CN107229762B - Microwave circuit characteristic analysis method containing semiconductor physical model - Google Patents

Microwave circuit characteristic analysis method containing semiconductor physical model Download PDF

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CN107229762B
CN107229762B CN201610169924.3A CN201610169924A CN107229762B CN 107229762 B CN107229762 B CN 107229762B CN 201610169924 A CN201610169924 A CN 201610169924A CN 107229762 B CN107229762 B CN 107229762B
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陈如山
朱琦
丁大志
樊振宏
陈士涛
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Nanjing University of Science and Technology
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Abstract

The invention discloses a microwave circuit characteristic analysis method containing a semiconductor physical model. The method mainly utilizes a field-path coupling algorithm of a time domain volume-surface integration method to analyze the microwave circuit structure containing the semiconductor physical model. The field coupling algorithm requires the same current and potential at the electromagnetic and circuit structure connection locations. And the physical characteristics of the semiconductor are solved numerically by a time domain spectral element method. Because the internal physical change process of the semiconductor is described by a drift diffusion equation, the physical characteristic of the semiconductor is nonlinear, a discrete Newton iteration method is required to be adopted in the electrical characteristic calculation process of the microwave circuit, and an improved strictly synchronous coupling solving process is adopted, so that the stability and the efficiency of the algorithm are improved.

Description

Microwave circuit characteristic analysis method containing semiconductor physical model
Technical Field
The invention relates to the technical field of electromagnetic simulation, in particular to a time domain volume-surface integration method capable of analyzing an actual microwave circuit structure, which is provided for the real physical characteristic analysis of a microwave semiconductor circuit.
Background
For simulation of field-by-field mixing problems, including integrated circuit modules and substrate systems, the time domain approach is very useful because it allows for accurate simulation of nonlinear components in the circuit and also for obtaining broadband information. The research on the field-one-way coupling problem of time domain simulation mainly depends on a differential equation method in the past, for example, a finite difference method is favored by people in the past because of the stability of the differential method and the easy realization of the addition of lumped circuit elements. However, with the development of the time domain integral equation solving technology, especially the improvement of the stability of the time domain integral equation solving technology at night, the reduction of the computational complexity and the enhancement of the computational performance are realized with the adoption of a fast algorithm, and the continuous research of a new simulation scheme aiming at the field-one-path coupling problem is carried out. These have all led to a wide range of attention being paid to the TDIE solution.
Originally, the TDIE method was based on a partial cell equivalent circuit (PEEC) method, and the key idea of PEEC is to convert the electromagnetic coupling between wires into an equivalent circuit and connect it with any other lumped circuit model to form a circuit simulator, like SPICE software. Recent improvements in stability and computational speed of TDIE led to the idea of combining the integral equation method with the circuit analysis method, first applied to the metal structure, and then expanded to the metal medium mixed structure. A circuit problem generally for metal/medium mixing is to combine the Modified Nodal Analysis (MNA) of the TDIE method with the circuit simulation method). The basis of this solution for the electromagnetic coupling of the circuit is the idea of coupling currents by which the circuit parts and the electromagnetic structure parts in the area are linked. Since this method can add both circuit excitation and field excitation, it can be used for signal integrity and EMI/EMC simulation.
Disclosure of Invention
The invention aims to provide a microwave circuit characteristic analysis method containing a semiconductor physical model, simultaneously considers equation description of a real physical process in a microwave semiconductor circuit and a field-path matrix equation coupled by adopting a field-path coupling algorithm, and finally solves the physical parameters of the circuit through strict synchronization of an improved Newton iteration method.
The technical solution for realizing the purpose of the invention is as follows: a microwave circuit characteristic analysis method containing a semiconductor physical model comprises the following steps:
firstly, establishing a solving model of a microwave circuit structure, subdividing the model by using triangles for a metal part in an electromagnetic structure, and subdividing a tetrahedron for a medium part to obtain structural information of the model, namely unit information of each triangle and each tetrahedron;
secondly, determining a time domain electric field integral equation of the electromagnetic target from a Maxwell equation system;
and thirdly, respectively dispersing the surface current of the metal and the electric flux density of the dielectric body in a space domain and a time domain. Here, the dispersion method of the surface current with respect to the metal surface is to spatially disperse using RWG basis functions, and the division method of the metal surface is to use a division form of a triangular patch. The processing of the dielectric body is different from the metal processing by a space dispersion mode of the electric flux density, the dispersion is carried out on a space domain by using an SWG basis function, and a tetrahedral body division mode is selected for dividing the dielectric body. Furthermore, in the time domain, the time domain volume-surface integral equation is discretized for both metal and media parts using a Lagrange interpolation time basis function of order 4.
Step four, substituting the expanded expressions of the metal surface current and the electric flux density of the dielectric body in the step three into the time domain electric field integral equation in the step two, and then respectively testing the discrete time domain electric field integral equation by adopting a point test in time and a Galerkin test in space to obtain a system impedance matrix equation;
fifthly, starting from a semiconductor drift-diffusion equation set, expanding the concentration and the potential of the current carrier to be solved on each node, testing the semiconductor drift-diffusion equation by adopting a Galerkin method, solving by utilizing a Newton iteration method to obtain the current carrier and the potential distribution of each node, and finally obtaining the internal physical parameters of the semiconductor;
and sixthly, establishing a strictly synchronous field-circuit coupling matrix equation according to the system impedance matrix equation obtained in the fourth step and the semiconductor physical parameters obtained in the fifth step through a field-circuit coupling idea, then obtaining time domain current distribution in the microwave circuit structure through improved Newton iteration solution, obtaining physical parameters according to the time domain current distribution, and completing the simulation process.
Compared with the prior art, the invention has the following remarkable advantages: (1) compared with a time domain surface integral equation method, the adopted time domain volume surface integral equation can process more complex three-dimensional electromagnetic structures, such as a metal-medium mixed microstrip transmission line structure and the like. (2) The physical characteristic equation of the microwave semiconductor circuit is based on a semiconductor drift-diffusion equation set, the concentration and the potential of a current carrier to be solved are expanded on each node, the equation is tested by adopting a Galerkin method, the current carrier and the potential distribution of each node are obtained by utilizing a Newton iteration method, the physical process of the PIN tube can be more accurately analyzed compared with an equivalent circuit model, and meanwhile, the electric-heat integration analysis of the microwave circuit can be further carried out. (3) The physical model equation of the semiconductor is combined into a time domain volume-surface integral equation based on MOT to form a strictly synchronous field-circuit coupling solving method, and an improved Newton iteration method is adopted in the solving process, so that the calculation accuracy of the field-circuit coupling solving can be ensured, and meanwhile, certain calculation efficiency is improved.
Drawings
FIG. 1 is a RWG basis function.
FIG. 2 is a SWG basis function.
Fig. 3 is a cross-sectional view of a MOSFET.
Fig. 4 is a three-dimensional electromagnetic structural model of a MOSFET tube amplifier circuit.
Fig. 5 is a simulation result of the MOSFET tube amplifier circuit under the action of a sinusoidal continuous signal.
Detailed Description
The invention combines the electromagnetic structure analysis process of the time domain volume-surface integral method based on time stepping (MOT) with the semiconductor circuit structure analysis process of the time domain spectral element method, namely, a nonlinear semiconductor physical equation is combined into the time domain volume-surface integral equation based on the MOT to form a mixed field path solution, thus the mutual coupling analysis calculation between the electromagnetic structure and the circuit structure is more consistent and effective. Compared with an equivalent analytical model, the physical model is more in line with a real physical process when the characteristics of an actual structure are analyzed, and the calculation and analysis are more accurate. However, the analysis of the physical model also consumes more time and computing resources, and an improved newton iteration solution is provided for the problem, so that a part of computing time can be saved. Because the simulation of a real physical process is complex, currently, there are few related reports of field-path coupling analysis semiconductor physical processes introducing the problem of microwave circuits, and the reports are not found in a time domain volume-surface integration method. This is also an innovation of the present invention.
The present invention is described in further detail below with reference to the attached drawing figures.
First, basic principle of time domain volume-surface integral method
It is assumed that a metal-dielectric mixed target exists in free space, wherein the surface of the metal is denoted by S, the volume of the dielectric body is denoted by V, and the dielectric is isotropic, nonmagnetic, non-dispersive, lossless, and has a dielectric constant ε (r). Dielectric constant of free space of epsilon0Magnetic permeability of mu0. When there is a time domain incident wave Einc(r, t) when the mixed object is irradiated, an induced surface current J is generated on the metal surface S and in the dielectric body V, respectivelys(r, t) and polarizer Current Jv(r, t). Then, the scattered field in the space includes the sum of the scattered fields generated by the two parts of the induced surface current and the polarizer current, that is:
Figure BDA0000948027560000031
and has:
Figure BDA0000948027560000032
Figure BDA0000948027560000041
further, in the dielectric body, the electric flux density D (r, t), and the polarizer current JvThe relationship between (r, t) and the total electric field E (r, t) satisfies the following expression:
D(r,t)＝ε(r)E(r,t) (1.4)
Figure BDA0000948027560000042
because two types of targets of metal and medium exist in the space at the same time, corresponding time domain integral equations are respectively constructed, the time derivative of the total electric field meeting the tangential direction on the metal surface S is zero, and the time derivative of the total electric field in the medium body V is equal to the sum of the time derivative of the incident electric field and the time derivative of the scattering electric field, namely:
Figure BDA0000948027560000043
Figure BDA0000948027560000044
the above equations (1.6) and (1.7) together form a time domain volume-surface integral equation suitable for analyzing metal-media mixed targets. Here, it is to be noted that the time domain volume-surface integral equation in the above equation operates on time derivatives on both sides of the equation.
In order to solve the above time domain volume-surface integral equation by a numerical method, the surface current J of the metal is requireds(r, t) and the electric flux density D (r, t) of the dielectric body are respectively dispersed in the space and time domains. Here, the surface current J for the metal surfacesAnd (r, t) a discrete mode, namely performing discrete by using RWG basis functions in space, and a subdivision mode of a triangular patch is used for subdividing the metal surface. The place for processing the dielectric body is different from the place for processing the metal is a space dispersion mode of the electric flux density D (r, t), the space domain is dispersed by using an SWG basic function, and a tetrahedral body division mode is selected for dividing the dielectric body. Furthermore, in the time domain, the time domain volume-surface integral equation is discretized for both metal and media parts using a Lagrange interpolation time basis function of order 4. Wherein, the RWG basis functions are defined as shown in FIG. 1, and the SWG basis functions are defined as shown in FIG. 1.
Each complete RWG basis function is composed of two distinct triangles, called the upper and lower triangles of the basis function, in the figure
Figure BDA0000948027560000045
And
Figure BDA0000948027560000046
together forming the nth basis function. lnSide length representing an n-th basis function unknown side，
Figure BDA0000948027560000047
Respectively represent the areas of the upper and lower triangles,
Figure BDA0000948027560000048
is a space vector. The nth basis function is:
Figure BDA0000948027560000051
the surface current J (r) of an ideal conductor is approximated by an expansion using the RWG basis functions given in FIG. 1, which can be expressed as
Figure BDA0000948027560000052
Here, N represents the total number of basis functions, I, obtained by triangulating the entire ideal conductor target surfacenRepresents the current coefficient corresponding to the nth RWG basis function, and J (r) is the current density (unit is ampere/meter or A/m).
In FIG. 2 the adjacent tetrahedra are
Figure BDA0000948027560000053
And
Figure BDA0000948027560000054
the common plane is an nth medium triangle with an area of an. In addition, the vector
Figure BDA0000948027560000055
Is the vector of the free vertex of the upper tetrahedron pointing to the source point r, and the opposite is known
Figure BDA0000948027560000056
Thus, the expression of the SWG basis function associated with the nth triangle patch can be written as:
Figure BDA0000948027560000057
herein, the
Figure BDA0000948027560000058
Corresponding to the volume of the upper and lower tetrahedron, respectively. In addition to the spatial basis functions described above, the 4 th order Lagrange interpolation temporal basis function used herein in addressing the metal-medium mixing problem is:
Figure BDA0000948027560000059
thus, J can be puts(r, t) and D (r, t) are discretely expanded by basis functions in space and time into the form:
Figure BDA0000948027560000061
Figure BDA0000948027560000062
wherein,
Figure BDA0000948027560000063
each being a RWG basis function and a SWG basis function, Ns、NvEach being an unknown number, N, of spatially basis functions after the discretization of the metal and the dielectric bodytThe number of unknowns representing the time basis function after the discretization of the hybrid object,
Figure BDA0000948027560000064
representing the unknown coefficients, T, associated with the basis functions of the metal and dielectric parts, respectivelyj(T) T (T-j Δ T), Δ T being the size of the time step.
Substituting the formula (1.12) and the formula (1.13) into the formula (1.6) and the formula (1.7), all the space basis functions are used
Figure BDA0000948027560000065
And
Figure BDA0000948027560000066
the discrete time domain volume-surface integral equation (1.6) and the equation (1.7) are respectively subjected to a Galerkin test in space, and each time tjThe point matching in time is carried out on the discrete time domain volume-surface integral equation, so that a series of equation sets can be obtained, and the equation sets can be written into the form of a matrix equation, namely:
Figure BDA0000948027560000067
wherein,
Figure BDA0000948027560000068
Figure BDA0000948027560000069
Figure BDA00009480275600000610
Figure BDA00009480275600000611
Figure BDA0000948027560000071
Figure BDA0000948027560000072
Figure BDA0000948027560000073
wherein j is 1tAnd < v >, > represents inner product. By solving the matrix equation for equation (1.14) at each time t ═ j Δ t, all N at each time step can be foundEM＝Ns+NvThe unknown coefficients corresponding to the unknown quantities of the basis functions can be solved in a time stepping mode aiming at the analysis of the metal-medium mixed target, and the formula (1.14) is also called a time domain volume surface integral equation based on the time stepping.
Second, physical model solution of semiconductor
The transient drift-diffusion equation of the MOSFET is solved by a coupling method, namely a Poisson equation and a current continuity equation are simultaneously solved, and the carrier concentration n, p and the potential are used
Figure BDA0000948027560000074
Are variables.
The transient model equation for the MOSFET includes:
normalized poisson equation:
Figure BDA0000948027560000075
Figure BDA0000948027560000076
in the Poisson equation of the above formula (2.1), gamma is the net doping concentration, epsilon1，ε2Dielectric constant, expressed as:
Figure BDA0000948027560000077
normalized electron current density equation:
Figure BDA0000948027560000078
Figure BDA0000948027560000079
normalized hole current density equation:
Figure BDA00009480275600000710
Figure BDA00009480275600000711
normalized electron current continuity equation:
Figure BDA00009480275600000712
Figure BDA00009480275600000713
normalized hole current continuity equation:
Figure BDA00009480275600000714
Figure BDA00009480275600000715
normalized composite rate model:
Figure BDA0000948027560000081
Figure BDA0000948027560000082
as shown in fig. 3, the boundary conditions of the MOSFET:
for poisson's equation, the solution area is the entire MOSFET, and the boundary conditions are:
gate, drain, source and base plates are fixed boundary conditions (metal boundary conditions):
Figure BDA0000948027560000083
Figure BDA0000948027560000084
parallel to the x-coordinate axis is a floating boundary condition
Figure BDA0000948027560000085
Figure BDA0000948027560000086
Si-SiO2 interface
Figure BDA0000948027560000087
Figure BDA0000948027560000088
For the current continuity equation, the solution region is semiconductor, excluding oxide, and the boundary conditions are:
drain, source and base plates are fixed boundary conditions (metal boundary conditions):
and an N region: n- Γ, P-1/Γ P region: n-1/Γ, p- Γ (2.10)
CD + EG + FH is a floating boundary condition
Figure BDA0000948027560000089
Figure BDA00009480275600000810
Note that the front and back surfaces in the three-dimensional model are set as floating boundary conditions.
Since both the current continuity equation and the poisson equation are nonlinear, taylor's expansion is used to linearize the equations.
Solving a drift-diffusion equation by adopting a full-coupling method, and writing the equation after Taylor expansion processing into a form of an equation (2.12):
Figure BDA0000948027560000091
the final matrix form is obtained by appropriate derivation:
Figure BDA0000948027560000092
in equation (2.13), each matrix block is as follows:
Figure BDA0000948027560000093
Figure BDA0000948027560000094
Figure BDA0000948027560000095
Figure BDA0000948027560000096
Figure BDA0000948027560000101
Figure BDA0000948027560000102
Figure BDA0000948027560000103
Figure BDA0000948027560000104
Figure BDA0000948027560000105
Figure BDA0000948027560000106
Figure BDA0000948027560000107
Figure BDA0000948027560000108
Figure BDA0000948027560000109
Figure BDA00009480275600001010
Figure BDA00009480275600001011
Figure BDA00009480275600001012
for the drift-diffusion model, the handling of the avalanche generation term needs to be particularly pointed out. The expression of it is shown as (2.14):
Figure BDA00009480275600001013
in the above formula (2.14), the ionization coefficients of electrons and holes are:
Figure BDA0000948027560000111
Figure BDA0000948027560000112
where T is the temperature at the current time inside the device, TrefIs the initial ambient temperature, An,Bn,Cn,DnAnd Ap,Bp,Cp,DpIs a constant.
Determining the quasi-Fermi potential phi of the electronnQuasi-fermi potential of the cavity phipAnd electric potential
Figure BDA0000948027560000113
Then, the current of each node of the corresponding plate can be obtained by the following formula.
Electron current at each node on the plate:
Figure BDA0000948027560000114
hole current at each point on the plate:
Figure BDA0000948027560000115
displacement current:
Figure BDA0000948027560000116
the current at each node is summed to produce the current from the corresponding carrier of the plate. In transient simulation, the displacement current is not negligible. The whole semiconductor solving process can be regarded as a current process for solving the output of the semiconductor transistor by knowing the value of the input voltage.
Three field path coupling algorithm
In FIG. 4, the RWG triangle boundary edges at the G and D positions of the electromagnetic structure connected to the loaded semiconductor are treated as equivalent voltage source edges, and the voltage on the source is taken
Figure BDA0000948027560000117
And
Figure BDA0000948027560000118
when viewed as a feed voltage of an equivalent voltage source, and further, the current flowing through the semiconductor is equal to the current flowing vertically through the loading edge, due to the current coefficient of the boundary edge at the G position
Figure BDA0000948027560000119
Indicating the current density flowing perpendicularly through the edge and thus through the edge
The current of a side being equal to the current coefficient multiplied by the side length a, i.e.
Figure BDA0000948027560000121
Obtaining a mixed field-path equation:
Figure BDA0000948027560000122
since the gate current of the MOSFET is small, it is treated as a zero value.
Figure BDA0000948027560000123
It is possible to obtain:
Figure BDA0000948027560000124
the field-path coupling system equation (3.3) of the time domain nonlinearity is simplified as follows:
Figure BDA0000948027560000125
non-linear term of the equation
Figure BDA0000948027560000126
Unknown quantity of only AND circuit
Figure BDA0000948027560000127
Relative, and number N of circuit unknownsCKTNumber N much smaller than field unknownsEMThen the dimension of the non-linear equations in the system of equations can be considered to be much smaller than the dimension of the linear equations. Thus, conventional solutions utilize criteriaThe newton iteration of (a) solves such a large matrix system as the whole equation (3.4), which is not a very efficient, optimized solution. In addition, the matrix dimension in equation (3.4) is N for each Newton iteration step at each time stepEM+NCKTThe jacobian matrix of (a) is variable, so solving matrix equations of such large dimensions, whether using direct or iterative solutions, is time consuming and cumbersome. Therefore, in order to solve the nonlinear coupled system equation (3.4) more efficiently,
the split is into two equations, namely:
Figure BDA0000948027560000131
Figure BDA0000948027560000132
the field unknowns in equation (3.5)
Figure BDA0000948027560000133
Using circuit unknowns
Figure BDA0000948027560000134
Can be expressed as:
Figure BDA0000948027560000135
then, substituting formula (3.7) into formula (3.6) to obtain the product:
Figure BDA0000948027560000136
the nonlinear equation (3.8) is expressed as:
Figure BDA0000948027560000137
Figure BDA0000948027560000138
equation (3.8) can be abbreviated as:
Figure BDA0000948027560000139
the nonlinear equation (3.11) is solved by discrete newton's iteration:
order to
Figure BDA00009480275600001310
Figure BDA00009480275600001311
Figure BDA00009480275600001312
Final solution xn+1＝xn-[F'(x)]-1·F(x)(3.14)
The solution vector of the equation, i.e., the circuit unknown at each time step, can be found
Figure BDA00009480275600001313
Then, substituting the circuit unknown quantity solved at the current moment into the formula (3.7), so as to obtain the field unknown quantity at the current moment
Figure BDA00009480275600001314
Wherein,
Figure BDA00009480275600001315
is a process representing the MOSFET solution.
Figure BDA00009480275600001316
Figure BDA0000948027560000141
Uj，IjThe electric field and current value of the last iteration step. U shape*＝UjΔ U, predetermined to 0.01V, and
Figure BDA0000948027560000142
to obtain the current I*. Then, the tentative voltage U is determined from (3.14)j+1And current Ij+1. And iterating in the above way until the iteration precision is met, and stopping. Updating Uj＝Uj+1,Ij＝Ij+1. Then, substituting the circuit unknown quantity solved at the current moment into the formula (3.7), so as to obtain the field unknown quantity at the current moment
Figure BDA0000948027560000143
It can be noted that the dimension of the above-mentioned non-linear equation (3.11) is exactly the number N of circuit unknownsCKTAnd thus the dimension N of the above-mentioned non-linear equationCKTIs much smaller than the dimension N of equation (3.4)EM+NCKTIn (1). Because the improved solution of the time domain nonlinear coupling system equation is only used for solving the nonlinear equation (3.11) by the Newton iteration method, the improved solution saves the solution time compared with the traditional solution, and the calculation efficiency is greatly improved. After Newton's iteration satisfies the precision, the current and voltage distribution of the electromagnetic part in the microwave circuit structure and the voltage and current change inside the semiconductor circuit can be obtained at each time step.
In the model of fig. 4, the length of the dielectric substrate is 17.526mm, the width of the dielectric substrate is 16.256mm, the height of the dielectric substrate is 0.7874mm, the relative dielectric constant of the dielectric is 2.33, the lengths of the two metal microstrip lines are both 7.763mm, the width of the two metal microstrip lines is 2.286mm, and the intermediate span of the two metal microstrip lines is 2 mm. The metal microstrip line of the model is divided into two sections, 4 ports are defined, and the two sections correspond to 4 RWG basis functions of the metal surface. The input end loads a sinusoidal small signal with the frequency of 1.34GHz and the voltage amplitude of 0.25V, the grid bias voltage is 0.5V, the drain bias voltage is 5V, and the bias and load resistance are both 50 ohm. The other two ports each represent the gate-source port and the drain-source port of the field effect transistor. It is through these two ports G and D that the two sections of metal microstrip lines are effectively connected together in the figure. And (2) subdividing the metal surface of the model by using a triangle, subdividing the dielectric body of the model by using a tetrahedron, obtaining 160 triangular patches after discretization, 460 tetrahedrons, unknown quantities in 215 metal pieces, unknown quantities in 1102 dielectric triangles, and selecting the time step size to be 0.002286 lm. And (4) obtaining the time domain oscillograms of the voltage signals of the input and output ports of the field effect tube through the field-path coupling algorithm analysis based on the time domain integral equation.

Claims (3)

1. A microwave circuit characteristic analysis method containing a semiconductor physical model is characterized by comprising the following steps:
firstly, establishing a solving model of a microwave circuit structure, subdividing the model by using triangles for a metal part in an electromagnetic structure, and subdividing a tetrahedron for a medium part to obtain structural information of the model, namely unit information of each triangle and each tetrahedron;
secondly, determining a time domain electric field integral equation of the electromagnetic target from a Maxwell equation system;
third, the surface current J of the metals(r, t) and the electric flux density D (r, t) of the dielectric body are respectively dispersed in the space domain and the time domain; the dispersion mode of the surface current of the metal surface is to spatially disperse by using RWG basis functions, and to spatially disperse the electric flux density by using SWG basis functions; in addition, in a time domain, a time domain volume surface integral equation disperses metal and medium parts by using a 4-order Lagrange interpolation time basis function;
step four, substituting the expanded expressions of the metal surface current and the electric flux density of the dielectric body in the step three into the time domain electric field integral equation in the step two, and then respectively testing the discrete time domain electric field integral equation by adopting a point test in time and a Galerkin test in space to obtain a system impedance matrix equation;
fifthly, starting from a semiconductor drift-diffusion equation set, expanding the concentration and the potential of the current carrier to be solved on each node, testing the semiconductor drift-diffusion equation by adopting a Galerkin method, solving the current carrier and the potential distribution of each node by utilizing a Newton iteration method, and finally obtaining the internal physical parameters of the semiconductor;
and sixthly, establishing a strictly synchronous field-circuit coupling matrix equation through field-circuit coupling according to the system impedance matrix equation obtained in the fourth step and the semiconductor physical parameters obtained in the fifth step, then solving the distribution of current carriers and electric potential in the semiconductor through improved Newton iteration, and finally obtaining the transient current distribution in the microwave semiconductor circuit structure to complete the simulation process.
2. The method of claim 1, wherein the microwave circuit includes a semiconductor physical model, and the method further comprises: the fourth step is specifically as follows:
RWG triangle edge k to be loaded with semiconductor1As an equivalent voltage source side, and the voltage V on the source1As a feed voltage of an equivalent voltage source, and the current flowing through the semiconductor is equal to the current flowing vertically through the loading side k1Due to the current of (k)1Current coefficient of edge
Figure FDA0002917734800000011
Indicating the current density flowing perpendicularly through the edge, the current flowing through the edge being equal to the current coefficient multiplied by the edge length
Figure FDA0002917734800000012
Namely, it is
Figure FDA0002917734800000013
Obtaining a mixed field-path equation:
Figure FDA0002917734800000021
wherein,
Figure FDA0002917734800000022
the derivative with respect to time is represented as,
Figure FDA0002917734800000023
representing the field excitation source value and the circuit excitation source value,
Figure FDA0002917734800000024
vector of current coefficients representing RWG basis functions at time j Δ t, matrix Z0And Zj-iRespectively, representing the mutual coupling between the RWG basis functions of the electromagnetic structure at the present time and at the past time.
3. The method of claim 1, wherein the microwave circuit includes a semiconductor physical model, and the method further comprises: establishing a strictly synchronous field-path coupling matrix equation in the sixth step, and then solving through improved Newton iteration, wherein the method comprises the following specific steps:
1) a coupling equation which can simultaneously solve a time domain integral equation and a semiconductor nonlinear equation is given, and a matrix equation is as follows:
Figure FDA0002917734800000025
wherein,
Figure FDA0002917734800000026
is a vector of node voltages and current circuit unknowns on the voltage source branch,
Figure FDA0002917734800000027
including values representing voltage or current sources in the circuit and the effect of an unknown in the circuit at a historical time on the current time,
Figure FDA0002917734800000028
is an unknown quantity of non-linear change, Z, in the circuitCEAnd ZECAre sparse matrices that are generated by the voltage-current relationship at the interface of the circuit and the electromagnetic structure, the matrix ZCERepresenting the influence of the circuit structure on the electromagnetic structure, and including the coupling voltage information of the circuit port; matrix ZECRepresenting the influence of an electromagnetic structure on a circuit structure, and including coupling current information of a circuit port; the matrix Y represents a linear time-invariant circuit element of size NCKT×NCKTOf a sparse admittance matrix of only NCKTA non-zero element; the calculation of the voltage-to-time derivation operation adopts a third-order backward difference formula criterion, namely:
Figure FDA0002917734800000029
v in the above formulaj、Vj-1、Vj-2、Vj-3Respectively are voltage values at j delta t, (j-1) delta t, (j-2) delta t and (j-3) delta t; matrix ZCEThe coefficients comprising the first term in the derivative expansion are all used to calculate
Figure FDA0002917734800000031
2) The above equations are solved by using an improved matrix equation solving scheme, and a specific implementation scheme is described as follows
The field-path coupling system equation (2) of time domain nonlinearity is split into two equations, namely:
Figure FDA0002917734800000032
Figure FDA0002917734800000033
the field unknowns in equation (3)
Figure FDA0002917734800000034
Using circuit unknowns
Figure FDA0002917734800000035
To represent, as:
Figure FDA0002917734800000036
then, substituting formula (5) into formula (4) yields:
Figure FDA0002917734800000037
the non-linear equation (6) is expressed as:
Figure FDA0002917734800000038
Figure FDA0002917734800000039
equation (6) is abbreviated as:
Figure FDA00029177348000000310
the nonlinear equation (9) is solved by discrete newton's iteration:
order to
Figure FDA00029177348000000311
Figure FDA00029177348000000312
Figure FDA00029177348000000313
Final solution xn+1＝xn-[F′(x)]-1F (x) to find the solution vector of the equation, i.e. the circuit unknown at each time step
Figure FDA0002917734800000041
Then, substituting the circuit unknown quantity solved at the current moment into the formula (3) to obtain the field unknown quantity at the current moment
Figure FDA0002917734800000042
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