MOSFET modeling method based on electrothermal coupling constraint neural network

Abstract

The invention discloses an MOSFET (Metal-Oxide-Semiconductor Field Effect Transistor) modeling method based on an electrothermal coupling constraint neural network, which comprises the following steps of: defining a two-dimensional profile solution domain of an MOSFET, and determining that input variables of an electrothermal coupling constraint neural network model comprise working conditions and two-dimensional space-time coordinates sampled in the two-dimensional profile solution domain; constructing an electrothermal coupling constraint neural network model, and predicting potential, electron concentration, hole concentration and temperature; a composite loss function composed of a data loss item and a physical loss item is defined, the data loss item is a mean square error of a predicted value and an actual value of the neural network model, and the physical loss item is the sum of a partial differential equation set residual error and a boundary condition residual error; and training the neural network model by minimizing the composite loss function until the loss function converges, thereby obtaining the neural network model capable of representing the electrothermal coupling characteristics of the MOSFET. According to the invention, on the premise of ensuring physical accuracy, rapid prediction of the electric thermal field in the device can be realized.

Description

Technical Field

[0001] This invention belongs to the field of MOSFET modeling, and specifically relates to a MOSFET modeling method based on an electrothermal coupling constraint neural network. Background Technology

[0002] Power MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors) are the core of power electronic systems. As device size continues to shrink and power density continues to increase, two-dimensional effects inside the device, such as short-channel effect, drain-induced barrier reduction (DIBL), and hot spot distribution, are becoming increasingly critical to the device's performance and reliability. Therefore, it is necessary to predict the internal electrothermal field distribution of MOSFETs through MOSFET modeling.

[0003] Traditional MOSFET modeling methods have the following limitations: (1) Physical analytical modeling has the advantages of strong physical intuition, fast calculation speed and clear parameter meaning. However, as device size continues to shrink to the nanoscale, physical effects (especially short-channel effect, quantum effect and parasitic effect) become extremely complex and inter-coupled. Purely physical-based analytical models are increasingly difficult to accurately describe all working regions of MOSFETs under advanced process nodes, and their solution process consumes huge computational resources.

[0004] (2) Physics-based TCAD simulation can accurately solve semiconductor equations and capture coupling effects, but it requires fine meshing of complex device structures, which is extremely costly and time-consuming (usually several hours to several days). It is not suitable for circuit-level simulation or system-level optimization design.

[0005] (3) Pure data-driven neural network models predict quickly, but require massive amounts of TCAD simulation or experimental data for training, and the models lack physical interpretability, and their calculation results may violate physical laws. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a MOSFET modeling method, computer device, computer-readable storage medium and computer program product based on electrothermal coupling constrained neural network, which can achieve rapid prediction of the internal electrothermal field of the device while ensuring physical accuracy.

[0007] To achieve the above objectives, one aspect of the present invention provides a MOSFET modeling method based on an electrothermal coupling constrained neural network, comprising: Define the two-dimensional profile solution domain of the MOSFET, and determine that the input variables of the electrothermal coupling constrained neural network model include the operating conditions and the two-dimensional spatiotemporal coordinates sampled in the two-dimensional profile solution domain. The operating conditions include at least the gate-source voltage and the drain-source voltage, and the two-dimensional spatiotemporal coordinates are composed of two-dimensional spatial coordinates and time coordinates. An electrothermal coupling constrained neural network model is constructed, with the operating conditions and two-dimensional spatiotemporal coordinates as inputs, and the potential, electron concentration, hole concentration and temperature of the MOSFET under the corresponding operating conditions and two-dimensional spatiotemporal coordinates as outputs. Define the composite loss function L as follows: L = w data Loss data + w physics Loss physics Among them, Loss data Loss is the data loss term. physics For physical loss terms, w data and w physics The weights of the data loss term and the physical loss term are respectively represented. The data loss term is the mean square error between the electric potential, electron concentration, hole concentration and temperature of multiple points calculated by the neural network model and the actual values. The physical loss term is the sum of the residuals of the partial differential equation system describing the two-dimensional electrothermal coupling and the residuals of the boundary conditions defined on the boundary of the solution domain of the two-dimensional profile. By minimizing the composite loss function using an optimization algorithm, the neural network model is trained until the loss function converges, thus obtaining a neural network model that can characterize the electrothermal coupling properties of MOSFETs.

[0008] Preferably, the partial differential equations include a two-dimensional Poisson equation describing the relationship between electric potential and space charge, coupled within the solution domain; a two-dimensional carrier continuity equation describing the concentration of electrons and holes based on a drift-diffusion model; and a two-dimensional heat conduction equation describing the change in temperature field.

[0009] Preferably, in the calculation of the physical loss term, the power loss function calculated from the potential, electron concentration and hole concentration output by the neural network model is used as the heat source term in the heat conduction equation; Temperature-dependent material parameters are calculated based on the temperature output of the neural network model, and these parameters are used in the residual calculation of the Poisson equation and the carrier continuity equation.

[0010] Preferably, the power loss function Q is calculated as follows: (x,y,t) : Q (x, y, t) =J (x, y, t) ·E (x, y, t) + q(RG) · (Eg / q) Where (x, y, t) are two-dimensional spatiotemporal coordinates, E (x, y, t) J is the electric field intensity vector. (x, y, t) Let q be the total current density vector, q be the elementary charge, (RG) be the net recombination rate of electron-hole pairs per unit volume, R be the recombination rate, G be the generation rate, and E be the total current density vector. g It refers to the semiconductor bandgap.

[0011] Preferably, the temperature-dependent material parameters include one or more of the following: carrier mobility, intrinsic carrier concentration, semiconductor bandgap, saturation drift velocity, and material thermal conductivity.

[0012] Preferably, the residual of the partial differential equation system is the mean square error of the residual value obtained by substituting the partial derivatives of the potential, electron concentration, hole concentration and temperature of multiple points calculated by the neural network model into the partial differential equation system; the boundary condition residual is the difference between the boundary conditions of the solution domain and the calculation results of the neural network model.

[0013] Preferably, the boundary includes a silicon dioxide-semiconductor interface, and the boundary conditions on the silicon dioxide-semiconductor interface include continuous electric displacement vector normal component and zero carrier current density normal component.

[0014] Another aspect of the present invention provides a computer device including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described above.

[0015] Another aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0016] Another aspect of the present invention provides a computer program product including a computer program that, when executed by a processor, implements the steps of the method described above.

[0017] According to the MOSFET modeling method, computer device, computer-readable storage medium, and computer program product based on the electrothermal coupling constrained neural network of the present invention, rapid prediction of the internal electrothermal field of the device can be achieved while ensuring physical accuracy. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the present invention, the accompanying drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort: Figure 1 This is a flowchart of a MOSFET modeling method based on an electrothermal coupling constrained neural network according to an embodiment of the present invention; Figure 2 This is a schematic cross-sectional view of a MOSFET according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of an electrothermal coupling constrained neural network model according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the electrothermal coupling mechanism according to an embodiment of the present invention; Figure 5 This is a structural diagram of a computer device according to an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0020] One embodiment of the present invention provides a MOSFET modeling method based on an electrothermal coupling constrained neural network, such as... Figure 1 As shown, the MOSFET modeling method of the electrothermal coupling constrained neural network in this embodiment of the invention includes steps S1 to S4.

[0021] Step S1: Define the model input and solution domain. First, determine the MOSFET structure and define its geometric solution domain Ω, such as... Figure 2 As shown. In this embodiment, the solution domain Ω is a two-dimensional cross-sectional solution domain. Then, the input variables of the electrothermal coupling constrained neural network model are determined, including the operating conditions (Vgs, Vds) and the two-dimensional spatiotemporal coordinate points (x, y, t) sampled within the solution domain Ω. The geometric solution domain includes the semiconductor region (source, drain, channel, substrate) and the gate region (gate and the gate oxide layer between the gate and the channel, mainly silicon dioxide). In actual calculations, the spatiotemporal coordinates of N points uniformly distributed within the solution domain are used as the overall solution domain.

[0022] Specifically, in this step, MOSFET data is acquired as the conditional input to the neural network. The data includes at least the gate-source voltage (Vgs) and drain-source voltage (Vds). Two-dimensional spatial coordinates (x, y) and time coordinates (t) are defined as the main inputs to the neural network, where the x-direction is the channel length direction and the y-direction is the substrate depth direction. The spatiotemporal coordinates (x, y, t) are sampled within the MOSFET profile solution domain.

[0023] Step S2: Construct an electrothermal coupled constrained neural network model. In one embodiment, such as... Figure 3 As shown, the core of this neural network model is a multilayer perceptron (MLP). Its input layer consists of the input variables defined in step S1 (operating conditions (Vgs, Vds), spatiotemporal coordinates (x, y, t)). The output layer consists of four physical quantities corresponding to the operating conditions and spatiotemporal coordinates: electric potential. The input vector is defined by the following parameters: (x, y, t), electron concentration n(x, y, t), hole concentration p(x, y, t), and temperature distribution T(x, y, t). Multiple hidden layers exist between the input and output layers, each containing several neurons. The input vector undergoes a non-linear transformation within these hidden layers before being output by the output layer.

[0024] Specifically, in this step, an electrothermal coupling constrained neural network model is constructed, using Vgs, Vds, and two-dimensional spatiotemporal coordinates (x, y, t) as inputs, and the potential inside the MOSFET at the corresponding spatiotemporal coordinates (x, y, t) as input. The outputs are (x, y, t), electron concentration n(x, y, t), hole concentration p(x, y, t), and temperature T(x, y, t).

[0025] Step S3: Define the composite loss function. Define a loss function consisting of the data loss term (Loss) data ) and electrothermal coupling physical loss term (Loss physics The weighted composite loss function L: L = w data Loss data + w physics Loss physics Among them, Loss data Loss is the data loss term. physics For the electrothermal coupling physical loss term, w data and w physics These represent the weights of the data loss term and the physical loss term, respectively. There is no specific rule for determining the weight values. Generally, they can be directly set as two numbers that add up to 1, such as 0.6 and 0.4, or they can be generated by other algorithms.

[0026] The data loss is the potential at N points calculated (predicted) by the neural network model. The mean square error between the actual values ​​of (x, y, t)_pred, electron concentration n(x, y, t)_pred, hole concentration p(x, y, t)_pred, and temperature T(x, y, t)_pred. The data loss is calculated as follows:

[0027] Physical losses are described by two-dimensional electrothermal coupling (such as...) Figure 4 The partial differential equation system and its boundary conditions constitute the residuals (as shown).

[0028] The partial differential equations set includes three basic equations coupled in the solution domain: a two-dimensional Poisson equation (1) describing the relationship between potential and space charge; a two-dimensional carrier continuity equation (2-1 is the electron continuity equation, and 2-2 is the hole continuity equation) describing the electron and hole concentrations based on the drift-diffusion model; and a two-dimensional heat conduction equation (3) describing the temperature field change.

[0029] (1) (2-1) (2-2) (3) (1) Middle It is a two-dimensional gradient operator. It is electric potential. It is the dielectric constant. It is the space charge density function, q is the elementary charge, and n and p are the electron and hole concentrations, respectively. and These are the donor and acceptor concentrations of ionization, respectively. (2-1) and (2-2) and These are the vector functions of the current density of electrons and holes, as shown in equations (4) and (5), where E is the electric field strength. and These are the mobility rates of electrons and holes, respectively. and These are the diffusion coefficients of electrons and holes, respectively. and These are the coincidence rates of electrons and holes, respectively.

[0030] (4) (5) (3) It is the material density. is specific heat capacity, k is thermal conductivity, and Q is the power loss function, i.e., the power dissipated by the electrical processes of the device.

[0031] The physical loss is the sum of the residuals of the partial differential equation system and the residuals of the boundary conditions, as shown below: Loss physics = Loss PDE + Loss BC Loss of residuals of partial differential equation system PDE Electric potential at N points calculated for a neural network model The residual values ​​are obtained by substituting the partial derivatives of (x, y, t)_pred, electron concentration n(x, y, t)_pred, hole concentration p(x, y, t)_pred, and temperature T(x, y, t)_pred into the partial differential equation system.

[0032]

[0033] in, , , and It is , , and The residual value is obtained by substituting it into the system of partial differential equations.

[0034] The boundary condition residual refers to the difference between the specific conditions that must be satisfied at the actual geometric boundary or interface of the solution domain and the calculation results of the neural network model. Taking the carrier motion at the interface between the gate oxide layer and the semiconductor as an example, the normal component of the carrier current density at this interface is zero. Sampling N points at this interface yields the boundary residual.

[0035] in, and These are the vector functions of the current density of electrons and holes, respectively. It is its normal component.

[0036] In this embodiment of the invention, the constructed electrothermal coupling constraint neural network model is a Physics-Informed Neural Network (PINN) model, in which the electrothermal coupling constraint is embedded in the physical loss term. physics The calculation process is specifically reflected in the following two aspects: Electric-thermal coupling: the potential V output by the PINN model (x,y,t) electron concentration n (x,y,t)and hole concentration p (x,y,t) The calculated power loss function Q (x,y,t) As the heat source in the heat conduction equation, the residual of the heat conduction equation The calculation implicitly includes the conversion relationship from electricity to heat. The process of minimizing the loss function forces the PINN model to learn the temperature field data under the influence of the electric field it predicts, thereby achieving electrothermal coupling.

[0037]

[0038] Thermo-electric coupling: The temperature function T output by the PINN model (x,y,t) As variables, these parameters are substituted into a pre-defined physical model (electric coefficient function of semiconductor materials) to calculate temperature-dependent material parameters, which are then used in the residual calculations of the Poisson equation and the carrier continuity equation. This calculation process implicitly incorporates the influence of thermal on electrical properties; minimizing the loss function also forces the PINN model to learn the electrical field data under the influence of its own predicted temperature field, thereby achieving thermoelectric coupling. The temperature-dependent material parameters include at least one or more of the following: carrier mobility μ... (T) Intrinsic carrier concentration ni (T) Semiconductor bandgap Eg (T) saturation drift velocity vsat (T) and the thermal conductivity k of the material (T) .

[0039] The power loss function Q (x,y,t) The formula for calculating the conversion process from electrical energy to thermal energy within a device is as follows: Q (x, y, t) =J (x, y, t) ·E (x, y, t) + q(RG) · (E g / q) in, J is the electric field intensity vector. (x, y, t) J is the total current density vector. (x, y, t) ·E (x, y, t) This is a calculation term for Joule heat. q is the elementary charge, (RG) is the net recombination rate of electron-hole pairs per unit volume, R is the recombination rate, G is the generation rate, and E... g It is the semiconductor bandgap, q(RG) · (E g / q) Composite thermal calculation term.

[0040] The physical loss term (Loss) physicsThe method also includes boundary condition residuals defined on the boundary of the two-dimensional profile solution domain, wherein the boundary includes at least a gate electrode, a source electrode, a drain electrode, a substrate electrode, and a silicon dioxide-semiconductor interface. The boundary conditions on the silicon dioxide-semiconductor interface include continuous electric displacement vector normal component and zero carrier current density normal component.

[0041] Step S4: Train the neural network model. Use an optimization algorithm (such as Adam) to adjust the weights and biases of the neural network to minimize the composite loss function. Train the neural network model until the loss function converges, obtaining a neural network model that can characterize the electrothermal coupling characteristics of the MOSFET.

[0042] After training, the model is evaluated. A qualified model can serve as an efficient surrogate model for quickly predicting the two-dimensional electrothermal characteristics of MOSFET devices under different operating conditions.

[0043] In summary, the method of this invention constructs a neural network that takes the MOSFET device operating conditions (Vgs, Vds) and two-dimensional spatiotemporal coordinates (x, y, t) as input, and outputs the two-dimensional potential field, carrier concentration field, and temperature field inside the device. The training process of this network is constrained by a set of partial differential equations (PDEs) describing the two-dimensional electrothermal coupling physical process and their boundary conditions, thereby making the trained model an efficient and physically consistent surrogate model. The method of this invention can quickly and accurately predict the electrothermal field distribution inside the MOSFET, and has the following beneficial effects: (1) Capturing two-dimensional physical effects: By solving coupled PDEs (partial differential equations) in two-dimensional space (channel length x, substrate depth y), the method of this embodiment can naturally capture key physical phenomena such as short-channel effect, DIBL, two-dimensional current distribution and hot spots. Since the above partial differential equations themselves satisfy these physical effects, the solution of the equations is used as training data, and the model of this invention can naturally capture the relevant physical phenomena.

[0044] (2) High efficiency and high accuracy: Compared with TCAD, the method of this embodiment does not require mesh subdivision, and the prediction speed is improved by several orders of magnitude; compared with one-dimensional model, the method of this embodiment has significantly improved accuracy due to the embedding of two-dimensional physical information.

[0045] (3) Physical consistency and low data dependence: The model of this invention is strongly constrained by physical laws and boundary conditions, which ensures the physical rationality of the two-dimensional field distribution and significantly reduces the dependence on expensive high-fidelity data.

[0046] Embodiments of the present invention also provide a computer device, which may be a server, and its internal structure diagram may be as follows: Figure 5 As shown. The computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database stores operating parameter data for various components. The network interface communicates with external terminals via a network connection. When executed by the processor, the computer program implements the steps of the method according to embodiments of the present invention.

[0047] Those skilled in the art will understand that Figure 5 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0048] Embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method of the embodiments of the present invention.

[0049] Embodiments of the present invention also provide a computer program product, including a computer program that, when executed by a processor, implements the steps of the method of the embodiments of the present invention.

[0050] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A MOSFET modeling method based on electrothermal coupling constrained neural network, characterized in that, include: Define the two-dimensional profile solution domain of the MOSFET, and determine that the input variables of the electrothermal coupling constrained neural network model include the operating conditions and the two-dimensional spatiotemporal coordinates sampled in the two-dimensional profile solution domain. The operating conditions include at least the gate-source voltage and the drain-source voltage, and the two-dimensional spatiotemporal coordinates are composed of two-dimensional spatial coordinates and time coordinates. An electrothermal coupling constrained neural network model is constructed, with the operating conditions and two-dimensional spatiotemporal coordinates as inputs, and the potential, electron concentration, hole concentration and temperature of the MOSFET under the corresponding operating conditions and two-dimensional spatiotemporal coordinates as outputs. Define the composite loss function L as follows: L = w data ·Loss data + w physics ·Loss physics Among them, Loss data Loss is the data loss term. physics For physical loss terms, w data and w physics The weights of the data loss term and the physical loss term are respectively represented. The data loss term is the mean square error between the electric potential, electron concentration, hole concentration and temperature of multiple points calculated by the neural network model and the actual values. The physical loss term is the sum of the residuals of the partial differential equation system describing the two-dimensional electrothermal coupling and the residuals of the boundary conditions defined on the boundary of the solution domain of the two-dimensional profile. By minimizing the composite loss function using an optimization algorithm, the neural network model is trained until the loss function converges, thus obtaining a neural network model that can characterize the electrothermal coupling properties of MOSFETs.

2. The method according to claim 1, characterized in that, The partial differential equations include a two-dimensional Poisson equation describing the relationship between electric potential and space charge, coupled within the solution domain; a two-dimensional carrier continuity equation describing the concentration of electrons and holes based on a drift-diffusion model; and a two-dimensional heat conduction equation describing changes in the temperature field.

3. The method according to claim 2, characterized in that, In the calculation of the physical loss term, the power loss function calculated from the potential, electron concentration and hole concentration output by the neural network model is used as the heat source term in the heat conduction equation. Temperature-dependent material parameters are calculated based on the temperature output of the neural network model, and these parameters are used in the residual calculation of the Poisson equation and the carrier continuity equation.

4. The method according to claim 3, characterized in that, The power loss function Q is calculated as follows. (x,y,t) : Q (x, y, t) =J (x, y, t) ·E (x, y, t) + q(R-G) · (E g / q) Where (x, y, t) are two-dimensional spatiotemporal coordinates, E (x, y, t) J is the electric field intensity vector. (x, y, t) Let q be the total current density vector, q be the elementary charge, (RG) be the net recombination rate of electron-hole pairs per unit volume, R be the recombination rate, G be the generation rate, and E be the total current density vector. g It refers to the semiconductor bandgap.

5. The method according to claim 3 or 4, characterized in that, The temperature-dependent material parameters include one or more of the following: carrier mobility, intrinsic carrier concentration, semiconductor bandgap, saturation drift velocity, and material thermal conductivity.

6. The method according to any one of claims 1-4, characterized in that, The residual of a partial differential equation system is the mean square error of the residual value obtained by substituting the partial derivatives of the potential, electron concentration, hole concentration and temperature at multiple points calculated by the neural network model into the partial differential equation system; the boundary condition residual is the difference between the boundary conditions of the solution domain and the calculation results of the neural network model.

7. The method according to any one of claims 1-4, characterized in that, The boundary includes a silicon dioxide-semiconductor interface, and the boundary conditions on the silicon dioxide-semiconductor interface include continuous electric displacement vector normal component and zero carrier current density normal component.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

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