CN117350130A - Optimized simulation method for transient heat conduction of gallium nitride device - Google Patents
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Abstract
A gallium nitride device transient heat conduction optimizing simulation method is characterized in that a three-dimensional geometric model of a gallium nitride device is constructed, and the model is subjected to discrete processing in a space domain to obtain a local refined grid; setting material properties and boundary conditions of the gallium nitride device, obtaining an equation in a matrix form through a finite volume method, and solving through a generalized alternating direction implicit method to obtain a transient thermal simulation result of the gallium nitride device. On the premise of ensuring the precision, the invention has the advantages of unconditional stability, high efficiency, less consumption of calculation resources and the like.
Description
Technical Field
The invention relates to a technology in the field of semiconductor design, in particular to an optimized simulation method for transient heat conduction of a gallium nitride device.
Background
Gallium nitride devices have significant advantages in radio frequency power electronics applications due to their superior material properties. As power density increases, efficient transient thermal conduction simulation techniques are needed to predict dynamic temperature changes of gallium nitride devices. The time-stepping solution method of the transient heat conduction equation comprises an implicit type and an explicit type. The explicit method has high solving efficiency, but proper time step is needed to be selected to meet the stability condition of solving, so that divergence is avoided; the implicit method is unconditionally stable, and does not need to consider the influence of time step on stability, but in the solving process, a large sparse matrix needs to be solved, and the problems of long calculation time and high calculation resource consumption are faced.
Disclosure of Invention
Aiming at the defect that the existing alternate direction implicit technology is only suitable for a scene that a calculation area is a structured grid, the invention provides an optimized simulation method for transient heat conduction of a gallium nitride device, and the method has the advantages of unconditional stability, high efficiency, low calculation resource consumption and the like on the premise of ensuring the precision.
The invention is realized by the following technical scheme:
the invention relates to an optimization simulation method of transient heat conduction of a gallium nitride device, which comprises the steps of constructing a three-dimensional geometric model of the gallium nitride device and performing discrete treatment on the model in a space domain to obtain a local refined grid; setting material properties and boundary conditions of the gallium nitride device, obtaining an equation in a matrix form through a finite volume method, and solving through a generalized alternating direction implicit method to obtain a transient thermal simulation result of the gallium nitride device.
The three-dimensional geometric model of the gallium nitride device comprises: the substrate layer and the gallium nitride layer, the thickness direction is the z direction, the length direction is the x direction, the width direction is the y direction, wherein: the cross section is the x-z plane.
The discrete processing refers to: unstructured grid dispersion is carried out on the x-z plane of the three-dimensional geometric model, a local refined grid is generated, and uniform grid dispersion is adopted in the y direction, specifically:
i) Generating a plurality of initial rectangular grids according to the grid size standard of each rectangular area in the x-z plane;
ii) continuously dividing at the midpoint of the side length of the rectangular grid until the generated grid size is smaller than the given standard and all grids are legal grids, namely, at most two adjacent sides are divided, and the division ratio of the adjacent grids is at most 2.
The local refinement grid includes: there is no type I mesh with edges segmented, a type II mesh with one edge segmented, and a type III mesh with two adjacent edges segmented, the mesh vertices are temperature nodes, each surrounded by a corresponding control volume.
The material properties include: specific heat capacity, density, and thermal conductivity.
The boundary conditions include: constant temperature boundary conditions, heat flow boundary conditions, and convection boundary conditions.
The equation in matrix form is obtained by the finite volume method, and specifically comprises the following steps:
1) According to the equation of heat conduction in the control volume VThe first term on the left of the equation satisfiesThe second term on the left is calculated as by the divergence theoremThe right term of the equation satisfies ≡ V q(r,t)dV≈q A V A Wherein: r is a position vector, T is a time variable, T is a temperature value, κ is the thermal conductivity of the material, ρ is the density, c p Is heat capacity, q is time-varying heat source, deltat is time step in transient simulation, V A Control volume corresponding to temperature node A, q A Is a heat source at a temperature node A, S is the outer surface of the control volume V, and is composed of m parts in total, S i For the i-th part of the outer surface, n i Is S i The temperature gradient is obtained through center difference approximation and linear interpolation;
2) In the three types of locally refined grids, the space temperature node A and the ambient temperature nodes A', B, C, E and G respectively meet the following conditions:
type I grid:
type II grid:
type III grid:
wherein: Δx, Δy, Δz are the discrete spatial steps in the x, y, z directions, S x ＝ΔyΔz/4,S y ＝ΔxΔz/4,S z ＝ΔxΔy/4,，κ x ，κ y And kappa (kappa) z Thermal conductivities in the x, y and z directions respectively,
3) By combining the equations of all temperature nodes, a linear system of equations is obtainedWherein: c is a heat capacity matrix, G is a heat conduction matrix, T is a temperature vector, and q is a heat source vector.
The generalized alternating direction implicit method specifically comprises the following steps:
a) According to a time stepping formula based on a backward difference methodThe rewriting is: (I+A) T n+1 ＝T n +q', wherein: a=Δtc -1 G，q'＝ΔtC -1 q, matrix a splits into five-directional heat transfer matrices, including:A 1 represents the x direction, A 2 Represents the y direction, A 3 Indicating the z direction, A 4 Indicating the left lower-right upper direction, A 5 Indicating the direction from lower right to upper left, substituted with +.>
b) The equation of step a) is divided into five substeps by an operator splitting method:the matrix equation of each sub-step is solved through a linear complexity catch-up method, and finally a transient thermal simulation result of the gallium nitride device is obtained.
The transient thermal simulation result comprises the step of predicting the working temperature of the gallium nitride device, and is further used for extracting the thermal resistance and the thermal capacity of the gallium nitride device and assisting in analyzing the thermal reliability of the gallium nitride device.
The invention relates to a system for realizing the method, which comprises the following steps: the system comprises a grid dividing module, a matrix assembling module and a time stepping solving module, wherein: the grid dividing module performs space discretization processing according to the three-dimensional geometric model of the gallium nitride device to obtain a local refined grid; the matrix assembly module constructs equations of all temperature nodes through a finite volume method according to the local refinement grid, given material properties and boundary conditions, and assembles the equations to obtain a matrix equation; the time stepping solving module splits an original matrix equation into five tri-diagonal matrixes according to a specified direction based on a generalized alternating direction implicit method, and solves the tri-diagonal matrixes by using a catch-up method to obtain a transient thermal simulation result of the gallium nitride device.
Technical effects
According to the invention, five specific directions are set through a generalized alternating direction implicit method based on unstructured local refinement grids, and when a time stepping equation is solved, a large sparse matrix is split into five tri-diagonal matrices according to the five specific directions, and the method can be solved through a catch-up method with linear complexity. The invention breaks through the limitation that the existing alternate direction implicit method cannot process unstructured grids. The algorithm has linear complexity, so that the method has remarkable advantage in simulation efficiency for transient thermal simulation of the gallium nitride device under the condition of large unknown quantity number.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a schematic structural diagram of a gallium nitride device;
FIG. 3 is a schematic diagram of three types of grids;
FIG. 4 is a schematic diagram of a generalized alternating direction approach;
FIG. 5 is a schematic diagram of a partially refined mesh of an embodiment of a multi-fingered gallium nitride device;
FIG. 6 is a plot of the viewpoint temperature response of an embodiment;
FIG. 7 is a schematic diagram of simulation time under different unknowns according to an embodiment.
Detailed Description
As shown in fig. 1, this embodiment relates to an optimized simulation method for transient heat conduction of a gallium nitride device, which adopts a local refinement grid to perform dispersion in a spatial domain by establishing a three-dimensional geometric model of the gallium nitride device; setting material properties and boundary conditions of a gallium nitride device, and obtaining an equation in a matrix form through a finite volume method; solving the equation by a generalized alternating direction implicit method to obtain a transient thermal simulation result of the gallium nitride device.
As shown in fig. 2, the three-dimensional geometric model of the gallium nitride device includes a substrate layer and a gallium nitride layer, the thickness direction is the z direction, the length direction is the x direction, and the width direction is the y direction.
As shown in fig. 3, the locally refined mesh can be classified into three types according to the segmentation edges: type I grids have no edges partitioned; the type II mesh has one edge partitioned; the type III grid has two adjacent edges segmented.
As shown in fig. 3, the grid vertices are temperature nodes, each surrounded by a corresponding control volume.
As shown in fig. 4, in the generalized alternate direction implicit method, five directions in three types of grids are respectively specified: direction 1 is the x-direction, direction 2 is the y-direction, direction 3 is the z-direction, direction 4 is the bottom-left-top-right-direction, and direction 5 is the bottom-left-top-right-direction.
As shown in fig. 5, a partially refined grid of a multi-finger gallium nitride device, in which the gallium nitride layer thickness is 2 μm, the silicon substrate thickness is 100 μm, and the length is 600 μm. The width and length of the gate fingers were 100 μm and 0.5 μm, and the gate finger pitch was 20 μm.
The bottom surface of the substrate is a constant temperature boundary 300K, which shows the function of a heat sink; the uniform heat flow boundary condition under the gate finger is used for representing a heat source, the size of the heat source is 3W/mm, the pulse width is 10us, and the duty ratio is 50%; the remaining outer surfaces are all insulated boundaries.
An observation point P1 is set at the center of the innermost gate finger. To verify the accuracy of the method, thermal simulations were performed by the conventional backward differential method and the inventive method, respectively, with a time step of 1ns, the temperature responses of which are compared in fig. 6. The average absolute error between them is less than 0.5K, which is a sufficient indication of the effectiveness of the method of the present invention.
Compared with the prior art, the method adopts the generalized alternating direction implicit method in the time stepping solving process, and compared with the backward differential method, the method does not need to solve a sparse matrix, only needs to solve a tri-diagonal matrix, has linear complexity, and remarkably reduces the simulation time. The simulation time consumption was calculated on a computer with a 3.2-GHz Intel Core i7-8700 processor and 48GB memory using the conventional backward differencing method and the inventive method, respectively, under different unknown quantities as shown in FIG. 7. It can be seen that the efficiency of the method of the present invention is improved by an order of magnitude over conventional methods, and that the required computation time increases linearly as the number of unknowns increases, fully illustrating the efficiency advantages of the method of the present invention.
The foregoing embodiments may be partially modified in numerous ways by those skilled in the art without departing from the principles and spirit of the invention, the scope of which is defined in the claims and not by the foregoing embodiments, and all such implementations are within the scope of the invention.
Claims (7)
1. The optimized simulation method of the transient heat conduction of the gallium nitride device is characterized in that a three-dimensional geometric model of the gallium nitride device is constructed and the model is subjected to discrete processing in a space domain to obtain a local refined grid; setting material properties and boundary conditions of the gallium nitride device, obtaining an equation in a matrix form through a finite volume method, and solving through a generalized alternating direction implicit method to obtain a transient thermal simulation result of the gallium nitride device;
the material properties include: specific heat capacity, density, and thermal conductivity;
the boundary conditions include: constant temperature boundary conditions, heat flow boundary conditions, and convection boundary conditions.
2. The method for optimizing the simulation of the transient heat conduction of the gallium nitride device according to claim 1, wherein the three-dimensional geometric model of the gallium nitride device comprises: the substrate layer and the gallium nitride layer, the thickness direction is the z direction, the length direction is the x direction, the width direction is the y direction, wherein: the cross section is an x-z plane;
the discrete processing refers to: unstructured grid dispersion is carried out on the x-z plane of the three-dimensional geometric model, a local refined grid is generated, and uniform grid dispersion is adopted in the y direction.
3. The method for optimizing and simulating transient heat conduction of a gallium nitride device according to claim 1 or 2, wherein the discrete processing is specifically:
i) Generating a plurality of initial rectangular grids according to the grid size standard of each rectangular area in the x-z plane;
ii) continuously dividing at the midpoint of the side length of the rectangular grid until the generated grid size is smaller than the given standard and all grids are legal grids, namely, at most two adjacent sides are divided, and the division ratio of the adjacent grids is at most 2.
4. The method for optimizing and simulating transient heat conduction of a gallium nitride device according to claim 1 or 2, wherein the locally refined grid comprises: there is no type I mesh with edges segmented, a type II mesh with one edge segmented, and a type III mesh with two adjacent edges segmented, the mesh vertices are temperature nodes, each surrounded by a corresponding control volume.
5. The method for optimizing the simulation of the transient heat conduction of the gallium nitride device according to claim 1, wherein the equation in the form of a matrix is obtained by a finite volume method, and the method specifically comprises the following steps:
1) According to the equation of heat conduction in the control volume VThe first term on the left of the equation satisfies +.>The second term on the left is calculated as by the divergence theoremThe right term of the equation satisfies ≡ V q(r,t)dV≈q A V A Wherein: r is a position vector, T is a time variable, T is a temperature value, κ is the thermal conductivity of the material, ρ is the density, c p Is heat capacity, q is time-varying heat source, deltat is time step in transient simulation, V A Control volume corresponding to temperature node A, q A Is a heat source at a temperature node A, S is the outer surface of the control volume V, and is composed of m parts in total, S i For the i-th part of the outer surface, n i Is S i The temperature gradient is obtained through center difference approximation and linear interpolation;
2) In the three types of locally refined grids, the space temperature node A and the ambient temperature nodes A', B, C, E and G respectively meet the following conditions:
type I grid:
type II grid:
type III grid:
wherein: Δx, Δy, Δz are the discrete spatial steps in the x, y, z directions, S x ＝ΔyΔz/4,S y ＝ΔxΔz/4,S z ＝ΔxΔy/4,κ x ，κ y And kappa (kappa) z Thermal conductivities in the x, y and z directions respectively,
3) By combining the equations of all temperature nodes, a linear system of equations is obtainedWherein: c is a heat capacity matrix, G is a heat conduction matrix, T is a temperature vector, and q is a heat source vector.
6. The optimized simulation method for transient heat conduction of a gallium nitride device according to claim 1, wherein the generalized alternating direction implicit method specifically comprises:
a) According to a time stepping formula based on a backward difference methodThe rewriting is: (I+A) T n+1 ＝T n +q', wherein: a=Δtc -1 G，q'＝ΔtC -1 q, matrix a splits into five-directional heat transfer matrices, including: />A 1 Represents the x direction, A 2 Represents the y direction, A 3 Indicating the z direction, A 4 Indicating the left lower-right upper direction, A 5 Indicating the direction from lower right to upper left, substituted with +.>
b) The equation of step a) is divided into five substeps by an operator splitting method:the matrix equation of each sub-step is solved through a linear complexity catch-up method, and finally a transient thermal simulation result of the gallium nitride device is obtained.
7. An optimized simulation system for transient heat conduction of a gallium nitride device implementing the method of any one of claims 1-6, comprising: the system comprises a grid dividing module, a matrix assembling module and a time stepping solving module, wherein: the grid dividing module performs space discretization processing according to the three-dimensional geometric model of the gallium nitride device to obtain a local refined grid; the matrix assembly module constructs equations of all temperature nodes through a finite volume method according to the local refinement grid, given material properties and boundary conditions, and assembles the equations to obtain a matrix equation; the time stepping solving module splits an original matrix equation into five tri-diagonal matrixes according to a specified direction based on a generalized alternating direction implicit method, and solves the tri-diagonal matrixes by using a catch-up method to obtain a transient thermal simulation result of the gallium nitride device.
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