CN116680875A - Timing jitter modeling method of silicon-based fully-integrated single photon avalanche diode - Google Patents
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Abstract
The invention discloses a timing jitter modeling method of a silicon-based fully integrated single photon avalanche diode, which comprises the following steps: acquiring electrical simulation data of a single photon avalanche diode and optical simulation data of the single photon avalanche diode; acquiring the microscopic ionization rate of electrons, the macroscopic ionization rate of electrons, the microscopic ionization rate of holes, the macroscopic ionization rate of holes and the initial avalanche current front propagation speed; processing by using a preset avalanche build-up time distribution model to obtain avalanche build-up time distribution; processing by using a preset avalanche propagation time distribution model to obtain avalanche propagation time distribution; processing by using a preset drift diffusion time distribution model to obtain the drift diffusion time distribution of the neutral region; and performing discrete convolution operation on the avalanche build-up time distribution, the avalanche propagation time distribution and the neutral region drift diffusion time distribution to obtain the timing jitter of the single photon avalanche diode. The method and the device can improve the timing jitter calculation efficiency of the single photon diode.
Description
Technical Field
The invention belongs to the technical field of microelectronic photoelectric devices, and particularly relates to a timing jitter modeling method of a silicon-based fully-integrated single photon avalanche diode.
Background
The Single Photon Avalanche Diode (SPAD) is an advanced single photon detection device, has the advantages of high sensitivity, high time resolution, high integration level and the like, and is the first choice for time resolution imaging application. In recent years, SPAD prepared by a compatible CMOS process has developed rapidly, and SPAD-based time-dependent single photon counting (TCSPC) optical sensing systems have been widely used in Positron Emission Tomography (PET), fluorescence Lifetime Imaging Microscopy (FLIM) and laser radar (LiDAR).
Timing jitter is an important parameter for evaluating the time response performance of SPAD, traditional analytical band or full-band monte carlo simulation can obtain response time distribution and timing jitter by largely simulating the SPAD avalanche breakdown process, but the calculation of the energy band structure is complex, and the monte carlo simulation is required to simulate the whole avalanche process, so that the model is very time-consuming and wastes calculation resources. The high-level analytical model can be combined with The Computer Aided Design (TCAD) simulation results of semiconductor processes and devices to directly calculate avalanche response time and timing jitter, but the calculation results will ignore statistical jitter caused by random ionization events during the initial establishment of avalanche, so that the calculation results are inaccurate.
Accordingly, there is a need to improve upon the deficiencies in the prior art.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a timing jitter modeling method of a silicon-based fully integrated single photon avalanche diode. The technical problems to be solved by the invention are realized by the following technical scheme:
in a first aspect, the present invention provides a timing jitter modeling method for a silicon-based fully integrated single photon avalanche diode, including:
performing steady-state and transient electrical simulation on a preset first single photon avalanche diode structure model, and acquiring electrical simulation data of the single photon avalanche diode;
carrying out optical simulation on a preset second single photon avalanche diode structure model, and acquiring optical simulation data of the single photon avalanche diode;
according to the electrical simulation data of part of single photon avalanche diode, respectively obtaining electron microscopic ionization rate, electron macroscopic ionization rate, hole microscopic ionization rate, hole macroscopic ionization rate and initial avalanche current front propagation speed;
gridding partial electrical simulation data, electron microscopic ionization rate and hole microscopic ionization rate, and processing by using a preset avalanche build-up time distribution model to obtain avalanche build-up time distribution;
performing gridding treatment on the macroscopic ionization rate of electrons, the macroscopic ionization rate of holes and the initial avalanche current front propagation speed, performing gridding treatment, and performing treatment by using a preset avalanche propagation time distribution model to obtain avalanche propagation time distribution;
performing gridding treatment on part of the electrical simulation data, and combining the optical simulation data, and processing by using a preset drift diffusion time distribution model to obtain the drift diffusion time distribution of the neutral region;
performing discrete convolution operation on the avalanche build-up time distribution, the avalanche propagation time distribution and the neutral region drift diffusion time distribution to obtain avalanche time response distribution;
the full width at half maximum of the avalanche time response distribution is extracted as the timing jitter of the single photon avalanche diode. The invention has the beneficial effects that:
the invention provides a timing jitter modeling method of a silicon-based fully integrated single photon avalanche diode, which comprises the steps of firstly, carrying out steady-state and transient electrical simulation on a preset first single photon avalanche diode structure model to obtain electrical simulation data of the single photon avalanche diode, and carrying out optical simulation on a 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, avalanche build-up time distribution, avalanche propagation time distribution and neutral zone drift diffusion time distribution are respectively obtained, and avalanche time response distribution is further built; finally, according to avalanche time response distribution, acquiring timing jitter of the single photon diode so as to further evaluate the performance of the single photon diode; the method simplifies the Monte Carlo model and the high-level analytical model, comprises the complete process of avalanche breakdown, improves the consistency and accuracy of the calculation result and theory, and can realize the calculation of the high-level model at different input points in parallel through the GPU acceleration platform, thereby improving the calculation efficiency.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
FIG. 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 invention;
FIG. 2 is a schematic diagram of a single photon avalanche diode structure provided in an embodiment of the present invention;
FIG. 3 is a flow chart of avalanche build time distribution model modeling provided by an embodiment of the present invention;
fig. 4 is a flow chart of avalanche propagation time distribution model modeling provided by an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but embodiments of the present invention are not limited thereto.
Aiming at the prior art, the statistical jitter caused by random ionization events during the initial establishment of avalanche is ignored, so that the avalanche response time and the timing jitter are calculated inaccurately; the invention provides a timing jitter modeling method of a silicon-based fully integrated single photon avalanche diode, which combines a simplified Monte Carlo model and a high-level analytic model, and further efficiently and accurately acquires the timing jitter of the single photon avalanche diode by acquiring avalanche setup time distribution, avalanche propagation time distribution and neutral zone drift diffusion time distribution so as to evaluate the performance of the single photon avalanche diode.
Referring to fig. 1, fig. 1 is a flowchart of a timing jitter modeling method of a silicon-based fully integrated single photon avalanche diode according to an embodiment of the present invention, where the timing jitter modeling method of the silicon-based fully integrated single photon avalanche diode includes:
s101, conducting steady-state and transient-state electrical simulation on a preset first single-photon avalanche diode structure model, and acquiring electrical simulation data of the single-photon avalanche diode.
Specifically, referring to fig. 2, fig. 2 is a schematic diagram of a single photon avalanche diode structure provided in an embodiment of the present invention, in this embodiment, first, a first single photon avalanche diode structure model is constructed; secondly, carrying out steady-state and transient-state electrical simulation on a preset first single photon avalanche diode structure model, and acquiring electrical simulation data of the single photon avalanche diode; wherein, under different diode reverse bias voltages, the electrical simulation data of the single photon avalanche diode comprises the intensity E (Z) of an electric field on a Z-direction section line and the saturated electron velocity v on the Z-direction section line esta (Z), velocity v of saturated hole on Z-direction section hsta (Z), X-Y section avalanche breakdown initial electric field intensity E at Z-direction multiplication main junction depth b (X, y), electric field strength E (X, y) after partial avalanche breakdown, current density J (X, y) after partial avalanche breakdown, electric field strength E in X direction of electrons in active region profile of device before avalanche breakdown x (x, Z), electron field strength E in Z direction of active region section of device before avalanche breakdown z (x, z), electron electric field intensity E (x, z) of the active region profile of the device before avalanche breakdown, electron movement velocity v of the active region profile of the device before avalanche breakdown e (x, z), hole movement velocity v of active region profile of device before avalanche breakdown h (x, z), breakdown probability P of P-type neutral region ne And breakdown probability P of n-type neutral region nh 。
In the embodiment shown in fig. 2, the XY section is shown as C1, the XZ section is shown as C2, and the Z-direction cross-section is shown as C3, and the embodiment shown in fig. 2 only schematically shows one structural schematic of the single photon avalanche diode, and does not represent the size thereof.
S102, carrying out optical simulation on a preset second single photon avalanche diode structure model, and acquiring optical simulation data of the single photon avalanche diode.
Specifically, in this embodiment, first, a second single photon avalanche diode structure model is constructed; secondly, carrying out optical simulation on a preset second single photon avalanche diode, and acquiring optical simulation data of the single photon avalanche diode; wherein the optical simulation data of the single photon avalanche diode comprises the absorptivity R of the p-type neutral region ne And an absorption rate R of an n-type neutral region nh The method comprises the steps of carrying out a first treatment on the surface of the It should be noted that the absorption rate of the heavily doped region may be ignored in the case of abrupt junctions.
S103, respectively acquiring the microscopic ionization rate of electrons, the macroscopic ionization rate of electrons, the microscopic ionization rate of holes, the macroscopic ionization rate of holes and the initial avalanche current front propagation speed according to the electrical simulation data of part of the single photon avalanche diode.
Specifically, in this embodiment, considering that carriers undergo an ionization threshold to trigger the impact ionization process, the microscopic ionization rate α of electrons is obtained by using the Okuto coefficient * The expression of (2) is:
wherein E is ie Electron ionization threshold energy, E r Is optical phonon energy, lambda r Is the average free path of optical phonons, q is the electron charge quantity, E is the electric field strength, exp {. Cndot. } is an exponential function;
obtaining microscopic ionization Rate of holes * The expression of (2) is:
wherein E is ih Is the hole ionization threshold energy.
The collision ionization process can be triggered without considering that the carriers undergo an ionization threshold, and the expression of acquiring the macroscopic ionization rate alpha of electrons by relying on a local electric field and generally using a Deman empirical coefficient is as follows:
α＝a e exp(-b e /E)；
wherein a is e And b e Are all experience coefficients;
the expression for obtaining the macroscopic ionization rate beta of the cavity is as follows:
β＝a h exp(-b h /E)；
wherein a is h And b h Are all empirical coefficients.
It should be noted that for silicon material, a e ＝7.03×10 5 cm -1 ；
b e ＝1.231×10 6 V cm -1 (1.75×10 5 E6.0×10 5 V cm -1 )；
a h ＝1.582×10 6 cm -1 ；
b h ＝2.036×10 6 V cm -1 (1.75×10 5 E4.0×10 5 V cm -1 )；
a h ＝6.71×10 5 cm -1 ；
b h ＝1.693×10 6 V cm -1 (4.0×10 5 E6.0×10 5 V cm -1 )。
Obtaining initial avalanche current front propagation velocity v s0 The expression of (2) is:
wherein D is the diffusion coefficient, τ 0 Is the initial avalanche time constant.
Note that τ 0 The calculation is divided into two types, one is fit parameter calculation, and the calculation formula is as follows:
wherein g is a fitting parameter, τ i Is an intrinsic time constantThe calculation formula is as follows:
wherein w is the depletion region width, v n Is the electron saturation velocity, v p Is the hole saturation velocity.
The other is no fitting parameter calculation, and the calculation formula is as follows:
in the embodiment, fitting parameter-free calculation can be realized, input parameters can be extracted and calculated through TCAD and FDTD simulation, and the predictability of timing jitter of a given device is improved.
S104, carrying out gridding treatment on part of electrical simulation data, the electron microscopic ionization rate and the hole microscopic ionization rate, and then using a preset avalanche build-up time distribution model to carry out treatment so as to obtain avalanche build-up time distribution.
Specifically, referring to fig. 3, fig. 3 is a flowchart of modeling an avalanche build-up time distribution model according to an embodiment of the present invention, in this embodiment, since an avalanche build-up time calculates a process of increasing an avalanche initial current to 1 μa, and the process current does not propagate in a large area, a 1-dimensional random path method (1D-RPL) is used as a simplified monte carlo method for modeling, and the avalanche build-up time distribution model processing procedure specifically includes:
s1041, microscopic ionization Rate of electrons alpha * Microscopic ionization Rate of hole beta * Saturated electron velocity v on Z-direction section esta (Z), velocity v of saturated hole on Z-direction section hsta (z), a first preset current threshold I b Inputting a preset avalanche to establish a time distribution model by a time step dt;
s1042 initializing parameters including setting initial carrier position z 0 [1]Random number r 1]=u (0, 1) and forward path length l 0 [1]＝0；
S1043, updating parameter avalanche build-up time t b Initializing the newly added carrier quantity n a ＝0；
S1044, for each current carrier, updating the advancing path length l and the position z, and judging whether the carrier reaches the depletion region boundary; wherein, the expression of updating the carrier advancing path length l is:
l＝l 0 +v sta ·dt；
wherein for electron v sta ＝v esta For cavity v sta ＝-v hsta ；
The expression for updating the carrier position z is:
z＝z 0 +l；
s1045, removing the carrier if the carrier reaches the depletion region boundary, and updating the carrier quantity;
s1046, if the carrier does not reach the depletion region boundary, judging whether collision ionization occurs to the carrier, wherein the probability S that the carrier does not undergo collision ionization at the position z is:
wherein h (z) is a collision ionization probability density function, z 0 [i]The initial position of the ith carrier, i is the ith carrier;
the electron impact ionization probability density function h e The expression of (z) is:
wherein d e Is the length of the electron dead space;
for holes, impact ionization probability density function h h The expression of (z) is:
s1047, judging whether the probability S of the carrier in the position z without collision ionization is smaller than or equal to a random number, namely, S is smaller than or equal to r; if so, the carriers add new electron hole pairs at the position z, and the newly added carrier quantity n is updated a Reset random number r and initial carrier position z 0 ；
S1048, judging whether the current I reaches a first preset current threshold I b If so, outputting avalanche build-up time t b The method comprises the steps of carrying out a first treatment on the surface of the If not, updating the avalanche build-up time t b Until the current I reaches the preset current threshold I b The method comprises the steps of carrying out a first treatment on the surface of the The expression for acquiring the current I is as follows:
I＝n·I q ；
wherein I is q The current contributed to a single carrier, v is the average carrier velocity, w is the depletion region width, n is the total number of carriers, and q is the electron charge amount;
s1049 repeating at least 10 3 Sub-calculation of avalanche build-up time t b Statistical to obtain avalanche build-up time distribution P b (t)。
In this embodiment, the simplified monte carlo model is used to calculate only the process of increasing the initial avalanche current to 1 μa, so that the calculation time and calculation resources are saved compared with the calculation of the complete avalanche process.
S105, carrying out gridding treatment on the macroscopic ionization rate of electrons, the macroscopic ionization rate of holes and the initial avalanche current front propagation speed, and then carrying out treatment by using a preset avalanche propagation time distribution model to obtain avalanche propagation time distribution.
Specifically, referring to fig. 4, fig. 4 is a flowchart of modeling an avalanche propagation time distribution model according to an embodiment of the present invention, where the above process specifically includes:
s1051, macroscopic ionization rate alpha of electrons, macroscopic ionization rate beta of holes, initial avalanche current front propagation velocity v s0 The grid spacing on the XY section is d 1 External voltage V r An external resistor R and a second preset current threshold I th Inputting the preset avalanche propagation time distribution model;
s1052, setting the initial avalanche propagation speed equal to the initial avalanche current front propagation speed, i.e. v s ＝v s0 And setting a second cycle parameter m=1, propagation time t=0, bias voltage v=v on the single photon avalanche diode r ；
S1053, calculate the propagation time t respectively s A propagation circle radius r and a total current I (m); wherein the propagation time t is obtained s The expression of (2) is:
t s ＝t s +d 1 /v s ；
the expression for obtaining the radius r of the propagation ring is:
r＝md 1 ；
the expression for obtaining the total current I (m) is:
wherein D (m) is a propagation circle region with a center of (x, y) and a radius r=md 1 ；
S1054, judging whether the total current I (m) reaches a second preset current threshold value I th If so, then the propagation time t is output s The method comprises the steps of carrying out a first treatment on the surface of the If not, the bias voltage V and avalanche propagation speed V on the single photon avalanche diode are updated s And a second cycle parameter m, wherein the bias voltage V on the single photon avalanche diode is determined by a specific external circuit according to the electric field E under the bias voltage V on the diode b E, updating the current tau until the total current reaches a second preset current threshold;
s1055 calculating avalanche propagation time t for each point on XY section s After statistics, avalanche propagation time distribution P is obtained s (t)。
And S106, performing gridding treatment on part of the electrical simulation data, and combining the optical simulation data, and processing by using a preset drift diffusion time distribution model to obtain the drift diffusion time distribution of the neutral region.
Specifically, in this embodiment, the above-mentioned process specifically includes:
s1061, using an electric field intensity vector as field distribution, generating a streamline corresponding to a point (x, z), and using the streamline as a motion path of carriers at the point; wherein, the distribution value of the P-type neutral area field is-E x and-E z The n-type neutral area field distribution takes on E x And E is z The method comprises the steps of carrying out a first treatment on the surface of the It should be noted that, the streamline generation can be realized through MATLAB streamline function;
s1062, processing the positions of each point in the streamline to obtain a coordinate matrix [ x ] l ，z l ]The number of coordinates is g;
s1063 according to the coordinate matrix [ x ] l ，z l ]Obtaining drift diffusion time t corresponding to a current path d The expression is:
wherein v (x l ,z l ) Electron movement velocity v of active region profile of device before avalanche breakdown corresponding to p-type neutral region e (x,z)，v(x l ,z l ) Hole movement velocity v of active region profile of device before avalanche breakdown corresponding to n-type neutral region h (x, z), k is the cycle parameter in the summation process;
s1064 calculating drift diffusion time t for each point on XZ section neutral zone d And absorb the absorption rate R in each neutral zone ne 、R nh And breakdown probability P ne 、P nh Weighting and counting to obtain neutral zone drift diffusion time distribution P d (t)。
In the gridding process, the grid pitch on the XY section is d 1 Grid spacing on XZ section is d 2 。
S107, performing discrete convolution operation on the avalanche build-up time distribution, the avalanche propagation time distribution and the neutral region drift diffusion time distribution to obtain avalanche time response distribution.
S108, extracting the full width at half maximum of the avalanche time response distribution as the timing jitter of the single photon avalanche diode.
In summary, according to the timing jitter modeling method of the silicon-based fully integrated single photon avalanche diode provided by the invention, firstly, steady state and transient state electrical simulation is performed on a preset first single photon avalanche diode structure model to obtain electrical simulation data of the single photon avalanche diode, and optical simulation is performed on a 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, avalanche build-up time distribution, avalanche propagation time distribution and neutral zone drift diffusion time distribution are respectively obtained, and avalanche time response distribution is further built; finally, according to avalanche time response distribution, acquiring timing jitter of the single photon diode so as to further evaluate the performance of the single photon diode; the method simplifies the Monte Carlo model and the high-level analytical model, comprises the complete process of avalanche breakdown, improves the consistency and accuracy of the calculation result and theory, and can realize the calculation of the high-level model at different input points in parallel through the GPU acceleration platform, thereby improving the calculation efficiency.
It should be noted that in this document relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in an article or apparatus that comprises the element. The terms "connected" or "connected," and the like, are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The orientation or positional relationship indicated by "upper", "lower", "left", "right", etc. is based on the orientation or positional relationship shown in the drawings, and is merely for convenience of description and to simplify the description, and is not indicative or implying that the apparatus or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Further, one skilled in the art can engage and combine the different embodiments or examples described in this specification.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (10)
1. The timing jitter modeling method of the silicon-based fully-integrated single photon avalanche diode is characterized by comprising the following steps of:
performing steady-state and transient electrical simulation on a preset first single photon avalanche diode structure model, and acquiring electrical simulation data of the single photon avalanche diode;
carrying out optical simulation on a preset second single photon avalanche diode structure model, and acquiring optical simulation data of the single photon avalanche diode;
according to the electrical simulation data of part of the single photon avalanche diode, respectively acquiring the microscopic ionization rate of electrons, the macroscopic ionization rate of electrons, the microscopic ionization rate of holes, the macroscopic ionization rate of holes and the initial avalanche current front propagation speed;
performing gridding treatment on part of the electrical simulation data, the electron microscopic ionization rate and the hole microscopic ionization rate, and then using a preset avalanche build-up time distribution model to perform treatment so as to obtain avalanche build-up time distribution;
performing gridding treatment on the macroscopic ionization rate of the electrons, the macroscopic ionization rate of the holes and the initial avalanche current front propagation speed, performing gridding treatment, and then performing treatment by using a preset avalanche propagation time distribution model to obtain avalanche propagation time distribution;
performing gridding treatment on part of the electrical simulation data, and combining the optical simulation data, and processing by using a preset drift diffusion time distribution model to obtain the drift diffusion time distribution of a neutral region;
performing discrete convolution operation on the avalanche build-up time distribution, the avalanche propagation time distribution and the neutral region drift diffusion time distribution to obtain avalanche time response distribution;
and extracting the full width at half maximum of the avalanche time response distribution as the timing jitter of the single photon avalanche diode.
2. The method for modeling timing jitter of a fully integrated single photon avalanche diode in accordance with claim 1, wherein said electrical simulation data of said single photon avalanche diode includes an intensity of an electric field E (Z) on a Z-direction cross-section, a saturated electron velocity v on a Z-direction cross-section esta (Z), velocity v of saturated hole on Z-direction section hsta (Z), X-Y section avalanche breakdown initial electric field intensity E at Z-direction multiplication main junction depth b (X, y), electric field strength E (X, y) after partial avalanche breakdown, current density J (X, y) after partial avalanche breakdown, electric field strength E in X direction of electrons in active region profile of device before avalanche breakdown x (x, z), avalanche breakdownElectron field strength E in Z direction of front device active region section z (x, z), electron electric field intensity E (x, z) of the active region profile of the device before avalanche breakdown, electron movement velocity v of the active region profile of the device before avalanche breakdown e (x, z), hole movement velocity v of active region profile of device before avalanche breakdown h (x, z), breakdown probability P of P-type neutral region ne And breakdown probability P of n-type neutral region nh 。
3. The method of modeling timing jitter of a fully integrated single photon avalanche diode in silicon based form of claim 1, wherein optical simulation data of said single photon avalanche diode includes an absorptivity R of a p-type neutral region ne And an absorption rate R of an n-type neutral region nh 。
4. The method for modeling timing jitter of a fully integrated single photon avalanche diode in silicon based according to claim 1, wherein a microscopic ionization rate α of said electrons is obtained * The expression of (2) is:
wherein E is ie Electron ionization threshold energy, E r Is optical phonon energy, lambda r Is the average free path of optical phonons, q is the electron charge quantity, E is the electric field strength, exp {. Cndot. } is an exponential function;
obtaining the microscopic ionization rate beta of the cavity * The expression of (2) is:
wherein E is ih Is the hole ionization threshold energy.
5. The method for modeling timing jitter of a fully integrated single photon avalanche diode in silicon-based according to claim 1, wherein the expression for obtaining the macroscopic ionization rate α of the electrons is:
α＝a e exp(-b e /E)；
wherein a is e And b e Are all experience coefficients;
the expression for obtaining the macroscopic ionization rate beta of the cavity is as follows:
β＝a h exp(-b h /E)；
wherein a is h And b h Are all empirical coefficients.
6. The method for modeling timing jitter of a fully integrated single photon avalanche diode in silicon based according to claim 1, wherein the initial avalanche current front propagation velocity v is obtained s0 The expression of (2) is:
wherein D is the diffusion coefficient, τ 0 Is the initial avalanche time constant.
7. The method for modeling timing jitter of silicon-based fully integrated single photon avalanche diode according to claim 1, wherein in gridding process, a grid pitch on XY section is d 1 Grid spacing on XZ section is d 2 。
8. The method for modeling timing jitter of a fully integrated single photon avalanche diode in accordance with claim 1, wherein said step of meshing a portion of said electrical simulation data and said electron microscopic ionization rate, and further processing using a predetermined avalanche build-up time distribution model to obtain an avalanche build-up time distribution comprises:
microscopic ionization Rate α of the electrons * Microscopic ionization Rate beta of the cavity * Saturated electron velocity v on Z-direction section esta (Z), velocity v of saturated hole on Z-direction section hsta (z), a first preset currentThreshold I b Inputting the time step dt into the preset avalanche to establish a time distribution model;
initializing parameters, including setting initial carrier positions z 0 [1]Random number r 1]=u (0, 1) and forward path length l 0 [1]＝0；
Update parameter avalanche build-up time t b Initializing the newly added carrier quantity n a ＝0；
For each current carrier, updating the advancing path length l and the position z, and judging whether the carrier reaches the depletion region boundary or not; wherein, the expression of updating the carrier advancing path length l is:
l＝l 0 +v sta ·dt；
wherein for electron v sta ＝v esta For cavity v sta ＝-v hsta ；
The expression for updating the carrier position z is:
z＝z 0 +l；
removing the carrier if the carrier reaches the depletion region boundary, and updating the carrier quantity;
if the carrier does not reach the depletion region boundary, judging whether collision ionization occurs to the carrier, wherein the probability s that the carrier does not undergo collision ionization at the position z is as follows:
wherein h (z) is a collision ionization probability density function, z 0 [i]The initial position of the ith carrier, i is the ith carrier;
judging whether the probability s of the carrier in the position z without collision ionization is smaller than or equal to a random number, namely, s is smaller than or equal to r; if so, the carriers add new electron hole pairs at the position z, and the newly added carrier quantity n is updated a Reset random number r and initial carrier position z 0 ；
Judging whether the current I reaches a first preset current threshold I b If it reachesThen output avalanche build-up time t b The method comprises the steps of carrying out a first treatment on the surface of the If not, updating the avalanche build-up time t b Until the current I reaches the preset current threshold I b The method comprises the steps of carrying out a first treatment on the surface of the The expression for acquiring the current I is as follows:
I＝n·I q ；
wherein I is q The current contributed to a single carrier, v is the average carrier velocity, w is the depletion region width, n is the total number of carriers, and q is the electron charge amount;
repeating at least 10 3 Sub-calculation of avalanche build-up time t b Statistical to obtain avalanche build-up time distribution P b (t)。
9. The method for modeling timing jitter of a fully integrated single photon avalanche diode in accordance with claim 1, wherein said step of gridding said electron's macroscopic ionization rate and said initial avalanche current front propagation speed, and then using a predetermined avalanche propagation time distribution model to obtain an avalanche propagation time distribution comprises:
the macroscopic ionization rate alpha of the electron, the macroscopic ionization rate beta of the hole and the initial avalanche current front propagation velocity v s0 The grid spacing on the XY section is d 1 External voltage V r An external resistor 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 a second cycle parameter m=1, propagation time t=0, bias voltage v=v on the single photon avalanche diode r ；
Respectively calculate the propagation time t s A propagation circle radius r and a total current I (m); wherein the propagation time t is obtained s The expression of (2) is:
t s ＝t s +d 1 /v s ；
the expression for obtaining the radius r of the propagation ring is:
r＝md 1 ；
the expression for obtaining the total current I (m) is:
wherein D (m) is a propagation circle region with a center of (x, y) and a radius r=md 1 ；
Judging whether the total current I (m) reaches a second preset current threshold value I th If so, then the propagation time t is output s The method comprises the steps of carrying out a first treatment on the surface of the If not, the bias voltage V and avalanche propagation speed V on the single photon avalanche diode are updated s And a second cycle parameter m until the total current reaches a second preset current threshold;
calculation of avalanche propagation time t for each point on XY section s After statistics, avalanche propagation time distribution P is obtained s (t)。
10. The method for modeling timing jitter of a fully integrated single photon avalanche diode in accordance with claim 1, wherein said step of meshing a portion of said electrical simulation data, in combination with said optical simulation data, using a predetermined drift diffusion time distribution model to obtain a neutral zone drift diffusion time distribution comprises:
generating a streamline corresponding to a point (x, z) by taking the electric field intensity vector as field distribution, and taking the streamline as a motion path of carriers at the point; wherein, the distribution value of the P-type neutral area field is-E x and-E z The n-type neutral area field distribution takes on E x And E is z ；
Processing the positions of each point in the streamline to obtain a coordinate matrix [ x ] l ，z l ]The number of coordinates is g;
according to a coordinate matrix [ x l ，z l ]Acquisition ofDrift diffusion time t corresponding to current path d The expression is:
wherein v (x l ,z l ) Electron movement velocity v of active region profile of device before avalanche breakdown corresponding to p-type neutral region e (x,z)，v(x l ,z l ) Hole movement velocity v of active region profile of device before avalanche breakdown corresponding to n-type neutral region h (x, z), k is the cycle parameter in the summation process;
calculating the drift diffusion time t for each point on the XZ section neutral zone d And absorb the absorption rate R in each neutral zone ne 、R nh And breakdown probability P ne 、P nh Weighting and counting to obtain neutral zone drift diffusion time distribution P d (t)。
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| CN117669030A (en) * | 2023-11-30 | 2024-03-08 | 北京航空航天大学 | Radio frequency radar signal HERF safety distance design method based on electron avalanche time |
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| CN117669030A (en) * | 2023-11-30 | 2024-03-08 | 北京航空航天大学 | Radio frequency radar signal HERF safety distance design method based on electron avalanche time |
| CN117669030B (en) * | 2023-11-30 | 2024-07-23 | 北京航空航天大学 | Radio frequency radar signal HERF safety distance design method based on electron avalanche time |
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