Method and apparatus for estimating thermal conductivity

Abstract

This invention provides a method and apparatus for estimating thermal conductivity of a sample in a simple and highly accurate manner. [Solution] The thermal conductivity estimation method according to the present invention comprises the steps of: measuring the temperature distribution of a sample when it is heated; performing a heat transfer simulation based on a plurality of combinations of a provisional thermal conductivity and heating conditions of a sample model having the same shape as the sample to be measured, and calculating the temperature distribution of the sample model; creating a regression model representing the relationship between the temperature distribution of the sample model and the thermal conductivity of the sample model using a machine learning method, using the plurality of combinations of provisional thermal conductivity and heating conditions and the calculation results of the temperature distribution of the sample model as training data; and inputting the measurement results of the temperature distribution of the sample to the regression model to estimate the thermal conductivity of the sample. The step of measuring the temperature distribution of the sample to be measured involves creating a temperature distribution using a plurality of temperature measurements taken at a plurality of measurement positions that are equally spaced in temperature.

Description

Technical Field

[0001] The present invention relates to a method for estimating thermal conductivity and an apparatus for estimating thermal conductivity.

Background Art

[0002] As a method for estimating the thermal conductivity of a substance, for example, Patent Document 1 proposes a method using a machine learning method. This method includes a step of heating a part of a measurement sample under predetermined heating conditions and measuring the temperature distribution on the surface of the measurement sample in a steady state, a step of performing a heat transfer simulation for a plurality of combinations of a hypothetical thermal conductivity of a sample model having the same shape as the measurement sample and heating conditions and calculating the temperature distribution on the surface of the sample model for each combination, a step of creating a regression model using a machine learning method with the plurality of combinations and the calculation results of the temperature distributions obtained from the plurality of combinations as training data, with the input being the temperature distribution on the surface of the measurement sample and the output being the thermal conductivity of the measurement sample, and a step of inputting the measurement result of the temperature distribution on the surface of the measurement sample into the regression model and estimating the thermal conductivity of the measurement sample.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] The above method for estimating thermal conductivity can simply estimate the thermal conductivity, but further improvement in estimation accuracy is required.

[0005] Therefore, an object of the present invention is to provide a method for estimating thermal conductivity and an apparatus for estimating thermal conductivity that can simply and accurately estimate the thermal conductivity of a sample.

Means for Solving the Problems

[0006] As a result of diligent research by the inventors of this invention, they have found that the measurement location is crucial in measuring the temperature distribution of a sample necessary for estimating thermal conductivity, and that further improvements in estimation accuracy can be expected by taking temperature measurements at an appropriate location.

[0007] The present invention is based on such technical knowledge, and the thermal conductivity estimation method according to the present invention comprises the steps of: heating a part of a sample to be measured under predetermined heating conditions to measure the temperature distribution of the sample; performing a heat transfer simulation based on a plurality of combinations of provisional thermal conductivity and heating conditions of a sample model having the same shape as the sample to calculate the temperature distribution of the sample model; using the plurality of combinations of provisional thermal conductivity and heating conditions used in the heat transfer simulation and the calculation results of the temperature distribution of the sample model obtained from the heat transfer simulation as training data to create a regression model representing the relationship between the temperature distribution of the sample model and the thermal conductivity of the sample model using a machine learning method; and inputting the measurement results of the temperature distribution of the sample to the regression model to estimate the thermal conductivity of the sample, wherein the step of measuring the temperature distribution of the sample to be measured is characterized in that the temperature distribution is created using a plurality of temperature measurement values ​​measured at a plurality of measurement positions that are equally spaced in temperature.

[0008] According to the present invention, not only can the thermal conductivity of a measurement sample be easily estimated, but the estimation accuracy can also be improved.

[0009] In the present invention, the plurality of measurement positions are preferably arranged in order toward the direction away from the heating position of the sample to be measured, and the distance between two adjacent points of the plurality of measurement positions is preferably longer as it moves away from the heating position. Alternatively, the plurality of measurement positions include a first measurement point, a second measurement point, and a third measurement point arranged in order toward the direction away from the heating position of the sample to be measured, and it is preferable that the first distance from the heating position to the first measurement point is shorter than the second distance from the first measurement point to the second measurement point, and the third distance from the second measurement point to the third measurement point is shorter than the second distance. This makes it possible to create the temperature distribution using a plurality of temperature measurements taken at a plurality of measurement positions that are temperaturely equal apart.

[0010] In the present invention, the step of measuring the temperature distribution of the sample to be measured preferably involves estimating the temperature distribution of the sample to be measured by a heat transfer simulation using the provisional thermal conductivity of the sample to be measured, and determining a plurality of measurement positions that are equally spaced in temperature from the estimated result of the temperature distribution of the sample to be measured.

[0011] In the present invention, the step of creating the regression model by machine learning is to create a regression model in which the input is the temperature distribution of the sample to be measured and the heating conditions at the time of measuring the temperature distribution, and the output is the thermal conductivity of the sample to be measured. The step of estimating the thermal conductivity is to input the measurement result of the temperature distribution and the heating conditions at the time of measuring the temperature distribution into the regression model to estimate the thermal conductivity of the sample to be measured.

[0012] In the present invention, the step of calculating the temperature distribution of the sample model is preferably performed by conducting a heat transfer simulation based on the same measurement system used when measuring the temperature distribution occurring in the sample.

[0013] In the present invention, the step of calculating the temperature distribution of the sample model preferably involves performing a heat transfer simulation under the same conditions as when the temperature distribution of the sample was measured. This improves the accuracy of estimating the thermal conductivity of the sample.

[0014] In the present invention, the measurement sample is preferably a component of a semiconductor crystal product manufacturing apparatus or a substitute material thereof. By using the estimated thermal conductivity of this measurement sample in a heat transfer simulation of the semiconductor single crystal or semiconductor substrate manufacturing process, and controlling the semiconductor single crystal or semiconductor substrate manufacturing apparatus based on the results of this heat transfer simulation, semiconductor crystal products with desired characteristics can be easily manufactured.

[0015] Furthermore, the thermal conductivity estimation device according to the present invention comprises: a measurement unit that measures the temperature distribution of a sample when a part of the sample is heated under predetermined heating conditions; a calculation unit that calculates the temperature distribution of a sample model by performing a heat transfer simulation based on a plurality of combinations of a provisional thermal conductivity and heating conditions of a sample model having the same shape as the sample; a machine learning unit that uses the plurality of combinations of the provisional thermal conductivity and heating conditions used in the heat transfer simulation and the calculation results of the temperature distribution of the sample model obtained from the heat transfer simulation as training data to create a regression model that represents the relationship between the temperature distribution of the sample model and the thermal conductivity of the sample model using a machine learning method; and an estimation unit that inputs the measurement results of the temperature distribution of the sample into the regression model to estimate the thermal conductivity of the sample, wherein the measurement unit creates the temperature distribution using a plurality of temperature measurements taken at a plurality of measurement positions that are equally spaced in temperature.

[0016] According to the present invention, not only can the thermal conductivity of a measurement sample be easily estimated, but the estimation accuracy can also be improved. [Effects of the Invention]

[0017] According to the present invention, it is possible to provide a method and apparatus for estimating thermal conductivity of a sample that can estimate the thermal conductivity of the sample simply and with high accuracy. [Brief explanation of the drawing]

[0018] [Figure 1] Figure 1 is a schematic diagram showing the configuration of a thermal conductivity estimation device and a thermal conductivity estimation method according to an embodiment of the present invention. [Figure 2] Figure 2 is a schematic diagram showing the configuration of the measurement unit. [Figure 3] Figure 3 is a schematic diagram showing an example of the installation position (temperature measurement position) of the thermocouple attached to the measurement sample. [Figure 4] Figure 4 is a schematic diagram showing the hierarchical structure of the neural network.

Mode for Carrying Out the Invention

[0019] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

[0020] Figure 1 is a schematic diagram showing the configuration of the thermal conductivity estimation device and the thermal conductivity estimation method according to an embodiment of the present invention.

[0021] As shown in Figure 1, the thermal conductivity estimation device 1 includes a measurement unit 2 that heats the measurement sample 10 under predetermined heating conditions and measures the temperature distribution on the surface of the measurement sample 10, a calculation unit 3 that performs a heat transfer simulation to calculate the temperature distribution of a sample model having the same shape as the measurement sample 10, a machine learning unit 4 that creates a regression model representing the relationship between the temperature distribution of the sample model and the thermal conductivity of the sample model using the calculation result of the temperature distribution of the sample model obtained from the heat transfer simulation as training data, and an estimation unit 5 that inputs the measurement result of the temperature distribution of the measurement sample 10 into the regression model and estimates the thermal conductivity of the measurement sample 10.

[0022] Examples of measurement samples 10 include the components themselves of manufacturing equipment for semiconductor crystal products such as silicon single crystals and silicon wafers, or substitute materials that are made of the same material as the components or have similar heat transfer properties. An example of a silicon single crystal manufacturing device is a single crystal pulling device using the Czochralski method. Examples of silicon wafer manufacturing devices include a silicon single crystal slicing device, a silicon wafer polishing device, and an epitaxial silicon wafer vapor phase growth device. Examples of components of the above-mentioned manufacturing devices include parts that make up the hot zone of a single crystal pulling device (chamber, crucible, heater, pulling cable, heat shield, insulation material), inner wall materials of single crystal pulling devices and vapor phase growth devices, susceptors of vapor phase growth devices, and various parts of slicing devices and polishing devices.

[0023] Figure 2 is a schematic diagram showing the configuration of the measurement unit 2.

[0024] As shown in Figure 2, the measurement unit 2 comprises a measurement case 21, a heating unit 22, a sample support unit 23, a temperature maintenance unit 24, an inert gas introduction unit 25, a thermocouple 26, and a control unit 28. In this embodiment, the shape and arrangement of the measurement sample 10, the measurement case 21, the heating unit 22, and the sample support unit 23 are axially symmetric cylindrical, that is, circular when viewed from above with their centers coinciding. However, these shapes do not have to be axially symmetric or cylindrical, and the arrangement may be such that the center of at least one component is offset from the centers of the other components. By making the components of the measurement system axially symmetric cylindrical, as in this embodiment, it becomes easier to construct the heat transfer simulation model in the calculation unit 3.

[0025] The measurement case 21 is formed in the shape of a hollow box with an outer shape that is roughly cylindrical. The heating section 22 is, for example, a resistance heater and is positioned in the center or bottom of the roughly cylindrical measurement sample 10.

[0026] The temperature maintenance unit 24 cools the measurement case 21 with water to maintain it at a constant temperature. The method for maintaining the measurement case 21 at a constant temperature is not limited to water cooling; air cooling or a heat sink may also be used.

[0027] The inert gas introduction section 25 replaces the inside of the measurement case 21 with an inert gas. Examples of inert gases include nitrogen and argon, but are not limited to these.

[0028] The thermocouple 26 is installed at a predetermined location on the sample 10 whose temperature is to be measured. The thermocouple 26 is electrically connected to the control unit 28. The thermocouple 26 measures the local temperature of the sample 10 at its installation location and outputs the measurement result to the control unit 28.

[0029] If the temperature maintenance unit 24 is configured to control the temperature by water cooling or air cooling, the control unit 28 controls the temperature maintenance unit 24 so that the measurement case 21 is at a constant temperature. The control unit 28 controls the inert gas introduction unit 25 to create an inert gas atmosphere inside the measurement case 21. The control unit 28 acquires the temperature distribution of the measurement sample 10 when a steady state is reached from the thermocouple 26 and outputs it to the estimation unit 5.

[0030] Figure 3 is a schematic diagram showing an example of the installation position (temperature measurement position) of the thermocouple attached to the measurement sample 10.

[0031] As shown in Figure 3, it is preferable that the thermocouples 26 on the measurement sample 10 be installed at positions that are equally spaced in temperature. In this case, the installation positions of the multiple thermocouples 26 are arranged sequentially in the direction away from the heating position of the measurement sample 10, and the distance between two adjacent points at the multiple measurement positions increases as the distance from the heating position increases. By determining the positions so that the temperature intervals between the thermocouples 26 are equal, the accuracy of estimating the thermal conductivity can be improved.

[0032] The reason why the accuracy of thermal conductivity estimation improves is presumed to be as follows: Machine learning programs estimate by mimicking known data, and if the known data is biased, the estimation accuracy for unknown data will worsen. When measuring the temperature of the sample 10, if measurements are taken at positions that are equally spaced geographically, the input values ​​will be biased because the temperature intervals are not equal. However, if measurements are taken at positions that are equally spaced temperaturely, the bias in the input values ​​can be suppressed, and the accuracy of thermal conductivity estimation can be improved.

[0033] Although the thermal conductivity of the measurement sample 10 is unknown, it is rare that its value is completely unknown. Therefore, the temperature distribution can be calculated by heat transfer simulation using an estimated value of the thermal conductivity, and the positions that are equally spaced in terms of temperature can be determined from the results of the temperature distribution calculation.

[0034] The calculation unit 3 creates training data. Training data (or teacher data) is a set of input-output pairs of a function, such as "desired output d for a given input x," used to define the function of the target network. The training data is used in the machine learning unit 4 to create a regression model using machine learning methods.

[0035] Creating regression models requires the collection of a large amount of training data, but this is difficult to achieve through experiments. Therefore, in this embodiment, training data is created through simulation using analysis software.

[0036] The calculation unit 3 performs heat transfer simulations for multiple combinations of hypothetical thermal conductivity and heating conditions of a sample model having the same shape as the measurement sample 10, and calculates the temperature distribution of the sample model for each of these combinations. In performing these calculations, the calculation unit 3 considers the electric heating inside and outside the measurement case 21 from the viewpoints of heat conduction, heat transfer, and thermal radiation, and performs heat transfer simulations based on known physical models.

[0037] The calculation unit 3 outputs the temperature distribution calculation results, the combination of the provisional thermal conductivity and heating conditions used in the temperature distribution calculation, as training data to the machine learning unit 4. The analysis software used in the calculation unit 3 is not particularly limited and commercially available software can be used.

[0038] The machine learning unit 4 uses the training data input from the calculation unit 3 to create a regression model using machine learning methods, where the input is the temperature distribution of the measurement sample 10 and the output is the thermal conductivity of the measurement sample 10. The machine learning unit 4 outputs the created regression model to the estimation unit 5. Examples of machine learning methods used by the machine learning unit 4 include methods using neural networks and genetic algorithms, but it is not particularly limited and well-known methods (such as support vector machines and sparse models) can be used.

[0039] Machine learning is a method that uses computers to discover patterns in large amounts of data and utilizes these patterns for data analysis and prediction. A major characteristic of machine learning is that, if the learning process is successful, it becomes possible to predict results even from unknown information that was not learned during training. Regression refers to defining a function that well reproduces the training data, for functions that take continuous values ​​such as numbers as outputs.

[0040] In this embodiment, the machine learning unit 4 creates a regression model using a neural network. A neural network is a technology that mimics the neural network of living organisms. The model used when performing regression on the regression model using the neural network will be described below.

[0041] Figure 4 is a schematic diagram showing the hierarchical structure of a neural network.

[0042] As shown in Figure 4, the neural network of this embodiment has a hierarchical structure including l, m, and n layers. The l layer is the input layer, to which the temperature distribution of the measurement sample 10 is input. The m layer is a hidden layer, of which there are two layers and 128 neurons. The n layer is the output layer, which outputs the thermal conductivity of the measurement sample 10. In this embodiment, the sigmoid function is used as the activation function, and Adam (Adaptive Moment Estimation) is used to adjust the learning rate.

[0043] The estimation unit 5 obtains the temperature distribution measurement result of the measurement sample 10 from the measurement unit 2, inputs the temperature distribution measurement result into a regression model, and estimates the thermal conductivity of the measurement sample 10.

[0044] Next, we will explain the method for estimating thermal conductivity using the thermal conductivity estimation device 1 described above.

[0045] As shown in Figure 1, the worker constructs the measuring unit 2 having the above configuration (step S1).

[0046] Before or after the processing in step S1, or in parallel with the processing in step S1, the calculation unit 3 constructs a simulation model that simulates the measurement unit 2 based on the operator's input settings (step S2). When constructing the simulation model, the size and physical properties of the components are set as known values. Examples of components whose size is set include the shape of the internal space of the measurement case 21, the measurement sample 10, and the heating unit 22. Examples of physical properties that are set include the temperature, pressure, atmosphere, and convection conditions inside the measurement case 21. Hereinafter, the configuration corresponding to the measurement sample 10 in the simulation model will be referred to as the "sample model".

[0047] After processing in step S2, the calculation unit 3 performs a heat transfer simulation based on the simulation model to generate training data (step S3). In this step S3 process, the calculation unit 3 sets a range for the provisional thermal conductivity of the sample model and a range for the heating temperature based on the operator's input, and then sets multiple calculation conditions by arbitrarily combining the provisional thermal conductivity and heating temperature within the above range. From the viewpoint of improving the accuracy of the regression model in the machine learning unit 4, it is preferable to set a large number of calculation conditions here.

[0048] The calculation unit 3 performs heat transfer simulations for each of these multiple calculation conditions and calculates the steady-state temperature distribution when only the lower surface of the sample model is heated. At this time, from the viewpoint of improving the accuracy of the regression model in the machine learning unit 4, it is preferable to perform calculations assuming the same measurement system and the same atmosphere as when the temperature distribution was measured in the measurement unit 2. The calculation unit 3 outputs a combination of a provisional thermal conductivity, heating temperature, and the temperature distribution obtained based on these as training data to the machine learning unit 4. Note that the training data may also be input to the machine learning unit 4 based on settings input by the operator.

[0049] After processing in step S3, the machine learning unit 4 uses the training data to create a regression model (step S4) in which the input is the temperature distribution measurement result of the measurement sample 10 from the measurement unit 2 and the heating conditions during the temperature distribution measurement, and the output is the thermal conductivity of the measurement sample 10. The machine learning unit 4 then outputs this regression model to the estimation unit 5. The regression model may also be input to the estimation unit 5 based on settings input by the operator.

[0050] Before or after the processing in steps S2 to S4, or in parallel with the processing in steps S2 to S4, the measurement unit 2 measures the temperature distribution of the measurement sample 10, which has the same shape as the sample model, under the same conditions as the simulation model constructed by the calculation unit 3 (step S5).

[0051] The control unit 28 acquires the temperature distribution measurement results of the measurement sample 10 at predetermined time intervals and outputs the temperature distribution when the change in temperature distribution over time ceases (when a steady state is reached) to the estimation unit 5.

[0052] In order to accurately estimate the thermal conductivity of the measurement sample 10 in the estimation unit 5, it is preferable to use the temperature distribution when only one point of the measurement sample 10 is heated, so that the temperature gradient is in one direction. For example, it is preferable to use the temperature distribution when the center of the measurement sample 10 is heated. Alternatively, the temperature distribution when the bottom of the measurement sample 10 is heated may be used.

[0053] Preferably, the control unit 28 controls the temperature maintenance unit 24 to adjust the temperature of the measurement case 21. With this configuration, it is possible to suppress changes in the ambient temperature around the measurement sample 10 due to the temperature outside the measurement case 21, and to measure the temperature distribution of the measurement sample 10 under the same conditions as the simulation model.

[0054] The control unit 28 preferably controls the inert gas introduction unit 25 to replace the inside of the measurement case 21 with an inert gas. With this configuration, oxidation of the surface of the measurement sample 10 due to heating can be suppressed, and the influence of oxides on the temperature distribution can be suppressed.

[0055] After the processing in steps S4 and S5, the estimation unit 5 inputs the temperature distribution measurement results from the measurement unit 2 and the heating conditions during the temperature distribution measurement into a regression model to estimate the thermal conductivity of the measurement sample 10 (step S6).

[0056] According to this embodiment, the thermal conductivity of a component of a semiconductor crystal product manufacturing apparatus, such as a semiconductor single crystal or a semiconductor substrate, or a substitute material with similar heat transfer properties, can be easily estimated by performing the above-described thermal conductivity estimation method on the measurement sample 10. The results of this thermal conductivity estimation can be used in a heat transfer simulation of the manufacturing process of the semiconductor single crystal or semiconductor substrate, and by controlling the manufacturing apparatus of the semiconductor single crystal or semiconductor substrate based on the results of this heat transfer simulation, semiconductor crystal products with desired properties can be easily manufactured.

[0057] The thermal conductivity estimation device 1 can perform a heat transfer simulation by setting the shape of the sample model to the same shape as the measurement sample 10, while not setting any material, and inputting a provisional thermal conductivity. Based on the heat transfer simulation results, the thermal conductivity estimation device 1 creates a regression model using machine learning, and estimates the thermal conductivity of the measurement sample 10 by inputting the temperature distribution measurement results of the measurement sample 10 into the regression model. Using this regression model, the thermal conductivity of various measurement samples 10 made of different materials can be easily estimated. Furthermore, the thermal conductivity can be easily estimated when performing various heat transfer analyses in the manufacturing process of semiconductor crystal products.

[0058] As described above, the thermal conductivity estimation method according to this embodiment comprises the steps of: step S1 preparing a measurement sample 10 and constructing a measurement unit 2; step S5 heating the measurement sample 10 and measuring the temperature distribution of the measurement sample 10 in a steady state; steps S2 and S3 performing a heat transfer simulation based on multiple combinations of provisional thermal conductivity and heating conditions of a sample model having the same shape as the measurement sample 10 to calculate the temperature distribution of the sample model; step S4 creating a regression model representing the relationship between the temperature distribution of the sample model and the thermal conductivity of the sample model using machine learning, with the multiple combinations of provisional thermal conductivity and heating conditions used in the heat transfer simulation and the calculation results of the temperature distribution of the sample model obtained from the heat transfer simulation as training data; and step S6 inputting the measurement results of the temperature distribution of the measurement sample into the regression model to estimate the thermal conductivity of the measurement sample. Step S5, which measures the temperature distribution of the measurement sample 10, creates the temperature distribution using multiple temperature measurement values ​​measured at multiple measurement positions that are equally spaced in temperature, so that the thermal conductivity of the measurement sample can be easily estimated, and the estimation accuracy can be improved.

[0059] Although preferred embodiments of the present invention have been described above, it goes without saying that the present invention is not limited to the above embodiments, and various modifications are possible without departing from the spirit of the invention, and these modifications are also included within the scope of the present invention.

[0060] For example, the configuration of the measurement unit 2 shown in Figure 2 is just one example, and various measurement systems can be used as long as they can measure the temperature distribution of the measurement sample 10. [Examples]

[0061] The temperature distribution of a measurement system containing a sample with an unknown thermal conductivity was calculated, and the thermal conductivity of the sample was estimated by inputting the calculation conditions and results into a machine learning program. RF board (registered trademark) manufactured by Nichias Corporation was used as the sample. RF board is an insulating material formed into a plate shape by adding inorganic and organic binders to alumina fiber, and it has low heat storage capacity and excellent insulation and processability. The nominal thermal conductivity of RF board is 0.15 W / m·K.

[0062] Next, a regression model was created to estimate the thermal conductivity of the sample. First, a simulation model simulating the measurement unit 2 was constructed using the calculation unit 3. The software used for the calculation unit 3 was "CGSim" from STR Corporation. The heating conditions shown in Table 1 below were set when constructing the simulation model.

[0063] [Table 1]

[0064] Next, the provisional thermal conductivity of the sample model was set to a range of 0.1 to 10 times 0.15 W / mK, and the heating temperature of the center of the sample model was set to 1000°C. Within this range, 1875 different calculation conditions were set by arbitrarily combining the provisional thermal conductivity and heating temperature. Using the calculation unit 3, a heat transfer simulation based on the simulation model was performed for each calculation condition to calculate the temperature distribution of the sample in a steady state.

[0065] In the evaluation of thermal conductivity using comparative examples, the temperatures of a total of 21 locations at equally spaced positions on the sample model were extracted from the calculation results above. This extracted temperature distribution, along with the combination of the provisional thermal conductivity and heating temperature used to calculate this temperature distribution, was input into the machine learning unit 4 as training data.

[0066] In the evaluation of thermal conductivity using the examples, based on the calculation results above, the temperatures at a total of three locations that are equally spaced in temperature on the sample model were extracted when the thermal conductivity of the RF board was set to the nominal value of 0.15 W / mK. This extracted temperature distribution, along with the combination of the provisional thermal conductivity and heating temperature used in the calculation of this temperature distribution, was input into the machine learning unit 4 as training data.

[0067] By inputting training data into the machine learning unit 4 and performing machine learning on the relationship between the hypothetical thermal conductivity of the sample model and the surface temperature distribution, regression models were created for comparative examples and examples, with the temperature distribution and heating conditions of the sample model as input and the thermal conductivity of the sample model as output. In creating the regression models, machine learning using a neural network was performed, and the following parameters were adopted for machine learning. In addition, Google's TENSORFLOW® was used as the software library for machine learning. Hidden layers: 2 layers Number of neurons: 128 Learning method: Adam Number of epochs: 1000 Activation function: Sigmoid Module: Keras

[0068] Next, the regression models were evaluated using the examples and comparative examples. First, 50 combinations of hypothetical thermal conductivity, heating conditions, and temperature distribution, which were not used in creating the regression model (not used as training data), were used as unknown test data for the regression model (trained model). The thermal conductivity of the measured sample was estimated by inputting the temperature distribution and heating conditions into the regression model. In order to accurately compare the regression models of the comparative examples and examples, the unknown test data were assumed to have the same thermal conductivity.

[0069] In estimating thermal conductivity using comparative examples, the temperatures of three measurement points that were equally spaced from the test data were selected and used as input to the regression model of the comparative examples. Specifically, when setting the first to third measurement points radially away from the heating point, the distance between any two adjacent points was set to 37.5 mm in all cases (see Figure 3).

[0070] In estimating thermal conductivity using the examples, temperatures were selected from the test data at three measurement points that were equally spaced in temperature, and these were used as input to the regression model of the examples. Specifically, when setting the first to third measurement points in order in the radial direction away from the heating position, the first distance from the heating section 22 to the first measurement point was set to 16 mm, the second distance from the first to the second measurement point was set to 24 mm, and the third distance from the second to the third measurement point was set to 38 mm, so that the temperature difference between all two adjacent points was the same at 225°C (see Figure 3). To accurately compare the two, the number of temperature measurement points was set to three in both cases. A measurement error of about 10°C is estimated for the temperature measurement.

[0071] Thus, the thermal conductivity of the samples was estimated using the regression models of the comparative examples and the examples, and the estimation accuracy Δ was determined by comparing it with the set value of the thermal conductivity obtained from the simulation.

[0072] k is the estimated thermal conductivity calculated using the regression model, and k is the answer to the thermal conductivity that can be obtained from the test data. T In this case, the estimation accuracy Δ can be calculated as follows.

[0073]

number

[0074] The estimation accuracy Δ is calculated by comparing the estimated thermal conductivity k of the regression model with the answer k from the test data. T This shows the difference as a ratio. Here, 50 test data points (n=50) were used. The results are shown in Table 2.

[0075] [Table 2]

[0076] The estimation accuracy Δ for the comparative example was 10.3, while the estimation accuracy Δ for the example was 8.01. From these results, it was found that using temperature distributions measured at temperature-equally spaced measurement positions resulted in better estimation accuracy of thermal conductivity than using temperature distributions measured at distance-equally spaced measurement positions.

[0077] In this embodiment, the temperature was measured at three points from the center on the sample model, but it goes without saying that the temperature could also be measured at four or more points. [Explanation of Symbols]

[0078] 1. Thermal conductivity estimation device 2 Measuring part 3 Calculation section 4. Machine Learning Department 5 Estimation part 10 Samples to be measured 21 Measurement Cases 22 Heating section 23 Sample support section 24 Temperature maintenance part 25 Inert gas introduction section 26 Thermocouples 28 Control Unit

Claims

1. A step of heating a portion of the sample to be measured under predetermined heating conditions and measuring the temperature distribution of the sample, The steps include: performing a heat transfer simulation based on multiple combinations of hypothetical thermal conductivity and heating conditions of a sample model having the same shape as the measured sample, and calculating the temperature distribution of the sample model; The steps include creating a regression model that represents the relationship between the temperature distribution of the sample model and the thermal conductivity of the sample model using a machine learning method, using the provisional thermal conductivity and multiple combinations of heating conditions used in the heat transfer simulation and the calculation results of the temperature distribution of the sample model obtained from the heat transfer simulation as training data, The system includes the step of inputting the measurement results of the temperature distribution of the sample into the regression model to estimate the thermal conductivity of the sample. The step of measuring the temperature distribution of the sample to be measured is characterized by creating the temperature distribution using a plurality of temperature measurements taken at a plurality of measurement positions that are equally spaced in temperature.

2. The plurality of measurement positions are arranged in order from the heating position of the measurement sample toward the heating position. The thermal conductivity estimation method according to claim 1, wherein the distance between two adjacent points of the plurality of measurement positions increases as the distance from the heating position increases.

3. The plurality of measurement positions include a first measurement point, a second measurement point, and a third measurement point, which are arranged in order in a direction away from the heating position of the measurement sample. The first distance from the heating position to the first measurement point is shorter than the second distance from the first measurement point to the second measurement point. The thermal conductivity estimation method according to claim 1, wherein the third distance from the second measurement point to the third measurement point is shorter than the second distance.

4. The method for estimating thermal conductivity according to claim 1, wherein the step of measuring the temperature distribution of the sample to be measured is to estimate the temperature distribution of the sample to be measured by a heat transfer simulation using the provisional thermal conductivity of the sample to be measured, and to determine a plurality of measurement positions that are equally spaced in temperature from the estimated result of the temperature distribution of the sample to be measured.

5. The step of creating the regression model using machine learning involves creating a regression model in which the input is the temperature distribution of the sample to be measured and the heating conditions during the measurement of the temperature distribution, and the output is the thermal conductivity of the sample to be measured. The thermal conductivity estimation method according to claim 1, wherein the step of estimating the thermal conductivity involves inputting the measurement results of the temperature distribution and the heating conditions at the time of the temperature distribution measurement into the regression model to estimate the thermal conductivity of the sample to be measured.

6. The method for estimating thermal conductivity according to claim 1, wherein the step of calculating the temperature distribution of the sample model is to perform a heat transfer simulation based on the same measurement system used when measuring the temperature distribution occurring in the measurement sample.

7. The method for estimating thermal conductivity according to claim 1, wherein the step of calculating the temperature distribution of the sample model is to perform a heat transfer simulation assuming the same atmosphere as when the temperature distribution of the measurement sample was measured.

8. The method for estimating thermal conductivity according to claim 1, wherein the measurement sample is a component of a semiconductor crystal product manufacturing apparatus or a substitute material thereof.

9. A measuring unit that measures the temperature distribution of a sample when a portion of the sample is heated under predetermined heating conditions, A calculation unit that performs a heat transfer simulation based on multiple combinations of hypothetical thermal conductivity and heating conditions of a sample model having the same shape as the measured sample, and calculates the temperature distribution of the sample model. A machine learning unit creates a regression model representing the relationship between the temperature distribution of the sample model and the thermal conductivity of the sample model using a machine learning method, using the provisional thermal conductivity and multiple combinations of heating conditions used in the heat transfer simulation and the calculation results of the temperature distribution of the sample model obtained from the heat transfer simulation as training data. The system includes an estimation unit that inputs the measurement results of the temperature distribution of the sample into the regression model to estimate the thermal conductivity of the sample. The thermal conductivity estimation device is characterized in that the measuring unit creates the temperature distribution using a plurality of temperature measurement values ​​taken at a plurality of measurement positions that are equally spaced in temperature.

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