A single photon avalanche diode photon detection probability modeling and prediction method

Abstract

The application provides a single-photon avalanche diode photon detection probability modeling and predicting method, considers dead space distance and non-ideal factor edge effect, input parameters are extracted from TCAD Sentaurus simulation, is based on actual manufacturing values and device layout, does not need to add additional fitting parameters, calculates breakdown probability of each point occurring on a two-dimensional profile, is very intuitive and easy to optimize device structure, then calculates photon detection probability according to optical simulation data and total breakdown probability. Moreover, the application can call GPU for parallel acceleration calculation in the Matlab platform, improves calculation efficiency, and therefore the application has good prediction effect and efficiency of the established model.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of microelectronic optoelectronic devices, and particularly relates to a single-photon avalanche diode photon detection probability modeling and prediction method. BACKGROUND

[0002] Single-photon avalanche diodes (SPADs) are of great interest in CMOS technology due to their high sensitivity at the single-photon level, picosecond-level high time resolution, and ease of integration. In recent years, micro-light detection technology based on SPADs has been continuously developed, and SPADs prepared using CMOS-compatible processes have been widely used in three-dimensional imaging, time-gated Raman spectroscopy, and laser radar (LiDAR) fields.

[0003] However, the existing photon-detection-probability (PDP) model based on a one-dimensional local-field model assumes that the motion in all regions of the device is along a straight line perpendicular to the surface, which makes the edge effect more serious due to the continuous reduction in the size of CMOS SPADs. In addition, the local-field model is affected by the path before the ionization threshold energy in the prediction process, resulting in poor prediction results. SUMMARY

[0004] To solve the above problems in the prior art, the application provides a single-photon avalanche diode photon detection probability modeling and prediction method. The technical problems to be solved by the application are solved by the following technical solutions:

[0005] The single-photon avalanche diode photon detection probability modeling and prediction method provided by the application comprises:

[0006] Step 1: obtaining the structure, working voltage, and incident light wavelength of the SPAD;

[0007] Step 2: obtaining electrical simulation data by electrically simulating the structure of the SPAD, and obtaining optical simulation data by optically simulating the structure of the SPAD;

[0008] The electrical simulation data includes potential, electric field intensity, transverse electric field intensity, and longitudinal electric field intensity, and the optical simulation data includes optical generation.

[0009] Step 3: gridizing the electrical simulation data and the optical simulation data to obtain a first grid and a second grid;

[0010] Step 4: taking the two-dimensional vector data formed by the transverse electric field intensity and the longitudinal electric field intensity as grid data, generating two streamlines on the basis of the first grid in combination with the second grid;

[0011] Wherein, all point coordinates of any streamline are taken as path coordinate matrix;

[0012] Step 5: Convert the coordinate values of the path coordinate matrix of each streamline into the indices of the parameters in the grid matrix of the first grid, which are used to index the imported electric field, electric potential and ionization rate;

[0013] Step 6: Take the indices of the first streamline as the electron motion path and the second streamline as the hole motion path to search the dead space region respectively; and according to the collision ionization probability density of all points in the dead space region and the non-dead space region on each motion path, calculate the electron collision ionization probability matrix and the hole collision ionization probability matrix of all intersection points in the second grid;

[0014] Step 7: Set the calculation accuracy, and for each type of collision ionization probability matrix, take the collision ionization probability matrix calculated each time as the input of the next time to calculate the breakdown probability matrix composed of the electron breakdown probability of all intersection points in the second grid;

[0015] Step 8: Calculate the total breakdown probability according to the electron breakdown probability matrix and the hole breakdown probability matrix;

[0016] Step 9: Calculate the photon detection probability according to the optical simulation data and the total breakdown probability.

[0017] Optionally, step 3 comprises:

[0018] Step 31: Grid the electrical simulation data and the optical simulation data in Origin to obtain data points distributed uniformly on the plane;

[0019] Step 32: Import the data points into matlab as numerical matrices to generate the first grid corresponding to the data points and the second grid for calculating the breakdown probability points;

[0020] Wherein, the first grid and the second grid each correspond to a grid matrix, and the parameters in the grid matrix represent the coordinates of the intersection points on the grid.

[0021] Optionally, step 4 comprises:

[0022] Take the intersection points on the first grid as coordinates, take the preset range of transverse electric field intensity and longitudinal electric field intensity as two-dimensional vector data, and take the intersection points on the second grid as starting points to generate two streamlines.

[0023] Optionally, step 6 comprises:

[0024] Step 61: searching from the starting point to a first target point with an electron motion path of the matrix subscript of the first stream line under the first grid and a potential rise of no less than the first potential or searching to a second target point with a hole motion path of the matrix subscript of the second stream line under the first grid and a potential drop of no more than the first potential;

[0025] wherein the curve between the starting point and the first target point or the second target point is an electron dead space or a hole dead space generated at the coordinates of the junction point on the first grid;

[0026] Step 62: calculating the collision ionization probability density of the dead space region and the non-dead space region on the electron motion path and the hole motion path respectively to obtain the electron collision ionization probability density and the hole collision ionization probability density;

[0027] Step 63: calculating the electron collision ionization probability matrix according to the electron collision ionization probability density and calculating the hole collision ionization probability matrix according to the hole collision ionization probability density.

[0028] Optionally, step 7 comprises:

[0029] Step 71: setting the calculation precision;

[0030] Step 72: for each type of collision ionization probability, taking the collision ionization probability calculated last time as the input data to calculate the electron breakdown probability of one junction point of the second grid;

[0031] Step 73: cyclically executing step 72 until the electron breakdown probability of all junction points is calculated to form a collision ionization probability matrix.

[0032] Optionally, step 8 comprises:

[0033] Step 81: calculating the breakdown probability matrix according to each collision ionization probability matrix;

[0034] Step 82: calculating the total breakdown probability under the light incidence condition according to the breakdown probability matrix.

[0035] Optionally, step 9 comprises:

[0036] Step 91: calculating the quantum efficiency according to the optical simulation data;

[0037] Step 92: multiplying the quantum efficiency and the total breakdown probability to obtain the photon detection probability.

[0038] Optionally, before step 5, the single-photon avalanche diode photon detection probability modeling and prediction method further comprises:

[0039] rounding off the coordinate values in the path coordinate matrix of each stream line to keep the same decimal point number as the first grid spacing.

[0040] The total breakdown probability is expressed as:

[0041]

[0042] Among them, P B =P E +P H -P E *P H , Indicates optical generation, P B Let λ represent the breakdown probability matrix, and λ represent the incident light wavelength.

[0043] The photon detection probability is expressed as:

[0044] PDP(λ)=η(λ)·P b,total (λ)

[0045] Where η(λ) represents the photon detection probability.

[0046] This invention provides a method for probabilistic modeling and prediction of single-photon avalanche diode (SPAD) photon detection. The method involves performing electrical and optical simulations of the SPAD structure to obtain simulation data; meshing the simulation data to obtain a first mesh and a second mesh; using two-dimensional vector data formed by the transverse and longitudinal electric field intensities as mesh data, and combining the first mesh with the second mesh to generate two streamlines; converting the coordinate values ​​of the path coordinate matrix of each streamline into subscripts of parameters in the mesh matrix of the first mesh, used to index the imported electric field, potential, and ionization rate; using the subscript of the first streamline as the electron motion path, and using the subscript of the second streamline as the electron path... The two streamlines serve as the hole movement path, searching the dead space region separately. Based on the collision ionization probability density of all points along each path, the electron collision ionization probability matrix and hole collision ionization probability matrix of all boundary points in the second grid are calculated. The calculation precision is set, and for each type of collision ionization probability matrix, the calculated collision ionization probability matrix is ​​used as the input for the next calculation to calculate the breakdown probability matrix composed of the electron breakdown probabilities of all boundary points in the second grid. The total breakdown probability is calculated based on the electron breakdown probability matrix and the hole breakdown probability matrix. The photon detection probability is calculated based on the optical simulation data and the total breakdown probability. This invention considers dead space distance and non-ideal edge effects. The input parameters are extracted from TCAD Sentaurus simulations, based on actual manufacturing values ​​and device layout, without the need for additional fitting parameters. The calculation of the breakdown probability at each point on the two-dimensional cross-section is very intuitive and easy to optimize the device structure. Furthermore, this invention can call GPUs in the Matlab platform for parallel acceleration calculations, improving computational efficiency.

[0047] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0048] Figure 1 This is a flowchart of two-dimensional photon detection probability modeling provided in an embodiment of the present invention;

[0049] Figure 2 The breakdown probability matrix P provided in the embodiments of the present invention E ,P H ,P B Calculation flowchart. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0051] like Figure 1 As shown, the single-photon avalanche diode photon detection probability modeling and prediction method provided by the present invention includes:

[0052] Step 1: Obtain the SPAD structure (TCAD Sentaurus SDE), operating voltage V, and incident light wavelength λ;

[0053] Step 2: Perform electrical simulation on the SPAD structure to obtain electrical simulation data, and perform optical simulation to obtain optical simulation data;

[0054] The electrical simulation data includes electric potential, electric field strength, transverse electric field strength, and longitudinal electric field strength, while the optical simulation data includes optical generation.

[0055] It is worth noting that: in TCAD Sentaurus Sdevice, electrical and optical simulations of this structure were performed, and the electric potential (Electric Field-V), electric field strength (Abs(Electric Field-V)), transverse electric field strength (Electric Field-X), longitudinal electric field strength (Electric Field-Y), and optical generation (OptIcal Generation) were extracted and exported, denoted as P, E, and E, respectively. X E Y G O .

[0056] In the dead-space model, electrons and holes acquire energies greater than or equal to the ionization threshold E during their motion. ie or E ih Only when collisional ionization occurs can this energy be obtained. The minimum distance that the carriers need to travel is called the dead space of the carriers.

[0057] In the two-dimensional dead space model, the dead space distance d of electrons (holes) e (x,y)(d h (x, y) can be expressed by the following formula:

[0058]

[0059]

[0060] Where E(x,y) is the electric field strength, E ie E is the electron ionization threshold energy. ih Let ΔP be the hole ionization threshold energy, and ΔP be the energy at path L. de L dh The potential increment on L de Let L be the curve representing the path of an electron generated at (x,y) to reach the ionization threshold energy. de The length is the dead space distance of the electron, L dh Let L be the curve representing the path along which a hole generated at (x,y) travels to acquire the ionization threshold energy. dh The length is the dead space distance of the cavity.

[0061] Step 3: Mesh the electrical simulation data and optical simulation data to obtain the first mesh and the second mesh;

[0062] This step can be achieved through the following process:

[0063] Step 31: Mesh the electrical and optical simulation data in Origin to obtain data points that are evenly distributed on the plane;

[0064] Step 32: Import the data points into Matlab as a numerical matrix, generate the first grid corresponding to the data points and the second grid for calculating the breakdown probability points;

[0065] Each of the first and second grids corresponds to a grid matrix, and the parameters in the grid matrix represent the coordinates of the intersection points on the grid.

[0066] It is worth noting that: the first grid [X,Y] with a spacing of d1 is generated to define the coordinates of the imported data; the second grid [x,y] with a spacing of d2 is generated to calculate the penetration probability, and the coordinate ranges of the two grids are consistent.

[0067] It is worth noting that in Origin, the exported data is gridded to generate data points evenly distributed on a plane, P, E, E X E Y The grid spacing is d1, G OGrid spacing d2, d2≤d1; the data generated in Origin is imported into Matlab as the numerical matrix of potential, electric field and photo-generated carriers.

[0068] Step 4: the two-dimensional vector data formed by the transverse electric field intensity and the longitudinal electric field intensity are taken as the grid data, the second grid is combined on the basis of the first grid, and two streamlines are generated;

[0069] Wherein, the coordinates of all points on any streamline are taken as the path coordinate matrix.

[0070] This step takes the junction points on the first grid as coordinates, takes the preset range of the transverse electric field intensity and the longitudinal electric field intensity as the two-dimensional vector data, and takes the junction points on the second grid as starting points to generate two streamlines.

[0071] It is worth noting that: taking [X, Y] as coordinates, [-Ex, -Ey] and [Ex, Ey] as two-dimensional vector data, and the junction points [x, y] of the second grid as starting points, the streamlines generated are taken as the motion paths of electrons and holes, and the coordinates of all points on each streamline are taken as the motion path coordinate matrix.

[0072] After obtaining the path coordinate matrix, the coordinate values in the path coordinate matrix of each streamline are rounded off to retain the same number of decimal places as the spacing of the first grid.

[0073] It is worth noting that: the path coordinate matrix of the electron (hole) generated by a point (x, y) is A e (A h ) (both are n x 2 matrices, and n is the number of points on the streamline), all coordinate values in the coordinate matrix are rounded off to retain the same number of decimal places as d1, and a new coordinate matrix A e1 =[A ex1 ,A ey1 ] (A h1 =[A hx1 ,A hy1 ) is generated.

[0074] Step 5: the coordinate values of the path coordinate matrix of each streamline are converted into the subscripts of the parameters in the grid matrix of the first grid, which are used for indexing the imported electric field, potential and ionization rate.

[0075] The coordinate values in A e1 and A h1 are converted into the matrix subscripts (i e (k),j e (k)) and (i h (k),j h of the [X, Y] grid.(k)) for indexing in imported electric field, electric potential and other parameters; the matrix subscript (i e1 (k),j e1 (k)) is expressed as:

[0076]

[0077]

[0078] the matrix subscript (i h1 (k),j h1 (k)) is expressed as:

[0079]

[0080]

[0081] wherein, A e1 = [A ex1 ,A ey1 ](A h1 = [A hx1 ,A hy1 ]), x min is the minimum value of X in the point coordinates [X, Y] of the first grid, y min is the minimum value of Y in [X, Y], d1 is the first grid spacing, and k represents the serial number of the coordinates.

[0082] Step 6: taking the subscript of the first stream line as the electron motion path and the second stream line as the hole motion path, searching the dead space region respectively; and according to the collision ionization probability density of the dead space region and the non-dead space region on each motion path, calculating the electron collision ionization probability matrix and the hole collision ionization probability matrix;

[0083] This step can be realized by the following process:

[0084] Step 61: taking the matrix subscript of the first stream line under the first grid as the electron motion path, searching from the starting point to the first target point with the electric potential rising no less than E ie or taking the matrix subscript of the second stream line under the first grid as the hole motion path, searching the second target point with the electric potential dropping no higher than E ih ;

[0085] wherein, the curve between the starting point and the first target point or the second target point is the electron dead space or hole dead space generated at the coordinates of the junction points on the first grid;

[0086] For the motion of the electron, (i e1 (k),j e1(k)) as the electron path of motion, from the starting point (i e1 (1),j e1 (1)) to search for a first target point (i ie (c),j e1 (c)) where the potential P is raised by E e1 (c)) can be expressed as:

[0087] P(i e1 (c),j e1 (c))-P(i e1 (1),j e1 (1))≥E ie

[0088] The segment of the curve from (A ex1 (1),A ey1 (1)) to (A ex1 (c),A ey1 (c)) on the path coordinate matrix is the dead space for the electron generated at (x,y), and the dead space distance d e The discrete coordinate points (equation (1)) are approximated as follows:

[0089]

[0090] For hole motion, (i h1 (k),j h1 (k)) as the hole path of motion, from the starting point (i h1 (1),j h1 (1)) to search for a second target point (i ih (c),j h1 (c)) where the potential P is lowered by E h1 (eV), which can be expressed as:

[0091] P(i h1 (1),j h1 (1))-P(i h1 (c),j h1 (c))≥E ih

[0092] The segment of the curve from (A hx1 (1),A hy1 (1)) to (A hx1 (c),A hy1 (c)) on the flow line coordinate matrix is the dead space for the hole generated at (x,y), and the dead space distance d h The discrete coordinate points (equation (2)) are approximated as follows:

[0093]

[0094] Step 62: calculate the collision ionization probability density of the dead space region and the non-dead space region on the electron motion path and the hole motion path respectively, to obtain the electron collision ionization probability density and the hole collision ionization probability density;

[0095] wherein the collision ionization probability density of each point on the electron motion path (formula (3)) can be discretely approximated as:

[0096]

[0097] Formula (3) is expressed as:

[0098]

[0099] represents the two-dimensional collision ionization probability density of the electron generated at (x, y) at the point (x0, y0) on its motion path, L e0 is the curve along the electron motion path from the initial position (x, y) to the point (x0, y0), and a is the electron ionization rate.

[0100] wherein a(i1(k),j1(k)) is the electron ionization rate indexed by the index of the transformed matrix in step 5, and the electron ionization rate is calculated by formula (4) as follows.

[0101]

[0102] wherein E(x, y) is the electric field strength, E r is the optical phonon energy, and λ r is the optical phonon mean free path.

[0103] The collision ionization probability density of each point on the hole motion path (formula (5)) can be discretely approximated as:

[0104]

[0105] wherein β(i1(k),j1(k)) is the hole ionization rate indexed by the index of the transformed matrix in step 5, and the hole ionization rate is calculated by formula (6).

[0106] Formula (5):

[0107]

[0108] represents the two-dimensional collision ionization probability density of the hole generated at (x, y) at the point (x0, y0) on its motion path, L h0 is the curve along the hole motion path from the initial position (x, y) to the point (x0, y0), and β is the hole ionization rate:

[0109]

[0110] Where E(x,y) is the electric field strength, E r For the optical phonon energy, λ r It is the mean free path of optical phonons.

[0111] Step 63: Calculate the electron collision ionization probability matrix based on the electron collision ionization probability density and the hole collision ionization probability matrix based on the hole collision ionization probability density.

[0112] The collisional ionization probability P of the electron generated at (x,y) ie The first term in equation (7) can be discretized and approximated as follows:

[0113]

[0114] Equation (7):

[0115] Equation 7 represents the probability P that the electron generated at (x,y) produces an infinite number of charge carriers (i.e., breakdown occurs). e (x,y).

[0116] The collision ionization probability P of the hole generated at (x,y) ih That is, the first term in equation (8) can be discretized and approximated as follows:

[0117]

[0118] Equation (8) can be used to calculate the probability P that a hole generated at (x,y) produces an infinite number of charge carriers. h (x,y).

[0119]

[0120] Among them, L e (L h ), which is the motion path curve of the electron (hole) generated at (x,y).

[0121] Find the collision ionization probability P at each boundary point in the second grid [x,y]. ie (Electronics), P ih The collision ionization probability matrix composed of (holes) is P. IE (Electronics), P IH (Empty hole).

[0122] Step 7: Set the calculation precision. For each type of collision ionization probability matrix, use the collision ionization probability matrix calculated each time as the input for the next time to calculate the breakdown probability matrix composed of the electron breakdown probabilities of all intersection points of the second grid.

[0123] Step 71: Set the calculation precision;

[0124] Step 72: For each type of collision ionization probability, calculate the electron breakdown probability of a junction point of the second grid using the last calculated collision ionization probability as input data;

[0125] Step 73: Loop step 72 until the electron breakdown probability of all junction points is calculated, forming a collision ionization probability matrix.

[0126] The process of solving the recursive equations (7), (8) through continuous iteration is shown in the calculation flowchart as Figure 2 :

[0127] In the first iteration, the last collision ionization probability calculation result P ie (P ih ) is taken as the initial electron (hole) breakdown probability P e,0 (P h,0 ), P IE , P IH are taken as the initial electron (hole) breakdown probability matrix P E,0 , P H,0

[0128] Since the interval of the second grid [x, y] of the breakdown probability point is d2, all coordinate values in the motion path coordinate matrix A e (A h ) at the junction point (x, y) of the second grid are rounded to the same number of decimal places as d2 to generate a new coordinate matrix A e2 = [A ex2 , A ey2 ] (A h2 = [A hx2 , A hy2 ]). The matrix subscript used when indexing P E (P H ) should be:

[0129]

[0130]

[0131] The electron breakdown probability P e,n at the discretized approximation (x, y) produced by the nth iteration of the recursive equation (7) is:

[0132]

[0133] The hole breakdown probability P h,n at the discretized approximation (x, y) produced by the nth iteration of the recursive equation (8) is:

[0134]

[0135] where P e,n ,P h,n The parameter subscript index of the transformation can be expressed by the following formula:

[0136] P e,n (A ex2 (k),A ey2 (k))=P E,n (i e2 (k),j e2 (k)) P h,n (A ex2 (k),A ey2 (k))=P H,n (i e2 (k),j e2 (k))

[0137] P e,n (A hx2 (k),A hy2 (k))=P E,n (i h2 (k),j h2 (k)) P h,n (A hx2 (k),A hy2 (k))=P H,n (i h2 (k),j h2 (k))

[0138] where, P E,n ,P H,n is the matrix composed of each point P e,n ,P h,n in the grid [x,y] generated in the nth iteration, and the above calculation process is repeated until each point on the [x,y] grid meets the calculation accuracy, and the iteration is stopped

[0139] P e,n+1 (x,y)-P e,n (x,y)≤ε

[0140] P h,n+1 (x,y)-P h,n (x,y)≤ε

[0141] The final generated electron and hole breakdown probability matrix of each point on the second grid [x,y] grid is P E ,P H .

[0142] Step 8: Calculate the total breakdown probability according to the electron breakdown probability matrix and the hole breakdown probability matrix;

[0143] This step can be implemented by the following process:

[0144] Step 81: Calculate the breakdown probability matrix according to each collision ionization probability matrix;

[0145] This step first calculates the breakdown probability matrix P E (x,y) according to the obtained P H (x,y) and P B (x,y) respectively.

[0146] P B (x,y) = P E (x,y) + P H (x,y) - P E (x,y) · P H

[0147] P b (x,y) = P e (x,y) + P h (x,y) - P e (x,y) · P h (x,y) (9)

[0148] Equation (9) represents the total breakdown probability Pb(x,y) of the generated carriers at (x,y).

[0149] Step 82: Calculate the total breakdown probability under the condition of light incidence according to the breakdown probability matrix.

[0150] The breakdown probability matrix is weighted by the optical generation G O (x,y) to obtain the total breakdown probability P b，total (λ) at the incident light wavelength λ by discretizing equation (10).

[0151]

[0152] Where m and n are the number of rows and columns of the [x,y] grid matrix respectively.

[0153]

[0154] Equation (10) can obtain the total breakdown probability P b,total (λ) at the incident light wavelength λ by weighting and integrating each breakdown probability with the photon absorption condition.

[0155] Where f(x,y) is the probability density of photon absorption at each point on the plane, and D is the two-dimensional cross-sectional area of the device.

[0156] Step 9: Calculate the photon detection probability according to the optical simulation data and the total breakdown probability.

[0157] The photon detection probability can be calculated using the following process:

[0158] Step 91: Calculate the quantum efficiency according to the optical simulation data;

[0159] Calculate the incident photon flux N in (λ) and the photo-generated carrier flux N opt (λ) according to the simulation results in 2);

[0160] N in (λ) can be calculated by the following formula:

[0161]

[0162] Where I in (λ) is the incident light intensity, A surf is the simulated SPAD surface area, E ph (λ) is the energy of the photon with wavelength λ; h is the Planck constant, and c is the speed of light.

[0163] N opt (λ) can be calculated by the following formula:

[0164]

[0165] Where L Z is the width of the simulated SPAD in the Z direction, and the integral term is the integral of the light generation rate G opt (unit cm -3 s -1 ) on the surface, which can be obtained by simulation. Substitute the calculated N in (λ) and N opt (λ) into formula (11) to obtain the quantum efficiency η(λ);

[0166]

[0167] Step 92: Multiply the quantum efficiency by the total breakdown probability to obtain the photon detection probability.

[0168] Substitute the quantum efficiency and the total breakdown probability into formula (12) to calculate the photon detection probability PDP:

[0169] PDP(λ) = η(λ) · P b,total (λ) (12)

[0170] The application provides a single-photon avalanche diode photon detection probability modeling and prediction method, which comprises the following steps: obtaining simulation data by performing electrical simulation and optical simulation on the structure of a SPAD; performing gridding on the simulation data to obtain a first grid and a second grid; taking two-dimensional vector data formed by a transverse electric field intensity and a longitudinal electric field intensity as grid data, generating two streamlines on the basis of the first grid in combination with the second grid; converting coordinate values of a path coordinate matrix of each streamline into subscripts of parameters in a grid matrix of the first grid, and using the subscripts to index imported electric fields, electric potentials and ionization rates; taking the first streamline as an electron motion path and the second streamline as a hole motion path, and searching for dead space regions respectively; calculating an electron collision ionization probability matrix and a hole collision ionization probability matrix of all intersection points of the second grid according to collision ionization probability densities of all points on each motion path; setting a calculation precision, taking each calculated collision ionization probability matrix as an input of the next calculation, and calculating a breakdown probability matrix composed of electron breakdown probabilities of all intersection points of the second grid; calculating a total breakdown probability according to the electron breakdown probability matrix and the hole breakdown probability matrix; and calculating a photon detection probability according to optical simulation data and the total breakdown probability. The application considers dead space distances and non-ideal factor edge effects, the input parameters are extracted from TCAD Sentaurus simulation, the calculation is based on actual manufacturing values and device layout, no additional fitting parameters are added, the breakdown probability of each point occurring on a two-dimensional profile is calculated, and the device structure is very intuitive and easy to optimize. Moreover, the application can call a GPU for parallel acceleration calculation in a Matlab platform, and the calculation efficiency is improved.

[0171] The above is a further detailed description of the application in combination with specific preferred embodiments, and the specific implementation of the application should not be limited to the description. For ordinary skilled persons in the technical field to which the application belongs, some simple deductions or replacements can be made without departing from the concept of the application, and all of them should be regarded as falling within the protection scope of the application.

Claims

1. A method for probabilistic modeling and prediction of single-photon avalanche diode photon detection, characterized in that, The application relates to a method for calculating the photon detection probability of a single photon avalanche diode (SPAD) and a device thereof. The method comprises the following steps: Step 1: obtaining the structure, working voltage and incident light wavelength of the SPAD; Step 2: performing electrical simulation on the structure of the SPAD to obtain electrical simulation data and performing optical simulation to obtain optical simulation data; The electrical simulation data comprises potential, electric field intensity, transverse electric field intensity and longitudinal electric field intensity, and the optical simulation data comprises optical generation; Step 3: meshing the electrical simulation data and the optical simulation data to obtain a first mesh and a second mesh; Step 4: taking the two-dimensional vector data formed by the transverse electric field intensity and the longitudinal electric field intensity as mesh data, combining the second mesh on the basis of the first mesh, and generating two streamlines; Any point coordinate on any streamline is taken as a path coordinate matrix; Step 5: converting the coordinate values of the path coordinate matrix of each streamline into the subscripts of the parameters in the mesh matrix of the first mesh, which are used for indexing the imported electric field, potential and ionization rate; Step 6: taking the subscript of the first streamline as an electron motion path and taking the second streamline as a hole motion path, searching for dead space regions respectively, and calculating the electron collision ionization probability matrix and the hole collision ionization probability matrix of all the junction points of the second mesh according to the collision ionization probability density of all the points in the dead space regions and the non-dead space regions on each motion path; Step 7: setting the calculation accuracy, taking each type of collision ionization probability matrix as the input of the next calculation, and calculating the breakdown probability matrix composed of the electron breakdown probabilities of all the junction points of the second mesh; Step 8: calculating the total breakdown probability according to the electron breakdown probability matrix and the hole breakdown probability matrix; 2. The method of claim 1, wherein, Step 9: calculating the photon detection probability according to the optical simulation data and the total breakdown probability. The step 3 comprises the following steps: Step 31: meshing the electrical simulation data and the optical simulation data in Origin to obtain data points uniformly distributed on a plane; Step 32: importing the data points into matlab as a numerical matrix to generate a first mesh corresponding to the data points and a second mesh for calculating the breakdown probability points; 3. The method of claim 1, wherein, The first mesh and the second mesh each correspond to a mesh matrix, and the parameters in the mesh matrix represent the coordinates of the junction points on the mesh. The step 4 comprises the following steps:

4. The method of claim 1, wherein, Taking the junction points on the first mesh as coordinates, taking the preset range of the transverse electric field intensity and the longitudinal electric field intensity as two-dimensional vector data, and taking the junction points on the second mesh as starting points, two streamlines are generated. The step 6 comprises the following steps: Step 61: taking the matrix subscript of the first streamline under the first mesh as an electron motion path, searching from a starting point to a first target point with a first potential that is not less than a first electric potential or taking the matrix subscript of the second streamline under the first mesh as a hole motion path, searching for a second target point with a first potential that is not higher than the first electric potential; The curve between the starting point and the first target point or the second target point is the electron dead space or the hole dead space generated at the coordinates of the junction points on the first mesh. Step 62: calculate the collision ionization probability density of the dead space region and the non-dead space region on the electron motion path and the hole motion path respectively, to obtain the electron collision ionization probability density and the hole collision ionization probability density; Step 63: calculate the electron collision ionization probability matrix according to the electron collision ionization probability density, and calculate the hole collision ionization probability matrix according to the hole collision ionization probability density.

5. The single photon avalanche diode photon detection probability modeling prediction method of claim 1, wherein, The step 7 comprises: Step 71: set the calculation precision; Step 72: for each type of collision ionization probability, take the last calculated collision ionization probability as the input data to calculate the electron breakdown probability of one junction point of the second grid; Step 73: loop step 72 until the electron breakdown probability of all junction points is calculated to form a collision ionization probability matrix.

6. The single photon avalanche diode photon detection probability modeling prediction method of claim 1, wherein, The step 8 comprises: Step 81: calculate the breakdown probability matrix according to each collision ionization probability matrix; Step 82: calculate the total breakdown probability under the light incidence condition according to the breakdown probability matrix.

7. The single photon avalanche diode photon detection probability modeling prediction method of claim 1, wherein, The step 9 comprises: Step 91: calculate the quantum efficiency according to the optical simulation data; Step 92: multiply the quantum efficiency by the total breakdown probability to obtain the photon detection probability.

8. The single photon avalanche diode photon detection probability modeling prediction method of claim 1, wherein, Before step 5, the single-photon avalanche diode photon detection probability modeling and prediction method further comprises: Round off the coordinate values in the path coordinate matrix of each streamline to keep the same number of decimal places as the first grid spacing.

9. The method of claim 7, wherein, The total breakdown probability is represented as: where P B = P E + P H - P E * P H , represents optical generation, P B represents a breakdown probability matrix, and λ represents an incident light wavelength.

10. The method of claim 9, wherein, The photon detection probability is represented as: PDP(λ) = η(λ) · P b,total (λ) Wherein, η(λ) represents the photon detection probability.

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