JP2006148013A - Positioning method and exposing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To precisely position a wafer W at a designated reference position on a rest frame prescribing the moving position of a body for each of a plurality of sectioned areas formed on a body. <P>SOLUTION: Shot areas SAp equally arranged on concentric circles C1 and C2 are selected as sample shot areas SA<SB>g</SB>whose position coordinates are measured to find coefficients of respective terms of a model expression (a model expression defining an array of a plurality of shot areas SAp on the wafer W) including as independent variables designed position coordinates (x, y) of the plurality of shot areas SA<SB>p</SB>on the wafer W and also including as subordinate variables information regarding the positions of the shot areas SA<SB>p</SB>on a stage coordinate system. Consequently, the sample shot areas SA<SB>g</SB>can equally be interspersed along an arbitrary straight line passing a nearly center point of the wafer W, so when the coefficients of the respective terms of the model expression are found from their measurement results by using a statistical method, an estimation error between a model expressed by the model expression and the real model expression can be reduced. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an alignment method and an exposure method, and more specifically, each of a plurality of partitioned regions formed on an object is defined with respect to a predetermined reference position in a stationary coordinate system that defines the movement position of the object. The present invention relates to a positioning method for positioning and an exposure method using the positioning method.

  In recent years, in a manufacturing process of a device such as a semiconductor element, an exposure apparatus such as a step-and-repeat system or a step-and-scan system, a wafer prober, or a laser repair apparatus is used. In these apparatuses, each of a plurality of shot areas arranged on a substrate is set to a predetermined reference point (for example, a rectangular coordinate system defined by a laser interferometer) that defines a moving position of the substrate (for example, Therefore, it is necessary to align (align) very precisely with respect to processing points of various apparatuses.

  In particular, in an exposure apparatus, a circuit pattern (reticle pattern) of 10 layers or more is superimposed and transferred onto a substrate (hereinafter referred to as “wafer”). The above characteristics can be inconvenient. In such a case, the chip does not satisfy the desired characteristics, and in the worst case, the chip becomes a defective product, which reduces the yield. Therefore, in the exposure apparatus, an alignment mark is previously attached to each of a plurality of shot areas on the wafer, and a stage coordinate system that is a stationary coordinate system that defines a moving position of a wafer stage that can hold and move the wafer. The position (coordinate value) of the mark is detected. Thereafter, wafer alignment is performed for aligning one shot area on the wafer with the reticle pattern based on the mark position information and the position information of a known reticle pattern (which is measured in advance).

  As one of the wafer alignments, there is a global alignment method in which each shot area is aligned by detecting alignment marks of several shot areas on the wafer and obtaining regularity of the arrangement of the shot areas. Among them, an enhanced global alignment (EGA) method that accurately specifies the regularity of the arrangement of shot areas on a wafer by a statistical method has become the mainstream (see, for example, Patent Document 1 and Patent Document 2).

  In the EGA method, first, position coordinates on a stage coordinate system of a plurality of shot areas (hereinafter also referred to as “sample shot areas”) on a wafer are actually measured. The design positions of a plurality (three or more, usually about 7 to 15) of sample shot areas on the arrangement coordinate system defined by the actual measurement values and the shot area arrangement on the wafer. At the time of the conversion, statistical analysis processing (for example, least square method) is used so that the fitting error with the position coordinates obtained when the coordinates are converted to the position coordinates on the stage coordinate system is as small as possible. Error parameter values such as scaling, rotation, and offset used in the above are obtained. Further, the position coordinates of each shot region in the stage coordinate system are calculated based on the regression model defined by the obtained error parameter values.

  Various improvements have been made to the EGA method in order to meet the demand for higher overlay accuracy of shot areas accompanying the recent miniaturization of device patterns. For example, as a statistical model defined by the error parameter, there is a method using a regression model that considers not only the first order component (rotation, magnification, offset) of the array of shot areas on the wafer but also the higher order component as a parameter. (See Patent Document 3).

  In regression analysis such as the EGA method, when selecting a sample shot area from shot areas, it is desirable to select an optimal arrangement from the viewpoint of model estimation accuracy. In this case, the sample shot area is selected under an arrangement that is empirically desirable, such as simply selecting shot areas that are scattered in a grid pattern. However, as described above, higher-order polynomials are gradually used as the model formula, and the number of sample shot areas necessary for the estimation is also increasing. In order to be high, a clear standard for the selection of the sample shot area has become necessary.

JP-A 61-44429 JP-A-62-84516 Japanese Patent No. 3230271

  In the present invention made under the above circumstances, from a first viewpoint, each of the plurality of partitioned areas formed on the object is set with respect to a predetermined reference position in a stationary coordinate system that defines the moving position of the object. A predetermined number of partition regions arranged substantially evenly on a plurality of concentric circles centered on an approximate center of the object from the plurality of partition regions. Selecting as a specific partition region; measuring a position coordinate of a partition region including the predetermined number of specific partition regions in the stationary coordinate system; performing statistical calculation based on a result of the measurement; Obtaining a coefficient of each term of a model equation of a predetermined order having the design position coordinates of each of the plurality of partitioned areas in as an independent variable and information relating to the position of the partitioned area as a dependent variable; Demand A first alignment method comprising; was based on the model equation, each of the plurality of divided areas, a step of aligning with respect to a predetermined reference position in the stationary coordinate system.

  According to this, a model formula (specifying the arrangement of multiple partitioned areas on an object is defined with the design position coordinates of each partitioned area on the object as an independent variable and the information on the position of the partitioned area as a dependent variable. In order to obtain the coefficient of each term of the model equation), a partitioned region that is evenly scattered on a concentric circle centered on the approximate center of the object is selected as the specific partitioned region for measuring the position coordinates. In this way, since it is possible to uniformly measure the position information of the divided areas that are radially arranged uniformly about the center on the object, from the measurement results, using a statistical method, When obtaining the coefficient of each term of the model formula, an estimation error between the estimated model expressed by the model formula and the true model formula can be reduced.

  According to a second aspect of the present invention, each of a plurality of partitioned areas formed on a substantially circular object is aligned with a predetermined reference position in a stationary coordinate system that defines the movement position of the object. A positioning method, wherein a predetermined number of partitioned areas arranged substantially uniformly in an arbitrary diameter direction of the object are selected from the plurality of partitioned areas as a specific partitioned area; and the stationary coordinate system Measuring a position coordinate of a partition area including the predetermined number of specific partition areas in the method; and performing a statistical calculation based on a result of the measurement to obtain a design position coordinate of each of the plurality of partition areas in the stationary coordinate system. Obtaining a coefficient of each term of a model equation of a predetermined order having an independent variable and information on the position of the partition area as a dependent variable; and, based on the model equation from which the coefficient of each term is obtained, A second alignment method comprising; each image region, a step of aligning with respect to a predetermined reference position in the stationary coordinate system.

  According to this, a model formula (specifying the arrangement of multiple partitioned areas on an object is defined with the design position coordinates of each partitioned area on the object as an independent variable and the information on the position of the partitioned area as a dependent variable. In order to obtain the coefficient of each term of the model equation), a predetermined number of partitioned areas arranged almost uniformly in an arbitrary diameter direction of the object are selected as specific partitioned areas for measuring position coordinates. In this way, since it is possible to measure the position information of the partition area arranged without deviation in the diameter direction of the object on the substantially circle, from the measurement results, using the statistical method, When obtaining the coefficient of each term, it is possible to reduce the estimation error between the estimated model expressed by the model formula and the true model formula.

  According to a third aspect of the present invention, there is provided an exposure method for sequentially exposing a plurality of partitioned areas arranged on an object to form a predetermined pattern in each partitioned area, and using the alignment method of the present invention, Aligning each of the plurality of partitioned areas with a predetermined reference position in a stationary coordinate system defining a movement position of the object; and exposing the aligned partitioned areas. Including an exposure method. In such a case, since each of the plurality of partitioned regions on the object is aligned with the reference position using the exposure method of the present invention, highly accurate overlay exposure can be realized.

  Hereinafter, an embodiment of the present invention will be described with reference to FIGS.

  FIG. 1 shows a schematic configuration of an exposure apparatus 100 according to an embodiment of the present invention. The exposure apparatus 100 is a step-and-scan projection exposure apparatus. The exposure apparatus 100 includes a reticle stage RST that holds a reticle R as a mask, a projection optical system PL, a wafer stage WST on which a wafer W as an object is mounted, an alignment detection system AS, and a main controller that controls the entire apparatus. 20 etc.

  On reticle stage RST, reticle R on which a circuit pattern or the like is drawn is fixed, for example, by vacuum suction. On the reticle R, illumination light IL from an illumination system (not shown) is illuminated uniformly. An illumination area on the reticle R by the illumination light IL is defined by a reticle blind (not shown) that is provided inside the illumination system and whose operation is controlled by the main controller 20. Reticle stage RST is perpendicular to the optical axis of an illumination system (not shown) (corresponding to optical axis AX of projection optical system PL described later) by a reticle stage drive unit (not shown) using a linear motor, a voice coil motor or the like as a drive source. In addition, it can be driven in a small amount in the XY plane, and can be driven at a scanning speed specified in a predetermined scanning direction (here, the Y-axis direction).

  The position of the reticle stage RST in the stage moving surface is always detected by a reticle laser interferometer (hereinafter abbreviated as “reticle interferometer”) 16 via a movable mirror 15 with a resolution of about 0.5 to 1 nm, for example. Is done. Here, actually, on the reticle stage RST, a moving mirror having a reflecting surface orthogonal to the Y-axis direction and a moving mirror having a reflecting surface orthogonal to the X-axis direction are provided, corresponding to these moving mirrors. A reticle Y interferometer and a reticle X interferometer are provided, but these are typically shown as a movable mirror 15 and a reticle interferometer 16 in FIG. Here, at least one of the reticle Y interferometer and the reticle X interferometer, for example, the reticle Y interferometer, is a two-axis interferometer having two measurement axes, and the reticle stage RST is based on the measurement value of the reticle Y interferometer. In addition to the Y position, the rotation amount (yawing amount) in the θz direction (rotation direction around the Z axis) can also be measured. Position information (including rotation information such as yawing amount) of reticle stage RST from reticle interferometer 16 is supplied to stage controller 19 and main controller 20 via this. The stage control device 19 drives and controls the reticle stage RST via a reticle stage drive unit (not shown) based on the position information of the reticle stage RST in response to an instruction from the main control device 20.

  The projection optical system PL is disposed below the reticle stage RST in FIG. 1, and the direction of the optical axis AX is the Z-axis direction. As the projection optical system PL, a birefringent optical system having a predetermined reduction magnification (for example, 1/5 or 1/4) is used.

  Wafer stage WST is arranged on a base (not shown) below projection optical system PL in FIG. Wafer holder 25 is placed on wafer stage WST. A wafer W is fixed on the wafer holder 25 by, for example, vacuum suction. Wafer stage WST is rotated by X, Y, Z, θz (rotation direction around Z axis), θx (rotation direction around X axis), and θy (rotation around Y axis) by wafer stage drive unit 24 in FIG. It is a single stage that can be driven in the direction of 6 degrees of freedom. For the remaining θz direction, wafer stage WST (specifically, wafer holder 25) may be configured to be rotatable, and yawing error of wafer stage WST is corrected by rotation on reticle stage RST side. It is also good.

  A movable mirror 17 that reflects a laser beam from a wafer laser interferometer (hereinafter abbreviated as “wafer interferometer”) 18 is fixed to a side surface of the wafer stage WST. The positions of the wafer stage WST in the X direction, the Y direction, and the θz direction (rotation direction about the Z axis) are always detected with a resolution of about 0.5 to 1 nm, for example.

  In the present embodiment, the X-axis and Y-axis interferometers are multi-axis interferometers having a plurality of measurement axes, and in addition to the X and Y positions of wafer stage WST, rotation (yawing (θz which is rotation around the Z axis) Rotation), pitching (θx rotation that is rotation around the X axis), and rolling (θy rotation that is rotation around the Y axis)) can also be measured.

  As described above, a plurality of wafer interferometers and moving mirrors are provided, but in FIG. 1, these are typically shown as a moving mirror 17 and a wafer interferometer 18. A stationary coordinate system that defines the movement position of wafer stage WST (wafer W held on wafer stage WST) defined by wafer interferometer 18 is hereinafter referred to as a “stage coordinate system”.

  A reference mark plate FM is fixed in the vicinity of wafer W on wafer stage WST. The surface of the reference mark plate FM is set to the same height as the surface of the wafer W, and at least a pair of reticle alignment reference marks and a reference mark for baseline measurement of the alignment detection system AS are formed on this surface. Has been.

  The alignment detection system AS is an off-axis alignment sensor disposed on the side surface of the projection optical system PL. As this alignment detection system AS, for example, a broadband detection light beam that does not sensitize a resist on a wafer is irradiated onto a target mark, and an image of the target mark formed on a light receiving surface by reflected light from the target mark is not shown. An image processing type FIA (Field Image Alignment) type sensor that captures an image of an index using an imaging device (CCD) or the like and outputs an image pickup signal thereof is used. In addition to the FIA system, a target mark is irradiated with coherent detection light, and scattered light or diffracted light generated from the target mark is detected, or two diffracted lights (for example, of the same order) generated from the target mark. Of course, it is possible to use an alignment sensor for detecting the interference by using them alone or in combination as appropriate. The imaging result of the alignment detection system AS is output to the main controller 20 via an alignment signal processing system (not shown).

  In FIG. 1, the control system is mainly configured by a main control device 20 and a stage control device 19 subordinate thereto. The main controller 20 includes a so-called microcomputer (or workstation) including an internal memory such as a CPU (Central Processing Unit), a ROM (Read Only Memory), and a RAM (Random Access Memory). , To control the entire device.

  The main controller 20 is a man-machine interface for an operator, for example, an input device including a pointing device such as a keyboard and a mouse, a display device such as a CRT display (or liquid crystal display), and various information. A storage device (not shown) for storage is connected externally. The main controller 20 performs, for example, synchronous scanning of the reticle R and the wafer W, stepping of the wafer W, and the like based on the measurement values of the reticle interferometer 16 and the wafer interferometer 18 so that the scanning exposure operation is performed accurately. Control.

  Further, the exposure apparatus 100 of the present embodiment supplies an image forming light beam for forming a plurality of slit images toward the best image forming surface of the projection optical system PL from an oblique direction with respect to the optical axis AX direction (not shown). And an oblique incidence type multi-point focus detection system comprising a light receiving system (not shown) that receives each reflected light beam of the imaging light beam on the surface of the wafer W through a slit. As this multipoint focus detection system, one having the same configuration as that disclosed in, for example, Japanese Patent Laid-Open No. 6-283403 can be used, and detailed description thereof is omitted here. The output of this multipoint focus detection system is supplied to the main controller 20. Main controller 20 drives wafer stage WST in the Z direction and the tilt direction via stage controller 19 and wafer stage drive unit 24 based on the wafer position information from the multipoint focus detection system.

  Next, with reference to FIG. 2 and FIG. 2, the exposure apparatus 100 according to the present embodiment configured as described above performs the exposure process for the second layer (second layer) and subsequent layers on the wafer W. 6, the top view of the wafer W, the processing algorithm of the CPU in the main controller 20 will be described with reference to the flowcharts of FIGS. 3, 4 and 5, and the graph shown in FIG. 7.

On the wafer W, as shown in FIG. 2, a plurality of (for example, p _max ) shot regions SA _p are formed on the array in the processing steps up to the previous layer. A coordinate system defined by the arrangement of the shot areas SA _p is defined as an αβ coordinate system. In this case, the α axis corresponds to the x axis, and the β axis corresponds to the y axis. A wafer alignment X mark (wafer X mark) MX _p and a wafer alignment Y mark (wafer Y mark) MY _p are formed on street lines having a width of about 100 μm between adjacent shot regions. Among these, the X position of the wafer X mark MX _p coincides with the X (α) coordinate of the shot area SA _p (center C _p ) by design, and the Y position of the wafer Y mark MY _p is the shot area SA _p ( Is designed to coincide with the Y (β) coordinate of the center C _p ). That is, in terms of design, the position coordinates of the shot area SA _p (center C _p ) (which is expressed as (MX _p , MY _p )) by the X position of the wafer X mark MX _p and the Y position of the wafer Y mark MY _p. Is required).

Incidentally, the shot area SA _p concerning information residing on the wafer W as described above (number of shots, shot size, placement, placement of the alignment mark, the type called shot map data for connections), the main control unit from a host computer of a lithography system It is assumed that it has been downloaded to 20 storage devices (not shown).

As shown in FIG. 3, first, in step 301, reticle R is loaded onto reticle stage RST via a reticle loader (not shown). When this reticle loading is completed, in the next step 303-> step 305, preparations such as reticle alignment using a reticle alignment system (not shown) and the above-described reference mark plate FM, baseline measurement using the alignment detection system AS, etc. Process. By this series of preparation processes, the relative positional relationship between the loaded reticle R and the stage coordinate system (XY coordinate system) is obtained, and the distance between the projection center of the reticle R and the detection center of the alignment detection system AS. A baseline is required. When this series of preparatory processing is completed, the main controller 20, wafer loading, the and overlay exposure for each shot area SA _p on the wafer W wafer alignment (wafer alignment by the EGA method in this case) performed. In the present embodiment, the position corresponding to the projection center of the reticle R in the stage coordinate system is the reference position in the overlay exposure in the stage coordinate system.

  First, in step 307, a shot map is acquired from a storage device (not shown) and held in an internal memory. With this shot map, the arrangement and number of sample shot areas (number of samples) as specific section areas for measuring position information in the stage coordinate system are determined as will be described later during wafer alignment described later. In the next step 309, the wafer W is loaded on the wafer stage WST (specifically, on the wafer holder 25) via a wafer loader (not shown). In this embodiment, prior to loading of the wafer W, a pre-alignment apparatus (not shown) is used to briefly describe the stage coordinate system (XY coordinate system) and the αβ coordinate system (hereinafter referred to as “wafer coordinate system”) in FIG. So that the rotational deviation and the center position deviation of the wafer W with respect to the wafer stage WST are adjusted with high precision, so that the rotation deviation and the center position of the wafer W are loaded after loading. It is assumed that so-called search alignment for adjusting the deviation is unnecessary.

In the next subroutine 311, wafer alignment processing is performed. In this wafer alignment process, the arrangement of shot areas SA _p on the wafer W in the stage coordinate system is estimated, and the position coordinates of the center C _p of all shot areas SA _p are calculated according to the arrangement. The wafer alignment process will be described later in detail.

Next, in step 313, 1 is set to the value of the counter p indicating the array number of the shot area (hereinafter referred to as “counter value p”), and the first shot area SA _p is set as the exposure target area.

Next, in step 315, based on the arrangement coordinates of the exposure area which is held in the internal memory is calculated in the subroutine 311 (center position coordinates of each shot area SA _p), the position of the wafer W is, the projection of the reticle R Back-calculating from the position corresponding to the center, the stage control device 19 and the wafer are positioned so as to be the acceleration start position for performing accurate overlay exposure by scanning exposure on the exposure target shot area SA _p on the wafer W. Wafer stage WST is moved via stage drive unit 24, and reticle stage RST is moved via stage control device 19 and reticle stage drive unit (not shown) so that the position of reticle R becomes the acceleration start position. .

In step 317, relative scanning of reticle stage RST and wafer stage WST is started. When both stages RST and WST reach their respective target scanning speeds and reach a constant speed synchronization state, the pattern area of the reticle R starts to be illuminated by illumination light IL from an illumination system (not shown), and scanning exposure is started. The Then, different areas of the pattern area of the reticle R are sequentially illuminated with the illumination light IL, and the scanning exposure is completed when the illumination on the entire pattern area is completed. Thus, the pattern of reticle R is reduced and transferred onto the shot area SA _p to be exposed on the wafer W via the projection optical system PL.

In step 319, referring to the counter value p, it is determined whether the exposure has been performed on all of the shot areas SA _p. Here, since p = 1, that is, only the first shot area SA ₁ has been exposed, the determination at step 319 is denied and the routine proceeds to step 321.

  In step 321, the counter value p is incremented (p ← p + 1), the next shot area is set as the exposure target area, and the process returns to step 315.

Thereafter, the processing and determination of step 315 → step 317 → step 319 → step 321 are repeated until the determination in step 319 is affirmed. When the pattern transfer to all the shot areas SA _p on the wafer W is completed, the determination in step 319 is affirmed, and the process proceeds to step 323.

  In step 323, an instruction to unload the wafer W is given to a wafer loader (not shown). As a result, the wafer W is unloaded from the wafer holder 25 and then transferred to a coater / developer (not shown) connected inline to the exposure apparatus 100 by a wafer transfer system (not shown).

  In the next step 325, it is determined whether or not the exposure of all the wafers W in the lot has been completed. If this determination is affirmative, the exposure process is terminated, and if negative, the process returns to step 309. Here, since the exposure of the first (first) wafer W in the lot has only been completed, the determination is denied and the process returns to step 309.

  Thereafter, step 309 (wafer load) → subroutine 311 (wafer alignment) → step 313 to step 321 (exposure) → step 323 (wafer unload) → step 325 (lot) until the determination in step 325 of FIG. 3 is affirmed. (End determination) loop processing is sequentially executed for each wafer W in the lot. If the determination in step 325 is affirmative, the series of exposure processing is terminated.

  That is, in the above exposure processing, wafer alignment processing and exposure processing are performed on wafers W in a lot, with wafers W sequentially loaded on wafer stage WST being processed.

≪Wafer alignment process≫
Next, the wafer alignment process in the subroutine 311 will be described. In this wafer alignment process, the EGA method is adopted. First, the high-order EGA method adopted in this embodiment will be described.

The actual formation position of the wafer marks MX _p and MY _p formed on the wafer W in the stage coordinate system deviates from the design position (that is, the formation position of the shot area SA _p deviates from the design position). This is due to a mismatch between the stage coordinate system (X, Y) that defines the movement position and the wafer coordinate system (α, β).

If the design position coordinate of the center position C _p of the shot area SA _p caused by this mismatch is (x, y) and the actual position coordinate in the stage coordinate system is (x ′, y ′), The model expression indicating the relationship between the position coordinates (x, y) of the actual position coordinates (x ′, y ′) is expressed by the following expression, that is, a polynomial of two variables of x and y.

ここで、ａ₀〜ａ₉、ｂ₀〜ｂ₉は、このモデル式の各項の係数であり、これを以下では、「ＥＧＡパラメータ」とも呼ぶ。

Here, a _{0 to} a ₉ and b _{0 to} b ₉ are coefficients of each term of this model formula, and are also referred to as “EGA parameters” below.

In the EGA method, the design position coordinates of the shot area SA _p are substituted into (x, y) of the model expression of the above expression (1), and (x ′, y ′) is substituted with the actual shot area SA _p . The position coordinates are obtained and used as the center position of the shot area SA _g in the stage coordinate system in the alignment. For this purpose, the EGA parameters a _{0 to} a ₉ , b in the above equation (1) are used. it is necessary to obtain the value of ₀ ~b _9. In order to obtain the EGA parameters a _{0 to} a ₉ and b _{0 to} b ₉ , in this embodiment, first, several sample shot areas SA selected from a shot area SA _p on the wafer W by a method to be described later are used. The position coordinates (MX _g , MY _g ) in the stage coordinate system of several (for example, h) wafer marks attached to _g (g = 1, 2,..., h) are actually measured. Then, using the actually measured position coordinates of the sample shot area SA _g and the design position in the in-shot coordinate system (coordinate system with the center of the shot area as the origin) of the h actually measured wafer marks, Based on the model expression shown in Expression (1), statistical processing (for example, the method of least squares) is executed, and the model of the above Expression (1) that minimizes the value of the evaluation function E shown in the following Expression The values of EGA parameters a _{0 to} a ₉ and b _{0 to} b _{9 in} the equation are estimated.

すなわち、この評価関数Ｅは、計測されるショット領域に対応する各ウエハマークＭＸ_g、ＭＹ_gの上記式（１）により求められる予想位置（ＭＸ_g’，ＭＹ_g’）とその位置の実測値（ＭＸ_g，ＭＹ_g）との残差の二乗和を、ウエハマークのサンプル数ｈで割ったもの（すなわち残差の二乗和の平均）である。

That is, the evaluation function E is obtained by _{calculating the} expected position (MX _g ′, MY _g ′) of the wafer marks MX _g and MY _g corresponding to the shot area to be measured, which is obtained by the above equation (1), and the actual value of the position. The residual sum of squares with (MX _g , MY _g ) is divided by the number h of wafer mark samples (that is, the average of the residual sum of squares).

  Hereinafter, the wafer alignment processing will be described along the flowchart of the subroutine 311 shown in FIG. As described above, this subroutine 311 is executed once for the wafer W every time the wafer W to be processed is switched (every time Steps 309 to 325 in FIG. 3 are repeated). Become.

In subroutine 401, the selection of sample shot areas SA _g to detect the position information in the stage coordinate system by the alignment detection system AS. Here, a description will be given of the principle of the selection method of the sample shot areas SA _g in this embodiment. FIG. 6 shows a shot map (shot arrangement) on the wafer W. In the present embodiment, in order to simplify the description, the description will be made assuming that a total of 269 square shot areas SA _p are formed on one wafer W, although more than usual.

In FIG. 6, two concentric circles C <b> 1 and C <b> 2 are indicated by dotted lines so as to be superimposed on the shot arrangement of the wafer W. The concentric circles C1 and C2 are circles centered on the approximate center of the wafer W. Concentric C2 is the size of the circle that passes through the outermost shot upper region SA _p on the wafer W, the radius of the ratio of the concentric circle C1 concentric C2 is 1: 2. In FIG. 6, sample shot areas SA _g selected from the plurality of shot areas SA _{p and} whose position coordinates in the stage coordinate system are measured by the alignment detection system AS are displayed with diagonal lines. That is, in this embodiment, as shown in FIG. 6, as the sample shot areas SA _g, the shot area SA _p disposed on a plurality of concentric circles C1, C2, which is shown, is selected.

The reason why the shot area SA _p on the plurality of concentric circles C1 and C2 is selected as the sample shot area SA _g will be described.

  First, in order to simplify the description, when estimating a coefficient of a polynomial having one variable x represented by the following equation instead of a polynomial having two variables x and y as represented by the above equation (1): think about.

ここで、ｘが取りうる値の範囲を規定する区間［ｔ₁，ｔ₂］内における複数のｘ位置ｘ_gについて、それぞれ複数のデータの組（ｘ_g，ｆ（ｘ_g））（１≦ｇ≦ｈ）が得られているとする。このデータ組（ｘ_g，ｆ（ｘ_g））から係数ｄ_kを推定する場合、すべての（ｘ_g，ｆ（ｘ_g））が上記式（３）を満たしていれば、係数ｄ_kを正しく推定することができる。しかし、区間［ｔ₁，ｔ₂］内における複数のデータの組（ｘ_g，ｆ（ｘ_g））のｆ（ｘ_g）が何らかの計測装置により計測された計測値であるような場合は、そのｆ（ｘ_g）に計測誤差が含まれるようになる。ここで、計測誤差εは、偶然誤差であり、平均０、分散σ₂の正規分布に従うものとし、その期待値を｜ε｜とする。すなわち、ここでは、区間［ｔ₁，ｔ₂］のいずれの計測点でｆ（ｘ_g）を計測しても、その計測誤差の期待値｜ε｜は同じであると仮定する。

Here, a plurality of data sets (x _g , f (x _g )) (1 ≦ 1) for a plurality of x positions x _g in the interval [t ₁ , t ₂ ] defining the range of values that x can take. It is assumed that g ≦ h) is obtained. When estimating the coefficient d _k from this data set (x _g , f (x _g )), if all (x _g , f (x _g )) satisfy the above equation (3), the coefficient d _k is _calculated. It can be estimated correctly. However, the interval [t _1, t _2] If such a plurality of sets of data _{(x g, f (x g} )) of f (x _g) are measured values by some measuring device within the The measurement error is included in the f (x _g ). Here, the measurement error ε is a coincidence error and follows a normal distribution with an average of 0 and a variance σ ₂ , and its expected value is | ε |. That is, here, it is assumed that the expected value | ε | of the measurement error is the same even if f (x _g ) is measured at any measurement point in the section [t ₁ , t ₂ ].

Here, by the coefficients d _k of each term that has been estimated that the coefficient e _k, the equation polynomial f (x) of (3), indicated the coefficient by the following equation to e _k g (x) Replace with

この推定された多項式（４）と上記式（３）の多項式（真のモデル）との誤差（推定誤差）（Δ（ｘ）とする）は、次式で示される。

The error (estimated error) (referred to as Δ (x)) between the estimated polynomial (4) and the polynomial (true model) of the above equation (3) is expressed by the following equation.

上記式（５）より、推定されたモデルと真のモデルとの間に生ずる推定誤差Δ（ｘ）もｎ次の多項式となることがわかる。

From the above equation (5), it can be seen that the estimation error Δ (x) generated between the estimated model and the true model is also an n-order polynomial.

In general, since such a polynomial diverges from x → ± ∞, when the magnitude of the estimation error | Δ (x) | is expressed by the above equation (5), the absolute value | x | As the value increases, the estimation error | Δ (x) | increases monotonously. Whether the monotonic increase of the estimation error | Δ (x) | starts from which x position depends on the property of the above equation (3), but both ends x of the section of the range x _g can take in the measured data. If measurement data near t = x ₁ and x = t ₂ is included, at least the measurement error | Δ (x) | near x = t ₁ and t ₂ should be expected to be about | ε |. Can do. On the other hand, the given measurement data includes only the x coordinate near the center of the section [t ₁ , t ₂ ], and x = t ₁ or x = t ₂ is expressed by the above equation (3). If it is included in the monotonically increasing region, the possibility that the measurement error | Δ (x) | near x = t ₁ and x = t ₂ will be larger than | ε | cannot be denied. . Therefore, in this case, in the measurement data, the interval [t _1, t _2] so that the measurement data points are always included close to both ends (i.e., measured close to the ends of the interval [t _1, t _2] It is desirable from the viewpoint of estimation accuracy to ensure that points are included.

In addition, since there are (n + 1) coefficients in an n-order polynomial of one variable, at least (n + 1) sets of measurement data are necessary to estimate the values of these coefficients. It is desirable that the measurement points from which (n + 1) sets of measurement data are acquired are evenly scattered within the interval that the variable x can take. This is because if the position of the measurement point from which measurement data is acquired is concentrated in a part of the section and the distribution in the section of the measurement point from which measurement data is acquired is biased, it exists in that part. the measurement error contained in the measurement data to the estimation result with so (equation (the value of the coefficient e _k 4)) is largely, possibly estimation error for a small number section of the measurement data is large Because there is.

As an example, the case where the polynomial to be estimated is a quadratic function as shown in FIG. 7 will be described. In this case, since there are three coefficients to be estimated, three sets of measurement data may be used for estimation. Here, from the viewpoint of the estimation accuracy described above, as described above, among the three sets of measurement data used for estimation, two sets of measurement data are measured data near x = t ₁ (x ₁ , f (x ₁ )) And measurement data near x = t ₂ (x ₂ , f (x ₂ )) are measured. In FIG. 7, on the assumption that these two sets of measurement data are used for estimation, the third set of measurement data is measured data in the middle of x = t ₁ and x = t ₂ , that is, x = x. _{When 3} measurement data (x ₃ , f (x ₃ )) are selected, and when x = x ₃ ′ measurement data (x ₃ ′, f (x ₃ ′)) near x = x ₂ The estimation results (quadratic functions g and g ′) estimated respectively in FIG. As can be seen from FIG. 7, 2 estimated when the three sets of measurement data are evenly scattered from the quadratic function g ′ estimated when the distribution of the arrangement state of the three sets of measurement data is biased. It can be seen that the quadratic function g is closer to the quadratic function f which is a true model.

  As described above, when estimating a single-variable polynomial from measurement data, it is desirable that measurement points from which measurement data near both ends of the range that the variable can take are obtained, and a plurality of measurement data It is desirable to arrange the measurement points from which are acquired to be evenly scattered. This tendency is the same for the estimation of the third-order or higher polynomial, where there are measurement points near both ends of the measurement range, and measurement points from which measurement data used for estimation are acquired are scattered as evenly as possible within the section. There is no substitute for what should be done.

  Next, polynomial coefficients of two variables (x, y) corresponding to the X-axis and Y-axis of the stage coordinate system as shown in the above equation (1) (a model equation for shot arrangement on the wafer W) are obtained. A case of estimation will be described. First, the model equation as shown in the above equation (1) is generally expressed as the following equation.

ウエハＷ内のサンプルショット領域ＳＡ_gで得られた計測データを（ｘ_g，ｙ_g）（１≦ｇ≦ｈ）とする（（ｘ_g，ｙ_g）が取りうる範囲は、ウエハＷ上の領域（ショット領域ＳＡ_pが形成されている範囲）である）。この場合にも、計測データを取得する計測点の中に、ｘ，ｙが取りうる範囲の端部の計測点が含まれているのが望ましい。この場合には、ウエハＷに対応する範囲がｘ，ｙの取りうる範囲となるので、ウエハＷの最外周のショット領域ＳＡ_pがサンプルショット領域ＳＡ_gとして選択されるのが望ましいということになる。

The measurement data obtained in the sample shot area SA _g in the wafer W is (x _g , y _g ) (1 ≦ g ≦ h), and the range that ((x _g , y _g ) can take is on the wafer W. Region (range in which the shot region SA _p is formed)). Also in this case, it is desirable that the measurement points for acquiring the measurement data include the measurement points at the end of the range that x and y can take. In this case, since the range corresponding to the wafer W is a range that can be taken by x and y, it is desirable that the outermost shot area SA _p of the wafer W is selected as the sample shot area SA _g. .

  Further, if an arbitrary straight line passing through the approximate center of the wafer W is y = cx (c is a real number) and only the measurement points on the straight line are considered, the above equation (6) can be converted into the following equation. it can.

このように、ｘ、ｙ２変数の多項式である上記式（６）を、ｘについてのｎ次の多項式に変換することができる。これにより、ｆ_x（ｘ，ｙ）、ｆ_y（ｘ、ｙ）の推定（得られた実測値による最小二乗法を用いた各係数ｐ_kl、ｑ_klの推定）には、ｘ座標が異なる計測データが、少なくともｎ＋１個必要であることがわかる。また、上述したように、２つの変数の多項式であっても、ｎ＋１個の計測データ各々が計測される計測点が、ｘ軸方向に均等に点在するようにそれらを配置するのが望ましい。

Thus, the above equation (6), which is a polynomial of x and y2 variables, can be converted into an nth-order polynomial for x. Thus, f _x (x, y), the f _y (x, y) estimation (each coefficient p _kl using the least squares method according to the obtained measured values, the estimation of q _kl) is, x-coordinate is different It can be seen that at least n + 1 pieces of measurement data are required. In addition, as described above, even in the case of a polynomial of two variables, it is desirable to arrange the measurement points at which each of n + 1 pieces of measurement data is evenly scattered in the x-axis direction.

  The above conversion (conversion from a polynomial of two variables x and y to a polynomial of one variable x) can be performed in the same way for y, and the measurement points at which individual measurement data can be obtained are equally distributed in the y-axis direction. It is desirable to arrange them so that they are interspersed.

For the reasons described above, in this embodiment, as shown in FIG. 6, the uniform distribution of measurement data in the X-axis direction and the Y-axis direction (in other words, the uniform distribution of measurement data in an arbitrary diameter direction of the wafer W). ) in order to realize a plurality of concentric circles C1, C2 (concentric C2 around the approximate center of the wafer W, on the corresponding) to the outermost of the shot area SA _p, and the shot area SA interspersed evenly selecting _p as sample shot areas SA _g.

Note that the number of concentric circles depends on the highest degree (n) of the polynomial to be estimated. In the present embodiment, the calculation formula for the number of concentric circles differs depending on whether the highest degree of the polynomial to be estimated is an odd number or an even number. As in the present embodiment, when the highest order n of the polynomial to be estimated is an odd number, n + 1 pieces of measurement data are required in an arbitrary linear direction passing through the approximate center of the wafer W. Therefore, the highest order n The number obtained by adding 1 to 1 and dividing by 2 is the number of concentric circles. For example, when the highest order n of the polynomial to be estimated is the third order (odd number) as shown in Expression (1), (3 + 1) / 2 = 2 is the number of concentric circles. Thereby, in the wafer W as shown in FIG. 6, two concentric circles C1 and C2 are selected. On the other hand, when the highest order n of the polynomial to be estimated is an even number, the number of concentric circles is the number obtained by dividing n by 2 to the highest order, and the shot area SA _p at the substantially center of the wafer W is sample shot. Add to region SA _g .

By the way, the number of coefficients of a polynomial as shown in the above formula (1) is (n + 1) (n + 2) / 2 per polynomial, where the highest order is n, and there are two formulas. , (N + 1) (n + 2). Therefore, if the number of sample shot areas SA _g in each concentric circle is the same, the number of sample shot areas on one concentric circle is (n + 1) (n + 2) / {(n + 1) / 2} = 2 (n + 2). Become. For example, in the present embodiment, since the highest degree n of the polynomial is 3, the number of coefficients of the polynomial of 10 pieces, the number of sample shot areas SA _g on one concentric circle, the ten. In Figure 6, a concentric C1, C2 10 pieces of shot areas SA _p respectively corresponding to each are displayed by hatching as sample shot areas SA _g.

On the other hand, when the highest degree n of the polynomial is an even number, the number of concentric circles is n / 2, and the sample shot area SA _g is added to the approximate center of the wafer W. Therefore, the sample shot area SA _g per concentric circle is added. Is the smallest integer of 2 {(n + 1) (n + 2) -1} / n or more.

Based on the above calculation principle, a processing procedure for selecting the sample shot area SA _g will be described. FIG. 5 shows a processing procedure of the subroutine 401. First, in step 501, it is determined whether or not the highest degree of the estimated polynomial is an odd number. If this determination is affirmed, steps 503 and 505 are continued, and if not, steps 507 and 509 are performed.

In step 503, (n + 1) / 2 is calculated and obtained as the number of concentric circles, and in step 505, 2 (n + 2) is calculated and obtained as the number of samples for each concentric circle. On the other hand, in step 507, n / 2 is calculated as the number of concentric circles, and in step 509, 2 {(n + 2) (n + 1) -1} / n is calculated as the number of samples for each concentric circle, and the number Find the smallest integer above. After the completion of step 505 or step 509, the process proceeds to step 511 to select a sample shot area SA _g. In step 511, a concentric circle is determined based on the determined number of concentric circles, the number of samples per concentric circle, and the shot map acquired in step 307 (see FIG. 3), and a shot area on the concentric circle. from the SA _p, determines the sample shot area SA _g. In the present embodiment, based on the obtained shot map, obtains a distance between the center of the shot area SA _p and the wafer W located at the outermost on the wafer W, on the basis of the distance, their outermost shot area A concentric circle C2 is determined as a circle corresponding to SA _p , and a concentric circle C1 having a radius half that of the concentric circle C2 is determined. Then, among the shot areas SA _p through which the concentric circles C1 and C2 pass, as shown in FIG. 6, the shot areas SA _p that are scattered almost uniformly are selected as the sample shot areas SA _g .

In the present embodiment, the processing procedure described above, the concentric circles C1, C2 shown in FIG. 6, the sample shot area SA _g is determined. After step 511 is completed, the subroutine 401 is ended and the process proceeds to step 403 in FIG.

In the next step 403, for example, from the wafer marks arranged in the sample shot areas SA _g being displayed by hatching in FIG. 6, a total of h in the stage coordinate system (i.e. (n + 1) (n + 2)) samples The position (MX _g , MY _g ) (g = 1, 2,..., H) of the shot area is measured. Specifically, the sample shot areas SA _g h pieces of wafer marks arranged in, based on the measurement order as the time required for position measurement of the wafer mark is as short as possible in all sample shot areas SA _g, alignment detection The wafer stage WST is moved in the XY plane so as to sequentially move within the detection field of the system AS, and the wafer mark is picked up by the alignment detection system AS, and the image pickup result is acquired. At the same time, the wafer stage WST at that time The measurement value of the wafer interferometer 18 is acquired as the position coordinate in the stage coordinate system. Since the position information of the wafer mark within the imaging field of view is sent from the alignment detection system AS, the wafer mark in the stage coordinate system is obtained from the position information of the wafer mark, the measurement value of the wafer interferometer 18 and the baseline. An actual measurement value of the position coordinates of the mark can be obtained. The actually measured value of the position coordinate of the obtained wafer mark in the stage coordinate system is held in the internal memory. In this way, the actual measurement values (MX _g , MY _g ) of the positions of the h wafer marks attached to the selected sample shot SA _g are acquired.

In the next step 405, the values of the EGA parameters a _k and b _k of the model formula of the above formula (1) when only the current measurement result is used are calculated. That is, the parameter a that minimizes the evaluation function E shown in the above equation (2) based on the actually measured values (MX _g , MY _g ) of the position of each wafer mark stored in the internal memory, that is, satisfies the following equation: The values of _k and b _k are obtained using the least square method (EGA calculation).

ここで、（ＭＸ_g’、ＭＹ_g’）は、上記式（１）により求められる位置座標なので、評価関数Ｅは、上記式（１）の成分を含んでおり、上記式（８）を条件にして、パラメータａ_k、ｂ_kの値を求めることができる。なお、この処理については、例えば特開昭６１−４４４２９号公報などに開示されているので、詳細な説明を省略する。

Here, (MX _g ′, MY _g ′) is a position coordinate obtained by the above equation (1), so the evaluation function E includes the component of the above equation (1), and the above equation (8) is a condition. Thus, the values of the parameters a _k and b _k can be obtained. Since this process is disclosed in, for example, Japanese Patent Laid-Open No. 61-44429, detailed description thereof is omitted.

In the next step 407, the position coordinates of all shot areas SA _p are calculated using the above equation (1) in which the values of the obtained parameters a _k and b _k are set, and the calculation results are held in the internal memory. To do. After step 407 ends, the processing of subroutine 311 ends.

  In the present embodiment, the wafer alignment in the subroutine 311 is performed on the wafer W thus loaded as described above.

  As is clear from the above description, in the present embodiment, the process of the subroutine 401 (FIG. 4) performed by the CPU of the main controller 20 corresponds to the “selecting process”, and the process of step 403 (FIG. 4). Corresponds to the “measurement process”, step 405 corresponds to the “coefficient calculation process”, and step 315 (FIG. 3) corresponds to the “positioning process”.

As described above in detail, according to the present embodiment, the design position coordinates (x, y) of each of the plurality of shot areas SA _p on the wafer W are set as independent variables, and the position of the shot area SA _p is related. Sample shot area SA in which position coordinates are measured in order to obtain coefficients a _k and b _k of each term of a model expression (model expression defining the arrangement of a plurality of shot areas SA _p on wafer W) having information as a dependent variable _{As the g} , shot areas SA _p arranged so as to be evenly scattered radially on the wafer W are selected. In this way, over the whole area on the wafer W, since the sample shot area SA _g can be uniformly scattered, from their measurement results, using a statistical method, each term in the model equation When obtaining the coefficients a _k and b _k , the estimation error between the model expressed by the model formula and the true model formula can be reduced.

Incidentally, if, regardless of the method according to the present embodiment, when selecting a shot area SA _p scattered in a grid pattern as sample shot areas SA _g is aligned in any linear direction through the approximate center of the wafer W the distance between the sample shot areas SA _g becomes different depending on the linear direction, it will change the estimation accuracy of the polynomial by the direction. For this case, as in the present embodiment, if the sample shot area SA _g on a plurality of concentric circles centered on the approximate center of the wafer W so as to intersperse on the wafer W, any linear direction (concentric because of the diameter direction) spacing of the sample shot areas SA _g is the same for, becomes almost uniform also estimation accuracy any linear direction (diameter direction), reducing the variation in the estimation accuracy of the polynomial over the entire wafer surface Can do.

Further, the sample shot area SA _g than evenly scattered in a grid pattern, as in the present embodiment, it was so as to intersperse the sample shot areas SA _g radially, in the region of the same size when attempting to estimate the same accuracy using the measurement data, the number of sample shot areas SA _g (measurement points) can be relatively small, which is advantageous in throughput.

In the present embodiment, the number of concentric circles for selecting the sample shot area SA _g is determined from the highest order n of the polynomial to be estimated. In this way, the number of measurement data necessary to estimate the coefficient of the polynomial is always obtained with respect to an arbitrary linear direction (wafer diameter direction) passing through the approximate center of the wafer W. The polynomial can be accurately estimated.

In the present embodiment, the calculation formulas for the highest order n of the polynomial and the number of concentric circles are changed depending on whether the highest order n of the estimated polynomial is an odd number or an even number. By changing the calculation formula, the sample shot area SA _g (ie, the diameter direction of an arbitrary wafer W passing through the approximate center of the wafer W, that is, whether the highest order n of the polynomial to be estimated is an odd number or an even number. Measurement points) can be evenly scattered on the wafer W. Note that when the highest order n of the polynomial is an even number, the number of coefficients to be obtained is an odd number, so that the shot area SA _p located at the approximate center of the wafer W is also selected as the sample shot area SA _g. realizes a justification for any measuring point of the sample shot areas SA _g about the diameter direction of the wafer W.

Figure 8 shows an example of a sample shot area SA _g is selected is shown when the highest degree n of the polynomial representing the shot sequence model that estimates were fourth order. As shown in FIG. 8, since the highest order n is the fourth order (even number), in the subroutine 401 of FIG. 5, steps 507 and 509 are executed, and 2 is determined as the number of concentric circles. Fifteen is determined as the number of sample shot areas SA _g per concentric circle. As shown in FIG. 8, the shot area SA _{p at} the substantially center of the wafer W is also selected as the sample shot area SA _g . However, the present invention is not limited to this, and even a shot area SA _p that is not on a concentric circle can be added to the sample shot area SA _g on condition that the measurement points are not biased to a part of the area.

FIG. 9 shows an example of the sample shot area SA _g when the highest order n of the polynomial to be estimated is 5th. In this case, the number of concentric circles 3 Tsutonari, the number of sample shot areas SA _g per one concentric becomes 14. The ratio of the radii of the three concentric circles is 1: 2: 3.

In the present embodiment, the number of concentric circles is (n + 1) / 2 when the highest degree n of the polynomial is an odd number, and n / 2 when the polynomial is an even number, but the number of concentric circles is , Or more than that. In this case, the number of sample shot areas SA _p per concentric circle may be a number obtained by dividing the total number of necessary sample shot areas SA _{g by} the number of concentric circles.

Further, in the present embodiment, among the plurality of concentric circles C1, C2 shown in FIG. 6, most outer circumference of the concentric circle C2, it is set so as to correspond to the shot areas SA _p located outermost on the wafer W . In this way, the measurement error value included in the measurement data on the outermost concentric circle, that is, the measurement data at the edge of the wafer W can be set to the expected value | ε | of each measurement data. Thus, the estimation error of the polynomial can be reduced. This is the same even when the highest degree of the polynomial is an even number as shown in FIG.

In the present embodiment, the expected value | ε | of the measurement error of the wafer mark position is the same for all the shot areas SA _p , but when the expected value differs depending on the position in the wafer W, for example, most if its expected value in the shot area SA _p of the outer periphery is that extremely large than its expected value of the inner periphery of the shot area SA _p is not an outermost shot area SA _p, measurement error may be selected concentric such that it can be of the outermost shot area SA _p of the expected value is small shot area SA _p and sample shot area SA _g.

In the present embodiment, the sample shot area SA _g to interspersed on a single concentric were the same number for each concentric circle, not limited thereto. FIG Choosing example of a sample shot area SA _g shown in 10, of the selected sample shot areas SA _g as shown in FIG. 6, in the sample shot areas SA _g disposed on the innermost concentric circle C1 Therefore, the number of shot areas SA _p is excluded, so that the number is 6. In this way, the frequency (distribution density) of the sample shot area SA _g near the outer periphery on the wafer W and the frequency (distribution density) of the sample shot area SA _g near the center are approximately equal to each other. To reduce the influence of measurement point density differences on measurement errors (that is, a phenomenon in which shot array estimation is greatly influenced by measurement results at measurement points near the center of the wafer W). Can do. Since the required total number of sample shot areas SA _g is determined by the highest order n of the polynomial to be estimated, in FIG. 10, the sample shot area SA _g on the concentric circle C2 is increased by the reduction number (four), thereby reducing the sample shot area SA _g. It is adjusted so that the number of SA _g does not decrease. Note that when increasing the sample shot area SA _g is not necessary to select the shot area SA _p of concentric C2, may be selected shot areas SA _p in other areas.

In this case, if the highest degree n of the polynomial is even, it may be excluded sample shot areas SA _g of substantially the center of the wafer W to be selected from the measurement target.

In the present embodiment, each of the plurality of shot areas SA _p on the wafer W is set to a reference position (reticle) based on the position coordinates of the shot area SA _p in the stage coordinate system obtained by using the above-described alignment method. Therefore, highly accurate overlay exposure can be realized.

The arrangement of the sample shot areas SA _g on concentric, FIG. 6, it is not limited to those of FIGS. 8 to 10 as a matter of course. In short, the sample shot areas SA _g may be selected so as to be evenly scattered on the concentric circles.

  In the above embodiment, for the sake of simplicity, the description has been given assuming that each shot area has a square shape and there are more than 200 shot areas. However, the actual number of shot areas in the wafer W is as follows. In many cases, the shape of the shot area is also rectangular. Even in this case, the application of the present invention is sufficiently possible, and a shot area on a concentric circle may be selected as a sample shot area. In this case, for example, when a wafer X mark is on a concentric circle and a wafer Y mark is far from the concentric circle for a certain sample shot area, the wafer X mark and wafer Y mark of different shot areas on the concentric circle May be selected as a mark to be measured. In short, the measurement points only need to be scattered on concentric circles.

  In addition, when a plurality of chip areas are formed in one shot area and a wafer mark is attached to each chip area, the areas shown in FIGS. 6 and 8 to 10 are regarded as chip areas and are concentrically arranged. The chip area arranged at the position may be selected as a sample area for measuring the position coordinates.

Further, it is not necessary to select the sample shot area SA _g completely arranged on the concentric circle, and the shot area SA _p near the concentric circle may be selected as the sample shot area SA _g . In short, it is only necessary that the plurality of sample shot areas SA _g are scattered evenly on substantially concentric circles as a whole.

In the above embodiment, the sample shot area SA _g is selected by the main controller 20 of the exposure apparatus 100. However, the selection is not limited to this. For example, the selection is performed in advance by a host computer that manages the lithography process. May be. In this case, the host computer sends information related to the shot map including information indicating which shot area SA _p is selected as the sample shot area SA _g to the main control apparatus 20, and the main control apparatus 20 uses the information. Wafer alignment may be performed based on the above.

  In the above embodiment, the FIA type alignment sensor is used as the alignment detection system AS. However, as described above, the laser beam is irradiated to the alignment mark in the form of a dot on the wafer W and is diffracted by the mark. The present invention can also be applied to an LSA (Laser Step Alignment) type alignment sensor that detects a mark position using scattered light, or an alignment sensor that appropriately combines the alignment sensor and the FIA method. . In addition, for example, an alignment sensor that irradiates a mark on the surface to be detected with a coherent detection light and causes two diffracted lights (for example, the same order) generated from the mark to interfere with each other is used alone, or the FIA method, the LSA. Of course, the present invention can be applied to an alignment sensor appropriately combined with a method or the like.

  The alignment detection system may be an on-axis method (for example, a TTL (Through The Lens) method). In addition, the alignment detection system is not limited to the one that detects the alignment mark in a state where the alignment mark is almost stationary in the detection visual field of the alignment detection system. Relative movement may be used (for example, the aforementioned LSA system or homodyne LIA system). In the case where the detection light and the alignment mark are moved relative to each other, it is desirable that the relative movement direction is the same as the movement direction of the wafer stage WST when detecting each of the alignment marks.

Further, although the light source of the exposure apparatus to which the present invention is applied is a KrF excimer laser, an ArF excimer laser, or an F ₂ laser, other pulse laser light sources in the vacuum ultraviolet region may be used. In addition, as the illumination light for exposure, for example, a fiber doped with erbium (or both erbium and ytterbium), for example, an infrared or visible single wavelength laser beam oscillated from a DFB semiconductor laser or fiber laser. Harmonics that are amplified by an amplifier and wavelength-converted to ultraviolet light using a nonlinear optical crystal may be used.

  An illumination optical system, a projection optical system, and an alignment detection system AS composed of a plurality of lenses are incorporated in the exposure apparatus main body, optically adjusted, and a reticle stage and wafer stage made up of a large number of mechanical parts are arranged in the exposure apparatus main body. The exposure apparatus of the above-described embodiment can be manufactured by connecting the wiring and pipes to each other and further performing general adjustment (electrical adjustment, operation check, etc.). The exposure apparatus is preferably manufactured in a clean room where the temperature, cleanliness, etc. are controlled.

  In the above embodiment, the step-and-scan type projection exposure apparatus has been described. However, the present invention is not limited to the step-and-repeat type projection exposure apparatus, and other exposure apparatuses such as a proximity-type exposure apparatus. Needless to say, this can also be applied. The present invention can also be suitably applied to a step-and-stitch reduction projection exposure apparatus that combines a shot area and a shot area. The present invention can also be applied to a twin stage type exposure apparatus having two wafer stages. Of course, the present invention can also be applied to an exposure apparatus using a liquid immersion method.

  The present invention is not limited to an exposure apparatus for manufacturing a semiconductor, but is used for manufacturing a display including a liquid crystal display element. An exposure apparatus for transferring a device pattern onto a glass plate and a device used for manufacturing a thin film magnetic head. The present invention can also be applied to an exposure apparatus that transfers a pattern onto a ceramic wafer, an exposure apparatus used for manufacturing an image sensor (CCD, etc.), an organic EL, a micromachine, and a DNA chip. A substrate such as a liquid crystal display element is usually rectangular and has a shape different from that of the wafer W described above, but the present invention can also be applied to this case.

  Further, in order to manufacture reticles or masks used in not only microdevices such as semiconductor elements but also light exposure apparatuses, EUV exposure apparatuses, X-ray exposure apparatuses, electron beam exposure apparatuses, etc., glass substrates or silicon wafers, etc. The present invention can also be applied to an exposure apparatus that transfers a circuit pattern.

  Further, the alignment method according to the present invention is not limited to the exposure apparatus, and several marks are selected and detected from a plurality of marks formed on the object, and the detected information is used. Any device that needs to align an object can be applied.

  The semiconductor device includes a step of designing a function and performance of the device, a step of manufacturing a reticle based on the design step, a step of manufacturing a wafer from a silicon material, and a reticle pattern on the wafer by the exposure apparatus 100 of the above-described embodiment. It is manufactured through a transfer step, a device assembly step (including a dicing process, a bonding process, and a packaging process), an inspection step, and the like.

  The alignment method of the present invention is suitable for aligning an object. The exposure method of the present invention is suitable for a lithography process for manufacturing a semiconductor element, a liquid crystal display element, and the like.

It is a figure which shows schematically the structure of the exposure apparatus which concerns on one Embodiment of this invention. It is a figure which shows an example of arrangement | positioning of the shot area | region on a wafer, and the wafer mark attached to this. It is a flowchart which shows the process algorithm of CPU of the main control apparatus in the case of the exposure process in the exposure apparatus which concerns on one Embodiment of this invention. It is a flowchart which shows a wafer alignment process. It is a flowchart which shows the process sequence of the subroutine of selection of a sample shot area | region. FIG. 6 is a diagram (part 1) illustrating an example of a selected sample shot region. It is a figure for demonstrating the difference of the estimation result according to arrangement | positioning of the measurement data used for estimation. FIG. 10 is a second diagram illustrating an example of a selected sample shot area. FIG. 10 is a third diagram illustrating an example of a selected sample shot area. FIG. 14 is a diagram (part 4) illustrating an example of a selected sample shot region;

Explanation of symbols

DESCRIPTION OF SYMBOLS 15 ... Moving mirror, 16 ... Reticle interferometer, 17 ... Moving mirror, 18 ... Wafer interferometer, 19 ... Stage controller, 20 ... Main controller, 24 ... Wafer stage drive part, 25 ... Wafer holder, 100 ... Exposure apparatus, a ₀ ~a ₉ ... coefficient, AS ... alignment detection system, AX ... optical axis, b ₀ ~b ₉ ... coefficient, the center of the C _p ... shot areas, IL ... illumination light, FM ... fiducial mark plate, h ... sample shot Number of regions, MX _p , MY _p ... wafer mark (wafer X, Y mark), PL ... projection optical system, p _max ... number of shot regions, R ... reticle, RST ... reticle stage, SA _p , SA _g ... shot Area (partition area), W ... wafer (object), WST ... wafer stage.

Claims (7)

An alignment method for aligning each of a plurality of partitioned areas formed on an object with respect to a predetermined reference position in a stationary coordinate system that defines a moving position of the object,
Selecting, from among the plurality of partitioned areas, a predetermined number of partitioned areas arranged substantially evenly on the circumference of a plurality of concentric circles centered on the approximate center of the object;
Measuring position coordinates of a partitioned area including the predetermined number of specific partitioned areas in the stationary coordinate system;
Performing a statistical calculation based on the measurement result, the design position coordinates of each of the plurality of partitioned areas in the stationary coordinate system as independent variables, and a model equation of a predetermined order having information on the position of the partitioned areas as a dependent variable Obtaining a coefficient of each term of
Aligning each of the plurality of partitioned areas with a predetermined reference position in the stationary coordinate system based on the model formula for which the coefficient of each term is obtained. When the highest order n (n is a natural number) of the model formula is an odd number, the number of concentric circles is set to (n + 1) / 2 or more,
When the highest order n of the model formula is an even number, the number of concentric circles is set to n / 2 or more, and a partition region located at the approximate center of the object is further selected as the specific partition region. The alignment method according to claim 1. When the maximum order n of the model formula is an odd number, the number of specific partition regions arranged on each concentric circle is 2 (n + 2),
When the highest order n of the model formula is an even number, the number of specific partition regions arranged on each concentric circle is set to a minimum integer equal to or greater than 2 {(n + 1) (n + 2) -1} / n. The alignment method according to claim 2, wherein:   4. The alignment method according to claim 1, wherein as the radius of the concentric circle becomes smaller, the number of specific partition regions located on the concentric circle is reduced.   The alignment method according to any one of claims 1 to 4, wherein an outermost concentric circle among the plurality of concentric circles corresponds to a partition region located on an outermost side on the object. . An alignment method for aligning each of a plurality of partitioned areas formed on a substantially circular object with respect to a predetermined reference position in a stationary coordinate system that defines a movement position of the object,
Selecting a predetermined number of partitioned areas arranged substantially evenly in an arbitrary diameter direction of the object from the plurality of partitioned areas as a specific partitioned area;
Measuring position coordinates of a partitioned area including the predetermined number of specific partitioned areas in the stationary coordinate system;
Performing a statistical calculation based on the measurement result, the design position coordinates of each of the plurality of partitioned areas in the stationary coordinate system as independent variables, and a model equation of a predetermined order having information on the position of the partitioned areas as a dependent variable Obtaining a coefficient of each term of
Aligning each of the plurality of partitioned areas with a predetermined reference position in the stationary coordinate system based on the model formula for which the coefficient of each term is obtained. An exposure method for sequentially exposing a plurality of partitioned areas arranged on an object to form a predetermined pattern in each partitioned area,
Using the alignment method according to any one of claims 1 to 6, each of the plurality of partitioned areas is aligned with a predetermined reference position in a stationary coordinate system that defines a moving position of the object. A process of performing;
Exposing each of the aligned partitioned areas.

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