Power configuration method of semiconductor heating device and semiconductor heating device

Abstract

The invention provides a power configuration method of a semiconductor heating device and the semiconductor heating device, and relates to the technical field of energy. Constructing a transient three-dimensional numerical model representing the heating process of the heating surface of the semiconductor heating device; calculating to obtain a temperature distribution rule of the heating surface in the whole heating process based on original power configuration, and determining a power compensation position of the heating surface; the heating medium of the heating surface is segmented, so that the heating medium is divided into multiple segments; and by taking the average temperature uniformity value as an optimization target, optimizing the power configuration of the heating medium of the target section at different heating stages by adopting an optimization algorithm. The temperature distribution of the semiconductor device at each moment in the whole heating process is obtained through transient numerical calculation, especially the temperature distribution of the most critical heating surface, so that the low-temperature area and the high-temperature area of the heating surface are obtained, and the temperature uniformity condition of the heating surface at each moment is determined; and the temperature uniformity of the heating surface is improved by increasing the temperature of the low-temperature area.

Description

Technical Field

[0001] This application relates to the field of energy technology, and in particular to a power configuration method for a semiconductor heating device and a semiconductor heating device. Background Technology

[0002] Existing three-dimensional heterogeneous integration technology, characterized by diverse functions, represents an important research and application direction for transcending Moore's Law. Three-dimensional integration is defined as stacking Moore's wafers or chips in a direction perpendicular to the wafer or chip plane. Semiconductor heating devices, as key equipment for this stacking process, require very high temperature uniformity on the heating surface.

[0003] Existing experimental methods are insufficient to obtain the temperature distribution of the entire heating surface. Although numerical simulation technology can obtain the temperature distribution of the entire heating surface, existing technologies only focus on the temperature uniformity of the heating surface during the isothermal stage. The temperature uniformity during the heating process also affects various performance characteristics of the molybdenum wafer or chip, and the temperature distribution pattern is not the same in different heating stages. Therefore, it is necessary to adopt reasonable solutions to improve the temperature uniformity of the heating surface. Summary of the Invention

[0004] In view of the above problems, this application proposes a power configuration method for a semiconductor heating device and a semiconductor heating device, overcoming the shortcomings of the prior art.

[0005] In a first aspect, embodiments of this application provide a power configuration method for a semiconductor heating device, including: A transient three-dimensional numerical model characterizing the heating process of the heating surface of the semiconductor heating device is constructed; Based on the transient three-dimensional numerical model, the temperature distribution law of the heating surface during the entire heating process based on the original power configuration is calculated, and the power compensation position of the heating surface is determined. Based on the power compensation position of the heating surface, the heating medium of the heating surface is segmented, so that the heating medium is divided into multiple segments; Using the average temperature uniformity as the optimization objective, an optimization algorithm is employed to optimize the power configuration of the heating medium in the target section at different heating stages, so that the temperature uniformity of the heating surface during the heating process meets the average temperature uniformity.

[0006] Optionally, a transient three-dimensional numerical model characterizing the heating process of the heating surface of the semiconductor heating device is constructed, including: A numerical calculation model is established using three-dimensional transient numerical simulation technology; The semiconductor heating device is given the correct boundary conditions and a preset number of grids are divided; The transient three-dimensional numerical model is constructed by combining the numerical calculation model, the correct boundary conditions, and the preset number of grids. The correct boundary conditions are determined based on the environmental conditions and materials in which the semiconductor heating device operates.

[0007] Optionally, the power compensation position of the heating surface is determined by calculating the temperature distribution pattern of the heating surface throughout the heating process based on the original power configuration, including: The calculations yielded the high-temperature and low-temperature zones of the heating surface at different heating stages throughout the entire heating process; Based on the high-temperature and low-temperature zones at each moment during different heating stages, the variation patterns of the high-temperature and low-temperature zones of the heating surface are formed; Based on the aforementioned variation pattern, the power compensation position of the heating surface is determined.

[0008] Optionally, each heating stage includes: a heating stage and a constant temperature stage; determining the power compensation position of the heating surface according to the change pattern includes: During the heating phase, the low-temperature zone and the high-temperature zone are defined as the power compensation locations of the heating surface; During the constant temperature stage, only the low temperature zone is identified as the power compensation location for the heating surface.

[0009] Optionally, based on the power compensation position of the heating surface, the heating medium of the heating surface is segmented, such that the heating medium is divided into multiple segments, including: During the heating phase, the center and upper left edge of the heating surface are the low-temperature zone, and the lower right edge of the heating surface is the high-temperature zone. During the constant temperature stage, the upper left edge of the heating surface is the low temperature zone; The heating medium is divided into three segments according to the center position and the upper left edge position of the heating surface. One segment corresponds to the center position of the heating surface, another segment corresponds to the upper left edge position of the heating surface, and the remaining heating medium is considered as one segment.

[0010] Optionally, the power configuration of the heating medium in the target section can be optimized at different heating stages, including: During the heating phase, the two sections of heating medium corresponding to the center and upper left edge of the heating surface are optimized by increasing their power by different amounts, while the remaining heating medium is optimized by decreasing its power. During the constant temperature stage, the power of the heating medium is increased only at the upper left edge of the heating surface, while the power of the other two heating medium sections is maintained.

[0011] Optionally, using the average temperature uniformity as the optimization objective, an optimization algorithm is employed to optimize the power configuration of the heating medium in the target section at different heating stages, including: Using the optimal Latin hypercube design, the initial design parameters are uniformly sampled to obtain sample data, and the input set of the sample database is constructed. The initial design parameters are a range value. The average temperature uniformity of the heating surface at each moment in different heating stages is taken as the optimization target. The average temperature uniformity of each sample data is calculated and used as the output set of the sample database. A proxy model is constructed using a Kriging model to establish a relationship between the power configuration optimization strategy and the average temperature uniformity. This proxy model takes the input set of the sample database as input and the output set of the sample database as output. Based on the Kriging model, the optimal design parameter values ​​for minimizing the average temperature uniformity under different heating stages are calculated using an adaptive simulated annealing algorithm. Using the aforementioned optimal design parameter values, the power configuration of the heating medium in the target section is optimized at different heating stages; The initial design parameters include multiple ratios, which are the ratios of the power density after each power increase at the power compensation position of the heating surface during each heating stage to the power density in the original power configuration.

[0012] Optionally, based on the Kriging model, the optimal design parameter values ​​for minimizing the average temperature uniformity at different heating stages are calculated using an adaptive simulated annealing algorithm, including: Based on the Kriging model, the optimal design parameter values ​​for minimizing the average temperature uniformity of the heating surface under different heating stages are calculated from the range of initial design parameter values ​​using an adaptive simulated annealing algorithm.

[0013] Optionally, the average temperature uniformity includes:

[0014]

[0015] In the above formula, T F This represents the average value of overall temperature uniformity. T FH This is the highest temperature of the heating surface. T FL This is the lowest temperature of the heating surface. T FAVE This represents the average temperature of the heating surface. T RThis represents the average radial temperature uniformity. This indicates the calculation of the standard deviation. T C The temperature at the radial center point of the heating surface. T E This represents the temperature difference at the radial edge of the heating surface.

[0016] Secondly, embodiments of this application provide a semiconductor heating device that uses the power configuration method of a semiconductor heating device as described in any of the first aspects for heating, the semiconductor heating device comprising: an upper structure, a lower structure, and a housing; The upper structure and the lower structure are attached to each other, with the contact surface being the heating surface, and both have heating media with the same structure inside, which are used to heat the heating surface; The upper structure and the lower structure are fixedly connected to the outer shell through a support structure. The upper structure and the lower structure are fitted together to form a whole, and the space between them and the outer shell is a vacuum environment. The heating medium inside both the upper structure and the lower structure includes: a multi-segment heating medium; Each segment of the sub-heating medium is connected to a power source; Any sub-heating medium in the upper structure and the corresponding sub-heating medium at the same heating position in the lower structure are connected to the same power source; The heating medium in the upper structure is distributed in a vortex pattern from the center of the upper structure outwards, and the heating medium in the lower structure is also distributed in a vortex pattern from the center of the lower structure outwards, overlapping the heating medium in the upper structure in the vertical direction.

[0017] The power configuration method for the semiconductor heating device proposed in this application creatively proposes a novel power configuration method. First, it constructs a transient three-dimensional numerical model characterizing the heating process of the heating surface of the semiconductor heating device. Then, based on the transient three-dimensional numerical model, it calculates the temperature distribution law of the heating surface throughout the heating process under the original power configuration, determining the power compensation position of the heating surface. Next, based on the power compensation position of the heating surface, it segments the heating medium of the heating surface, dividing it into multiple segments. Finally, using the average temperature uniformity as the optimization objective, it employs an optimization algorithm to optimize the power configuration of the target segment heating medium at different heating stages, ensuring that the temperature uniformity of the heating surface meets the average temperature uniformity during the heating process (whether in the isothermal or heating-up stage), greatly improving the temperature uniformity of the heating surface.

[0018] The power configuration method for the semiconductor heating device proposed in this application obtains the temperature distribution of the semiconductor device at every moment during the entire heating process through transient numerical calculation, especially the temperature distribution of the most critical heating surface. This allows for the identification of low-temperature and high-temperature regions on the heating surface, determination of the temperature uniformity of the heating surface at each moment, and improvement of the temperature uniformity of the heating surface by increasing the temperature of the low-temperature region. This method has broad application prospects and high practicality. Attached Figure Description

[0019] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart illustrating a power configuration method for a semiconductor heating device according to an embodiment of this application; Figure 2 This is a schematic diagram illustrating a segmented heating medium according to an embodiment of this application; Figure 3 The adaptive simulated annealing algorithm flowchart exemplified in the embodiments of this application is shown in the figure. Figure 4 This is a comparison chart illustrating the change in overall temperature uniformity over time during the entire heating process before and after optimization, as exemplified in the embodiments of this application. Figure 5 This is a comparison diagram of the radial temperature uniformity over time before and after optimization during the entire heating process, as illustrated in the embodiments of this application. Figure 6 This is an overall structural diagram of a semiconductor heating device according to an embodiment of this application. Detailed Implementation

[0020] The embodiments of this application will now be described in detail. Examples of these embodiments are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0021] Wafer bonding technology refers to the physical or chemical connection of multiple wafers in a direction perpendicular to a plane by heating and pressurizing. It is a key means to improve the performance of semiconductor devices and realize miniaturization, and has broad application prospects in emerging fields such as microelectronics manufacturing, advanced packaging, and multifunctional chip integration.

[0022] The inventors discovered that existing semiconductor heating devices, as key equipment for stacking, have very high requirements for temperature uniformity of the heating surface. Temperature uniformity plays a decisive role in interface atomic diffusion, wafer stress distribution, and bonding strength, and is a core indicator of the performance of semiconductor heating devices. Poor temperature uniformity during bonding will cause uneven expansion of the wafer from the center outwards in all directions, easily leading to defects such as interface voids and residual stress concentration.

[0023] In recent years, computer simulation technology has developed rapidly and has been widely used in the study of heat transfer and temperature field in various power systems and devices. This technology provides a brand-new research method for temperature uniformity research. By establishing a global three-dimensional heat transfer numerical model using numerical simulation, and using simulation to guide experiments and experiments to verify simulation results, the influencing factors and their effects on temperature uniformity can be studied. This is of great significance for improving temperature uniformity, shortening product development cycles, and reducing development costs.

[0024] Further research by the inventors revealed that there is currently very little research on the temperature uniformity of semiconductor heating devices, and the few existing technologies only optimize the uniformity at the highest heating temperature. There is no research on the temperature uniformity throughout the entire heating process from room temperature to the highest temperature. Temperature uniformity during heating also affects various wafer properties, and the temperature distribution patterns differ at different heating stages. Therefore, it is urgent to develop a reasonable approach to improve temperature uniformity.

[0025] Existing testing methods are insufficient to obtain the temperature distribution of the entire heating surface. Current technologies only focus on the temperature uniformity of the heating surface during the isothermal stage. The temperature uniformity during the heating process also affects various performance characteristics of the molybdenum wafer or chip. Furthermore, the temperature distribution pattern is not the same in different heating stages. Therefore, it is necessary to adopt reasonable solutions to improve the temperature uniformity of the heating surface.

[0026] To address the aforementioned problems, the inventors have creatively proposed a power configuration method for a semiconductor heating device and a semiconductor heating device as described in this application. The technical solution of this application will be explained and described in detail below.

[0027] The power configuration method for a semiconductor heating device proposed in this application refers to... Figure 1 The flowchart shown includes: Step 101: Construct a transient three-dimensional numerical model characterizing the heating process of the heating surface of the semiconductor heating device.

[0028] To achieve power configuration of the heating surface, this application requires obtaining the real-time temperature of the heating surface. To obtain this real-time temperature, a transient three-dimensional numerical model characterizing the heating process of the semiconductor heating device's heating surface is first constructed. The transient three-dimensional numerical model obtains the real-time temperature of the heating surface through simulation calculations.

[0029] The aforementioned transient three-dimensional numerical model can be constructed using existing technologies. In one embodiment of this application, a preferred method for constructing a transient three-dimensional numerical model characterizing the heating process of a semiconductor heating device's heating surface includes: First, a numerical calculation model is established using three-dimensional transient numerical simulation technology. This model can be used to subsequently calculate the real-time temperature of the heating film and the temperature distribution throughout the heating process when the heating surface is formed based on the original power configuration. The numerical calculation model can be obtained using known numerical calculation equations, for example: Continuity equation: .

[0030] Momentum equation:

[0031]

[0032]

[0033] Energy equation:

[0034] In the ascending equation, The velocity vector is in m / s. , , Let x, y, and z be the velocity components of the fluid element in the x, y, and z directions, respectively, in m / s; Density, kg / m³ 3 ; For time, s; The pressure on the fluid element is expressed in Pa. Let N be the mass force on the fluid element; The value is the dynamic viscosity coefficient, in Pa·s; Specific heat at constant pressure, J / (kg·K); Temperature, K; The thermal conductivity is W / (m·K); For the heat source term defined on the heating medium, W / m 3 ; For the radiative heat source term, W / m 3 .

[0035] For radiative heat transfer between non-adjacent walls in a semiconductor heating device, a discrete coordinate (DO) radiation model is used in the simulation calculation. The solution is based on the radiation transport equation:

[0036] In the above formula, For position Along the direction The radiation intensity, W / (m 2 ·sr); Let m be the absorption coefficient of the medium; Let m be the scattering coefficient of the medium; The refractive index; The Stefan-Boltzmann constant, =5.67×10⁻⁸W / (m²) 2 ·K 4 ); The total number of discrete directions; Let be the scattering phase function, describing the scattering from the direction arrive The scattering probability; For direction The weighting factor is determined by the angle discretization.

[0037] Next, correct boundary conditions are applied to the semiconductor heating device, and a predetermined number of meshes are created. Applying correct boundary conditions and creating a predetermined number of meshes is to enable the model to obtain more accurate numerical simulation results. The correct boundary conditions are determined based on the environmental conditions and materials of the semiconductor heating device during operation. For example, typically, the heating surface is formed by the close contact of the upper and lower structures within the semiconductor heating device. The outer wall surface formed by the combination of the upper and lower structures can employ a mixed convection and radiation boundary condition, such as setting the convection heat transfer coefficient to 5 W / (m²). 2 ·K), with a surface emissivity of 0.28, etc.; the inner wall surface that contacts the vacuum cavity (the cavity between the upper and lower structures and the solid shell of the semiconductor heating device is the vacuum cavity) after the upper and lower structures are combined can adopt coupled boundary conditions, and different emissivity can be selected according to the wall material, such as: the emissivity of graphite is 0.8, and the emissivity of other metal parts is 0.28, etc.

[0038] Since a larger mesh count increases the complexity and computation time of the model, a polyhedral mesh is preferred for meshing the semiconductor heating device to reduce the mesh count. Specifically, the mesh at the heating medium is finer due to its relatively complex structure and the presence of a significant temperature gradient near the heat source. Extensive testing revealed that when the mesh count is below 5.23 million, the maximum temperature of both the heating surface and the heating medium gradually increases with the mesh count; however, when the mesh count exceeds 5.23 million, the maximum temperatures of both the heating surface and the heating medium show no significant fluctuations. Therefore, a mesh count of 5.23 million is optimal for calculation.

[0039] After all the above are completed, the transient three-dimensional numerical model can be constructed by combining the numerical calculation model, the correct boundary conditions, and the preset number of grids.

[0040] Step 102: Based on the transient three-dimensional numerical model, calculate the temperature distribution law of the heating surface during the entire heating process based on the original power configuration, and determine the power compensation position of the heating surface.

[0041] After constructing the transient three-dimensional numerical model, the temperature distribution pattern of the heating surface during the entire heating process based on the original power configuration can be obtained by using the model for calculation, thereby determining the power compensation position of the heating surface.

[0042] In one embodiment of this application, a preferred method for determining the power compensation position of the heating surface includes: First, the high-temperature and low-temperature zones of the heating surface at each moment during different heating stages are calculated throughout the entire heating process. Then, based on the high-temperature and low-temperature zones at each moment during different heating stages, the variation patterns of the high-temperature and low-temperature zones of the heating surface are formed. Finally, the power compensation position of the heating surface is determined according to the variation patterns.

[0043] Generally, a stepped heating strategy is used in the heating process of semiconductor heating devices. This strategy means that after each heating period, the heating surface is kept at a constant temperature for a period of time. In other words, assuming there are seven different heating stages, each stage includes a heating stage and a holding stage. Each stage involves heating for a period of time followed by a holding stage before moving to the next stage, until the target temperature is reached.

[0044] Ideally, temperature changes should be calculated continuously at every moment to obtain the most accurate data and optimize the uniformity of the heating surface temperature. However, this method requires extremely powerful hardware and is relatively time-consuming. Therefore, a better approach is to select multiple moments for calculation within each stage, such as 10 moments within the entire heating phase and 10 moments within the entire isothermal phase. This ensures a relatively accurate data foundation, better temperature uniformity control, and requires less powerful hardware while also being less time-consuming. The specific method used can be determined based on actual conditions and needs.

[0045] During the calculation, the vacuum environment inside the vacuum chamber can be achieved by setting the physical property parameters of the air inside the chamber. The density is calculated using the incompressible ideal gas equation of state. The outer wall of the chamber shell in contact with the air and the outer wall of the cooling water pipe adopt convective-radiative mixed boundary conditions, while the inner wall in contact with the vacuum chamber adopts coupled boundary conditions. The cooling water inlet adopts a velocity inlet and the outlet adopts a pressure outlet. The optimal cooling water inlet temperature can be selected as 296K, and the optimal inlet velocity can be selected as 1m / s.

[0046] The above calculations reveal the high-temperature and low-temperature zones of the heating surface at different heating stages throughout the entire heating process, thus establishing the variation patterns of these two regions. During the heating phase, both the low-temperature and high-temperature zones are designated as power compensation locations for the heating surface; during the isothermal phase, only the low-temperature zone is designated as the power compensation location. This arrangement is based on the following reasoning: Through extensive testing, the inventors discovered that the high-temperature zone of the heating surface is located in the lower right corner of the heating surface during each heating stage. Particularly in the first heating stage, the high-temperature zone is almost flush with the lower right edge of the heating surface, while its lowest temperature point is located in the center of the heating surface. In the remaining heating stages, the lowest temperature point is located in the upper left corner of the heating surface. Comparing the heating stages reveals that the low-temperature phenomenon in the center of the heating surface gradually weakens as the heating temperature increases, until it completely disappears in the last heating stage. For the isothermal stage, the temperature distribution of the heating surface is relatively similar in each stage, with the high-temperature zone located in the center of the heating surface towards the lower right corner, and the low-temperature zone located in the upper left edge area. Therefore, during the heating stage, both the low-temperature and high-temperature zones are identified as power compensation locations for the heating surface; during the isothermal stage, only the low-temperature zone is identified as the power compensation location for the heating surface.

[0047] Step 103: Based on the power compensation position of the heating surface, the heating medium of the heating surface is segmented, so that the heating medium is divided into multiple segments.

[0048] After obtaining the power compensation position of the heating surface, the heating medium can be segmented based on this position, resulting in multiple segments. Since the heating surface relies on the heating medium, which is typically located within the upper and lower structures and has identical structures, the heating media in both structures appear identical from a top-down view after being attached. However, due to the different power compensation positions, segmentation of the heating medium is necessary. This allows for individual control of the power of a specific segment, resulting in higher power, higher heat output, and faster temperature rise, or lower power, reduced heat output, and slower temperature rise.

[0049] In one embodiment of this application, a preferred method for segmenting the heating medium of a heating surface, such that the heating medium is divided into multiple segments, includes: During the heating stage, the center and upper left edge of the heating surface are low-temperature zones, while the lower right edge is a high-temperature zone. During the constant-temperature stage, the upper left edge of the heating surface is a low-temperature zone. Based on the center and upper left edge of the heating surface, the heating medium is divided into three sections: one section corresponds to the center of the heating surface, another section corresponds to the upper left edge, and the remaining heating medium is considered as one section.

[0050] To better understand the above segmentation, refer to... Figure 2 The diagram shown is a segmented heating medium. Figure 2 The diagram uses a common square arrangement of heating media as an example. To make it easier to understand, a color diagram is used and the top, bottom, left, and right sides are marked schematically, making it more intuitive. Figure 2 The heating medium at the center of the corresponding heating surface is marked in red, the heating medium at the upper left edge of the corresponding heating surface is marked in green, and the heating medium at the rest of the corresponding heating surface is marked in blue.

[0051] Step 104: Using the average temperature uniformity as the optimization target, an optimization algorithm is used to optimize the power configuration of the heating medium in the target section at different heating stages, so that the temperature uniformity of the heating surface during the heating process meets the average temperature uniformity.

[0052] After the aforementioned three steps are completed, the average temperature uniformity is used as the optimization target. An optimization algorithm is then employed to optimize the power configuration of the heating medium in the target section at different heating stages, so that the temperature uniformity of the heating surface during the heating process meets the average temperature uniformity.

[0053] Specifically, in conjunction with the foregoing content, we have: During the heating phase, the power of the two heating media sections corresponding to the center and upper left edge of the heating surface is increased by different amounts, while the power of the remaining heating media is decreased. During the isothermal phase, only the heating media section corresponding to the upper left edge of the heating surface is optimized by increasing its power, while maintaining the power of the other two sections. This optimization method ensures that the temperature at the center and upper left edge of the heating surface rises faster in each heating phase, while the temperature at the remaining locations rises more slowly, quickly meeting the temperature uniformity requirements of the heating surface. In the isothermal phase, only the power at the upper left edge of the heating surface is increased to make its temperature rise faster, while the temperature at the remaining locations maintains the initial rate of temperature increase, thus quickly meeting the temperature uniformity requirements of the heating surface.

[0054] In one embodiment of this application, to meet the requirement of uniform temperature of the heating surface, it is naturally necessary to use the average temperature uniformity as the optimization target, and to employ an optimization algorithm to optimize the power configuration of the heating medium in the target section at different heating stages. A preferred method for optimizing the power configuration of the heating medium in the target section at different heating stages using an optimization algorithm includes: First, using the optimal Latin hypercube design, the initial design parameters are uniformly sampled to obtain sample data, and the input set of the sample database is constructed. The initial design parameters are a range value, including multiple ratios. The ratio refers to the ratio of the power density after each power increase at the power compensation position of the heating surface in each heating stage to the power density in the original power configuration.

[0055] After the input set is constructed, the average temperature uniformity of the heating surface at each time point in different heating stages is used as the optimization objective. The average temperature uniformity of each sample data is calculated and used as the output set of the sample database.

[0056] After the input and output sets are constructed, a surrogate model is constructed using a Kriging model to establish a relationship between the power configuration optimization strategy and the average temperature uniformity. This surrogate model uses the input set of the sample database as the input quantity and the output set of the sample database as the output quantity. Based on the Kriging model, the optimal design parameter values ​​are calculated using an adaptive simulated annealing algorithm to minimize the average temperature uniformity at different heating stages. Finally, the power configuration of the heating medium in the target section is optimized at different heating stages using the optimal design parameter values.

[0057] Kriging models are used to construct surrogate models. This type of model is an interpolation function model that predicts the response values ​​of unknown sample points by performing spatially weighted interpolation on the response values ​​of known sample points. Compared to other surrogate models, Kriging models have better global convergence and higher fitting accuracy, and are now widely used. In a Kriging model, the expression for the unknown function is: In this formula, The unknown constant, also known as the global trend model, represents The expected value of the mathematical expression; It has a mean of 0 and a variance of A static random process. The covariance matrix can be expressed as: In this formula: The correlation function is only related to spatial distance and satisfies the condition that it equals 1 when the distance is 0 and equals 0 when the distance is infinite. The correlation decreases as the distance increases.

[0058] Using the multiple correlation coefficient R 2 To test the accuracy of the Kriging model, R 2 The value ranges from 0 to 1; the closer it is to 1, the higher the precision. In engineering, R is generally required to be... 2 A value greater than 0.9 indicates that R... 2 The calculation formula is as follows:

[0059]

[0060] In the above formula, This represents the actual output. To predict the output, It is the average of n actual output values.

[0061] Based on the aforementioned Kriging model, the optimal design parameter values ​​are calculated from the range of initial design parameter values ​​to minimize the average temperature uniformity of the heating surface under different heating stages using an adaptive simulated annealing algorithm.

[0062] The main idea of ​​simulated annealing is to simulate the physical annealing process of solids. However, when applied to solving optimization problems, the classical simulated annealing algorithm is often inefficient due to the need for numerous iterations. The adaptive simulated annealing algorithm used in this application improves the rate of temperature decrease T by replacing linear decrease with exponential decrease. This improvement significantly enhances the algorithm's convergence speed and gives it superior global solution capabilities. The cooling strategy of the adaptive simulated annealing algorithm is as follows:

[0063] In the above formula, Let K be the initial temperature; C be a constant coefficient used to control the cooling rate; K be the current iteration number; and D be the spatial dimension of the target problem. The adaptive simulated annealing algorithm flow is as follows: Figure 3 As shown, after it starts, an initial solution is generated randomly. i Calculate the objective function E( i Random perturbations are generated based on the Cauchy distribution to produce new solutions. i new Calculate the objective function E( i new ).

[0064] set up ,like Then accept the new solution. i new and objective function E ( i new );like If this is not true, then probability P accepts the new solution. i new and objective function E ( i new Next, determine if the termination temperature has been reached. If yes, end the process; otherwise, adjust the annealing rate according to the number of annealing cycles, perform a cooling operation, and return to the process: generate a new solution by producing a random perturbation based on the Cauchy distribution. i new Calculate the objective function E( i new ).

[0065] The ultimate goal is to achieve an average temperature uniformity, which includes:

[0066]

[0067] In the above formula, T F This represents the average value of overall temperature uniformity. T FH This is the highest temperature of the heating surface. T FL This is the lowest temperature of the heating surface. T FAVE This represents the average temperature of the heating surface. T R This represents the average radial temperature uniformity. This indicates the calculation of the standard deviation. T C The temperature at the radial center point of the heating surface. T E This represents the temperature difference at the radial edge of the heating surface.

[0068] The reason for setting such an average temperature uniformity is that the temperature uniformity requirements of semiconductor heating devices are mainly reflected in the overall temperature uniformity and radial temperature uniformity of the heating surface. In order to evaluate the temperature uniformity of the heating surface of the semiconductor heating device from different perspectives, the average overall temperature uniformity is defined. T F and radial temperature uniformity average value T R Overall temperature uniformity is average. T F Taking into account the temperature differences across all areas of the heating surface, it can intuitively reflect the overall temperature uniformity level of the heating surface. Average radial temperature uniformity. T R The main focus is on the consistency of the temperature gradient of the heating surface in different radial directions, emphasizing the uniformity of temperature change in the radial direction.

[0069] The temperature uniformity of the heating surface is improved by optimizing the power of the heating medium corresponding to the low-temperature zone of the heating surface. The same power optimization method is used for both the upper and lower heating media. Based on the heating process analysis under the original power configuration scheme of the semiconductor heating device, the power optimization method is divided into two categories according to time nodes. For example, in the heating phase of the first heating process, the power of the heating medium at the center and the upper left corner of the heating surface is increased, while the power of the remaining heating media is decreased. In other time periods, since the overall temperature uniformity fluctuation is relatively small, and the lowest temperature point of the heating surface always occurs in the upper left corner region, the power of the heating medium at the upper left corner of the heating surface edge region is only increased. Furthermore, to reduce the number of heating medium segments, when compensating the power of the heating medium in the upper left corner, only the outermost ring of the heating medium is compensated. Figure 2 (Green area); Measurements show that the low-temperature zone in the first heating stage is concentrated within a circular area with a radius of approximately 31.8 mm around the center of the heating surface. Therefore, compensation is only applied to the heating medium within this area. Figure 2 (Middle red area).

[0070] Heating medium power optimization is achieved by increasing the heating medium power density in a certain area. The ratio of the compensated power density to the original power density is defined as the initial design parameter X. The optimization design is divided into two segments, with the end of the heating phase in the first heating stage as the critical point. Before the end of the heating phase, the optimization parameters are the heating medium power density ratio X1 in the central area and X2 in the upper left corner of the edge area. After the end of the heating phase, the optimization parameter is the heating medium power density ratio X3 in the upper left corner of the edge area. The heating medium power density ratio in the remaining areas remains constant at 1 throughout the entire heating process.

[0071] Through multiple trials, the value ranges of each initial design parameter were determined to be: X1=2-5; X2=1-2; X3=1-2. To quantify the temperature uniformity level of the entire heating process, the average temperature uniformity of the entire heating process was taken as the optimization target. First, X1 and X2 were determined to minimize the average temperature uniformity during the heating stage of the first heating process, and then X3 was optimized for the subsequent heating processes.

[0072] The sample database obtained using the optimal Latin hypercube design suggests a sample size of 2×(n+1)×(n+2) in optimal Latin hypercube sampling, where n is the number of input variables. Two input variables, X1 and X2, are defined before the end of the heating phase, generating 25 sets of sample data; in the remaining phases, only one input variable, X3, is used, generating 12 sets of sample data.

[0073] X1 and X2 are the initial design parameters obtained from optimal Latin hypercube sampling. The average temperature uniformity was obtained by calculating the transient three-dimensional numerical model. To evaluate the predictive performance of the surrogate model, cross-validation was used to analyze its error. Ten sample points were randomly selected, and the predicted output of the surrogate model was compared with the actual output of the numerical calculation. The actual value and the predicted value were approximately equal. R before the end of the heating stage... 2 The value of 0.97 indicates that the aforementioned surrogate model has high prediction accuracy.

[0074] X1 has a greater impact on the average temperature uniformity than X2, and there is an interaction term X1-X2. Except for X1-X2, all other variables have a positive impact on the average temperature uniformity. An adaptive annealing algorithm was used to optimize the solution within the design space, yielding optimal design parameters of X1=2.57 and X2=1.35 before the end of the heating stage. At this point, the surrogate model predicted an average temperature uniformity of 2.70% before the end of the heating stage. To verify the accuracy of this prediction, the optimal design parameters for this stage were substituted into a transient three-dimensional numerical model for simulation calculation, yielding an average surface temperature uniformity of 2.61%, with a deviation of only 0.09% from the optimization algorithm's prediction, further demonstrating the reliability of the constructed surrogate model and the optimization algorithm's solution.

[0075] Based on the optimal parameters before the end of the heating stage, the temperature uniformity after the end of the heating stage is further optimized to obtain its R. 2The value is 0.99. This process has only one design parameter, X3, which plays a dominant role in the average temperature uniformity. As X3 increases, the average temperature uniformity first decreases and then increases. Using an adaptive annealing algorithm to optimize the solution in the sample space, the optimal design parameter after the heating stage is obtained as X3 = 1.39. At this point, the surrogate model predicts an average surface temperature uniformity of 2.05%. Substituting the optimal design parameter into the transient three-dimensional numerical model simulation, the average temperature uniformity after the heating stage is found to be 2.06%. This demonstrates the reliability of the constructed surrogate model and the solution obtained by the optimization algorithm.

[0076] After optimization, both the overall temperature uniformity and radial temperature uniformity at each moment of the entire heating process were improved. (Refer to...) Figure 4 The graph shown compares the overall temperature uniformity over time throughout the heating process. (Refer to...) Figure 5 The comparison graph showing the radial temperature uniformity change over time throughout the entire heating process demonstrates that, compared to the original power configuration scheme where the maximum overall temperature uniformity exceeded 14%, the optimized method of this application significantly improves the overall temperature uniformity. Furthermore, the average overall temperature uniformity throughout the entire heating process is reduced from 2.91% to 2.03%. In addition, the average radial temperature uniformity is reduced from 0.872℃ to 0.37℃. This demonstrates the effectiveness of the power configuration method proposed in this application.

[0077] Furthermore, this application also proposes a semiconductor heating device, which utilizes the power configuration method of the semiconductor heating device described in any one of steps 101-104 above for heating. A schematic diagram of the overall structure of the semiconductor heating device is provided below. Figure 6 As shown, it includes: an upper structure 1, a lower structure 2 and a shell 3; the upper structure 1 and the lower structure 2 are bonded together, the bonding surface is the heating surface 4, and both are provided with heating medium 5 with the same structure inside, which is used to heat the heating surface.

[0078] The upper structure 1 and the lower structure 2 are fixedly connected to the outer shell 3 through the support structure 6. The upper structure 1 and the lower structure 2 are fitted together to form a whole, and the space between them and the outer shell 3 is a vacuum environment, which forms a vacuum chamber 7. The heating medium 5 inside the upper structure 1 and the lower structure 2 both include multi-segment heating medium.

[0079] Each heating medium is connected to a power source ( Figure 6(Not shown in the diagram) Connection; any sub-heating medium in the upper structure 1 and the corresponding sub-heating medium at the same heating position in the lower structure 2 are connected to the same power source; the heating medium 5 in the upper structure 1 is distributed in a vortex pattern from the center outwards, and the heating medium 5 in the lower structure 2 is also distributed in a vortex pattern from the center outwards, overlapping with the heating medium 5 in the upper structure 1 in the vertical direction. That is, the heating media inside the two structures are symmetrically distributed with the heating surface as the plane of symmetry.

[0080] In summary, the power configuration method for the semiconductor heating device proposed in this application creatively proposes a novel power configuration method. First, it constructs a transient three-dimensional numerical model characterizing the heating process of the heating surface of the semiconductor heating device. Then, based on the transient three-dimensional numerical model, it calculates the temperature distribution law of the heating surface throughout the heating process under the original power configuration, determining the power compensation position of the heating surface. Next, based on the power compensation position of the heating surface, it segments the heating medium of the heating surface, dividing it into multiple segments. Finally, using the average temperature uniformity as the optimization objective, it employs an optimization algorithm to optimize the power configuration of the target segment heating medium at different heating stages, ensuring that the temperature uniformity of the heating surface meets the average temperature uniformity during the heating process (whether in the isothermal or heating-up stage), greatly improving the temperature uniformity of the heating surface.

[0081] The power configuration method for the semiconductor heating device proposed in this application obtains the temperature distribution of the semiconductor device at every moment during the entire heating process through transient numerical calculation, especially the temperature distribution of the most critical heating surface. This allows for the identification of low-temperature and high-temperature regions on the heating surface, determination of the temperature uniformity of the heating surface at each moment, and improvement of the temperature uniformity of the heating surface by increasing the temperature of the low-temperature region. This method has broad application prospects and high practicality.

[0082] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0083] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0084] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims. All of these forms are within the protection scope of this application.

Claims

1. A power configuration method for a semiconductor heating device, characterized in that, include: A transient three-dimensional numerical model characterizing the heating process of the heating surface of the semiconductor heating device is constructed; Based on the transient three-dimensional numerical model, the temperature distribution law of the heating surface during the entire heating process based on the original power configuration is calculated, and the power compensation position of the heating surface is determined. Based on the power compensation position of the heating surface, the heating medium of the heating surface is segmented, so that the heating medium is divided into multiple segments; Using the average temperature uniformity as the optimization objective, an optimization algorithm is employed to optimize the power configuration of the heating medium in the target section at different heating stages, so that the temperature uniformity of the heating surface during the heating process meets the average temperature uniformity.

2. The power configuration method according to claim 1, characterized in that, Constructing a transient three-dimensional numerical model characterizing the heating process of the heating surface of the semiconductor heating device includes: A numerical calculation model is established using three-dimensional transient numerical simulation technology; The semiconductor heating device is given the correct boundary conditions and a preset number of grids are divided; The transient three-dimensional numerical model is constructed by combining the numerical calculation model, the correct boundary conditions, and the preset number of grids. The correct boundary conditions are determined based on the environmental conditions and materials in which the semiconductor heating device operates.

3. The power configuration method according to claim 1, characterized in that, The calculation yields the temperature distribution pattern of the heating surface throughout the heating process based on the original power configuration, and determines the power compensation position of the heating surface, including: The calculations yielded the high-temperature and low-temperature zones of the heating surface at different heating stages throughout the entire heating process; Based on the high-temperature and low-temperature zones at each moment during different heating stages, the variation patterns of the high-temperature and low-temperature zones of the heating surface are formed; Based on the aforementioned variation pattern, the power compensation position of the heating surface is determined.

4. The power configuration method according to claim 3, characterized in that, Each heating stage includes a heating phase and a constant temperature phase; based on the aforementioned variation pattern, the power compensation position of the heating surface is determined, including: During the heating phase, the low-temperature zone and the high-temperature zone are defined as the power compensation locations of the heating surface; During the constant temperature stage, only the low temperature zone is identified as the power compensation location for the heating surface.

5. The power configuration method according to claim 4, characterized in that, Based on the power compensation position of the heating surface, the heating medium of the heating surface is segmented, resulting in multiple segments, including: During the heating phase, the center and upper left edge of the heating surface are the low-temperature zone, and the lower right edge of the heating surface is the high-temperature zone. During the constant temperature stage, the upper left edge of the heating surface is the low temperature zone; The heating medium is divided into three segments according to the center position and the upper left edge position of the heating surface. One segment corresponds to the center position of the heating surface, another segment corresponds to the upper left edge position of the heating surface, and the remaining heating medium is considered as one segment.

6. The power configuration method according to claim 5, characterized in that, The power configuration of the heating medium in the target section is optimized at different heating stages, including: During the heating phase, the two sections of heating medium corresponding to the center and upper left edge of the heating surface are optimized by increasing their power by different amounts, while the remaining heating medium is optimized by decreasing its power. During the constant temperature stage, the power of the heating medium is increased only at the upper left edge of the heating surface, while the power of the other two heating medium sections is maintained.

7. The power configuration method according to claim 1, characterized in that, Using the average temperature uniformity as the optimization objective, an optimization algorithm is employed to optimize the power configuration of the heating medium in the target section at different heating stages, including: Using the optimal Latin hypercube design, the initial design parameters are uniformly sampled to obtain sample data, and the input set of the sample database is constructed. The initial design parameters are a range value. The average temperature uniformity of the heating surface at each moment in different heating stages is taken as the optimization target. The average temperature uniformity of each sample data is calculated and used as the output set of the sample database. A proxy model is constructed using a Kriging model to establish a relationship between the power configuration optimization strategy and the average temperature uniformity. This proxy model takes the input set of the sample database as input and the output set of the sample database as output. Based on the Kriging model, the optimal design parameter values ​​for minimizing the average temperature uniformity under different heating stages are calculated using an adaptive simulated annealing algorithm. Using the aforementioned optimal design parameter values, the power configuration of the heating medium in the target section is optimized at different heating stages; The initial design parameters include multiple ratios, which are the ratios of the power density after each power increase at the power compensation position of the heating surface during each heating stage to the power density in the original power configuration.

8. The power configuration method according to claim 7, characterized in that, Based on the Kriging model, the optimal design parameter values ​​for minimizing the average temperature uniformity at different heating stages are calculated using an adaptive simulated annealing algorithm, including: Based on the Kriging model, the optimal design parameter values ​​for minimizing the average temperature uniformity of the heating surface under different heating stages are calculated from the range of initial design parameter values ​​using an adaptive simulated annealing algorithm.

9. The power configuration method according to claim 1, characterized in that, The average temperature uniformity includes: In the above formula, T F This represents the average value of overall temperature uniformity. T FH This is the highest temperature of the heating surface. T FL This is the lowest temperature of the heating surface. T FAVE This represents the average temperature of the heating surface. T R This represents the average radial temperature uniformity. This indicates the calculation of the standard deviation. T C The temperature at the radial center point of the heating surface. T E This represents the temperature difference at the radial edge of the heating surface.

10. A semiconductor heating device, characterized in that, The semiconductor heating device is heated using the power configuration method of the semiconductor heating device as described in any one of claims 1-9, and the semiconductor heating device includes: an upper structure, a lower structure, and a housing; The upper structure and the lower structure are attached to each other, with the contact surface being the heating surface, and both have heating media with the same structure inside, which are used to heat the heating surface; The upper structure and the lower structure are fixedly connected to the outer shell through a support structure. The upper structure and the lower structure are fitted together to form a whole, and the space between them and the outer shell is a vacuum environment. The heating medium inside both the upper structure and the lower structure includes: a multi-segment heating medium; Each segment of the sub-heating medium is connected to a power source; Any sub-heating medium in the upper structure and the corresponding sub-heating medium at the same heating position in the lower structure are connected to the same power source; The heating medium in the upper structure is distributed in a vortex pattern from the center of the upper structure outwards, and the heating medium in the lower structure is also distributed in a vortex pattern from the center of the lower structure outwards, overlapping the heating medium in the upper structure in the vertical direction.

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