A PIN diode modeling and simulation method based on LP-CDI-FDTD

Abstract

The application discloses a PIN diode modeling and simulation method based on LP-CDI-FDTD, belongs to the field of computational electromagnetics, microwave technology and circuit simulation, and comprises the following steps: firstly, an equivalent lumped parameter model of a semiconductor device is established, and a voltage-current relationship thereof is obtained; then, the relationship is converted into an equivalent current density, and is embedded into a Maxwell curl equation according to the relationship between an electric field and a voltage, so as to construct an electromagnetic-circuit coupling equation set; further, a leapfrog compliant divergence unconditional stable time domain finite difference method is adopted to discretize the coupling equation set, and a discrete updating equation is obtained; finally, iterative calculation is carried out according to the equation, and electromagnetic fields and device states are synchronously updated. The method realizes the inherent strong coupling between full-wave electromagnetic fields and semiconductor physical processes, and breaks through the time step restriction caused by a CFL condition in traditional methods by using the unconditional stability of the algorithm, so that the calculation efficiency can be significantly improved when simulating a device containing a fine structure.

Description

Technical Field

[0001] This invention belongs to the fields of computational electromagnetics, microwave technology and circuit simulation, and particularly relates to a PIN diode modeling and simulation method based on LP-CDI-FDTD. Background Technology

[0002] As a key radio frequency (RF) dynamic tuning element, the PIN diode can switch its impedance between low-resistance (on) and high-resistance (off) states by changing its bias voltage. This characteristic makes it play a central role in advanced microwave technologies such as reconfigurable antennas and smart metasurfaces. To accurately evaluate the electromagnetic performance of devices integrating PIN diodes, efficient numerical simulation is required. Currently, the main simulation methods include field-circuit co-simulation using commercial software and full-wave electromagnetic analysis methods based on finite-difference time-domain (FDTD).

[0003] However, existing simulation techniques have significant limitations. First, commercial software's field-circuit co-simulation typically employs loose coupling, making it difficult to accurately reflect the close interaction between the electromagnetic field and semiconductor carrier transport processes during transient events, thus limiting simulation accuracy. Second, while traditional explicit FDTD methods can perform full-wave analysis, their time steps are strictly constrained by the Courant-Friedrich-Lévy (CFL) stability condition. When the simulation model includes fine structures such as the extremely thin intrinsic regions of PIN diodes, the extremely dense mesh used to meet spatial resolution forces a drastic reduction in the time step, leading to an exponential increase in computation time and extremely low simulation efficiency, making it difficult to meet the rapid iteration requirements of engineering designs. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a PIN diode modeling and simulation method based on LP-CDI-FDTD, comprising: Establish an equivalent lumped parameter model of the semiconductor device and obtain its voltage-current relationship under a given bias state; The voltage-current relationship is converted into an equivalent current density, and based on the physical relationship between electric field and voltage, the equivalent current density is embedded into the current density term of Maxwell's curl equation to construct a coupled electromagnetic-circuit equation system. The coupled equations are spatially and temporally discretized using the frog-leap compliance divergence unconditionally stable time-domain finite-difference method to obtain discretized update equations. Simultaneously, iterative calculations are performed based on the discretized update equation, and the spatial electromagnetic field distribution and the state variables of the semiconductor device are updated synchronously at each time step.

[0005] Optionally, establishing the equivalent lumped parameter model of the semiconductor device includes: Based on the physical characteristics of the semiconductor device under forward bias, it is equivalent to a series structure of parasitic inductance and on-resistance. Meanwhile, based on the physical characteristics of the semiconductor device under reverse bias, it is equivalent to a structure in which the junction capacitance and high resistance are connected in parallel, and then connected in series with the parasitic inductance.

[0006] Optionally, the conversion of the voltage-current relationship into an equivalent current density includes: The voltage-current relationship is determined based on the voltage between the two nodes of the semiconductor device and the current flowing through it. Based on the relationship that the line integral of the electric field along the path between the nodes equals the voltage, the current is converted into current density; and The current density is introduced as a source term into the corresponding position in Maxwell's curl equation.

[0007] Optionally, when the semiconductor device is forward biased, determining the equivalent current density based on the voltage-current relationship includes: The voltage equation of a series circuit containing inductance and resistance is discretized by center difference, and the current density value at the discrete time step is obtained by combining the geometric conversion relationship between current and current density.

[0008] Optionally, when the semiconductor device is reverse biased, determining the equivalent current density based on the voltage-current relationship includes: The current equation of a circuit containing a capacitor and a high impedance in parallel is discretized by central difference, and the current density value at the discrete time step is obtained by combining the geometric conversion relationship between current and current density.

[0009] Optionally, the discretization using the frog-jump compliance divergence unconditionally stable time-domain finite-difference method includes: The Maxwell curl equation is rewritten in matrix form with auxiliary variables; The equation in matrix form is decomposed locally into one dimension to obtain update operators for two sub-steps; Based on the update operator, an explicit set of update equations for the electric field, magnetic field, and auxiliary variables is derived.

[0010] Optionally, the iterative calculation includes the following steps performed sequentially: Update the auxiliary variables for the current time step based on the electric field value of the previous time step; Based on the updated auxiliary variables and the magnetic field value of the previous time step, update the magnetic field value of the current half-time step. Based on the updated magnetic field value and the equivalent current density, update the intermediate auxiliary variables and current density term for the current half-time step; and Based on the updated intermediate auxiliary variables, update the electric field value for the next whole time step.

[0011] Optionally, the method is applied to the electromagnetic simulation of a reconfigurable antenna or metasurface unit containing the semiconductor device; The semiconductor device is a PIN diode; The spatial discretization uses a grid size that is less than or equal to one-tenth of the critical physical size of the semiconductor device, and the time discretization uses a time step that is not limited by the Courant-Friedrich-Levy condition.

[0012] On the other hand, the present invention also provides an electronic device including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0013] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0014] Compared with the prior art, the present invention has the following advantages and technical effects: This invention first achieves strong intrinsic coupling between the full-wave electromagnetic field and semiconductor physical processes by tightly embedding the lumped-parameter model of a PIN diode into Maxwell's equations in the form of equivalent current density, significantly improving the physical realism and computational accuracy of the simulation model. Secondly, this invention employs the unconditionally stable CDI-FDTD algorithm as the solution framework, completely eliminating the constraints of the CFL condition in traditional explicit FDTD methods. This allows for stable calculations with time steps tens to hundreds of times larger than traditional methods, even with small spatial grids required for analyzing fine structures. Thus, while maintaining accuracy, it improves the simulation efficiency of PIN diode models with high structural contrast by one to two orders of magnitude. Furthermore, this invention provides a general and unified modeling framework, facilitating its extension to the electromagnetic co-simulation of other lumped-parameter components or complex circuits. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of the CDI-FDTD method according to an embodiment of the present invention; Figure 2 This is an equivalent circuit diagram of a PIN diode according to an embodiment of the present invention; Figure 3 This is a circuit diagram of a sinusoidal voltage source driving a PIN diode according to an embodiment of the present invention; Figure 4 The following is a simulation diagram of a PIN diode driven by a sinusoidal voltage source according to Embodiment 2 of the present invention, wherein (a) is a mesh partitioning diagram and (b) is a sampling voltage diagram; Figure 5 This is a structural diagram of a single-pole antenna model according to an embodiment of the present invention; Figure 6 This is a simulation diagram of the PIN diode cutoff in Embodiment 3 of the present invention; Figure 7 This is a simulation diagram of the PIN diode conduction in Embodiment 3 of the present invention. Detailed Implementation

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0018] Example 1 This embodiment provides a PIN diode modeling and simulation method based on LP-CDI-FDTD, including: Establish an equivalent lumped parameter model of the semiconductor device and obtain its voltage-current relationship under a given bias state; The voltage-current relationship is converted into an equivalent current density, and based on the physical relationship between electric field and voltage, the equivalent current density is embedded into the current density term of Maxwell's curl equation to construct a coupled electromagnetic-circuit equation system. The coupled equations are spatially and temporally discretized using the frog-leap compliance divergence unconditionally stable time-domain finite-difference method to obtain discretized update equations. Simultaneously, iterative calculations are performed based on the discretized update equation, and the spatial electromagnetic field distribution and the state variables of the semiconductor device are updated synchronously at each time step.

[0019] Specifically, it includes: like Figure 1 As shown, the core of this technology lies in constructing a coupled solution system, which couples the influence of lumped parameter elements into electromagnetic calculations, and uses the LP-CDI-FDTD method for efficient iterative solution.

[0020] 1. Establishment of the equivalent model and governing equations: The BAP64-02 is a silicon PIN diode manufactured by Nexperia. PIN diodes are core components in radio frequency (RF) and optoelectronics, enabling key functions such as switching, attenuation, and photodetection through flexible bias control. Under forward bias (e.g., 10 mA), the series resistance is extremely low, allowing continuous adjustment of the I-layer carrier concentration to change the resistance value and achieve adjustable RF attenuation. Under reverse bias (e.g., -2 V), the typical junction capacitance is only about 0.25 pF, ensuring good isolation at high frequencies. The BAP64-02 achieves nanosecond-level switching speeds and is frequently used in antenna switching modules. The BAP64-02 uses an SOD-323 surface mount package, which is extremely small (approximately 1.7 x 1.25 x 0.95 mm), making it ideal for modern wireless devices with high-density PCB layouts.

[0021] The equivalent circuit of a PIN diode differs depending on its bias condition. A forward-biased PIN diode can be equivalent to a series structure of parasitic inductance Ls and on-resistance Rd; a reverse-biased PIN diode can be equivalent to a junction capacitance Cd connected in parallel with a high resistance Rp, followed by a series parasitic inductance Ls. (See appendix) Figure 2 .

[0022] In numerical simulations of antennas and microwave devices, the current through a lumped-parameter element can be expressed as the applied current density J. i Expressed using Maxwell's equations: (1) The characteristics of a lumped-parameter element placed between two nodes are determined by the relationship between the voltage between these two nodes and the current flowing through them. This relationship can be incorporated into Maxwell's equations through the relationship between voltage and electric field: (2) Taking the z-direction as an example, the relationship between current Iz and current density (Jz) is given by equation (3), where Δx and Δy are the spatial step sizes in the x and y directions, respectively: (3) The equivalent circuits for forward-biased and reverse-biased PIN diodes are different (zero bias is not considered), so they will be discussed separately. When the PIN diode is forward-biased, to calculate the equivalent current density of the diode, the voltage between the two nodes is defined as U; the current flowing through it is defined as I. z The voltage across the inductor is U. L The voltage across the resistor is U. R .

[0023] (4) By discretizing the central difference of formula (4), we can obtain: (5) Substituting formula (3) into formula (5), the current density Jn+1 / 2 at time n+1 / 2 can be calculated, where Δt is the time step: (6) Similarly, when the PIN diode is reverse biased, since the high resistance is >10kΩ, it can be considered an open circuit, and Jn+1 / 2 can be calculated: (7) 2. The CDI-FDTD discrete and coupling strategies include: Maxwell's curl equation can be written in the following form: (8) (9) In the formula, H is the magnetic field strength, measured in amperes per meter (A / m); E is the electric field strength, measured in volts per meter (V / m); J is the current density, measured in amperes per square meter (A / m²); M is the magnetic flux density, measured in volts per square meter (V / m²); ε is the permittivity, measured in farads per meter (F / m); and μ is the permeability, measured in henries per meter (H / m).

[0024] Solving Maxwell's equations using the LOD-FDTD method yields: (10) (11) Where In is the n-order identity matrix, M=[E,H]T; S=[-Jx / ε,-Jy / ε, -Jz / ε,0,0,0]T; Jx represents the component of the current density in the x-direction; Jy represents the component of the current density in the y-direction; Jz represents the component of the current density in the z-direction; the coefficient matrices A and B are respectively: , , , , , , 03 represents a 3rd order zero matrix.

[0025] Mcn+1 / 2 and Mcn+1 are defined as follows: (12) (13) Therefore, we can conclude that: (14) (15) Substituting formula (12) into formula (15) yields: (16) Therefore, the expression for Ec at time n+1 can be calculated as follows: (17) Where Si = [-Jx / ε, -Jy / ε, -Jz / ε]T. Substituting formula (13) into formula (14) yields: (18) Therefore, the expression for Ec at time n is calculated as follows: (19) Subtracting formula (17) from formula (19) yields the update formula for Ec: (20) Similarly, the update formula for Hc can be calculated: (twenty one) Formulas (20) and (21) are the solution formulas for CDI-FDTD, but they are complex to calculate because they involve matrix inversion. Therefore, auxiliary variables are defined to simplify the formulas, and the expressions are (22), (23), and (24).

[0026] (twenty two) (twenty three) (twenty four) The simplified formula is: (25) (26) The simplified iterative formula of CDI-FDTD is discretized. The iterative formulas for Hc in each direction at time n+1 / 2 are as follows: (27) In the formula, Hcxn+1 / 2(i,j+1 / 2,k+1 / 2) represents the x-direction component of the magnetic field Hc at the grid with coordinates (i,j+1 / 2,k+1 / 2) at time n+1 / 2; Hcxn-1 / 2(i,j+1 / 2,k+1 / 2) represents the x-direction component of the magnetic field Hc at the grid with coordinates (i,j+1 / 2,k+1 / 2) at time n-1 / 2; ecyn(i,j+1 / 2,k+1) represents the y-direction component of the auxiliary variable ec at the grid with coordinates (i,j+1 / 2,k+1) at time n; ecyn(i,j+1 / 2,k) represents the y-direction component of the auxiliary variable ec at the grid with coordinates (i,j+1 / 2,k) at time n; eczn(i,j+1,k+1 / 2) represents the y-direction component of the auxiliary variable ec at the grid with coordinates (i,j+1,k+1 / 2 ...,k+1 / 2) at time n The z-direction component of the auxiliary variable ec at the grid (i, j, k+1 / 2); eczn(i, j, k+1 / 2) represents the z-direction component of the auxiliary variable ec at the grid (i, j, k+1 / 2) at time n.

[0027] (28) In the formula, Hcyn+1 / 2(i+1 / 2,j,k+1 / 2) represents the y-direction component of the magnetic field Hc at the grid with coordinates (i+1 / 2,j,k+1 / 2) at time n+1 / 2; Hcyn-1 / 2(i+1 / 2,j,k+1 / 2) represents the y-direction component of the magnetic field Hc at the grid with coordinates (i+1 / 2,j,k+1 / 2) at time n-1 / 2; eczn(i+1,j,k+1 / 2) represents the z-direction component of the auxiliary variable ec at the grid with coordinates (i+1,j,k+1 / 2) at time n; eczn(i,j,k+1 / 2) represents the z-direction component of the auxiliary variable ec at the grid with coordinates (i,j,k+1 / 2) at time n; ecxn(i+1 / 2,j,k+1 / 2) represents the z-direction component of the auxiliary variable ec at the grid with coordinates (i,j,k+1 / 2) at time n; and ecxn(i+1 / 2,j,k+1 / 2) represents the z-direction component of the auxiliary variable ec at the grid with coordinates (i,j,k+1 / 2) at time n. The x-direction component of the auxiliary variable ec at grid (i+1), i+1, j, k; ecxn(i+1 / 2, j, k) represents the x-direction component of the auxiliary variable ec at grid (i+1 / 2, j, k) at time n.

[0028] (29) In the formula, Hczn+1 / 2(i+1 / 2,j+1 / 2,k) represents the z-direction component of the magnetic field Hc at the grid with coordinates (i+1 / 2,j+1 / 2,k) at time n+1 / 2; Hczn-1 / 2(i+1 / 2,j+1 / 2,k) represents the z-direction component of the magnetic field Hc at the grid with coordinates (i+1 / 2,j+1 / 2,k) at time n-1 / 2; ecxn(i+1 / 2,j+1 / 2,k) represents the x-direction component of the auxiliary variable ec at the grid with coordinates (i+1 / 2,j+1 / 2,k) at time n; ecxn(i+1 / 2,j,k) represents the x-direction component of the auxiliary variable ec at the grid with coordinates (i+1,j+1 / 2,k) at time n; ecyn(i+1,j+1 / 2,k) represents the x-direction component of the auxiliary variable ec at the grid with coordinates (i+1,j+1 / 2,k) at time n; and ecyn(i+1,j+1 / 2,k) represents the x-direction component of the auxiliary variable ec at the grid with coordinates (i+1,j+1 / 2,k) at time n. k) The y-direction component of the auxiliary variable ec at the grid; ecyn(i,j+1 / 2,k) represents the y-direction component of the auxiliary variable ec at the grid at coordinate (i, j+1 / 2, k) at time n.

[0029] The iterative formulas for Ec in each direction at time n+1 are as follows: (30) (31) (32) The update formula for the auxiliary variable is as follows: (33) (34) (35) (36) (37) (38) (39) (40) (41) In summary, the calculation order of the CDI-FDTD method is as follows: First, solve for the value of the auxiliary variable ec at time n; then update the field value of Hc at time n+1 / 2; next, update the values ​​of hc and si at time n+1 / 2; finally, update the field value of Ec at time n+1. This process is repeated cyclically.

[0030] This computational method incorporates the influence of lumped-parameter elements on the electromagnetic field into Maxwell's equations through the relationship between voltage and electric field, and then discretizes the Maxwell's equations using the LP-CDI-FDTD method. The influence of lumped-parameter elements on the electromagnetic field is continuously corrected during the iteration process. This computational approach provides a more efficient modeling of electromagnetic structures containing lumped-parameter parameters such as PIN diodes, including reconfigurable antennas and metasurface antennas.

[0031] Example 2 This embodiment provides a PIN diode modeling and simulation method based on LP-CDI-FDTD, including: In this embodiment, a sinusoidal voltage source is used to excite the PIN diode. Figure 3 Two of the same size (8mm) Two parallel PEC boards (2mm apart) are spaced 4mm apart. The PEC boards have a relative permittivity of 1, a relative permeability of 1, and a conductivity of 10¹⁰ S / m. A voltage source with a 50Ω external resistor is connected to the left end of each PEC board, and a current-limiting resistor and a PIN diode are connected in series to the right end. The voltage source operates at a frequency of 500MHz and a voltage of 2V.

[0032] Define the size of the cell mesh as 0.1. 0.1 The particles are 0.1 mm thick and distributed along the x, y, and z axes, respectively. To ensure simulation accuracy, a PML (Perfectly Matched Layer) is applied as an absorbing boundary at all mesh boundaries. Figure 4 As shown in (a), the target is spaced 10 grids from the boundary. This space is filled with air. The simulation time step is 3000 steps. The signal source is configured as a voltage source, and the waveform is a sine wave. According to... Figure 4 As can be seen in (b), the experimental results are basically consistent with the parameters of BAP64-02.

[0033] Example 3 This embodiment provides a PIN diode modeling and simulation method based on LP-CDI-FDTD, including: This embodiment is a single-pole reconfigurable antenna. In this case, a PIN diode is used to achieve the reconfigurability function. Figure 5 The image shows a top-down view of the model. This model has a three-layer structure: the top layer consists of a microstrip line (green) and a PIN diode (red); the middle layer is a square dielectric substrate; and the bottom layer (orange) is GND. The specific dimensions are: L=40 mm, W=11 mm, W1=3.6 mm, W2=2 mm, L1=4.4 mm, L2=7.2 mm, R1=10.4 mm, R2=23.2 mm. The power supply is located between the bottom of the microstrip line and GND.

[0034] Define the size of the cell mesh as 0.1. 0.1 0.1 mm, distributed along the x, y, and z axes respectively. The initial coordinates are (0, 0, 0). To ensure simulation accuracy, a PML (Perfect Match Layer) is applied as an absorbing boundary at all mesh boundaries. The boundary thickness is 8 meshes. The target is spaced 5 meshes from the boundary, filled with air. The simulation time step is 7000 steps. Both the upper microstrip line and the lower GND are PEC. In the HFSS simulation, the on / off state of the PIN diode is simulated by controlling the boundary conditions in the red area. The boundary condition is set to 2Ω when on and 0.35pF when off. Figures 6-7 As shown, the HFSS simulation results are in good agreement with the MATLAB experimental results.

[0035] On the other hand, this embodiment also provides an electronic device, including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0036] On the other hand, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0037] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A PIN diode modeling and simulation method based on LP-CDI-FDTD, characterized in that, include: Establish an equivalent lumped parameter model of a semiconductor device and obtain its voltage-current relationship under a given bias state; The voltage-current relationship is converted into an equivalent current density, and based on the physical relationship between electric field and voltage, the equivalent current density is embedded into the current density term of Maxwell's curl equation to construct a coupled electromagnetic-circuit equation system. The coupled equations are spatially and temporally discretized using the frog-leap compliance divergence unconditionally stable time-domain finite-difference method to obtain discretized update equations. Simultaneously, iterative calculations are performed based on the discretized update equation, and the spatial electromagnetic field distribution and the state variables of the semiconductor device are updated synchronously at each time step.

2. The method according to claim 1, characterized in that, The establishment of the equivalent lumped parameter model of the semiconductor device includes: Based on the physical characteristics of the semiconductor device under forward bias, it is equivalent to a series structure of parasitic inductance and on-resistance. Meanwhile, based on the physical characteristics of the semiconductor device under reverse bias, it is equivalent to a structure in which the junction capacitance and high resistance are connected in parallel, and then connected in series with the parasitic inductance.

3. The method according to claim 2, characterized in that, Converting the voltage-current relationship into an equivalent current density includes: The voltage-current relationship is determined based on the voltage between the two nodes of the semiconductor device and the current flowing through it. Based on the relationship that the line integral of the electric field along the path between the nodes equals the voltage, the current is converted into current density; and The current density is introduced as a source term into the corresponding position in Maxwell's curl equation.

4. The method according to claim 3, characterized in that, When the semiconductor device is forward biased, determining the equivalent current density based on the voltage-current relationship includes: The voltage equation of a series circuit containing inductance and resistance is discretized by center difference, and the current density value at the discrete time step is obtained by combining the geometric conversion relationship between current and current density.

5. The method according to claim 3, characterized in that, When the semiconductor device is reverse biased, determining the equivalent current density based on the voltage-current relationship includes: The current equation of a circuit containing a capacitor and a high impedance in parallel is discretized by central difference, and the current density value at the discrete time step is obtained by combining the geometric conversion relationship between current and current density.

6. The method according to claim 1, characterized in that, The discretization using the frog-jump compliance divergence unconditionally stable time-domain finite-difference method includes: The Maxwell curl equation is rewritten in matrix form with auxiliary variables; The equation in matrix form is decomposed locally into one dimension to obtain update operators for two sub-steps; Based on the update operator, an explicit set of update equations for the electric field, magnetic field, and auxiliary variables is derived.

7. The method according to claim 6, characterized in that, The iterative calculation includes the following steps performed sequentially: Update the auxiliary variables for the current time step based on the electric field value of the previous time step; Based on the updated auxiliary variables and the magnetic field value of the previous time step, update the magnetic field value of the current half-time step. Based on the updated magnetic field value and the equivalent current density, update the intermediate auxiliary variables and current density term for the current half-time step; and Based on the updated intermediate auxiliary variables, update the electric field value for the next whole time step.

8. The method according to claim 1, characterized in that, The method is applied to the electromagnetic simulation of a reconfigurable antenna or metasurface unit containing the semiconductor device. The semiconductor device is a PIN diode; The spatial discretization uses a grid size that is less than or equal to one-tenth of the critical physical size of the semiconductor device, and the time discretization uses a time step that is not limited by the Courant-Friedrich-Levy condition.

9. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that, When the processor executes the computing program, it implements the method of any one of claims 1-8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-8.

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