Optimized simulation method for transient heat conduction of gallium nitride devices

Abstract

The application discloses a simulation method for optimizing transient heat conduction of a gallium nitride device, which comprises the following steps: constructing a three-dimensional geometric model of the gallium nitride device, and discretely processing the model in a space domain to obtain a local refined grid; setting material properties and boundary conditions of the gallium nitride device, obtaining a matrix equation by using a finite volume method, and solving the equation by using a generalized alternating direction implicit method to obtain a transient heat simulation result of the gallium nitride device. The application has the advantages of unconditional stability, high efficiency, and low consumption of computing resources under the premise of ensuring accuracy.

Description

Technical Field

[0001] This invention relates to a technology in the field of semiconductor design, specifically an optimization simulation method for transient thermal conduction in gallium nitride devices. Background Technology

[0002] Gallium nitride (GaN) devices offer significant advantages in radio frequency (RF) power electronics applications due to their superior material properties. As power density increases, efficient transient heat conduction simulation techniques are needed to predict the dynamic temperature changes of GaN devices. Time-stepped solutions to transient heat conduction equations fall into two categories: implicit and explicit. Explicit methods are highly efficient, but require selecting an appropriate time step to meet stability conditions and avoid divergence. Implicit methods are unconditionally stable and do not require consideration of the time step's impact on stability; however, they involve solving large sparse matrices, resulting in long computation times and high computational resource consumption. Summary of the Invention

[0003] This invention addresses the limitation of existing alternating direction implicit techniques, which are only applicable to scenarios where the computational domain is a structured mesh. It proposes an optimized simulation method for transient heat conduction in gallium nitride devices, which, while ensuring accuracy, has advantages such as unconditional stability, high efficiency, and low computational resource consumption.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to an optimized simulation method for transient thermal conduction of gallium nitride (GaN) devices. The method involves constructing a three-dimensional geometric model of the GaN device and discretizing the model in the spatial domain to obtain a locally refined mesh. The material properties and boundary conditions of the GaN device are set, and the matrix equations are obtained through the finite volume method. The transient thermal simulation results of the GaN device are then obtained by solving the equations using the generalized alternating direction implicit method.

[0006] The three-dimensional geometric model of the gallium nitride device includes a substrate layer and a gallium nitride layer, with the thickness direction in the z-direction, the length direction in the x-direction, and the width direction in the y-direction, wherein the cross-section is the xz plane.

[0007] The discretization process refers to: discretizing an unstructured mesh in the xz plane of the three-dimensional geometric model to generate a locally refined mesh, and discretizing with a uniform mesh in the y direction, specifically:

[0008] i) Generate several initial rectangular meshes based on the mesh size standard of each rectangular region in the xz plane;

[0009] ii) Continuously divide the rectangular grid at the midpoint of the side length until the generated grid size is smaller than the given standard and all grids are valid grids, that is, at most only two adjacent sides are divided and the division ratio of adjacent grids is at most 2.

[0010] The localized refined mesh includes: a Type I mesh with no edge division, a Type II mesh with one edge division, and a Type III mesh with two adjacent edges division. The mesh vertices are temperature nodes, and each temperature node is surrounded by a corresponding control volume.

[0011] The material properties mentioned include: specific heat capacity, density, and thermal conductivity.

[0012] The boundary conditions include: isothermal boundary conditions, heat flux boundary conditions, and convection boundary conditions.

[0013] The equations obtained in matrix form using the finite volume method specifically include:

[0014] 1) Based on the heat conduction equation within the control volume V The first term on the left side of the equation satisfies The second term on the left is calculated using the divergence theorem as follows: The terms on the right side of the equation satisfy ∫ V q(r,t)dV≈q A V A Where: r is the position vector, t is the time variable, T is the temperature value, κ is the thermal conductivity of the material, ρ is the density, and c p Let V be the heat capacity, q be the time-varying heat source, Δt be the time step in the transient simulation, and V be the heat capacity. A Let q be the control volume corresponding to temperature node A. A Let S be the heat source at temperature node A, and let S be the outer surface of the control volume V, which is composed of m parts in total. i Let n be the outer surface of the i-th part. i For S i The external normal vector and the temperature gradient are obtained through central difference approximation and linear interpolation;

[0015] 2) In the three types of locally refined meshes, the spatial temperature node A and the surrounding temperature nodes A', B, C, E, and G respectively satisfy:

[0016] Type I mesh:

[0017] Type II grid:

[0018] Type III mesh:

[0019] Where: Δx, Δy, Δz are the spatial step sizes after discretization in the x, y, and z directions, respectively, and S x =ΔyΔz / 4,S y =ΔxΔz / 4,S z =ΔxΔy / 4, , κ x , κ y and κ z These are the thermal conductivity in the x, y, and z directions, respectively.

[0020] 3) By combining the equations for all temperature nodes, a system of linear equations is obtained. Where: C is the heat capacity matrix, G is the thermal conductivity matrix, T is the temperature vector, and q is the heat source vector.

[0021] The aforementioned generalized alternating direction implicit method specifically includes:

[0022] a) Based on the time stepping formula of the backward difference method Rewritten as: (I+A)T n+1 =T n +q', where: A=ΔtC -1 G, q' = ΔtC -1 q, matrix A is split into heat transfer matrices in five directions, including: A1 represents the x-direction, A2 represents the y-direction, A3 represents the z-direction, A4 represents the bottom-left to top-right direction, and A5 represents the bottom-right to top-left direction. Substituting these values, we get...

[0023] b) Using the operator splitting method, the equation in step a) is divided into five sub-steps: The matrix equations for each sub-step are solved using a linear-competition method, ultimately yielding the transient thermal simulation results for the gallium nitride device.

[0024] The transient thermal simulation results include predictions of the operating temperature of gallium nitride (GaN) devices, which are further used to extract the thermal resistance and thermal capacity of GaN devices to assist in the analysis of their thermal reliability.

[0025] This invention relates to a system for implementing the above-mentioned method, comprising: a mesh generation module, a matrix assembly module, and a time-stepping solution module, wherein: the mesh generation module performs spatial discretization processing based on the three-dimensional geometric model of the gallium nitride device to obtain a locally refined mesh; the matrix assembly module constructs equations for all temperature nodes using the finite volume method based on the locally refined mesh and given material properties and boundary conditions, and assembles the matrix equations; the time-stepping solution module, based on the generalized alternating direction implicit method, splits the original matrix equations into five tridiagonal matrices according to a specified direction, and solves the tridiagonal matrices using the chasing method to obtain the transient thermal simulation results of the gallium nitride device. Technical effect

[0026] This invention employs a generalized, alternating-direction implicit method based on unstructured, locally refined meshes. Five specific directions are defined, and when solving the time-stepping equations, a large sparse matrix is ​​split into five tridiagonal matrices according to these five directions, allowing for solution using a linearly complex chasing method. This invention overcomes the limitation of existing alternating-direction implicit methods in handling unstructured meshes. Due to the algorithm's linear complexity, it offers significant advantages in simulation efficiency for transient thermal simulations of gallium nitride devices with a large number of unknowns. Attached Figure Description

[0027] Figure 1 This is a flowchart of the present invention;

[0028] Figure 2 This is a schematic diagram of a gallium nitride device.

[0029] Figure 3 This is a schematic diagram of three types of grids;

[0030] Figure 4 This is a schematic diagram of the generalized alternating direction method;

[0031] Figure 5 This is a schematic diagram of a locally refined mesh in a specific embodiment of a multi-finger gallium nitride device.

[0032] Figure 6 This is a temperature response curve at the observation point of a specific embodiment;

[0033] Figure 7 This is a simulation time diagram for a specific embodiment under different numbers of unknowns. Detailed Implementation

[0034] like Figure 1 As shown in the figure, this embodiment relates to an optimization simulation method for transient heat conduction of gallium nitride (GaN) devices. By establishing a three-dimensional geometric model of the GaN device, a locally refined mesh is used for discretization in the spatial domain. The material properties and boundary conditions of the GaN device are set, and the matrix equation is obtained by the finite volume method. The equation is solved by the generalized alternating direction implicit method to obtain the transient thermal simulation results of the GaN device.

[0035] like Figure 2 As shown, the three-dimensional geometric model of the gallium nitride device includes a substrate layer and a gallium nitride layer, with the thickness direction in the z-direction, the length direction in the x-direction, and the width direction in the y-direction.

[0036] like Figure 3 As shown, the localized mesh refinement can be categorized into three types based on the dividing edges: Type I mesh has no dividing edges; Type II mesh has one dividing edge; and Type III mesh has two adjacent dividing edges.

[0037] like Figure 3 As shown, the grid vertices are temperature nodes, and each temperature node is surrounded by a corresponding control volume.

[0038] like Figure 4 As shown, the generalized alternating direction implicit method defines five directions in three types of meshes: direction 1 is the x-direction, direction 2 is the y-direction, direction 3 is the z-direction, direction 4 is the lower left-upper right direction, and direction 5 is the lower right-upper left direction.

[0039] like Figure 5 The image shows a locally refined grid of a multi-finger gallium nitride (GaN) device, where the GaN layer is 2 μm thick, the silicon substrate is 100 μm thick, and the length is 600 μm. The gate fingers have a width of 100 μm and a length of 0.5 μm, and the gate finger pitch is 20 μm.

[0040] The bottom surface of the substrate is a constant temperature boundary of 300K, representing the function of the heat sink; the area below the gate finger is a uniform heat flow boundary condition, representing the heat source, with a size of 3W / mm, a pulse width of 10µs, and a duty cycle of 50%; the remaining outer surfaces are all adiabatic boundaries.

[0041] An observation point P1 is set at the center of the innermost gate finger. To verify the accuracy of the method, thermal simulations are performed using both the traditional backward difference method and the method of this invention, with a time step of 1 ns. The temperature response is observed at... Figure 6 A comparison was made. The average absolute error between them was less than 0.5K, which fully demonstrates the effectiveness of the method of the present invention.

[0042] Compared with existing technologies, this method employs a generalized alternating direction implicit method during the time-stepping solution process. Compared to the backward difference method, it does not require solving for a sparse matrix, only a tridiagonal matrix, thus exhibiting linear complexity and significantly reducing simulation time. Simulations were performed on a computer with a 3.2-GHz Intel Core i7-8700 processor and 48GB of memory, using both the traditional backward difference method and the method of this invention, with varying numbers of unknowns. The simulation time consumption is as follows: Figure 7 As shown, compared with traditional methods, the efficiency of the method of the present invention is improved by an order of magnitude, and the required calculation time increases linearly with the increase of the number of unknowns, which fully demonstrates the efficiency advantage of the method of the present invention.

[0043] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. An optimized simulation method for transient thermal conduction in gallium nitride devices, characterized in that, A three-dimensional geometric model of a gallium nitride (GaN) device was constructed, and the model was discretized in the spatial domain to obtain a locally refined mesh. The material properties and boundary conditions of the GaN device were set, and the matrix equations were obtained through the finite volume method. The transient thermal simulation results of the GaN device were obtained by solving the equations through the generalized alternating direction implicit method. The material properties mentioned include: specific heat capacity, density, and thermal conductivity; The boundary conditions include: isothermal boundary conditions, heat flux boundary conditions, and convection boundary conditions; The three-dimensional geometric model of the gallium nitride device includes: a substrate layer and a gallium nitride layer, with the thickness direction in the z-direction, the length direction in the x-direction, and the width direction in the y-direction, wherein the cross-section is the xz plane; The discretization process refers to: performing unstructured mesh discretization on the xz plane of the three-dimensional geometric model to generate a locally refined mesh, and using a uniform mesh discretization in the y direction; The discrete processing specifically refers to: i) Generate several initial rectangular meshes based on the mesh size standard of each rectangular region in the xz plane; ii) Continuously divide the rectangular grid at the midpoint of the side length until the generated grid size is smaller than the given standard and all grids are valid grids, that is, at most only two adjacent sides are divided and the division ratio of adjacent grids is at most 2. The localized refined mesh includes: a Type I mesh with no edge division, a Type II mesh with one edge division, and a Type III mesh with two adjacent edges division. The mesh vertices are temperature nodes, and each temperature node is surrounded by a corresponding control volume. The equations obtained in matrix form using the finite volume method specifically include: 1) Based on the heat conduction equation within the control volume V The first term on the left side of the equation satisfies The second term on the left is calculated using the divergence theorem as follows: The terms on the right side of the equation satisfy Where: r is the position vector, t is the time variable, T is the temperature value, κ is the thermal conductivity of the material, ρ is the density, and c p Let V be the heat capacity, q be the time-varying heat source, Δt be the time step in the transient simulation, and V be the heat capacity. A Let q be the control volume corresponding to temperature node A. A Let S be the heat source at temperature node A, and let S be the outer surface of the control volume V, which is composed of m parts in total. i Let n be the outer surface of the i-th part. i For S i The external normal vector and temperature gradient are obtained through central difference approximation and linear interpolation; 2) In the three types of locally refined meshes, the spatial temperature node A and the surrounding temperature nodes A', B, C, E, and G respectively satisfy: Type I mesh: ; Type II grid: ; Type III mesh: ; Where Δx, Δy, and Δz are the spatial step sizes after discretization in the x, y, and z directions, respectively. , κ x , κ y and κ z These are the thermal conductivity in the x, y, and z directions, respectively. , ; 3) By combining the equations for all temperature nodes, a system of linear equations is obtained. Where: C is the heat capacity matrix, G is the thermal conductivity matrix, T is the temperature vector, and q is the heat source vector; The aforementioned generalized alternating direction implicit method specifically includes: a) Based on the time stepping formula of the backward difference method Rewritten as: ,in: Matrix A is split into heat transfer matrices in five directions, including: A1 represents the x-direction, A2 represents the y-direction, A3 represents the z-direction, A4 represents the bottom-left to top-right direction, and A5 represents the bottom-right to top-left direction. Substituting these values, we get... ; b) Using the operator splitting method, the equation in step a) is divided into five sub-steps: The matrix equations for each sub-step are solved using a linear-competition method, and finally, the transient thermal simulation results of the gallium nitride device are obtained.

2. An optimized simulation system for transient thermal conduction of gallium nitride devices implementing the method of claim 1, characterized in that, include: The system comprises a mesh generation module, a matrix assembly module, and a time-stepping solution module. The mesh generation module discretizes the three-dimensional geometric model of the gallium nitride (GaN) device to obtain a locally refined mesh. The matrix assembly module constructs equations for all temperature nodes using the finite volume method based on the locally refined mesh and given material properties and boundary conditions, assembling the equations into a matrix form. The time-stepping solution module, based on a generalized alternating direction implicit method, splits the matrix equations into five tridiagonal matrices according to a specified direction, and solves the tridiagonal matrices using a chasing method to obtain the transient thermal simulation results of the GaN device.

Images