WO2014078191A1 - Low-overhead multi-patterning design rule check - Google Patents

Abstract

Roughly described, a system enables quick and accurate depiction to a user of multi-patterning layout violations so that they may be corrected manually and in real time, and without interfering with normal manual editing process. In one embodiment, the system involves iteratively building tree structures with nodes identifying islands and arcs identifying multi-patterning spacing violations between the connected islands. The system detects coloring violations during the building of these tree structures, using the relationships previously inserted. The coloring violations preferably are reported to a user in the form of visual indications of the cycles among the candidate spacing violations, with the candidate spacing violations also themselves indicated visually and individually. The user can see intuitively how to move the islands around, and in which directions and by what distance, in order to remove a multi-patterning spacing violation and thereby break the cycle.

Description

LOW-OVERHEAD MULTI-PATTERNING DESIGN RULE CHECK

BACKGROUND

[0001] The invention relates to electronic design automation, and more particularly, to methods and apparatuses for rapid checking of design rules in a circuit layout.

[0002] Advancements in process technology have impacted integrated circuit manufacturing in at least two key ways. First, scaling of device geometry achieved through sub- wavelength lithography has facilitated packing more devices on a chip. Second, different process recipes have enabled manufacturing of heterogeneous devices with different threshold and supply voltages on the same die. A consequence of these improvements, however, has been an explosion in the number of design rules that need to be obeyed in the layout. Instead of simple width and spacing rules, modern fabrication technologies prescribe complex contextual rules that have to be obeyed for manufacturability.

[0003] The increase in the number of rules has complicated the task of creating design rule clean layouts, i.e., layouts that do not have design rule violations. Creating design rule clean layouts for digital circuit designs can be facilitated by the use of standard cell layouts as building blocks, and placement and routing tools that are extended to address the design rules.

[0004] Unfortunately, this approach usually does not work for analog, RF and custom circuit designs. Layouts for such designs are typically created manually using layout editors, and because of the number and complexity of the design rules, checking them was a laborious process.

[0005] A conventional design rule check (DRC) system requires a powerful two- dimensional geometry engine which supports geometric operations such as Boolean operations like AND, OR, NOT, XOR; sizing operations like grow / shrink horizontal/vertical/diagonal; other operations like merge, shift, flip, cut, smooth; as well as all-angle geometry for true Euclidean distance calculations. Individual rules are typically checked individually over an entire layout region. This is also true of individual rule values of same rule (e.g. a check against the minimum value for a rule, and another check against a preferred value for the same rule). Each check basically runs an independent sequence of geometry operations, and numerous passes through the layout region are required.

[0006] For example, a conventional series of operations to check a minimum spacing rule in a Manhattan only layout, might include steps of

• Merge all same layer shapes into separate islands; Grow all islands by half the minimum spacing value;

Perform an AND (intersection) operation among the islands; and

Draw DRC violation markers based on the resulting shapes of the AND operation.

[0007] As another example, a conventional series of operations to check a minimum width rule in a Manhattan only layout, might include steps of

• Merge all same layer shapes into separate islands;

• Shrink all islands by (half the minimum width value + epsilon)

• Eliminate all resulting islands of zero area;

• Grow back the resulting islands by (half the minimum width value + epsilon);

• Perform a NOT operation between the original merged islands and grown back islands; and

• Draw DRC violation markers based on the shapes resulting from the NOT operation.

[0008] So long as a good geometry engine is available, the conventional DRC techniques are simple to code, at least for simple rules. They are also flexible and powerful if the geometry engine has a scripting API for relevant geometry operations, and it is relatively straightforward to massively parallelize the DRC process among numerous CPUs.

[0009] On the other hand, it can be seen that checking even simple design rules like those above is extremely expensive computationally. Massive parallelization usually is possible only for offline checks, which typically are performed only between layout iterations. Even then they often can require hours to complete. The conventional approach also suffers from roughly linear growth of the total run time with respect to the number of rules to be checked, with multiple values for a rule counted as separate rules. This makes it very hard to reduce the total run time without turning off selected rules. The conventional approach also suffers from linear growth of run time for individual rule checks, with respect to the length of the geometry operation sequence, i.e., the complexity of the rule. The conventional approach also involves separate checks for Euclidean measurements, and also requires extensive education and training in order to optimize the performance of the customer scripts.

[0010] Recently, the march toward increasingly smaller technology nodes has pushed fabrication vendors to support double-patterning technology (DPT). If integrated circuit features on a layer are laid out too near each other for adequate separation when exposed through a lithographic mask, then the features are apportioned onto two different masks, each mask having only some of the features for the layer. During fabrication, the wafer is exposed twice, once with each mask. In this way features can be defined on the integrated circuit which are too finely spaced for them to be defined clearly and reliably by a single mask. Double-patterning technology can be extended to triple-patterning technology, in which the features for a layer are apportioned onto three different masks, and so on. Apportionment onto higher numbers of masks is possible as well, and these techniques are sometimes referred to generally as "multi-patterning technology".

[0011] Typically the mask fabricator (which often is also the chip fabricator) uses its own algorithm to allocate shapes among the two or more masks. However, in some arrangements of layout shapes an allocation is not possible since a particular shape cannot be allocated to any of the masks without violating the spacing rules for features on that mask. In a layout layer which has not yet been split, these situations can be detected by a design rule checking algorithm which assigns different "colors" (corresponding to different lithographic masks) to any pair of shapes which are nearer to each other than the minimum multi-patterning spacing constraint for a single mask. Chains of such features are detected, each feature forcing the next feature to have a different color. In the double-patterning case, each next feature is assigned the color opposite to the former feature in the chain. In the multi-patterning case multiple colors are used, and it is sufficient that each next feature be assigned a different (also called non-conflicting) color.

[0012] If a chain loops back onto itself, then it forms a "cycle". A cycle is not itself bad, unless there is no way to avoid two adjacent features in the chain being assigned the same color. In the double-patterning situation, if a cycle contains an even number of features, then there is no conflict because a color conflict can be avoided. The arrangement can then be allocated among the two masks without violating the single-mask spacing rules. If a cycle contains an odd number of features in the double-patterning case, however, then a coloring conflict exists and the arrangement, if not modified, cannot be allocated among the two masks without violating the single-mask spacing rules. The latter situation is sometimes referred to herein as a "DPT odd cycle violation". (In the extension to multi-patterning, coloring conflicts are sometimes referred to herein as "multi-patterning coloring violations".)

[0013] A number of techniques exist for handling odd cycle violations. But if none of them work, then one or more of the features must be moved away from one or more other features, in order to break the cycle. Since this solution can reduce circuit density, it would be desirable to move features only so far as needed in order to solve the problem. For a manual layout editor, this would ideally involve real time DPT odd cycle detection, so that after every movement or other edit of a shape the user can see immediately whether the violation remains. But checking for DPT odd cycle violations can be extremely time consuming by conventional methods, and prohibitively slow for such real time layout editing.

SUMMARY

[0014] A need therefore exists for a robust solution to the problem of real time manual layout editing, in a manner that avoids double-patterning or multi-patterning violations.

[0015] Roughly described, a system enables quick and accurate depiction to a user of multi-patterning layout violations so that they may be corrected manually and in real time, and without interfering with normal manual editing process. In one embodiment, the system involves iteratively building a data structure (such as a forest structure) identifying a plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships in a tree indicating that the pair of islands related by the relationship violates a multi-patterning spacing constraint. The system detects multi-patterning coloring violation among islands represented in the data structure, during the building of this data structure, and using the relationships that have been inserted into the data structure. The coloring violations preferably are reported to a user in the form of visual indications of the cycles among the inter-island multi- patterning candidate spacing violations, with the candidate spacing violations also themselves indicated visually and individually. Preferably the visual indications of the involved multi- patterning spacing violations are depicted with visual markers, the size of which depend upon the value of the multi-patterning spacing constraint being violated. In this way the user can see intuitively how to move the islands around, and in which directions and by what distance, in order to remove a multi-patterning spacing violation and thereby break the cycle.

[0016] Preferably, the system pre-populates a database identifying a plurality of multi- patterning candidate spacing violations before searching the database for multi-patterning coloring violations as above. At least some of the candidate violations can be detected and inserted into the database during a predecessor process of traversing the corners of shapes in a subject layout region, and for each corner, populating a layout topology database with values that depend on the respective corner locations. Preferably corner traversal is performed using scan lines scanning in at least two dimensions, and stopping only at corner positions. The layout topology database is populated with what information can be gleaned based on the current scan line. During this process, at least some types of the candidate violations are detected and inserted into the multi-patterning candidate spacing violations database. [0017] Additional aspects of the invention are set forth herein for handling pre-coloring, pre-groups, triple patterning violation detection, and so-called "split-and-stitch" mitigation of multi-patterning violations.

[0018] The above summary of the invention is provided in order to provide a basic understanding of some aspects of the invention. This summary is not intended to identify key or critical elements of the invention or to delineate the scope of the invention. Its sole purpose is to present some concepts of the invention in a simplified form as a prelude to the more detailed description that is presented later. Particular aspects of the invention are described in the claims, specification and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The invention will be described with respect to specific embodiments thereof, and reference will be made to the drawings, in which:

[0020] Fig. 1 shows a simplified representation of an illustrative digital integrated circuit design flow.

[0021] Fig. 2 is a flow chart illustrating an example user experience when using an embodiment of the system as described herein.

[0022] Fig. 3 is a flow chart of the overall system flow for an embodiment of the invention.

[0023] Figs. 4, 7-10, 12-18, 20, 23-27, 29-34 and 36-38 are flow chart details of the overall system flow in Fig. 3.

[0024] Fig. 5 illustrates part of a sweep x data structure referred to in Fig. 4.

[0025] Fig. 5A illustrates a simple portion of a layout.

[0026] Fig. 6 illustrates part of a sweep y data structure referred to in Fig. 4.

[0027] Figs. 1 1A and 1 IB illustrate simple portions of a layout, highlighting convex and concave corners of a layout shape, respectively.

[0028] Figs. 19A, 19B and 19C illustrate certain corner relationships between layout shapes.

[0029] Fig. 19D illustrates two layout shapes for the purpose of a particular design rule check.

[0030] Fig. 19E illustrates three layout shapes together forming an island.

[0031] Figs. 21A-21E illustrate example visual indications of design rule violations and near- violations. [0032] Fig. 22 is a simplified block diagram of a computer system that can be used to implement software incorporating aspects of the present invention.

[0033] Figs. 28A and 28B illustrate examples of editing edges determined from a selection command.

[0034] Fig. 35 is a flow chart detail of step 1715, for a particular layer.

[0035] Fig. 35 illustrates an example visual indication of a layout region showing DPT odd cycle violations.

DETAILED DESCRIPTION

[0036] The following description is presented to enable any person skilled in the art to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein.

Overall Design Process Flow

[0037] Fig. 1 shows a simplified representation of an illustrative digital integrated circuit design flow. At a high level, the process starts with the product idea (step 100) and is realized in an EDA (Electronic Design Automation) software design process (step 1 10). When the design is finalized, it can be taped-out (step 127). At some point after tape out, the fabrication process (step 150) and packaging and assembly processes (step 160) occur resulting, ultimately, in finished integrated circuit chips (result 170).

[0038] The EDA software design process (step 1 10) is itself composed of a number of steps 1 12-130, shown in linear fashion for simplicity. In an actual integrated circuit design process, the particular design might have to go back through steps until certain tests are passed. Similarly, in any actual design process, these steps may occur in different orders and combinations. This description is therefore provided by way of context and general explanation rather than as a specific, or recommended, design flow for a particular integrated circuit.

[0039] A brief description of the component steps of the EDA software design process

(step 1 10) will now be provided. [0040] System design (step 1 12): The designers describe the functionality that they want to implement, they can perform what- if planning to refine functionality, check costs, etc.

Hardware-software architecture partitioning can occur at this stage. Example EDA software products from Synopsys, Inc. that can be used at this step include Model Architect, Saber, System Studio, and Design Ware® products.

[0041] Logic design and functional verification (step 114): At this stage, the VHDL or

Verilog code for modules in the system is written and the design is checked for functional accuracy. More specifically, the design is checked to ensure that it produces correct outputs in response to particular input stimuli. Example EDA software products from Synopsys, Inc. that can be used at this step include VCS, VERA, DesignWare®, Magellan, Formality, ESP and LED A products.

[0042] Synthesis and design for test (step 116): Here, the VHDL/Verilog is translated to a netlist. The netlist can be optimized for the target technology. Additionally, the design and implementation of tests to permit checking of the finished chip occurs. Example EDA software products from Synopsys, Inc. that can be used at this step include Design Compiler®, Physical Compiler, DFT Compiler, Power Compiler, FPGA Compiler, TetraMAX, and DesignWare® products.

[0043] Netlist verification (step 1 18): At this step, the netlist is checked for compliance with timing constraints and for correspondence with the VHDL/V erilog source code. Example EDA software products from Synopsys, Inc. that can be used at this step include Formality, PrimeTime, and VCS products.

[0044] Design planning (step 120): Here, an overall floor plan for the chip is constructed and analyzed for timing and top-level routing. Example EDA software products from Synopsys, Inc. that can be used at this step include Astro and Custom Designer products.

[0045] Physical implementation (step 122): The placement (positioning of circuit elements) and routing (connection of the same) occurs at this step. Example EDA software products from Synopsys, Inc. that can be used at this step include the Astro, IC Compiler, and Custom Designer products. Aspects of the invention can be performed during this step 122.

[0046] Analysis and extraction (step 124): At this step, the circuit function is verified at a transistor level, this in turn permits what- if refinement. Example EDA software products from Synopsys, Inc. that can be used at this step include AstroRail, PrimeRail, PrimeTime, and Star- RCXT products.

[0047] Physical verification (step 126): At this step various checking functions are performed to ensure correctness for: manufacturing, electrical issues, lithographic issues, and circuitry. Example EDA software products from Synopsys, Inc. that can be used at this step include the Hercules product. Aspects of the invention can be performed during this step 126 as well.

[0048] Tape-out (step 127): This step provides the "tape-out" data to be used (after lithographic enhancements are applied if appropriate) for production of masks for lithographic use to produce finished chips. Example EDA software products from Synopsys, Inc. that can be used at this step include the IC Compiler and Custom Designer families of products.

[0049] Resolution enhancement (step 128): This step involves geometric manipulations of the layout to improve manufacturability of the design. Example EDA software products from Synopsys, Inc. that can be used at this step include Proteus, ProteusAF, and PSMGen products.

[0050] Mask data preparation (step 130): This step provides mask-making-ready "tape- out" data for production of masks for lithographic use to produce finished chips. Example EDA software products from Synopsys, Inc. that can be used at this step include the CATS(R) family of products. Often this step includes partitioning or fracturing non-rectangular shaped islands into rectangles. An example method for performing such fracturing can be found in U.S. patent No. 8, 151,236, incorporated herein by reference.

Overview of the Technique

[0051] While DRC layout rules are becoming more and more complex at smaller and smaller technology nodes, most if not all of them still can be decomposed into a combination of the relationships among the edges, the corners, and the contours of shapes in the layout.

Relationships "among" shapes as used herein includes relationships about a single shape as well. In embodiments herein, multiple perpendicular scan lines are used to collect all the required data in one pass, so that the combinatorial checking on the data is virtually free. The pass speed is improved even further by stopping the scan lines only at corner positions. Note that scans in multiple directions can also be combined an a particular embodiment, so that the algorithm effectively jumps from corner to corner, considering each corner only once.

[0052] In a Manhattan layout, all edges of all shapes are oriented either horizontally or vertically. In this case two scan lines would be used, one vertical (scanning horizontally) and one horizontal (scanning vertically). In each case the scan line stops only at endpoints that it encounters of the edges that are oriented perpendicularly to the scan line. The vertical scan line, for example, stops only at endpoints of horizontally oriented edges, and the horizontal scan line stops only at endpoints of vertically oriented edges. In 45 degree layouts, edges can also be oriented at a 45 degree angle or a 135 degree angle. In this case four scan lines can be used, each scanning in a direction perpendicular to a respective one of the orientations in which edges are included in the layout. While scanning the layout region in each particular direction, "corner" data structures are populated for each corner, with whatever information is easily obtainable from the edge endpoints at the corner, and from other edges that intersect the same scan line. The combined information collected from all the scan lines as they encounter the corner, is sufficient to fully populate the corner data structure.

[0053] For most of the design rules defined on derived layers, the shapes in the derived layers never need to be explicitly derived in embodiments herein. Instead, information about their shape edges is inserted into the corner data structures for physical corners that they intersect. While such information can be said to "describe" the derived shapes, only information at these physical corners need be calculated, since most of the derived layer rules are defined on corners of virtual shapes, and these corners all derive from at least one corner position of an ancestor (parent, grandparent, etc.) physical layer. The X,Y position of a derived corner might not coincide with a single physical corner, but if not, then the X position derives from one physical corner and the Y position derives from another physical corner.

[0054] Again, this can occur as part of the scan of the layout region in each particular direction. There need be no limitation on the depth or width of the derived layer graph.

[0055] Other data structures are also populated during a scan, such as information about an island (such as its area), and information about vias.

[0056] Once all the data is collected into a layout topology database, design rule checking is accomplished merely by comparing the numeric values in the layout topology database with the constraint values in the design rule data set. Unlike geometry engine approaches, the approach described herein can be performed extremely quickly, often within milliseconds, allowing for design rule checking in real time, immediately as the layout designer makes each alteration in the layout.

[0057] Moreover, since most if not all of the design rules can be framed in terms of topological relationships among edges and corners, including design rules defined on derived layers, it can be seen that the same basic information, collected during the scan, can be used in checking most if not all of the design rules, including design rules defined on derived layers, and including DPT odd cycle detection. In most embodiments, there is no need to re-scan the layout region in order to check different design rules; one scan is sufficient for collecting all the needed data. Still further, since the number of topological relationships that can be involved in checking design rules is itself limited, there is little if any additional data collection needed during the scan in order to check new and ever more complex rules. The time required to perform DRC increases less than linearly with increasing numbers of rules, and tapers off to nearly zero.

[0058] For example, if minSpacing is supported already, then minSameNetSpacing and minNotchSpacing can be supported for free (no runtime overhead). If minArea is supported already, then minRectArea can be supported for free (no runtime overhead). If ID spacing is supported already, then ID extension can be supported easily regardless of whether they share the same "width". It can be seen that the more rules that are to be checked, the greater the likelihood that the next "new rule" can be supported for free or with a little extra overhead.

Example Implementation

[0059] Fig. 2 illustrates an example user experience when using an embodiment of the system as described herein. The flow chart of Fig. 2 occurs within step 122 (Fig. 1).

[0060] In step 210, the user develops a preliminary layout from a circuit design. As used herein, the term "circuit design" refers to the gate or transistor level design, before layout. The circuit design is often represented internally to the system in a netlist file. The layout is represented internally to the system in a geometry file which defines, among other things, all the shapes to be formed on each mask that will be used to expose the wafer during fabrication. The geometry file can have any of several standard formats, such as GDSII, OASIS, CREF, and so on, or it can have a non-standard format. The file describes the layout of the circuit design in the form of a mask definition for each of the masks to be generated. Each mask definition defines a plurality of polygons. At the time if Fig. 2, no resolution enhancement (RET) has yet been performed. Thus the layout geometries with which the user is working in Fig. 2 are in a sense idealized, since they do not yet take into account the imperfections of lithographic printing using optical wavelengths comparable or larger in size than the size of the geometries in the layout. For example, rectangles are rectangular, and are not yet pre-corrected for diffractive effects.

[0061] In step 212, the user views the layout on a computer monitor. The user typically selects a region of the layout for magnified viewing, so that only that region is visible on the monitor.

[0062] In step 214, the user, using a mouse or other pointing device, selects a group of one or more shapes from the visible layout region and drags them to a different location. In step 216, as the user drags the shapes, the system shows on the monitor any design rule violations in real time. In step 218, the user continues to drag the selected shapes until a position is found at which all design rule violations disappear. The user then performs the next desired editing step, which could be another drag-and-drop as in steps 214-218.

[0063] It can be seen how useful real time immediate design rule checking, enabled by the system herein, can be in manual layout or layout modification efforts.

Relationship Master

[0064] Before discussing the methods used by an implementation of the system, it will be useful to discuss design rules in general, and how they can be represented within the system. Design rules are a set of rules that are provided by a semiconductor manufacturer, which specify minimum or maximum geometric relationships among the features of a layout. A semiconductor manufacturing process always has some variability, and the purpose of design rules is to ensure that sufficient margin is included in the layout geometries to minimize the likelihood that the variability will result in loss of yield. A set of design rules is specific to a particular

semiconductor manufacturing process, so new rules are provided to designers or EDA vendors for each new process or significant process change. Despite their specificity to a particular process, there are many design rules which are similar, except for one or more numeric values, across many processes.

[0065] Design rules range from very simple to very complex. Most, however, can be framed as a set of one or more constraint parameters, and a set of one or more constraint values for the constraint parameters. (As used herein, a "parameter" is merely a slot or container for one or more values. It is not itself a value.) For example, a simple design rule is minimum edge-to- edge spacing (sometimes called minSpacing). This rule has one parameter (edge-to-edge spacing), and one value which is the minimum spacing allowed by the rule between edges in a single layer (physical or derived) of the layout. Many design rules specify more than one value for a particular parameter, such as an "absolute minimum" value and a "preferred minimum" value. As used herein, a "physical" layer is one for which geometries are specified in the geometry file.

[0066] More complex rules can have multiple parameters. An End-of-line spacing rule, for example, specifies the minimum spacing between the end of a line and its neighboring geometry. Again, this rule can be defined on any layer, including a derived layer. The constraint applies only if the width of the wire is less than a specified value, eolWidth. The constraint applies when any geometry occurs within a region defined by the minimum spacing, where the region includes the distance from each side of the wire. This distance is referred to as a lateral verification distance eolWithin. The constraint applies only if one parallel edge is within a specified rectangular region from the corners of the wire, or it applies only if two parallel edges are within a specified rectangular region from the corners of the wire. These parameters are referred to as parWithin and parSpace. The constraint applies when no parallel edges occur within the region defined by the minimum spacing, or one parallel edge occurs within the region defined by the minimum spacing, or two parallel edges. This rule has the spacing parameter itself, eolSpacing, as well as the following parameters: eolWidth, eolWithin, parWithin and parSpace.

[0067] Design rules can also specify constraints on edges in different layers. The

MinDualExtension layer pair constraint, for example, specifies the minimum distance a shape on one layer must extend past a shape on a second layer. The first or second layer or both or neither can be derived layers. This rule has one parameter for extensions in the horizontal direction and another parameter for extensions in the vertical directions. This rule can also specify additional pairs of parameters, keyed by wire width. Other more complex parameters are also available for this rule, including optional parameters to qualify when the rule applies.

[0068] Design rule sets also often include area rules, such as the minimum area of an island or a hole in a layer. They can also include via rules, which specify constraints on geometric dimensions in the "cut" layer (also sometimes called the via layer), the island in the "cover" layer above the via, and the island in the "cover" layer below the via. These rules, too, can be defined on derived layers.

[0069] Derived layers are defined in the design rule sets. A derived layer can be defined by specifying a name for the derived layer, a layer number, the parent layers for the particular derived layer, and an operator for calculating the derived layer as a function of the parent layers. In one embodiment, only one or two parent layers can be specified, meaning a derived layer must have no more than two parent layers. In another embodiment, more than two parent layers can be specified. The derived layer operator can in one embodiment be a simple Boolean logic function (And, Or, XOR, or NOT). In another embodiment, the derived layer operator can be a more complex Boolean logic expression such as 'Layerl AND (Layer2 OR Layer3)'. Also, the parent(s) of a derived layer need not be physical (layout) layers; one or more of them can be other derived layers, thereby allowing a nesting of derived layers. As used herein, a "parent" layer refers to an immediate parent layer. Grandparents and other ancestors (including parents) are referred to herein as "ancestor" layers.

[0070] Ultimately, each derived layer has one or more ultimate ancestor which is a physical layer, though the number of derived layers in between the particular layer and the ancestor physical layer on one side of the family tree may be different from the number on another side of the family tree. For example, a first derived layer Dl may be dependent upon physical layers P I and P2, and a second derived layer D2 may be dependent upon D l and physical layer P3. Then one ancestor physical layer P3 of derived layer D2 has zero derived layers in between, whereas ancestor physical layers PI and P2 each have one derived layer in between the layer D2 and the respective physical layer PI or P2. As used herein, the "rank" of a particular derived layer is equal to the maximum of the number of derived layers to and including the particular derived layer from each of its ancestor physical layers. The rank of a physical layer is considered to be zero, and the rank of a particular derived layer can be calculated as one plus the maximum rank of all its parent layers.

[0071] The design rules that reference derived layers are of many of the same kinds as those that reference only physical layers, and are expressed in the design rule set in the same way. For example, they can be framed as a set of one or more constraint parameters and one or more constraint values for the constraint parameters. They can include rules that apply to shapes on the particular derived layer (such as minimum edge-to-edge spacing and end-of-line spacing), as well as rules that specify constraints among different layers (such as MinDualExtension). Rules that reference more than one layer are not restricted to referencing only physical layers or only derived layers; then can also reference layers of both kinds, such as the minimum extension of a shape in a derived layer relative to a shape in a physical layer.

[0072] As a simplified example, a design rule set may include a rule that sets a minimum longitudinal spacing between transistor gate conductors. In many fabrication processes, a transistor gate conductor can be identified as the geometric intersection where a polysilicon line crosses a diffusion region. In order to establish this design rule, the design rule set may specify a derived layer G defined as LI AND L2, where LI is layer defining the polysilicon lines, and L2 is the layer defining the diffusion implants. In this case the derivation operator for derived layer G is "LI AND L2". The design rule set then specifies a design rule that references layer G, recites a parameter for specifying the minimum spacing between shapes on layer G, and recites a value for that parameter.

[0073] As used herein, a design rule "references" a particular derived layer typically by identifying the derived layer. For example, a minimum extension rule, which specifies the minimum distance by which a shape in a derived layer must extend beyond the edge of a shape in a physical layer, or vice-versa, references both layers that the rule constrains (including the derived layer) by explicitly identifying both layers (including the derived layer). Also as used herein, a derivation operator "references" a particular layer by identifying it as one of its parent layers. In the simplified example above, the derivation operator for layer G "references" both layers LI and L2.

[0074] In an embodiment of the invention, all of the values specified by the design rules are provided to the system in the form of a design rule data set. As used herein, the term "data set" does not imply any particular organization. For example, it includes maps, multimaps, trees, as well as ordinary tables, and other data organizations as well. The term also does not necessarily imply any unity or regularity of structure. For example, two or more separate data sets, when considered together, still constitute a "data set" as that term is used herein. The terms "database" and "data structure" are also intended to have the same meaning as "data set".

[0075] In the present embodiment, the design rule data set is sometimes referred to herein as the relationship master. A class definition for an example relationship master, in pseudo-C++, is as follows. In order to simplify the discussion, only some of the parameters are shown. A relationship_master object exists for each layer on which design rules are defined, including derived layers. class relationship_master

{

layer_number m_layer; // layer number for this instantiation std : : set<layer_number> m_layers_above; // identification of layers above current layer

std : : set<layer_number> m_layers_below; // identification of layers below current layer

// the worst case value for spacing relationship on the

// same layer, 0 if there is no design rule asking for

// min_spacing relationship

int m_spacing;

// the worst case value for dimension relationship on the

// same layer, 0 if not applicable (minimum line width)

int m_dimension;

// the worst case value for neighbor_spacing relationship on

// the same layer, 0 if not applicable

// (also called parallel spacing)

int m_neighbor_spacing;

// the worst case value for neighbor_within relationship on

// the same layer, 0 if not applicable

int m_neighbor_within;

// the worst case value for neighbor_dimension relationship on

// the same layer int m_neighbor_width;

int m_area; // minimum island area

int hole_area;

int m_common_run_length;

std : : map<layer_number , int> m_common_run_clearance_vector_map;

// extensions from this layer to other layers

std : : map<layer_number , int> m_cover_layers;

// extensions from other layers to this layer

std : : map<layer_number , int> m_cut_layers;

/ / wors t case dif ferent layer clearance , from this layer to other layers std : : map<layer_number , int> m_clearance_layers;

// for via rules

std: : set<layer_number> m_overlap_layers ;

std: : set<layer_number> m_dual_cover_layers;

};

[0076] In addition to the above, relationship master also includes a plurality of DPT rules. Among these are the following: width_threshold: if an edge is longer than this value, then call it a side_edge; otherwise, call it end_edge;

end end spacing: the DPT minimum spacing between two end edges; smaller than this value, this edge-edge relationship becomes a DPT spacing candidate and can be used to form a cycle;

end side spacing: the DPT minimum between an end edge and a side edge; smaller than this value, this edge-edge relationship becomes a DPT spacing candidate and can be used to form a cycle;

side_side_spacing: the DPT minimum between two side_edges; smaller than this value, this edge-edge relationship becomes a DPT spacing candidate and can be used to form a cycle;

corner corner spacing: the DPT minimum between two corners; smaller than this value, this edge-edge relationship becomes a DPT spacing candidate and can be used to form a cycle.

[0077] Note that as used herein, a "DPT spacing candidate" can be either a DPT edge- edge spacing candidate or a DPT corner-corner spacing candidate. Other types of candidates are also possible in different embodiments. A "DPT edge-edge" spacing candidate can be either a DPT end-end spacing candidate, a DPT end-side spacing candidate, or a DPT side-side spacing candidate. Again, other types of edge-edge spacing candidates are also possible in different embodiments. These terms are sometimes abbreviated herein, by omitting "spacing" or "DPT" or both.

Design Rule Checking Flow with PRC Assist

[0078] Fig. 3 is a flow chart of the overall system flow for real time visual layout design rule checking. The reader will recognize that the flow can be easily modified for use as a batch job instead. As with all flowcharts herein, it will be appreciated that many of the steps in Fig. 3 can be combined, performed in parallel or performed in a different sequence without affecting the functions achieved. In some cases a re-arrangement of steps will achieve the same results only if certain other changes are made as well, and in other cases a re-arrangement of steps will achieve the same results only if certain conditions are satisfied. However, as described in detail hereinafter, there are certain steps which are performed prior to other steps, in order to obtain benefits of the invention.

[0079] In step 310, the relationship master data set is built from a set of design rules for the target fabrication process. This can be done manually, or in some embodiments it can be automated. It is provided to the DRC system either electronically or via a computer readable medium, and it is stored accessibly to the system on a computer readable medium. As used herein, a computer readable medium is one on which information can be stored and read by a computer system. Examples include a floppy disk, a hard disk drive, a RAM, a CD, a DVD, flash memory, a USB drive, and so on. The computer readable medium may store information in coded formats that are decoded for actual use in a particular data processing system. A single computer readable medium, as the term is used herein, may also include more than one physical item, such as a plurality of CD ROMs or a plurality of segments of RAM, or a combination of several different kinds of media. A computer readable medium, as the term is used herein, excludes transitory media on which content is represented on a signal during propagation.

[0080] In step 312, the system displays on a monitor the layout or layout region selected by the user. As used herein, the term "region" refers to a portion as viewed from above, including whatever layers are pertinent. As a degenerate case, the entire layout is also a "region". The user can manipulate (edit) objects in the layout using familiar editing commands, such as keyboarder mouse-based behaviors recognized by the system. For example, the user can select a group of objects by clicking and dragging the mouse pointer to form a rectangle around them. Only objects on physical layers can be selected; derived layers are created only to facilitate the specification of certain error checking rules and are not visible to the user editing a layout. The user can then move the objects as a group by clicking within the rectangle and dragging it.

Editing commands are recognized by the operating system and delivered to the application program by way of events in a well known manner. For example, user dragging of a group of objects might cause a series of events to be delivered to the application program, one after each movement by some number of pixels, or some number of milliseconds. The application program receives these events and determines for itself what the event represents. Step 312 can include a conventional event loop, whereby the application program repeatedly checks for new events. When it receives an event, step 312 determines that it represents a layout editing command such as user dragging of a group of shapes across the layout.

[0081] In step 313, the system determines the type of the editing command. Typically for a drag operation, the dragging behavior is preceded by one or more predecessor behaviors which indicate a predecessor command which indicates what to do in response to the dragging behavior. One predecessor command, for example, can involve selection of a group of one or more editing shapes to be moved to a different position in response to dragging behavior.

Another command can involve selection of an edge or a corner, so that shape(s) will be stretched or contracted in response to dragging behavior. Yet another command, known sometimes as an array copy, can involve selection of one or more shapes to be copied, with ever increasing spacing among the copies, in response to dragging behavior. At a minimum, all of the predecessor commands relevant to the embodiment of Fig. 3 include an aspect of object selection, where the object(s) can include shapes, edges or corners or other geometries in the layout.

[0082] Initially in step 313, if the current editing command includes neither object selection nor dragging, then it is handled in a step 330. The operation of step 330 is not important for an understanding of the invention.

[0083] If the current editing command includes an object selection, then the system takes advantage of such a selection event in order to pre-calculate design rule bounds, which indicate the distance that the shapes can move before a design rule is violated. Flow passes to step 314, in which the system collects all the editing shapes, which are the ones that are being edited by the user. For a click-and-drag behavior, the editing shapes are the ones that are being moved to a different position in the layout. For a shape re-sizing command, the editing shapes are the ones being resized. [0084] In step 315, the system populates edge speed ratios for each edge of each selected shape based on the editing command. The edge speed ratio is the ratio of edge movement distance per unit of cursor movement distance, as appropriate for the current selection command. Typically this ratio is 0 or 1 , but could be anything from negative infinity to positive infinity, and need not necessarily be integral in all embodiments. Speed ratios can be better understood by reference to the illustrations in Figs. 28A and 28B (collectively Fig. 28). Fig. 28A illustrates two shapes 2810 and 2812. Shape 2812 has been selected for a simple drag operation. For a simple drag, all edges of the shape move in the layout by the same distance that the cursor moves during the drag. Thus the speed ratio for all edges on shape 2812 is 1. In Fig. 28B, corner 2814 of shape 2816 has been selected. The subsequent drag operation will either stretch or contract shape 2816. Edge 2820, a horizontal edge, will move vertically in the layout by the same distance that the cursor moves vertically during the drag (upward or downward), so the speed ratio for edge 2820 is 1. Similarly, edge 2822, a vertical edge, will move horizontally in the layout by the same distance that the cursor moves horizontally during the drag (leftward or rightward), so the speed ratio for edge 2822, too, is 1. Edges 2824 and 2826 will not move during the drag, so their speed ratio is 0. Other command are more complicated, but can still be modeled with edge speed ratios. For example, for a 3x4 array copy of a source shape, all the edges of three copies of the shape will remain stationary during the drag and therefore have speed ratio 0. All the edges of the next three copies of the shape have a speed ratio of 1. All the edges of the next three copies have a speed ratio of 2, and all the edges of the final three copies have a speed ratio of 3. It is noteworthy that all the speed ratios are determinable from the command itself. The direction and extent of all the movements, which will not be known until the drag behavior commences, are not necessary to determine the speed ratios.

[0085] For a derived edge, its speed ratio is determined from its ancestor physical edge(s). If all the physical ancestor edges having the same speed ratio A, then the derived edge will have the same speed ratio A. If some of the physical ancestor edges having different speed ratios, that implies that the derived geometries are about to experience a sudden change. In this case the system forces the speed ratio to zero for the derived edge. In practice, most derived edges have only a single ancestor physical edge, so these kinds of sudden derived geometry changes are infrequent. In addition, derived layers are mostly defined on lower physical layers, practically all encapsulated inside a P-CELL, so they tend to move together. That is, all the ancestor physical edges tend to have the same speed ratios. This further decreases the likelihood of sudden derived geometry changes. The ancestor physical edges are obtained from the 'current edge group' as described in conjunction with steps 2422 of Fig. 24 and 2622 of Fig. 26. In addition to the Boolean status vector of derived edges, the system also caches the derived speed ratio (a single float value) for this purpose.

[0086] In a later step, the system will use the edge speed ratios to pre-calculate values indicating bounds imposed by the design rules on the distance in various directions that the selected objects can be moved. In one embodiment these design rule bounds are indicated by left, right, upward, downward and radial distances that the selected objects can be moved before one of the design rules will be violated. In another embodiment they are represented by a distance in each direction that the cursor can be moved before one of the design rules will be violated during a drag of the selected objects. This latter representation is sometimes referred to herein as a 'slack' distance, and is the one used in the embodiment described herein. In yet another embodiment the bounds are represented by the final bounding position in the layout to which the selected objects can be moved before one of the design rules will be violated. Other ways of indicating these bounds will be apparent. Also, in an embodiment, the set of design rules enabled to impose bounds in DRC assist mode need not include all the design rules. Fewer than all can be included in such a set in a particular embodiment.

[0087] Three types of bounds are calculated in the present embodiment: linear bounds (in the four linear directions), corner bounds and conditional bounds. Roughly described, the linear design rule bounds are calculated in the present embodiment by calculating them for each edge and successively and retaining only the most restrictive bound in each direction at each iteration. The corner and conditional bounds are applied later to further restrict the overall bounds to avoid violating any of the enabled design rules by any of the objects in the selection. Linear bounds and corner bounds need not be calculated immediately sequentially, and in present embodiment they are not. Rather, each type of bound is calculated where most cost-effective to calculate it. In fact, the calculation of vertical linear bounds is spread out during the horizontal scan to populate the corner data structures, and the calculation of horizontal linear bounds is spread out during the vertical scan to populate the corner data structures. Similarly, calculation of corner bounds is performed during the scan of corners to check corner-to-corner design rules, and the calculation for conditional bounds is performed during the check of other corner-based design rules such as the end-of-line spacing rule.

[0088] In step 316, the system collects all the surrounding shapes, which in a click-and- drag command, are the shapes near the new position of the editing shapes. Again, only real shapes, not those on derived layers, are included. A selection algorithm is used here which errs on the side of collecting more shapes than necessary, since while inclusion of additional shapes could impact performance, the exclusion of relevant shapes will impact accuracy. One efficient way to collect appropriate shapes is to create a bounding box around the editing shapes in their new position, then extend the box in all four directions by 1.5 times the worst case minimum spacing or the worst case minimum inter-layer clearance, whichever is larger. All shapes at least partially overlapping with the expanded bounding box, in any layer, are then included in the result. A conventional range search engine can be used for this step. Geometry processing is not needed.

[0089] In step 318, horizontal and vertical scan line trees sweep x and sweep y are built from all of the collected shapes, including both the editing shapes and the static shapes. The horizontal scan line tree sweep x is a map of particular vertical scan lines, and will be scanned horizontally across the selected layout region, from left to right. The vertical scan line tree sweep_y is a map of particular horizontal scan lines, and will be scanned vertically across the selected layout region, from bottom to top.

[0090] Fig. 4 is a flow chart of step 318, and as can be seen, it includes a step 410 of building sweep_x and another step 412 of building sweep_y.

[0091] Fig. 5 illustrates pertinent parts of the sweep x data structure 510. It contains two tree data structures, called enter_tree 512 and exit_tree 514. Enter-tree is a map of the vertical scan lines, and the vertical position on such scan lines, of the left-hand endpoints of the horizontal edges. Exitjxee is a map of the vertical scan lines, and the vertical position on such scan lines, of the right-hand endpoints of the horizontal edges. No additional entries are provided in the map to account for endpoints of edges on derived layers, because the great majority of the derived layer rules operate on corners of shapes on the derived layers whose x/y positions coincide with at least one corner position of ancestor physical layers, and information regarding the derived edges can be stored in conjunction with the coincident corner position(s) on the ancestor physical layers. Any rules that require additional information are handled separately. (As used herein, the "corner position", or the "location" of a corner, refers to the (x,y) location of the corner and is not specific to layer number or depth within the ultimate integrated circuit chip.)

[0092] Map 516 is an expansion of exitjxee 514; enterjxee 512 has the same structure and is therefore not shown in Fig. 5. It comprises key-value pairs, in which all the keys indicate horizontal positions and all the values are structures of class 'edge-tree', and represent vertical scan lines. A "map" is a standard structure which allows only one entry for each unique key. Thus exitjxee organizes all the vertical scan lines, and there is one vertical scan line for each horizontal position included. Note that by representing only specific vertical scan lines, the horizontal scanning algorithm will be able to jump over all horizontal positions that do not contain any corners.

[0093] Multimap 518 is an expansion of one of the edge tree structures 520. The other edge_trees have the same structure and therefore are not shown in Fig. 5. Edge_tree 520 also comprises key-value pairs, except that as a "multimap", multiple entries are allowed having the same key. In edgejxee 520 the keys indicate vertical positions, and all the values are structures of class 'edge', representing an edge having an endpoint on the current vertical scan line. Since this is part of the exitjxee 514, only those horizontal edges having right-hand endpoints at this horizontal position are included in edge_tree 520. (In the enter_tree 512, only edges having left- hand endpoints at a given horizontal position are included in the edge tree for the vertical scan line at the given horizontal position.) A multimap is used here rather than a map, in order to accommodate multiple edges having a right-hand endpoint at the same x and y position in the layout region. Multiple edges are possible because some could be on different layers in the layout, or some could even be superimposed on each other in a single layer. Again, these are physical edges only; edges located in derived layers do not have their own entries. In another embodiment, however, derived layer edges can be given their own edge entries in multimap 518.

[0094] Block 522 is an expansion of one of the edge structures 524. The other edges have the same structure and therefore are not shown in Fig. 5. Edge 524 contains information about a particular horizontal edge of one of the shapes in the layout region, and also acts as a holding area for certain information developed during the scan as described hereinafter. At least the following information is included:

• edge ID: an identifying value for the edge;

• layer ID: an indication of the layer number on which the edge lies;

• edge start (x,y): the x and y coordinates of the left-hand endpoint of the edge;

• edge end (x,y): the x and y coordinates of the right-hand endpoint of the edge;

• edge against scan line? (T/F): a Boolean indicating whether the edge is the bottom edge of a shape (True if it is a bottom edge, False otherwise);

• quadrant depth vector: four slots indicating how many shapes overlap each other in the current layer at the right-hand endpoint of the edge (for exiting edges) or the left- hand endpoint (for entering edges) or the intersection point of the edge and the vertical scan line (for all other edges in the current scan line), in each of the four quadrants centered at that point (for an embodiment that supports 45 degree geometries, this is an octant depth vector containing eight slots); • neighbor map: a map of neighboring edges;

• derived edge status map 526: a map of edge status at the current X_pos, y_pos for various derived layers.

[0095] Block 528 is an expansion of derived edge status map 526. It contains information about horizontal edges in some of the derived layers, which edges terminate at or pass through the current vertical scan line at the current vertical position on that scan line. Each entry contains the derived layer ID, in association with a status vector for the edge. The status vector for a derived edge is similar to a quadrant depth vector (discussed later), in that it contains four values indicating status in the four respective quadrants centered at the current x- and y-position. It differs from a quadrant depth vector in that each entry of the vector can contain only a 1 or a 0: a 1 indicates that the current derived layer does have an island in that quadrant, and a 0 indicates that it does not (or vice- versa). There is no need to indicate the number of superimposed shapes in the quadrant within a derived layer, because the shapes are defined in a Boolean operation: in a given location a shape is either present or absent.

[0096] Fig. 5A illustrates the functioning of a derived layer status vector. The figure illustrates a vertical scan line 530 and three vertical positions numbered, from bottom to top, 532, 534 and 536. A derived shape 538 has its right-hand edge aligned with vertical scan line 530, and its bottom and top edges located at vertical positions 532 and 536, respectively. As with quadrant depth vectors, the quadrants in a derived layer status vector are numbered counterclockwise beginning in the top-right quadrant. The status vector at vertical position 532 is (0, 1,0,0), indicating that the y-position 532 on the vertical scan line 530 is the lower-right corner of a shape. Similarly, the status vector at vertical position 536 is (0,0, 1,0), indicating that the y- position 536 on the vertical scan line 530 is the upper-right corner of a shape. The status vector at vertical position 534 is (0, 1,1,0), indicating that the shape extends to the left and above and below the y-position 532 on the vertical scan line 530.

[0097] It can be seen that a status vector having one T and three O's indicates a convex corner of the derived shape, whereas a status vector having one '0' and three Ts indicates a concave corner of a derived shape. A status vector of (0,0, 1,1), (0, 1, 1,0), (1, 1,0,0) or (1,0,0, 1) indicates a non-corner edge of a derived shape. A status vector of (0,1,0, 1) or (1,0, 1,0) indicates two derived shapes meeting at a common corner; a situation that will usually violate design rules. Note that only edges and corners of a derived shape appear in derived edge status maps. If the status vector at a particular x/y position for a derived layer is (0,0,0,0), then this derived layer has no shape at that position. If it is (1, 1, 1,1), then the current x/y position is inside a derived shape. In either case, no entry is made for the current derived layer in the derived edge status map 526.

[0098] It will be appreciated that each x/y position of corners on physical layers may be represented numerous times in the Sweep x data structure. It may be represented in both Enter_tree 512 and Exit_tree 514. It might also be represented at multiple physical layers (multiple entries in block 518 all having a common y_pos key). Because many of the derived edges at a particular x/y position can be stored in a single map 526, there may be multiple edge data structures 522 which would serve as an appropriate place to store each derived edge status map 526. Different embodiments can implement different conventions on this point. In one embodiment, the status vectors for all the derived edges on a particular derived layer are inserted into an edge data structure for the "first" physical layer that is one of its physical ancestors. Preferably the "first" physical layer is defined as whichever layer is used to break a tie when vertical positions of edges are the same in the current vertical scan line. In the embodiment of Fig. 5, it is the physical layer with the smallest layer number.

[0099] Fig. 6 illustrates pertinent parts of the sweep y data structure 610. Like sweep x, sweep_y contains two tree data structures, called enterjxee 612 and exitjxee 614. In sweep_y, enter-tree is a map of the horizontal scan lines, and the horizontal position on such scan lines, of the lower endpoints of the vertical edges. Exitjxee is a map of the horizontal scan lines, and the horizontal position on such scan lines, of the upper endpoints of the vertical edges. Like sweep_x, no additional entries are provided in the map to account for endpoints of edges on derived layers.

[00100] Map 616 is an expansion of exitjxee 614; enter tree 612 has the same structure and is therefore not shown in Fig. 6. It comprises key-value pairs, in which all the keys indicate vertical positions and all the values are structures of class 'edge-tree', and represent horizontal scan lines. Thus exitjree organizes all the vertical scan lines, and since exitjree is a map, there is only one horizontal scan line for each vertical position included. Note that by representing only specific horizontal scan lines, the vertical scanning algorithm, like the horizontal scanning algorithm, will be able to jump over all vertical positions that do not contain any corners.

[00101] Multimap 618 is an expansion of one of the edge tree structures 620. The other edgejrees have the same structure and therefore are not shown in Fig. 6. Edgejree 620 also comprises key-value pairs, except that as a "multimap", multiple entries are allowed having the same key. In edgejree 620 the keys indicate horizontal positions, and all the values are structures of class 'edge', representing an edge having an endpoint on the current horizontal scan line. Since this is part of the exitjree 614, only those vertical edges having upper endpoints at this vertical position are included in edgejxee 620. (In the enterjxee 612, only edges having lower endpoints at a given vertical position are included in the edgejxee for the horizontal scan line at the given vertical position.) Again, these are physical edges only; edges located in derived layers do not have their own entries. In another embodiment, however, derived layer edges can be given their own edge entries in multimap 618.

[00102] Block 622 is an expansion of one of the edge structures 624. The other edges have the same structure and therefore are not shown in Fig. 6. Edge 624 contains information about a particular vertical edge of one of the shapes in the layout region, and also acts as a holding area for certain information developed during the scan as described hereinafter. At least the following information is included:

• edge ID: an identifying value for the edge;

• layer ID: an indication of the layer number on which the edge lies;

• edge start (x,y): the x and y coordinates of the lower endpoint of the edge;

• edge end (x,y): the x and y coordinates of the upper endpoint of the edge;

• edge against scan line? (T/F): a Boolean indicating whether the edge is the left edge of a shape (it will be True if it is a left edge, False otherwise);

• quadrant depth vector: four slots indicating how many shapes overlap each other in the current layer at the lower endpoint of the edge (for exiting edges) or the upper endpoint (for entering edges) or the intersection point of the edge and the horizontal scan line (for all other edges in the current scan line), in each of the four quadrants centered at that point (for an embodiment that supports 45 degree geometries, this is an octant depth vector containing eight slots);

• neighbor map: a map of neighboring edges;

• derived edge status map 626: a map of edge status at the current X_pos, y_pos for various derived layers.

[00103] Block 628 is an expansion of derived edge status map 626. It contains information about vertical edges in some of the derived layers, which edges terminate at or pass through the current horizontal scan line at the current horizontal position on that scan line. Each entry contains the derived layer ID, in association with a status vector for the edge. Like for derived edge information stored in the Sweep_x data structure, the status vectors for all the vertical derived edges on a particular derived layer are inserted into an edge data structure 624 for the smallest numbered physical layer that is one of the ancestors of the particular derived layer. [00104] As can be seen, sweep_x contains only horizontal edges (physical and derived) and sweep_y contains only vertical edges (physical and derived). Thus the scan lines in each data structure are perpendicular to the edges that will be encountered during a traversal of the structure. In an embodiment supporting diagonal edges as well, two more sweep data structures are present as well: one containing scan lines oriented parallel to one diagonal and the other containing scan lines oriented parallel to the other diagonal. Each data structure includes only edges oriented perpendicularly to its scan lines, so again, a scan line sweep of the scan lines in each structure will encounter only those edges oriented perpendicularly to the scan line.

[00105] Fig. 7 is a flow chart detail of a method 410 for building the horizontal scan line tree sweep_x. In step 710, a list is formed of all the horizontal edges of all shapes in the selected region, including editing shapes. Only shapes on physical layers are considered in Fig. 7; derived layer information is not yet inserted. In step 712, the list is sorted by the horizontal position of all the left-hand endpoints of the edges. There may be multiple edges whose left-hand endpoints have the same horizontal position, and these would be grouped together in the sort.

[00106] In step 714, enter tree is created for sweep x. This is accomplished by, at each unique horizontal position represented in the sorted list (step 716), creating a scan line multimap (of class 'edgejxee') for a vertical scan line at that horizontal position (step 718). In step 720, the scan line multimap at that horizontal position is populated with all the edges (structures of class 'edge') in the list having left-hand endpoints at the current horizontal position.

[00107] After enter tree has been created and populated for sweep x, the list from step 710 is re-sorted by horizontal position of all the right-hand endpoints of the edges. Again, there may be multiple edges whose right-hand endpoints have the same horizontal position. In step 724, exitjxee is created for sweep_x. Similarly to the creation of enterjxee, this is accomplished by, at each unique horizontal position represented in the sorted list (step 726), creating a scan line multimap (of class 'edgejxee') for a vertical scan line at that horizontal position (step 718). In step 720, the scan line multimap at that horizontal position is populated with all the edges (structures of class 'edge') in the list having right-hand endpoints at the current horizontal position.

[00108] Fig. 8 is a flow chart detail of a method 412 for building the horizontal scan line tree sweep_y. In step 810, a list is formed of all the vertical edges of all shapes in the selected region, including editing shapes. In step 812, the list is sorted by the vertical position of all the lower endpoints of the edges. Again, there may be multiple edges whose lower endpoints have the same vertical position, and these would be grouped together in the sort. [00109] In step 814, enter tree is created for sweep y. This is accomplished by, at each unique vertical position represented in the sorted list (step 812), creating a scan line multimap (of class 'edgejxee') for a horizontal scan line at that vertical position (step 818). In step 820, the scan line multimap at that vertical position is populated with all the edges (structures of class 'edge') in the list having lower endpoints at the current vertical position.

[00110] After enter tree has been created and populated for sweep y, the list from step 810 is re-sorted by horizontal position of all the upper endpoints of the edges. Again, there may be multiple edges whose upper endpoints have the same vertical position. In step 824, exitjxee is created for sweep_y. As before, this is accomplished by, at each unique vertical position represented in the sorted list (step 822), creating a scan line multimap (of class 'edgejxee') for a horizontal scan line at that vertical position (step 818). In step 820, the scan line multimap at that vertical position is populated with all the edges (structures of class 'edge') in the list having upper endpoints at the current vertical position.

[00111] Returning now to Fig. 3, after the horizontal and vertical scan line trees have been built (step 318), all of the required topographical relationships among the shapes in the layout region are now extracted (step 320). The linear design rule bounds are calculated during this step as well.

[00112] Fig. 9 is a flow chart of step 320, and as can be seen, it includes a step 910 of scanning the horizontal scan tree sweep_x and another step 912 of scanning the vertical scan tree sweep_y. Vertical linear design rule bounds for DRC assist are calculated during step 910, and horizontal linear design rule bounds are calculated during step 912. Note that in another embodiment the vertical scan can be performed first and the horizontal scan thereafter. In yet another embodiment, the two scans can be performed in an alternating manner. In a particularly advantageous embodiment, since the two scans are independent of each other, and discover different items of information for populating the corner data structures, the two scans are performed simultaneously on two different processor cores. In yet another embodiment, the two scans are coordinated with each other so that they proceed from corner to corner, with all data for a given corner populated before jumping to the next corner. As used herein, the two scans are said to be performed "concurrently" with each other if they overlap in time in such a way that corner data is extracted from at least one endpoint of at least one horizontal edge before corner data is extracted from at least one endpoint of at least one vertical edge, and corner data is extracted from at least one endpoint of at least one vertical edge before corner data is extracted from at least one endpoint of at least one horizontal edge. [00113] Fig. 10 is a flow chart of step 910, for scanning the horizontal scan tree sweep x.

In step 1008, the vertical scan line edge-tree multimap object current scan line is created. In step 1010, current scan line traverses both enter tree and the exit tree together so that the vertical scan lines from both trees are considered in monotonically varying sequence, left to right. Since these two trees contain only those vertical scan lines on which an endpoint of a horizontal physical edge lies, intervening vertical scan lines are skipped during this scan. The existence of derived edges does not alter this plan since it is assumed for this part of the algorithm that all derived edge endpoints are co-located with (coincident with) at least one physical edge endpoint. The current vertical scan line is maintained in a multimap object of class edge_tree, having the structure of edge_tree 520 (Fig. 5). It has a current horizontal scanning position, and stores the information shown in block 522 for each horizontal edge that intersects a vertical line at the current horizontal scanning position.

[00114] In step 1012, current scan line is updated by adding all horizontal edges having a left-hand endpoint located at the current horizontal scan position. In step 1014, the quadrant depth vector (Fig. 5) for each edge in the current vertical scan line multimap is updated. In order to illustrate this step, reference is made to Figs. 1 1A and 1 IB, which illustrate simple portions of a layout. Fig. 1 1A highlights a convex corner 11 14, whereas Fig. 1 IB highlights a concave corner 1 134. In Fig. 1 1A, 1 110 is the current vertical scan line and 1 112 is a particular edge being considered. Edge 1 112 is represented in the enter tree and in current scan line, and has a left-hand endpoint 1 114 located on vertical scan line 11 10. Edge 11 12 also forms the upper edge of a rectangle 11 16. Four other rectangles are also shown in the figure, 11 18, 1 120, 1 122 and 1 124. Four quadrants, centered at endpoint 1 114 and numbered I, II, III and IV for purposes of the present discussion, are also shown in Fig. 11A. Similarly, in Fig. 1 IB, 1130 is the current vertical scan line and 1 132 is a particular edge being considered. Edge 1 132 is represented in the enter tree, and has a left-hand endpoint 1 134 located on vertical scan line 1 110. Edge 1 132 also forms the upper edge of a rectangle 1 136. Four other rectangles are also shown in the figure, 1 138, 1140, 1 142 and 1144. The four quadrants I, II, III and IV, centered at endpoint 1134, are also shown in Fig. 1 IB.

[00115] The quadrant depth vector indicates the number of shapes in a particular layer that border a particular edge endpoint in each of the four quadrants centered at that endpoint. In Fig. 1 1A, quadrants I, II and III contain no shapes that border endpoint 1 114, and quadrant IV contains one such shape 1 116. Thus the quadrant depth vector at endpoint 1 114 is (0,0,0,1). On the other hand, in Fig. 1 IB, quadrant II contains no shapes that border endpoint 1134, whereas quadrants I, III and IV each contain one such shape. Thus the quadrant depth vector at endpoint 1 134 is (1,0, 1,1). It can be seen that if exactly one quadrant depth is zero, then the point represents a concave corner of an island, as in Fig. 1 IB. If exactly two values are zero, and they are in adjacent quadrants, then the endpoint is not on a corner of an island. If the two zeros are in diagonally opposite quadrants, then the endpoint is a corner of two diagonally adjacent islands, sharing the one corner. If exactly three values are zero, as in Fig. 1 1 A, then the endpoint represents a convex corner of an island, island 11 16 in Fig. 1 1A. If none of the values are zero, then the endpoint is inside an island and does not represent a corner of an island. The quadrant depth vector is used in later steps, as described hereinafter.

[00116] In step 1014, the updating of the quadrant depth vector for an edge in the enter_tree (i.e. an edge whose left-hand endpoint lies on the current vertical scan line), involves incrementing the value for either quadrant I or quadrant IV by one. The value for quadrant I is incremented if the "edge against scan line?" Boolean for the edge 1 112 indicates True (i.e. the edge is the bottom edge of a shape), or the value for quadrant IV is incremented if the "edge against scan line?" Boolean for the edge 11 12 indicates False (i.e. the edge is the top edge of a shape). Similarly, the updating of the quadrant depth vector for an edge in the exit tree (i.e. an edge whose right-hand endpoint lies on the current vertical scan line), involves decrementing the value for either quadrant I or quadrant IV by one. The value for quadrant I is decremented if the "edge against scan line?" Boolean for the exiting edge indicates True (i.e. the edge is the bottom edge of a shape), or the value for quadrant IV is decremented if the "edge against scan line?" Boolean for the exiting edge indicates False (i.e. the edge is the top edge of a shape). It can be seen that the quadrant depth vector increments quantities as the vertical scan line encounters shapes while moving left-to-right across the region. It decrements quantities as the scan line moves past shapes.

[00117] In step 1015, the derived layer information is populated for each derived layer having an edge intersecting the current scan line. Fig. 24 is a flow chart detail of step 1015. Referring to Fig. 24, in step 2410, a loop is begun to traverse through all the y_positions, bottom to top, at which one or more physical horizontal edges intersect the current vertical scan line. These edges are collinear with each other, in plan view. Some may be on different layers, and some may occupy the same layer and be superimposed on each other. This group of collinear edges intersecting the current vertical scan line at current y _position is sometimes referred to herein as an "edge group".

[00118] In step 2412, the system collects all the "related" physical layers related to any of the physical horizontal edges in current edge group. As used in Fig. 24, two physical layers are considered "related" if they are both ancestors of a common derived layer. Preferably, the collections of "related" layers have been precompiled and cached for easy retrieval in this step 2412.

[00119] In step 2414, at the current y_position on current vertical scan line, the Boolean status vector for each related physical layer is determined and written into a map object referred to herein as a related_edge_status map. At this step, the related_edge_status map is populated only for physical layers.

[00120] In step 2416, all the derived layers derived ultimately from physical layers containing any of the edges in current edge group are collected. The system sorts these monotonically according to their rank. Thus derived layers that involve fewer derivation steps appear earlier in this collection than those that involve more derivation steps. This arrangement ensures that during a traversal of the collection in sorted order to calculate derived layer information, those derived layers which are ancestors of a child derived layer will already have been calculated by the time the child derived layer is reached.

[00121] In step 2418, a loop is begun through the derived layers in the collection, in sorted order. In step 2420, the derivation operator for the current derived layer is used to derive the Boolean status vector for the derived edge on the current derived layer at the current x/y position. The four elements of the Boolean status vector are calculated simply by applying the derivation operator for the current derived layer separately to each of the four elements of the Boolean status of the parent layer(s) referred to by the derivation operator for the current derived layer. For example, if the derivation operator for derived layer Dl is "P I AND P2", where P I and P2 are physical layers, and the Boolean status vectors for P 1 and P2 at the current x/y position are (a,b,c,d) and (e,f,g,h), respectively, then the Boolean status vector for the derived edge on the current derived layer at the current x/y position is calculated as (a^»e, b^»f, c^»g, d^»h).

[00122] In step 2422, the Boolean status vector just calculated for current derived layer at current y _position on current vertical scan line is inserted into the m derived edge status map in the edge object 524 for the first physical edge of current edge group. In step 2424, the Boolean status vector just calculated is also inserted into the related edge status map for the current derived layer, at the current y _position on the current vertical scan line. This prepares the related_edge_status map in case a subsequent derived layer of higher rank refers to the current derived layer in its derivation operator.

[00123] In step 2426, it is determined whether there are any more derived layers in the collection prepared in step 2416. If so, then the system returns to step 2418 to derive the Boolean status vector for the next such derived layer. If not, then the system returns to step 2410 to address the edge group intersecting the current vertical scan line at the next y-position. If there are no more such y-positions, then step 1015 for populating the derived layer information for derived layers having an edge intersecting the current vertical scan line is complete (step 2428). It can be seen that in the embodiment of Fig. 24, no shapes are actually calculated for the derived layers. Only certain information about the derived edges are calculated and stored at positions where they intersect the specific vertical scan lines that correspond to endpoints of horizontal physical edges in the layout. As used herein, any information about the location or shape of derived shapes is considered to constitute "shape information". In addition, it will be seen that the shape information that the system derives in step 1015 about derived shapes includes, among other things, sufficient information to indicate the locations of the corners of the derived shape.

[00124] Returning to Fig. 10, in step 1016, each of the edges whose left-hand endpoint lies on the current scan line are processed. These are the edges represented in enterjxee. As they are processed, a "corner" data structure for the endpoint is populated. The vertical linear design rule bounds imposed by these particular edges are calculated here as well. The corner data structure, which is used for both physical and derived corners, stores the information illustrated in Figs. 1 1A and 1 IB. It can be described in a C++ like pseudocode class definition as follows: class corner

{

edge* m_origin_x; // ori_x vertical edge meeting at the

corner. Of the edge endpoints, only the x- coordinates are populated,

edge* m_origin_y; // ori_y horizontal edge meeting at the

corner. Of the edge endpoints, only the y- coordinates are populated,

edge* m_target_x; // tar_x nearest vertical edge, walking

horizontally along shape contour from corner edge* m_target_y; // tar_y nearest horizontal edge, walking

vertically along shape contour from corner edge* m_space_ray_x; // s_ray_x nearest vertical facing edge,

walking horizontally from corner, away from shape

edge* m_space_ray_y; // s_ray_y nearest horizontal facing edge, walking vertically from corner, away from shape

edge* m_dimension_ray_x; // d_ray_x last vertical edge walking

horizontally into shape, before exiting shape edge* m_dimension_ray_y; // d_ray y last horizontal edge walking vertically into shape, before exiting shape std : : list<corner*> m_neighbor_list; // list of nearest neighbor

corners

bool m_is_convex; // whether the corner is convex or concave ray* create_space_ray_x ( ) {

ray* p_ray = new ray (this);

// the first point is the corner position, i.e., the tail of the arrow p_ray->m_pl . x = m_origin_x->m_pointl . x;

p_ray->m_pl . y = m_origin_y->m_pointl . y;

// the second point is the x position of the m_space_ray_x, i.e., the head of the arrow

p_ray->m_p2. x = m_space_ray_x->m_pointl . x;

p_ray->m_p2. y = m_origin_y->m_pointl . y;

return p_ray;

}; ray* create_space_ray_y ( ) {

ray* p_ray = new ray (this);

// the first point is the corner position, i.e., the tail of the arrow p_ray->m_pl . x = m_origin_x->m_pointl . x;

p_ray->m_pl . y = m_origin_y->m_pointl . y;

// the second point is the y position of the m_space_ray_y, i.e., the head of the arrow

p_ray->m_p2. x = m_origin_x->m_pointl . x;

p_ray->m_p2. y = m_space_ray_y->m_pointl . y;

return p_ray;

}; ray* create_dimension_ray_x ( ) {

ray* p_ray = new ray (this);

// the first point is the corner position, i.e., the tail of the arrow p_ray->m_pl . x = m_origin_x->m_pointl . x;

p_ray->m_pl . y = m_origin_y->m_pointl . y;

// the second point is the x position of the m_dimension_ray_x, i.e., the head of the arrow

p_ray->m_p2. x = m_space_dimension_x->m_pointl . x;

p_ray->m_p2. y = m_origin_y->m_pointl . y;

return p_ray; ray* create_dimension_ray_y ( ) {

ray* p_ray = new ray (this);

// the first point is the corner position, i.e., the tail of the arrow

p_ray->m_pl . x = m_origin_x->m_pointl . x;

p_ray->m_pl . y = m_origin_y->m_pointl . y;

// the second point is the y position of the m_dimension_ray_y, i.e., the head of the arrow

p_ray->m_p2. x = m_origin_x->m_pointl . x;

p_ray->m_p2. y = m_space_dimension_y->m_pointl . y;

return p_ray;

};

};

[00125] Note that for derived corners, the edge* objects in the above class all represent physical edges. Only the position of the edge* are useful (borrowed) for derived edges.

[00126] A ray object represents essentially an arrow with a head point and tail point. All the tail points coincide with the current corner. For Manhattan layouts the rays are either horizontal or vertical, though in 45 degree layouts it can also have either of the two diagonal orientations. The 'ray' class is described in a C++ like pseudocode class definition as follows: class ray

{

corner* m_parent

bool is_s_ray;

point m_pl;

point m_p2;

}

[00127] The corner data structures developed during the scan are maintained as entries in a synchronized corner map structure. This structure is a map, in which the keys identify a physical or derived layer number and an x and y position on that layer, and the values are objects of class 'corner'. Only edges on physical layers are handled in this step 1016; derived layer edges are processed in step 1019.

[00128] Fig. 12 is a flow chart detail of step 1016, for processing the entering edges. In step 1210, each of the physical entering edges represented in the current vertical scan line are considered. In Fig. 11A, this will be only edge 1 112. In Fig. 1 IB, this will be edge 1 132, as well as the top and bottom edges of rectangle 1 138. In step 1214, it is determined whether the left- hand endpoint of the current edge is a corner of an island. This is determined by reference to the current quadrant vector, as described previously. If it is not a corner of an island, then the edge is skipped.

[00129] In step 1216, a corner data structure for the left-hand endpoint of the current edge is instantiated in synchronized corner map if it does not already exist. The corner data structure might already exist in synchronized corner map if, for example, the corner had already been encountered because of a different horizontal edge on the same layer that starts at the same point (such as the bottom edge of rectangle 1138 in Fig. 1 IB), or as part of the vertical scan in an embodiment in which the vertical scan precedes or operates concurrently with the horizontal scan. In step 1218, the system walks upward and downward along the current vertical scan line from the current horizontal edge, populating the available corner information as it is learned. In particular, referring to the corner data structure definition above and the illustrations in Figs. 11 A and 1 IB, the edges s_ray_y, tar_y and d_ray_y, as well as any others required by the design rules, are populated. Note that these values identify the shape edges at the head of the respective ray. The ray itself is identified separately in the corner data structure, as previously mentioned.

[00130] In one embodiment, all design rule checks are performed only after all scans are complete. However, the present embodiment incorporates a feature in which the system performs certain simple edge-based rule checks as part of step 1218. For example, if the current edge is a top edge and the walk upwards along the current vertical scan line meets the bottom edge of a shape in the same layer, then s_ray_y is populated in the corner data structure and the minimum spacing rule is checked as well. This check involves comparing the length of s_ray_y with the minimum spacing value in the relationship master. If the current edge is a top edge and the walk upwards along the current vertical scan line meets the top edge of a shape in a different layer, then the minimum extension rule is checked by comparing the distance walked to the minimum extension value for the appropriate layer pair in the relationship master. If the current edge is a bottom edge and the walk upwards along the current vertical scan line meets the top edge of a shape in the same layer, then d ray y is populated, and also the minimum dimension rule is checked. This check involves comparing the value of d_ray_y with the minimum dimension value in the relationship master. If the current edge is a bottom edge and the walk upwards along the current vertical scan line meets the top edge of a shape in a different layer, then the minimum overlap rule is checked. Similar checks are performed during the walk downward from the current edge. If during the walks up and down the current vertical scan line, the distance walked exceeds the worst case limit from the relationship master, there is no design rule violation encountered and it is not necessary to populate further items in the corner data structure that would be encountered in the current walking direction.

[00131] In an embodiment which checks for DPT odd cycle variations, though not essential, it is also preferable at this point to detect edge-edge DPT candidates discernable from the above . Thus if the length of s_ray_y is less than the largest of the edge-edge DPT minimum spacing values set forth in the DPT design rules in the relationship master, then a

DPT edge marker object is inserted into a structure DPT edge marker set. This object identifies the current edge and the edge at the far end of s_ray_y, as well as the current scanline position.

[00132] After the available corner structure information items have been populated, the system then calculates the vertical linear design rule bounds for the current entering edge in the current vertical scan line (step 1220). In order to best understand this calculation, call the current horizontal edge el and call the next lower horizontal entering edge in the current vertical scan line e2. Assume the current distance between them is d, and the minimum rule value is r.

Depending on the particular design rule being evaluated, r could be a minimum spacing value, minimum width, minimum extension, minimum overlap, and so on. Further assume that el has a speed ratio (determined in step 315) of s 1 and e2 has a speed ratio of s2. According to the calculation, if s l=s2, then the two edges will remain the same distance from each other vertically during the drag operation. Thus no vertical linear design rule bound is created. If s l<s2, that means el will move more slowly than s2 during the drag operation. If the drag has a vertically downward vector component, then the spacing between the two edges will increase during the drag and no minimum distance rule will be violated. Again, therefore, no vertical linear design rule bound is created for downward linear movement. But if the drag has a vertically upward vector component, then the spacing between the two edges will decrease during the drag and eventually violate the design rule. The maximum distance that edge el can be allowed to move upward is then given by (d-r), which corresponds to a maximum allowable upward cursor movement (i.e. the linear upward slack distance) of d/|s2-sl |-r. Thus a linear upward slack distance is cached for the current horizontal edge el .

[00133] Note that vertical movement of el relative to the next higher horizontal entering edge in the current vertical scan line must be considered as well, and that might result in a linear downward slack distance and/or a further restriction on the linear upward slack distance.

Subsequent calculations (in step 1018 for example, for exiting edges) might further restrict the distance that edge el can move upward or downward, thereby further restricting the linear upward or downward slack. Furthermore, slack calculations for other horizontal edges intersecting the current vertical scan line or any other vertical scan line in the vertical scan line multimap can still further restrict the distance that the cursor should be allowed to move vertically upward or downward during the drag. Since only the one most restrictive slack distance need be stored for the upward direction and one for the downward direction, each new calculation of a slack distance overwrites the previous slack distance if the new slack distance is more restrictive (smaller). This procedure also occurs for each design rule in the set of design rules enabled for DRC assist, including design rules setting a maximum rule value r rather than a minimum rule value, with always the most restrictive slack distance overwriting a less restrictive slack distance in the same direction.

[00134] After the available corner structure information items have been populated, then the system returns to step 1210 to consider the next entering edge in the current vertical scan line.

[00135] Fig. 13 is a flow chart detail of step 1018 for processing exiting edge corners.

Again, only physical edges are addressed in step 1018. In step 1310, each of the exiting physical edges represented in the current vertical scan line are considered. In step 1314, it is determined whether the right-hand endpoint of the current edge is a corner of an island. This is determined by reference to the current quadrant vector, as described previously. If it is not a corner of an island, then the edge is skipped.

[00136] In step 1316, a corner data structure for the right-hand endpoint of the current edge is instantiated in synchronized_corner_map if it does not already exist. Again, the corner data structure might already exist in synchronized corner map if, for example, the corner had already been encountered because of a different horizontal edge on the same layer that ends at the same point, or as part of the vertical scan in an embodiment in which the vertical scan precedes or operates concurrently with the horizontal scan. In step 1318, the system walks upward and downward along the current vertical scan line from the current horizontal edge, populating the available corner information as it is learned. In particular, referring to the corner data structure definition above and the illustration in Figs. 1 1A and 1 IB, the edges s_ray_y, tar_y and d_ray_y, as well as any others required by the design rules, are populated.

[00137] In addition, preferably but not essentially, the system also in step 1318 performs the same edge-based rule checks for the exiting edges as performed and described above with respect to step 1218 for entering edges.

[00138] In an embodiment which checks for DPT odd cycle variations, though not essential, edge-edge DPT candidates discernable from the above preferably are detected in the same way as set forth above with respect to step 1218 for entering edges. Marker objects are inserted into DPT edge marker set which indicate the current edge and the edge at the far end of s_ray_y, as well as the current scanline position. Note that if the new marker object duplicates one already in DPT edge marker set, it is not inserted again.

[00139] After the available corner structure information items have been populated, the system then calculates additional vertical linear design rule bounds for the current exiting edge in the current vertical scan line (step 1320). These bounds are calculated similarly as set forth above with respect to step 1220, and again, only the most restrictive upward and downward vertical slack distances are retained.

[00140] After the available corner structure information items have been populated, then the system returns to step 1310 to consider the next exiting edge in the current vertical scan line.

[00141] Returning to Fig. 10, after both the entering and exiting physical edges having an endpoint on the current vertical scan line are processed, the system processes all the derived corners in the current vertical scan line (step 1019). Fig. 25 is a flow chart detail of step 1019. Because derived edge status vectors are by convention kept on the first physical edge of each unique position in the current scan line in the present embodiment, it is not useful to loop separately through edges in Enterjxee separately from edges in Exitjxee. Instead, one loop is performed vertically along the current vertical scan line, from bottom to top, stopping at each unique vertical position at which there is an edge object. Thus referring to Fig. 25, in step 2510, the current vertical scan line is walked from bottom to top, stopping at each unique vertical position at which an edge object exists. In step 2512, it is determined whether the first physical edge object at the current vertical position contains any derived edge status vectors. Only the first physical edge object need be checked at each vertical position, because by convention in the present embodiment, that is where the derived edge status map for all horizontal derived edges at the current x/y position are kept. If it is determined that there are no derived edges in the first physical edge object at the current vertical position, then the system returns to step 2510 to consider the next unique vertical position in the current vertical scan line.

[00142] If there are derived edges, then in step 2514 the system begins another loop through all the derived edges in the derived edge status map in the first physical edge object at the current vertical position. In step 2516, it is determined whether the Boolean status of the current derived edge indicates a valid corner. As previously explained, so long as the Boolean status is neither all zeros nor all ones, the corner is valid. If the current derived edge is not a corner, then the edge is skipped.

[00143] If the current derived edge is a valid corner, then in step 2518, a corner data structure for the current derived edge is instantiated in synchronized corner map if it does not already exist. In step 2520, the system walks upward and downward along the current vertical scan line from the current derived edge, populating the available derived corner information as it is learned. In particular, as for physical layer edges, s_ray_y, tar_y and d_ray_y, as well as any others required by the design rules, are populated. Also in step 2520, like in step 1218 for physical layer edges, the system performs certain simple edge-based rule checks such as minimum spacing and minimum dimension on the current derived layer, and minimum extension and minimum overlap relative to other layers (physical or derived). All the same design rule checks are performed on the derived layers as set forth above with respect to step 1218.

Additionally, like in step 1218, if during the walks up and down the current vertical scan line on the current derived layer, the distance walked exceeds the worst case limit from the relationship master, there is no design rule violation encountered and it is not necessary to populate further items in the corner data structure that would be encountered in the current walking direction.

[00144] In step 2524, the system then calculates additional vertical linear design rule bounds for the current derived edge. These bounds are calculated similarly as set forth above with respect to step 1220, and again, only the most restrictive upward and downward vertical slack distances are retained.

[00145] After the available derived corner structure information items have been populated, and the vertical design rule bounds imposed by the current derived edge have been taken into account, then the system returns to step 2514 to consider the next derived edge in the current physical edge object. If there are no more derived edges in the current physical edge object, then the system returns to step 2510 to move to the next unique vertical position in the current vertical scan line. If there are no more vertical positions represented in the current vertical scan line, then step 1019 concludes (step 2522).

[00146] Returning to Fig. 10, after both the physical and derived layer edges at the current vertical scan line are processed, the system populates or updates information about islands (step 1020). Islands are represented in objects of class 'island', and maintained in a map of class 'island map'. They are instantiated as the vertical scan line encounters them as it scans horizontally, and are updated as the vertical scan line moves across them horizontally, corner to corner. Islands are determined and checked on both physical layers and derived layers. Pertinent parts of the 'island' data structure are described in a C++ like pseudocode class definition as follows: class i sland

{ // For horizontal scan, this is the iterator in

// current_scan_line of the bottom_most_edge of the island

edge_tree : : iterator m_start_iterator ;

// For horizontal scan, this is the iterator in

// current_scan_line of the top_most_edge of the island

edge_tree : : iterator m_end_iterator ;

// the unique id of the island.

// Islands are split or merged during the horizontal scan.

// When an island is split, the island id is not split

// (i.e., multiple islands will share same id), so we know

// these islands are actually sub-islands of a larger island;

// When multiple islands merge together, the smallest island

// id is used as the shared id for all the islands merged together.

int m_island_id;

// accumulating the common run length against the same layer.

// For efficiency, 2D spacing rules are checked during scan,

// not after. In another embodiment they could be checked afterwards. int m_last_valid_common_run_position ;

// accumulating the common run length against different layers

std : : map<layer_number, int> m_last_valid_top_position_vector;

std: : map<layer_number, int> m_last_valid_bottom_position_vector ;

// accumulating the area of this island so far

int m_area;

// accumulating the area of the potential hole right above this island, int m_hole_area;

// Horizontal position that current_scan_line stopped last time

int m_last_position_updated;

[00147] Among other things, the island data structure accumulates the following information about a particular island during the process of the horizontal scan: area of the island, area of a hole just above the island, common run lengths against other islands in the same layer and islands in other layers. For clarity of illustration, the present description will concentrate primarily on the island area as an example of island-based rule checking. Reference will be made to Fig. 19E, which illustrates a sample layout region having three overlapping rectangles 1932, 1934 and 1936, all on a single physical layer. Because they overlap on a single layer, they form a single island 1930.

[00148] Roughly described, island area is accumulated during the horizontal scan by using the shape corners to divide the island into non-overlapping "island rectangles", the area of which are easily determined from the horizontal edges represented in the current vertical scan line. In the example of Fig. 19E, the method divides the island 1930 into five island rectangles bounded horizontally by the broken vertical lines 1938. Like for the extraction of corner data, the updating of island data takes place only at those vertical scan lines containing a corner of the island. Horizontal scanning does not stop anywhere between corners. A rectangle (not shown) disposed entirely within rectangle 1932, for example, will not bear on any island design rule and does not become a stopping place during the scan. A high level description of the process is illustrated in the flow chart of Fig. 23.

[00149] Referring to Fig. 23, as mentioned, the islands are stored in a map called island_map. The keys of island map identify the lower left corner of a respective island. In step 2310, each island having a corner lying on the current vertical scan line is considered. In step 2312, if the corner represents an island being encountered for the first time during the scan, a new island data structure is instantiated in island_map (step 2314). The area is set to zero (step 2316), and in step 2324, the value of m last _position_updated for the new island is set equal to the x-position of the current vertical scan line.

[00150] If the current island is already represented in island map, then effectively a vertical slice is made through the current island at the current vertical scan line; and the area of the left-adjacent rectangle is added to the area being accumulated. Accordingly, in step 2318, the height H of the left-adjacent rectangle is calculated as the distance along the current vertical scan line from the bottom edge of the current island to the top edge of the current island. This information is available in current scan line, because at least one of the top and bottom edges is a corner, and the y-position of the corner is available as the left- or right-hand endpoint of a horizontal edge in the current vertical scan line. The other of the top and bottom edges may also be a corner, or may be an edge that merely intersects the current vertical scan line. In either case its y-position is available as well in current_scan_line. In step 2320, the width W of the left- adjacent rectangle is calculated as the horizontal position of the current scan line minus the last scan line position at which island information was updated, which is the value in

m_last_position_updated. In step 2322 the product of H and W is added to the area value for the current island.

[00151] In step 2324, as mentioned above, the value of m last _position_updated for the new island is set equal to the x-position of the current vertical scan line. The method then returns to step 2310 for consideration of the next island having a corner on the current vertical scan line.

[00152] Once all islands having a corner on the current vertical scan line have been considered, then any two or more of such islands that are now vertically-adjacent are merged into a single island in step 2326 and their area values summed. In step 2328, any island that is now split into two, perhaps separated vertically by a newly encountered hole or notch, are split. The details of the merging and splitting operations are not important for an understanding of the invention. Note that whereas island area information is captured during the horizontal scan, it is not compared to the design rule values in the present embodiment until later. Note also that whereas Fig. 19E and the flow chart of Fig. 23 have been described with respect to an island on a physical layer, the process is the same for islands on a derived layer.

[00153] Returning to Fig. 10, after the island data has been updated based on the current scan line, in step 1022, as a time saving technique, the quadrant depth vectors for each of the entering horizontal edges in the current vertical scan line are copied from the right-hand quadrants to the corresponding left-hand quadrants. In this manner the left-hand quadrant depth values can be incremented or decremented as the vertical scan line moves rightward, and will contain accurate values when the scan line reaches the right hand endpoint of the edge. No such updating is required for the status vectors for edges on derived layers. In step 1024, all the exiting edges are removed from the current vertical scan line. The routine then returns to step 1010 for the next horizontal scan position.

[00154] Returning to Fig. 9, after the horizontal scan tree has been scanned, the vertical scan tree is scanned (step 912). Fig. 14 is a flow chart of step 912, for scanning the vertical scan tree sweep_y.

[00155] Fig. 14 is a flow chart of step 912, for scanning the vertical scan tree sweep_y. In step 1408, the horizontal scan line edge-tree multimap object current scan line is created. In step 1410, current_scan_line traverses both enterjxee and the exitjxee together so that the horizontal scan lines from both trees are considered in monotonically varying sequence, bottom to top. Since these two trees contain only those horizontal scan lines on which an endpoint of a vertical edge lies, intervening horizontal scan lines are skipped during this scan. Again, the existence of derived edges does not alter this plan since it is assumed for this part of the algorithm that all derived edge endpoints are co-located with at least one physical edge endpoint. The current horizontal scan line is maintained in a multimap object of class edge tree, having the structure of edge_tree 620 (Fig. 6). It has a current horizontal scanning position, and stores the information shown in block 622 for each vertical edge that intersects a horizontal line at the current vertical scanning position.

[00156] In step 1412, current scan line is updated by adding all vertical edges having a lower endpoint located at the current horizontal scan position. In step 1414, the quadrant depth vector (Fig. 6) for each edge in the current horizontal scan line multimap is updated. This step involves, for an edge in the enterjxee (i.e. a vertical edge whose lower endpoint lies on the current horizontal scan line), incrementing the value for either quadrant I or quadrant II by one. The value for quadrant I is incremented if the "edge against scan line?" Boolean for the edge 1 112 indicates True (i.e. the edge is the left-hand edge of a shape), or the value for quadrant II is incremented if the "edge against scan line?" Boolean for the edge 1 112 indicates False (i.e. the edge is the right-hand edge of a shape). Similarly, the updating of the quadrant depth vector for an edge in the exit_tree (i.e. an edge whose upper endpoint lies on the current horizontal scan line), involves decrementing the value for either quadrant I or quadrant II by one. The value for quadrant I is decremented if the "edge against scan line?" Boolean for the exiting edge indicates True (i.e. the edge is the left-hand edge of a shape), or the value for quadrant II is decremented if the "edge against scan line?" Boolean for the exiting edge indicates False (i.e. the edge is the right-hand edge of a shape). It can be seen that the quadrant depth vector increments quantities as the horizontal scan line encounters shapes while moving upward across the region. It decrements quantities as the scan line moves past shapes.

[00157] In step 1415, the derived layer information is populated for each derived layer having an edge intersecting the current scan line. Fig. 26 is a flow chart detail of step 1415. Referring to Fig. 26, in step 2610, a loop is begun to traverse through all the x_positions, left-to- right, at which one or more physical vertical edges intersect the current horizontal scan line. These edges are collinear with each other, in plan view. Some may be on different layers, and some may occupy the same layer and be superimposed on each other. Like in Fig. 24, this group of collinear edges intersecting the current horizontal scan line at current x_position is sometimes referred to herein as an "edge group".

[00158] In step 2612, the system collects all the "related" physical layers related to any of the physical vertical edges in current edge group. Again, as used in Fig. 26, two physical layers are considered "related" if they are both ancestors of a common derived layer. Preferably, the collections of "related" layers have been precompiled and cached for easy retrieval in this step 2612.

[00159] In step 2614, at the current x_position on current horizontal scan line, the Boolean status vector for each related physical layer is determined and written into a related_edge_status map. At this step, the related_edge_status map is populated only for physical layers.

[00160] In step 2616, all the derived layers derived ultimately from physical layers containing any of the edges in current edge group are collected. The system sort these monotonically according to their rank, for the same reason as set forth above with respect to step 2416. [00161] In step 2618, a loop is begun through the derived layers in the collection, in sorted order. In step 2620, the derivation operator for the current derived layer is used to derive the Boolean status vector for the derived edge on the current derived layer at the current x/y position. The four elements of the Boolean status vector are calculated by applying the derivation operator for the current derived layer separately to each of the four elements of the Boolean status of the parent layer(s) referred to by the derivation operator for the current derived layer.

[00162] In step 2622, the Boolean status vector just calculated for current derived layer at current x _position on current horizontal scan line is inserted into the m derived edge status map in the edge object 524 for the first physical edge of current edge group. In step 2624, the Boolean status vector just calculated is also inserted into the related_edge_status map for the current derived layer, at the current x _position on the current horizontal scan line. This prepares the related_edge_status map in case a subsequent derived layer of higher rank refers to the current derived layer in its derivation operator.

[00163] In step 2626, it is determined whether there are any more derived layers in the collection prepared in step 2616. If so, then the system returns to step 2618 to derive the Boolean status vector for the next such derived layer. If not, then the system returns to step 2610 to address the edge group intersecting the current horizontal scan line at the next x-position. If there are no more such x-positions, then step 1415 for populating the derived layer information for derived layers having an edge intersecting the current horizontal scan line is complete (step 2628). It can be seen again that in the embodiment of Fig. 26, no shapes are actually calculated for the derived layers. Only certain information about the derived edges are calculated and stored at positions where they intersect the specific horizontal scan lines that correspond to endpoints of vertical physical edges in the layout.

[00164] Returning to Fig. 14, in step 1416, each of the physical edges whose lower endpoint lies on the current scan line are processed. These are the edges represented in enter_tree. As they are processed, the "corner" data structure for the endpoint is populated in synchronized_corner_map. As mentioned, the relevant corner data structure may already exist from a previously encountered different vertical edge on the same layer that starts at the same point, or as part of the horizontal scan in an embodiment in which the horizontal vertical scan precedes or operates concurrently with the vertical scan. The horizontal linear design rule bounds imposed by these particular edges are calculated here as well.

[00165] Fig. 15 is a flow chart detail of step 1416, for processing the entering edges. In step 1510, each of the entering physical edges represented in the current horizontal scan line are considered. In step 1514, it is determined whether the lower endpoint of the current edge is a corner of an island. This is determined by reference to the current quadrant vector, as described previously. If it is not a corner of an island, then the edge is skipped.

[00166] In step 1516, a corner data structure for the left-hand endpoint of the current edge is instantiated in synchronized_corner_map if it does not already exist. In step 1518, the system walks leftward and rightward along the current horizontal scan line from the current vertical edge, populating the available corner information as it is learned. In particular, referring to the corner data structure definition above and the illustrations in Figs. 1 1A and 1 IB, the edges s_ray_x, tar_x and d_ray_x, as well as any others required by the design rules, are populated.

[00167] In an embodiment, certain edge-based rule checks are also performed as part of step 1518, similar to those performed in step 1218. For example, if the current edge is a right- hand edge and the walk rightward along the current horizontal scan line meets the left-hand edge of a shape in the same layer, then s ray x is populated in the corner data structure and the minimum spacing rule is checked as well. This check involves comparing the length of s_ray_x with the minimum spacing value in the relationship master. If the current edge is a right-hand edge and the walk rightwards along the current horizontal scan line meets the right-hand edge of a shape in a different layer, then the minimum extension rule is checked by comparing the distance walked to the minimum extension value for the appropriate layer pair in the relationship master. If the current edge is a left-hand edge and the walk rightwards along the current horizontal scan line meets the right-hand edge of a shape in the same layer, then d ray x is populated, and also the minimum dimension rule is checked. This check involves comparing the value of d ray x with the minimum dimension value in the relationship master. If the current edge is a left-hand edge and the walk rightwards along the current horizontal scan line meets the right-hand edge of a shape in a different layer, then the minimum overlap rule is checked. Similar checks are performed during the walk leftward from the current edge. If during the walks leftward and rightward along the current horizontal scan line, the distance walked exceeds the worst case limit from the relationship master, there is no design rule violation encountered and it is not necessary to populate further items in the corner data structure that would be encountered in the current walking direction.

[00168] In an embodiment which checks for DPT odd cycle variations, though not essential, it is also preferable at this point to detect edge-edge DPT candidates discernable from the above. Thus if the length of s_ray_x is less than the largest of the edge-edge DPT minimum spacing values set forth in the DPT design rules in the relationship master, then a

DPT edge marker object is inserted into DPT edge marker set as set forth with respect to step 1218. This object identifies the current edge and the edge at the far end of s_ray_x, as well as the current scanline position.

[00169] After the available corner structure information items have been populated, the system then calculates the horizontal linear design rule bounds for the current entering edge in the current horizontal scan line (step 1520). This calculation is similar to that set forth above with respect to step 1220, but will be adapted here for clarity. Call the current vertical edge el and call the next lower vertical entering edge in the current horizontal scan line e2. Assume the current distance between them is d, and the minimum rule value is r. Further assume that el has a speed ratio (determined in step 315) of si and e2 has a speed ratio of s2. If s l=s2, then the two edges will remain the same distance from each other horizontally during the drag operation and no horizontal linear design rule bound is created. If s l<s2, that means el will move more slowly than s2 during the drag operation. If the drag has a horizontally leftward vector component, then the spacing between the two edges will increase during the drag and no minimum distance rule will be violated. Again, therefore, no horizontal linear design rule bound is created for leftward linear movement. But if the drag has a horizontally rightward vector component, then the spacing between the two edges will decrease during the drag and eventually violate the design rule. The maximum distance that edge el can be allowed to move rightward is then given by (d- r), which corresponds to a maximum allowable rightward cursor movement (i.e. the right linear slack distance) of d/|s2-s 1 |-r. Thus a right linear slack distance is cached for the current vertical edge el.

[00170] Again, horizontal movement will also be restricted by left and right linear slacks calculated for the same and other edges of the selected objects, as well as for satisfaction of other design rules. Since only the one most restrictive linear slack distances need be stored for drag vector components in each of the leftward and rightward directions, each new calculation of a slack distance overwrites the previous slack distance if the new slack distance is more restrictive (smaller). Only one linear slack distance in each direction remains.

[00171] After the available corner structure information items have been populated, then the system returns to step 1510 to consider the next entering edge in the current horizontal scan line.

[00172] Fig. 16 is a flow chart detail of step 1418 for processing exiting edge corners.

Again, only physical edges are addressed in step 1418. In step 1610, each of the exiting edges represented in the current horizontal scan line are considered. In step 1614, it is determined whether the upper endpoint of the current edge is a corner of an island. This is determined by reference to the current quadrant vector, as described previously. If it is not a corner of an island, then the edge is skipped.

[00173] In step 1616, a corner data structure for the upper endpoint of the current edge is instantiated in synchronized corner map if it does not already exist. Again, the corner data structure might already exist in synchronized_corner_map. In step 1618, the system walks leftward and rightward along the current horizontal scan line from the current vertical edge, populating the available corner information as it is learned. In particular, referring to the corner data structure definition above and the illustration in Figs. 1 1A and 1 IB, the edges s ray x, tar_x and d_ray_x, as well as any others required by the design rules, are populated.

[00174] In addition, preferably but not essentially, the system also in step 1618 performs similar edge-based rule checks for the exiting edges as performed and described above with respect to step 1318.

[00175] In an embodiment which checks for DPT odd cycle variations, though not essential, edge-edge DPT candidates discernable from the above preferably are detected in the same way as set forth above with respect to step 1518 for entering edges. Marker objects are inserted into DPT edge marker set which indicate the current edge and the edge at the far end of s_ray_x, as well as the current scanline position. Note that if the new marker object duplicates one already in DPT edge marker set, it is not inserted again.

[00176] After the available corner structure information items have been populated, the system then calculates additional horizontal linear design rule bounds for the current exiting edge in the current horizontal scan line (step 1620). These bounds are calculated similarly as set forth above with respect to step 1520, and again, only the most restrictive left and right linear slacks are retained.

[00177] After the available corner structure information items have been populated, then the system returns to step 1610 to consider the next exiting edge in the current horizontal scan line.

[00178] Returning to Fig. 14, after both the entering and exiting physical edges having an endpoint on the current horizontal scan line are processed, the system processes all the derived corners in the current horizontal scan line (step 1419). Fig. 27 is a flow chart detail of step 1419. Because derived edge status vectors are by convention kept on the first physical edge of each unique position in the current scan line in the present embodiment, it is not useful to loop separately through edges in Enterjxee separately from edges in Exitjxee. Instead, one loop is performed horizontally along the current horizontal scan line, from left to right, stopping at each unique horizontal position at which there is an edge object. Thus referring to Fig. 27, in step 2710, the current horizontal scan line is walked from left to right, stopping at each unique horizontal position at which an edge object exists. In step 2712, it is determined whether the first physical edge object at the current horizontal position contains any derived edge status vectors. Only the first physical edge object need be checked at each horizontal position, because by convention in the present embodiment, that is where the derived edge status map for all vertical derived edges at the current x/y position are kept. If it is determined that there are no derived edges in the first physical edge object at the current horizontal position, then the system returns to step 2710 to consider the next unique horizontal position in the current horizontal scan line.

[00179] If there are derived edges, then in step 2714 the system begins another loop through all the derived edges in the derived edge status map in the first physical edge object at the current horizontal position. In step 2716, it is determined whether the Boolean status of the current derived edge indicates a valid corner. As previously explained, so long as the Boolean status is neither all zeros nor all ones, the corner is valid. If the current derived edge is not a corner, then the edge is skipped.

[00180] If the current derived edge is a valid corner, then in step 2718, a corner data structure for the current derived edge is instantiated in synchronized corner map if it does not already exist. In step 2720, the system walks left and right along the current horizontal scan line from the current derived edge, populating the available derived corner information as it is learned. Also in step 2720, like in step 1218 for physical layer edges, the system performs certain simple edge-based rule checks such as minimum spacing and minimum dimension on the current derived layer, and minimum extension and minimum overlap relative to other layers (physical or derived). All the same design rule checks are performed on the derived layers as set forth above with respect to step 1218. Additionally, like in step 1218, if during the walks to the left and right along the current horizontal scan line on the current derived layer, the distance walked exceeds the worst case limit from the relationship master, there is no design rule violation encountered and it is not necessary to populate further items in the corner data structure that would be encountered in the current walking direction.

[00181] In step 2724, the system then calculates additional horizontal linear design rule bounds for the current derived edge in the current horizontal scan line. These bounds are calculated similarly as set forth above with respect to step 1520, and again, only the most restrictive left and right linear slacks are retained.

[00182] After the available derived corner structure information items have been populated and horizontal linear slacks have been updated, then the system returns to step 2714 to consider the next derived edge in the current physical edge object. If there are no more derived edges in the current physical edge object, then the system returns to step 2710 to move to the next unique horizontal position in the current horizontal scan line. If there are no more horizontal positions represented in the current horizontal scan line, then step 1419 concludes (step 2722).

[00183] Returning to Fig. 14, after both the physical and derived layer edges at the current horizontal scan line are processed, it is not necessary to populate or update information about islands. This was done during the horizontal scan (step 1020 in Fig. 10), and no additional information will be determined during the vertical scan. For example, the area of an island, determined as a vertical scan line scans across the island horizontally, will not be any different than the area determined as a horizontal scan line scans across the island vertically.

[00184] In step 1422, as a time saving technique, the quadrant depth vectors for each of the entering vertical edges in the current horizontal scan line are copied from the upper quadrants to the corresponding lower quadrants. In this manner the lower quadrant depth values can be incremented or decremented as the horizontal scan line moves upward, and will contain accurate values when the scan line reaches the upper endpoint of the edge. It is not necessary to update status vectors for derived edges in the same manner. In step 1424, all the exiting edges are removed from the current horizontal scan line. The routine then returns to step 1410 for the next vertical scan position.

[00185] Returning to Fig. 3, after step 320, all the topographical relationships needed to perform the checks in the design rule set have been collected into a layout topology database. This includes all the needed relationships on both physical and derived layers, as well as those needed to perform DPT odd cycle detection. As mentioned, the term 'database' as used herein does not imply any unity or regularity of structure, and in the present embodiment the layout topology database includes synchronized corner map, island map and via map, and other collections of data as well. In step 322, the values in the layout topology database are compared to those in the relationship master, in order to check all the design rules. In one embodiment, all design rule violations are reported, whereas in another embodiment, only those violations involving editing shapes are reported. The corner and conditional design rule bounds are calculated during this step as well.

[00186] Fig. 17 is a flow chart detail of step 322. These are illustrative examples of design rules that are checked in the present embodiment only after the scans across the layout region have been completed. The grouping of these checks as shown in Fig. 17 is only for convenience of the present description; it may or may not correspond to any grouping in any particular embodiment. For purposes of the present description, the design rules that are checked in Fig. 17 are grouped as follows. Corner-to-corner rules are checked in step 1710, and other corner-based rules are checked in step 1712. Island-based rules are checked in step 1714, and DPT multi- patterning rule checks such as DPT odd cycle detection is performed in step 1715. Other rules (such as via-based rules) are checked in step 1716. Details are provided herein regarding some of the corner-to-corner rules, some other corner-based rules, some island-based rules, and DPT odd cycle detection. All of the design rule checks described below with respect to steps 1710-1716 are checked for both physical and derived layer features if they are identified in the design rule set. Design rules that reference derived layers are checked in the steps of Fig. 17, as well as those that reference only physical layers.

[00187] Corner design rule bounds are calculated as part of the check of corner-to-corner rules in step 1710. Conditional design rule bounds are calculated as part of the check of other corner-based rules in step 1712.

[00188] Fig. 18 is a flow chart detail of step 1710, for checking the corner-to-corner rules.

In step 1810, the system builds a map of space and dimension rays from the ray information previously populated into the synchronized corner map. Rays from all layers are included, from both physical and derived layers, but only those space_rays that extend from convex corners, and only those dimension_rays that extend from concave corners, are included in this ray map. In addition, instead of the rays representing the shape edges encountered when walking away from the corner, the rays in the ray map formed in step 1810 represent true rays from the corner to the encountered edge.

[00189] In step 1812, the ray map is scanned left-to-right to identify intersections of the rays. A conventional scan line algorithm can be used for this purpose.

[00190] In step 1814, it is determined whether the current ray intersection is an intersection of two space_rays. The two corners from which these space_rays extend both have to be convex, so the situation is as illustrated in Fig. 19A, where s_rays 1910 and 1912 intersect.

In this case the corner-to-corner Euclidean spacing 1914 is calculated. If the two shapes are located on the same layer, the spacing 1914 is compared to the minimum corner-to-corner spacing value in relationship_master. If they are on different layers, it is compared to the minimum corner-to-corner clearance in relationship master (step 1816).

[00191] In an embodiment which checks for DPT odd cycle variations, though not essential, it is also preferable at this point to detect corner-corner DPT candidates discernable from the above. Thus in step 1817, if the two shapes are located on the same layer, the spacing

1914 is compared also to the DPT minimum corner-to-corner spacing value in

relationship master. If the distance between the corners is shorter, then a DPT corner marker object is inserted into DPT_edge_marker_set as set forth with respect to step 1218. A DPT corner marker identifies the two corners, which in turn identify the x and y positions of each corner. Note that in one embodiment, the Euclidean distance between the two corners is used whereas in another embodiment the Manhattan distance is used. In yet another embodiment the Euclidean distance is used in certain conditions and the Manhattan distance is used in other situations. In still other embodiments, yet another kind of distance measurement is used.

[00192] Returning to Fig. 18, if the intersecting rays are not both space rays, then in step

1818 it is determined whether they are both dimension_rays in the same layer. The two corners from which these dimension_rays extend both have to be concave, so the situation is as illustrated in Fig. 19B, where d rays 1916 and 1918 intersect. In this case the corner-to-corner Euclidean dimension 1920 is again calculated and compared to the minimum dimension rule value in relationship_master (step 1820).

[00193] If the intersecting rays are not both dimension rays, then in step 1822 it is determined whether one is a space_ray on one layer, and the other is a dimension_ray on a different layer. Since the corner from which the space_ray extends is convex, and the corner from which the dimension ray extends in concave, the situation is as illustrated in Fig. 19C. In this figure, s_ray 1922 from a corner of shape 1921 intersects d_ray 1924 from a corner of shape 1923, and the two shapes are on different layers. In this case the distance that the shape on one layer extends past the edge of the shape the other layer is calculated in both dimensions, and compared to the minExtension or minDualExtension value in relationship_master (step 1824).

[00194] Various other corner-based design rule checks can be performed within this loop as well, not shown in Fig. 18. Corner slacks are then calculated in step 1826, and the routine then loops back to step 1812 to continue scanning for more intersecting rays.

[00195] A corner slack is the slack between two corners, i.e. one pair of horizontal and one pair of vertical edges. A corner slack has two linear slack values, one horizontal (either left or right) and one vertical (either up or down). These horizontal and vertical linear slack components of the corner slack are calculated in the same way that the horizontal and vertical linear slack values are calculated within step 320. However, the values calculated for corner slacks are cached separately and not merged with those calculated for the linear slacks.

[00196] Fig. 20 is a flow chart detail of step 1712, for checking certain other corner-based rules. These rules are checked inside a loop 2010 which traverses the synchronized corner map. In step 2012, the edge length rule is checked from the current corner. For the horizontal edge meeting at this corner, this involves subtracting the x-position of the corner (ori_x) from the x- position of the nearest vertical edge, walking horizontally along the shape contour (tar_x) and comparing the absolute value of the difference to the minimum edge length value in the relationship_master. For the vertical edge meeting at this corner, this involves subtracting the y- position of the corner (ori_y) from the y-position of the nearest horizontal edge, walking vertically along the shape contour (tar_y) and comparing the absolute value of the difference to the minimum edge length value in the relationship master.

[00197] In step 2014, it is determined whether the current corner is concave or convex. If it is concave, then in step 2016 the concave corner edge length rule is checked. This rule requires that at least one of the two adjacent edges forming a concave corner have at least a minimum length. This test can be performed using the same values from the corner data structure as used in step 2012 (ori_x, tar_x, ori_y and tar_y). The lengths determined for the two edges are compared to the minimum concave corner edge length value in the relationship master.

[00198] In step 2018, the notch rule is checked. This rule requires that a 'notch' in an island have at least a specified minimum width. Framed in terms of corners, the rule requires that two adjacent concave corners be at least a specified distance apart. This rule need be checked for a horizontally-adjacent corner only of the horizontally-adjacent corner is concave, and need be checked for a vertically-adjacent corner only of the vertically -adjacent corner is concave. For example, in the illustration of Fig. 1 IB, only the horizontally-adjacent corner need be checked for violation of the notch rule. The notch rule can be tested by subtracting the x-position of the current corner (ori_x) from the x-position of the nearest vertical facing edge, walking horizontally from corner, away from the shape, which is already available in the current corner data structure as space ray x. The absolute value of the difference is then compared to the minimum notch width value in the relationship master. For a notch formed with a vertically- adjacent concave corner, the y-position of the current corner (ori_y) is subtracted from the y- position of the nearest horizontal facing edge, walking vertically from the current corner, away from the shape, which is already available in the current corner data structure as space_ray_y. The absolute value of the difference is then compared to the minimum notch width value in the relationship master.

[00199] If in step 2014, it is determined that the current corner is convex, then in step

2020 the convex corner edge length rule is checked. This rule requires that at least one of the two adjacent edges forming a convex corner have at least a minimum length. This test can be performed using the same values from the corner data structure as used in step 2012 (ori_x, tar_x, ori_y and tar_y). The lengths determined for the two edges are compared to the minimum convex corner edge length value in the relationship_master.

[00200] In step 2022, an end-of-line spacing rule is checked. In its simplest form, this rule requires that at the end of a line, a specified minimum spacing is required to the neighboring geometry. Referring to Fig. 19D, where the line in question is line 1926, the rule requires that for an end-of-line width eolWidth less than one specified value, the end-of-line spacing eolSpace must be at least another specified value. If the current corner is convex corner 1828, then the width of the line 1926 in the horizontal dimension is easily determined by subtracting the x- position of the current corner (ori_x) from the x-position of the last vertical edge walking horizontally into shape, before exiting shape, which is already available in the current corner data structure as d_ray_x. The spacing to the next neighboring geometry is available in the current corner data structure as s_ray_y. Thus the absolute value of the subtraction is compared to the value for eolWidth in the relationship master, and if small enough to invoke the rule, s_ray_y is then compared to the value for eolSpace in the relationship_master. For a

horizontally-oriented line, the width of the line in the vertical dimension is determined by subtracting the y-position of the current corner (ori_y) from the y-position of the last horizontal edge walking vertically into shape, before exiting shape, which is already available in the current corner data structure as d_ray_y. The spacing to the next neighboring geometry is available in the current corner data structure as s ray x. Thus the absolute value of the subtraction is compared to the value for eolWidth in the relationship master, and if small enough to invoke the rule, s ray x is then compared to the value for eolSpace in the relationship master.

[00201] After all the desired rules are checked for the current corner, conditional design rule bounds are calculated in step 2026. The routine then returns to step 2010 to consider the next corner in synchronized corner map.

[00202] A conditional slack is the slack for a general conditional rule context. Complex design rules with multiple sub-rules, such as for example some of the design rules checked in Fig. 20, can be handled with such a slack. Multiple groups of pairs of edges are considered, with a conjunctive relationship of conditions inside each group and a disjunctive relationship among groups. A conditional slack has multiple groups of horizontal and linear slack values, each of which is calculated in the same way that the horizontal and vertical linear slack values are calculated within step 320.

[00203] Returning to Fig. 17, after the corner-based rules have been checked in steps 1710 and 1712, island-based rules are then checked in step 1714. Example island-based design rules that can be checked here include the minimum island area rule, the minimum hole area rule, minimum common run dependent separation against other islands in the same layer, and minimum common run dependent separation against islands in other layers. In an embodiment, these are all checked within a single traversal of island map, where the values for all required topological relationships in the layout region have already been populated. For example, the area of each island in island map has already been populated during the horizontal scan. The step of checking the minimum island area rule, therefore, is accomplished simply by comparing the stored island area for the current island with the minimum area value in the relationship master. Note that in an embodiment, during the horizontal scan, accumulation of island area is aborted once the accumulated area exceeds the worst case minimum required in the relationship master. The stored area values will still be determined in this step 1714 to satisfy the minimum island area rule.

[00204] In step 1715, DPT odd cycle detection is performed. In an embodiment that supports triple-patterning-technology (TPT) design rule violation detection, this can be performed as part of step 1715 as well. The embodiment of Fig. 17 detects TPT design rule violations mainly as an add-on to DPT odd cycle detection, but in another embodiment, it can be done natively.

[00205] Fig. 29 is a flow chart detail of step 1715, for a particular layer. Step 1715 can be repeated for each physical layer to be considered. The routine begins with dpt_edge_marker_set and dpt_corner_marker_set as populated during the scanning process as previously described. Dpt edge marker set identifies all the candidate edge pairs that are spaced more closely than the appropriate DPT edge-edge minimum, and dpt corner marker set identifies all the candidate corner pairs that are spaced more closely than the DPT corner-corner minimum. Though many relationships are determined and stored during the scanning process as previously described, the only objects that are actually used in the present embodiment for DPT odd cycle detection are those that were inserted into dpt_edge_marker_set and dpt_corner_marker_set. For edge-edge DPT spacing candidates, at a minimum in the present embodiment this includes an identification of the two islands which are more near each other than one or more of the DPT edge-edge spacing rules. In addition, recall that detection of DPT edge-edge spacing candidate violations in one dimension need only the s_ray_x values, and detection of DPT edge-edge spacing candidate violations in the perpendicular dimension need only the s_ray_y values. While it is optimal that all these relationships have been determined within the subject region before step 1715 begins, it will be appreciated that a benefit will be obtained so long as a plurality (more than one) of the relationships have been determined before step 1715 begins.

[00206] In the embodiment of Fig. 29, DPT odd cycle violation detection operates by iterating through all the islands on the current layer in the region of interest. The iteration involves a nested discovery of islands that are connected to each other by DPT candidate relationships in either dpt edge marker set or dpt corner marker set. As islands are discovered, a spanning tree is built in which each of the nodes represents an island, and each of the arcs represents a DPT candidate relationship. As each island is added to a tree it is colored oppositely of the color of the island to which it will be connected in the tree. If an island is discovered which is already on the tree, then connecting it again would create a cycle. And if it is already colored in conflict with the color of the island (node) to which it would be newly connected, then a DPT odd cycle violation has been found. In the embodiment of Fig. 29, no arcs are actually drawn which form cycles; the only record that is maintained is a list of odd cycle violations, for later display to a user. In another embodiment arcs which form cycles could be drawn.

[00207] As used herein, a "graph" is a set of nodes connected together by arcs. A "tree", as used herein, means a connected graph with no cycles. Thus a process of "building a tree" also constitutes a process of "building a graph", although it is a special case of a graph. A "forest", as used herein, is a graph containing only disconnected trees, and a single tree is considered herein to be a degenerate case of a Forest. In aspects of the present invention, there is no requirement that any particular node of a tree be designated as a root node, though it is useful to do so and the embodiment herein does so.

[00208] Referring to Fig. 29, three new multimaps are first created from

dpt_edge_marker_set and dpt_corner_marker_set. Together, these two sets are sometimes considered herein to constitute a single 'data structure'. In step 2910, the edge-edge candidates from dpt edge marker set are first written into a l^st_edge_map multimap, sorted by the head edge of each candidate. Then the same candidates are also written into a 2^nd_edge_map multimap, this time sorted by the tail edge of each candidate. In step 2912, the corner-corner candidates from dpt corner marker set are written into a corner map multimap, twice: once keyed by the head corner of each candidate, and the second time keyed by the tail corner of each candidate. As used herein, 1 st edge map, 2nd_edge_map and corner map multimap are sometimes considered a single 'data structure'. The three multimaps together indicate all the islands within the region to be checked, mostly more than once. In the DPT odd cycle checking process below, islands are discovered and referenced by a "root corner", which can be any corner on the island. Corners are discovered by iterating through corner_map, which identifies corners explicitly, as well as through l^st_edge_map multimap and 2^nd_edge_map, in which corners are identified implicitly as one end or the other of the included edges. The corner-corner or edge- edge entries in the three multimaps are erased as they are considered in the DPT odd cycle checking process until they are empty.

[00209] In step 2914, the routine begins to iterate through all the available islands represented in the three multimaps. Each new island to consider is identified at this point by a particular corner of the island, which has been designated as the "root" corner. Fig. 30 is a flow chart detail of step 2914. It utilizes an additional, temporary map known as

candidate corner map, to hold corners discovered during the iteration and which might identify new islands not yet considered. The corner which the routine outputs as the next corner to be considered in the iteration (the root corner of the next island to be considered in the iteration) is referred to in Fig. 30 as the "selected" corner.

[00210] Referring to Fig. 30, in step 3010, the routine first determines whether the candidate corner map is empty. If not, then in step 3012, the first available corner in candidate corner map is taken as the selected corner. In step 3014 the selected corner is erased from candidate corner map. In step 3016 it is determined whether the selected corner is already colored. If so, then the island has already been considered in the iteration and need not be considered again. The routine returns to step 3010 to determine whether candidate corner map contains any more candidate corners. If in step 3016 the selected corner is determined to not yet be colored, then in step 3018 the selected corner is returned as the root corner of the first (or next) available island to consider in the iteration.

[00211] If in step 3010 it is determined that candidate corner map is empty, then the routine next looks in corner map. In step 3020, if corner map is not empty, then in step 3022, the first available corner in corner_map is taken as the selected corner. As this corner was not found by way of a relationship with a previously-considered corner or edge, it is presumed (at least initially) to be disjoint from any existing tree. In step 3024, therefore, a new tree is started with its root as the island identified by the selected corner. In an embodiment which supports predefined color groups, the pre-groups value for the tree is set initially to no_color. The selected corner is then returned in step 3018 as the root corner of the first (or next) available island to consider in the iteration. No color is assigned to the island yet; it will be assigned when the island is connected to a tree.

[00212] If in step 3020 it is determined that corner map is empty, then the routine next looks in l^st_edge_map. In step 3030, if l^st_edge_map is not empty, then in step 3032, one of the endpoints (corners) of an available edge in l^st_edge_map is taken as the selected corner. It will be recalled that l^st_edge_map is a multimap, keyed according to the head edge of the edge-edge candidates. It will also be appreciated that both endpoints of any given edge are disposed on the same island. Thus since the iteration of step 2914 is ultimately for identifying islands rather than edges or corners, step 3032 merely involves selecting one of the key edges in l^st_edge_map, and then selecting as the selected corner one of the endpoints from the selected edge. It does not matter which key edge is selected nor which endpoint of that edge is selected. Again, as the selected corner was not found by way of a relationship with a previously -considered corner or edge, it is presumed (at least initially) to be disjoint from any existing tree. In step 3024, therefore, a new tree is started with its root as the island identified by the selected corner. In an embodiment which supports predefined color groups, the pre-groups value for the tree is set initially to no color. The selected corner is then returned in step 3018 as the root corner of the first (or next) available island to consider in the iteration. No color is assigned to the island yet; it will be assigned when the island is connected to a tree.

[00213] If in step 3030 it is determined that l^st_edge_map is empty, then the routine next looks in 2^nd_edge_map. In step 3040, if 2^nd_edge_map is not empty, then in step 3042, one of the endpoints (corners) of the first available edge in 2^nd_edge_map is taken as the selected corner. It will be recalled that 2^nd_edge_map is a multimap, keyed according to the tail edge of the edge- edge candidates. It will also be appreciated that both endpoints of any given edge are disposed on the same island. Thus since the iteration of step 2914 is ultimately for identifying islands rather than edges or corners, step 3042 merely involves selecting one of the key edges in

2^nd_edge_map, and then selecting as the selected corner one of the endpoints from the selected edge. It does not matter which key edge is selected nor which endpoint of that edge is selected. Again, as the selected corner was not found by way of a relationship with a previously- considered corner or edge, it is presumed (at least initially) to be disjoint from any existing tree. In step 3034, therefore, a new tree is started with its root as the island identified by the selected corner. In an embodiment which supports predefined color groups, the pre-groups value for the tree is set initially to no_color. The selected corner is then returned in step 3018 as the root corner of the first (or next) available island to consider in the iteration. No color is assigned to the island yet; it will be assigned when the island is connected to a tree.

[00214] If in step 3040 it is determined that 2^nd_edge_map is empty as well, then the routine returns NULL to indicate that the iteration is complete (step 3050).

[00215] Returning to Fig. 29, after the iterating step 2914 returns the next island to consider, in step 2916, the routine walks the island contour, from the root corner identified in step 2914, looking for odd cycles formed with other islands. It does not matter whether the contour walk proceeds clockwise or counterclockwise, or in some other sequence. It can also visit corners and edges of the contour in any desired sequence. In the present embodiment the contour can be walked most easily clockwise or counterclockwise in step 2916, because each of the corner data structures has already collected the horizontal and vertical edges connected to it, and the next corner of the island at the far end of each edge. Specifically, the following information has already been collected about each corner on the island: the edge adjacent to the corner in one direction (clockwise or counterclockwise; both are collected in the present embodiment but only one is needed to walk the contour); and the far corner of that edge. Note that in some embodiments individual corners or edges can be skipped in this contour walk, for example if because of other information it is already known that such corner or edge

geometrically cannot be involved in a multi-patterning spacing candidate violation.

[00216] Fig. 31 is a flow chart detail of step 2916. Referring to Fig. 31, in step 31 10, all corner-corner candidates that involve the current corner are processed, looking for corner-corner candidates whose far island is already on the current tree and already colored. If one is found, and the far island is already colored in conflict with the color of the current island, then a DPT odd cycle violation has been found.

[00217] Fig. 32 is a flow chart detail of step 31 10 of Fig. 31. Referring to Fig. 32, in step

3210, the routine first iterates through all the corner-corner candidates in corner map involving the current corner. In step 3212, the far corner of the current candidate is identified. If it is not already assigned to an existing island (step 3214), then in step 3216 it is merely inserted into candidate_corner_map as identifying a newly discovered island to be considered later (see step 3012 (Fig. 30)). The routine then returns to step 3210 to consider the next corner-corner candidate in corner map involving the current corner.

[00218] If the far corner is already assigned to an island (step 3214), then in step 3218 it is determined whether that island (now sometimes called the far island) has been colored. If not, then it is not yet connected to a tree. In this case, in step 3220, it is connected to the current tree. The arc for the new connection is the current corner-corner candidate, and the color assigned to the far island is whatever color is opposite of the current island. In an embodiment, assigning a color to an island can involve merely populating a color parameter in a node data structure with an integer or enum representing one of the range of available colors. The routine then returns to step 3210 to consider the next corner-corner candidate in corner map involving the current corner.

[00219] In an embodiment that supports TPT design rule violation detection, after it is determined in step 3214 that the current far corner is already assigned to an island, then in step 3217 an identification of the island pair is inserted into a new map called TPT island map, which is used as described below. Additionally, in an embodiment that supports multi-patterning pre-coloring, after the newly discovered island is connected to the current tree and colored (step 3220), the current tree is checked for a multi -patterning pre-coloring violation (step 3222). Still further, in an embodiment that supports multi-patterning pre-groups, after the newly discovered island is connected to the current tree and colored (step 3220), the current tree is checked for a multi-patterning pre-grouping violation (step 3224).

[00220] Returning to step 3218, if the far island is already colored, then it is already connected to a tree. In this case, adding an arc to it would create a cycle. Thus in step 3226 it is determined whether the cycle is even or odd. If the two islands are colored oppositely, then the cycle is even and nothing need be done, connected or stored. The routine merely returns to step 3210 to consider the next corner-corner candidate in corner map involving the current corner. If the two islands have the same color, however, then the cycle is odd. In step 3228 the odd cycle is inserted into an odd cycle collection structure for later presentation to the user. Again, there is no need to connect the new arc in the tree, so the routine merely returns to step 3210 to consider the next corner-corner candidate in corner map involving the current corner.

[00221] A cycle is represented in the DPT odd cycle collection structure as a list of markers each identifying a DPT spacing violation that forms an element of the cycle. Each of these markers is either a corner-corner marker, in which case it identifies the specific corners of the two islands that are place too near each other; or an edge-edge marker, in which case it identifies the specific edges of the two islands that are placed too near each other. It will be appreciated that this information is sufficient to draw the marker visibly for the user.

[00222] After all the corner-corner candidates in corner map involving the current corner have been considered (step 3210), all the corner-corner candidates keyed by the current corner are erased from corner_map (step 3230). The routine then returns (step 3232) to the contour walking process (Fig. 31).

[00223] Fig. 36 is a flow chart detail of step 3222 (Fig. 32) for checking for a multi- patterning pre-coloring violation. For various reasons it might be the case that some islands in a layout are pre-designated by the designer to be formed on a particular one of the multi-patterning masks. As an overview, the present embodiment detects such pre-coloring violations as follows. While growing the spanning tree for detecting DPT coloring violations, if an island has a pre- color consistent with an assigned color, mark it as positive; if an island has a pre-color inconsistent with the assigned color, mark it as negative; whenever there are both positive and negative islands detected on a single tree, then there is a pre-color violation, and the conflict path is the path from positive to negative on the tree. Note that neither pre-coloring nor the methods described herein to detect a pre-coloring violation, are restricted to environments using only two multi-patterning masks.

[00224] Referring to Fig. 36, in step 2610, it is first determined whether the newly connected island (step 3220) has been pre-designated for a particular mask. If not, then in step 3612 the process returns to Fig. 32 since there is no pre-coloring to violate. If the new island is pre-colored, then in step 3614 it is determined whether the current tree has already been marked "consistent" or "inconsistent" by a previous pre-color, or not yet marked. If it has not yet been marked, then in step 3616, if the pre-color of the island is the same as the color assigned to the island in step 3220 then the current tree is marked "consistent". If different, then the current tree is marked "inconsistent". The current island is then saved as a pre color island, and in step 3612 the process returns to Fig. 32.

[00225] If in step 3614 it was determined that the current tree has already been marked as

"inconsistent", then in step 3620 it is determined whether the pre-color of the island is the same as the color assigned to the island in step 3220. If not, then there is no pre-color violation and in step 3612 the process returns to Fig. 32. On the other hand, if in step 3614 it was determined that the current tree has already been marked as "consistent", then in step 3622 it is again determined whether the pre-color of the island is the same as the color assigned to the island in step 3220. If so, then again there is no pre-color violation and in step 3612 the process returns to Fig. 32. It is only if the current tree has already been marked as "inconsistent" and the pre-color of the island is the same as the color assigned to the island in step 3220, or the tree has already been marked as "consistent" and the pre-color of the island is not the same as the color assigned to the island in step 3220, that a pre-color violation has been found. In these cases, in step 3624, the path between the current island and the pre color island on the current tree is saved for display to the user or other reporting. In step 3612 the process then returns to Fig. 32.

[00226] Fig. 37 is a flow chart detail of step 3224 (Fig. 32) for checking for a DPT pre- grouping violation. As for pre-coloring, for various reasons it might be the case that all islands in a "pre-group" of islands are required to be formed on a particular a single one of the DPT masks - though it does not matter which mask. A pre-grouping violation occurs when the requirement cannot be met with respect to a particular one of the pre-groups. In the present embodiment such pre-grouping violations are detected roughly as follows: While growing the spanning tree for detecting DPT coloring violations, whenever two islands in the same pre-group are found with different colors assigned, then a pre-grouping violation has been found, and the conflict path is the path between the two islands on the tree. Note that like pre-coloring, neither pre-grouping nor the methods described herein to detect a pre- grouping violation, are restricted to environments using only two multi-patterning masks.

[00227] Referring to Fig. 37, in step 3710 a loop is begun which iterates through a preexisting list of pre-groups. In step 3712 it is determined whether the current pre-group contains the current island. If not, then iteration continues to the next pre-group (step 3710). If so, then it is next determined in step 3714 whether the current pre-group has already been given a color. If not, then in step 3716 the current pre-group is assigned the same color as was assigned to the current island (from step 3220), and no pre-grouping violation has occurred. The iteration then continues to the next pre-group (step 3710). If in step 3714 it is determined that the current pre- group is already colored, then in step 3718 it is determined whether that color is the same as the color of the current island. If so then no pre-grouping violation has occurred and the iteration then continues to the next pre-group (step 3710). If the color of the current pre-group differs from the color of the current island, then a pre-group violation has been found. In step 3720 the path is found between the current island and an a color island of the current pre-group, and that path is saved for display to the user or other reporting. The iteration then continues to the next pre-group (step 3710). When the iteration completes checking all pre-groups, in step 3722 the process then returns to Fig. 32.

[00228] As mentioned, in Fig. 32, after all the corner-corner candidates in corner map involving the current corner have been considered and appropriate ones erased from corner map (step 3230), the routine returns to the contour walking process (Fig. 31). In Fig. 31, the contour walking process next, in step 31 12, refers to the corner data structure of the current corner to identify an edge of the current island that is adjacent to the current corner. Referring to Fig. 11A, for example, this can be either ori_x or ori_y, depending on whether the next edge in the contour walk is a vertical edge or a horizontal edge. Ori x and ori y each point to an edge data structure, which in turn identifies the two endpoints of the edge. All edge-edge candidates that involve the current edge are then processed, looking for edge-edge candidates whose far island is already on the current tree and already colored. Again, if one is found, and the far island is already colored in conflict with the color of the current island, then a DPT odd cycle violation has been found. In step 31 12, only those edge-edge candidates whose head end is represented as a key in the l^st_edge_map multimap, are considered in step 31 12.

[00229] Fig. 33 is a flow chart detail of step 31 12 of Fig. 31. As it bears many similarities with the flow chart of Fig. 32, the description of Fig. 32 applies to Fig. 33 as well to the extent not in conflict with this description of Fig. 33. Referring to Fig. 33, in step 3310, the routine first iterates through all the edge-edge candidates in l^st_edge_map for which the current edge is the key edge. In step 3312, the far edge of the current candidate is identified. If it is not already assigned to an existing island (step 3314), then in step 3316 one corner of the far edge is merely inserted into candidate_corner_map as identifying a newly discovered island to be considered later (see step 3012 (Fig. 30)). It does not matter which endpoint of that edge is selected as the corner to be inserted into candidate corner map since both endpoints would identify the same island. The endpoint can be determined easily because the edge data structure already identifies both endpoints of the edge. The routine then returns to step 3310 to consider the next edge-edge candidate in l^st_edge_map involving the current corner.

[00230] If the far corner is already assigned to an island (step 3314), then in step 3318 it is determined whether that island (now sometimes called the far island) has been colored. If not, then it is not yet connected to a tree. In this case, in step 3320, it is connected to the current tree. The arc for the new connection is the current edge-edge candidate, and the color assigned to the far island is whatever color is opposite of the current island. The routine then returns to step 3310 to consider the next edge-edge candidate in lst_edge_map involving the current edge.

[00231] In an embodiment that supports TPT design rule violation detection, after it is determined in step 3314 that the current far corner is already assigned to an island, then in step 3317 an identification of the island pair is inserted into TPT island map. Additionally, in an embodiment that supports multi-patterning pre-coloring, after the newly discovered island is connected to the current tree and colored (step 3320), the current tree is checked for a multi- patterning pre-coloring violation (step 3322). The method of Fig. 36 can be used to perform this check. Still further, in an embodiment that supports multi-patterning pre-groups, after the newly discovered island is connected to the current tree and colored (step 3320), the current tree is checked for a multi-patterning pre-grouping violation (step 3324). The method of Fig. 37 can be used to perform this check.

[00232] Returning to step 3318, if the far island is already colored, then it is already connected to a tree. In this case, adding an arc to it would create a cycle. Thus in step 3326 it is determined whether the cycle is even or odd. If the two islands are colored oppositely, then the cycle is even and nothing need be done, connected or stored. The routine merely returns to step 3310 to consider the next edge-edge candidate in lst_edge_map involving the current edge. If the two islands have the same color, however, then the cycle is odd. In step 3328 the odd cycle is inserted into the odd cycle collection structure for later presentation to the user. Again, there is no need to connect the new arc in the tree, so the routine merely returns to step 3310 to consider the next edge-edge candidate in lst_edge_map involving the current edge.

[00233] After all the edge-edge candidates in lst edge map involving the current edge have been considered (step 3310), all the edge-edge candidates keyed by the current edge are erased from lst_edge_map (step 3330). The routine then returns (step 3332) to the contour walking process (Fig. 31).

[00234] Returning to Fig. 31, the contour walking process next, in step 3114, processes all edge-edge candidates that involve the current edge, this time considering only those edge-edge candidates whose tail end is represented as a key in the 2ⁿ _edge_map multimap. Fig. 34 is a flow chart detail of step 31 14 of Fig. 31, which is similar to that in Fig. 33. The descriptions of Figs. 32 and 33 apply to Fig. 34 as well, to the extent not in conflict with this description of Fig. 34.

[00235] Referring to Fig. 34, in step 3410, the routine first iterates through all the edge- edge candidates in 2^nd_edge_map for which the current edge is the key edge. In step 3412, the far edge of the current candidate is identified. If it is not already assigned to an existing island (step 3414), then in step 3416 one corner of the far edge is merely inserted into candidate_corner_map as identifying a newly discovered island to be considered later (see step 3012 (Fig. 30)). It does not matter which corner of that edge is selected, since both corners would identify the same island. The corner can be determined easily because the edge data structure already identifies both endpoints of the edge. The routine then returns to step 3410 to consider the next edge-edge candidate in 2^nd_edge_map involving the current corner.

[00236] If the far edge is already assigned to an island (step 3414), then in step 3418 it is determined whether the far island has already been colored. If not, then it is not yet connected to a tree. In this case, in step 3420, it is connected to the current tree. The arc for the new connection is the current edge-edge candidate, and the color assigned to the far island is whatever color is opposite of the current island. The routine then returns to step 3410 to consider the next edge-edge candidate in 2^nd_edge_map involving the current edge.

[00237] In an embodiment that supports TPT design rule violation detection, after it is determined in step 3414 that the current far corner is already assigned to an island, then in step 3417 an identification of the island pair is inserted into TPT island map. Additionally, in an embodiment that supports multi-patterning pre-coloring, after the newly discovered island is connected to the current tree and colored (step 3420), the current tree is checked for a multi- patterning pre-coloring violation (step 3422). The method of Fig. 36 can be used to perform this check. Still further, in an embodiment that supports multi-patterning pre-groups, after the newly discovered island is connected to the current tree and colored (step 3420), the current tree is checked for a multi-patterning pre-grouping violation (step 3424). The method of Fig. 37 can be used to perform this check.

[00238] Returning to step 3418, if the far island is already colored, then it is already connected to a tree. In this case, adding an arc to it would create a cycle. Thus in step 3426 it is now determined whether the cycle that would be created by adding a new arc is even or odd. If the two islands are colored oppositely, then the cycle is even and nothing need be done, connected or stored. The routine merely returns to step 3410 to consider the next edge-edge candidate in 2ⁿ _edge_map involving the current edge. If the two islands have the same color, however, then the cycle is odd. In step 3428 the odd cycle is inserted into the odd cycle collection structure for later presentation to the user. Again, as there is no need to connect the new arc in the tree, the routine then returns to step 3410 to consider the next edge-edge candidate in 2^nd_edge_map involving the current edge.

[00239] Note that whereas arcs that would form cycles are never inserted into the tree being built in Figs. 32, 33 and 34, in another embodiment they might be. In such an embodiment the graph being build would no longer be strictly a "tree" structure, but it would remain more generally a "graph" structure. Also note that the building of the trees in Figs. 32, 33 and 34 is not preceded by any step of fracturing the islands into rectangles. Fracturing is not performed until, preferably, the mask data preparation step 130 (Fig. 1). Thus each of the nodes in the forest represents an entire island, many if not most of which are non-rectangular. No island is represented by more than one node in the forest. The inclusion of non-rectangular islands also means that more than one candidate violation can occur between a single pair of islands.

[00240] After all the edge-edge candidates in 2^nd_edge_map involving the current edge have been considered (step 3410), all the edge-edge candidates keyed by the current edge are erased from 2^nd_edge_map (step 3430). The routine then returns (step 3432) to the contour walking process (Fig. 31).

[00241] Returning to Fig. 31, after all the candidates from the current corner and the immediately adjacent edge of the current island have been processed, in step 31 16 the current corner is replaced by the corner at the far end of the adjacent edge considered in steps 3112 and 3114. In step 3118 it is determined whether the new current corner has already been considered and processed. If not, then the routine returns to step 31 10 to process the corner-corner candidate involving this new corner. If the new current corner has already been considered and processed, then the entire contour of the current island has been walked and in step 3120 the routine returns to Fig. 29.

[00242] In Fig. 29, after the current island contour has been walked in step 2916 and all discovered DPT odd cycle violations have been written into the odd cycle collection structure, the routine returns to step 2914 to proceed to another island from which to detect more violations. Once the iteration completes and there are no more islands to consider, triple patterning rule checks can be performed (step 2917), as well as triple patterning rule checks with pre-coloring (step 2919).

[00243] Fig. 38 is a flow chart detail of step 2917 for checking for triple patterning coloring violations. As an overview, a triple patterning coloring violation arises if the graph of islands interconnected by multi-patterning candidate spacing violations cannot be colored by three different colors. Because any cycle that does not constitute a DPT odd cycle can by definition be colored with only two colors, all TPT coloring violations can be found by starting with only those islands that form a DPT odd cycle. The present embodiment therefore begins with the odd cycles found in the iteration of steps 2914 and 2916 and searches for one more island (a "common" island) which has a multi-patterning candidate spacing violation against all of the islands in the cycle. If one such island can be found, then another color is needed to color the graph beyond the three or more needed to color the DPT odd cycle. The graph thus cannot be colored with only three colors and a triple patterning coloring violation has been found.

[00244] Referring to Fig. 38, in step 3810, the violation check starts a loop through all the odd cycles collected previously in steps 3228, 3328 and 3428 (Figs. 32, 33 and 34). In step 3812, from the current odd cycle, a starting island is selected for beginning the search for a common island. For convenience, this starting island is referred to herein as island A. In step 3814, a loop is begun through all the far islands which form multi-patterning candidate spacing violations with the current island A. The current far island in this loop is referred to herein as island B. In step 3816, a tentative TPT violation set X is cleared, and the island pair BA is inserted into the set. In step 3818, another loop is begun through the remaining islands (other than starting island A) from the current odd cycle. The islands visited in this loop are referred to herein as islands C. In step 3820, it is determined whether island B (the current far island) forms a multi-patterning candidate spacing violation with current island C from the current odd cycle. If so, then the island pair BC is inserted into the tentative TPT violation set X (step 3822), and the loop 3818 continues to the next island C from the current odd cycle. If island B does not form a multi- patterning candidate spacing violation with current island C, then current far island B is not a "common" island with which to form a TPT coloring violation. The routine therefore returns to step 3814 to consider the next far island B forming a multi-patterning candidate spacing violation with the starting island A in the current odd cycle. If there are no more far islands B forming a multi-patterning candidate spacing violation with the starting island A, then no TPT coloring violation has been found based on the current odd cycle. The loop then returns to step 3810 to check the next odd cycle in the odd cycle collection.

[00245] Returning to step 3818, if the loop through all the next islands C from the current odd cycle completes, and the loop did not break because one of the islands C did not form a multi-patterning candidate spacing violation with the current far island B, then far island B constitutes a "common" island which has a multi-patterning candidate spacing violation against all of the islands in the current odd cycle. In step 3824, therefore, a TPT coloring violation has been found and the current odd cycle is saved, along with the current set X, for display to the user or other reporting. Loop 3810 then continues with the next odd cycle in the odd cycle collection.

[00246] When all of the odd cycles in the odd cycle collection have been considered, the routine terminates (step 3826).

[00247] Returning to fig. 29, after triple patterning rule checks and triple patterning rule checks with pre-coloring are performed (steps 2917 and 2919), the odd cycle collection structure is then cleaned up by deleting duplicate cycles (step 2920) and deleting cycles that do not include a moving object (step 2922). Pre-coloring paths and pre-grouping paths are also cleaned up in the same way. It is useful in real time editing to delete cycles and paths that do not include a moving object (step 2922) because the multi-patterning rule check is performed in response to each tick of the mouse as the user drags objects into desired positions. What the user is most interested in during this process is how near to other objects the moving objects can be moved before the violation occurs. The user is less interested in existing violations involving static shapes, which pre-existed the moving operation. By deleting cycles that do not include a moving object, pre-existing violations involving only static shapes are not shown to the user and do not clutter the display. This step can be omitted in a different embodiment. The routine then returns to Fig. 17.

[00248] In Fig. 17, after the DPT rules are checked in step 1715, other rules, such as via- based rules, are checked in step 1716.

[00249] Returning to Fig. 3, after step 322, in step 326, the system saves the design rule bounds calculated in steps 320 and 322 to a cache.

[00250] Also after step 322, in step 324 the system reports any design rule violations to the user or to another entity. In one embodiment, if the current editing command did not involve any movement of shapes, then nothing is output in this step. It will be seen however that another iteration through steps 314-322 occurs when the user begins dragging behavior, in which case any design rule violations can be reported. If reported to the user, the report can take place promptly (e.g. for real time feedback) or later (e.g. if performed as a batch job). Where the violations are reported to the user promptly, this enables the user to modify the layout to correct for the design rule violations. Whereas any form of reporting can be used, preferably the design rule violations are reported by way of visual indications on the user's monitor, as markers on the layout region itself. In an embodiment, near violations are also indicated. Marker information can be anything that can be used to render a visual indicator of the violation, but preferably it identifies a rectangle for designating the location of the violation within the layout region. In an embodiment, the rectangle is shown in a size which indicates the magnitude of the primary value of the rule being violated. This information can be very useful as it indicates graphically how much is needed to correct the violation. For near-violations, it can be a ruler indicating the current spacing. For example, if the violation is a minimum spacing violation, a rectangle might encompass the (too-small) spacing area, or a ruler disposed across the space might indicate actual spacing if it is larger than the minimum. Where violations are reported later, this can take the form of a log file or other record of the violations found. In addition, if the system proceeds directly to an automated step of correcting violations, reporting can take the form of the modified layout resulting from the corrections.

[00251] All of the design rule checks output marker information for any violation. The marker information is collected in a map structure. In step 324, the marker information is converted to visible form on the user's monitor or provided to another entity.

[00252] As shown in Fig. 3, once design rule bounds have been saved to cache and any markers have been output, the system returns to step 312 to await the next editing command. Significantly, since design rule bounds calculated in steps 314-322 do not depend on the knowing the direction or distance of the subsequent drag operation, they are performed prior to receipt by the system of the next user command. There is no need to await the next drag operation before performing these calculations. Since knowing the design rule bounds greatly simplifies the determination of whether the drag violates a design rule, or what is the best DRC- clean position if it does, the pre-calculation of such bounds before receipt of such next user command can enable immediate user feedback and true real-time rapid manual editing of the layout with optimum DRC-clean placement of geometries.

[00253] Returning to step 313, if the current editing command involves dragging selected objects, then the design rule bounds that were pre-calculated during a previous traversal through steps 314-322 are used to assist the placement of the objects at the design rule boundary nearest the user's desired destination point. Note that the current drag operation may be just the next increment of a longer drag, in which case the most recent traversal through steps 314-322 (and therefore the most recent pre-calculation of design rule bounds) will have been in response to a previous drag command rather than the selection command just described. Either way, in step 328 the system determines whether the destination position of the drag event exceeds the pre- calculated design rule bounds. If not, then the system merely moves the editing objects to the target position. If so, then the system adjusts the target position to the position nearest the user's target position, but which does not violate any of the design rules in the set of design rules enabled for DRC-assist. Push-through is also performed here. [00254] Note further that the present embodiment is intended to assist in continuous geometry changes associated with mouse drag. In the case of sudden geometry changes associated with the drag, which is possible for some of the user commands, step 328 will not do anything to block them. The operation is treated the same as push-through.

[00255] The following pseudocode describes the pertinent aspects of step 328. The starting position of the objects selected for editing is pl(x,y), and the user's destination or target position is p2(x,y):

Let the pre-calculated left, right, up and down linear slacks be called Ls, Rs, Us and Ds, respectively.

If any of Ls, Rs, Us and Ds is negative, this means there is already DRC violation. Continue to step 314 without adjusting p2.

If p2 (x) > pi (x) , that means the mouse movement has a rightward vector component. Set horizontal slack Hs=Rs . Otherwise, if p2 (x) < pi (x) , that means the mouse movement has a leftward vector component. Set horizontal slack Hs=Ls .

If p2 (y) > pi (y) , that means the mouse movement has an upward vector component. Set vertical slack Vs=Us. Otherwise, if p2 (y) < pi (y) , that means the mouse movement has a downward vector component. Set vertical slack Vs=Ds. Set Δχ = |p2 (x) - pi (x) |

Set Ay = |p2 (y) - pi (y) |

If (Δχ - Hs >= a push_through_threshold OR Ay - Vs >=

push_through_threshold) , this means the user has pushed through. Continue to step 314 without adjusting p2. Objects will appear to jump to destination position if they had been stopped and a DRC-clean position earlier in the drag behavior. Note that push-through can be disabled by setting the push_through_threshold to infinity.

If (Δχ <= Hs) , then no horizontal DRC bound has been reached. Do not adjust p2 (x)

Else if Δχ > Hs, then the horizontal slack distance has been exceeded.

If p2 is moving to the right, adjust p2 (x) = p2 (x) - (Δχ - Hs) .

If p2 is moving to the left, adjust p2 (x) = p2 (x) + (Δχ - Hs) .

If (Ay <= Vs) , then no horizontal DRC bound has been reached. Do not adjust p2 (y)

Else if Ay > Vs, then the vertical slack distance has been exceeded.

If p2 is moving upward, adjust p2 (y) = p2 (y) - (Ay - Vs).

If p2 is moving downward, adjust p2 (y) = p2 (y) + (Ay - Vs) .

[00256] The above pseudocode blocks the user's drag operation from exceeding any of the linear slacks, and operates by adjusting the destination position p2 to the nearest position that prevents any such violation. Next, the system checks the corner and conditional slacks, based on the adjusted destination position p2, and further adjusts p2 to avoid violating any of those. This latter process involves adjusting the destination point in two separate monotonic sequences. The first sequence is X_first, and the second sequence is Y_first. Each sequence is monotonic in the sense that no step in the sequence backtracks either horizontally or vertically. For example, for an adjustment toward the upper right, the X first sequence is to the right, then upward, then to the right, and so on until either the destination point is reached, or both the right and upward directions are blocked. The corresponding Y_first sequence is the same, except that it begins with an adjustment upward. At each step inside the sequence, the destination point is adjusted by a small amount, and the four linear slacks (Ls, Rs, Bs, Ts) are recalculated based on adjusted positions and all the corner and conditional slacks.

[00257] Whether or not step 328 results in any adjustment of the destination position p2 as signaled by the user's drag command, the system next traverses steps 314-326 again to check the new position against the design rules and output markers if appropriate, and to pre-calculate, in advance of the next editing command, a new set of design rule bounds based on the new position p2 of the selected objects. The system then returns to step 312 to await the next editing command. This may be as simple as another slight movement of the current editing shapes being dragged across the layout region, which would result in another traversal through steps 314-326 of Fig. 3, thus causing a change in the visual indicator as seen by the user and yet another precalculation of design rule bounds in preparation for yet another editing command. Because of the efficiency of the design rule checking techniques and the DRC assistance techniques described herein, in the embodiment herein the new markings will appear nearly immediately with each drag of the editing shapes and a movement which exceeds a design rule bound will be immediately stopped.

[00258] Fig. 21 A is an example visual indication of a violation of a minimum spacing rule. In this drawing, editing rectangle 21 12 has been moved too close to static rectangle 21 10, and a box 2114 appears indicating how much end-of-line spacing is required by the rule. If the minimum spacing value that is being violated is an absolute value, then the box 2114 might appear in one color, whereas if it is a preferred value that is being violated, then the box 2114 might appear in another color. A third color can be used to indicate a most preferred value, and so on. As the user pulls the editing shape 2112 apart from static shape 21 10, the box 2114 disappears and a ruler appears, such as ruler 2116 in Fig. 2 IB. Ruler 21 16 indicates the actual distance between the end of editing shape 21 12 and the nearest edge of static shape 2110, and thereby indicates how much closer shape 2112 can be brought to shape 21 10 before the minimum spacing rule will be violated.

[00259] Fig. 21 C is an example visual indication of a violation of a corner-to-corner spacing rule. In this drawing, editing rectangle 21 12 has been moved too close to a corner of static rectangle 2110, and a box 21 18 appears indicating the violation. Again, the box 2118 can appear in either of two colors to indicate violation of an absolute or preferred value for this design rule. As the user pulls the editing shape 21 12 apart from static shape 2110, the box 2114 disappears and a ruler appears, such as corner-to-corner ruler 2120 in Fig. 21D. Ruler 2120 indicates the actual corner-to-corner distance between the end of editing shape 21 12 and the nearest edge of static shape 2110.

[00260] Fig. 2 IE is an example visual indication of a violation of a corner-to-corner minimum dimension rule. In this drawing, a corner of editing rectangle 21 12 overlaps a corner of a same layer static rectangle 21 10, but the overlap is too small to satisfy the minimum dimension rule. A box 2122 appears indicating the violation.

[00261] Fig. 35 is an example visual indication of a layout region showing two DPT odd cycle violations. The hatched regions 3510, 3512 and 3514 represent three islands, while the markers (rectangles with crossing diagonals) 3520, 3522, 3524, 3526 and 3528 are markers produced by the DPT violation checker indicating DPT spacing candidates. The candidates illustrated are no longer merely candidates in Fig. 35, since they do form actual odd cycle violations. However, they are still referred to sometimes herein as "candidates" for convenience of discussion. Marker 3520 indicates a corner-corner candidate, in which one corner of island 3510 is closer to a corner of island 3512 than the DPT minimum corner-corner spacing. The size of the rectangle indicates the minimum corner-corner spacing called for by the DPT rules, so its corners may overlap the corners of the islands. The extent of the overlap indicates visually to the user roughly by how far the island corners must be moved apart in order to remove that particular corner-corner spacing violation. Similarly, markers 3522, 3524, 3526 and 3528 all indicate edge-edge candidates, in which an edge of one island is closer to an edge of another island than the relevant DPT edge-edge spacing rule. The length of the rectangle in the dimension along the gap between the two edges is merely the length of the overlap of the two edges. The length of the rectangle in the dimension across the gap between the two edges indicates the minimum edge-edge spacing called for by the relevant DPT rule, so the rectangle may overlap the two edges in this dimension. The extent of the overlap indicates visually to the user roughly by how far the island edges must be moved apart in order to remove that particular edge-edge spacing violation. [00262] The "relevant DPT edge-edge spacing rule" applied above is whichever applies of

(a) the DPT minimum end-edge spacing, (b) the DPT minimum side-edge spacing, or (c) the DPT minimum side-side spacing. As previously mentioned an edge is either an "end-edge" or a "side-edge", depending on a comparison with the width threshold value in the DPT spacing rules, and different spacing values apply depending on whether the relationship between the two edges of a candidate is end-edge side-edge spacing, or side-side. In Fig. 35 only candidate 3528 indicates an end-side violation whereas markers 3522, 3524 and 3526 all indicate side-side violations. For purposes of the visual indication, however, no distinction is made among the types of edge-edge violations because the user's response is the same: move the involved edges apart until the marker disappears. Note that DPT odd cycles themselves do not distinguish at all among the different kinds of violations; cycles are formed regardless of the types of violations that make up the cycle. The corner-corner candidates are treated separately from the edge-edge candidates in the present embodiment only to simplify the implementation.

[00263] Fig. 35 uses polygons 3530 and 3532 with broken lines to indicate cycles. Since each of these cycles connect an odd number of islands (three each), they indicate to the user two DPT odd cycle violations. The user need only remove one of the DPT spacing violations in a cycle in order to remove the entire DPT odd cycle violation. Not only would the marker indicating the removed spacing violation disappear, but the broken lines indicating the odd cycle violation would also then disappear, as would all of the DPT candidate markers involved in that cycle (unless they are also part of another DPT odd cycle violation). If the number of islands making up a cycle is even, then no broken lines would be drawn for that cycle as no DPT violation has occurred. Nor would the spacing markers for DPT spacing violations be drawn for that cycle, again unless they are also part of a DPT odd cycle violation.

[00264] Importantly, the candidate markers identify to the user not only which islands are too near each other, but also (a) which kind of violation has occurred (edge-edge or corner- corner), (b) exactly which edges and corners are involved in the violation, and (c) roughly how far the islands need to move away from each other in order to remove each of the DPT spacing violations. This helps the user to know, visually and intuitively, which islands need to be moved and in which direction, and roughly by how far, in order to remove the violation. Also importantly, the cycles are indicated among the candidates, not the islands. In particular, the broken lines 3530 and 3532 interconnect the centerpoints of the markers identifying the individual spacing violations which form the cycle, not the islands which form the cycle. This arrangement again indicates much more intuitively to the user which islands need to be moved and in which direction. That information can be more difficult to gather where the DPT odd cycle violation polygon has its vertices placed somewhere in the middle of the islands themselves.

[00265] It can be seen that the islands in the example of Fig. 35 are not all pure rectangles.

Island 3512, in particular, is non-rectangular. It is an advantageous feature of the DPT odd cycle detection methods described herein that layout shapes do not need to be partitioned or fractured into rectangles before searching for violations. In part this results from the portion of the method which walks the island contour, and in part it results from the availability of sufficient corner and edge information developed in advance.

[00266] Similar visual indicators to indicate violations of other design rules will be apparent to the reader. In addition, note that all of the design rule checks indicated in Figs. 21A- 2 IE can reference derived layers or physical layers or both. It can be seen that the markings provide nearly immediate feedback to the user as the layout is edited, thereby greatly facilitating the manual layout effort. It should be noted that the absence of any visual indication to the user also constitutes a notification to the user that no design rule violation has been detected.

[00267] In the embodiments described herein, all the corner data structures are completely populated before the corner-based rules are checked. This is the most advantageous arrangement, but some benefits of the invention can be obtained even if only some (i.e. more than one;

preferably more than two) of the corner data structures are completely populated before the corner-based rules are checked. For DPT odd cycle checking, not all the data gathered for each corner is required. Therefore, while again it is most advantageous to populate at least two of the corner data structures completely before the DPT odd cycle rules are checked, some benefits of the invention can be obtained even if only the following information about such corners are populated in advance: (x,y), s_ray_x, and s_ray_y. In addition, ori_x and ori_y should be populated in advance if a contour walking technique such as in step 2916 (Fig. 29) is used.

[00268] Similarly, all island data structures are completely populated before the island- based rules are checked. Again, while this is the most advantageous arrangement, some benefits of the invention can be obtained even if only some (i.e. more than one; preferably more than two) of the island data structures are completely populated before the island-based rules are checked.

[00269] In the embodiments described herein, multi-patterning minimum spacing constraint violations and coloring violations formed by cycles of such violations, have been given as examples. It will be appreciated, however, that aspects of the invention also apply to other types of multi-patterning rules as well. In some embodiments, multi-patterning rules can become as complex as, or more complex than, the single-layer design rules described elsewhere herein.

Hardware

[00270] Fig. 22 is a simplified block diagram of a computer system 2210 that can be used to implement software incorporating aspects of the present invention. Computer system 2210 includes a processor subsystem 2214 which communicates with a number of peripheral devices via bus subsystem 2212. These peripheral devices may include a storage subsystem 2224, comprising a memory subsystem 2226 and a file storage subsystem 2228, user interface input devices 2222, user interface output devices 2220, and a network interface subsystem 2216. The input and output devices allow user interaction with computer system 2210. Network interface subsystem 2216 provides an interface to outside networks, including an interface to

communication network 2218, and is coupled via communication network 2218 to

corresponding interface devices in other computer systems. Communication network 2218 may comprise many interconnected computer systems and communication links. These

communication links may be wireline links, optical links, wireless links, or any other mechanisms for communication of information. While in one embodiment, communication network 2218 is the Internet, in other embodiments, communication network 2218 may be any suitable computer network.

[00271] The physical hardware component of network interfaces are sometimes referred to as network interface cards (NICs), although they need not be in the form of cards: for instance they could be in the form of integrated circuits (ICs) and connectors fitted directly onto a motherboard, or in the form of macrocells fabricated on a single integrated circuit chip with other components of the computer system.

[00272] User interface input devices 2222 may include a keyboard, pointing devices such as a mouse, trackball, touchpad, or graphics tablet, a scanner, a touch screen incorporated into the display, audio input devices such as voice recognition systems, microphones, and other types of input devices. In general, use of the term "input device" is intended to include all possible types of devices and ways to input information into computer system 2210 or onto computer network 2218.

[00273] User interface output devices 2220 may include a display subsystem, a printer, a fax machine, or non-visual displays such as audio output devices. The display subsystem may include a cathode ray tube (CRT), a flat-panel device such as a liquid crystal display (LCD), a projection device, or some other mechanism for creating a visible image. The display subsystem produces the images illustrated in Figs. 21A-21E, for example. The display subsystem may also provide non-visual display such as via audio output devices. In general, use of the term "output device" is intended to include all possible types of devices and ways to output information from computer system 2210 to the user or to another machine or computer system.

[00274] Storage subsystem 2224 stores the basic programming and data constructs that provide the functionality of certain embodiments of the present invention. For example, the various modules implementing the functionality of certain embodiments of the invention may be stored in storage subsystem 2224. These software modules are generally executed by processor subsystem 2214.

[00275] Memory subsystem 2226 typically includes a number of memories including a main random access memory (RAM) 2230 for storage of instructions and data during program execution and a read only memory (ROM) 2232 in which fixed instructions are stored. File storage subsystem 2228 provides persistent storage for program and data files, and may include a hard disk drive, a floppy disk drive along with associated removable media, a CD-ROM drive, an optical drive, or removable media cartridges. The databases and modules implementing the functionality of certain embodiments of the invention may be stored by file storage subsystem 2228. The host memory 2226 contains, among other things, computer instructions which, when executed by the processor subsystem 2214, cause the computer system to operate or perform functions as described herein. As used herein, processes and software that are said to run in or on "the host" or "the computer system", execute on the processor subsystem 2214 in response to computer instructions and data in the host memory subsystem 2226 including any other local or remote storage for such instructions and data.

[00276] Bus subsystem 2212 provides a mechanism for letting the various components and subsystems of computer system 2210 communicate with each other as intended. Although bus subsystem 2212 is shown schematically as a single bus, alternative embodiments of the bus subsystem may use multiple busses.

[00277] Computer system 2210 itself can be of varying types including a personal computer, a portable computer, a workstation, a computer terminal, a network computer, a television, a mainframe, or any other data processing system or user device. Due to the ever-changing nature of computers and networks, the description of computer system 2210 depicted in Fig. 22 is intended only as a specific example for purposes of illustrating certain embodiments of the present invention. In another embodiment, the invention can be

implemented using multiple computer systems, such as in a server farm. Many other configurations of computer system 2210 are possible having more or less components than the computer system depicted in Fig. 22.

[00278] In an embodiment, the steps set forth in the flow charts and descriptions herein are performed by a computer system having a processor such as processor subsystem 2214 and a memory such as storage subsystem 2224, under the control of software which includes instructions which are executable by the processor subsystem 2214 to perform the steps shown. The software also includes data on which the processor operates. The software is stored on a computer readable medium, which as mentioned above and as used herein, is one on which information can be stored and read by a computer system. Examples include a floppy disk, a hard disk drive, a RAM, a CD, a DVD, flash memory, a USB drive, and so on. The computer readable medium may store information in coded formats that are decoded for actual use in a particular data processing system. A single computer readable medium, as the term is used herein, may also include more than one physical item, such as a plurality of CD-ROMs or a plurality of segments of RAM, or a combination of several different kinds of media. When the computer readable medium storing the software is combined with the computer system of Fig. 22, the combination is a machine which performs the steps set forth herein. Means for performing each step consists of the computer system (or only those parts of it that are needed for the step) in combination with software modules for performing the step. The computer readable medium storing the software is also capable of being distributed separately from the computer system, and forms its own article of manufacture.

[00279] Additionally, the geometry file or files storing the layout, the relationship master dataset, and the layout topology database are themselves stored on computer readable media. Such media can be distributable separately from the computer system, and form their own respective articles of manufacture. When combined with a computer system programmed with software for reading, revising, and writing the geometry files, and for design rule checking, they form yet another machine which performs the steps set forth herein.

[00280] As used herein, the "identification" of an item of information does not necessarily require the direct specification of that item of information. Information can be "identified" in a field by simply referring to the actual information through one or more layers of indirection, or by identifying one or more items of different information which are together sufficient to determine the actual item of information. In addition, the term "indicate" is used herein to mean the same as "identify".

[00281] As used herein, a given signal, event or value is "responsive" to a predecessor signal, event or value if the predecessor signal, event or value influenced the given signal, event or value. If there is an intervening processing element, step or time period, the given signal, event or value can still be "responsive" to the predecessor signal, event or value. If the intervening processing element or step combines more than one signal, event or value, the signal output of the processing element or step is considered "responsive" to each of the signal, event or value inputs. If the given signal, event or value is the same as the predecessor signal, event or value, this is merely a degenerate case in which the given signal, event or value is still considered to be "responsive" to the predecessor signal, event or value. "Dependency" of a given signal, event or value upon another signal, event or value is defined similarly.

[00282] The foregoing description of preferred embodiments of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Obviously, many modifications and variations will be apparent to practitioners skilled in this art. In particular, and without limitation, any and all variations described, suggested or incorporated by reference in the Background section of this patent application are specifically incorporated by reference into the description herein of embodiments of the invention. The embodiments described herein were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims and their equivalents.

[00283] The following clauses describe aspects of various examples of the invention.

[00284] Clause 1. A method for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands,

for use by a computer system having access to a design rule data set indicating values for multi-patterning spacing constraints among islands in a particular layer, the method comprising the steps of:

the computer system iteratively building a data structure identifying the plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships indicating that the pair of islands related by the relationship violates one of the multi-patterning spacing constraints;

during the step of building a data structure, and before all of the relationships are included in the data structure, in dependence upon the relationships that are included in the data structure, detecting a multi-patterning coloring violation among islands represented in the data structure; and

reporting the multi-patterning coloring violation to a user. [00285] Clause 2. A method according to clause 1, wherein the multi-patterning spacing constraints are double-patterning spacing constraints.

[00286] Clause 3. A method according to any of clauses 1-2, wherein the data structure comprises a graph having a plurality of nodes and a plurality of arcs interconnecting the nodes, each of the nodes representing one of the islands and each of the arcs representing one of the relationships.

[00287] Clause 4. A method according to clause 3, wherein each of the nodes represents an entire island,

wherein no island is represented by more than one node,

and wherein one of the islands represented by a node is non-rectangular.

[00288] Clause 5. A method according to any of clauses 3-4, wherein the step of building the data structure comprises steps of:

inserting into the graph a root node representing a first one of the islands in the plurality; and

iteratively inserting arcs into the graph which interconnect further nodes in the graph until a particular arc is found the insertion of which would form a cycle in the graph.

[00289] Clause 6. A method according to clause 5, wherein the step of detecting a multi- patterning coloring violation comprises a step of detecting that the cycle has an odd number of arcs.

[00290] Clause 7. A method according to any of clauses 5-6, further comprising steps of: assigning a color to the root node in conjunction with the step of inserting the root node into the graph; and

in conjunction with the insertion of each given arc in the step of iteratively inserting arcs, the given arc interconnecting a given one of the further nodes with a respective parent node in the graph, assigning a color to the given further node which does not conflict with the color assigned to the respective parent node,

and wherein the step of detecting a multi-patterning coloring violation comprises a step of detecting that the particular arc would interconnect two nodes in the graph whose colors conflict.

[00291] Clause 8. A method according to clause 7, further comprising a step of inserting into a multi-patterning cycle coloring violation data structure, an identification of the cycle.

[00292] Clause 10. A method according to any of clauses 5-8, further comprising a step of resuming the step of iteratively inserting arcs, without inserting the particular arc into the graph. [00293] Clause 1 1. A method according to any of clauses 1-10, wherein the pair of islands related by one of the relationships in the data structure violates more than one of the multi- patterning spacing constraints.

[00294] Clause 12. A method according to any of clauses 1-1 1, wherein the step of the computer system iteratively building a data structure comprises steps of:

iterating among islands in the plurality of islands;

for each current island in the iteration among islands, iterating among corners of the current island; and

for each current corner in the iteration among corners:

determining whether a multi-patterning candidate spacing constraint violation involving the current corner exists between the current island and a far island different from the current island; and

if so, then at least if the far island is not yet in the data structure, inserting into the data structure a particular one of the relationships, the particular relationship indicating that the current island and the far island violate one of the multi-patterning spacing constraints.

[00295] Clause 13. A method according to clause 12, wherein the step of iterating among corners of the current island comprises a step of iterating among corners of the current island sequentially.

[00296] Clause 14. A method according to any of clauses 12-13, wherein the step of detecting a multi-patterning coloring violation among islands represented in the data structure comprises, during the iteration among corners of the current island, steps of:

determining that the multi-patterning candidate spacing constraint violation involving the current corner does exist between the current island and the far island;

determining that the far island is already in the data structure; and

determining that a multi-patterning coloring violation is formed by the particular relationship.

[00297] Clause 15. A method according to any of clauses 12-14, further comprising steps of:

for the current island in the iteration among islands, iterating among edges of the current island; and

for each current edge in the iteration among edges: determining whether a multi-patterning candidate spacing constraint violation involving the current edge exists between the current island and another island different from the current island; and

if so, then at least if the other island is not yet in the data structure, inserting into the data structure a given one of the relationships, the given relationship indicating that the current island and the other island violate one of the multi-patterning spacing constraints.

[00298] Clause 16. A method according to clause 15, wherein the steps of for each current island iterating among corners of the current island, and for the current island iterating among edges of the current island, collectively comprise steps of visiting all corners and all edges of the current island.

[00299] Clause 17. A method according to any of clauses 1-16, wherein the multi- patterning coloring violation comprises a pre-coloring violation.

[00300] Clause 18. A method according to any of clauses 1-17, wherein the multi- patterning coloring violation comprises a pre-grouping violation.

[00301] Clause 19. A method according to any of clauses 1-18, wherein the multi- patterning coloring violation comprises a triple-patterning coloring violation.

[00302] Clause 20. A method according to any of clauses 1-19, wherein the step of reporting the multi-patterning coloring violation to a user comprises the step of indicating the multi-patterning coloring violation to the user visually.

[00303] Clause 21. A method according to clause 20, wherein the step of indicating the multi-patterning coloring violation to the user visually comprises a step of pointing out the multi- patterning spacing constraint violations which make up a cycle.

[00304] Clause 22. A method according to any of clauses 20-21, wherein the step of indicating the multi-patterning coloring violation to the user visually comprises a step of representing a particular one of the multi-patterning spacing constraint violations which make up a cycle by using a visual marker, the size of the marker being dependent upon a value of a multi- patterning spacing constraint being violated.

[00305] Clause 23. A method according to clause 22, wherein the particular multi- patterning spacing constraint violation comprises a corner-corner multi-patterning spacing violation,

and wherein the marker representing the particular constraint violation comprises a rectangle visually interconnecting a pair of island corners which violate the corner-corner multi- patterning spacing constraint. [00306] Clause 24. A method according to clause 23, wherein the rectangle has a size which indicates visually a minimum spacing called for by the corner-corner multi-patterning spacing constraint.

[00307] Clause 25. A method according to any of clauses 22-24, wherein the particular multi-patterning spacing constraint violation comprises an edge-edge multi-patterning spacing violation,

and wherein the marker representing the particular constraint violation comprises a rectangle visually interconnecting a pair of island edges which violate the edge-edge multi- patterning spacing constraint.

[00308] Clause 26. A method according to clause 25, wherein the rectangle has a length in a dimension perpendicular to the two edges which indicates a minimum spacing called for by an edge-edge multi-patterning spacing constraint.

[00309] Clause 27. A method according to any of clauses 22-26, wherein the step of the computer system iteratively building a data structure is performed in response to a user behavior in which a set of at least one of the islands in the plurality of islands is edited,

wherein the step of reporting the multi-patterning coloring violation to a user comprises the step of indicating the multi-patterning coloring violation to the user sufficiently promptly after the user behavior so that the user can correct the multi-patterning coloring violation in real time.

[00310] Clause 28. A method according to any of clauses 22-26, wherein the step of the computer system iteratively building a data structure is performed in response to a user selecting a set of at least one portion of the islands in the plurality of islands, depressing a mouse button and dragging the selected portion to a modified position in the layout,

and wherein the step of reporting a design rule violation to a user is completed before the user releases the mouse button.

[00311] Clause 29. A system for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands, comprising: a computer system having access to a design rule data set indicating values for multi- patterning spacing constraints among islands in a particular layer, the computer system further having access to computer instructions and data which, when applied to the computer system, perform the steps of:

iteratively building a data structure identifying the plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships indicating that the pair of islands related by the relationship violates one of the multi-patterning spacing constraints; while building the data structure, and before all of the relationships are included in the data structure, in dependence upon the relationships that are included in the data structure, detecting any multi-patterning coloring violations among islands represented in the data structure; and

where a multi-patterning coloring violation is detected among islands represented in the data structure, reporting it to a user.

[00312] Clause 30. A system according to clause 29, wherein the data structure comprises a graph having a plurality of nodes and a plurality of arcs interconnecting the nodes, each of the nodes representing one of the islands and each of the arcs representing one of the relationships, and wherein iteratively building a data structure comprises:

inserting into the graph a root node representing a first one of the islands in the plurality; and

iteratively inserting arcs into the graph which interconnect further nodes in the graph until a particular arc is found the insertion of which would form a cycle in the graph.

[00313] Clause 31. A system according to clause 30, wherein the computer instructions and data, when applied to the computer system, perform further steps of:

assigning a color to the root node in conjunction with the step of inserting the root node into the graph; and

in conjunction with the insertion of each given arc in the step of iteratively inserting arcs, the given arc interconnecting a given one of the further nodes with a respective parent node in the graph, assigning a color to the given further node which does not conflict with the color assigned to the respective parent node,

and wherein the step of detecting a multi-patterning coloring violation comprises a step of detecting that the particular arc would interconnect two nodes in the graph whose colors conflict.

[00314] Clause 32. A system according to any of clauses 29-31, wherein iteratively building a data structure comprises:

iterating among islands in the plurality of islands;

for each current island in the iteration among islands, iterating among corners of the current island; and

for each current corner in the iteration among corners:

determining whether a multi-patterning candidate spacing constraint violation involving the current corner exists between the current island and a far island different from the current island; and if so, then at least if the far island is not yet in the data structure, inserting into the data structure a particular one of the relationships, the particular relationship indicating that the current island and the far island violate one of the multi-patterning spacing constraints.

[00315] Clause 33. A system according to clause 32, wherein detecting a multi-patterning coloring violation among islands represented in the data structure comprises, during the iteration among corners of the current island:

determining that the multi-patterning candidate spacing constraint violation involving the current corner does exist between the current island and the far island;

determining that the far island is already in the data structure; and

determining that a multi-patterning coloring violation is formed by the particular relationship.

[00316] Clause 34. A system according to any of clauses 32-33, wherein the computer instructions and data, when applied to the computer system, perform further steps of:

for the current island in the iteration among islands, iterating among edges of the current island; and

for each current edge in the iteration among edges:

determining whether a multi-patterning candidate spacing constraint violation involving the current edge exists between the current island and another island different from the current island; and

if so, then at least if the other island is not yet in the data structure, inserting into the data structure a given one of the relationships, the given relationship indicating that the current island and the other island violate one of the multi-patterning spacing constraints.

[00317] Clause 35. A system according to any of clauses 29-34, wherein the multi- patterning coloring violation comprises a member of the group consisting of: a pre-coloring violation, a pre-grouping violation, and a triple-patterning coloring violation.

[00318] Clause 36. A system according to any of clauses 29-35, wherein reporting the multi-patterning coloring violation to a user comprises indicating the multi-patterning coloring violation to the user visually.

[00319] Clause 37. A system according to clause 36, wherein indicating the multi- patterning coloring violation to the user visually comprises representing a particular one of the multi-patterning spacing constraint violations which make up a cycle by using a visual marker, the size of the marker being dependent upon a value of a multi-patterning spacing constraint being violated.

[00320] Clause 38. A system according to clause 37, wherein the particular multi- patterning spacing constraint violation comprises a corner-corner multi-patterning spacing violation,

and wherein the marker representing the particular constraint violation comprises a rectangle visually interconnecting a pair of island corners which violate the corner-corner multi- patterning spacing constraint.

[00321] Clause 39. A system according to clause 38, wherein the rectangle has a size which indicates visually a minimum spacing called for by the corner-corner multi-patterning spacing constraint.

[00322] Clause 40. A system according to any of clauses 37-39, wherein the particular multi-patterning spacing constraint violation comprises an edge-edge multi-patterning spacing violation,

and wherein the marker representing the particular constraint violation comprises a rectangle visually interconnecting a pair of island edges which violate the edge-edge multi- patterning spacing constraint.

[00323] Clause 41. A system according to clause 40, wherein the rectangle has a length in a dimension perpendicular to the two edges which indicates a minimum spacing called for by an edge-edge multi-patterning spacing constraint.

[00324] Clause 42. A system according to any of clauses 36-41, wherein iteratively building a data structure is performed in response to a user behavior in which a set of at least one of the islands in the plurality of islands is edited,

and wherein reporting the multi-patterning coloring violation to a user comprises indicating the multi-patterning coloring violation to the user sufficiently promptly after the user behavior so that the user can correct the multi-patterning coloring violation in real time.

[00325] Clause 43. A system according to any of clauses 36-42, wherein iteratively building a data structure is performed in response to a user selecting a set of at least one portion of the islands in the plurality of islands, depressing a mouse button and dragging the selected portion to a modified position in the layout,

and wherein reporting a design rule violation to a user is completed before the user releases the mouse button.

[00326] Clause 44. A computer program product for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands, for use by a computer system having access to a design rule data set indicating values for multi-patterning spacing constraints among islands in a particular layer, the computer program product comprising:

a computer readable storage medium having stored thereon a plurality of software code portions and data which when executed by the computer system perform the steps of:

iteratively building a data structure identifying the plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships indicating that the pair of islands related by the relationship violates one of the multi-patterning spacing constraints; while building the data structure, and before all of the relationships are included in the data structure, in dependence upon the relationships that are included in the data structure, detecting any multi-patterning coloring violations among islands represented in the data structure; and

where a multi-patterning coloring violation is detected among islands represented in the data structure, reporting it to a user.

[00327] Clause 45. A method for checking a set of multi-patterning layout design rules on a particular layer of a region of an integrated circuit layout, the layout including a plurality of shapes,

for use by a computer system having access to a design rule data set indicating values for multi-patterning spacing constraints among islands in the particular layer, the method comprising steps of:

for each edge in a subset of at least two edges of the shapes in the plurality of shapes, the computer system populating a layout topology database with values in dependence upon the respective edge location;

in dependence upon values populated into the layout topology database in the step of the computer system populating, but before populating the layout topology database with values in dependence upon all of the edge locations in the subset of edges, detecting a subset of at least one candidate violation of the multi-patterning spacing constraints;

after detecting all the candidate violations in the subset, searching the candidate violations in the subset for multi-patterning coloring violations; and

where a multi-patterning coloring violation is detected, reporting it to a user.

[00328] Clause 46. A method according to clause 45, wherein the step of populating a layout topology database with values in dependence upon the respective edge location comprises a step of populating the layout topology database with values in dependence upon a location of an endpoint of the respective edge. [00329] Clause 47. A method according to any of clauses 45-46, wherein the step of populating a layout topology database with values in dependence upon the respective edge location comprises a step of populating the layout topology database with a distance from a first one of the edges to a second one of the edges of a shape in the plurality of shapes, the first and second edges being on different islands,

and wherein the step of detecting a subset of at least one candidate violation of the multi- patterning spacing constraints, comprises a step of comparing the distance with a value of an edge-edge multi-patterning spacing constraint in the design rule data set.

[00330] Clause 48. A method according to any of clauses 45-47, comprising a step of, in conjunction with each detection of a candidate violation in the step of detecting, inserting an identification of the candidate violation into a database of candidate violations of the multi- patterning spacing constraints,

and wherein the step of searching the candidate violations in the subset for multi- patterning coloring violations comprises a step of searching the database of candidate violations for multi-patterning coloring violations,

further comprising a step of inserting into database of candidate violations identifications of a plurality of detected violations of a corner-corner multi-patterning spacing constraint in the design rule data set, prior to the step of searching the candidate violations in the subset for multi- patterning coloring violations.

[00331] Clause 49. A method according to clause 48, further comprising steps of:

for each of a plurality of detected convex-corner-to-convex-corner geometric relationships among islands in the particular layer, calculating a corner-corner distance between the corners;

comparing the corner-corner distance with a minimum corner-to-corner spacing value in the design rule data set; and in conjunction therewith,

comparing the corner-corner distance with a value of a corner-corner multi-patterning spacing constraint in the design rule data set;

and where a violation of the corner-corner multi-patterning spacing constraint is found, inserting into the database of candidate violations an identification of the island corners involved in the violation.

[00332] Clause 50. A method according to any of clauses 45-49, wherein the step of searching the candidate violations in the subset for multi-patterning coloring violations comprises steps of: the computer system, in dependence upon the database of candidate violations, iteratively building a data structure identifying the plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships indicating that the pair of islands related by the relationship violates one of the multi-patterning spacing constraints; and

during the step of building a data structure, and before all of the relationships are included in the data structure, in dependence upon the relationships that are included in the data structure, detecting a multi-patterning coloring violation among islands represented in the data structure.

[00333] Clause 51. A method according to any of clauses 45-50, wherein the multi- patterning spacing constraints are double-patterning spacing constraints.

[00334] Clause 52. A method according to any of clauses 45-51, wherein the step of searching the candidate violations in the subset for multi-patterning coloring violations, comprises a step of searching for pre-coloring violations.

[00335] Clause 53. A method according to any of clauses 45-52, wherein the step of searching the candidate violations in the subset for multi-patterning coloring violations, comprises a step of searching for pre-grouping violations.

[00336] Clause 54. A method according to any of clauses 45-53, wherein the step of searching the candidate violations in the subset for multi-patterning coloring violations, comprises a step of searching for triple-patterning coloring violations.

[00337] Clause 55. A system for checking a set of multi-patterning layout design rules on a particular layer of a region of an integrated circuit layout, the layout including a plurality of shapes, comprising:

a computer system having access to a design rule data set indicating values for multi- patterning spacing constraints among islands in the particular layer, the computer system further having access to computer instructions and data which, when applied to the computer system, perform the steps of:

for each edge in a subset of at least two edges of the shapes in the plurality of shapes, the computer system populating a layout topology database with values in dependence upon the respective edge location;

in dependence upon values populated into the layout topology database in the step of the computer system populating, but before populating the layout topology database with values in dependence upon all of the edge locations in the subset of edges, detecting a subset of at least one candidate violation of the multi-patterning spacing constraints; after detecting all the candidate violations in the subset, searching the candidate violations in the subset for multi-patterning coloring violations; and

where a multi-patterning coloring violation is detected, reporting it to a user.

[00338] Clause 56. A system according to clause 55, wherein searching the candidate violations in the subset for multi-patterning coloring violations comprises:

in dependence upon the database of candidate violations, iteratively building a data structure identifying the plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships indicating that the pair of islands related by the relationship violates one of the multi-patterning spacing constraints; and

during the building a data structure, and before all of the relationships are included in the data structure, in dependence upon the relationships that are included in the data structure, detecting a multi-patterning coloring violation among islands represented in the data structure.

[00339] Clause 57. A system according to any of clauses 55-56, wherein the multi- patterning spacing constraints are double-patterning spacing constraints.

[00340] Clause 58. A system according to any of clauses 55-57, wherein searching the candidate violations in the subset for multi-patterning coloring violations, comprises a member of the group consisting of: searching for pre-coloring violations, searching for pre-grouping violations, and searching for triple-patterning coloring violations.

[00341] Clause 59. A computer program product for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of shapes, for use by a computer system having access to a design rule data set indicating values for multi-patterning spacing constraints among islands in the particular layer, the computer program product comprising:

a computer readable storage medium having stored thereon a plurality of software code portions and data which when executed by the computer system perform the steps of:

for each edge in a subset of at least two edges of the shapes in the plurality of shapes, the computer system populating a layout topology database with values in dependence upon the respective edge location;

in dependence upon values populated into the layout topology database in the step of the computer system populating, but before populating the layout topology database with values in dependence upon all of the edge locations in the subset of edges, detecting a subset of at least one candidate violation of the multi-patterning spacing constraints;

after detecting all the candidate violations in the subset, searching the candidate violations in the subset for multi-patterning coloring violations; and where a multi-patterning coloring violation is detected, reporting it to a user.

[00342] Clause 60. A method for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands,

for use by a computer system having access to a design rule data set indicating values for multi-patterning spacing constraints among islands in a particular layer, the method comprising the steps of:

the computer system detecting a set of islands forming a double-patterning coloring violation;

detecting a triple-patterning coloring violation among all the islands in the set and a common island outside the set; and

reporting the triple-patterning coloring violation to a user.

[00343] Clause 61. A method according to clause 60, wherein the step of detecting a triple-patterning coloring violation comprises detecting that the common island is located too near to each of the islands in the set to satisfy all of the multi-patterning spacing constraints with respect to each of the islands in the set.

[00344] Clause 62. A method according to clause 61, wherein the step of detecting the set of islands forming a double-patterning coloring violation comprises detecting an odd-length cycle of islands in the plurality of islands for which each particular island in the cycle is located too near to its next island in the cycle to satisfy all of the multi-patterning spacing constraints.

[00345] Clause 63. A method according to any of clauses 61-62, wherein the step of detecting that the common island is located too near to each of the islands in the set comprises steps of:

for a selected starting island in the set, and for each candidate common island which is located too near to the starting island to satisfy all of the multi-patterning spacing constraints, at least until the common island is found:

determining whether the candidate common island is also located too near to each island in the set other than the starting island, to satisfy all of the multi-patterning spacing constraints.

[00346] Clause 64. A system for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands, comprising: a computer system having access to a design rule data set indicating values for multi- patterning spacing constraints among islands in a particular layer, the computer system further having access to computer instructions and data which, when applied to the computer system, perform the steps of: detecting a set of islands forming a double-patterning coloring violation; searching for a triple-patterning coloring violation among all the islands in the set and a common island outside the set; and

where a triple-patterning coloring violation is found, reporting it to a user.

[00347] Clause 65. A system according to clause 64, wherein detecting a triple-patterning coloring violation comprises detecting that the common island is located too near to each of the islands in the set to satisfy all of the multi-patterning spacing constraints with respect to each of the islands in the set.

[00348] Clause 66. A computer program product for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands, for use by a computer system having access to a design rule data set indicating values for multi-patterning spacing constraints among islands in a particular layer, the computer program product comprising:

a computer readable storage medium having stored thereon a plurality of software code portions and data which when executed by the computer system perform the steps of:

detecting a set of islands forming a double-patterning coloring violation;

searching for a triple-patterning coloring violation among all the islands in the set and a common island outside the set; and

where a triple-patterning coloring violation is found, reporting it to a user.

[00349] Clause 67. A method for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands, comprising: detecting a multi-patterning coloring violation among islands represented in the data structure; and

reporting the multi-patterning coloring violation to a user visually.

[00350] Clause 68. A method according to clause 67, wherein the step of reporting the multi-patterning coloring violation to the user visually comprises a step of pointing out the multi- patterning spacing constraint violations which make up a cycle.

[00351] Clause 69. A method according to any of clauses 67-68, wherein the step of reporting the multi-patterning coloring violation to the user visually comprises a step of representing a particular one of the multi-patterning spacing constraint violations which make up a cycle by using a visual marker, the size of the marker being dependent upon a value of a multi- patterning spacing constraint being violated. [00352] Clause 70. A method according to clause 69, wherein the particular multi- patterning spacing constraint violation comprises a corner-corner multi-patterning spacing violation,

and wherein the marker representing the particular constraint violation comprises a rectangle visually interconnecting a pair of island corners which violate the corner-corner multi- patterning spacing constraint.

[00353] Clause 71. A method according to clause 70, wherein the rectangle has a size which indicates visually a minimum spacing called for by the corner-corner multi-patterning spacing constraint.

[00354] Clause 72. A method according to any of clauses 69-71, wherein the particular multi-patterning spacing constraint violation comprises an edge-edge multi-patterning spacing violation,

and wherein the marker representing the particular constraint violation comprises a rectangle visually interconnecting a pair of island edges which violate the edge-edge multi- patterning spacing constraint.

[00355] Clause 73. A method according to clause 72, wherein the rectangle has a length in a dimension perpendicular to the two edges which indicates a minimum spacing called for by an edge-edge multi-patterning spacing constraint.

[00356] Clause 74. A method according to any of clauses 69-73, wherein the step of detecting a multi-patterning coloring violation is performed in response to a user behavior in which a set of at least one of the islands in the plurality of islands is edited,

wherein the step of reporting the multi-patterning coloring violation to a user comprises the step of indicating the multi-patterning coloring violation to the user sufficiently promptly after the user behavior so that the user can correct the multi-patterning coloring violation in real time.

[00357] Clause 75. A method according to any of clauses 69-74, wherein the step of detecting a multi-patterning coloring violation is performed in response to a user selecting a set of at least one portion of the islands in the plurality of islands, depressing a mouse button and dragging the selected portion to a modified position in the layout,

and wherein the step of reporting a design rule violation to a user is completed before the user releases the mouse button.

Claims

1. A method for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands,

for use by a computer system having access to a design rule data set indicating values for multi-patterning spacing constraints among islands in a particular layer, the method comprising the steps of:

the computer system iteratively building a data structure identifying the plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships indicating that the pair of islands related by the relationship violates one of the multi-patterning spacing constraints;

during the step of building a data structure, and before all of the relationships are included in the data structure, in dependence upon the relationships that are included in the data structure, detecting a multi-patterning coloring violation among islands represented in the data structure; and

reporting the multi-patterning coloring violation to a user.

2. A method according to claim 1, wherein the data structure comprises a graph having a plurality of nodes and a plurality of arcs interconnecting the nodes, each of the nodes representing one of the islands and each of the arcs representing one of the relationships.

3. A method according to claim 2, wherein each of the nodes represents an entire island,

wherein no island is represented by more than one node,

and wherein one of the islands represented by a node is non-rectangular.

4. A method according to any of claims 2-3, wherein the step of building the data structure comprises steps of:

inserting into the graph a root node representing a first one of the islands in the plurality; and

iteratively inserting arcs into the graph which interconnect further nodes in the graph until a particular arc is found the insertion of which would form a cycle in the graph.

5. A method according to any of claims 1-4, wherein the pair of islands related by one of the relationships in the data structure violates more than one of the multi-patterning spacing constraints.

6. A method according to any of claims 1-5, wherein the step of the computer system iteratively building a data structure comprises steps of: iterating among islands in the plurality of islands;

for each current island in the iteration among islands, iterating among corners of the current island; and

for each current corner in the iteration among corners:

determining whether a multi-patterning candidate spacing constraint violation involving the current corner exists between the current island and a far island different from the current island; and

if so, then at least if the far island is not yet in the data structure, inserting into the data structure a particular one of the relationships, the particular relationship indicating that the current island and the far island violate one of the multi-patterning spacing constraints.

7. A method according to claim 6, further comprising steps of:

for the current island in the iteration among islands, iterating among edges of the current island; and

for each current edge in the iteration among edges:

determining whether a multi-patterning candidate spacing constraint violation involving the current edge exists between the current island and another island different from the current island; and

if so, then at least if the other island is not yet in the data structure, inserting into the data structure a given one of the relationships, the given relationship indicating that the current island and the other island violate one of the multi-patterning spacing constraints.

8. A method according to any of claims 1-7, wherein the multi-patterning coloring violation comprises a pre-coloring violation.

9. A method according to any of claims 1-8, wherein the multi-patterning coloring violation comprises a pre-grouping violation.

10. A method according to any of claims 1-9, wherein the multi-patterning coloring violation comprises a triple-patterning coloring violation.

11. A method according to any of claims 1-10, wherein the step of reporting the multi-patterning coloring violation to a user comprises the step of indicating the multi-patterning coloring violation to the user visually.

12. A method according to claim 1 1, wherein the step of indicating the multi- patterning coloring violation to the user visually comprises a step of representing a particular one of the multi-patterning spacing constraint violations which make up a cycle by using a visual marker, the size of the marker being dependent upon a value of a multi-patterning spacing constraint being violated.

13. A method according to any of claims 11-12, wherein the step of the computer system iteratively building a data structure is performed in response to a user behavior in which a set of at least one of the islands in the plurality of islands is edited,

wherein the step of reporting the multi-patterning coloring violation to a user comprises the step of indicating the multi-patterning coloring violation to the user sufficiently promptly after the user behavior so that the user can correct the multi-patterning coloring violation in real time.

14. A method according to any of claims 11-13, wherein the step of the computer system iteratively building a data structure is performed in response to a user selecting a set of at least one portion of the islands in the plurality of islands, depressing a mouse button and dragging the selected portion to a modified position in the layout,

and wherein the step of reporting a design rule violation to a user is completed before the user releases the mouse button.

15. A system for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands, comprising:

a computer system having access to a design rule data set indicating values for multi- patterning spacing constraints among islands in a particular layer, the computer system further having access to computer instructions and data which, when applied to the computer system, perform the steps of:

iteratively building a data structure identifying the plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships indicating that the pair of islands related by the relationship violates one of the multi-patterning spacing constraints; while building the data structure, and before all of the relationships are included in the data structure, in dependence upon the relationships that are included in the data structure, detecting any multi-patterning coloring violations among islands represented in the data structure; and

where a multi-patterning coloring violation is detected among islands represented in the data structure, reporting it to a user.

16. A computer program product for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands, for use by a computer system having access to a design rule data set indicating values for multi- patterning spacing constraints among islands in a particular layer, the computer program product comprising:

a computer readable storage medium having stored thereon a plurality of software code portions and data which when executed by the computer system perform the steps of:

iteratively building a data structure identifying the plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships indicating that the pair of islands related by the relationship violates one of the multi-patterning spacing constraints; while building the data structure, and before all of the relationships are included in the data structure, in dependence upon the relationships that are included in the data structure, detecting any multi-patterning coloring violations among islands represented in the data structure; and

where a multi-patterning coloring violation is detected among islands represented in the data structure, reporting it to a user.

17. A method for checking a set of multi-patterning layout design rules on a particular layer of a region of an integrated circuit layout, the layout including a plurality of shapes,

for use by a computer system having access to a design rule data set indicating values for multi-patterning spacing constraints among islands in the particular layer, the method comprising steps of:

for each edge in a subset of at least two edges of the shapes in the plurality of shapes, the computer system populating a layout topology database with values in dependence upon the respective edge location;

in dependence upon values populated into the layout topology database in the step of the computer system populating, but before populating the layout topology database with values in dependence upon all of the edge locations in the subset of edges, detecting a subset of at least one candidate violation of the multi-patterning spacing constraints;

after detecting all the candidate violations in the subset, searching the candidate violations in the subset for multi-patterning coloring violations; and

where a multi-patterning coloring violation is detected, reporting it to a user.

18. A method according to claim 17, wherein the step of populating a layout topology database with values in dependence upon the respective edge location comprises a step of populating the layout topology database with values in dependence upon a location of an endpoint of the respective edge.

19. A method according to any of claims 17-18, wherein the step of populating a layout topology database with values in dependence upon the respective edge location comprises a step of populating the layout topology database with a distance from a first one of the edges to a second one of the edges of a shape in the plurality of shapes, the first and second edges being on different islands,

and wherein the step of detecting a subset of at least one candidate violation of the multi- patterning spacing constraints, comprises a step of comparing the distance with a value of an edge-edge multi-patterning spacing constraint in the design rule data set.

20. A method according to any of claims 17-19, comprising a step of, in conjunction with each detection of a candidate violation in the step of detecting, inserting an identification of the candidate violation into a database of candidate violations of the multi-patterning spacing constraints,

and wherein the step of searching the candidate violations in the subset for multi- patterning coloring violations comprises a step of searching the database of candidate violations for multi-patterning coloring violations,

further comprising a step of inserting into database of candidate violations identifications of a plurality of detected violations of a corner-corner multi-patterning spacing constraint in the design rule data set, prior to the step of searching the candidate violations in the subset for multi- patterning coloring violations.

21. A method according to claim 20, further comprising steps of:

for each of a plurality of detected convex-corner-to-convex-corner geometric relationships among islands in the particular layer, calculating a corner-corner distance between the corners;

comparing the corner-corner distance with a minimum corner-to-corner spacing value in the design rule data set; and in conjunction therewith,

comparing the corner-corner distance with a value of a corner-corner multi-patterning spacing constraint in the design rule data set;

and where a violation of the corner-corner multi-patterning spacing constraint is found, inserting into the database of candidate violations an identification of the island corners involved in the violation.

22. A method according to any of claims 17-21, wherein the step of searching the candidate violations in the subset for multi-patterning coloring violations comprises steps of: the computer system, in dependence upon the database of candidate violations, iteratively building a data structure identifying the plurality of islands and a plurality of relationships among respective pairs of the islands, each of the relationships indicating that the pair of islands related by the relationship violates one of the multi-patterning spacing constraints; and during the step of building a data structure, and before all of the relationships are included in the data structure, in dependence upon the relationships that are included in the data structure, detecting a multi-patterning coloring violation among islands represented in the data structure.

23. A system for checking a set of multi-patterning layout design rules on a particular layer of a region of an integrated circuit layout, the layout including a plurality of shapes, comprising:

a computer system having access to a design rule data set indicating values for multi- patterning spacing constraints among islands in the particular layer, the computer system further having access to computer instructions and data which, when applied to the computer system, perform the steps of:

for each edge in a subset of at least two edges of the shapes in the plurality of shapes, the computer system populating a layout topology database with values in dependence upon the respective edge location;

in dependence upon values populated into the layout topology database in the step of the computer system populating, but before populating the layout topology database with values in dependence upon all of the edge locations in the subset of edges, detecting a subset of at least one candidate violation of the multi-patterning spacing constraints;

after detecting all the candidate violations in the subset, searching the candidate violations in the subset for multi-patterning coloring violations; and

where a multi-patterning coloring violation is detected, reporting it to a user.

24. A computer program product for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of shapes, for use by a computer system having access to a design rule data set indicating values for multi- patterning spacing constraints among islands in the particular layer, the computer program product comprising:

a computer readable storage medium having stored thereon a plurality of software code portions and data which when executed by the computer system perform the steps of:

for each edge in a subset of at least two edges of the shapes in the plurality of shapes, the computer system populating a layout topology database with values in dependence upon the respective edge location;

in dependence upon values populated into the layout topology database in the step of the computer system populating, but before populating the layout topology database with values in dependence upon all of the edge locations in the subset of edges, detecting a subset of at least one candidate violation of the multi-patterning spacing constraints;

after detecting all the candidate violations in the subset, searching the candidate violations in the subset for multi-patterning coloring violations; and

where a multi-patterning coloring violation is detected, reporting it to a user.

25. A method for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands,

for use by a computer system having access to a design rule data set indicating values for multi-patterning spacing constraints among islands in a particular layer, the method comprising the steps of:

the computer system detecting a set of islands forming a double-patterning coloring violation;

detecting a triple-patterning coloring violation among all the islands in the set and a common island outside the set; and

reporting the triple-patterning coloring violation to a user.

26. A system for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands, comprising:

a computer system having access to a design rule data set indicating values for multi- patterning spacing constraints among islands in a particular layer, the computer system further having access to computer instructions and data which, when applied to the computer system, perform the steps of:

detecting a set of islands forming a double-patterning coloring violation;

searching for a triple-patterning coloring violation among all the islands in the set and a common island outside the set; and

where a triple-patterning coloring violation is found, reporting it to a user.

27. A computer program product for checking a set of multi-patterning layout design rules on a region of an integrated circuit layout, the layout including a plurality of islands, for use by a computer system having access to a design rule data set indicating values for multi- patterning spacing constraints among islands in a particular layer, the computer program product comprising:

a computer readable storage medium having stored thereon a plurality of software code portions and data which when executed by the computer system perform the steps of:

detecting a set of islands forming a double-patterning coloring violation; searching for a triple-patterning coloring violation among all the islands in the set and a common island outside the set; and

where a triple-patterning coloring violation is found, reporting it to a user.