JP6135611B2 - Point defect concentration calculation method, Grown-in defect calculation method, Grown-in defect in-plane distribution calculation method, and silicon single crystal manufacturing method using them - Google Patents

Description

  The present invention relates to a point defect concentration calculation method, a grown-in defect calculation method, a grown-in defect in-plane distribution calculation method, and a silicon single crystal manufacturing method using them.

  In recent years, with high integration of devices, high quality requirements for silicon single crystal wafers have become strict. High quality means that there are few or no defects near the wafer surface where the device operates. Wafers that can achieve these include epitaxial wafers, annealed wafers, and low / defect-free crystal PW (polished wafers). Among these, low / defect-free crystals PW that can be reduced in cost have been widely used. This is a wafer cut out from a crystal in which a grown-in defect formed during crystal growth is controlled to produce a crystal having low defects or no defects.

  The Grown-in defect is a defect formed by aggregating point defects during crystal growth. There are two types of point defects: Vacancy (vacancies) in which Si atoms at lattice points are missing, and Interstitial-Si (interstitial Si) in which Si atoms enter between lattices. The formation state of this Grown-in defect varies depending on the growth rate of the single crystal and the cooling conditions of the single crystal pulled from the silicon melt. For example, it is known that vacancy becomes dominant when a single crystal is grown at a relatively high growth rate. A collection of this vacancy is called a void defect, and the name differs depending on how it is detected. Is done. When these defects are taken into the oxide film formed on the silicon substrate, it is considered that the breakdown voltage of the oxide film is caused.

  On the other hand, when a single crystal is grown at a relatively low growth rate, it is known that Interstitial-Si (hereinafter referred to as I-Si) becomes dominant. When this I-Si aggregates and collects, LEP (Large Etch Pit = dislocation cluster defect), which is considered to be a cluster of dislocation loops, is detected. It is said that when a device is formed in a region where this dislocation cluster defect occurs, a serious failure such as current leakage occurs.

  Therefore, if the crystal is grown under an intermediate condition between the vacancy dominant condition and the I-Si dominant condition, there is no vacancy or I-Si, or a small amount that does not form void defects or dislocation cluster defects. It is known that a defect-free region that does not exist can be obtained. Even if there is no defect, the region where the vacancy is dominant is called the Nv region, and the region where the I-Si is dominant is called the Ni region. In order to obtain such a defect-free region, it is necessary to adjust the thermal environment of the crystal to be grown. Even if this adjustment is performed on a trial and error basis, a defect-free region cannot be easily obtained, and an enormous cost is required. Therefore, attempts have been made to obtain conditions for obtaining defect-free crystals by simulating the thermal environment in the furnace and the formation of defects.

  As a formation theory of a Grown-in defect in a silicon single crystal, a model proposed by Boronkov is widely known. This is because the concentration of point defects is determined by three factors: diffusion due to concentration gradient, diffusion due to temperature gradient, and decrease due to pair annihilation. In many cases, calculations are performed based on this theory.

  Patent Document 1 proposes a model in which this model is simplified and the point defect concentration is determined depending on the ratio V / G between the growth rate V and the temperature gradient G in the vicinity of the interface. When V / G is large, the vacancy concentration is dominant, and when V / G is small, I-Si is dominant. By controlling to V / G where the vacancy concentration and the I-Si concentration antagonize, the concentration of point defects can be reduced and the grown-in defects are prevented from growing. The distribution of defects is determined by the radial distribution of V / G. Patent Document 2 shows that a defect-free crystal can be obtained by controlling the ratio (V / G) between the temperature gradient G and the crystal growth rate V at the crystal growth interface. This model is simple and effective because the defect distribution can be predicted only by obtaining the temperature distribution of the crystal. However, this model does not consider outward diffusion toward the outer surface, which is a sink for point defects. For this reason, the actual defect in-plane distribution, in particular, the distribution shape in the outer periphery cannot be expressed. In recent years, higher quality is desired even in a defect-free region, and the defect distribution in the outer periphery has become important. Therefore, a simulation method that can accurately calculate the defect distribution in the outer peripheral portion is required.

  Therefore, the defect distribution simulation method disclosed in Patent Documents 3-5 determines the temperature in the crystal by changing the length of the crystal, and then determines the concentration of point defects (Vacancy and I-Si) based on the diffusion equation, A portion having a small difference between both point defect densities is obtained as a defect-free region. By performing these calculations in multiple dimensions, it seems that the influence of out-diffusion is taken into account. However, the defect distribution obtained in Patent Document 5 does not appear to accurately represent the actual distribution. In addition, such multi-dimensional calculation takes a very long time because the amount of calculation increases dramatically. For this reason, there is a problem that it is not possible to easily perform the operation of finding the optimum growth conditions while changing the in-furnace parts. Although the calculation considered to be multidimensional is performed also in patent document 6, as described in the paragraph (0034), the distribution of the peripheral portion of the crystal is not suitable, and the radial diffusion of I-Si is deleted. Yes. Even in this case, there is a problem that the defect distribution is not correctly expressed and a huge amount of calculation is required.

Japanese Patent Application Laid-Open No. 11-1393 JP-A-11-157996 JP 2001-302394 A JP 2002-47096 A JP 2004-26567 A JP 2003-73192 A

  The present invention has been made in view of the above problems, and is a point defect concentration calculation method capable of calculating a point defect concentration accurately in a short time and a size of a grown-in defect accurately in a short time. An object of the present invention is to provide a Grown-in defect calculation method. It is another object of the present invention to provide a Grown-in defect in-plane distribution calculation method capable of easily obtaining an accurate defect distribution. It is another object of the present invention to provide a silicon single crystal manufacturing method utilizing these calculation results.

  To achieve the above object, according to the present invention, in the method for calculating the concentration of point defects in a growing silicon single crystal, the diffusion of point defects includes diffusion parallel to the crystal growth axis and diffusion in the crystal diameter direction. Is calculated as a one-dimensional diffusion, respectively, and a point defect concentration calculation method is provided.

  With this method of calculating diffusion and calculating the point defect concentration, the point defect concentration can be accurately obtained in a short time by a very simple calculation.

  Further, it is preferable to use different point defect diffusion coefficients for calculating the diffusion parallel to the crystal growth axis and for calculating the diffusion in the crystal diameter direction.

  With such a point defect concentration calculation method, the calculation result of diffusion in the crystal diameter direction (outward diffusion) can be made closer to the actual measurement result of a silicon single crystal.

  Further, the diffusion parallel to the crystal growth axis and the diffusion in the crystal diameter direction is one or both of diffusion due to a concentration gradient of point defects and diffusion due to a temperature gradient, diffusion due to the concentration gradient, diffusion due to the temperature gradient. It is preferable to obtain the point defect concentration by calculating one or both of these, or by calculating the effect of reducing the point defect concentration due to pair annihilation.

  Such a point defect concentration calculation method is preferable because the obtained point defect concentration value is closer to the point defect concentration value of an actual silicon single crystal.

  The point defect concentration is preferably calculated from the melting point to the defect formation temperature.

  With such a point defect concentration calculation method, the point defect concentration can be calculated more efficiently.

  Further, the present invention is characterized in that a Grown-in defect size is obtained by calculating agglomeration of point defects in a defect formation temperature zone from the point defect concentration obtained by the point defect concentration calculation method of the present invention. A Grown-in defect calculation method is provided.

  With such a grown-in defect calculation method, the size of the grown-in defect can be accurately calculated in a short time.

  In this case, a region where the Grown-in defect size is a certain value or less can be determined as a defect-free region.

  With such a Grown-in defect calculation method, it can be easily determined whether or not the silicon single crystal has a defect-free region.

  Moreover, it is preferable to perform the calculation of the point defect concentration and the calculation of the aggregation of the point defects based on the temperature distribution in the growth furnace obtained by the comprehensive heat transfer analysis software.

  Such software is easy to use and has an interface, etc., and since each has a track record, a reliable result can be expected when used under certain conditions.

  Furthermore, in the present invention, the defect in-plane distribution shape is obtained by plotting the growth rate to be a defect-free region of each of the vacancy type and the interstitial type obtained by the Grown-in defect calculation method of the present invention, against the crystal diameter. A Grown-in defect in-plane distribution calculation method is provided.

  With such a Grown-in defect in-plane distribution calculation method, an accurate defect distribution can be easily obtained.

  Furthermore, in the present invention, based on the results calculated by the point defect concentration calculation method, the Grown-in defect calculation method or the Grown-in defect in-plane distribution calculation method of the present invention, the growth furnace structure, in-furnace parts, temperature environment and Provided is a method for producing a silicon single crystal, characterized in that any one or more of operating conditions are changed and a real crystal is grown under the growing conditions.

  With such a silicon single crystal manufacturing method, a silicon single crystal with few or no defects can be obtained at low cost.

  With the point defect concentration calculation method of the present invention, the point defect concentration can be obtained accurately in a short time. Further, according to the Grown-in defect calculation method of the present invention, the Grown-in defect size can be accurately calculated in a short time. With the Grown-in defect in-plane distribution calculation method of the present invention using these calculation results, an accurate defect distribution can be easily obtained. Furthermore, the silicon single crystal manufacturing method in which the growth conditions are set based on the calculation result of the point defect concentration calculation method, the grown-in defect calculation method, or the grown-in defect in-plane distribution calculation method of the present invention has few defects. Alternatively, no silicon single crystal can be obtained at low cost.

It is a figure showing the crystal diameter direction distribution of the growth rate of the upper limit and minimum which can obtain the defect-free area | region obtained in the Example. It is the figure which showed the example of the X-ray topograph of the vertically divided sample obtained by experiment. It is the figure explaining the effect of the point defect outward diffusion in the defect in-plane distribution. It is the figure showing the outline of the single crystal growth furnace which can be used for the silicon single crystal manufacturing method of this invention. It is a figure showing the crystal diameter direction distribution of the growth rate of the upper limit and minimum which can obtain the defect-free area | region obtained by the comparative example.

  Hereinafter, the present invention will be described in more detail.

  As described above, there is a need for a point defect concentration calculation method that can accurately calculate a point defect concentration in a short time.

  The diffusion of point defects in crystals is a phenomenon that occurs three-dimensionally, and it is desirable to solve the diffusion equation in three dimensions. However, it is generally difficult to solve the diffusion equation, and when the calculation by the difference method or the like is performed, the calculation amount increases drastically as the dimension increases. As shown in Patent Document 1 and Patent Document 2, an approximate defect distribution can be estimated with a one-dimensional simplified model in the growth axis direction. That is, in the vicinity of the center of the crystal, the concentration gradient in the crystal growth axis direction is large, but the concentration gradient in the crystal diameter direction is not large. However, since the surface that is the sink of point defects is close to the outer periphery of the crystal, the influence of outward diffusion that the point defects diffuse toward the surface becomes large.

  In order to take into account the influence of such outward diffusion, if the diffusion is calculated in a multi-dimensional manner, there arises a problem that the amount of calculation increases dramatically as described above. Thus, in the conventional method, it has been impossible to achieve both reduction in the amount of calculation of diffusion and accurate calculation of the point defect concentration.

  As a result of diligent studies to solve the above problems, the inventors of the present invention calculated a point defect concentration in a growing silicon single crystal by making point defect diffusion parallel to the crystal growth axis. The point defect concentration calculation method for calculating the diffusion and the diffusion in the crystal diameter direction as one-dimensional diffusion can be solved, and the point defect concentration calculation method of the present invention has been completed.

  Hereinafter, embodiments of the present invention will be described in detail, but the present invention is not limited thereto.

[Point defect concentration calculation method]
As described above, according to the point defect concentration calculation method of the present invention, the point defect diffusion is calculated as one-dimensional diffusion for diffusion parallel to the crystal growth axis and diffusion in the crystal diameter direction (outward diffusion). It is a method to do. In this way, in the present invention for obtaining the final point defect concentration by calculating the diffusion parallel to the crystal growth axis and the outward diffusion in the crystal diameter direction in one dimension, the amount of calculation of the diffusion is reduced. The point defect density can be accurately calculated while decreasing.

  For example, after calculating the one-dimensional diffusion parallel to the crystal growth axis and calculating the point defect concentration considering only the diffusion parallel to the crystal growth axis, the outward diffusion (diffusion in the crystal diameter direction) is calculated, The final point defect concentration can be obtained by correcting the concentration of point defects on the outer periphery of the crystal. By performing these calculations in one dimension, the point defect density can be obtained with high accuracy by a very simple calculation.

  At this time, it is preferable to use different point defect diffusion coefficients for calculating the diffusion parallel to the crystal growth axis and for calculating the outward diffusion in the crystal diameter direction. When calculating outward diffusion in one dimension, it is preferable to use a diffusion coefficient different from that for calculating diffusion parallel to the crystal growth axis for several reasons as follows.

Usually, since there is no pressure change in a solid, the equilibrium concentration Ce and the diffusion coefficient D are Ce = Coexp (−Ec / kT), D = Doexp (−Ed / kT), Equation 1
Ec, Ed: Activation energy, Co, Do: Coefficients, there are no major problems. However, non-uniform internal stress is acting in the growing crystal. For this reason, the equation 1 takes into account the pressure Ce = Coexp (− (Ec + pVc) / kT), D = Doexpp (− (Ed + pVd) / kT).
It is considered preferable to express Vc, Vd: activation volume and p: pressure.

  Here, it is not easy to discuss the pressure dependence of the diffusion coefficient, but it is relatively easy to imagine the equilibrium concentration. That is, it is considered that Vacancy is stable when the pressure is high and I-Si is stable when the pressure is low.

  On the other hand, the intracrystalline stress is estimated to be compressed near the center and tensile at the outer periphery. Therefore, it is considered that the equilibrium concentration of I-Si is high in the periphery, and therefore, the degree of supersaturation is considered to be low in the periphery. Contributing to the formation of a Grown-in defect or a driving force for diffusion is considered to be a point defect that is supersaturated beyond the equilibrium concentration. Therefore, there are two effects: (1) it is difficult to form I-Si defects in the periphery, and (2) I-Si diffusion toward the periphery is likely to occur. In Vacancy, the opposite effect to I-Si can be considered. Due to the effects of (1) and (2) due to the stress difference between the vicinity of the crystal center and the outer periphery, I-Si has an apparently large diffusion coefficient, and Vacancy has an apparently small diffusion coefficient.

  Furthermore, it is necessary to consider the effect of calculating the outward diffusion in one dimension. It is (3) the volume difference between the central part and the outer peripheral part. In the growing silicon single crystal having a cylindrical shape, the volume of the outer peripheral portion is larger than the volume of the central portion. For this reason, I-Si that easily diffuses outward due to the stress effect has an area that can be diffused spreads two-dimensionally and is very easy to diffuse. In the case of vacancy, it is difficult to diffuse.

  As described above, when I-Si is considered, (1) the supersaturation concentration (supersaturation degree) is reduced in the vicinity, and thus the effect of making it difficult to form a grown-in defect. (2) the supersaturation concentration is reduced in the vicinity. There are three effects: (3) the effect that diffusion toward the periphery tends to occur, and (3) the effect that diffusion toward the periphery easily occurs due to the volume difference between the central portion and the outer periphery. Considering these as apparent outward diffusion coefficients that are carried by the diffusion coefficient, the apparent outward diffusion coefficient of I-Si increases. Vacancy's apparent outward diffusion coefficient is the opposite. Therefore, when calculating the outward diffusion in one dimension, it is desirable to use an apparent outward diffusion coefficient that is different from the case of calculating the diffusion parallel to the crystal growth direction.

  The diffusion parallel to the crystal growth axis and the diffusion in the crystal diameter direction (diffusion of point defects) is preferably one or both of diffusion due to the concentration gradient of point defects and diffusion due to the temperature gradient. In this case, the point defect concentration can be obtained by calculating one or both of diffusion due to the concentration gradient and diffusion due to the temperature gradient, or by calculating the effect of decreasing the point defect concentration due to pair annihilation. Thereby, the obtained point defect concentration value can be made closer to the actual point defect concentration value of the silicon single crystal.

  The calculation of the point defect concentration is preferably performed from the melting point to the defect formation temperature. That is, it is efficient to calculate the point defect diffusion and pair annihilation from the melting point of the silicon single crystal to the defect formation temperature to obtain the point defect concentration.

  The temperature at which the Grown-in defect is formed is obtained from an experiment that rapidly changes the growth rate, and is, for example, 1150 ° C.-1080 ° C. in Japanese Patent Laid-Open No. 8-337490. Therefore, the change in concentration due to the diffusion of point defects is preferably calculated from the melting point to the temperature at which the grown-in defect is formed. When the calculation is actually performed, the diffusion coefficient decreases as the temperature decreases, and the amount of increase in the supersaturation concentration decreases, so that the point defect concentration becomes a constant concentration by about 1150 ° C. Therefore, it is understood that it is sufficient to calculate the point defect concentration from the melting point of the silicon single crystal to the defect formation temperature. The melting point of the silicon single crystal is about 1412 ° C. The defect formation start temperature is a temperature around 1150 ° C., but is not limited to this temperature.

[Grown-in defect calculation method]
Next, the Grown-in defect calculation method of the present invention will be described. The Grown-in defect calculation method of the present invention is a calculation method for obtaining the Grown-in defect size by calculating the aggregation of point defects in the defect formation temperature zone from the point defect concentration obtained by the above point defect concentration calculating method. It is. As described above, the Grown-in defect calculation method using the point defect concentration obtained by the above method can accurately calculate the Grown-in defect size in a short time.

  For example, from the point defect concentration obtained from the melting point of the silicon single crystal to the defect formation temperature, the process of agglomeration of point defects in the defect formation temperature zone can be calculated to determine the Grown-in defect size.

  At this time, a region where the Grown-in defect size is a certain value or less can be determined as a defect-free region. In this case, by using the growth rate of the silicon single crystal as a variable, agglomeration of point defects and the like are calculated, and by obtaining a region where the Grown-in defect size is a certain value or less, a vacancy-type defect-free region or interstitial type is obtained. The growth rate of a silicon single crystal that can obtain a defect-free region can be obtained.

  In the defect formation temperature zone, it is considered that the point defects that have been supersaturated so far aggregate to form a grown-in defect. Therefore, it is possible to calculate the Grown-in defect size by calculating the aggregation process of point defects in this temperature range. Moreover, it is also possible to determine a defect size equal to or smaller than a certain defect size among the defect sizes obtained as described above as a defect-free region. If the Grown-in defect size can be known, for example, conditions for growing a crystal having a size that easily disappears by annealing treatment can be obtained. On the other hand, the region determined to be defect-free changes due to the improvement of the oxygen concentration and the defect detection capability, so that a size equal to or smaller than the size corresponding to the detection capability at that time can be determined as the defect-free region. At present, this size can be set to about 10 to 30 nm. The defect-free region is a growth rate range in which the Grown-in defect size is a certain value or less, and is a position (region) in the crystal where the Grown-in defect size is a certain value or less. The temperature range of the defect formation temperature zone is not particularly limited, but is, for example, 1150 ° C.-1080 ° C.

[Grown-in defect in-plane distribution calculation method]
Next, the Grown-in defect in-plane distribution calculation method of the present invention will be described. The Grown-in defect in-plane distribution calculation method of the present invention plots the growth rate to be a defect-free region of each of the vacancy type and the interstitial type obtained by the above Grown-in defect calculation method against the crystal diameter. This is a calculation method for obtaining the distribution shape in the defect plane. In this way, the defect in-plane distribution shape can be simplified by plotting the growth rate determined to be defect-free for each of the vacancy type and interstitial type obtained by calculating the process of point defect aggregation. Can be requested.

  When the above-mentioned diffusion / pair annihilation / aggregation of point defects is calculated using the growth rate of the silicon single crystal as a variable, the difference Cv-Ci between the Vacancy supersaturation concentration Cv and the I-Si supersaturation concentration Ci decreases from a high speed to a low speed. As it becomes, it goes from positive to negative. As the grown-in defect size decreases from high speed to low speed, the vacancy aggregate size decreases in the vicinity of the defect-free region (vacancy-type defect-free region) in the range of Cv-Ci> 0, and Cv-Ci = 0. The I-Si aggregate size increases in the vicinity of the defect-free region (interstitial defect-free region) in the range of Cv-Ci <0. The growth rate at which the Vacancy agglomerates are below a certain size (defect-free upper limit growth rate) and the growth rate at which the I-Si agglomerates are below a certain size (defect-free lower limit growth rate) are plotted in the crystal diameter direction. By doing so, the in-plane distribution shape of the defect can be obtained. This corresponds to the defect distribution obtained with an actual crystal while gradually reducing the growth rate. By using this defect in-plane distribution, it is possible to easily determine whether a defect-free region can be obtained in the crystal plane.

  The above calculation (calculation of point defect concentration and point defect agglomeration) can be performed based on the temperature distribution in the growth furnace determined by the comprehensive heat transfer analysis software or the like.

  Software for obtaining the temperature distribution in the single crystal growth furnace includes several software including an integrated heat transfer analysis program FEMAG (see F. Dupret et al .; Int. J. Heat Mass Transfer, 33, 1849 (1990)). Is commercially available. These analysis softwares are easy to use with a well-developed interface, etc., and since each has proven results, reliable results can be expected to some extent when used under certain conditions. Therefore, it is advantageous to use those calculated by these software for the temperature distribution that is the basis of calculation of diffusion, pair annihilation, and point defect aggregation.

[Silicon single crystal manufacturing method]
The silicon single crystal manufacturing method of the present invention is based on the results calculated by the above point defect concentration calculation method, Grown-in defect calculation method or Grown-in defect in-plane distribution calculation method of the present invention, This is a manufacturing method in which one or more growth conditions of a product, a temperature environment, and an operation condition are changed, and a real crystal is grown under the changed growth condition. As described above, it is preferable to grow the actual crystal under conditions reflecting the results by changing the growth conditions and calculating and evaluating the crystal growth temperature environment using the calculation method of the present invention.

  The greatest purpose of performing the above-described calculation is to easily and accurately obtain the optimum conditions for growing an actual crystal. In addition, in order to obtain the optimum conditions, various thermal environment conditions are calculated and evaluated by this calculation method, and the actual crystal is pulled up under conditions (optimum conditions) suitable for the purpose. Growing a real crystal in all the thermal environments and evaluating the defect distribution would take enormous time and cost. If this can be done by calculation, several thermal environments can be tried in a short time at a very low cost. This makes it easy to find the optimal environment. By pulling up the actual crystal under this optimum condition, it is possible to reduce the cost for developing a low defect or defect-free crystal all at once.

  If it is the silicon single crystal manufacturing method of this invention, since the growth conditions are set using the calculation method of this invention, the defect-free single crystal used in the most advanced field can be obtained at low cost. From such a single crystal, a silicon wafer used as a substrate for a semiconductor device such as a memory, CPU, or power device can be cut out.

  Here, a single crystal growth furnace (CZ single crystal production apparatus) that can be used in the silicon single crystal production method of the present invention will be described with reference to FIG. 4, but the growth furnace is not limited thereto.

  The external appearance of the silicon single crystal manufacturing apparatus shown in FIG. 4 includes a main chamber 1, a top chamber 11 that communicates with the main chamber 1, and a pulling chamber 2 that communicates with the top chamber 11. A graphite crucible 6 and a quartz crucible 5 are installed inside the main chamber 1. A heater 7 is provided so as to surround the graphite crucible 6, and the raw material silicon polycrystal accommodated in the quartz crucible 5 is melted by the heater 7 to form a raw material melt 4. Further, a heat insulating member 8 is provided to prevent the radiant heat from the heater 7 from directly hitting a metal instrument such as the main chamber 1.

  On the melt surface of the raw material melt 4, a heat shield member 13 is disposed opposite the melt surface at a predetermined interval to block radiant heat from the raw material melt surface. After immersing the seed crystal in the crucible, the rod-shaped single crystal rod 3 is pulled up from the raw material melt 4. The crucible can be moved up and down in the direction of the crystal growth axis, and the raw material melt 4 is raised by raising the crucible during the growth so as to compensate for the lowering of the liquid surface of the raw material melt 4 that has decreased as the growth of the single crystal proceeds. The height of the melt surface is kept approximately constant.

  Further, an inert gas such as argon gas is introduced from the gas inlet 10 as a purge gas during single crystal growth, and after passing between the single crystal rod 3 being pulled and the gas purge cylinder 12, the heat shield member 13 and the raw material It passes between the melt surface of the melt 4 and is discharged from the gas outlet 9. By controlling the flow rate of gas to be introduced and the amount of gas discharged by a pump or valve, the pressure in the chamber being pulled up is controlled.

  Hereinafter, detailed description will be given using actual data.

[Experiment]
When evaluating a grown-in defect region in a silicon single crystal, a crystal having a gradually reduced crystal growth rate is grown, and this is vertically divided to investigate the defect distribution. An example evaluated in this manner is shown in FIG. This was evaluated by X-ray topography after subjecting the vertically divided crystal to precipitation heat treatment at 650 ° C. for 2 hours + 800 ° C. for 4 hours + 1000 ° C. for 16 hours. In such a vertically-divided crystal with a gradually decreasing growth rate, the distribution is generally such that the I-rich region hangs down on the outer periphery of the crystal and the OSF region hangs down on the outer periphery. It is considered that the defect distribution shape in the outer peripheral portion is determined by the outward diffusion of point defects. It can be explained as follows.

  FIG. 3 is a diagram illustrating the effect of point defect outward diffusion in the defect in-plane distribution. If out diffusion is not considered, it is assumed that the defect distribution in the crystal diameter direction is flat (see FIG. 3A). Next, consider the case where I-Si diffuses outward toward the surface, which is an infinite sink of point defects, near the periphery of the crystal (see FIG. 3B). Due to the outward diffusion of I-Si, the I-rich / Ni region boundary, the Ni / Nv region boundary, the Nv / OSF region boundary, and the OSF / V-rich region boundary bend to the lower side which is the I region at the outer periphery. This is because I-Si decreases in the outer periphery of the I-rich region and becomes the Ni region, and the outer periphery of the Ni region becomes the Nv region. The Nv region and the OSF region are vacancy-dominated regions, but since I-Si diffuses outward at the outer peripheral portion and vacancy dominance increases, the Nv region and the OSF region also bend downward.

  Further, consider the case where vacancy diffuses outward toward the surface in the vicinity of the crystal periphery (see FIG. 3C). Vacancy In predominates which was Nv Vacancy is reduced, the area neither dominant because it also reduced I-Si which outdiffused first. Therefore, the linear Nv / Ni region boundary becomes wider toward the outside. The vacancy is diffused outward in the outer periphery of the OSF region and becomes the Nv region, and becomes the OSF region in the outer periphery of the V-rich region. As a result, the Nv / OSF region boundary and the OSF / V-rich region boundary bend upward in the V region.

  Considering the above, the defect distribution of the actual SE gradually decreasing vertically divided crystal as shown in FIG. 2 can be well explained. When attention is paid to the OSF / Nv region boundary in this actually vertically divided sample, it hangs down from the center to the periphery and then jumps up. That is, it can be seen that the outward diffusion region of I-Si bites inward more than the outward diffusion region of Vacancy. From this, it is considered that the apparent outward diffusion coefficient Di ′ of I-Si is larger than the apparent outward diffusion coefficient Dv ′ of Vacancy.

  As described above, the apparent outward diffusion coefficients Dv ′ and Di ′ include three effects. In other words, when considered in terms of I-Si, (1) the supersaturation concentration is reduced in the vicinity, so that the growth-in defect is less likely to be formed, and (2) the supersaturation concentration is reduced in the periphery, so that diffusion toward the periphery occurs. This is an effect that is likely to occur, and (3) an effect that diffusion toward the peripheral portion is likely to occur due to a volume difference between the central portion and the outer peripheral portion. For this reason, it is preferable to distinguish from Dv and Di when considering diffusion parallel to the crystal growth axis. Dv and Di have been studied conventionally and various values have been reported. However, Dv 'and Di' are not disclosed. Then, next, approximate values of Dv ′ and Di ′ are experimentally obtained.

  The growth rate gradually decreasing vertical defect distribution as shown in FIG. 2 was obtained under several conditions with different thermal environments. Next, Vacancy outward diffusion distance (Lv) and I-Si outward diffusion distance (Li) were determined. Lv was determined as the distance from the part where the OSF / Nv region boundary jumped up to the outer periphery, and Li was determined as the distance from the part where the Nv / Ni boundary hangs down to the outer periphery.

On the other hand, the crystal temperature distribution was determined by FEMAG under the conditions in which the growth rate was gradually reduced and the crystal was grown. The defect formation temperature zone from the melting point (Tm) in the outer periphery of about 30mm of the temperature distribution (Td = 1150 ℃) until the out-diffusion distance _{^{Lv = √∫ Tm Td Dv'tdT, Li}} = √∫ Tm Td Di'tdT · ..Formula 3
t: It was determined as the diffusion time. Dv ′ and Di ′ are apparent outward diffusion coefficients. Dv ′ = 0.006exp (−0.4 / kT), Di ′ = 4420exp (−2.0 / kT) Equation 4
In this case, a 1: 1 correspondence was obtained with Lv and Li previously measured from the vertical defect distribution. Therefore, the value of Equation 4 is appropriate as an apparent outward diffusion coefficient. This value is particularly large for I-Si as compared with the generally reported diffusion coefficient. These are considered to be the effects of the stress and volume ratio described above in (1) to (3).

  EXAMPLES Hereinafter, although an Example and a comparative example are shown and this invention is demonstrated more concretely, this invention is not limited to this Example.

(Example)
In the silicon single crystal growth apparatus schematically shown in FIG. 4, the temperature distribution in the furnace when the diameter of the crystal was 306 mm and the length of the straight body was 100 cm was determined by steady analysis of FEMAG. The temperature distribution in the growth axis direction in the crystal was extracted from the obtained temperature. Extraction positions were 0 cm, 1 cm, 2 cm,..., 14 cm, 14.3 cm, and 15 cm every 1 cm with the center of the crystal being 0 cm. At each position, the temperature was extracted every 5 mm in the direction parallel to the growth axis from the crystal interface = melting point.

  At each of these positions, the diffusion parallel to the crystal growth direction was calculated. As described above, a model proposed by Boronkov is widely known as the formation theory of a grown-in defect in a silicon single crystal. This is because the concentration of point defects is determined by three factors: diffusion due to concentration gradient, diffusion due to temperature gradient, and decrease due to pair annihilation. In particular, the concentration of point defects is determined depending on the ratio V / G between the growth rate V and the temperature gradient G near the interface. If V / G is large, the vacancy concentration is dominant, and if V / G is small, I-Si is dominant. It is known that The factor that V / G greatly influences is the diffusion due to the temperature gradient, that is, the equilibrium concentration of point defects decreases as the temperature decreases, and therefore, the effect that the point defects that are supersaturated diffuse in the opposite direction of the concentration gradient. It is thought that there is. This effect is called slope diffusion. There are various calculation methods such as whether concentration diffusion is emphasized, slope diffusion is emphasized, or a coefficient for pair annihilation is set. Since the equilibrium concentration and diffusion coefficient of point defects vary depending on the calculation method, various values have been reported. In this method, the calculation related to the crystal growth axis direction may be any method as long as it is consistent with the actual defect distribution. In this example, the diffusion was calculated mainly for slope diffusion, and the supersaturated concentration of point defects was obtained.

Specifically, the diffusion was calculated about every 10-20 ° C. from the melting point parallel to the crystal growth axis. The calculation was performed as follows. First, the difference between the equilibrium concentration at the previous temperature and the equilibrium concentration at the next temperature was defined as the supersaturated concentration, and the concentration after this was diffused in one dimension was determined. Next, since the difference between the concentration after diffusion and the equilibrium concentration at the next temperature becomes a supersaturated concentration, the concentration after diffusion in one dimension was obtained. This was repeated from the melting point to 1150 ° C. where defect formation started. Since the diffusion time and distance depend on the growth rate, these concentrations are obtained as a function of the growth rate. The values of equilibrium concentration and diffusion coefficient used for the calculation at this time are Cev = 4.5 × 10 ²⁶ exp (−3.9 / kT), Cei = 2.5 × 10 ²⁸ exp (−4.5 / kT)
Dv = 40exp (−1.6 / kT), Di = 6.6 × 10 ⁻³ exp (−0.55 / kT)
It is. After obtaining the supersaturated concentration after diffusion in Vacancy and I-Si, the difference was obtained as the point defect supersaturated concentration.

  Next, the final supersaturation concentration was calculated by one-dimensionally diffusing the obtained point defect supersaturation concentration in the crystal diameter direction using the apparent outward diffusion coefficient obtained previously. Here, in order to make the calculation easier, the outward diffusion was calculated after calculating the diffusion parallel to the growth direction. You may repeat performing one-dimensional calculation of a growth direction and one-dimensional calculation of a radial direction for every temperature.

  Next, the process of agglomeration of point defects was calculated from the finally obtained supersaturation point concentration. The temperature range for aggregation was 1150 ° C to 1080 ° C. Aggregation is affected by the diffusion distance determined from the transit time and diffusion coefficient of this temperature range. Here, the maximum defect size that all point defects within the diffusion distance range gathered was determined, and this was determined as the average defect size normalized by the Grown-in defect average size confirmed in the actual crystal. In the actual crystal, the point defects are repeatedly agglomerated and split while diffusing, and those that are larger than the critical nucleus radius grow into grown-in defects. For this reason, it is considered that defects having a density distribution below the maximum defect size are formed. It is more correct to calculate this process, but for the sake of simplicity, only the average defect size is obtained here. The Void size obtained by this method increases as Cv-Ci increases as the growth rate increases, and further increases at higher speeds because the transit time is shorter and the diffusion distance is shorter, resulting in a realistic result. Is obtained.

  Next, among the calculated defect sizes, a size smaller than a certain size was determined as a defect-free region. The size below a certain level was determined as follows. While gradually reducing the growth rate under a certain condition, a crystal as shown in FIG. 2 was grown, and the growth rate at the upper end of the Nv region and the growth rate at the lower end of the Ni region were obtained. This condition is calculated by the above-described method, and the vacancy agglomerated defect size at the growth rate at which the Nv upper end is obtained and the I-Si agglomerated defect size at the growth rate at which the Ni lower end is obtained are set to a certain size or less. Asked.

  The supersaturated concentration of point defects and the grown-in defect size described above are obtained as a function of the growth rate. From this relationship, a growth rate range in which a defect-free region in which the defect size is a certain value or less is obtained. The upper and lower growth rates at which this defect-free region can be obtained were first determined at 0 cm of the crystal center and then at 1 cm, and this was repeated up to 15 cm. FIG. 1 is a plot of this in the crystal diameter direction. In addition to the upper limit growth rate and the lower limit growth rate, the growth rate at which Cv−Ci = 0 is also described. The vertical axis represents the relative growth rate normalized by the growth rate at which Cv−Ci = 0 at the center of the crystal. In FIG. 1, it can be seen that a characteristic distribution is reproduced in which the I-rich region as obtained in FIG. 2 hangs down at the outer periphery of the crystal and the OSF region hangs down at the outer periphery.

  A range between the defect-free upper limit speed and the lower limit speed obtained in this way is determined as a defect-free area. If there is a growth rate that falls within this range at any part in the plane, it can be considered that a crystal having no defect is obtained over the entire crystal diameter direction (defect-free condition). It can be determined that the margin for obtaining a defect-free region is large if the width of the growth rate at which defect-free growth occurs over the entire surface is large. In this way, the furnace environment can be changed to optimize the thermal environment so that the manufacturing margin is maximized.

  The time required for evaluation using this method depends on conditions, but if the temperature distribution calculation by comprehensive heat transfer analysis is steady analysis, it takes about 1 hour for point defect diffusion, pair annihilation, and grown-in defects. This calculation takes about tens of seconds with Microsoft spreadsheet software EXCEL. It takes about ten minutes because the temperature data is manually transferred, but it takes about an hour and a half. Actually, the calculation proceeds in equilibrium, so it is about one hour per condition. Of course, these calculation times depend on the number of meshes and temperature divisions. On the other hand, when a real crystal is grown, a sample is cut out from this, and defect distribution evaluation is performed, it takes at least about one week although it depends on the evaluation method and the like. Therefore, the evaluation time by this method is a short time of about 1/100 of the actual crystal. Furthermore, this method is low enough to be negligible except for the initial cost for software installation.

  As described in the middle, there are various calculation methods other than those shown in this embodiment. Depending on the calculation method, the equilibrium concentration and the value of the diffusion coefficient may vary. In that case, it is only necessary to make adjustments according to reality. The feature of this technique is to calculate one-dimensional diffusion in the crystal growth direction and the radial direction, respectively. At this time, it is desirable to use different diffusion coefficient values. The final object of the present invention is to reduce the cost of crystal development by growing a real crystal under the conditions that optimize the thermal environment using the calculation method of the present invention.

(Comparative example)
Except for not calculating the outward diffusion, the crystal diameter direction distribution of the upper limit and the lower limit growth rate at which a defect-free region is obtained was obtained by the same operation as in the example. The results are shown in FIG. In the vicinity of the center of the crystal, the defect distribution shape is the same as in FIG. 1, but in the vicinity of the outer periphery, the speed at which a defect-free region is obtained has shifted to the low speed side. This is clearly different from the actual defect distribution shown in FIG. 2, and the reality cannot be expressed.

  The present invention is not limited to the above embodiment. The above-described embodiment is an exemplification, and the present invention has substantially the same configuration as the technical idea described in the claims of the present invention, and any device that exhibits the same function and effect is the present invention. It is included in the technical scope of the invention.

1 ... main chamber, 2 ... pulling chamber, 3 ... single crystal rod,
4 ... Raw material melt, 5 ... Quartz crucible, 6 ... Graphite crucible,
7 ... Heater, 8 ... Heat insulation member, 9 ... Gas outlet,
10 ... Gas inlet, 11 ... Top chamber, 12 ... Gas purge cylinder,
13: Heat shielding member.

Claims (9)

  In the method of calculating the concentration of point defects in the growing silicon single crystal, the calculation of the point defect diffusion is performed as one-dimensional diffusion for diffusion parallel to the crystal growth axis and diffusion in the crystal diameter direction. A characteristic point defect density calculation method.   2. The point defect concentration calculation according to claim 1, wherein a diffusion coefficient of different point defects is used when calculating diffusion parallel to the crystal growth axis and when calculating diffusion in the crystal diameter direction. Method.   Diffusion parallel to the crystal growth axis and diffusion in the crystal diameter direction is one or both of diffusion due to a concentration gradient of point defects and diffusion due to a temperature gradient, and either diffusion due to the concentration gradient or diffusion due to the temperature gradient. 3. The point defect concentration according to claim 1, wherein the point defect concentration is calculated by calculating one or both of them, or by calculating an effect of reducing the point defect concentration due to pair annihilation. Method of calculation.   The point defect concentration calculation method according to any one of claims 1 to 3, wherein the point defect concentration is calculated from a melting point to a defect formation temperature.   The Grown-in defect size is calculated by calculating agglomeration of point defects in the defect formation temperature zone from the point defect concentration obtained by the point defect concentration calculation method according to any one of claims 1 to 4. A Grown-in defect calculation method characterized by comprising:   6. The grown-in defect calculation method according to claim 5, wherein a region in which the grown-in defect size is a predetermined value or less is determined as a defect-free region.   The calculation of the point defect concentration and the calculation of the aggregation of the point defects are performed based on the temperature distribution in the growth furnace obtained by comprehensive heat transfer analysis software. Grown-in defect calculation method.   The in-plane distribution shape by plotting the growth rate to be a defect-free region of each of the vacancy type and the interstitial type obtained by the Grown-in defect calculation method according to claim 6 or 7 against the crystal diameter A method for calculating a Grown-in defect in-plane distribution.   The point defect concentration calculation method according to any one of claims 1 to 4, the Grown-in defect calculation method according to any one of claims 5 to 7, or the Growth according to claim 8. -Based on the result calculated by the in-plane distribution calculation method, change one or more growth conditions of the growth furnace structure, in-furnace parts, temperature environment and operation conditions, and change the actual crystal under the growth conditions. A method for producing a silicon single crystal, characterized by growing.