Automatic calibration method and automatic calibration system

Abstract

The invention discloses an automatic calibration method and an automatic calibration system. An automatic calibration method according to at least one example embodiment may include: receiving at least one internal equation, input data associated with a semiconductor device design, and hardware data associated with the semiconductor device design; generating at least one approximation function based on the input data and the hardware data; determining at least one loss function based on the generated at least one approximation function; determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation such that a value of the at least one loss function is 0; and selectively adjusting the semiconductor device design based on the determined at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation.

Description

[0001] This application claims the benefit of priority to Korean Patent Application No. 10-2023-0170035, filed on November 29, 2023, with the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference in its entirety. Technical Field

[0002] Various example embodiments of the inventive concept relate to an automatic calibration method, apparatus, system, and / or non-transitory computer-readable medium, etc. More specifically, one or more of the example embodiments of the inventive concept relate to an automatic calibration method, apparatus, system, and / or non-transitory computer-readable medium capable of improving and / or optimizing at least one parameter of at least one internal equation without performing a technology computer-aided design (TCAD) simulation. Background Art

[0003] A design simulator (such as a TCAD simulator) can be used to predict the characteristics of a manufactured semiconductor in a field such as semiconductor manufacturing. To accurately predict the characteristics of a semiconductor design through a design simulator, output data indicating the characteristics of the semiconductor design can be observed by variably inputting input data indicating the layout, ion implantation, etc. of the semiconductor design into the design simulator, and calibration of the semiconductor design for matching the output data with target output data can be performed. However, because the semiconductor manufacturing process is complex, the number of influencing factors to be considered for simulation increases, making it difficult to perform calibration manually. Although deep learning-based calibration can be used to solve this difficulty, deep learning-based calibration expects and / or requires a large amount of TCAD data, resulting in additional computational costs and expenses. Summary of the Invention

[0004] Various example embodiments of the inventive concept provide a method, apparatus, system, and / or non-transitory computer-readable medium capable of directly solving at least one equation used in TCAD and improving and / or optimizing parameters related to at least one internal equation without performing a technology computer-aided design (TCAD) simulation.

[0005] Various example embodiments of the inventive concept also provide a method, apparatus, system, and / or non-transitory computer-readable medium capable of simultaneously determining several solutions of at least one parameter related to at least one internal equation without performing a TCAD simulation.

[0006] According to at least one example embodiment of the inventive concept, an automatic calibration method is provided.

[0007] The method includes: receiving at least one internal equation, input data associated with a semiconductor device design, and hardware data associated with the semiconductor device design; generating at least one approximation function based on the input data and the hardware data; determining at least one loss function based on the generated at least one approximation function; determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation such that the value of the loss function is 0; and selectively adjusting the semiconductor device design based on the determined at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation.

[0008] According to at least one exemplary embodiment of the inventive concept, an automatic calibration system is provided.

[0009] The system includes: a non-transitory storage medium storing computer-readable instructions; and a processing circuit configured to: execute the computer-readable instructions to perform an automatic calibration method.

[0010] According to at least one exemplary embodiment of the inventive concept, a non-transitory computer-readable storage medium is provided.

[0011] The non-transitory computer-readable storage medium stores computer-readable instructions that, when executed by a processing circuit, cause the processing circuit to: receive at least one internal equation, input data associated with a semiconductor device design, and hardware data associated with the semiconductor device design; generate at least one approximation function based on the input data and the hardware data; determine at least one loss function based on the generated at least one approximation function; determine at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation such that the value of the loss function is 0; and selectively adjust the semiconductor device design based on the determined at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation.

[0012] According to at least one exemplary embodiment of the inventive concept, an automatic calibration system is provided.

[0013] The system includes a processing circuit configured to: receive at least one internal equation associated with a semiconductor device design and hardware data associated with the semiconductor device design as inputs; generate at least one approximation function based on the hardware data; generate at least one loss function based on the at least one approximation function; determine at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation such that the generated at least one loss function is 0; and selectively adjust the semiconductor device design based on the determined at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Various exemplary embodiments of the inventive concept will be more clearly understood from the following detailed description in conjunction with the accompanying drawings.

[0015] Figure 1A is a flowchart schematically showing an auto - calibration method according to at least one exemplary embodiment of the inventive concept.

[0016] Figure 1B 、 Figure 1C and Figure 1D are flowcharts schematically showing operations of the auto - calibration method of Figure 1A according to some exemplary embodiments, respectively.

[0017] Figure 2A and Figure 2B is a flowchart showing a calibration method according to a comparative example.

[0018] Figure 3 is a flowchart showing a calibration method according to at least one exemplary embodiment.

[0019] Figure 4 is a block diagram showing an auto - calibration system according to at least one exemplary embodiment.

[0020] Figure 5 is a block diagram showing an auto - calibration system according to at least one exemplary embodiment.

[0021] Figure 6 is a flowchart showing a function used in an auto - calibration method and system according to at least one exemplary embodiment.

[0022] Figures 7A to 7C is a flowchart showing an auto - calibration method according to at least one exemplary embodiment.

[0023] Figure 8 is a flowchart showing an auto - calibration method according to at least one exemplary embodiment.

[0024] Figure 9 is a detailed flowchart showing an auto - calibration method according to at least one exemplary embodiment.

[0025] Figure 10 is a detailed flowchart showing an auto - calibration method according to at least one exemplary embodiment.

[0026] Figure 11 is a detailed flowchart showing an auto - calibration method according to at least one exemplary embodiment.

[0027] Figure 12 is a block diagram showing a computer system according to at least one exemplary embodiment. Detailed implementation manners

[0028] In the following, various exemplary embodiments will be described with reference to the accompanying drawings.

[0029] Figure 1A is a flowchart schematically showing an automatic calibration method according to at least one exemplary embodiment of the inventive concept. Figure 1A The automatic calibration method of may be executed by the automatic calibration system to be described below, but is not limited thereto, and the automatic calibration method may be executed on other comparable devices and / or systems, etc. According to at least one exemplary embodiment, Figure 1A The automatic calibration method of may be executed by at least one processor (e.g., a processing circuit) of the automatic calibration system to be described below, but is not limited thereto. As Figure 1A shown in, the operations executed by the automatic calibration system may include a plurality of operations S100, S200, and / or S300, etc., but are not limited thereto.

[0030] Referring to Figure 1A operation S100 of, the internal equation and the hardware data may be input into the automatic calibration system.

[0031] The term "internal equation" may represent any one of various equations used in a technology computer-aided design (TCAD) simulator software. For example, the internal equation may be a partial differential equation (PDE), etc., but the exemplary embodiment is not limited thereto.

[0032] The term "hardware data" may represent the result data obtained through actual experiments, and may be output when the input data is input into the relevant equations related to the internal equation, design requirements, user requirements, etc. The hardware data may represent both the input data and the result data, or may only represent the result data. For example, the term "input data" may include information about the layout, ion implantation, etc., time conditions, depth conditions, etc. of the semiconductor device design and / or information related to the layout, ion implantation, etc., time conditions, depth conditions, etc. of the semiconductor device design, but is not limited thereto. As another example, the term "result data" may represent the electrical / structural characteristics of the semiconductor device and / or product, etc. and / or information related to the electrical / structural characteristics of the semiconductor device and / or product, etc.

[0033] The term "calibration" may represent adjusting one or more parameters (e.g., variables, etc.) included in one or more internal equations such that when the input data is input into one or more internal equations, a desired target value is output. Optionally or additionally, the term "calibration" may represent adjusting one or more parameters included in at least one approximation function such that when the input data is input into at least one approximation function, a desired target value is output.

[0034] The term "associated equation" may represent at least one accurate equation represented as a result of solving an internal equation.

[0035] The term "deep neural network" may represent at least one network model using at least one deep learning algorithm. For example, a deep neural network model, a deep neural network, a neural network, a machine learning network, an artificial intelligence network, etc. may have the same meaning and may be used interchangeably.

[0036] Referring to Figure 1A In operation S200, the automatic calibration system may calibrate at least one parameter of at least one internal equation and solve at least one internal equation based on at least one approximation function approximated to satisfy hardware data and the internal equation.

[0037] The automatic calibration system may generate an approximation function that can satisfy hardware data (and / or design requirements, user requirements, etc.). According to at least one exemplary embodiment, the approximation function may be approximated by a neural network or the like. According to at least one exemplary embodiment, the approximation function may be generated such that the approximation function uses input data as at least one variable and includes at least one deep learning parameter.

[0038] The automatic calibration system may learn and / or determine at least one parameter of the internal equation and the approximation function based on the input internal equation, hardware data, and / or approximation function, and may perform calibration by adjusting, improving, and / or optimizing the parameters. Additionally, through calibration, the internal equation may be solved, and the semiconductor device design may be selectively adjusted, improved, and / or optimized based on the calibrated and / or solved internal equation, etc.

[0039] Referring to Figure 1A In operation S300, the automatic calibration system may construct a selectively adjusted, improved, and / or optimized TCAD environment by applying the parameters selectively adjusted, improved, and / or optimized in operation S200 to the TCAD emulator, or in other words, selectively adjust, improve, and / or optimize the semiconductor device design.

[0040] In the automatic calibration method according to at least one example embodiment, the parameters of the internal equation may be selectively adjusted, improved and / or optimized without using a TCAD simulator (e.g., without performing a TCAD simulation). The automatic calibration method according to at least one example embodiment may be based on an internal equation including a PDE and a deep neural network. The automatic calibration method according to at least one example embodiment of the inventive concept may perform calibration of a semiconductor device design by directly solving a TCAD internal equation described as a PDE using a deep neural network and simultaneously adjusting, improving and / or optimizing the parameters of the PDE that satisfies the hardware data. Because the automatic calibration system according to at least one example embodiment of the inventive concept is not based on data, the generation of TCAD data for creating and / or generating a deep neural network is not required. According to at least one example embodiment of the inventive concept, because the deep neural network is based on the PDE, a TCAD simulation for updating is not necessary. In addition, because the adjustment, improvement and / or optimization starts from a wide parameter region, global optimization (e.g., global adjustment, global improvement, etc.) of the semiconductor device design may be feasible.

[0041] Figure 1B , Figure 1C and Figure 1D are schematically illustrating the Figure 1A Flow chart of the operation of the automatic calibration method.

[0042] Figure 1B It is shown Figure 1A 2 is a flowchart of an example of operation S100 of the automatic calibration method, but example embodiments are not limited thereto.

[0043] Referring to operation S100, an internal equation related to a semiconductor device design and hardware data related to a semiconductor device design may be input to an automatic calibration system. Figure 1B , the approximate function may be initialized in operation S100a. By doing so, a neural network function (NN) of the approximate function may be generated S100a1.

[0044] In operation S100b, a PDE may be input. According to at least one example embodiment, the PDE may correspond to an internal equation. In operation S100b1, the input PDE may be processed, and thus, a calibration parameter S100b2 using the PDE and a first loss function S100b3 may be output.

[0045] In operation S100c, at least one boundary condition may be input. The at least one boundary condition may be associated with the PDE. In operation S100c1, the input at least one boundary condition may be processed to output a third loss function S100c2.

[0046] In operation S100d, hardware data can be input. In operation S100d1, the hardware data can be processed to output a second loss function S100d2.

[0047] Figure 1C is a flowchart showing an example of operation S200 of an Figure 1A automatic calibration method according to at least one example embodiment.

[0048] Referring to operation S200, the internal equation can be solved by calibrating at least one parameter of the internal equation based on an approximation function approximated to satisfy the hardware data and / or internal equation, etc.

[0049] The neural network function S100a1, the first loss function S100b3, the calibration parameter S100b2, the second loss function S100d2, and the third loss function S100c2 output in operation S100 can be used to calculate and / or determine the final loss value. The neural network function S100a1 used herein can undergo an approximation function calculation operation S200a and learn and / or determine the approximation function in operation S200b.

[0050] A loss value calculation operation S200c can be performed such that the sum of all loss values is 0. The loss value S200d obtained by performing the loss value calculation operation S200c can be processed by applying a gradient descent algorithm to the loss value S200d in operation S200e, but the example embodiment is not limited thereto.

[0051] If the process is sufficiently iterated (Yes in operation S200f), then the adjusted, improved, and / or optimized neural network function S200g and the adjusted, improved, and / or optimized calibration parameter S200h can be output; otherwise, if the process is not sufficiently iterated (No in operation S200f), then the loss function can be recalculated and / or determined by applying another calibration parameter to the loss function.

[0052] Figure 1D is a flowchart showing an example of operation S300 of an Figure 1A automatic calibration method according to at least one example embodiment.

[0053] Referring to operation S300, the adjusted, improved, and / or optimized parameters can be applied to TCAD to construct a selectively adjusted, improved, and / or optimized TCAD environment, or in other words, selectively adjust, improve, and / or optimize the semiconductor device design. Referring to Figure 1D, a simulation can be performed in operation S300b by using adjusted, improved, and / or optimized calibration parameters S300a. The performed simulation can be a TCAD simulation, but is not limited thereto. As a result of performing the simulation in operation S300b, a simulation result S300c with applied calibration can be output (e.g., a selectively adjusted, improved, and / or optimized semiconductor device design that meets the consistency S300d).

[0054] More specific examples will be described in detail below with reference to the accompanying drawings.

[0055] Figure 2A and Figure 2B are flowcharts showing calibration methods according to comparative examples. Referring to Figure 2A and Figure 2B , an example embodiment of adjusting parameters by using TCAD data generated by a TCAD simulator is shown.

[0056] Figure 2A and Figure 2B The TCAD simulators 20 and 21 shown in Figure 2A and Figure 2B can be physics-based computational simulators. The calibration methods shown in Figure 2A and Figure 2B can be methods for predicting performance by approximating experiments in fields that require high experimental costs (such as semiconductor manufacturing, etc.). In order to make a semiconductor product have desired electrical / structural characteristics, a designer of the semiconductor product can set desired and / or necessary parameters through a design simulator (e.g., a TCAD simulator) to obtain target output data including information about the desired electrical / structural characteristics. For accurate approximation and performance prediction, calibration between simulation and experiment is desired and / or necessary. However, in order to enhance and / or improve the consistency of simulations of complex manufacturing processes, the TCAD simulation time and the TCAD simulator license cost increase, and the cost of existing calibration accompanying the TCAD simulation also increases. Referring to the comparative examples in Figure 2A and Figure 2B , a TCAD simulator is used in the calibration process, TCAD data can be generated in the process of using the TCAD simulator, the accumulation of multiple TCAD data is a huge burden on the memory, and it may not be efficient in terms of time and cost.

[0057] According to Figure 2A 's comparative example, in Figure 2A 's comparative example, it is shown that parameter 10 is input to the TCAD simulator 20. Here, the TCAD simulator 20 can perform multiple simulations to obtain multiple TCAD data 30.

[0058] In operation 40, the obtained TCAD data 30 is calibrated to adjust the parameters included in the TCAD emulator 20, and the TCAD emulator 20 performs a TCAD simulation 50 to check and / or determine whether the calibration has been accurately performed. In operation 60, the operator and / or user can determine whether the output value Out output by the TCAD simulation 50 matches the hardware data HW. If the output value Out output by the TCAD simulation 50 matches the hardware data HW (Yes in operation 60), then the calibrated parameters are output in operation 80. Otherwise, if the output value Out output by the TCAD simulation 50 does not match the hardware data HW (No in operation 60), then the operator and / or user can add data in operation 70 to proceed to operation 40 to perform calibration again, and this process can be iterated until the parameter values through which an output value matching the hardware data HW is obtained are found and / or determined.

[0059] Referring to Figure 2A , multiple TCAD data can be accumulated during multiple TCAD simulations and the like.

[0060] According to Figure 2B the comparative example of, it is shown that parameter 11 is input into the TCAD emulator 21, but it is not limited thereto. Here, the TCAD emulator 21 can perform multiple simulations for semiconductor device design, thereby obtaining multiple TCAD data 31 and the like associated with and / or corresponding to the semiconductor device design.

[0061] The obtained TCAD data 31 is input into the deep learning network model 41 to learn, adjust, determine, etc. one or more parameters, and the TCAD emulator can perform a TCAD simulation 51 to determine the accuracy of the learning result data. The user and / or operator can determine in operation 61 whether the output value Out output by the TCAD simulation 51 matches the hardware data HW. If the output value Out output by the TCAD simulation 51 matches the hardware data HW (Yes in operation 61), then the calibrated parameters are output in operation 81. Otherwise, if the output value Out output by the TCAD simulation 51 does not match the hardware data HW (No in operation 61), then data can be added in operation 71 to proceed to operation 41 to retrain the deep learning network model 41, and this process can be iterated until the parameter values through which an output value matching the hardware data HW is obtained are found.

[0062] Referring to Figure 2B , multiple TCAD data can be accumulated during multiple TCAD simulations for semiconductor device design.

[0063] In the following, when at least one exemplary embodiment of the automatic calibration method described below is used, TCAD calibration can be performed without performing and / or using a TCAD simulation (e.g., without performing a TCAD simulation and / or without using a TCAD simulator, etc.), thereby ensuring more efficient processing in terms of time, cost reduction, etc.

[0064] Figure 3 is a flowchart showing a calibration method according to at least one exemplary embodiment. Referring to Figure 3 , a TCAD simulator is not used, and thus, TCAD data, which is an output result of simulating a semiconductor device design using a TCAD simulator, also does not exist.

[0065] Referring to Figure 3 , at least one parameter 12 and an internal equation 22 in the TCAD simulator can be input to the automatic calibration system 32 and learned and / or determined. The automatic calibration system 32 can receive the internal equation 22, at least one parameter 12, and / or hardware data (not shown) and immediately complete calibration in operation 42 by learning and / or determining an equation related to the received information using a deep learning network. The automatic calibration system 32 according to at least one exemplary embodiment of the inventive concept can immediately complete calibration without iterating the output result (e.g., without performing any additional iterations). Referring to Figure 3 at least one exemplary embodiment of Figure 2A and Figure 2B a comparative example of Figure 3 , since at least one parameter can be adjusted, improved, and / or optimized even without using a TCAD simulator and TCAD data, the TCAD license cost can be reduced, and since the adjustment, improvement, and / or optimization are performed even without performing a TCAD simulation, at least one exemplary embodiment of Figure 3 can also be economical in terms of time, reducing the consumed computing resources, etc. The automatic calibration system, device, non-transitory computer-readable medium, and automatic calibration method are specifically described below.

[0066] Figure 4 is a block diagram showing an automatic calibration system 100 according to at least one exemplary embodiment. Figure 5 is a block diagram showing an automatic calibration system 200 according to at least one exemplary embodiment.

[0067] Referring to Figure 4, the automatic calibration system 100 may include an approximation function generator 110 and / or an optimization processor 120, etc., but the exemplary embodiments are not limited thereto. For example, the automatic calibration system 100 may include a greater or smaller number of constituent components. According to some exemplary embodiments, one or more of the approximation function generator 110, the optimization processor 120, etc. may be implemented as a processing circuit. The processing circuit may include: hardware or a hardware circuit including a logic circuit; a hardware / software combination (such as a processor that executes software and / or firmware); or a combination thereof. For example, the processing circuit may more specifically include, but is not limited to, a central processing unit (CPU), an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate array (FPGA), a system on chip (SoC), a programmable logic unit, a microprocessor, an application specific integrated circuit (ASIC), etc., but is not limited thereto.

[0068] The approximation function generator 110 may receive an internal equation I_Eq and / or hardware data HW data, etc. as inputs, but is not limited thereto. Here, the internal equation I_Eq may be any one of a plurality of equations included in the TCAD emulator. According to at least one exemplary embodiment, the internal equation I_Eq may be a PDE for calculating and / or determining result data in an environment associated with and / or corresponding to a desired TCAD design (such as a semiconductor device design, etc.) using the automatic calibration system 100 according to at least one exemplary embodiment of the inventive concept. According to at least one exemplary embodiment, the hardware data HW data may be output data obtained when input data is actually input into an equation related to the internal equation I_Eq in an environment using the automatic calibration system 100 according to at least one exemplary embodiment of the inventive concept or when an experiment related to and / or corresponding to the desired TCAD design and / or an actual semiconductor device is actually performed using the input data.

[0069] According to at least one exemplary embodiment, the approximation function generator 110 may generate an approximation function C_Eq that can yield the hardware data HW data based on the hardware data HW data. According to at least one exemplary embodiment of the inventive concept, the approximation function generator 110 may generate an approximation function C_Eq that can output hardware data corresponding to the input data based on the input data and the hardware data corresponding to the input data.

[0070] According to at least one exemplary embodiment, the approximation function generator 110 may include at least one neural network model. The approximation function generator 110 may generate an approximation function C_Eq that satisfies (such as matches, fulfills, etc.) the hardware data HW based on the neural network model. The approximation function generator 110 is not limited to the neural network model and may include various deep learning network models, artificial intelligence models, etc.

[0071] The optimization processor 120 can adjust, improve, and / or optimize the parameter C_para included in the approximate function C_Eq output from the approximate function generator 110. Additionally, the optimization processor 120 can adjust, improve, and / or optimize the parameter I_para included in the internal equation I_Eq input to the approximate function generator 110.

[0072] The optimization processor 120 can adjust, improve, and / or optimize and output a related equation O_eq, which is the result of solving and / or calculating, determining, etc. the internal equation I_Eq input to the approximate function generator 110, the parameter I_para included in the internal equation I_Eq, and the parameter C_para included in the approximate function C_Eq.

[0073] Referring to Figure 5 , the automatic calibration system 200 can include an approximate function generator 210 and / or an optimization processor 220, etc. Because Figure 5 the approximate function generator 210 of Figure 4 can correspond to Figure 4 the approximate function generator 110 of

[0074] the description made with reference to

[0075] will not be repeated here.

[0074] The optimization processor 220 can include a loss function processor 221 and / or a learner 222, etc., but is not limited thereto. The loss function processor 221 can calculate and / or determine the loss function Loss based on the difference between the approximate function C_Eq input to the optimization processor 220 and the information input to the automatic calibration system 200. According to some example embodiments, one or more of the approximate function generator 210, the optimization processor 220, the loss function processor 221, the learner 222, etc. can be implemented as a processing circuit. The processing circuit can include: hardware or a hardware circuit including a logic circuit; a hardware / software combination (such as a processor executing software and / or firmware); or a combination thereof. For example, the processing circuit can more specifically include, but is not limited to, a central processing unit (CPU), an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate array (FPGA), a system on a chip (SoC), a programmable logic unit, a microprocessor, an application specific integrated circuit (ASIC), etc., but is not limited thereto.

[0075] The term "loss function" may represent a function that represents the difference between an approximation function and existing data. According to at least one exemplary embodiment, the loss function may be a function that obtains an average value (e.g., an average value) by substituting the approximation function into an internal equation and summing all the differences. According to another exemplary embodiment, the loss function may be a function that obtains an average value by substituting the approximation function into hardware data and summing all the differences. However, the exemplary embodiments of calculating and / or determining the loss function are not limited thereto, and may be widely analyzed as a function that obtains the difference between the approximation function approximated by a neural network and existing given data.

[0076] According to at least one exemplary embodiment, the loss function processor 221 may determine a first loss function by applying the approximation function C_Eq to the internal equation I_Eq. According to at least one exemplary embodiment, the loss function processor 221 may calculate and / or determine the first loss function by calculating and / or determining the difference between the approximation function C_Eq input to the optimization processor 220 and the internal equation I_Eq input to the approximation function generator 210. According to at least one exemplary embodiment, the loss function processor 221 may calculate and / or determine a second loss function by calculating and / or determining the difference between the approximation function C_Eq input to the optimization processor 220 and the HW data. According to at least one exemplary embodiment, the loss function processor 221 may calculate and / or determine a third loss function by calculating and / or determining the difference between the approximation function C_Eq input to the optimization processor 220 and at least one boundary condition of the internal equation I_Eq.

[0077] The loss function processor 221 may send the first loss function, the second loss function, and / or the third loss function to the learner 222. According to at least one exemplary embodiment, at least one of the first loss function, the second loss function, and the third loss function output from the loss function processor 221 may be a function related to at least one parameter of the internal equation I_Eq and / or at least one parameter of the approximation function C_Eq.

[0078] The learner 222 can learn and / or determine both at least one parameter of the internal equation I_Eq and at least one parameter of the approximation function C_Eq such that the sum of the first loss function, the second loss function, and the third loss function output from the loss function processor 221 is 0. The learner 222 can simultaneously find, calculate, and / or determine several solutions of at least one parameter of the internal equation I_Eq. The learner 222 can calibrate at least one parameter of the internal equation I_Eq and at least one parameter of the approximation function C_Eq based on the gradient descent algorithm. According to at least one example embodiment, the learner 222 can include a deep learning model. The learner 222 can learn, calculate, and / or determine at least one parameter of the internal equation I_Eq and at least one parameter of the approximation function C_Eq based on the deep learning model.

[0079] The automatic calibration systems 100 and 200 according to at least one example embodiment of the inventive concept can perform calibration of a physics-based design and / or simulation by directly using an internal equation and a deep learning network. The automatic calibration systems 100 and 200 according to at least one example embodiment of the inventive concept can be applied to all physics-based designs and / or simulations (e.g., TCAD devices, TCAD processes, TCAD quantum, electronic computer-aided design (ECAD), etc.). The automatic calibration system according to at least one example embodiment of the inventive concept can be applied to all simulation fields and / or variables for which calibration is desired and / or required. Additionally, global optimization (e.g., global tuning, etc.) can be performed by finding, calculating, and / or determining multiple solutions at once. Additionally, the automatic calibration system according to at least one example embodiment of the inventive concept can be applied to fields such as machine learning-based physics model simulation. Figure 4 of the automatic calibration system 100 or Figure 5 of the automatic calibration system 200 can be included in a computing system (e.g., Figure 12 the computer system 160), but the example embodiment is not limited thereto.

[0080] Figure 6 is a flowchart showing functions used in an automatic calibration method and system according to at least one example embodiment.

[0081] Referring to Figure 6 operation S110, input data , hardware data and the internal equation C can be input into the automatic calibration system. According to at least one example embodiment, the input data can be data related to depth x and time t, but the example embodiment is not limited thereto. According to at least one example embodiment, the hardware data can be data obtained by using the input data The result data of the actual experiment of depth x and time t. The internal equation C can be the PDE of is the equation for obtaining the hardware data According to at least one exemplary embodiment, the function disclosed in operation S110 of Figure 6 can be the function used in operation S100 of FIG. 1.

[0082] Referring to Figure 6 operation S210 of and the hardware data an approximate function can be generated based on the input data . The approximate function can be generated by a neural network model, but is not limited thereto. The approximate function can be generated to satisfy the input data and the hardware data within the range of, and may include at least one parameter of the approximate function .

[0083] Referring to Figure 6 operation S220 of a loss function can be generated based on the approximate function

[0084] Referring to Figure 6 operation S230 of a loss function can be generated by comparing the approximate function generated in operation S210 with the internal equation C input in operation S110 and the hardware data According to at least one exemplary embodiment, the loss function can be calculated and / or determined by substituting the approximate function into the internal equation C and / or substituting the approximate function into the hardware data and the input data According to at least one exemplary embodiment, the loss function including at least one parameter I_para of the internal equation C and at least one parameter C_para of the approximate function can be generated based on the relationship between the approximate function the internal equation C and the hardware data .

[0085] Referring to Figure 6 operation S240 of the internal equation can be simultaneously learned, calculated, and / or determined based on the gradient descent algorithmAt least one parameter I_para of C and an approximation function At least one parameter C_para of (), but not limited thereto. According to at least one exemplary embodiment, the loss function can be determined based on the gradient descent algorithm. According to at least one exemplary embodiment, each parameter can be learned based on the gradient descent algorithm such that the loss function is 0.

[0086] Referring to Figure 6 Operation S250 of, the internal equation as the learning result of operation S240 can be adjusted, improved, and / or optimized and determined At least one parameter I_para of C and an approximation function At least one parameter C_para of, and the approximation function can be solved .

[0087] According to at least one exemplary embodiment, in Figure 6 The functions and parameters disclosed in operations S210, S220, S230, S240, and S250 can be the functions and parameters used in operation S200 of FIG. 2, but not limited thereto.

[0088] Figures 7A to 7C Is a flowchart showing an automatic calibration method according to at least one exemplary embodiment.

[0089] Referring to Figure 7A , exemplary internal equations are disclosed in , however, the exemplary embodiments are not limited thereto, and other equations can be used for the automatic calibration method. The internal equation can be a PDE obtained by a TCAD simulator or the like.

[0090] Figure 7A The internal equation of is reproduced in Equation 1 below, but the exemplary embodiments are not limited thereto.

[0091] [Equation 1] .

[0092] In Equation 1, C represents the dopant concentration, t represents time, Represents the first parameter and the second parameter of the internal equation, Represents based on the first parameter and the second parameter of the internal equation Internal parameter function of, and x represents depth, but the exemplary embodiments are not limited thereto. The range of depth x and the range of time t can be determined as conditions.

[0093] Referring to Figure 7A, in operation S10, (x, t) can be input as input data into the automatic calibration system. Additionally, hardware data corresponding to the input data (x, t) can be input. Thus, in operation S20, a neural network for approximating the dopant concentration C can be defined based on the depth and time (x, t) as the input data. The neural network can approximate any function (by the universal approximation theorem), and if the initial conditions and boundary conditions are determined, the solution of the PDE is unique. Examples of hardware data according to at least one exemplary embodiment can be represented as follows, but are not limited thereto.

[0094] [Equation 2] 。

[0095] [Equation 3] 。

[0096] Equation 2 can indicate the hardware data when t is 0 at depth x, for example, under the initial conditions. Equation 3 can indicate the hardware data corresponding to the result when t is at its maximum value T at depth x (e.g., when the experiment is completed).

[0097] [Equation 4] 。

[0098] Equation 4 represents the approximation function approximated in operation S30 by considering the hardware data obtained from Equation 2 and Equation 3 and using the approximation function to calculate and / or determine the dopant concentration and the approximation function , but the exemplary embodiments are not limited thereto.

[0099] Once the approximation function is generated, the approximation function approximated by the neural network can be compared with the internal equation and the hardware data to define and calculate and / or determine the loss function. According to at least one exemplary embodiment, the loss function can be defined as follows, but the exemplary embodiments are not limited thereto.

[0100] [Equation 5] 。

[0101] Referring to Equation 5, one example (operation S42): Substitute the approximation function approximated by the neural network into Equation 1 as the internal equation, and calculate and / or determine the difference of the corresponding equation as the first loss function such that the result of substituting the approximation function into Equation 1 is satisfied. According to at least one exemplary embodiment, the first loss function can indicate the first parameter of the internal equation and a second parameter deviates from the approximation function by how much.

[0102] [Equation 6] .

[0103] Referring to Equation 6, an example (operation S43): Substitute the approximation function approximated by the neural network into the hardware data, and calculate and / or determine the difference between the approximation function and the hardware data as , but the example embodiment is not limited thereto. According to at least one example embodiment, the second loss function may indicate how much the approximation function deviates from the hardware data.

[0104] [Equation 7] .

[0105] Referring to Equation 7, Figure 7A the loss function in may be the same as the value obtained by adding the first loss function and the second loss function in operation S50, but the example embodiment is not limited thereto.

[0106] Referring to Figure 7A and Figure 7B , the loss function can be used to simultaneously learn the parameters of the neural network function as well as the first parameter of the internal equation and the second parameter , but the example embodiment is not limited thereto. According to at least one example embodiment, Equations 8, 9, and 10 can be used to learn the parameters, but are not limited thereto.

[0107] [Equation 8] .

[0108] [Equation 9] .

[0109] [Equation 10] .

[0110] Equation 8 can be an equation for learning the first parameter of the internal equation . Equation 9 can be an equation for learning the second parameter of the internal equation . Equation 10 can be an equation for learning the parameters of the neural network function .

[0111] According to at least one exemplary embodiment, Equation 8, Equation 9, and Equation 10 may be equations to which a gradient descent algorithm is applied. In Equation 8, Equation 9, and Equation 10, Loss represents a loss function and represents a learning rate. The learning rate may be a predefined value or a variable value. By learning a first parameter that satisfies Equation 8, the first parameter through which the loss function Loss satisfies 0 can be calibrated. By learning a second parameter that satisfies Equation 9, the second parameter through which the loss function Loss satisfies 0 can be calibrated. By learning a parameter of a neural network function that satisfies Equation 10, the parameter of the neural network function through which the loss function Loss satisfies 0 can be calibrated.

[0112] Referring to Figure 7C operation S41, the first parameter and the second parameter can be set in a vector form ( , ). By doing so, multiple solutions for the first parameter and the second parameter can be found at once.

[0113] [Equation 11] .

[0114] Referring to Equation 11, multiple solutions for the first parameter can be found, as well as multiple solutions for the second parameter corresponding to the first parameter . Similar to Equation 8, Equation 9, and Equation 10, the gradient descent algorithm can be applied to Equation 11.

[0115] Figure 8 is a flowchart showing an automatic calibration method according to at least one exemplary embodiment. According to at least one exemplary embodiment, Figure 8 at least one exemplary embodiment of Figures 7A to 7C may be an extended exemplary embodiment of at least one exemplary embodiment of

[0116] Referring to Figure 8 , in operation S11, (x, t) may be input as input data, but the exemplary embodiment is not limited thereto. Once the input data (x, t) is input into the automatic calibration system, an approximate function based on the input data (x, t) can be generated in operation S21 . Included in the approximation function among can be at least one parameter included in the approximation function . Referring to Figure 8 , in operation S31, the output data obtained through the approximation function can be represented by .

[0117] [Equation 12] .

[0118] [Equation 13] .

[0119] [Equation 14] .

[0120] [Equation 15] .

[0121] According to at least one exemplary embodiment of the inventive concept, a deep neural network model, at least one internal equation, and at least one parameter of the internal equation can be used to construct an approximation function configured to adjust, improve, and / or optimize the hardware data (e.g., design requirements, user requirements, etc.) of the network. As an example, Equation 12 can be an example of a PDE included in a TCAD simulator. In Equation 12, represents the function obtained by taking the partial derivative of the function u(x,t) with respect to t, and represents the partial derivative function with respect to u(x,t) including the parameter . The left side of Equation 12 can correspond to the left side of the internal equation of Figure 7A , and the right side of Equation 12 can correspond to the right side of the internal equation of Figure 7A . However, Equation 12 is not limited to the internal equation of Figure 7A .

[0122] Equation 13 can be a function of the boundary conditions related to Equation 12, but the exemplary embodiment is not limited thereto. can be a function indicating the boundary conditions of u(x,t).

[0123] Equation 14 and Equation 15 can respectively indicate the hardware data under the initial conditions and the hardware data as the final result after the total time has passed, but are not limited thereto.

[0124] can generate an approximation function based on Equation 12, Equation 13, Equation 14, and Equation 15. The approximation function It can be generated by Equation 16.

[0125] [Equation 16] .

[0126] According to at least one example embodiment, the parameters included in the deep neural network and the parameters of the internal equation can be configured as learning parameters to perform initialization. According to at least one example embodiment, the approximation function can be adjusted, improved, and / or optimized by transforming the internal equation into a learnable objective function . Once the approximation function is determined, the loss function can be calculated and / or determined based on the approximation function .

[0127] [Equation 17] .

[0128] [Equation 18] .

[0129] [Equation 19] .

[0130] Equation 17 can be an example of the first loss function obtained by substituting the approximation function into the internal equation and calculating and / or determining the difference between the approximation function and the internal equation. Equation 18 can be an example of the third loss function obtained by substituting the approximation function into the boundary conditions and calculating and / or determining the substitution result. Equation 19 can be an example of the second loss function obtained by comparing the approximation function with the hardware data and calculating and / or determining the difference between the approximation function and the hardware data. Learning can be performed using Equation 17, Equation 18, and Equation 19 such that the sum of the first loss function, the second loss function, and the third loss function is 0, but the example embodiments are not limited thereto.

[0131] According to at least one example embodiment, the parameters of the internal equation can be fixed and then the approximation function approximated by the deep neural network can be adjusted, improved, and / or optimized to adjust, improve, and / or optimize the parameters included in the deep neural network such that the approximation function approximates the internal equation. Thereafter, the parameters of the internal equation and the parameters included in the deep neural network , to approximate the internal equations and hardware data. Here, the parameters of the internal equations Can be constructed in vector form so that several solutions can be adjusted, improved and / or optimized at once.

[0132] According to at least one example embodiment of the inventive concept, the adjusted, improved and / or optimized parameters of the PDE can be converted into Directly applied to TCAD to construct a calibrated TCAD environment. According to at least one example embodiment of the inventive concept, since equations based on approximate functions, internal equations, and hardware data are used, a TCAD environment can be constructed without TCAD data.

[0133] According to at least one example embodiment of the inventive concepts, at least one parameter of the internal equation may be adjusted, improved, and / or optimized by using a user-defined equation (eg, internal equation) as an input, etc., but example embodiments are not limited thereto.

[0134] In addition, according to at least one example embodiment of the inventive concept, since solution discovery and calibration are performed simultaneously, uncalibrated intermediate results may not exist. According to the comparative example, since solution discovery and calibration cannot be performed simultaneously, iterative simulation is necessary and uncalibrated TCAD intermediate results must be generated.

[0135] In addition, according to at least one example embodiment of the inventive concepts, a TCAD license is not desired and / or required, thereby reducing costs, and calibration may be performed by directly solving equations based on a deep neural network.

[0136] Figure 9 is a detailed flow chart illustrating an automatic calibration method according to at least one example embodiment.

[0137] exist Figure 9 In operation S400, an approximate function based on the hardware data may be determined. According to at least one example embodiment of the inventive concept, an approximate function using a deep neural network may be generated based on the hardware data to satisfy the hardware data (and / or design requirements, user requirements, etc.). In the process of generating the approximate function, an internal equation (e.g., PDE), at least one parameter of the internal equation, etc. may be used, and at least one parameter is determined by a random number, but example embodiments are not limited thereto.

[0138] exist Figure 9In operation S500, at least one parameter included in the approximation function and at least one parameter included in the PDE can be adjusted, improved, and / or optimized based on a loss function. The PDE can indicate an internal equation input to the automatic calibration system. In operation S500, at least one parameter included in the PDE can be learned such that the loss function is 0, and a deep neural network approximating the approximation function can be trained. The parameters can be learned simultaneously and obtained as multiple solutions at once.

[0139] In Figure 9 operation S600, the adjusted, improved, and / or optimized parameters of the PDE can be applied to TCAD. Thus, even without TCAD data, the TCAD environment can be adjusted, improved, and / or optimized.

[0140] Figure 10 is a detailed flowchart showing an automatic calibration method according to at least one example embodiment.

[0141] According to at least one example embodiment, Figure 10 operations S510 to S550 can be included in Figure 9 operation S500, but is not limited thereto.

[0142] In Figure 10 operation S510, at least one parameter of the PDE can be fixed. In the case where multiple parameters are adjusted, improved, and / or optimized, at least one parameter of the PDE can be mainly fixed to a random number, but is not limited thereto.

[0143] In Figure 10 operation S520, at least one parameter included in the approximation function can be learned to approximate the PDE of operation S510. In operation S520, at least one parameter included in the approximation function can be learned in a state reflecting the fixed parameters of the PDE.

[0144] In Figure 10 operation S530, at least one parameter of the PDE can be randomized. In operation S530, in order to adjust, improve, and / or optimize the parameters of the PDE, the parameters can be randomized and learned.

[0145] In Figure 10 operation S540, at least one parameter included in the approximation function and at least one parameter of the PDE can be learned to approximate hardware data. In operation S540, multiple parameters can be learned to satisfy both the hardware data (e.g., design requirements, user requirements, etc.) and the PDE, but the example embodiment is not limited thereto.

[0146] In Figure 10In operation S550, it can be determined whether the desired and / or predefined number of iterations of the auto - calibration method has been satisfied. If the learning has been performed for the desired and / or predefined number of iterations, the learning ends, and if the learning has not been performed for the desired and / or predefined number of iterations, the learning can be performed again. The desired and / or predefined number of iterations can be determined by the auto - calibration system, set by the user, etc.

[0147] Figure 11 is a detailed flowchart showing an auto - calibration method according to at least one example embodiment.

[0148] According to at least one example embodiment, Figure 11 Operations S511 to S551 can be included in Figure 9 operation S500.

[0149] Figure 11 Operation S511 can correspond to Figure 10 operation S510, but the example embodiment is not limited thereto. Figure 11 Operation S521 can correspond to Figure 10 operation S520, but the example embodiment is not limited thereto. Figure 11 Operation S531 can correspond to Figure 10 operation S530, but the example embodiment is not limited thereto. Figure 11 Operation S541 can correspond to Figure 10 operation S540, but the example embodiment is not limited thereto. Figure 11 Operation S551 can correspond to Figure 10 operation S550, but the example embodiment is not limited thereto.

[0150] Referring to Figure 11 , in operation S542, at least one parameter of the PDE can be constructed and / or generated in vector form and learning can be performed on at least one parameter of the PDE. By doing so, multiple pairs of solutions of the parameters of the PDE can be obtained.

[0151] Figure 12 is a block diagram showing a computer system 160 according to at least one example embodiment.

[0152] In some example embodiments, Figure 12 the computer system 160 can train the learning model used in the auto - calibration method described above and can be referred to as an auto - calibration system, but the example embodiment is not limited thereto, and other computer systems can be used to perform the auto - calibration method of one or more of the example embodiments.

[0153] The computer system 160 may be referred to as a computer system including general hardware executing dedicated computer-readable instructions for implementing at least one example embodiment of the automatic calibration method discussed herein, a dedicated computing system including dedicated hardware for executing at least one example embodiment of the automatic calibration method discussed herein, or any combination thereof. For example, the computer system 160 may include a personal computer, a server computer, a laptop computer, a household appliance, etc. As Figure 12 shown, the computer system 160 may include at least one processor 161, a memory 162, a storage system 163, a network adapter 164, an input / output (I / O) interface 165, and / or a display 166, etc., but is not limited thereto.

[0154] The at least one processor 161 may execute a program module that includes dedicated computer system executable instructions for implementing one or more aspects of at least one method of at least one example embodiment.

[0155] For example, the program module may include routines, programs, objects, components, logics, data structures, etc., which are configured to perform specific tasks and / or implement specific abstract data types associated with one or more operations of one or more of the methods discussed above. The memory 162 may include a computer system readable medium of a volatile memory type (such as, a random access memory (RAM)). The at least one processor 161 may access the memory 162 and execute the computer-readable instructions loaded on the memory 162. The storage system 163 may store information in a non-volatile manner and may include at least one program product, the at least one program product including a program module configured to train and adjust, improve and / or optimize a learning model for one or more of the automatic calibration methods described above. As a non-limiting example, the program may include an operating system, at least one application, other program modules, and / or program data, etc.

[0156] The network adapter 164 may provide a connection to a local area network (LAN), a wide area network (WAN), a public network (such as, the Internet), etc. The input / output interface 165 may provide a communication channel with peripheral devices (such as, a keyboard, a pointing device, and / or an audio system). The display 166 may output various information such that the user can identify the information.

[0157] In some example embodiments, the training of the learning model for the automatic calibration method described above may be implemented by a dedicated computer program product. The dedicated computer program product may include a non-transitory computer-readable medium (e.g., a storage medium, etc.), the non-transitory computer-readable medium containing computer-readable instructions that allow at least one processor 161 to process images and / or train the model according to at least one example embodiment. As a non-limiting example, the computer-readable instructions may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state configuration data, and / or source code or object code edited using at least one programming language, etc.

[0158] The non-transitory computer-readable medium may be a type of memory medium capable of non-transitorily holding and storing instructions to be executed by at least one processor 161 and / or instruction-executable devices, but is not limited thereto. The non-transitory computer-readable medium may be an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or a combination thereof, but is not limited thereto. For example, the non-transitory computer-readable medium may be a portable computer disk, a hard disk, RAM, read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory, static random access memory (SRAM), a compact disc (CD), a digital versatile disc (DVD), a memory stick, a floppy disk, a mechanical encoding device (such as a punched card), or a combination thereof.

[0159] Although various example embodiments of the inventive concept have been specifically shown and described, it will be understood that various changes in form and detail may be made therein without departing from the spirit and scope of the appended claims.

Claims

1. An automatic calibration method, comprising: receiving at least one internal equation, input data associated with a semiconductor device design, and hardware data associated with the semiconductor device design; generating at least one approximation function based on the input data and the hardware data; determining at least one loss function based on the generated at least one approximation function; Determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation so that a value of the at least one loss function is 0; as well as A semiconductor device design is selectively adjusted based on the determined at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation.

2. The automatic calibration method according to claim 1, wherein: The at least one internal equation comprises a partial differential equation.

3. The automatic calibration method according to claim 1, wherein: The step of determining the at least one loss function based on the generated at least one approximation function further comprises: A first loss function is determined by applying the at least one approximation function to the at least one internal equation.

4. The automatic calibration method according to claim 1, wherein: The step of determining the at least one loss function based on the generated at least one approximation function further comprises: A second loss function is determined by comparing the at least one approximation function with the hardware data.

5. The automatic calibration method according to claim 1, wherein: The step of determining the at least one loss function based on the generated at least one approximation function further comprises: A third loss function is determined by comparing the at least one approximation function to at least one boundary condition of the at least one internal equation.

6. The automatic calibration method according to claim 1, wherein: The step of determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation further comprises: The at least one loss function is determined based on a gradient descent algorithm.

7. The automatic calibration method according to claim 6, wherein: The step of determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation further comprises: At least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation are determined simultaneously.

8. The automatic calibration method according to claim 6, wherein: The step of determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation further comprises: At least one parameter of the at least one internal equation is configured in vector form to determine a plurality of solutions of the at least one parameter of the at least one internal equation.

9. The automatic calibration method according to claim 1, wherein: The step of determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation further comprises: fixing at least one parameter of the at least one internal equation to determine at least one parameter of the at least one approximation function; and At least one parameter of the at least one internal equation is randomized to determine at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation.

10. The automatic calibration method according to claim 9, wherein: The step of fixing at least one parameter of the at least one internal equation further comprises: performing the step of determining at least one parameter of the at least one approximation function so that the at least one parameter of the at least one approximation function approximates the at least one internal equation; and The step of randomizing at least one parameter of the at least one internal equation to determine at least one parameter of the at least one approximate function and at least one parameter of the at least one approximate function also includes: determining at least one parameter of the at least one approximate function and at least one parameter of the at least one internal equation so as to approximate the hardware data.

11. An automatic calibration system, comprising: a non-transitory storage medium storing computer-readable instructions; as well as A processing circuit is configured to: execute the computer-readable instructions to perform the automatic calibration method according to any one of claims 1 to 10.

12. A non-transitory computer-readable storage medium storing computer-readable instructions that, when executed by a processing circuit, cause the processing circuit to: receiving at least one internal equation, input data associated with a semiconductor device design, and hardware data associated with the semiconductor device design; generating at least one approximation function based on the input data and the hardware data; determining at least one loss function based on the generated at least one approximation function; Determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation so that a value of the at least one loss function is 0; as well as A semiconductor device design is selectively adjusted based on the determined at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation.

13. An automatic calibration system, comprising: The processing circuit is configured to: receiving as input at least one internal equation associated with a semiconductor device design and hardware data associated with the semiconductor device design; generating at least one approximation function based on the hardware data; generating at least one loss function based on the at least one approximation function; Determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation so that the generated at least one loss function is 0; and A semiconductor device design is selectively adjusted based on the determined at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation.

14. The automatic calibration system according to claim 13, wherein: The processing circuit is further configured to: The at least one approximate function is generated using a deep learning network so that the hardware data is satisfied.

15. The automatic calibration system according to claim 13, wherein: The processing circuit is further configured to: generating the at least one loss function based on the at least one approximation function; and At least one parameter of the at least one approximate function and at least one parameter of the at least one internal equation are simultaneously learned so that an output of the at least one loss function is 0.

16. The automatic calibration system according to claim 15, wherein: The processing circuit is further configured to: Output each of a first loss function determined by applying the at least one approximate function to the at least one internal equation, a second loss function determined by comparing the at least one approximate function with the hardware data, and a third loss function determined by comparing the at least one approximate function with at least one boundary condition of the at least one internal equation.

17. The automatic calibration system according to claim 16, wherein: The processing circuit is further configured to: At least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation are determined so that a sum of the first loss function, the second loss function, and the third loss function is zero.

18. The automatic calibration system according to claim 15, wherein: The processing circuit is further configured to: The at least one loss function is determined based on a gradient descent algorithm.

19. The automatic calibration system according to claim 15, wherein: The processing circuit is further configured to: At least one parameter of the at least one internal equation is configured in vector form to determine a plurality of solutions of the at least one parameter of the at least one internal equation.

20. The automatic calibration system according to claim 15, wherein: The processing circuit is further configured to: fixing at least one parameter of the at least one internal equation to determine at least one parameter of the at least one approximation function; and At least one parameter of the at least one internal equation is randomized to determine at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation.

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