CN113076669A - Numerical simulation method and system for rapid ionization device - Google Patents
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Abstract
The invention provides a numerical simulation method and a numerical simulation system for a rapid ionization device, wherein the numerical simulation method comprises the following steps: determining a region to be simulated of the rapid ionization device and the size of the region to be simulated, dividing the region to be simulated into a plurality of grids by utilizing mutually vertical line segments, and giving a doping concentration value of each grid point according to the doping condition of the rapid ionization device corresponding to each grid point; selecting a drift diffusion model and corresponding model parameters, an electron and hole mobility model, a recombination rate model and a generation rate model to solve the device characteristics of the rapid ionization device in the dynamic triggering process; discretizing a differential equation in the drift diffusion model based on the doping concentration value of each grid point to obtain a discretized drift diffusion model; and simultaneously solving the device characteristic parameters on each grid point by adopting a Newton iteration method based on the discretized model so as to complete numerical simulation of the device characteristics at different moments in the dynamic triggering process of the device. The invention can be used for simulating the dynamic process of the device.
Description
Technical Field
The invention belongs to the field of semiconductor analysis, and particularly relates to a numerical simulation method and a numerical simulation system for a rapid ionization device.
Background
The fast ionization device is a power semiconductor device with the highest conduction speed in non-light-operated semiconductor devices, and has wide application prospect in the technical field of pulse power. The conduction mechanism of the fast ionization device is the delayed avalanche breakdown phenomenon, and this special physical phenomenon is still under study at present. For the research of the delayed avalanche breakdown phenomenon, it is necessary to simulate the physical process inside the device by means of numerical simulation of the semiconductor device. In addition, the optimal characteristic parameters of the device can be determined through numerical simulation of the semiconductor device, and the method is further used for production and preparation of the rapid ionization device.
The numerical simulation of the semiconductor device can carry out simulation prediction on the characteristics of the semiconductor device, is an essential important tool in the design of the device, provides guidance for the production and preparation of the device, and can reduce the production cost of the device.
Software for semiconductor device simulation is called TCAD (technology Computer aid design) software, and nowadays, there are many commercial TCAD software in the world. However, since the conduction mechanism of the fast ionization device is still under study, the TCAD software used in the study is required to have the flexibility and modification space as large as possible. The current commercial TCAD software has limited flexibility due to protection of the software, and provides very little modifiable space for users. Therefore, commercial TCAD software is not suitable for research and numerical simulation of fast ionization devices.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a numerical simulation method and a numerical simulation system for a rapid ionization device, and aims to solve the problem that the existing software is not suitable for the simulation of the rapid ionization device.
In order to achieve the above object, in a first aspect, the present invention provides a numerical simulation method for a fast ionization device, including the steps of:
determining a region to be simulated of the rapid ionization device and the size of the region to be simulated, dividing the region to be simulated into a plurality of grids by utilizing mutually vertical line segments, and giving a doping concentration value of each grid point according to the doping condition of the rapid ionization device corresponding to each grid point;
selecting a drift diffusion model and corresponding model parameters, and a related electron and hole mobility model, a recombination rate model and a generation rate model to solve the device characteristics of the fast ionization device in the dynamic triggering process;
discretizing a differential equation in the drift diffusion model by using a finite difference method based on the doping concentration value of each grid point to obtain a discretized drift diffusion model;
and simultaneously solving the device characteristic parameters on each grid point by adopting a Newton iteration method based on the discretized drift diffusion model so as to complete the numerical simulation of the device characteristics of the rapid ionization device at different moments in the dynamic triggering process.
In an alternative example, the drift diffusion model of the fast ionization device is:
wherein, the formula (1) and the formula (2) are respectively current density equations of electrons and holes, the formula (3) and the formula (4) are respectively current continuity equations of the electrons and the holes, and the formula (5) is a Poisson equation; n is the electron density inside the rapid ionization device, p is the hole density inside the rapid ionization device,
to rapidly ionize the potential inside the device, JnFor rapid ionization of electron current density inside the device, JpFor rapid ionization of the hole current density inside the device, DnFor rapid ionization of the electron diffusion coefficient inside the device, DpTo rapidly ionize the hole diffusion coefficient inside the device,
is the rate of change of electron density with time,
is the rate of change of hole density over time,
is the divergence of the electron current density,
is the divergence of the hole current density, munFor rapid ionization of electron mobility, μpFor rapid ionization of hole mobility inside the device, GnFor rapid ionization of electron generation rate inside the device, GpFor fast ionization of the hole generation rate inside the device, UnFor rapid ionization of electron recombination rate, U, inside the devicepTo rapidly ionize the hole recombination rate inside the device, ElIs the electric field vector inside the fast ionizing device, t is time variable, q is unit charge constant, epsilon is semiconductor dielectric constant, N0To rapidly ionize the effective doping concentration of the device.
In an optional example, the discretizing a differential equation in the drift diffusion model by using a finite difference method specifically includes:
determining the structural parameters of the rapid ionization device; the structural parameters include: the length, the width and the doping concentration of each region of the rapid ionization device are changed;
carrying out grid division on the rapid ionization device according to the structural parameters of the rapid ionization device, and determining the doping concentration value of each discrete grid point by combining the position corresponding relation of each grid point and each region of the rapid ionization device; and converting a differential equation in the drift diffusion model into a differential equation to obtain the drift diffusion model based on discretization.
In an optional example, the method for simultaneously solving the device characteristic parameters on each grid point by using a newton iteration method based on the discretized drift diffusion model specifically includes:
s1, obtaining the sum of the variables n, p and n on each discrete grid point under the initial zero voltage bias state of the rapid ionization device by the non-coupling method
An initial value of (1);
s2, calculating the calculation value of the voltage at two ends of the fast ionization device at the current time point by linear extrapolation, iterating the discretized drift diffusion model by using a Newton iteration method, and calculating the variables n, p and
to find the current flowing through the fast ionization device;
s3, solving the current of the fast ionization device according to the circuit equation of the fast ionization device, comparing the current of the fast ionization device solved in the step S2, if the error between the current of the fast ionization device and the current of the fast ionization device is less than a preset threshold value, solving the variables n, p and n on each grid point inside the fast ionization device at the current time point
The voltage and current values of the fast ionization device corresponding to the current time point can be obtained, iteration is carried out on the next time point, otherwise, the voltage calculation value in the step S2 is changed, and the step S2 is returned to continue calculation;
and S4, comparing the iteration time at the moment with the set iteration time, stopping the iteration process if the set iteration time is reached, and otherwise, continuing the calculation of the step S2.
In an alternative example, the circuit equation of the fast ionization device is: u is equal to UFID+R·IFID；
Wherein U is voltage of voltage source, UFIDFor rapid ionization of the voltage across the device, IFIDR is the load resistance for the current flowing through the fast ionization device.
In a second aspect, the present invention provides a numerical simulation system for rapidly ionizing a device, comprising:
the simulation area determining unit is used for determining an area to be simulated of the rapid ionization device and the size of the area to be simulated, dividing the area to be simulated into a plurality of grids by utilizing mutually vertical line segments, and endowing the doping concentration value of each grid point according to the doping condition of the rapid ionization device corresponding to each grid point;
the model and parameter determining unit is used for solving the device characteristics of the rapid ionization device in the dynamic triggering process by selecting a drift diffusion model and corresponding model parameters as well as a related electron and hole mobility model, a recombination rate model and a generation rate model;
the model discretization unit is used for discretizing a differential equation in the drift diffusion model by using a finite difference method based on the doping concentration value of each grid point to obtain a discretized drift diffusion model;
and the numerical simulation unit is used for simultaneously solving the device characteristic parameters on each grid point by adopting a Newton iteration method based on the discretized drift diffusion model so as to complete numerical simulation of the device characteristics of the rapid ionization device at different moments in the dynamic triggering process.
In an optional example, the drift diffusion model of the fast ionization device selected by the model and parameter determination unit is:
wherein, the formula (1) and the formula (2) are respectively current density equations of electrons and holes, the formula (3) and the formula (4) are respectively current continuity equations of the electrons and the holes, and the formula (5) is a Poisson equation; n is the electron density inside the rapid ionization device, p is the hole density inside the rapid ionization device,
to rapidly ionize the potential inside the device, JnFor rapid ionization of electron current density inside the device, JpFor rapid ionization of the hole current density inside the device, DnFor rapid ionization of the electron diffusion coefficient inside the device, DpTo rapidly ionize the hole diffusion coefficient inside the device,
is the rate of change of electron density with time,
is the rate of change of hole density over time,
is the divergence of the electron current density,
is the divergence of the hole current density,μnfor rapid ionization of electron mobility, μpFor rapid ionization of hole mobility inside the device, GnFor rapid ionization of electron generation rate inside the device, GpFor fast ionization of the hole generation rate inside the device, UnFor rapid ionization of electron recombination rate, U, inside the devicepTo rapidly ionize the hole recombination rate inside the device, ElIs the electric field vector inside the fast ionizing device, t is time variable, q is unit charge constant, epsilon is semiconductor dielectric constant, N0To rapidly ionize the effective doping concentration of the device.
In an optional example, the sharp model discretization unit determines structural parameters of the rapid ionization device; the structural parameters include: the length, the width and the doping concentration of each region of the rapid ionization device are changed; carrying out grid division on the rapid ionization device according to the structural parameters of the rapid ionization device, and determining the doping concentration value of each discrete grid point by combining the position corresponding relation of each grid point and each region of the rapid ionization device; and converting a differential equation in the drift diffusion model into a differential equation to obtain the drift diffusion model based on discretization.
In an optional example, the numerical simulation unit specifically solves the device characteristic parameters at each grid point by the following steps: s1, obtaining the sum of the variables n, p and n on each discrete grid point under the initial zero voltage bias state of the rapid ionization device by the non-coupling method
An initial value of (1); s2, calculating the calculation value of the voltage at two ends of the fast ionization device at the current time point by linear extrapolation, iterating the discretized drift diffusion model by using a Newton iteration method, and calculating the variables n, p and
to find the current flowing through the fast ionization device; s3, solving the fast ionization according to the circuit equation of the fast ionization deviceComparing the device current with the fast ionization device current obtained in step S2, and if the error between the device current and the fast ionization device current is smaller than a preset threshold, obtaining the sum of the variables n, p and n at each grid point inside the fast ionization device at the current time point
The voltage and current values of the fast ionization device corresponding to the current time point can be obtained, iteration is carried out on the next time point, otherwise, the voltage calculation value in the step S2 is changed, and the step S2 is returned to continue calculation; and S4, comparing the iteration time at the moment with the set iteration time, stopping the iteration process if the set iteration time is reached, and otherwise, continuing the calculation of the step S2.
In an alternative example, the circuit equation of the fast ionization device is: u is equal to UFID+R·IFID(ii) a Wherein U is voltage of voltage source, UFIDFor rapid ionization of the voltage across the device, IFIDR is the load resistance for the current flowing through the fast ionization device.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
the invention provides a numerical simulation method and a numerical simulation system for a rapid ionization device, which can modify the structure of the device and the doping concentration of the device according to research needs, can customize a physical effect model for simulating the dynamic process of the device, and are favorable for deeply researching the conduction mechanism of the rapid ionization device. The established numerical simulation platform can also be used for optimizing the structural parameters of the device through simulation before the device is produced and prepared, so that the production cost of the rapid ionization device is reduced.
Drawings
FIG. 1 is a flow chart of a numerical simulation method for a fast ionization device according to an embodiment of the present invention;
FIG. 2 is a block diagram of a fast ionization device according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of various doping concentrations of the rapid ionization device shown in FIG. 2 according to an embodiment of the present invention;
fig. 4 is a circuit structure diagram of a fast ionization device provided by an embodiment of the present invention;
FIG. 5 is a schematic diagram of voltage and current waveforms across a fast ionization device provided by an embodiment of the present invention;
FIG. 6 is a flow chart of a numerical simulation of a fast ionization device according to an embodiment of the present invention;
fig. 7 is a diagram of a numerical simulation system architecture for a fast ionization device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a method and a system for numerical simulation of a rapid ionization device, and the constructed numerical simulation program has great flexibility and can be used for research on a conduction mechanism of the rapid ionization device and design of device parameters before production and preparation.
FIG. 1 is a flow chart of a numerical simulation method for a fast ionization device according to an embodiment of the present invention; as shown in fig. 1, the method comprises the following steps:
s101, determining a region to be simulated of the rapid ionization device and the size of the region to be simulated, dividing the region to be simulated into a plurality of grids by utilizing mutually perpendicular line segments, and giving a doping concentration value of each grid point according to the doping condition of the rapid ionization device corresponding to each grid point;
s102, solving the device characteristics of the rapid ionization device in the dynamic triggering process by using a drift diffusion model and corresponding model parameters as well as a related electron and hole mobility model, a recombination rate model and a generation rate model;
s103, discretizing a differential equation in the drift diffusion model by using a finite difference method based on the doping concentration value of each grid point to obtain a discretized drift diffusion model;
and S104, simultaneously solving the device characteristic parameters on each grid point by adopting a Newton iteration method based on the discretized drift diffusion model so as to complete numerical simulation of the device characteristics of the rapid ionization device at different moments in the dynamic triggering process.
In an optional example, the discretizing a differential equation in the drift diffusion model by using a finite difference method specifically includes:
determining the structural parameters of the rapid ionization device; the structural parameters include: the length, the width and the doping concentration of each region of the rapid ionization device are changed;
carrying out grid division on the rapid ionization device according to the structural parameters of the rapid ionization device, and determining the doping concentration value of each discrete grid point by combining the position corresponding relation of each grid point and each region of the rapid ionization device; and converting a differential equation in the drift diffusion model into a differential equation to obtain the drift diffusion model based on discretization.
In an optional example, the method for simultaneously solving the device characteristic parameters on each grid point by using a newton iteration method based on the discretized drift diffusion model specifically includes:
s1, obtaining the sum of the variables n, p and n on each discrete grid point under the initial zero voltage bias state of the rapid ionization device by the non-coupling method
An initial value of (1);
s2, calculating the calculation value of the voltage at two ends of the fast ionization device at the current time point by linear extrapolation, iterating the discretized drift diffusion model by using a Newton iteration method, and calculating the variables n, p and
to find the current flowing through the fast ionization device;
s3, solving the current of the fast ionization device according to the circuit equation of the fast ionization device, comparing the current of the fast ionization device solved in the step S2,if the error between the two is smaller than the preset threshold value, solving the sum of the variables n, p and the sum of the variables on each grid point in the rapid ionization device at the current time point
The voltage and current values of the fast ionization device corresponding to the current time point can be obtained, iteration is carried out on the next time point, otherwise, the voltage calculation value in the step S2 is changed, and the step S2 is returned to continue calculation;
and S4, comparing the iteration time at the moment with the set iteration time, stopping the iteration process if the set iteration time is reached, and otherwise, continuing the calculation of the step S2.
The numerical simulation method for the rapid ionization device adopts a basic drift diffusion model. The drift diffusion model is a set of equations describing the characteristics of the semiconductor device, and is shown in formulas (1) to (5), wherein the formulas (1) and (2) are electron and hole current density equations respectively, the formulas (3) and (4) are electron and hole current continuity equations respectively, and the formula (5) is a Poisson equation.
N, p and
to solve for the variables. Wherein n is the electron density inside the rapid ionization device, p is the hole density inside the rapid ionization device,
to rapidly ionize the potential inside the device, JnFor rapid ionization of electron current density inside the device, JpFor rapid ionization of the hole current density inside the device, DnFor rapid ionization of the electron diffusion coefficient inside the device, DpFor fast ionization of the hole diffusion coefficient, mu, inside the devicenFor rapid ionization of electron mobility, μpFor rapid ionization of hole mobility inside the device, GnFor rapid ionization of electron generation rate inside the device, GpFor fast ionization of the hole generation rate inside the device, UnFor rapid ionization of electron recombination rate, U, inside the devicepTo rapidly ionize the hole recombination rate inside the device, ElIs the electric field vector inside the fast ionizing device, t is time variable, q is unit charge constant, epsilon is semiconductor dielectric constant, N0To rapidly ionize the effective doping concentration of the device.
As can be seen from the above equation set, the equation set includes partial differential equations, and there is a coupling relationship between the equations with respect to the three variables to be solved. To facilitate computer solution, partial differential equations need to be discretized.
Specifically, the discretized drift diffusion model is as follows:
wherein:
wherein, (M, N) represents the position of the corresponding grid point after discretizing the device structure by a finite difference method, M represents the abscissa, N represents the ordinate, N 'represents the midpoint of N and N +1, and M' represents the midpoint of M and M + 1. x represents the x-direction, y represents the y-direction, p represents the hole-related function, and n represents the electron-related function.
The electron and hole mobility model, recombination rate model, and generation rate model are as follows:
the mobility model is:
wherein:
wherein μ is electron or mobility, μmin，μmax，Nref，α，β，vmaxFor the constants involved in the calculation of the mobility in the formula, different values are taken when calculating the electron and hole mobilities, respectively.
The specific parameters are shown in table 1:
TABLE 1
The recombination rate model is:
wherein:
wherein R isSRHIs the SRH recombination rate, RAugIs Auger recombination rate, niAnd piIs the intrinsic carrier concentration, τnAnd τpElectron and hole lifetimes, N, respectivelyDAnd NARespective donor and acceptor doping concentrations, τ0，NT，Ccn，CcpIn order to calculate the constants involved in the recombination rate, different values were taken in the calculation of the electron and hole recombination rates,
the specific parameters are shown in table 2:
TABLE 2
The production rate model is:
wherein:
αnis the electron ionization rate, alphapThe ionization rate of holes, a, b and m are constants involved in the calculation of the ionization rate, different values are respectively adopted in the calculation of the ionization rate of electrons and holes, and specific parameters are shown in table 3:
TABLE 3
In one particular embodiment, the device structure model is created as shown in FIG. 2. The doping concentration of the corresponding two-dimensional plane of the device is shown in fig. 3. The circuit model used in the simulation is shown in fig. 4, where U is the voltage source, R is the 50 Ω load resistance, and FID is the fast ionization device shown in fig. 2.
The voltage current across the device obtained by the above numerical simulation is shown in fig. 5. At the initial moment, the bias voltage at the two ends of the device is 1 kV. When the trigger is triggered, the voltage source provides trigger pulses with the voltage rising rate of 5kV/ns, after the voltage at two ends of the device reaches 12703V, the voltage at two ends of the device is rapidly reduced to 4282V within about 100ps, and the current flowing through the device is rapidly increased to about 188A. The device exhibits sub-nanosecond turn-on characteristics.
Therefore, in order to solve the numerical model of the semiconductor device by using a computer, the model needs to be discretized by using a finite difference method, differential operation is converted into four arithmetic operations of addition, subtraction, multiplication and division, and then, in order to solve three variables simultaneously, a newton iteration method is used for iteratively solving the three variables. A numerical simulation program for designing a semiconductor device was designed using the following steps as shown in fig. 6:
1) defining basic physical constants used in calculation, such as unit charge q, dielectric constant epsilon, device temperature T and the like, and parameters used for establishing a device structure, such as length, width, doping concentration and the like of each region;
2) carrying out grid division on the defined device structure, and giving a doping concentration value to each discrete grid point;
3) obtaining the n, p and of the variable at each discrete point in the device under the initial zero-voltage bias state of the device by the non-coupling method
An initial value of (1);
4) calculating the calculation value of the voltage at two ends of the device at the current time point by a linear extrapolation method, iterating the discretized drift diffusion model by a Newton iteration method, and calculating the sum of the variables n, p and p at each discrete point in the device at the current time point
To calculate the current flowing through the device;
5) solving the current of the device according to a circuit equation, comparing the current solved in the step 4), if the error is small enough, solving the variable n, p and on each discrete point in the device at the current time point
Calculating the voltage and current values of the device, performing iteration at the next time point, otherwise changing the voltage calculation value in the step 4), and returning to the step 4) to continue calculation;
6) comparing the iteration time at the moment with the set iteration time, stopping the iteration process if the set iteration time is reached, and otherwise, continuing the calculation of the step 4).
The two-dimensional numerical simulation program of the rapid ionization device constructed according to the method can modify the structure of the device and the doping concentration of the device according to research needs, can customize a physical effect model for simulating the dynamic process of the device, and is favorable for deeply researching the conduction mechanism of the rapid ionization device. The established numerical simulation platform can also be used for optimizing the structural parameters of the device through simulation before the device is produced and prepared, so that the production cost of the rapid ionization device is reduced.
Fig. 7 is a diagram of a numerical simulation system architecture for a fast ionization device according to an embodiment of the present invention, as shown in fig. 7, including:
a simulation region determining unit 710, configured to determine a region to be simulated of the fast ionization device and a size thereof, divide the region to be simulated into multiple grids by using mutually perpendicular line segments, and assign a doping concentration value to each grid point according to a doping condition of the fast ionization device corresponding to each grid point;
a model and parameter determining unit 720, configured to select a drift diffusion model and corresponding model parameters, and solve device characteristics of the fast ionization device in a dynamic triggering process by using a related electron and hole mobility model, recombination rate model, and generation rate model;
the model discretization unit 730 is configured to discretize a differential equation in the drift diffusion model by using a finite difference method based on the doping concentration value of each grid point to obtain a discretized drift diffusion model;
and the numerical simulation unit 740 is configured to simultaneously solve the device characteristic parameters on each grid point by using a newton iteration method based on the discretized drift diffusion model, so as to complete numerical simulation of device characteristics at different times in the dynamic triggering process of the fast ionization device.
Specifically, the functions of each unit can be referred to the detailed description in the foregoing method embodiments, and are not described herein again.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A numerical simulation method for a rapid ionization device is characterized by comprising the following steps:
determining a region to be simulated of the rapid ionization device and the size of the region to be simulated, dividing the region to be simulated into a plurality of grids by utilizing mutually vertical line segments, and giving a doping concentration value of each grid point according to the doping condition of the rapid ionization device corresponding to each grid point;
selecting a drift diffusion model and corresponding model parameters, and a related electron and hole mobility model, a recombination rate model and a generation rate model to solve the device characteristics of the fast ionization device in the dynamic triggering process;
discretizing a differential equation in the drift diffusion model by using a finite difference method based on the doping concentration value of each grid point to obtain a discretized drift diffusion model;
and simultaneously solving the device characteristic parameters on each grid point by adopting a Newton iteration method based on the discretized drift diffusion model so as to complete the numerical simulation of the device characteristics of the rapid ionization device at different moments in the dynamic triggering process.
2. The numerical simulation method of claim 1, wherein the drift diffusion model of the fast ionization device is:
wherein, the formula (1) and the formula (2) are respectively current density equations of electrons and holes, the formula (3) and the formula (4) are respectively current continuity equations of the electrons and the holes, and the formula (5) is a Poisson equation; n is the electron density inside the rapid ionization device, p is the hole density inside the rapid ionization device,
to rapidly ionize the potential inside the device, JnFor rapid ionization of electron current density inside the device, JpFor rapid ionization of the hole current density inside the device, DnFor rapid ionization of the electron diffusion coefficient inside the device, DpTo rapidly ionize the hole diffusion coefficient inside the device,
is the rate of change of electron density with time,
is the rate of change of hole density over time,
is the divergence of the electron current density,
is the divergence of the hole current density, munFor rapid ionization of electron mobility, μpFor rapid ionization of hole mobility inside the device, GnFor rapid ionization of electron generation rate inside the device, GpFor fast ionization of the hole generation rate inside the device, UnFor rapid ionization of electron recombination rate, U, inside the devicepTo rapidly ionize the hole recombination rate inside the device, ElIs the electric field vector inside the fast ionizing device, t is time variable, q is unit charge constant, epsilon is semiconductor dielectric constant, N0To rapidly ionize the effective doping concentration of the device.
3. The numerical simulation method according to claim 2, wherein the discretization of the differential equation in the drift diffusion model by using the finite difference method is specifically:
determining the structural parameters of the rapid ionization device; the structural parameters include: the length, the width and the doping concentration of each region of the rapid ionization device are changed;
carrying out grid division on the rapid ionization device according to the structural parameters of the rapid ionization device, and determining the doping concentration value of each discrete grid point by combining the position corresponding relation of each grid point and each region of the rapid ionization device; and converting a differential equation in the drift diffusion model into a differential equation to obtain the drift diffusion model based on discretization.
4. The numerical simulation method according to claim 3, wherein the method for simultaneously solving the device characteristic parameters at each grid point based on the discretized drift diffusion model by using a Newton iteration method specifically comprises:
s1, obtaining the sum of the variables n, p and n on each discrete grid point under the initial zero voltage bias state of the rapid ionization device by the non-coupling method
An initial value of (1);
s2, calculating the calculation value of the voltage at two ends of the fast ionization device at the current time point by linear extrapolation, iterating the discretized drift diffusion model by using a Newton iteration method, and calculating the variables n, p and
to find the current flowing through the fast ionization device;
s3, solving the current of the fast ionization device according to the circuit equation of the fast ionization device, comparing the current of the fast ionization device solved in the step S2, if the error between the current of the fast ionization device and the current of the fast ionization device is less than a preset threshold value, solvingThe variables n, p and on each grid point in the rapid ionization device at the current time point are obtained
The voltage and current values of the fast ionization device corresponding to the current time point can be obtained, iteration is carried out on the next time point, otherwise, the voltage calculation value in the step S2 is changed, and the step S2 is returned to continue calculation;
and S4, comparing the iteration time at the moment with the set iteration time, stopping the iteration process if the set iteration time is reached, and otherwise, continuing the calculation of the step S2.
5. The numerical simulation method of claim 4, wherein the circuit equation of the fast ionization device is: u is equal to UFID+R·IFID；
Wherein U is voltage of voltage source, UFIDFor rapid ionization of the voltage across the device, IFIDR is the load resistance for the current flowing through the fast ionization device.
6. A numerical simulation system for a rapid ionization device, comprising:
the simulation area determining unit is used for determining an area to be simulated of the rapid ionization device and the size of the area to be simulated, dividing the area to be simulated into a plurality of grids by utilizing mutually vertical line segments, and endowing the doping concentration value of each grid point according to the doping condition of the rapid ionization device corresponding to each grid point;
the model and parameter determining unit is used for solving the device characteristics of the rapid ionization device in the dynamic triggering process by selecting a drift diffusion model and corresponding model parameters as well as a related electron and hole mobility model, a recombination rate model and a generation rate model;
the model discretization unit is used for discretizing a differential equation in the drift diffusion model by using a finite difference method based on the doping concentration value of each grid point to obtain a discretized drift diffusion model;
and the numerical simulation unit is used for simultaneously solving the device characteristic parameters on each grid point by adopting a Newton iteration method based on the discretized drift diffusion model so as to complete numerical simulation of the device characteristics of the rapid ionization device at different moments in the dynamic triggering process.
7. The numerical simulation system of claim 6, wherein the model and parameter determining unit selects a drift diffusion model of the fast ionization device as:
wherein, the formula (1) and the formula (2) are respectively current density equations of electrons and holes, the formula (3) and the formula (4) are respectively current continuity equations of the electrons and the holes, and the formula (5) is a Poisson equation; n is the electron density inside the rapid ionization device, p is the hole density inside the rapid ionization device,
to rapidly ionize the potential inside the device, JnFor rapid ionization of electron current inside the deviceDensity, JpFor rapid ionization of the hole current density inside the device, DnFor rapid ionization of the electron diffusion coefficient inside the device, DpTo rapidly ionize the hole diffusion coefficient inside the device,
is the rate of change of electron density with time,
is the rate of change of hole density over time,
is the divergence of the electron current density,
is the divergence of the hole current density, munFor rapid ionization of electron mobility, μpFor rapid ionization of hole mobility inside the device, GnFor rapid ionization of electron generation rate inside the device, GpFor fast ionization of the hole generation rate inside the device, UnFor rapid ionization of electron recombination rate, U, inside the devicepTo rapidly ionize the hole recombination rate inside the device, ElIs the electric field vector inside the fast ionizing device, t is time variable, q is unit charge constant, epsilon is semiconductor dielectric constant, N0To rapidly ionize the effective doping concentration of the device.
8. The numerical simulation system according to claim 7, wherein the model discretization unit determines structural parameters of a fast ionization device; the structural parameters include: the length, the width and the doping concentration of each region of the rapid ionization device are changed; carrying out grid division on the rapid ionization device according to the structural parameters of the rapid ionization device, and determining the doping concentration value of each discrete grid point by combining the position corresponding relation of each grid point and each region of the rapid ionization device; and converting a differential equation in the drift diffusion model into a differential equation to obtain the drift diffusion model based on discretization.
9. The numerical simulation system according to claim 8, wherein the numerical simulation unit solves the device characteristic parameters at the respective grid points by specifically: s1, obtaining the sum of the variables n, p and n on each discrete grid point under the initial zero voltage bias state of the rapid ionization device by the non-coupling method
An initial value of (1); s2, calculating the calculation value of the voltage at two ends of the fast ionization device at the current time point by linear extrapolation, iterating the discretized drift diffusion model by using a Newton iteration method, and calculating the variables n, p and
to find the current flowing through the fast ionization device; s3, solving the current of the fast ionization device according to the circuit equation of the fast ionization device, comparing the current of the fast ionization device solved in the step S2, if the error between the current of the fast ionization device and the current of the fast ionization device is less than a preset threshold value, solving the variables n, p and n on each grid point inside the fast ionization device at the current time point
The voltage and current values of the fast ionization device corresponding to the current time point can be obtained, iteration is carried out on the next time point, otherwise, the voltage calculation value in the step S2 is changed, and the step S2 is returned to continue calculation; and S4, comparing the iteration time at the moment with the set iteration time, stopping the iteration process if the set iteration time is reached, and otherwise, continuing the calculation of the step S2.
10. The numerical simulation system of claim 9, wherein the circuit equation of the fast ionization device is: u is equal to UFID+R·IFID(ii) a Wherein U is voltage of voltage source, UFIDFor rapid ionization of the voltage across the device, IFIDR is the load resistance for the current flowing through the fast ionization device.
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