Method and system for controlling temperature during crystal growth

Abstract

The present invention discloses a temperature control method and system for crystal growth, which includes the steps of constantly adjusting the power of each heater and simulating using software to calculate the corresponding thermal field at the solid-liquid interface and its vicinity, determining whether the solid-liquid interface and the total thermal energy are in thermal equilibrium by coupling the thermal field with a moving grid, storing the power of each heater that has reached thermal equilibrium at both the solid-liquid interface and the total thermal energy, and plotting a thermal equilibrium diagram based on the power of each heater, and controlling the temperature gradient at the solid-liquid interface by selecting the power of each heater from the plotted thermal equilibrium diagram during the crystal growth process.

Description

[Technical field]

[0001] The present disclosure relates generally to methods and systems for controlling temperature during crystal growth, and more specifically to methods and systems for controlling axial temperature gradients at solid-liquid interfaces by adjusting heater power during crystal growth. [Background technology]

[0002] With the miniaturization of the critical dimensions of semiconductor devices, semiconductor factories have increasingly higher requirements for the quality of semiconductor silicon wafers, especially for surface defects (LLS), flatness, surface metal impurities, and bulk metal impurities. In order to reduce the number of surface defects on silicon wafers, silicon wafer manufacturers try to remove the crystal defects generated during crystal growth by controlling the thermal history during the growth of silicon single crystals, thereby reducing the number of surface defects. How to remove crystal defects during the crystal growth process is currently interpreted by the theory proposed by Voronkov. Voronkov proposes that in order to remove crystal defects generated during the growth of single crystals in the crystal growth process, the axial temperature gradient of the crystal between the solid-liquid interface must maintain a certain degree of uniformity in the radial direction, and the ratio of the crystal growth rate to the axial temperature gradient at the solid-liquid interface must be controlled within a certain range. In other words, in order to remove crystal defects generated during single crystal growth in the crystal growth process, the ratio V / G of the crystal growth rate to the axial temperature gradient at the solid-liquid interface must be controlled within a certain range.

[0003] However, in the actual crystal growth process, although the crystal growth rate can be programmed, the axial temperature gradient of the crystal at the solid-liquid interface cannot be directly obtained by measurement, so other measurement methods must be developed to obtain the value in an indirect way so that it can be monitored and controlled in real time during the crystal growth process.

[0004] CN108754599A discloses a method for controlling the growth temperature of silicon single crystal based on finite element numerical simulation. In the prior art, the control method for silicon single crystal growth cannot meet the crystal temperature control, which solves the problem of crystal dislocation defects. However, the amount of calculation is too large when using finite element simulation analysis, and only the crystal within a certain axial range is simulated. In addition, the heat source is only distributed in the axial range, which is significantly different from the actual crystal growth environment, and is not suitable for direct use in temperature control during the actual crystal growth process.

[0005] CN100374628C discloses a method for producing silicon single crystals, which includes the steps of drawing a single crystal growing on a growing crystal face from a melt held in a rotating crucible according to the Zokolaski method, and rotating the single crystal and the crucible in the same direction, and supplying heat to the center of the growing crystal face by a heat source acting on the center of the growing crystal face such that the heat reaching the center of the growing crystal face per unit time is greater than the heat reaching the edge region of the growing crystal face near the center. However, the method for producing silicon single crystals in this invention does not provide a detailed description of how to adjust the power of each heater.

[0006] Therefore, there is a need for a method that can significantly reduce the amount of calculations during actual crystal growth and control the axial temperature gradient at the solid-liquid interface by adjusting the power of each heater in real time using automatic control software. Summary of the Invention [Problem to be solved by the invention]

[0007] In view of the above background, the present disclosure provides a temperature control method in a crystal growth process, comprising the steps of: constantly adjusting the power of each heater, and calculating the corresponding thermal field at and near the solid-liquid interface by simulating using software; determining whether the solid-liquid interface and the total thermal energy are both in thermal equilibrium by coupling the thermal field with a moving grid; storing the power of each heater that has brought both the solid-liquid interface and the total thermal energy into thermal equilibrium, and drawing a thermal equilibrium diagram based on the power of each heater; and selecting the power of each heater from the drawn thermal equilibrium diagram during the crystal growth process to control the temperature gradient at the solid-liquid interface. In one embodiment, the method further comprises the steps of: maintaining a constant level of the molten metal in a continuous supply manner during the crystal growth process. [Means for solving the problem]

[0008] In one embodiment, the step of selecting the power of each heater from the thermal equilibrium diagram drawn during the crystal growth process includes the step of selecting the power of each heater from the thermal equilibrium diagram drawn during the crystal growth process, which satisfies the condition of perfect crystal growth. In one embodiment, the condition of perfect crystal growth is V / G=0.112-0.142 mm 2 / min·℃, preferably V / G=0.117-0.139mm 2 / min·°C and Gc>=Ge, where V is the crystal growth rate, G is the axial temperature gradient at the solid-liquid interface, Gc is the G at the crystal center, and Ge is the G at the crystal edge.

[0009] In one embodiment, the method further includes determining a crystal growth rate in real time during the crystal growth process. In one embodiment, the heat balance diagram is a plurality of heat balance diagrams corresponding to a plurality of crystal growth rates, and selecting a power for each heater from the heat balance diagrams plotted during the crystal growth process includes selecting a power for each heater from a heat balance diagram corresponding to the real-time determined crystal growth rate in the plurality of heat balance diagrams during the crystal growth process. In one embodiment, determining the crystal growth rate in real time includes detecting the crystal growth rate in real time using a sensor. In another embodiment, determining the crystal growth rate in real time includes retrieving a preset crystal growth rate from a device associated with the crystal growth.

[0010] In one embodiment, the step of constantly adjusting the power of each heater comprises adjusting the power of two or three different heaters selected from the group consisting of side heaters, bottom heaters and top heaters at predetermined intervals or randomly. In another embodiment, the step of constantly adjusting the power of each heater comprises setting the power of one heater selected from the group consisting of side heaters, bottom heaters and top heaters to each of a predetermined number of values ​​and correspondingly adjusting the power of the other two heaters of the group at predetermined intervals or randomly.

[0011] In one embodiment, when there are multiple groups of heater powers in the thermal balance diagram that satisfy the thermal balance conditions, during the crystal growth process, the heater power of one group is randomly selected from the heater powers of the multiple groups to control the temperature gradient at the solid-liquid interface, or the heater power of one group that is closest to the current heater power overall from the heater powers of the multiple groups is selected to control the temperature gradient at the solid-liquid interface, or the heater power of one group that is closest to the current thermal field distribution of the system after controlling the heaters accordingly is selected from the heater powers of the multiple groups to control the temperature gradient at the solid-liquid interface.

[0012] In one embodiment, the thermal balance diagram is in the form of a table storing the powers of multiple groups of heaters that satisfy the thermal balance condition. In one embodiment, the thermal balance diagram is in the form of a graph formed by connecting the powers of multiple groups of heaters that satisfy the thermal balance condition. In one embodiment, in the thermal balance diagram, two of the powers of the side heaters, the powers of the bottom heaters, and the powers of the top heaters exhibit a linear relationship, and during the crystal growth process, the two of the powers of the side heaters, the powers of the bottom heaters, and the powers of the top heaters are adjusted according to the linear relationship.

[0013] The present disclosure further provides a system for controlling temperature during crystal growth, comprising a single crystal growth furnace including a heater and a continuous feeder for maintaining a constant level of the melt, a processor, a memory storing instructions that, when executed, cause the processor to perform the method for controlling temperature during crystal growth described herein, and a controller coupled to and controlling the single crystal growth furnace, the heater, the continuous feeder and the memory. In one embodiment, the system further comprises a sensor for detecting a crystal growth rate in real time. Effect of the Invention

[0014] Using the method disclosed in the present disclosure, a crystal can be grown by selecting and controlling the power of each heater directly based on a pre-obtained thermal equilibrium diagram during the crystal growth process. Furthermore, a crystal growth rate can be determined in real time, and a crystal can be grown by selecting and controlling the power of each heater directly based on a thermal equilibrium diagram corresponding to the determined crystal growth rate among a plurality of thermal equilibrium diagrams related to the crystal growth rate. Furthermore, a perfect crystal without crystal defects can be grown by selecting the power of each heater that satisfies the growth conditions of the perfect crystal from the thermal equilibrium diagram. Accordingly, a temperature gradient at the solid-liquid interface can be controlled by controlling the power of each heater directly based on a pre-calculated thermal equilibrium diagram during the crystal growth process. This avoids the need to calculate the power of each heater on-site through experiments in actual production. Moreover, the amount of calculation can be greatly reduced, and rapid and efficient control of the power of each heater can be realized, thereby improving the quality of the grown crystal.

[0015] Features, aspects, and advantages of the present disclosure will become apparent upon reading the following detailed description in conjunction with the drawings, which are briefly described below. The present disclosure includes any combination of two, three, four, or more features or elements described in the present disclosure, regardless of whether those features or elements are expressly combined or otherwise described in the specific examples described herein. The present disclosure is intended to be read in its entirety such that any separable features or elements of the present disclosure, in any of its various aspects and exemplary embodiments, are deemed combinable unless otherwise clearly specified in the context of the present disclosure. [Brief description of the drawings]

[0016] Having thus generally described the present disclosure, reference is now made to the drawings, which are not necessarily drawn to scale. [Figure 1] FIG. 2 is a diagram showing a temperature control system in a crystal growth process according to an embodiment. [Diagram 2]FIG. 4 is a diagram showing the flow direction of heat generated in each heater during the crystal growth process in the embodiment. [Diagram 3] FIG. 1 is a flowchart showing a method for controlling temperature in a crystal growth process according to an embodiment. [Figure 4] FIG. 13 is a diagram showing a thermal equilibrium diagram obtained as a result of the embodiment. [Figure 5A] FIG. 13 is a diagram showing the selection of the power of each heater to satisfy the perfect crystal growth conditions according to an embodiment. [Figure 5B] FIG. 13 is a diagram showing the selection of the power of each heater to satisfy the perfect crystal growth conditions according to an embodiment. [Figure 5C] FIG. 13 is a diagram showing the selection of the power of each heater to satisfy the perfect crystal growth conditions according to an embodiment. [Figure 5D] FIG. 13 is a diagram showing the selection of the power of each heater to satisfy the perfect crystal growth conditions according to an embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] As used herein, for example, the singular forms "1," "one," and "the" include plural referents unless the context clearly dictates otherwise. Reference may be made herein to quantitative measures, values, relationships, and the like. Unless otherwise specified, any one or more of these, but not all of these, may be absolute or approximate, taking into account possible variations in acceptable ranges, such as those due to engineering tolerances. Note that when ordinals such as "first," "second," and "third" are used to modify something in this specification, this does not necessarily mean that the thing is "first," "second," or "third" chronologically or spatially, but is merely for convenience of explanation. Also, things described with the ordinals "first," "second," or "third" may be used interchangeably without departing from the scope of this disclosure. It should be further noted that, as would be commonly understood by one of ordinary skill in the art, the term "perfect crystal" or "defect-free crystal" as used herein does not refer to an absolutely perfect crystal or a crystal without any defects, but rather to one that tolerates the presence of one or more crystal defects in a very small amount, not enough to cause a significant change in certain electrical or mechanical properties of the crystal or the resulting wafer that would degrade the performance of an electronic device made therewith.

[0018] Some embodiments of the present disclosure will now be described more fully with reference to the drawings, which show only a portion of the present disclosure and not all embodiments. Indeed, various embodiments of the present disclosure may be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein, but rather, these exemplary embodiments are provided to better convey the scope of the present disclosure to those skilled in the art.

[0019] FIG. 1 illustrates a temperature control system 100 for a crystal growth process according to an embodiment, the system 100 including a processor, a memory, a controller, and a single crystal growth furnace. The processor in the system 100 refers to a processing unit capable of executing an operating system (OS) and applications. The processor may include one or more individual processors. Each individual processor may include a single processing unit, a multi-core processing unit, or a combination thereof. The processing unit may be a main processor such as a CPU (Central Processing Unit), a peripheral processor such as a GPU (Graphics Processing Unit), or a combination thereof. The memory in the system may include various types of memory, such as volatile memory and non-volatile memory. The volatile memory may include dynamic volatile memory, for example, DRAM (Dynamic Random Access Memory) such as Synchronous DRAM (SDRAM), or some variants. The non-volatile memory device is a block addressable memory device such as NAND or NOR technology. Thus, the memory device may further include a 3D cross-point memory device, other byte addressable non-volatile memory devices, or memory devices using chalcogenide phase change materials (e.g., chalcogenide compound glasses) and other non-volatile devices developed in the future. The memory and processor in the system 100 may be communicatively coupled wirelessly or by wire. The memory in the system 100 may store computer readable instructions and data. The instructions, when executed, cause the processor in the system 100 to perform the crystal growth temperature control method described herein. The controller in the system 100 may include controller circuits or devices used for one or more memories of the system 100 and controller circuits and devices for controlling a single crystal growth furnace. The memory controller may access the memory, and the memory controller may generate control logic for memory access instructions in response to execution of operations by the processor.The controller circuit and device for controlling the single crystal growth furnace includes one or more sub-controller circuits and devices, and is used to control the crystal growth rate (V), heater power (e.g., side heater power, top heater power, and bottom heater power), crystal cooling rate, and molten metal supply amount and supply rate, etc. The controller in the system 100 is wirelessly or wired connected to the processor and memory so that it can be controlled by the processor to execute corresponding control. Although not shown in FIG. 1, any two or more of the processor, memory, controller, and single crystal growth furnace in the system 100 can be electrically or mechanically connected as necessary.

[0020] The single crystal growth furnace shown in FIG. 1 is a single crystal growth furnace for growing single crystals by the CCZ (continuous Czochralski) method. However, it should be noted that the temperature control method and system in the crystal growth process described herein are not limited to single crystal growth by the Czochralski method. In other words, the method described herein can be adapted to apply to other single crystal growth methods such as the FZ method and still fall within the scope of the present invention. The CCZ single crystal growth furnace shown in FIG. 1 includes a low thermal conductivity insulation layer 9, a graphite support 10, a heat shield (or draft tube) 6, a cooling member 4, a continuous feeder 11, a molten metal 8, an electrode foot 5, an upper heater 3, a side heater 1, a bottom heater 2, and a crystal rod 7 to be drawn.

[0021] During the single crystal growth process, the power of the top heater 3, the side heater 1, and the bottom heater 2 are each configured to generate adequate heat to maintain the melt in a molten state. The positions of the top heater 3, the side heater 1, and the bottom heater 2 in FIG. 1 are exemplary and do not necessarily mean that the top heater 3 is located at the top of the single crystal growth furnace. Similarly, the bottom heater 2 is not necessarily located at the bottom of the single crystal growth furnace. In other words, the positions of the top heater 3, the side heater 1, and the bottom heater 2 in FIG. 1 are relative. Also, for the purpose of illustration, only one pair of top heaters 3, one pair of side heaters 1, and one pair of bottom heaters 2 are shown in FIG. 1. In fact, the single crystal growth furnace may include any number of top heaters 3, side heaters 1, and bottom heaters 2. In some embodiments, one or two of the top heater 3, side heater 1, and bottom heater 2 may be omitted. Also, the top heater 3, side heater 1, and bottom heater 2 may be the same or different types of heaters, and they may have the same or different ranges of heating power.

[0022] The low thermal conductivity insulating layer 9 may be made of known conventional insulating materials such as graphite, carbon felt, and novel insulating materials such as vacuum sheet and aerogel felt. The low thermal conductivity insulating layer 9 allows the heat generated by each heater to be mainly concentrated on the molten metal, thus improving the heat utilization efficiency. To reduce the heat loss, the heat shield 6 may include multiple layers, such as an outer heat shield layer, an inner heat shield layer, and an intermediate insulating layer.

[0023] During the single crystal growth process, each heater is turned on and the power of each heater is adjusted. This allows the crystal rod 7 to be drawn out while rotating the molten metal 8. The cooling member 4 is connected to the crystal rod 7 so that the drawn crystal rod 7 is maintained below the melting point of the crystal and is not melted by heat. The cooling member 4 (e.g., water) may be continuously circulated and flowed, so that the cooling member 4, which is always at a very low temperature (e.g., 0°C), cools the crystal rod 7. In addition to water cooling or a combination of water cooling, the cooling member 4 may further use any other cooling method known or developed in the future, such as air cooling. To maintain a constant amount of the molten metal 8, the continuous feeder 11 constantly adds molten metal, granular material, or small block material to the single crystal growth furnace. The amount of molten metal added by the continuous feeder 11 each time or at regular intervals is automatically controlled by an automatic control method (e.g., PID method) well known in the industry, so that the liquid level of the molten metal can be kept substantially constant. Although not shown in detail in FIG. 1 , the single crystal growth furnace may further include other assemblies such as, but not limited to, a magnetic assembly for generating a magnetic field to increase a temperature gradient, an assembly for controlling the rotation speed of the molten metal, and sensors for measuring the crystal growth rate and the molten metal level.

[0024] In the process of single crystal growth by the Czochralski method, the success or failure of single crystal growth and the quality of the single crystal are determined by the temperature distribution of the thermal field. In a thermal field with an appropriate temperature distribution, the single crystal grows smoothly and has high quality. If the temperature distribution of the thermal field is not very reasonable, various defects are likely to occur in the single crystal growth process, affecting the quality, and in serious cases, crystal change phenomenon may occur and the single crystal may not grow. Therefore, in the crystal growth process, it is necessary to configure the most reasonable thermal field based on the growth device, and thereby ensure the quality of the single crystal produced. In the single crystal growth process by the Czochralski method, the temperature gradient is usually used to describe the temperature distribution situation of the thermal field, where the temperature gradient at the solid-liquid interface is the most crucial.

[0025] FIG. 2 is a diagram showing the flow direction of heat generated by each heater in the crystal growth process according to the embodiment. The top heater is located below the heat shield 6, as shown in FIG. 1. Here, the location of the top heater below the heat shield 6 may refer to the top heater being directly below the heat shield 6, or wrapping around the bottom or side of the inside of the device. Alternatively, only the side heater and the bottom heater may be used without using the top heater. As can be seen from FIG. 2, the heat B generated from the bottom heater flows upward through the crucible containing the molten metal and is conducted into the molten metal. The heat A generated from the side heater is conducted into the molten metal through the crucible wall along the radial direction. The heat F generated from the top heater located below the heat shield 6 is conducted to the interface of the crystal rod. A part of the heat D in the molten metal is conducted into the crystal rod via the solid-liquid interface. The other part C is conducted into the single crystal growth furnace via the surface of the molten metal. And a part of the heat E conducted into the crystal rod is further diffused into the single crystal growth furnace via the surface of the crystal rod.

[0026] To simulate the thermal field distribution in a single crystal growth furnace, the method of numerical simulation is usually used. Numerical simulation is low-cost and utilizes detailed information provided by computer calculations to support real (and expensive) experiments. Because numerical simulation provides a process close to reality, this technique can be used to easily determine the impact of any type of change (geometric dimensions, insulating materials, heaters, surrounding environment, etc.) on crystal quality. There are various software for simulating the thermal field of a single crystal furnace, including but not limited to process-oriented simulation software FEMAG, CGSIM software, COMSOL, etc. The present disclosure calculates the corresponding thermal field by constantly adjusting the power of each heater and simulating it using CGSIM software, and then selects the power of each heater that satisfies the thermal equilibrium condition from there to draw a thermal equilibrium diagram. In the actual crystal growth process, the power of each heater can be controlled based on the directly obtained thermal equilibrium diagram.

[0027] 3 is a diagram showing a flow chart of a temperature control method in a crystal growth process according to an embodiment. The idea of ​​the method is to constantly change the power of the side heater, the power of the top heater, and the power of the bottom heater, and to use software to simulate and calculate the thermal field distribution at the corresponding solid-liquid interface and its vicinity in the single crystal growth furnace, and to select a combination of the power of each heater that satisfies the thermal equilibrium condition from all combinations of the power of the side heater, the power of the top heater, and the power of the bottom heater that satisfies the thermal equilibrium condition, and to draw a thermal equilibrium diagram based on the combination. In one embodiment, the method includes the steps of setting the power of the side heater to a certain value, and constantly changing the power of the top heater and the power of the bottom heater in response thereto, and traversing the power of the top heater and the power of the bottom heater at certain intervals over a certain range, or randomly changing the power of the top heater and the power of the bottom heater over a certain range by the software to achieve a predetermined quantity, and then setting the power of the side heater to another value, and repeating the above process until the corresponding power of the top heater and the power of the bottom heater that satisfies the thermal equilibrium condition for all the predetermined number of the powers of the side heaters are calculated. In another embodiment, the method may include the steps of setting the power of the top heater or the power of the bottom heater and constantly varying the power of the remaining two heaters while leaving the other steps unchanged.

[0028] The term "thermal equilibrium diagram" referred to in the present disclosure means all combinations of the power of the top heater, the power of the bottom heater, and the power of the side heater that satisfy the thermal equilibrium condition. In one embodiment, the thermal equilibrium diagram may be a point, a line, a surface, or a body in a three-dimensional space with the power of the top heater, the power of the bottom heater, and the power of the side heater as coordinate axes, respectively. In one embodiment, the equilibrium diagram is in the form of a table, and the table lists all combinations of the power of the top heater, the power of the bottom heater, and the power of the side heater that satisfy the thermal equilibrium condition. In another embodiment, the thermal equilibrium diagram may be a plurality of thermal equilibrium diagrams associated with the crystal growth rate V.

[0029] In one embodiment, the method disclosed herein further includes the step of selecting the power of each heater from a direct heat diagram during the crystal growth process and controlling the axial temperature gradient at the solid-liquid interface based on the power of each heater from the direct heat diagram. In another embodiment, based on the current crystal growth rate, a heat diagram corresponding to the current crystal growth rate can be selected from a plurality of heat diagrams related to the crystal growth rate and controlling the axial temperature gradient at the solid-liquid interface based on the current crystal growth rate.

[0030] The specific steps of the method shown are described in detail below in conjunction with FIG. 3. Step 102 draws the geometric structure of the relevant assemblies in the single crystal growth furnace, such as the shape and dimensions of the crucible containing the molten metal, the drawn crystal rod, etc. It should be noted that the present disclosure is applicable to growing crystals of any required dimensions, such as 4 inches, 6 inches, 8 inches, 12 inches, etc. Step 104 sets the material and parameters, such as setting the material, specific heat, density, etc. of the single crystal to be grown. The method disclosed in the present disclosure for controlling the power of each heater in the single crystal growth furnace is suitable for controlling the power of each heater not only in the growth process of single crystal silicon, but also in the growth process of other crystals (e.g., sapphire, etc.). In addition, the method disclosed in the present disclosure is not limited to single crystal growth on a specific crystal plane, but can be applied to single crystal growth on any crystal plane.

[0031] In step 106, the governing equations and boundary conditions are established. When using the software to simulate the thermal field in the single crystal growth furnace, the basic model is assumed to be two-dimensional axisymmetric, that is, the temperature change at the position axisymmetric around the crystal is zero, as shown in equation (1). It is assumed that the fluid is an incompressible Newtonian fluid and the gas satisfies the ideal gas equation of state, and according to the heat conduction theory and the fluid dynamics theory, the coupled calculation of the thermal field and the flow field is used, where the heat source in the thermal field is an individual heater, and the thermal energy Q generated thereby generates resistance heat in the form of heat conduction (equation (2)). The resistance heat is transferred to the entire model through the boundary equation of surface-to-surface thermal radiation. The boundary equation includes the crystal surface (equation (3)), the molten metal surface (equation (4)), and other surfaces (equation (5)). Each solid and fluid transfers thermal energy (equation (6)) inside the object through heat conduction. It is assumed that the model periphery is used for heat dissipation of the flow passage and maintains a constant temperature of 300K (equation (7)). TIFF0007675742000001.tif67170

[0032] The method of Figure 3 then proceeds to step 108, where a grid is created or divided, for example, by methods well known to those skilled in the art. Step 110 adjusts the power of the side heaters and solves the thermal field. In one embodiment, when the method of Figure 3 is run for the first time, step 110 includes setting the power of each heater (including setting the power of the side heaters, the power of the top heater, and the power of the bottom heater) and solving the thermal field at and near the corresponding solid-liquid interfaces, and when step 110 is run again, the power of the side heaters is adjusted and the thermal field at and near the corresponding solid-liquid interfaces is solved.

[0033] The continuous feeder 11 constantly adds the molten metal 8 into the single crystal growth furnace to maintain a constant amount of the molten metal in the crucible. However, in the actual crystal growth process, the interface between the crystal rod and the liquid surface of the molten metal is dynamically changing. The moving boundary is related to the Stefan problem. For the Stefan boundary problem, the solid-liquid equation and the surface-surface equation are formulated, and the ambient temperature set point can be obtained by iterative iteration. In step 114, the thermal field and the flow field are coupled to each other by the energy equation (Equation (8)), and in step 112, the thermal field at the solid-liquid interface and its vicinity is solved by mutual iteration of the boundary equation (Stefan), the total thermal energy Q, and the crystal growth velocity V. A limit can be set on the number of iterations for the iterations in step 112, and if the limit is exceeded but convergence is not achieved, the method proceeds to step 122. TIFF0007675742000002.tif19170

[0034] After solving the coupled equilibrium of the thermal and flow fields of the global model, in step 116, it is determined whether the calculation has converged. If the convergence value has not been obtained, the method proceeds to step 122 to modify the grid and set a new convergence condition. If the convergence value has been calculated, the temperature field distribution and the velocity field distribution are obtained. Similarly, the shape of the solid-liquid interface and the power distribution can be obtained. The method proceeds to step 118 to determine whether both the solid-liquid interface and the total thermal energy are both in equilibrium. If it is determined in step 118 that both the solid-liquid interface and the total thermal energy are in equilibrium, the method proceeds to step 120 to store the power of each heater and analyze the results. In one embodiment, in step 120, the obtained power of each heater can be stored in a memory in the system 100 in the form of a table. In another embodiment, in step 120, the obtained power of the multiple groups of heaters is analyzed and the discipline of the power of each heater that satisfies the thermal equilibrium condition is statistically calculated, including the range of the power of each heater, the discipline of the change of the power of the other heaters when the power of one heater changes, including the range of the power of each heater, the linear change, the exponential change, or the unrelated change. In another embodiment, the result statistics and analysis may be performed by a processor in the system 100 or by other computing devices external to the system 100. In yet another embodiment, the result statistics and analysis may utilize data analysis methods and models commonly used in statistics, including machine learning. In one embodiment, in step 120, the result statistics and analysis includes storing the thermal field distribution at and near the solid-liquid interfaces, including the axial temperature gradients of the corresponding solid-liquid interfaces corresponding to the power of each heater that satisfies the thermal equilibrium condition of the system, including the edge temperature gradient Ge and the center temperature gradient Gc along the radial direction of the crystal. If, in step 118, it is determined that one or both of the solid-liquid interfaces and the total thermal energy are not in equilibrium, the top heater power and the bottom heater power are readjusted, and the above process is repeated until the side heater power has traversed a predetermined range or number of top heater power and bottom heater power based on a certain rule (e.g., at a certain interval or randomly). After this, the side heater power is set to another value, and the above process is repeated.

[0035] It should be noted that the method of the flowchart in FIG. 3 is merely illustrative, and one or more steps of the method may be omitted or performed multiple times. Also, the method of the flowchart in FIG. 3 is merely illustrative and not exhaustive, and the steps may be divided into multiple substeps and performed, and additional steps may be present. Also, the method of the flowchart in FIG. 3 calculates the power of each heater that satisfies the thermal equilibrium condition by setting the power of the side heater to a certain value and constantly changing the power of the top heater and the power of the bottom heater, but in other embodiments, the power of each heater that satisfies the thermal equilibrium condition of the system may be calculated by setting one or two of the power of the side heater, the power of the top heater, and the power of the bottom heater, and constantly changing the remaining two or one. Also, in other embodiments, any of the side heater, the top heater, and the bottom heater may be omitted.

[0036] FIG. 4 is a diagram showing a thermal balance diagram obtained as a result of the embodiment. In the present disclosure, the power of the side heater is set to 10, 30, 50, 70, and 90 KW, respectively, and the power of the top heater and the power of the bottom heater are constantly changed to calculate the thermal balance diagram. When the power of the side heater is set to 10 KW, the power of the top heater and the power of the bottom heater are adjusted so that both the solid-liquid interface and the total thermal energy are in thermal equilibrium. Points that satisfy the thermal equilibrium condition are drawn on a plane with the power of the top heater and the power of the bottom heater as the abscissa and ordinate, respectively, and are connected to a line as shown by line A in FIG. 4. The other lines B, C, D, and E are obtained by sequential analogy.

[0037] As can be seen from FIG. 4, lines A, B, C, D, and E are straight lines that are almost parallel to each other. In other words, when the power of the side heater is set to a certain value, the power of the top heater and the power of the bottom heater that satisfy the thermal equilibrium condition exhibit a linear relationship. The power of the side heater is constantly adjusted to obtain a thermal equilibrium region such as the region surrounded by the dotted line in the lower left corner of FIG. 4. In other words, when the power of the top heater and the power of the bottom heater are within the thermal equilibrium region, the crystal can be grown smoothly. Note that what is calculated in the experiment is the combination of the power of each heater that satisfies the thermal equilibrium condition, that is, the points indicated by different symbols in the thermal equilibrium region shown in FIG. 4. The boundary of the thermal equilibrium region is estimated from the distribution tendency embodied in many points that satisfy the thermal equilibrium condition calculated in the thermal equilibrium diagram. The boundary surrounding the thermal equilibrium diagram is composed of four dotted parts. The dotted parts that overlap with the abscissa axis (i.e., the power of the bottom heater) indicate that the power of the top heater is zero. The dotted line overlapping the ordinate axis (i.e., the power of the top heater) indicates that the power of the bottom heater is zero. The region that continues to extend beyond the topmost dotted line (overlapping the solid condensation line) is the condensation region. This indicates that the power of the top heater is too high, but the power of the bottom heater is too low, and the temperature is too low, the energy of the molten metal is insufficient, the bottom part hardens first, the thermal equilibrium of the crystal growth region is disturbed, and it is harmful to the crystal growth environment. The topmost dotted line is inclined upward. This means that the higher the power of the side heater (i.e., the closer to the bottom left of the thermal equilibrium region), the lower the power of the ultimate bottom heater that satisfies the thermal equilibrium condition. This also coincides with the experience of adjusting the power of each heater in the actual crystal growth process. The rightmost dotted line indicates that the power of the side heater is zero. Since the side heater is the main heater and supports the energy source of the entire system, condensation will occur if it continues to extend beyond the rightmost dotted line, and the condensation will start from the side.

[0038] In order to verify whether the points of lines A, B, C, D, and E in the heat balance diagram shown in FIG. 4 can achieve the heat balance of the system, in the present disclosure, when the power of the top heater is fixed to 10KW and the power of the side heater is 10, 30, 50, 70, and 90KW, the power of the bottom heater that satisfies the heat balance condition is simulated and calculated by the method shown in FIG. 3. The power of the side heater, the power of the bottom heater, and the power of the top heater that satisfies the heat balance condition are specifically obtained as 90-7-10, 70-30-10, 50-54-10, 30-77-10, and 10-102-10. Among these power combinations, the power of the bottom heater is almost the same as the result of the heat balance diagram shown in FIG. 4 (i.e., the power of the bottom heater corresponding to the intersection points (not shown) between the horizontal line (not shown) where the power of the top heater is fixed to 10KW and the lines A, B, C, D, and E in the heat balance diagram). Therefore, in an actual crystal growth process, in order to grow a crystal smoothly, the power of each heater can be directly selected or adjusted based on the thermal balance diagram, or the power of each heater can be directly selected or adjusted based on the (e.g., linear) relationship of the power of each heater that achieves the thermal equilibrium condition shown in the thermal balance diagram. For example, even if the thermal equilibrium of the system is not achieved with the power of each heater selected according to the balance diagram or the discipline shown therein due to an error, it is not necessary to randomly try or guess the selection of the power of each heater over a large range of the power of each heater over a long period of time, but only to fine-tune the power of each heater selected or near one or two of them, which can greatly save the amount of calculation and the calculation time, and can grow a crystal with better quality.

[0039] In the present disclosure, the heat balance diagram is calculated by setting the power of the side heater to 10, 30, 50, 70, and 90KW and constantly changing the power of the top heater and the bottom heater, but in other embodiments, the heat balance diagram can be calculated by setting the power of the side heater to another value and constantly changing the power of the top heater and the bottom heater. In other words, there are other lines that are approximately parallel to lines A, B, C, D, and E in the heat balance diagram shown in Figure 4, and points on these lines also satisfy the heat balance condition.

[0040] It should be noted that the thermal equilibrium diagram shown in FIG. 4 is obtained when the crystal growth rate is 0.6 mm / min. In other embodiments, the crystal growth rate may be other values, and a similar thermal equilibrium diagram can be obtained. Thus, in one embodiment, the thermal equilibrium diagram may be a plurality of thermal equilibrium diagrams associated with a plurality of crystal growth rates, and thus, during the crystal growth process, the thermal equilibrium diagram corresponding to the current crystal growth rate can be selected from the plurality of thermal equilibrium diagrams, and the heaters can be controlled by selecting the power of each heater from the thermal equilibrium diagram. Note that in FIG. 4, for convenience of explanation, the thermal equilibrium is shown as one thermal equilibrium area on a two-dimensional plane and several lines fixed by the power of the side heaters. However, in other embodiments, the thermal equilibrium diagram may have other formats, such as a table format, a point, a line, a surface, a body, or the like, or other object format in three-dimensional space with the power of each heater as the coordinate axis.

[0041] In the actual crystal growth process, the power of each heater can be selected according to the thermal equilibrium diagram in Figure 4 to ensure crystal growth. However, to grow a perfect crystal, there are requirements for the crystal growth rate V and the temperature gradient G at the solid-liquid interface. Generally, the theoretical value of V / G (C crit =2.1*10 ‐5 cm 2 / s·K=0.126mm 2 / min·℃) is the window region for perfect crystallography, that is, the V / G value range is 0.112-0.142 mm 2 / min·℃ and Gc>=Ge. If these two conditions are met, perfect crystals can be grown. Preferably, 0.92-1.1 times the theoretical V / G value is the window region for perfect crystals, that is, the range of V / G values ​​is 0.117-0.139 mm. 2 / mm·℃. In the actual crystal growth process, the crystal growth rate V=0.4-0.8 mm / min. This range is the crystal growth rate range that can grow crystals stably, reliably, and smoothly in most crystal growth systems currently. In other and future developed crystal growth systems, there may be crystal growth rates in other ranges. For example, the crystal growth rate can be higher so that the crystals can be grown more quickly and efficiently.

[0042] When the crystal growth rate ranges from V=0.4-0.8 mm / min, in order to grow perfect crystals, 7.14 K / mm>=G>=2.8 K / mm, i.e. 7140 K / m>=G>=2800 K / m, and at the same time Gc>=Ge must be satisfied. In other embodiments, the crystal growth rate is in other ranges, and the G value range is accordingly in the V / G value range of 0.112-0.142 mm. 2 / min·℃ or preferably V / G value range 0.117-0.139mm 2 / min·℃ and at the same time, Gc >= Ge.

[0043] Here, referring to Figs. 5A-5D, a method for further selecting the power of each heater that satisfies the perfect crystal growth condition from the thermal balance diagram shown in Fig. 4 that satisfies the thermal balance condition of the system will be described. Based on the power of each heater that satisfies the thermal balance condition of the system, the corresponding thermal field distribution and the axial temperature gradient Ge of the edge along the radial direction of the corresponding crystal and the axial temperature gradient Gc of the crystal center can be calculated using the computer simulation method shown in Fig. 3. In one embodiment, the axial temperature gradients including Ge and Gc corresponding to the power of each group of heaters that satisfies the thermal balance condition recorded in step 120 in Fig. 3 can be directly retrieved from the memory. Calculate whether the axial temperature gradient satisfies the above-described G value window for growing a perfect crystal, which is associated with the current crystal growth rate, and the condition of Gc>=Ge. If so, adjust and control each heater based on the power of the corresponding group of heaters to grow a perfect crystal. The calculation can be performed by a processor in the system 100 or a processor or other computing device outside the system 100. Note that due to range limitations, the G value window for a perfect crystal shown at the top of Figures 5A-5D may only be a portion of the total window.

[0044] When the power of the side heater, the power of the bottom heater and the power of the top heater are 10-102-10KW respectively, the condition for growing perfect crystals at the same time can be met, as shown in FIG. 5A. When the power of the side heater, the power of the bottom heater and the power of the top heater are 30-80-8KW respectively, the condition for growing perfect crystals at the same time can be met, as shown in FIG. 5B. When the power of the side heater, the power of the bottom heater and the power of the top heater are 50-70-1KW respectively, the condition for growing perfect crystals at the same time can be met, as shown in FIG. 5C. When the power of the side heater, the power of the bottom heater and the power of the top heater are 70-47-4KW respectively, the condition for growing perfect crystals at the same time can be met, as shown in FIG. 5D. Based on the power of the heaters of each group above, perfect crystals can be grown. It should be noted that there may be other groups of heater powers that meet the condition for growing perfect crystals. In addition, in an actual crystal growth process, when there are multiple groups of heater powers that satisfy the thermal equilibrium condition or the condition for growing a perfect crystal, the temperature gradient at the solid-liquid interface can be controlled by randomly selecting the heater power of one group from among them, or by selecting the optimal heater power of one group from among them. In one embodiment, the optimal heater power of one group may refer to the heater power of one group that is closest to the current heater power overall so that the power of each heater can be converted to the desired power most quickly. In one embodiment, the optimal heater power of one group refers to the heater power of the system that is closest to the current thermal field distribution (specifically, the solid-liquid interface and the thermal field in the vicinity thereof) after controlling the heaters based on the optimal heater power, so that the thermal field distribution of the system is least changed when the current heater power is adjusted to the heater power of the group. In other embodiments, the optimal heater power of one group can satisfy other limiting conditions.

[0045] It will be apparent to those skilled in the art that modifications and variations made based on the method and system of the present invention are perceptible and fall within the scope of the present invention. The drawings are exemplary. The specific embodiments described above with reference to the drawings are merely illustrative and are not intended to limit the scope of the present invention, which is limited by the appended claims.

Claims

1. A step of constantly adjusting the power of two or three heaters among the top heater, the bottom heater, and the side heater, and calculating the corresponding thermal field at the solid-liquid interface and its vicinity by simulating the thermal field during the silicon crystal growth process using software, wherein the top heater is a heater located on the top surface of the molten metal, the bottom heater is a heater located at the bottom of the molten metal, and the side heater is a heater located on the side of the molten metal; determining whether or not both the solid-liquid interface and the total thermal energy are in thermal equilibrium by coupling the thermal field with the mesh; storing the electric power of each heater that brings both the solid-liquid interface and the total thermal energy into thermal equilibrium, and drawing a thermal equilibrium diagram based on the electric power of each heater; and controlling the temperature gradient at the solid-liquid interface by selecting the power of each heater from the thermal equilibrium diagram drawn during the crystal growth process; Further comprising a step of determining a crystal growth rate in real time during the crystal growth process, The temperature control method for a crystal growth process, wherein the thermal equilibrium diagram is a plurality of thermal equilibrium diagrams corresponding to a plurality of crystal growth rates, and the step of selecting the power of each heater from the thermal equilibrium diagrams drawn during the crystal growth process includes the step of selecting the power of each heater from the thermal equilibrium diagram corresponding to the crystal growth rate determined in real time among the plurality of thermal equilibrium diagrams during the crystal growth process.

2. 2. The method according to claim 1, further comprising the step of maintaining a constant level of the molten metal by a continuous supply method during the crystal growth process.

3. 2. The method according to claim 1, wherein the step of selecting the power of each heater from the thermal equilibrium diagram drawn during the crystal growth process includes the step of selecting the power of each heater from the thermal equilibrium diagram drawn during the crystal growth process that satisfies the conditions for perfect crystal growth.

4. The condition for perfect crystal growth is V / G = 0.112 mm ２ / min・℃-0.142mm ２ / min ° C. and Gc >= Ge, where V denotes the crystal growth rate, G denotes the axial temperature gradient at the solid-liquid interface, Gc denotes G at the crystal center, and Ge denotes G at the crystal edge.

5. The condition for perfect crystal growth is V / G = 0.117 mm ２ / min・℃-0.139mm ２ / min ° C. and Gc >= Ge, where V denotes the crystal growth rate, G denotes the axial temperature gradient at the solid-liquid interface, Gc denotes G at the crystal center, and Ge denotes G at the crystal edge.

6. 10. The method of claim 1, wherein determining the crystal growth rate in real time comprises utilizing a sensor to detect the crystal growth rate in real time.

7. The method according to any one of claims 1 to 5, wherein the step of constantly adjusting the power of two or three of the top heater, bottom heater and side heater comprises adjusting the power of two or three different heaters selected from the group consisting of the side heater, the bottom heater and the top heater at predetermined intervals or randomly.

8. The method according to any one of claims 1 to 5, wherein the step of constantly adjusting the power of two or three of the top heater, bottom heater and side heater comprises setting the power of one heater selected from the group consisting of the side heater, the bottom heater and the top heater to each of a predetermined number of values, and adjusting the power of the other two heaters of the group at predetermined intervals or randomly.

9. 6. The method according to claim 1, wherein, when there are multiple groups of heater powers that satisfy the thermal equilibrium condition in the thermal equilibrium diagram, the heater power of one group is randomly selected from the multiple groups of heater powers during the crystal growth process to control the temperature gradient at the solid-liquid interface.

10. 6. The method according to claim 1, wherein, when there are multiple groups of heater powers that satisfy the thermal equilibrium condition in the thermal equilibrium diagram, during the crystal growth process, the heater power of one group that is closest to the current heater power overall from the heater powers of the multiple groups is selected to control the temperature gradient at the solid-liquid interface.

11. The method according to any one of claims 1 to 5, wherein, in the thermal equilibrium diagram, when there are multiple groups of heater powers that satisfy the thermal equilibrium condition, during the crystal growth process, the method comprises selecting from the multiple groups of heater powers, the group of heater powers that makes the thermal field distribution of the system closest to the current thermal field distribution after controlling each heater accordingly, and controlling the temperature gradient at the solid-liquid interface.

12. The method according to any one of claims 1 to 5, wherein the thermal balance diagram is in the form of a table that stores the powers of a plurality of groups of heaters that satisfy a thermal balance condition.

13. The method according to any one of claims 1 to 5, wherein the format of the heat balance diagram is a graph formed by connecting the electric power of a plurality of groups of heaters that satisfy a heat balance condition.

14. A method according to any one of claims 1 to 5, wherein in the thermal balance diagram, two of the power of the side heater, the power of the bottom heater and the power of the top heater exhibit a linear relationship, and during the crystal growth process, the two of the power of the side heater, the power of the bottom heater and the power of the top heater are adjusted according to the linear relationship.

15. a single crystal growth furnace including a heater and a continuous feeder for keeping the liquid surface position of the molten metal constant; A processor; a memory on which are stored instructions which, when executed, cause the processor to carry out a method according to any one of claims 1 to 14; a controller for controlling the single crystal growth furnace, its heater, continuous feeder and memory by coupling with them; A temperature control system for the crystal growth process including:

16. 16. The system of claim 15, further comprising a sensor for detecting the crystal growth rate in real time.

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