WO2021044907A1

WO2021044907A1 - Thermic fluid state computation apparatus

Info

Publication number: WO2021044907A1
Application number: PCT/JP2020/032026
Authority: WO
Inventors: 俊太原田; 将輝 ▲高▼石; 幸典小山; 徹宇治原
Original assignee: 国立大学法人東海国立大学機構
Priority date: 2019-09-03
Filing date: 2020-08-25
Publication date: 2021-03-11
Also published as: JP7162937B2; JPWO2021044907A1

Abstract

Provided is technology with which the temperature distribution and the flow velocity distribution of an entire thermic fluid can be ascertained. This thermic fluid state computation apparatus acquires and decomposes multiple sets of a simulation value of the temperature distribution and a simulation value of the flow velocity distribution in a J-dimensional region (J is any value of 1, 2, and 3) representing a portion of the thermic fluid to extract two or more sets of a characteristic temperature distribution and a characteristic flow velocity distribution. The thermic fluid state computation apparatus linearly adds the two or more sets of a characteristic temperature distribution and a characteristic flow velocity distribution to compute a predicted value of the temperature distribution and a predicted value of the flow velocity distribution in the J-dimensional region. The thermic fluid state computation apparatus performs computation such that a predicted temperature distribution value for a predetermined region indicating the temperature distribution in the predetermined region matches a measured temperature distribution value for the predetermined region measured by a measurement unit.

Description

Thermo-fluid state arithmetic unit

This application claims priority based on Japanese Patent Application No. 2019-160600 filed on September 3, 2019. The entire contents of that application are incorporated herein by reference. This specification discloses a technique relating to a thermo-fluid state arithmetic unit.

It may be necessary to grasp the overall temperature distribution and flow velocity distribution of the thermal fluid. For example, when a semiconductor crystal is grown by a solution growth method. As an example, International Publication WO2012 / 127703 discloses a technique for growing a SiC single crystal by accommodating a Si solution inside a graphite crucible and bringing a SiC seed crystal into contact with the Si solution.

The thermal fluid container structure is complicated and strict. Therefore, the observable region of the state of the thermal fluid (eg, temperature, flow velocity, etc.) may be limited to a local region such as a part of the surface of the thermal fluid. In this case, it is difficult to grasp the overall temperature distribution and flow velocity distribution of the thermal fluid.

This specification discloses a thermo-fluid state calculation device. The thermo-fluid state calculation device acquires a plurality of sets of temperature distribution simulation values and flow velocity distribution simulation values in a J-dimensional region (J is a value of 1, 2, or 3) indicating a part of the thermo-fluid. It has a part. Multiple sets are acquired based on a plurality of parameter groups, each having a different value. The thermo-fluid state calculation device includes an extraction unit that extracts two or more sets of characteristic temperature distribution and characteristic flow velocity distribution by decomposing each of a plurality of sets of temperature distribution simulation value and flow velocity distribution simulation value. The thermo-fluid state calculation device includes a measuring unit for measuring a predetermined region temperature distribution measurement value, which is a temperature distribution of a predetermined region which is a region of a part of the thermal fluid and is included in the J-dimensional region. The thermo-fluid state arithmetic unit is an arithmetic unit that calculates the predicted temperature distribution value and the predicted flow velocity distribution value in the J-dimensional region by linearly summing two or more sets of the characteristic temperature distribution and the characteristic flow velocity distribution. Be prepared. In the calculation unit, the predetermined region temperature distribution predicted value included in the calculated temperature distribution predicted value, and the predetermined region temperature distribution predicted value indicating the temperature distribution in the predetermined region is the predetermined region temperature distribution measured value measured by the measuring unit. Calculate to match.

Since the temperature distribution and the flow velocity distribution are closely related from the viewpoint of heat transport, the simulation value of the temperature distribution and the simulation value of the flow velocity distribution can be decomposed as one. Then, by extracting two or more sets of the characteristic temperature distribution and the characteristic flow velocity distribution and linearly summing them with each other, the overall temperature distribution and the flow velocity distribution of the thermal fluid can be predicted. At this time, the linear sum is performed so that the temperature distribution predicted value of the predetermined region obtained by the measurement matches the temperature distribution predicted value of the predetermined region obtained by the measurement. This makes it possible to predict the overall thermofluid state based on the measured values in a local predetermined region. It is possible to grasp the overall temperature distribution and flow velocity distribution of the thermal fluid.

The extraction unit may standardize each of a plurality of sets of the temperature distribution simulation value and the flow velocity distribution simulation value, and then perform the decomposition. To standardize the temperature distribution simulation values, obtain the average temperature distribution of multiple temperature distribution simulation values, obtain the deviation from the average temperature distribution for each of the multiple temperature distribution simulation values, and obtain one deviation from the multiple average temperature distributions. It may be performed by obtaining the standard deviation of the temperature distribution and dividing each of the deviations from the plurality of average temperature distributions by the standard deviation of the temperature distribution. To standardize the flow velocity distribution simulation values, obtain the average flow velocity distribution of multiple flow velocity distribution simulation values, obtain the deviation from the average flow velocity distribution for each of the multiple flow velocity distribution simulation values, and obtain one from the deviations from the plurality of average flow velocity distributions. It may be performed by obtaining the flow velocity standard deviation and dividing each of the deviations from the plurality of average flow velocity distributions by the flow velocity standard deviation.

The thermal fluid may be a melt of a semiconductor crystal material. The plurality of parameter groups may include the rotation speed of the container containing the thermal fluid and the rotation speed of the semiconductor crystal in contact with the melt.

The semiconductor crystal may be a SiC crystal. The acquisition unit may further acquire the carbon concentration distribution simulation value in the J-dimensional region. The extraction unit may further extract the characteristic carbon concentration distribution. The calculation unit may further calculate the predicted carbon concentration distribution value.

The predetermined region may be a part of the upper surface of the melt.

Further, a control unit that feedback-controls the rotation speed of the container and the rotation speed of the semiconductor crystal so that each of the predicted temperature distribution value and the predicted flow velocity distribution value calculated by the calculation unit are suitable values for the growth of the semiconductor crystal. You may have it.

When the J-dimensional region is a two-dimensional region including the XY plane and the flow velocity distribution simulation value includes the X-direction flow velocity distribution simulation value and the Y-direction flow velocity distribution simulation value, the acquisition unit performs K rows on the XY plane. And L columns (K and L are natural numbers of 1 or more) may be treated as a matrix. Each of the temperature distribution simulation value, the X-direction flow velocity distribution simulation value, and the Y-direction flow velocity distribution simulation value may be represented by a matrix of rows K and columns L. The matrix X to be decomposed by singular value may be represented by a matrix of N rows and M columns (N and M are natural numbers of 1 or more). The value of N may be the number of a plurality of parameter groups. The components of the i-th row (i is a natural number of 1 or more and N or less) of the matrix X are standardized in the K × L column that unifies the standardized temperature distribution simulation values in the i-th parameter group and in the i-th parameter group. It has a component in which a K × L column that unifies the X-direction flow velocity distribution simulation values and a K × L column that unifies the standardized Y-direction flow velocity distribution simulation values in the i-th parameter group are arranged in order. May be good.

It is a schematic block diagram of a crystal growth system 1. It is a figure which shows the operation flow of the crystal growth system 1. It is a figure which shows the 2D model of the crystal growth apparatus 3. It is a figure explaining the standardization of a temperature distribution simulation value. It is a figure explaining the standardization of a temperature distribution simulation value. It is a figure which shows the generation method of the matrix X. It is a figure which shows the singular value decomposition of a matrix X. It is a figure explaining the calculation method of the predicted value of a temperature distribution and a flow velocity distribution. It is a surface photograph of the SiC crystal grown in the comparative experimental example. It is a surface photograph of the SiC crystal grown in this experimental example.

<Structure of crystal growth system 1>
FIG. 1 shows a schematic configuration diagram of the crystal growth system 1. The crystal growth system 1 includes a solution state calculation device 2 and a crystal growth device 3.

The crystal growth device 3 is a device that grows a SiC crystal in liquid phase by the TSSG (Top-Seeded Solution Growth) method. The crystal growth device 3 includes a housing 10, a crucible accommodating unit 11, a rotating unit 12, a driving unit 12a, a crystal supporting unit 13, a driving unit 13a, a high frequency coil 14, a crucible 15, and a thermocamera (infrared thermography) 20. The housing 10 has an outer wall surface on the outer surface of a cylinder, and houses a high-frequency coil 14 and a crucible accommodating portion 11. A window portion 10w is arranged on the upper part of the housing 10. The crucible accommodating section 11 accommodates the crucible 15. The surface of the crucible accommodating portion 11 is covered with a heat insulating material. The thermo camera 20 measures the temperature distribution of a part of the surface of the melt 17 through the gap between the window portion 10w and the upper portion of the crucible accommodating portion 11.

Crucible 15 is made of carbon material (graphite). The drive unit 12a is a portion for rotating the crucible accommodating unit 11 and the crucible 15 via the rotating unit 12. The crystal support portion 13 is a member that rotatably supports the seed crystal 16 and the grown SiC crystal 18. The drive unit 13a is a portion for rotating the crystal support unit 13. The central axes CA of the rotating portion 12 and the crystal supporting portion 13 are aligned. The high-frequency coil 14 receives power from a power supply device (not shown) to induce and heat the crucible 15. The relative positions of the high-frequency coil 14 and the crucible 15 can be changed by a drive mechanism (not shown). Thereby, the temperature distribution of the crucible 15 at the time of heating can be changed.

The crucible 15 contains the melt 17. The melt 17 is a solution of Si. Carbon atoms melt from the crucible 15. Therefore, the SiC crystal 18 can be grown starting from the seed crystal 16 which is a SiC template.

The solution state calculation device 2 includes an acquisition unit 30, an extraction unit 32, a storage unit 34, a measurement unit 36, a calculation unit 38, and a control unit 40. The acquisition unit 30, the extraction unit 32, the calculation unit 38, and the control unit 40 are, for example, CPUs. The contents of these parts will be described later. The measurement unit 36 is an interface for acquiring the measurement result of the thermo camera 20. The storage unit 34 is a portion that stores the simulation results described later and various data used in the calculation unit 38. The storage unit 34 may be a combination of RAM, flash memory, HDD, and the like. The control unit 40 is a portion that controls the rotation speed of the rotating unit 12 and the crystal support unit 13, the relative position between the high-frequency coil 14 and the crucible 15, the current value of the high-frequency coil 14, and the like.

<Outline of Crystal Growth System 1>
In the SiC solution growth process, control of the temperature distribution and the flow velocity distribution of the melt 17 is important for improving the quality of the SiC crystal 18. Therefore, the crystal growth system 1 predicts the temperature distribution and the flow velocity distribution of the entire melt 17 based on the measured values of the temperature distribution of a part of the surface of the melt 17. Then, by feedback-controlling the parameter group (eg, the rotation speed of the rotating portion 12 and the rotation speed of the crystal support portion 13) based on the prediction result, the temperature distribution and the flow velocity distribution of the melt 17 can be controlled by the growth of the SiC crystal 18. Keep it in a suitable condition.

FIG. 2 shows the operation flow of the crystal growth system 1. The operation flow is roughly classified into a simulation value acquisition step S10, a feature amount extraction step S20, a temperature distribution and velocity distribution calculation step S30, and a feedback control step S40. Each step will be described below.

<Simulation value acquisition step>
In the technique of the present specification, a regression model for predicting the temperature distribution and the flow velocity distribution of the entire melt 17 is created. Creating such a regression model requires the collection of large amounts of data, but it is difficult to collect by experiment. Therefore, data is acquired by simulation using thermo-fluid calculation software.

In S11, the acquisition unit 30 creates a two-dimensional model of the crystal growth apparatus 3. As shown in FIG. 3, an axisymmetric model for the central axis CA is created. FIG. 3 is a view showing the right half side of the cross-sectional view passing through the central axis CA. The horizontal direction from the central axis CA is defined as the X direction, and the upward direction of the central axis CA is defined as the Y direction. This XY plane shows a part of the melt 17 stored in the crucible 15. A grid (mesh) is virtually set on this XY plane. Specifically, the XY plane is treated as a matrix of 41 rows and 120 columns. The grid in the XY plane of FIG. 3 is an example, and is not 41 rows and 120 columns.

As shown in FIG. 3, a predetermined region R1 that is not hidden by the seed crystal 16 exists on the surface of the melt 17. The predetermined region R1 is a part of the upper surface of the melt 17, and is a region that can be observed by the thermo camera 20 (FIG. 1, arrow A11). Further, the predetermined region R1 is a region included in the XY plane.

In S12, the acquisition unit 30 sets a plurality of parameter groups. In this embodiment, the rotation speed of the crucible 15, the rotation speed of the crystal support portion 13, and the relative position of the high-frequency coil 14 with respect to the crucible 15 are used as the parameter group. Then, a plurality of parameter groups having various different combinations of the rotation speed of the crucible 15, the rotation speed of the crystal support portion 13, and the relative position of the high-frequency coil 14 with respect to the crucible 15 were set. The inner and outer diameters of the crucible 15, the thickness of the bottom surface and the side wall of the crucible 15, the diameter of the seed crystal 16, the size of the crucible accommodating portion 11, and the like were set to constant values. Therefore, when changing these values, it is necessary to recreate them from the axisymmetric model of FIG.

In S13, the acquisition unit 30 performs a simulation calculation using each of the plurality of parameter groups. Each time the simulation is performed, one output result (a set of a temperature distribution simulation value in the XY plane, an X direction flow velocity distribution simulation value, and a Y direction flow velocity distribution simulation value) is obtained for one parameter group. The temperature distribution simulation value, the X-direction flow velocity distribution simulation value, and the Y-direction flow velocity distribution simulation value are matrices of 41 rows and 120 columns, respectively. By repeating the simulation, for example, results of 10 patterns or more and 100 million patterns or less can be obtained. The number of patterns may be appropriately determined in consideration of the required simulation accuracy and calculation load. In this example, 98 patterns of results were obtained based on 98 parameter groups. The results are stored in the storage unit 34.

<Feature quantity extraction step>
In the feature amount extraction step (S20), the feature amount is extracted by singular value decomposition. Specifically, the temperature distribution and the flow velocity distribution are integrated into a singular value decomposition. This is because the temperature distribution and the flow velocity distribution are closely related from the viewpoint of heat transport. This step is performed by the extraction unit 32.

In S21, the extraction unit 32 executes standardization of a plurality of sets of temperature distribution simulation values, standardization of a plurality of sets of X-direction flow velocity distribution simulation values, and standardization of a plurality of sets of Y-direction flow velocity distribution simulation values. The reason for standardization is to align the scales of different physical quantities. This makes it possible to generate a matrix X by arranging physical quantities having different dimensions of "temperature" and "velocity" in the next step. There are standardization methods such as "minimum value 0, maximum value 1" and standardization such that "mean 0, variance 1". Although the latter standardization method is used in the present specification, various standardization methods can be used without this limitation.

The standardization of a plurality of sets of temperature distribution simulation values will be described with reference to FIGS. 4A and 4B. _{One average temperature distribution MTD is obtained from 98} temperature distribution simulation values TDS ₁ to TDS 98 (FIG. 4A, arrow A0). Next, the average temperature distribution MTD is subtracted from each of the temperature distribution simulation values TDS ₁ to TDS _{98 (FIG. 4A, arrow A1).} _{As a result, the deviations TDV 1} to TDV ₉₈ from the average temperature distribution MTD can be obtained for each of the temperature distribution simulation values TDS ₁ to TDS _98.

From the deviations TDV ₁ to TDV ₉₈ , one temperature distribution standard deviation TSD is obtained (FIG. 4B, arrow A2). The temperature distribution standard deviation TSD can be obtained by finding the positive square root of the value obtained by dividing the sum of the squares of _{the deviations TDV 1} to TDV _{98 by the total number of data (98).} Then, by dividing each of the deviations TDV ₁ to TDV ₉₈ by the temperature distribution standard deviation TSD, the standardized temperature distribution simulation values STS ₁ to STS ₉₈ can be obtained. (FIG. 4B, arrow A3). The temperature distribution simulation value TDS, average temperature distribution MTD, deviation TDV, temperature distribution standard deviation TSD, and standardized temperature distribution simulation value STS are all a matrix of "41 rows x 120 columns".

Similarly, standardization of a plurality of sets of X-direction flow velocity distribution simulation values will be described. From 98 X-direction flow velocity distribution simulation values XFS ₁ to XFS ₉₈ , one average X-direction flow velocity distribution MXF is obtained. Next, for each of the X-direction flow velocity distribution simulation values XFS ₁ to XFS ₉₈ _{, the deviations XDV 1} to XDV ₉₈ from the average X-direction flow velocity distribution MXF are obtained. From the deviations XDV ₁ to XDV ₉₈ , one X-direction flow velocity standard deviation XSD is obtained. By dividing each of the deviations XDV ₁ to XDV ₉₈ by the X-direction flow velocity standard deviation XSD, the standardized X-direction flow velocity distribution simulation values SXS ₁ to SXS ₉₈ can be obtained. The X-direction flow velocity distribution simulation value XFS, the average X-direction flow velocity distribution MXF, the deviation XDV, the X-direction flow velocity standard deviation XSD, and the standardized X-direction flow velocity distribution simulation value SXS are all a matrix of “41 rows × 120 columns”.

Similarly, the standardization of a plurality of sets of Y-direction flow velocity distribution simulation values will be described. From 98 Y-direction flow velocity distribution simulation values YFS ₁ to YFS ₉₈ , one average Y-direction flow velocity distribution MYF is obtained. Next, for each of the Y-direction flow velocity distribution simulation values YFS ₁ to YFS ₉₈ _{, the deviations YDV 1} to YDV ₉₈ from the average Y-direction flow velocity distribution MYF are obtained. From the deviations YDV ₁ to YDV ₉₈ , one Y-direction flow velocity standard deviation YSD is obtained. By dividing _{each of the deviations YDV 1} to YDV ₉₈ by the Y-direction flow velocity standard deviation YSD, the standardized Y-direction flow velocity distribution simulation values SYS ₁ to SYS ₉₈ can be obtained. The Y-direction flow velocity distribution simulation value YFS, the average Y-direction flow velocity distribution MYF, the deviation YDV, the Y-direction flow velocity standard deviation YSD, and the standardized Y-direction flow velocity distribution simulation value SYS are all a matrix of “41 rows × 120 columns”.

In S22, the extraction unit 32 generates a matrix X to be decomposed into singular values. FIG. 5 shows a method of generating the matrix X. The matrix X is an N-row and M-column matrix. The value of N is the number of parameter groups, which is "98" in this embodiment. The value of M is "14760" as described later.

_{Standardized temperature distribution simulation values STS 1} to STS ₉₈ are arranged in the region RC1 from the first column to the 4920th column. Here, the standardized temperature distribution simulation values STS ₁ to STS ₉₈ are arranged after being unified from the matrix of "41 rows x 120 columns" to "1 row x 4920 columns". Similarly, in the region RC2 from the 4921th column to the 9840th column, the standardized X-direction flow velocity distribution simulation values SXS ₁ to SXS ₉₈ are arranged in a unified manner in “1 row × 4920 columns”. Similarly, in the region RC3 from the 9841 column to the 14760 column, normalized Y-direction flow velocity distribution simulation values _SYS 1 ~ _{SYS 98} is arranged on which a centralized "1 row × 4920 columns."

As shown in FIG. 5, the components of the i-th row (i is a natural number of 1 or more and N or less) of the matrix X are the standardized X-direction flow velocity distribution simulation value SXS _i in the unified 4920 columns and the standardized X-direction flow velocity distribution simulation value. It _{has a component in which 4920 columns in which the SXS i} is unified and 4920 columns in which the standardized Y-direction flow velocity distribution simulation value SYS _i is unified are arranged in order. Therefore, the matrix X has "14760 columns".

By arranging the temperature distribution and the velocity distribution in this way to generate the matrix X, in the next step, the temperature distribution and the flow velocity distribution can be integrated into a singular value decomposition.

In S23, the matrix X is decomposed into singular values. That is, as shown in FIG. 6, the matrix X (N × M matrix) can be represented by the product of the matrix U (N × s matrix), the matrix S (s × s matrix), and the matrix V (s × M matrix). it can. As described above, the value of N is "98" and the value of M is "14760". s is the number of singular values. The larger the value of s, the smaller the error in the predicted values of the temperature distribution and the flow velocity distribution obtained by the calculation of S33 described later. However, the burden of calculation becomes large. For example, the value of s may be determined so that the root mean square error (RMSE) of the error of the predicted value with respect to the actual value is equal to or less than a predetermined value. In this embodiment, the value of s is set to "10".

As a result, as shown in the matrix V of FIG. 6, the characteristic temperature distributions CTD ₁ to CTD _s , the characteristic X-direction flow velocity distributions CXF ₁ to CXF _s , and the characteristic Y-direction flow velocity distributions CYF ₁ to CYF _s can be obtained. it can. In other words, s (10) sets consisting of the characteristic temperature distribution CTD, the characteristic X-direction flow velocity distribution CXF, and the characteristic Y-direction flow velocity distribution CYF can be extracted. The characteristic temperature distribution CTD, the characteristic X-direction flow velocity distribution CXF, and the characteristic Y-direction flow velocity distribution CYF are a matrix unified into "1 row × 4920 columns". These characteristic distributions cannot be obtained by observation, but can be obtained only by calculation, so it can be said that they are potential solution states.

In S24, the conversion is performed so that the values of the elements of the matrix U and the matrix V are about "1". Specifically, as shown in the following equations (1) to (3), each of the matrices U, S, and V is converted into the matrices U', S', and V'. Here, "N" is the number of rows in the matrix X, and "M" is the number of columns in the matrix X.
U'= U × N ^1/2 ... Equation (1)
S'= S / (N × M) ^1/2 ... Equation (2)
V'= V × M ^1/2 ... Equation (3)

Explain the effect of conversion. The value of each element of the matrix U and the matrix V is a small value of 1 or less due to the characteristics of the singular value decomposition. Then, in the linear sum calculation process (S33) described later, it is necessary to handle the number of digits after the decimal point, which increases the calculation load. Therefore, the calculation load can be reduced by suppressing the number of digits after the decimal point by the conversion process.

<Calculation step of temperature distribution and velocity distribution>
The calculation step (S30) of the temperature distribution and the velocity distribution is performed by the calculation unit 38. In S31, the crystal growth system 1 starts the growth of the SiC crystal 18. In S32, the measuring unit 36 measures the temperature distribution of the predetermined region R1 on the surface of the melt 17 by using the thermo camera 20 (see FIGS. 1 and 3).

In S33, the calculation unit 38 calculates the predicted values of the temperature distribution and the flow velocity distribution. This will be specifically described with reference to FIG. 7. Linear by multiplying each of the 10 sets of characteristic temperature distributions CTD ₁ to CTD ₁₀ , characteristic X-direction flow velocity distributions CXF ₁ to CXF ₁₀ , and characteristic Y-direction flow velocity distributions CYF ₁ to CYF _{10 by coefficients θ1 to θ10.} Reconcile. The temperature distribution predicted value TDP can be calculated from the linear sum of the characteristic temperature distributions CTD ₁ to CTD _10. Further, the X-direction flow velocity distribution predicted value XFP can be calculated from the linear sum of the characteristic X-direction flow velocity distributions CXF ₁ to CXF _10. Further, the Y-direction flow velocity distribution predicted value YFP can be calculated from the linear sum of the characteristic Y-direction flow velocity distributions CYF ₁ to CYF _10. The characteristic temperature distribution CTD, the characteristic X-direction flow velocity distribution CXF, the characteristic Y-direction flow velocity distribution CYF, the temperature distribution predicted value TDP, the X-direction flow velocity distribution predicted value XFP, and the Y-direction flow velocity distribution predicted value YFP are all "41". It is a matrix of "rows x 120 columns".

The calculated temperature distribution predicted value TDP includes a predetermined region R1p (see FIG. 7). This is an area corresponding to a predetermined area R1 (see FIG. 3) that can be observed by the thermo camera 20. Then, the coefficients θ1 to θ10 are searched so that the predicted temperature distribution value in the predetermined region R1p matches the measured temperature distribution value in the predetermined region R1 measured by the thermo camera 20. In other words, the coefficients θ1 to θ10 are optimized so as to minimize the error between the measured value and the predicted value in the temperature distribution of the local region (predetermined region R1). As a result, from the measured value of the temperature distribution in the local region (predetermined region R1), the temperature distribution and velocity distribution (temperature distribution predicted value TDP, X-direction flow velocity distribution predicted value XFP, Y-direction flow velocity distribution predicted value YFP) of the entire melt 17 are obtained. ) Can be predicted accurately.

It is very difficult to optimize the coefficients θ1 to θ10. Therefore, in this example, optimization was performed using a genetic algorithm. Specifically, a multi-objective optimization algorithm (NSGAII) was used. The objective function was the root mean square error (RMSE) of the error between the measured and predicted values in the temperature distribution within the predetermined region R1. The coefficient optimization method is not limited to the genetic algorithm, and various methods can be used.

<Feedback control step>
The feedback control step (S40) is performed by the control unit 40. In S41, the control unit 40 sets each of the temperature distribution predicted value TDP, the X-direction flow velocity distribution predicted value XFP, and the Y-direction flow velocity distribution predicted value YFP calculated by the calculation unit 38 as ideal values for the growth of the SiC crystal 18. Therefore, the rotation speed of the crucible 15, the rotation speed of the crystal support portion 13, and the relative position of the high-frequency coil 14 with respect to the crucible 15 are feedback-controlled. For example, when the X-direction flow velocity distribution predicted value XFP or the Y-direction flow velocity distribution predicted value YFP is smaller than the ideal value, the rotation speed of the crucible 15 or the crystal support portion 13 may be increased.

In S42, it is determined whether or not the SiC crystal 18 is completed. If a negative determination is made (S42: NO), the processes of S32, S33, and S41 are repeated. If affirmative judgment is made (S42: YES), the flow is terminated.

Explain the effect. In the technique of this example, a small number of characteristic distributions (characteristic temperature distributions CTD ₁ to CTD ₁₀ , characteristic X-direction flow velocity distributions CXF ₁ to CXF) selected from the characteristic distributions extracted by the singular value decomposition (S23). _{10. The} overall temperature distribution and velocity distribution can be predicted by linearly summing the characteristic Y-direction flow velocity distributions CYF ₁ to CYF _10). That is, various and complicated temperature distributions and flow velocity distributions can be approximated (low-rank approximation) with as few features as possible. Since the burden of the arithmetic processing (S33) can be reduced, high-speed solution state prediction becomes possible. Therefore, it is possible to perform feedback control by following the momentary change of the temperature distribution and the velocity distribution.

<Comparative experiment of crystal growth>
Comparative experiments were performed to confirm the superiority of the simulations described herein. In the comparative experimental example, the parameters of SiC crystal growth were determined without using the simulation according to the present specification. On the other hand, in this experimental example, the parameters of SiC crystal growth were determined based on the simulation according to the present specification. Examples of the parameters include the rotation speed of the rotating portion 12, the rotation speed of the crystal support portion 13, the heating temperature, and the like.

FIG. 8 shows a surface photograph of the SiC crystal grown in the comparative experimental example. It can be seen from FIG. 8 that the unevenness of the crystal surface is extremely severe. This is because polycrystals have grown and adhered to the surface due to improper parameter control. Moreover, since the surface is covered with SiC polycrystals, defect evaluation could not be performed. Although the parameters were tried and errored and comparative experiments were performed several times, only polycrystals could be grown in each case.

FIG. 9 shows a surface photograph of the SiC crystal grown in this experimental example. The diameter of the grown crystal is about 3 inches. It can be seen from FIG. 9 that the crystal surface is sufficiently smooth as compared with the comparative experimental example (FIG. 8). This is because the parameter control can be appropriately performed based on the simulation according to the present specification, and the single crystal can be grown. In addition, defect evaluation was performed by synchrotron radiation topography. As a result, no penetrating spiral dislocations and basal plane dislocations were observed in a part of the region (10 × 10 mm ^2). In this experimental example, it can be seen that a high-quality single crystal with few defects can be grown.

The SiC crystal grown in the comparative example is polycrystalline and cannot be used as a semiconductor substrate. On the other hand, the SiC crystal grown in this experimental example is a single crystal and can be practically used as a semiconductor substrate. Moreover, since there are few defects, it is possible to produce a semiconductor device having good electrical characteristics. From the above, the performance and superiority of the simulation of this specification can be confirmed.

<Modification example>
Although the examples of the present invention have been described in detail above, these are merely examples and do not limit the scope of claims. The techniques described in the claims include various modifications and modifications of the specific examples illustrated above.

The solution state that is the subject of the prediction technique of this specification is not limited to the temperature distribution and the flow velocity distribution. For example, since the carbon concentration distribution is closely related to the temperature distribution and the flow velocity distribution, it can be predicted by the technique of the present specification. In this case, the carbon concentration distribution simulation value may be acquired (S13), and the carbon concentration distribution simulation value may be added to the matrix X (S22) by standardizing (S21) and making it one-dimensional. The characteristic carbon concentration distribution may be extracted by performing a singular value decomposition (S23) by integrating the temperature distribution, the flow velocity distribution, and the carbon concentration distribution. Then, in addition to the predicted value of the temperature distribution and the predicted value of the flow velocity distribution, the predicted value of the carbon concentration distribution may be calculated (S33).

In this specification, the case where the singular value decomposition is used as the matrix factorization method has been described, but the present invention is not limited to this form. Various methods such as an eigendecomposition method, a QZ decomposition method, and a Takagi decomposition method can be used.

In this specification, the case where the "two-dimensional" simulation result is treated as a "matrix" has been described, but the present invention is not limited to this form. It is also possible to treat the "three-dimensional" simulation result as a "third-floor tensor". This makes it possible to predict the temperature distribution and velocity distribution in three dimensions (three-dimensional).

The plane to be simulated when performing a "two-dimensional" simulation is not limited to the XY plane illustrated in FIG. It is possible to set a free plane such as a YY plane or an XX plane as a simulation target.

The number of matrices on the XY plane (41 rows and 120 columns) is an example. The virtual grid size and the number of matrices can be set arbitrarily. The calculation load increases as the grid size decreases and the matrix size increases. Therefore, the grid size and the number of matrices may be appropriately determined in consideration of the spatial resolution and the calculation load required in the simulation result. The number of parameter groups (98) and the number of singular values (10) are all examples. These values may be appropriately determined from the required accuracy and computing power.

In this specification, the liquid of the semiconductor crystal material has been described as an example of the thermal fluid, but the present invention is not limited to this form. Thermal fluid is a concept that also includes gas (high temperature gas). Further, the field of application of the prediction technique of the present specification is not limited to the growth of semiconductor crystals. It can also be applied to various fields such as the growth of oxide crystals other than semiconductors and the refining of metals.

The application of the technology of this specification is not limited to the thermal fluid stored in the "container". For example, gas filled inside the device without using a container is also applicable. Therefore, the techniques herein are also applicable to other crystal growth methods and processes that do not use containers.

The parameter group described in this specification is an example. Examples of other parameters include the frequency and current amount of the high frequency coil 14, the relative position of the high frequency coil 14 with respect to the crucible 15, the dimensions of the high frequency coil 14, the composition of the melt 17, and the thickness of the side wall and bottom of the crucible 15. , The pressure of the gas filled in the crystal growth apparatus 3, the material and thickness of the heat insulating material, and the like.

The physical quantity measured in the predetermined region R1 is not limited to the temperature distribution. Physical quantities such as flow velocity distribution and concentration distribution are also measured. Further, the predetermined region R1 is not limited to a part of the surface of the melt 17. It may be a region where the physical quantity of the melt 17 can be indirectly measured. For example, the predetermined region R1 may be a region inside the crystal growth apparatus 3.

The means for measuring the temperature distribution of the predetermined region R1 of the melt 17 is not limited to the thermo camera 20, and various means can be used.

The crystal to be grown by the crystal growth device 3 is not limited to SiC. Various semiconductor crystals such as GaN, GaAs, and AlN can be grown.

The technical elements described in the present specification or the drawings exhibit technical usefulness alone or in various combinations, and are not limited to the combinations described in the claims at the time of filing. In addition, the techniques illustrated in the present specification or drawings can achieve a plurality of purposes at the same time, and achieving one of the purposes itself has technical usefulness.

The XY plane is an example of the J-dimensional region. Crucible 15 is an example of a container. The melt 17 is an example of a thermal fluid.

Claims

An acquisition unit that acquires a plurality of sets of temperature distribution simulation values and flow velocity distribution simulation values in a J-dimensional region (J is a value of 1, 2, or 3) indicating a part of a thermal fluid. The acquisition unit and the acquisition unit, in which the set is acquired based on a plurality of parameter groups each having a different value,
An extraction unit that extracts two or more sets of characteristic temperature distribution and characteristic flow velocity distribution by decomposing each of a plurality of sets of the temperature distribution simulation value and the flow velocity distribution simulation value.
A measuring unit that measures a predetermined region temperature distribution measurement value, which is a temperature distribution of a predetermined region that is a partial region of the thermal fluid and is a region included in the J-dimensional region.
A calculation unit that calculates the predicted temperature distribution value and the predicted flow velocity distribution value in the J-dimensional region by linearly summing two or more sets of the characteristic temperature distribution and the characteristic flow velocity distribution. The predetermined region temperature distribution predicted value included in the temperature distribution predicted value, which indicates the temperature distribution of the predetermined region, is the predetermined region temperature distribution measured value measured by the measuring unit. With the above-mentioned calculation unit, which calculates so as to match with
A thermo-fluid state arithmetic unit.
The extraction unit standardizes each of the plurality of sets of the temperature distribution simulation value and the flow velocity distribution simulation value, and then performs the decomposition.
The standardization of the temperature distribution simulation value is
Obtain the average temperature distribution of the plurality of temperature distribution simulation values,
The deviation from the average temperature distribution was obtained for each of the plurality of temperature distribution simulation values.
Obtain one temperature distribution standard deviation from the deviations from the plurality of average temperature distributions.
It is performed by dividing each of the deviations from the plurality of average temperature distributions by the temperature distribution standard deviation.
The standardization of the flow velocity distribution simulation value is
Obtain the average flow velocity distribution of the plurality of flow velocity distribution simulation values, and obtain
The deviation from the average flow velocity distribution was obtained for each of the plurality of flow velocity distribution simulation values.
Obtain one flow velocity standard deviation from the deviations from the plurality of average flow velocity distributions.
It is performed by dividing each of the deviations from the plurality of average flow velocity distributions by the flow velocity standard deviations.
The thermo-fluid state calculation device according to claim 1.
The thermal fluid is a melt of a semiconductor crystal material and is
The thermal fluid according to claim 1 or 2, wherein the plurality of parameter groups include the rotation speed of the container containing the thermal fluid and the rotation speed of the semiconductor crystal in contact with the melt. State arithmetic unit.
The semiconductor crystal is a SiC crystal and
The acquisition unit further acquires the carbon concentration distribution simulation value in the J-dimensional region, and further acquires the carbon concentration distribution simulation value.
The extraction unit further extracts the characteristic carbon concentration distribution.
The thermo-fluid state calculation device according to claim 3, wherein the calculation unit further calculates a carbon concentration distribution predicted value.
The thermo-fluid state arithmetic unit according to claim 3 or 4, wherein the predetermined region is a part region on the upper surface of the melt.
The rotation speed of the container and the rotation speed of the semiconductor crystal are fed back so that each of the temperature distribution predicted value and the flow velocity distribution predicted value calculated by the arithmetic unit are suitable values for the growth of the semiconductor crystal. The thermo-fluid state calculation device according to any one of claims 3 to 5, further comprising a control unit for controlling.
When the J-dimensional region is a two-dimensional region including the XY plane and the flow velocity distribution simulation value includes the X-direction flow velocity distribution simulation value and the Y-direction flow velocity distribution simulation value, the acquisition unit is the XY. Treat the plane as a matrix of rows K and columns L (K and L are natural numbers greater than or equal to 1).
Each of the temperature distribution simulation value, the X-direction flow velocity distribution simulation value, and the Y-direction flow velocity distribution simulation value is represented by a matrix of rows K and columns L.
The matrix X to be decomposed is represented by a matrix of N rows and M columns (N and M are natural numbers of 1 or more).
The value of N is the number of the plurality of parameter groups.
The component of the i-th row of the matrix X (i is a natural number of 1 or more and N or less) is
A K × L sequence that unifies the standardized temperature distribution simulation values in the i-th parameter group, and
A K × L sequence that unifies the standardized X-direction flow velocity distribution simulation values in the i-th parameter group, and
The heat according to any one of claims 1 to 6, which has a component in which a K × L sequence in which the standardized Y-direction flow velocity distribution simulation value in the i-th parameter group is unified and the K × L sequence are arranged in order. Fluid state arithmetic unit.