A timing jitter modeling method for a silicon-based fully integrated single-photon avalanche diode

Abstract

The application discloses a kind of silicon-based fully integrated single-photon avalanche diode's timing jitter modeling method, comprising: obtaining the electrical simulation data of single-photon avalanche diode and the optical simulation data of single-photon avalanche diode;Obtain the microscopic ionization rate of electron, the macroscopic ionization rate of electron, the microscopic ionization rate of hole, the macroscopic ionization rate of hole and initial avalanche current front propagation speed;Using preset avalanche build time distribution model processing, obtain avalanche build time distribution;Using preset avalanche propagation time distribution model processing, obtain avalanche propagation time distribution;Using preset drift diffusion time distribution model processing, obtain neutral zone drift diffusion time distribution;Avalanche build time distribution, avalanche propagation time distribution and neutral zone drift diffusion time distribution are carried out discrete convolution operation, and the timing jitter of single-photon avalanche diode is acquired.The application can improve the timing jitter calculation efficiency of single-photon diode.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of microelectronic optoelectronic devices, and particularly relates to a timing jitter modeling method for a silicon-based fully integrated single-photon avalanche diode. BACKGROUND

[0002] A single-photon avalanche diode (SPAD) is an advanced single-photon detection device, has high sensitivity, high time resolution, high integration, and other advantages, and is the first choice for time-resolved imaging applications. In recent years, SPADs prepared by compatible CMOS processes have developed rapidly, and time-correlated single-photon counting (TCSPC) optical sensing systems based on SPADs have been widely used in positron emission tomography (PET), fluorescence lifetime imaging microscopy (FLIM), and laser radar (LiDAR).

[0003] Timing jitter is an important parameter for evaluating the time response performance of a SPAD. Traditional analytical band or full-band Monte Carlo simulation can obtain a response time distribution and timing jitter by simulating a large number of SPAD avalanche breakdown processes. However, considering the calculation complexity of the energy band structure and the need to simulate the entire avalanche process in Monte Carlo simulation, such a model is very time-consuming and wastes computing resources. A high-level analytical model can directly calculate the avalanche response time and timing jitter by combining semiconductor process and computer-aided design (TCAD) simulation results. However, the calculation results will ignore the statistical jitter caused by random ionization events during the initial establishment of the avalanche, resulting in inaccurate calculation results.

[0004] Therefore, it is urgent to improve the defects in the prior art. SUMMARY

[0005] To solve the above problems in the prior art, the application provides a timing jitter modeling method for a silicon-based fully integrated single-photon avalanche diode. The technical problem to be solved by the application is solved by the following technical scheme:

[0006] In a first aspect, the application provides a timing jitter modeling method for a silicon-based fully integrated single-photon avalanche diode, comprising:

[0007] Performing steady-state and transient electrical simulation on a preset first single-photon avalanche diode structure model, and obtaining electrical simulation data of the single-photon avalanche diode;

[0008] Performing optical simulation on a preset second single-photon avalanche diode structure model, and obtaining optical simulation data of the single-photon avalanche diode;

[0009] According to the electrical simulation data of part of the single-photon avalanche diodes, the micro ionization rate of electrons, the macro ionization rate of electrons, the micro ionization rate of holes, the macro ionization rate of holes, and the initial avalanche current front propagation speed are obtained, respectively;

[0010] The partial electrical simulation data, the micro ionization rate of electrons and the micro ionization rate of holes are grid processed, and then the preset avalanche establishment time distribution model is used for processing to obtain an avalanche establishment time distribution;

[0011] The macro ionization rate of electrons, the macro ionization rate of holes and the initial avalanche current front propagation speed are grid processed, and then the preset avalanche propagation time distribution model is used for processing to obtain an avalanche propagation time distribution;

[0012] The partial electrical simulation data are grid processed, combined with optical simulation data, and the preset drift diffusion time distribution model is used for processing to obtain a neutral region drift diffusion time distribution;

[0013] The avalanche establishment time distribution, the avalanche propagation time distribution and the neutral region drift diffusion time distribution are discretely convolved to obtain an avalanche time response distribution;

[0014] The full width at half maximum of the avalanche time response distribution is extracted as the timing jitter of the single-photon avalanche diode.

[0015] The timing jitter modeling method of the silicon-based fully integrated single-photon avalanche diode provided by the application comprises the following steps: firstly, a preset first single-photon avalanche diode structure model is subjected to steady-state and transient electrical simulation to obtain electrical simulation data of the single-photon avalanche diode, and a preset second single-photon avalanche diode structure is subjected to optical simulation to obtain optical simulation data of the single-photon avalanche diode; secondly, according to the electrical simulation data and the optical simulation data, an avalanche establishment time distribution, an avalanche propagation time distribution and a neutral region drift diffusion time distribution are obtained, and an avalanche time response distribution is further constructed; finally, according to the avalanche time response distribution, the timing jitter of the single-photon diode is obtained to further evaluate the performance of the single-photon diode; the application simplifies the Monte Carlo model and the high-level analytical model, contains the complete process of avalanche breakdown, improves the consistency and accuracy of the calculation results with the theory, and the calculation of the high-level model at different input points can be realized in parallel through a GPU acceleration platform, thereby improving the calculation efficiency.

[0016] The application will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a flowchart of the timing jitter modeling method of the silicon-based fully integrated single-photon avalanche diode provided by the embodiment of the application;

[0018] Figure 2 is a schematic diagram of the single-photon avalanche diode structure provided by the embodiment of the application;

[0019] Figure 3 is a flow chart of avalanche rise time distribution modeling provided by an embodiment of the present application;

[0020] Figure 4 is a flow chart of avalanche transit time distribution modeling provided by an embodiment of the present application. DETAILED DESCRIPTION

[0021] The present application will be further described in conjunction with specific embodiments, but the embodiments of the present application are not limited thereto.

[0022] In the prior art, statistical jitter caused by random ionization events during the initial establishment of the avalanche is ignored, which causes inaccurate calculation of the avalanche response time and timing jitter. The present application provides a timing jitter modeling method for a silicon-based fully integrated single-photon avalanche diode. The method combines a simplified Monte Carlo model and a high-level analytical model to obtain avalanche rise time distribution, avalanche transit time distribution and neutral region drift diffusion time distribution, and further efficiently and accurately obtains the timing jitter of the single-photon avalanche diode to evaluate the performance of the single-photon avalanche diode.

[0023] Please refer to Figure 1 , and Figure 1 is a flow chart of a timing jitter modeling method for a silicon-based fully integrated single-photon avalanche diode provided by an embodiment of the present application. The timing jitter modeling method for a silicon-based fully integrated single-photon avalanche diode provided by the present application comprises:

[0024] S101, steady-state and transient-state electrical simulation is performed on a preset first single-photon avalanche diode structure model, and electrical simulation data of the single-photon avalanche diode is obtained.

[0025] Specifically, please refer to Figure 2 , and Figure 2 is a schematic diagram of a single-photon avalanche diode structure provided by an embodiment of the present application. In the embodiment, first, a first single-photon avalanche diode structure model is constructed. Then, steady-state and transient-state electrical simulation is performed on the preset first single-photon avalanche diode structure model, and electrical simulation data of the single-photon avalanche diode is obtained. Under different diode reverse voltages, the electrical simulation data of the single-photon avalanche diode includes the intensity E(z) of the electric field on the Z-direction cross-section, the saturated electron velocity v esta (z) on the Z-direction cross-section, the saturated hole velocity v hsta (z) on the Z-direction cross-section, the XY cross-section avalanche breakdown initial electric field intensity E b (x,y) at the Z-direction multiplication main junction depth, the electric field intensity E(x,y) after local avalanche breakdown, the current density J(x,y) after local avalanche breakdown, the X-direction electric field intensity E x(x,z), the electron field intensity E(x,z) of the active region profile of the device before avalanche breakdown z (x,z), the electron field intensity E(x,z) of the active region profile of the device before avalanche breakdown e (x,z), the electron field intensity E(x,z) of the active region profile of the device before avalanche breakdown h (x,z), the breakdown probability P of the P-type neutral region ne (x,z), the breakdown probability P of the P-type neutral region nh .

[0026] It should be noted that, Figure 2 In the embodiment shown, the XY cross section is shown as C1, the XZ cross section is shown as C2, the Z-direction cross section is shown as C3, and Figure 2 The embodiment shown only schematically shows a structure of a single-photon avalanche diode, and does not represent the size thereof.

[0027] S102, optical simulation is performed on the preset second single-photon avalanche diode structure model, and optical simulation data of the single-photon avalanche diode is obtained.

[0028] Specifically, in the embodiment, first, a second single-photon avalanche diode structure model is constructed; second, optical simulation is performed on the preset second single-photon avalanche diode, and optical simulation data of the single-photon avalanche diode is obtained; wherein the optical simulation data of the single-photon avalanche diode includes the absorption rate R ne of the P-type neutral region and the absorption rate R nh of the N-type neutral region; it should be noted that if it is a sudden junction, the absorption rate of the heavily doped region can be ignored.

[0029] S103, according to the electrical simulation data of part of the single-photon avalanche diode, the microscopic ionization rate of the electron, the macroscopic ionization rate of the electron, the microscopic ionization rate of the hole, the macroscopic ionization rate of the hole and the initial avalanche current front propagation speed are obtained.

[0030] Specifically, in the embodiment, considering that the carrier can trigger the collision ionization process only after passing through the ionization threshold energy, the Okuto coefficient is usually used to obtain the microscopic ionization rate α * of the electron, and the expression thereof is:

[0031]

[0032] wherein E ie is the electron ionization threshold energy, E r is the optical phonon energy, λ r is the average free path of the optical phonon, q is the electron charge, E is the electric field intensity, and exp{·} is the exponential function.

[0033] Microscopic ionization rate β of holes * The expression is:

[0034]

[0035] Where E ih is the ionization threshold energy of holes.

[0036] Without considering that the carriers can trigger the collision ionization process only after experiencing the ionization threshold energy, depending on the local electric field, the expression for the macroscopic ionization rate α of electrons is usually obtained using the Deman empirical coefficient:

[0037] α = a e exp(-b e / E);

[0038] Where a e and b e are empirical coefficients;

[0039] The expression for the macroscopic ionization rate β of holes is:

[0040] β = a h exp(-b h / E);

[0041] Where a h and b h are empirical coefficients.

[0042] It should be noted that for silicon material, a e = 7.03 x 10 5 cm -1 ;

[0043] b e = 1.231 x 10 6 V cm -1 (1.75 x 10 5 E 6.0 x 10 5 V cm -1 );

[0044] a h = 1.582 x 10 6 cm -1 ;

[0045] b h = 2.036 x 10 6 V cm -1 (1.75 x 10 5 E 4.0 x 10 5 V cm -1 );

[0046] ah = 6.71 x 10 5 cm -1 ;

[0047] b h = 1.693 x 10 6 V cm -1 (4.0 x 10 5 E 6.0 x 10 5 V cm -1 ).

[0048] The expression for obtaining the initial avalanche current front propagation speed v s0 is as follows:

[0049]

[0050] where D is a diffusion coefficient, and τ0 is an initial avalanche time constant.

[0051] It should be noted that τ0 calculation is divided into two kinds, one is to calculate with fitting parameters, and the calculation formula is as follows:

[0052]

[0053] where g is a fitting parameter, and τ i is an intrinsic time constant, and the calculation formula is as follows:

[0054]

[0055] where w is a depletion region width, v n is an electron saturation speed, and v p is a hole saturation speed.

[0056] The other is to calculate without fitting parameters, and the calculation formula is as follows:

[0057]

[0058] In this embodiment, the calculation without fitting parameters can be realized, and the input parameters can be extracted and calculated through TCAD and FDTD simulation, so as to improve the predictability of the timing jitter of a given device.

[0059] In S104, the partial electrical simulation data, the microscopic ionization rate of electrons and the microscopic ionization rate of holes are grid processed, and then processed by using a preset avalanche establishment time distribution model to obtain an avalanche establishment time distribution.

[0060] Specifically, as shown in Figure 3 , Figure 3A flowchart of an avalanche rise time distribution model provided by the embodiment of the present application, in the embodiment, since the avalanche rise time calculates the process of the initial current growth of the avalanche to 1 mu A, the current does not spread in a large area, so 1D-RPL (1D-RPL) is used as a simplified Monte Carlo method modeling, and the avalanche rise time distribution model processing process is specifically:

[0061] S1041, the micro ionization rate of the electron α * , the micro ionization rate of the hole β * , the saturation electron velocity v esta (z) on the Z direction section line, the saturation hole velocity v hsta (z) on the Z direction section line, the first preset current threshold I b , and the time step dt input the preset avalanche rise time distribution model;

[0062] S1042, initialize parameters, including setting the initial carrier position z0[1], random number r[1]=U(0,1) and forward path length l0[1]=0;

[0063] S1043, update the parameters of the avalanche rise time t b , initialize the number of new carriers n a =0;

[0064] S1044, for each carrier at present, update the forward path length l and the position z, and judge whether the carrier reaches the depletion region boundary; wherein, the expression for updating the forward path length l of the carrier is:

[0065] l=l0+v sta ·dt;

[0066] Wherein, for electron v sta =v esta , for hole v sta =-v hsta ;

[0067] The expression for updating the carrier position z is:

[0068] z=z0+l;

[0069] S1045, if the carrier reaches the depletion region boundary, remove the carrier, and update the number of carriers;

[0070] S1046, if the carrier does not reach the depletion region boundary, judge whether the carrier has collision ionization, wherein the probability s that the carrier does not have collision ionization at the position z is:

[0071]

[0072] where h(z) is the collision ionization probability density function, z0[i] is the starting position of the i-th carrier, and i is the i-th carrier;

[0073] It should be noted that for an electron, the expression of the collision ionization probability density function h(z) is: e

[0074]

[0075] where d is the electron dead space length; e

[0076] For a hole, the expression of the collision ionization probability density function h(z) is: h

[0077]

[0078] S1047, determine whether the probability s that the carrier does not undergo collision ionization at the position z is less than or equal to the random number, i.e., s≤r; if yes, add a new electron-hole pair to the carrier at the position z, update the number of newly added carriers n a , and reset the random number r and the initial carrier position z0.

[0079] S1048, determine whether the current I reaches a first preset current threshold I b ; if yes, output the avalanche build-up time t b ; if not, update the avalanche build-up time t b until the current I reaches the preset current threshold I b ; wherein the expression for obtaining the current I is:

[0080] I = n · I q .

[0081]

[0082] where I q is the current contributed by a single carrier, v is the average carrier velocity, w is the width of the depletion region, n is the total number of carriers, and q is the electronic charge.

[0083] S1049, repeat the calculation of the avalanche build-up time t b for at least 10 3 times, and obtain the avalanche build-up time distribution P b (t) after statistics.

[0084] In this embodiment, the simplified Monte Carlo model is used to only calculate the process of the initial current growth of the avalanche to 1 μA, which saves the calculation time and calculation resources compared with calculating the complete avalanche process. ​​​

[0085] S105, the macroscopic ionization rate of electrons, the macroscopic ionization rate of holes and the initial avalanche current front propagation speed are grid processed, and then a preset avalanche propagation time distribution model is used for processing to obtain the avalanche propagation time distribution.

[0086] Specifically, please refer to Figure 4 as shown, Figure 4 is a flow chart of the avalanche propagation time distribution model modeling provided by the embodiment of the present application, and in the embodiment, the above process is specifically:

[0087] S1051, the macroscopic ionization rate α of electrons, the macroscopic ionization rate β of holes and the initial avalanche current front propagation speed v s0 , the grid spacing on the XY cross section is d1, the external voltage V r , the external resistance R and the second preset current threshold I th , the preset avalanche propagation time distribution model is input;

[0088] S1052, the initial avalanche propagation speed is set to be equal to the initial avalanche current front propagation speed, that is, v s =v s0 , the second loop parameter m is set to be 1, the propagation time t is set to be 0, and the bias voltage V on the single-photon avalanche diode is set to be V r ;

[0089] S1053, the propagation time t s , the propagation circular ring radius r and the total current I(m) are calculated respectively; wherein the expression of the propagation time t s is:

[0090] t s =t s +d1 / v s ;

[0091] The expression of the propagation circular ring radius r is:

[0092] r=md1;

[0093] The expression of the total current I(m) is:

[0094]

[0095] Wherein, D(m) is the propagation circular area, the center of which is (x, y) and the radius of which is r=md1;

[0096] S1054, whether the total current I(m) reaches the second preset current threshold I th , if yes, the propagation time t s; if not, updating the bias voltage V on the single photon avalanche diode, the avalanche propagation speed v s and the second cycle parameter m, wherein the bias voltage V on the single photon avalanche diode is determined by a specific external circuit, and the electric field E under the diode bias voltage V b and E is updated to the current τ until the total current reaches the second preset current threshold;

[0097] S1055, calculating the avalanche propagation time t of each point on the XY section s , and obtaining the avalanche propagation time distribution P s (t) after statistics.

[0098] S106, performing grid processing on part of the electrical simulation data, combining the optical simulation data, and using a preset drift diffusion time distribution model for processing to obtain a neutral region drift diffusion time distribution.

[0099] Specifically, the above process in the embodiment specifically includes:

[0100] S1061, taking the electric field intensity vector as the field distribution to generate the streamlines corresponding to the point (x, z), and taking the streamlines as the motion path of the carriers of the point; wherein the P-type neutral region field distribution takes the value of -E x and -E z , and the n-type neutral region field distribution takes the value of E x and E z ; it should be noted that the streamline generation can be realized by the MATLAB streamline function;

[0101] S1062, processing the positions of the points in the streamlines to obtain the coordinate matrix [x l , z l ], and the number of coordinates is g;

[0102] S1063, obtaining the drift diffusion time t d corresponding to the current path according to the coordinate matrix [x l , z l ], and the expression is:

[0103]

[0104] wherein v(x l ,z l ) is the electron motion speed v e (x, z) of the device active area profile corresponding to the avalanche breakdown in the p-type neutral region, v(x l ,z l ) is the hole motion speed v h (x, z) of the device active area profile corresponding to the avalanche breakdown in the n-type neutral region, and k is the cycle parameter in the summation process.

[0105] S1064, calculate the drift diffusion time t of each point on the neutral region in the XZ section d , and the neutral region absorption rate R ne , R nh and breakdown probability P ne , P nh are weighted, and the neutral region drift diffusion time distribution P d (t) is obtained by statistical calculation.

[0106] It should be noted that in the gridding process, the grid spacing on the XY section is d1, and the grid spacing on the XZ section is d2.

[0107] S107, discrete convolution operation is performed on the avalanche build-up time distribution, the avalanche propagation time distribution and the neutral region drift diffusion time distribution to obtain the avalanche time response distribution.

[0108] S108, the full width at half maximum of the avalanche time response distribution is extracted as the timing jitter of the single photon avalanche diode.

[0109] In summary, the timing jitter modeling method of the silicon-based fully integrated single photon avalanche diode provided by the present application firstly performs steady-state and transient electrical simulation on the preset first single photon avalanche diode structure model to obtain electrical simulation data of the single photon avalanche diode, and performs optical simulation on the preset second single photon avalanche diode structure to obtain optical simulation data of the single photon avalanche diode; secondly, according to the electrical simulation data and the optical simulation data, the avalanche build-up time distribution, the avalanche propagation time distribution and the neutral region drift diffusion time distribution are obtained respectively, and the avalanche time response distribution is further constructed; finally, according to the avalanche time response distribution, the timing jitter of the single photon diode is obtained to further evaluate the performance of the single photon diode; the present application simplifies the Monte Carlo model and the high-level analytical model, contains the complete process of avalanche breakdown, improves the consistency and accuracy of the calculation results with the theory, and the calculation of the high-level model at different input points can be realized in parallel through the GPU acceleration platform, which can improve the calculation efficiency.

[0110] It is to be understood that the terminology "first", "second", and the like used herein is merely intended to differentiate one element from another element, and does not imply or suggest any actual relationship or sequence between the elements. Also, the terms "comprise", "comprising", or any other variant thereof are intended to cover non-exclusive inclusions, such that an item or apparatus that comprises a list of elements does not exclude other elements not expressly listed. An element defined by the phrase "comprising a..." does not exclude the presence of additional identical elements in the item or apparatus comprising the element. The terms "connected" or "coupled" or similar terms are not limited to a direct physical or mechanical connection, but can also include an electrical connection, whether direct or indirect. The terms "upper", "lower", "left", "right", and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are merely intended to facilitate the description of the present application and simplify the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0111] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific feature or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. The illustrative expressions of the above terms in the present specification do not necessarily refer to the same embodiment or example. Also, the specific features or characteristics described can be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate different embodiments or examples described in the present specification.

[0112] The above is a further detailed description of the present application in conjunction with specific preferred embodiments, and cannot be considered as a limitation of the specific implementation of the present application. For those skilled in the art, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, which should be considered as falling within the scope of protection of the present application.

Claims

1. A method of timing jitter modeling for a silicon-based fully integrated single-photon avalanche diode, the method comprising: The method comprises the following steps: carrying out steady-state and transient-state electrical simulation on a preset first single-photon avalanche diode structure model, and obtaining electrical simulation data of the single-photon avalanche diode; carrying out optical simulation on a preset second single-photon avalanche diode structure model, and obtaining optical simulation data of the single-photon avalanche diode; obtaining a micro ionization rate of electrons, a macro ionization rate of electrons, a micro ionization rate of holes, a macro ionization rate of holes and an initial avalanche current front propagation speed according to part of the electrical simulation data of the single-photon avalanche diode; carrying out grid processing on part of the electrical simulation data, the micro ionization rate of electrons and the micro ionization rate of holes, and then processing by using a preset avalanche establishment time distribution model to obtain an avalanche establishment time distribution; carrying out grid processing on the macro ionization rate of electrons, the macro ionization rate of holes and the initial avalanche current front propagation speed, and then processing by using a preset avalanche propagation time distribution model to obtain an avalanche propagation time distribution; carrying out grid processing on part of the electrical simulation data, combining the optical simulation data, and processing by using a preset drift-diffusion time distribution model to obtain a neutral region drift-diffusion time distribution; carrying out discrete convolution operation on the avalanche establishment time distribution, the avalanche propagation time distribution and the neutral region drift-diffusion time distribution to obtain an avalanche time response distribution; extracting a full width at half maximum of the avalanche time response distribution as a timing jitter of the single-photon avalanche diode.

2. The method of claim 1, wherein the method is performed by a processor. The electrical simulation data of the single-photon avalanche diode includes the electric field intensity E(z) along the Z-direction cross section and the saturated electron velocity v along the Z-direction cross section. esta (z), Saturated hole velocity v on the Z-direction cutoff line hsta (z) Initial electric field intensity E of avalanche breakdown at the depth of the XY section in the Z-direction multiplying master node. b (x,y), electric field intensity E(x,y) after local avalanche breakdown, current density J(x,y) after local avalanche breakdown, and electric field intensity E of electrons in the X-direction of the active region profile of the device before avalanche breakdown. x (x,z), the electric field intensity E of electrons in the Z-direction of the active region profile of the device before avalanche breakdown. z (x,z), electron electric field intensity E(x,z) in the active region profile of the device before avalanche breakdown, and electron velocity v in the active region profile of the device before avalanche breakdown. e (x,z), the hole velocity v in the active region profile of the device before avalanche breakdown. h (x,z), the breakdown probability P of the P-type neutral region ne The breakdown probability P of the n-type neutral region nh .

3. The method of claim 1, wherein the method is performed by a processor. The optical simulation data of the single-photon avalanche diode includes an absorption rate R of a p-type neutral region ne and an absorption rate R of an n-type neutral region nh .

4. The method of claim 1, wherein the method is performed by a processor. obtaining a micro ionization rate α of the electrons * The expression is: where E ie electron ionization threshold energy, E r is the optical phonon energy, λ r is the optical phonon mean free path, q is the electron charge, E is the electric field strength, and exp{•} is the exponential function; obtaining a micro-ionization rate β of the voids * The expression is: where E ih is the ionization threshold energy for holes.

5. The method of claim 1, wherein the method is performed by a processor. An expression of the macro ionization rate of electrons α is obtained as follows: a = a e exp(-b e / E) wherein a e and b e are empirical coefficients; An expression of the macro ionization rate of holes β is obtained as follows: β = a h exp(-b h / E); wherein a h and b h are empirical coefficients.

6. The method of claim 1, wherein: obtaining the initial avalanche current front propagation speed v s0 The expression for v is: wherein D is a diffusion coefficient, and τ0 is an initial avalanche time constant.

7. The method of claim 1, wherein the method is performed by a processor. In the grid processing, the grid spacing on the XY section is d1, and the grid spacing on the XZ section is d2.

8. The method of claim 1, wherein: The process of carrying out grid processing on part of the electrical simulation data and the micro ionization rate of electrons, and then processing by using a preset avalanche establishment time distribution model to obtain an avalanche establishment time distribution comprises the following steps: a micro-ionization rate α of the electrons * a micro-ionization rate β of the holes * a saturation electron velocity v esta (z) in the Z-direction cross-section line hsta (z), a first preset current threshold I b and a time step dt input the preset avalanche build-up time distribution model; initializing parameters, including setting an initial carrier position z0[1], a random number r[1]=U(0,1) and a forward path length l0[1]=0; Updating parameter avalanche build-up time t b , initializing new carrier number n a = 0; for each current carrier, updating the forward path length l and the position z, and judging whether the carrier reaches the depletion region boundary; wherein an expression of updating the forward path length l of the carrier is as follows: l = lo + v sta • dt; where, for electrons v sta = v esta , for holes v sta = -v hsta ; an expression of updating the position z of the carrier is as follows: z=z0+l; if the carrier reaches the depletion region boundary, the carrier is removed, and the number of carriers is updated; if the carrier does not reach the depletion region boundary, it is judged whether the carrier is subjected to collision ionization, wherein a probability s that the carrier is not subjected to collision ionization at the position z is as follows: wherein h(z) is a collision ionization probability density function, z0[i] is a starting position of the i th carrier, and i is the i th carrier. determining whether the probability s that the carrier does not undergo collision ionization at the position z is less than or equal to a random number, i.e., s≤r; if so, adding a new electron-hole pair to the carrier at the position z, updating the number of newly added carriers n a resetting the random number r and the initial carrier position z0; determining whether the current I reaches a first preset current threshold I b , if yes, outputting the avalanche build-up time t b , if no, updating the avalanche build-up time t b until the current I reaches the preset current threshold I b ; wherein the expression for obtaining the current I is: I = n • I q ; where I q is the current contributed by a single carrier, v is the average carrier velocity, w is the width of the depletion region, n is the total number of carriers, and q is the electronic charge. Repeat at least 10 3 times to calculate avalanche build-up time t b , and count the number of times t b is less than or equal to t.

9. The method of claim 1, wherein: The process of carrying out grid processing on the macro ionization rate of electrons and the initial avalanche current front propagation speed, and then processing by using a preset avalanche propagation time distribution model to obtain an avalanche propagation time distribution comprises the following steps: a macroscopic ionization rate of the electron α, a macroscopic ionization rate of the hole β, a propagation speed of the initial avalanche current front v s0 , a grid spacing d1 on the XY cross section, an external voltage V r , an external resistance R and a second preset current threshold I th inputting the preset avalanche propagation time distribution model; Setting the initial avalanche propagation speed equal to the initial avalanche current front propagation speed, i.e. v s = v s0 , and setting the second loop parameter m = 1, the propagation time t = 0, and the bias voltage on the single photon avalanche diode V r = V ; The propagation time t is calculated for each of the two signals s , the propagation circle radius r and the total current I (m); wherein the propagation time t s is obtained from the expression: t s = t s + d1 / v s ; An expression for obtaining a propagation circle radius r is: r = md1; An expression for obtaining a total current I(m) is: where D(m) is a propagation circle area, a center of which is (x, y) and a radius of which is r = md1; determining whether the total current I(m) reaches a second preset current threshold I th if yes, outputting the propagation time t s if not, updating the bias voltage V, the avalanche propagation speed v s and the second loop parameter m on the single-photon avalanche diode until the total current reaches the second preset current threshold; The avalanche propagation time t is calculated for each point on the XY section s The avalanche propagation time distribution P(t) is obtained by statistics s (t).

10. The method of claim 1, wherein: The process of performing the gridding processing on the part of the electrical simulation data, combining the optical simulation data, and processing using a preset drift diffusion time distribution model to obtain a neutral region drift diffusion time distribution includes: With the electric field intensity vector as the field distribution, a stream line corresponding to the point (x, z) is generated, and the stream line is taken as the motion path of the carrier of the point; wherein the field distribution of the P-type neutral region is -E x and -E z , and the field distribution of the n-type neutral region is E x and E z ; The position of each point in the flow line is processed to obtain a coordinate matrix [x l , z l ] with g coordinates; According to the coordinate matrix [x l , z l ], the drift diffusion time t d corresponding to the current path is obtained, and the expression is as follows: Where, v(x) l ,z l The electron velocity v in the active region profile of the device before avalanche breakdown in the p-type neutral region. e (x,z), v(x) l ,z l The hole velocity v in the active region profile of the device before avalanche breakdown in the n-type neutral region. h (x,z), where k is the loop parameter in the summation process; The drift diffusion time t is calculated for each point in the neutral zone of the XZ cross section d The neutral zone absorption rate R ne , R nh and the breakdown probability P ne , P nh are weighted, and the neutral zone drift diffusion time distribution P d (t) is statistically obtained.

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