Method and device for simulating carrier capture dynamics in irradiated semiconductors

Abstract

The present invention discloses a method and device for simulating the dynamics of carrier capture in an irradiated semiconductor, the method comprising: obtaining a defect reaction event and a parameter list in the semiconductor required for annealing; based on the defect reaction event and the parameter list, calculating the spatial distribution of cascade defects after annealing; based on the spatial distribution of cascade defects after annealing, obtaining the radius of the effective cascade where the defect to be simulated is located and the average concentration of defects in the cascade; using the radius and average concentration of the defect to be simulated, as well as the parameter list as input, solving the improved rate equation based on the SRH theory, and obtaining the dynamic behavior of defect-captured carriers. The present invention considers the influence of spatial non-uniformity of cascade defects and complex cascade local potential on carrier capture, adopts a more realistic defect distribution, strictly solves the cascade local potential, and tries to be independent of or less dependent on adjustable parameters, and accurately simulates the dynamic behavior of deep energy level defects capturing electrons / holes.

Description

Technical Field

[0001] The invention relates to the field of semiconductor technology, and in particular to a method and a device for simulating carrier capture dynamics in an irradiated semiconductor. Background Art

[0002] Semiconductor devices serving in space or nuclear energy environments are often exposed to high-energy neutron irradiation, which causes the lattice atoms of semiconductor materials to be dislocated, resulting in a series of irregular and varying collision cascades. The dislocated defects in the cascade (especially deep energy level defects) will capture electrons / holes (carriers), enhance the recombination of electrons and holes, and cause the performance of semiconductor devices to degrade or even permanently fail. In addition, when the defects in the cascade capture carriers, they will form a local potential barrier near the cascade, thereby preventing the defects from further capturing carriers, which will further change the electrical properties of the semiconductor. Therefore, it is very important to study the kinetic behavior of carrier capture and explore its capture process and mechanism.

[0003] However, neutron reactors are currently in short supply, and neutron irradiation experiments are also relatively risky. More importantly, current experimental methods make it difficult to directly observe the capture process of defects on carriers, let alone reveal the capture mechanism, so theoretical simulation methods have emerged. Among them, atomic-scale methods, especially time-dependent density functional theory (TDDFT), can very accurately simulate the capture behavior of defects on carriers, but this method has low computational efficiency, covers a small spatial scale, and a short time scale. Therefore, the mesoscopic-scale rate equation based on the Shockey-Read-Hall (SRH) theory is currently commonly used to describe the capture dynamics of carriers. This method requires first determining the initial concentrations of defects and carriers, but defect cascades have strong spatial localization, the cascade sizes vary, and the defect distribution within the cascade is very uneven, which makes it difficult to solve the local potential formed by carrier capture.

[0004] In the relevant literature, either the spatial non-uniformity of cascade defects and the influence of local potential on carriers are not considered, or they are based on the spatial distribution of initial irradiation defects and rely on too many empirical parameters, which lacks certain authenticity.

[0005] In the related art, the invention patent application with publication number CN 110459269 A discloses a multi-scale coupling simulation method for irradiation damage of nuclear reactor materials. This method uses MD to simulate the cascade collision process, and the simulation results are used as the input of KMC. KMC is used to simulate the annealing process of cascade defects, and the simulation results are used as the input of CD. CD is used to simulate the long-term evolution of irradiation defects, which can achieve large-scale spatiotemporal simulation from defect generation to microstructure characterization. This method simulates the dynamic behavior of defects in metal core materials, rather than the dynamic behavior of defects in semiconductor materials. Due to the interaction between defects and carriers, defects in semiconductors will carry charges, making semiconductor defect simulation more difficult than metals.

[0006] The invention patent with publication number CN 106528493 B discloses a numerical simulation method for effectively separating deep energy level transient spectrum test signals. For each temperature point T i , using the global initial value as the initial guess value, solve for the reverse bias voltage V r The steady-state compound semiconductor partial differential equations are obtained at a temperature of T i , and solve for the reverse bias voltage V r The node values ​​of the physical variables to be solved, the semiconductor basic differential equations include: Poisson equation reflecting electrostatic potential, continuity equation reflecting carrier quasi-Fermi potential distribution and energy flow equation reflecting carrier ensemble temperature, all of which are second-order partial differential elliptic equations; discrete methods include: finite volume method, finite difference method and finite element method, and the solution of nonlinear equations adopts global Newton-Raphson method for iteration. This method is to separate the coupled deep energy level defects in deep energy level transient spectrum through deep energy level transient spectrum experiment combined with theoretical calculation, rather than the capture of carriers by defects in defect annealing and cascade.

[0007] Therefore, how to design a large-scale and efficient method for simulating carrier capture dynamics in irradiated semiconductors that takes into account more realistic defect distribution and local potential is an urgent problem to be solved. Summary of the invention

[0008] The technical problem to be solved by the present invention is to propose a large-scale and efficient method and device for simulating carrier capture dynamics in irradiated semiconductors that takes into account more realistic defect distribution and local potential.

[0009] The present invention solves the above technical problems through the following technical means:

[0010] In one aspect, the present invention provides a method for simulating carrier capture dynamics in an irradiated semiconductor, the method comprising:

[0011] Obtain a list of defect reaction events and parameters in the semiconductor required for annealing;

[0012] Based on the defect reaction event and the parameter list, calculating the spatial distribution of cascade defects after annealing;

[0013] Based on the spatial distribution of the cascade defects after annealing, obtaining the radius of the effective cascade where the defect to be simulated is located and the average concentration of defects in the cascade;

[0014] The radius of the effective cascade where the defect to be simulated is located, the average defect concentration in the cascade, and the parameter list are used as input to solve the improved rate equation based on the SRH theory to obtain the kinetic behavior of defect-captured carriers.

[0015] The present invention uses the spatial distribution of cascade defects after annealing to calculate the radius of the effective cascade where the defect to be simulated is located and the average defect concentration in the cascade, and adopts the improved rate equation based on SRH theory to obtain the kinetic behavior of defect-captured carriers; considering the influence of spatial non-uniformity of cascade defects and complex cascade local potential on carrier capture, a more realistic defect distribution is adopted, and based on reasonable assumptions, the cascade local potential is strictly solved, and it is as independent of or less dependent on adjustable parameters as possible, so as to accurately simulate the kinetic behavior of deep energy level defects capturing electrons / holes.

[0016] Furthermore, the step of obtaining a list of defect reaction events and parameters in the semiconductor required for annealing includes:

[0017] With reference to the theoretical calculation and experimental measurement results of DFT and molecular dynamics methods, the defect reaction events and the parameter list in the semiconductor required for annealing are obtained, wherein the defect reaction events include all defect types in the semiconductor and reaction paths between defects, and the parameter list includes semiconductor material parameters and semiconductor defect parameters.

[0018] Furthermore, the calculating of the spatial distribution of cascade defects after annealing based on the defect reaction event and the parameter list includes:

[0019] Taking the primary dislocated atomic energy spectrum caused by neutrons as input conditions and the parameter list as input parameters, a Monte Carlo method based on two-body collision approximation is used to calculate the spatial distribution of initial cascade defects;

[0020] The initial cascade defect spatial distribution is used as an initial condition, the defect reaction event and the parameter list are used as input, and the solid dynamics Monte Carlo method is used to calculate the cascade defect spatial distribution after annealing.

[0021] Furthermore, based on the spatial distribution of the cascade defects after annealing, obtaining the radius of the effective cascade where the defect to be simulated is located and the average concentration of defects in the cascade includes:

[0022] Using the spatial distribution of the cascade defects after annealing, a radial distribution of defects to be simulated in a specific semiconductor under neutron irradiation is obtained;

[0023] The radial distribution of the defect is fitted using an exponential function, and the exponential function is:

[0024] N(r)=N0exp(-r / λ)

[0025] Among them, N0 and λ are the defect number present factor and attenuation length respectively;

[0026] Approximating the exponential function and the set truncation by using a step function, obtaining the radius of the effective cascade where the defect to be simulated is located and the average number of defects in the cascade;

[0027] The effective cascade is regarded as a sphere, the volume of the effective cascade is calculated using a sphere volume calculation formula, and the average defect concentration in the cascade is obtained by dividing the average number of defects in the cascade by the volume of the effective cascade.

[0028] Furthermore, the improved rate equation based on SRH theory is:

[0029]

[0030] in, is the thermal motion rate of electrons / holes, X j is a defect X with charge j, is a defect X that carries a charge j-1 or j+1 by capturing electrons / holes, is the charged defect X in the cascade j Cross section for capturing electrons / holes, N CV is the conduction band / valence band effective state density, Charged defect The activation energy of emitting electrons / holes to the bottom of the conduction band / top of the valence band, For the charged defects at different times The concentration of is the average electron / hole density in the effective cascade at time t, Defect X is charged at different times j The concentration, k B is the Boltzmann constant and T is the temperature.

[0031] Furthermore, the radius of the effective cascade where the defect to be simulated is located, the average defect concentration in the cascade, and the parameter list are used as input to solve the improved rate equation based on the SRH theory to obtain the kinetic behavior of defect-captured carriers, including:

[0032] a), taking the radius of the effective cascade where the defect to be simulated is located, the average concentration of defects in the cascade, and the parameter list as inputs of the improved rate equation based on SRH theory;

[0033] b) Using the bisection method to iteratively solve the average electron / hole density in the effective cascade at time t Obtaining an average electron density in the effective cascade of the defect to be simulated, for solving the improved rate equation based on the SRH theory;

[0034] c) using the open source differential equation solver lsoda to iteratively solve the improved rate equation based on SRH theory to obtain the concentration of charged defects at the next moment;

[0035] Repeat steps b) to c) until the improved rate equation based on the SRH theory reaches equilibrium, the concentration of charged defects and their corresponding electron density remain unchanged, the self-consistent solution is completed, and the electrostatic potential barrier, the carrier density in the cascade, and the defect charge state transition ratio at any time are obtained.

[0036] Furthermore, the average electron / hole density in the effective cascade at time t is The calculation formula is as follows:

[0037]

[0038] in, is the electron / hole density before irradiation, E peb (t) is the potential energy barrier of electrons / holes when the defects in the cascade capture carriers at time t, which can be expressed as:

[0039]

[0040] Where q is the unit charge, and are the average potential in the effective cascade at time t and the potential at infinity, respectively.

[0041] Furthermore, the steps of calculating the average potential in the effective cascade at time t and the potential at infinity include:

[0042] Constructing an effective polarization region model, in which when the defect captures carriers, polarization occurs near the cascade to form two spherically symmetrical regions with opposite charges, one spherically symmetrical region is the effective cascade region where the deep energy level defect is located, and the other spherically symmetrical region is the carrier depletion region surrounding the effective cascade region;

[0043] Based on the effective polarization region model, taking infinity as the potential energy zero point, the Poisson equation is solved to obtain the average potential in the effective cascade at time t and the potential at infinity.

[0044] Furthermore, the formula of the effective polarization area model is expressed as follows:

[0045]

[0046] Among them, ε is the semiconductor dielectric constant; r0 is the effective radius of the effective cascade where the defect is located; Q1 is the concentration of net charge in the depletion layer surrounding the effective cascade region, which is approximated as the semiconductor donor / acceptor concentration; Q0(t) is the concentration of net charge in the effective cascade region at time t; r1(t) is the radius of the entire spherical region including the effective cascade region and the depletion region at time t.

[0047] In addition, the present invention also proposes a device for simulating carrier capture dynamics in an irradiated semiconductor, the device comprising:

[0048] An acquisition module, used for acquiring a list of defect reaction events and parameters in a semiconductor required for annealing;

[0049] A defect space calculation module, used to calculate the cascade defect space distribution after annealing based on the defect reaction event and the parameter list;

[0050] A defect characteristic calculation module, used to obtain the radius of the effective cascade where the defect to be simulated is located and the average defect concentration in the cascade based on the spatial distribution of the cascade defects after annealing;

[0051] The kinetic simulation module is used to solve the improved rate equation based on SRH theory by taking the radius of the effective cascade where the defect to be simulated is located, the average defect concentration in the cascade, and the parameter list as input to obtain the kinetic behavior of defect-captured carriers.

[0052] The advantages of the present invention are:

[0053] (1) The present invention uses a more realistic spatial distribution of cascade defects after annealing to calculate the radius of the effective cascade where the defect to be simulated is located and the average defect concentration in the cascade, and uses an improved rate equation based on SRH theory to obtain the kinetic behavior of defect-captured carriers; considering the influence of the spatial non-uniformity of cascade defects and the complex cascade local potential on carrier capture, a more realistic defect distribution is used, based on reasonable assumptions, the cascade local potential is strictly solved, and it is as independent of or less dependent on adjustable parameters as possible, so as to accurately simulate the kinetic behavior of deep energy level defects capturing electrons / holes.

[0054] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flow chart of a method for simulating carrier capture dynamics in an irradiated semiconductor according to the present invention;

[0056] Figure 2 is a spatial distribution diagram of the initial cascade defects of neutron-irradiated silicon of the present invention;

[0057] Figure 3 is a spatial distribution diagram of cascade defects obtained after annealing by the OKMC method of the present invention;

[0058] Figure 4 The radial distribution and effective radius of divacancy (V2) and vacancy-oxygen pair (VO) defects obtained by cascading 5000 annealings in the present invention;

[0059] Figure 5 It is a radial distribution diagram of charge density and electrostatic potential when V2 and VO of the present invention capture electrons;

[0060] Figure 6 It is a graph showing the change of potential energy barrier and electron density over time when V2 and VO capture electrons in the present invention;

[0061] Figure 7 It is a graph showing the change of the conversion ratio of the two defect charge states with time when V2 and VO capture electrons and the comparison of their superposition conversion ratio and experiment;

[0062] Figure 8 It is a structural diagram of the carrier capture dynamics simulation device in irradiated semiconductor of the present invention. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] Reference Figure 1 An embodiment of the present invention provides a method for simulating carrier capture dynamics in an irradiated semiconductor, the method comprising the following steps:

[0065] S10, obtaining a list of defect reaction events and parameters in the semiconductor required for annealing;

[0066] S20, calculating and obtaining the spatial distribution of cascade defects after annealing based on the defect reaction event and the parameter list;

[0067] S30, based on the spatial distribution of the cascade defects after annealing, obtaining the radius of the effective cascade where the defect to be simulated is located and the average concentration of defects in the cascade;

[0068] S40, using the radius of the effective cascade where the defect to be simulated is located, the average defect concentration in the cascade, and the parameter list as input, solving the improved rate equation based on the SRH theory to obtain the kinetic behavior of defect-captured carriers.

[0069] The present invention uses a more realistic spatial distribution of cascade defects after annealing to calculate the radius of the effective cascade where the defect to be simulated is located and the average defect concentration in the cascade, and adopts an improved rate equation based on SRH theory to obtain the kinetic behavior of defect-captured carriers; considering the influence of spatial non-uniformity of cascade defects and complex cascade local potential on carrier capture, a more realistic defect distribution is used, based on reasonable assumptions, the cascade local potential is strictly solved, and it is as independent of or less dependent on adjustable parameters as possible, so as to accurately simulate the kinetic behavior of deep energy level defects capturing electrons / holes.

[0070] In one embodiment, the step S10 includes:

[0071] With reference to the theoretical calculation and experimental measurement results of DFT and molecular dynamics methods, the defect reaction events and the parameter list in silicon (Si) required for annealing are obtained, wherein the defect reaction events include all defect types in the semiconductor and reaction paths between defects, and the parameter list includes semiconductor material parameters and semiconductor defect parameters.

[0072] It should be noted that the semiconductors described in this embodiment include, but are not limited to, germanium, gallium nitride, silicon carbide, silicon, etc. Different semiconductor types have different defect reaction events and parameter values ​​set when using this method, and the specific implementation steps are the same. Taking the simulation of carrier capture dynamics in the irradiated semiconductor at 130K after neutron irradiation of the collector of a 2N2222 Si bipolar transistor as an example, the defect reaction event includes all possible defect types in Si and accurate reaction paths between defects; the parameter list includes Si material parameters, such as band gap, conduction band / valence band effective state density, dielectric constant and off-position threshold energy, as well as defect parameters in Si, such as defect formation energy, migration energy, energy level position and binding energy.

[0073] In one embodiment, the step S20 includes the following steps:

[0074] S21, using the primary dissociated atomic energy spectrum caused by neutrons as input conditions and the parameter list as input parameters, and using a Monte Carlo method based on two-body collision approximation to calculate the spatial distribution of initial cascade defects;

[0075] It should be noted that, in this embodiment, the PKA spectrum of neutron-irradiated Si is used as input conditions, and the semiconductor material parameters (mainly the off-site threshold energy) are used as input parameters, and the open source Monte Carlo (MC) program IM3D is used to calculate the spatial distribution of the initial cascade defects, such as Figure 2 shown.

[0076] S22. Taking the initial cascade defect spatial distribution as an initial condition, taking the defect reaction event and the parameter list as input, and applying the entity dynamics Monte Carlo method, calculate the cascade defect spatial distribution after annealing.

[0077] It should be noted that, in this embodiment, the initial cascade defect spatial distribution calculated by IM3D is used as the initial condition, the defect reaction event and the parameter list are used as the input, and the open source object kinetic Monte Carlo (OKMC) program MMonCa is used to calculate the cascade defect spatial distribution after annealing, as shown in FIG. Figure 3 shown.

[0078] In one embodiment, the step S30 includes the following steps:

[0079] S31, using the spatial distribution of the cascade defects after annealing to obtain the radial distribution of defects to be simulated in a specific semiconductor under neutron irradiation;

[0080] It should be noted that the defects to be simulated in the semiconductor include important defects V2 and VO. The radial distribution of important defects V2 and VO in neutron-irradiated Si is obtained by using the spatial distribution of multiple cascades after annealing, as shown in Figure 4 shown.

[0081] S32, using exponential functions to fit the radial distribution of the defect, the exponential function is:

[0082] N(r)=N0exp(-r / λ)

[0083] Among them, N0 and λ are the defect number present factor and attenuation length respectively;

[0084] It should be noted that the exponential function is used to fit the radial distribution of V2 and VO, and the fitting parameter defect number factors are 13145 and 7888, respectively, and the attenuation lengths are 16nm and 42nm, respectively. Figure 4 shown.

[0085] S33, using a step function to approximate the exponential function and the set truncation to obtain the radius of the effective cascade where the defect to be simulated is located and the average number of defects in the cascade;

[0086] It should be noted that the exponential function is approximated by a step function and a reasonable cutoff is set to obtain the effective radius and the average number of defects in the effective cascade corresponding to V2 and VO. The effective radii are 91nm and 239nm, respectively, as shown in Figure 4 As shown, the average number of defects is 41 and 66 respectively.

[0087] The setting process of truncation is as follows: select a parameter, i.e., a multiple of the attenuation length, take the product of the parameter and the attenuation length as the effective radius, and take the effective radius as the truncation. In addition, within the effective radius, the defect concentration is uniform, and outside the effective radius, the defect concentration is negligible.

[0088] Specifically, the criterion for the step function to approximate the exponential function is that the areas enclosed by the two functions and the coordinate axis are equal. The expression of the exponential function can be fitted, so its area can be obtained by integrating from a radius of 0 to infinity, while the expression of the step function is unknown. Therefore, one of the average number of defects or the effective radius must be determined first, and the other can be determined by the area equality criterion. In this embodiment, the effective radius is first determined, and the effective radius is considered to be a multiple of the attenuation length. The multiple is used as a parameter. The parameter is not selected arbitrarily, and there are the following criteria: 1) In the same semiconductor, under the same irradiation conditions, the multiple parameters corresponding to different types of deep energy level defects are the same; 2) The integral area of ​​the exponential function within the effective radius obtained must reach more than 90% of the original area.

[0089] S34, regarding the effective cascade as a sphere, using a sphere volume calculation formula to calculate the volume of the effective cascade, and dividing the average number of defects in the cascade by the volume of the effective cascade to obtain an average defect concentration in the cascade.

[0090] It should be noted that in this embodiment, the cascade is regarded as a sphere, and the average number of defects is divided by the volume of the effective cascade to calculate the concentrations of V2 and VO in the effective cascade to be 1.39×10 22 m -3 and 1.14×10 21 m -3 .

[0091] It should be noted that due to the uneven distribution of cascades, the sizes of different cascades are also different, resulting in uneven concentration distribution, and the cascade radius is difficult to determine. Therefore, it is necessary to simulate the spatial distribution of as many (more than one thousand) annealed cascades as possible, and cleverly use the exponential function to replace (fit) the radial distribution of the cascade, and the fitting effect is very good. Then use the step function to approximate the exponential function to obtain the effective radius and average concentration of the cascade.

[0092] In one embodiment, in step S30, the improved rate equation based on SRH theory is:

[0093]

[0094] in, is the thermal motion rate of electrons / holes, X j is a defect X with charge j, is a defect X that carries a charge j-1 or j+1 by capturing electrons / holes, is the charged defect X in the cascade j Cross section for capturing electrons / holes, N CV is the conduction band / valence band effective state density, Charged defect The activation energy of emitting electrons / holes to the bottom of the conduction band / top of the valence band, For the charged defects at different times The concentration of is the average electron / hole density in the effective cascade at time t, Defect X is charged at different times j The concentration, k B is the Boltzmann constant and T is the temperature.

[0095] In the traditional rate equation, the carrier concentration is constant, but in this embodiment, based on the defect distribution after annealing and the effective polarization region model mentioned above, an improved cascade internal potential is obtained and introduced into the traditional rate equation to correct the carrier density. The corrected carrier density changes with the potential.

[0096] It should be noted that the improved rate equation based on SRH theory takes into account a more realistic local electrostatic potential and can accurately describe the dynamic behavior of defect-captured carriers.

[0097] Specifically, in this embodiment, the average electron / hole density in the effective cascade at time t is defined as the difference between the average potential energy in the cascade and the potential energy at infinity, then The calculation formula is as follows:

[0098]

[0099] in, is the electron / hole density before irradiation, E peb (t) is the potential energy barrier of electrons / holes when the defects in the cascade capture carriers at time t;

[0100]

[0101] Where q is the unit charge (including the sign, the q values ​​corresponding to the electron and hole cases are opposite to each other), and are the average potential in the effective cascade at time t and the potential at infinity, respectively.

[0102] Furthermore, the average potential in the effective cascade at time t and the potential at infinity and By solving the Poisson equation, the steps are as follows:

[0103] (1) An effective polarization region model is proposed. This model assumes that when the defect captures carriers, polarization will occur near the cascade to form two spherically symmetrical regions with opposite charges. One is the effective cascade region where the deep energy level defect is located, and the other is the carrier depletion region surrounding the effective cascade region. Based on this model, taking infinity as the potential energy zero point and solving the Poisson equation, the potential calculation formula can be obtained:

[0104]

[0105] Among them, ε is the semiconductor dielectric constant; r0 is the effective radius of the effective cascade where the defect is located; Q1 is the concentration of the net charge in the depletion layer surrounding the effective cascade region, which is approximated as the semiconductor donor / acceptor concentration; Q0(t) is the concentration of the net charge in the effective cascade region at time t, which has the following form:

[0106]

[0107] Where C0 is the concentration of the fixed charge existing before capture; r1(t) is the radius of the entire spherical region including the effective cascade region and the depletion region at time t, which can be determined by charge conservation as follows:

[0108]

[0109] From this, we can get and The calculation formulas are:

[0110]

[0111] It should be noted that for the above-mentioned improved rate equation based on SRH theory, the kinetic behavior of the important defects V2 and VO in neutron-irradiated Si realizing the valence state transition of (= / -) and (- / 0) by capturing electrons can be obtained by self-consistently solving it through the numerical solution method of differential equations.

[0112] In one embodiment, the step S40 includes the following steps:

[0113] a), taking the radius of the effective cascade where the defect to be simulated is located, the average concentration of defects in the cascade, and the parameter list as inputs of the improved rate equation based on SRH theory;

[0114] It should be noted that the necessary parameters for the self-consistent solution include the effective radius r0 corresponding to the defect, the semiconductor donor / acceptor concentration, and the electron / hole density before irradiation. The concentration of fixed charges in the cascade before electron / hole capture, C0 (equal to the average defect concentration or 0, depending on the situation) and the defect Concentration (Initially set to 0).

[0115] The effective radii of defects V2 and VO are 91 nm and 239 nm, respectively, and the Si donor concentration is 9.0×10 20 m -3 The electron / hole density at 130K before irradiation is 8.878×10 20 m -3 , for V2 (= / -), the fixed charge already existing in the cascade before electron capture The concentration is the average concentration of V2. For VO(- / 0), the fixed charge concentration is 0 and the charged defect and VO - The initial concentrations were set to 0.

[0116] b) Using the bisection method to iteratively solve the average electron / hole density in the effective cascade at time t Obtaining an average electron density in the effective cascade of the defect to be simulated, for solving the improved rate equation based on the SRH theory;

[0117] It should be noted that this embodiment uses the bisection method to iteratively solve the average electron / hole density in the effective cascade at time t The calculation equations are used to obtain the effective average electron density in the cascade for V2 (= / -) and VO (- / 0), respectively.

[0118] c) using the open source differential equation solver lsoda to iteratively solve the improved rate equation based on SRH theory to obtain the concentration of charged defects at the next moment;

[0119] Repeat steps b) to c) until the improved rate equation based on the SRH theory reaches equilibrium, the concentration of charged defects and their corresponding electron density remain unchanged, the self-consistent solution is completed, and the electrostatic potential barrier, the carrier density in the cascade, and the defect charge state transition ratio at any time are obtained.

[0120] It should be noted that this embodiment uses the open source differential equation solver lsoda to iteratively solve the improved rate equation based on SRH theory to obtain the charged defect V2 at the next moment. 2- and VO - , output the electron density and charged defect concentration V2 for V2(= / -) and VO(- / 0) at this moment respectively2- and VO - and electrostatic potential energy barriers.

[0121] It should be noted that the information such as charge density, local electrostatic potential, electrostatic potential barrier, carrier density in the cascade and defect charge state transition ratio can be calculated by the above formula after each cycle. The typical time (1.0×10 -6 s) The spatial distribution of charge density and local electrostatic potential is as follows Figure 5 The obtained potential energy barrier and electron density change with time are shown as Figure 6 As shown in Figure 2, the change of the defect charge state conversion ratio of V2 (= / -) and VO (- / 0) with time and the comparison of the superposition conversion ratio and the experiment are shown in Figure 2. Figure 7 shown.

[0122] It should be noted that the self-consistent solution algorithm in this embodiment couples the open source program lsoda that can efficiently solve stiff differential equations and various iterative algorithms such as the bisection method and Newton iteration method, and can accurately and efficiently solve the complex differential equations proposed in the present invention.

[0123] According to the background partial adjustment, the defect cascade has a strong spatial localization, the cascade sizes are different, and the defect distribution within the cascade is very uneven, which makes it difficult to solve the local potential formed by carrier capture. This embodiment proposes an effective polarization region model based on spherical symmetry approximation, and cleverly obtains the size and charge density of the two polarization regions, so that the local potential can be directly solved by Poisson. In addition, the defect distribution after annealing is used to help determine the size and charge density of the effective cascade region, making the potential solution more accurate.

[0124] In addition, refer to Figure 8 The embodiment of the present invention further provides a device for simulating carrier capture dynamics in an irradiated semiconductor, the device comprising:

[0125] An acquisition module 10 is used to acquire a list of defect reaction events and parameters in the semiconductor required for annealing;

[0126] A defect space calculation module 20, configured to calculate the cascade defect space distribution after annealing based on the defect reaction event and the parameter list;

[0127] A defect characteristic calculation module 30, for obtaining the radius of the effective cascade where the defect to be simulated is located and the average defect concentration in the cascade based on the spatial distribution of the cascade defects after annealing;

[0128] The kinetic simulation module 40 is used to solve the improved rate equation based on the SRH theory by taking the radius of the effective cascade where the defect to be simulated is located, the average defect concentration in the cascade, and the parameter list as input to obtain the kinetic behavior of defect-captured carriers.

[0129] The present invention uses a more realistic spatial distribution of cascade defects after annealing to calculate the radius of the effective cascade where the defect to be simulated is located and the average defect concentration in the cascade, and adopts an improved rate equation based on SRH theory to obtain the kinetic behavior of defect-captured carriers; considering the influence of spatial non-uniformity of cascade defects and complex cascade local potential on carrier capture, a more realistic defect distribution is used, based on reasonable assumptions, the cascade local potential is strictly solved, and it is as independent of or less dependent on adjustable parameters as possible, so as to accurately simulate the kinetic behavior of deep energy level defects capturing electrons / holes.

[0130] In one embodiment, the defect reaction events and the parameter list in Si required for the annealing can be obtained by referring to the theoretical calculation and experimental measurement results of DFT and molecular dynamics methods, wherein the defect reaction events include all defect types in the semiconductor and the reaction paths between defects, and the parameter list includes semiconductor material parameters and semiconductor defect parameters.

[0131] It should be noted that the defect reaction events include all possible defect types in Si and the accurate reaction paths between defects; the parameter list includes the material parameters of Si, such as band gap, conduction band / valence band effective state density, dielectric constant and off-site threshold energy, as well as the defect parameters in Si, such as defect formation energy, migration energy, energy level position and binding energy.

[0132] In one embodiment, the defect space calculation module 20 includes:

[0133] An initial cascade defect spatial distribution calculation unit is used to calculate the spatial distribution of the initial cascade defect using the primary dislocated atomic energy spectrum caused by neutrons as an input condition and the parameter list as an input parameter, and using a Monte Carlo method based on two-body collision approximation;

[0134] The post-annealing cascade defect spatial distribution calculation unit is used to calculate the post-annealing cascade defect spatial distribution using the initial cascade defect spatial distribution as an initial condition, the defect reaction event and the parameter list as input, and the entity dynamics Monte Carlo method.

[0135] In one embodiment, the defect feature calculation module 30 includes:

[0136] A calculation unit, used to obtain the radial distribution of defects to be simulated in a specific semiconductor under neutron irradiation by using the spatial distribution of the cascade defects after annealing;

[0137] The fitting unit is used to fit the radial distribution of the defect using an exponential function, where the exponential function is:

[0138] N(r)=N0exp(-r / λ)

[0139] Among them, N0 and λ are the defect number present factor and attenuation length respectively;

[0140] A feature acquisition unit, used to use a step function to approximate the exponential function and the set truncation to acquire the radius of the effective cascade where the defect to be simulated is located and the average number of defects in the cascade;

[0141] The concentration calculation unit is used to regard the effective cascade as a sphere, calculate the volume of the effective cascade using a sphere volume calculation formula, and obtain the average defect concentration in the cascade by dividing the average number of defects in the cascade by the volume of the effective cascade.

[0142] In one embodiment, the improved rate equation based on SRH theory is:

[0143]

[0144] in, is the thermal motion rate of electrons / holes, X j is a defect X with charge j, is a defect X that carries a charge j-1 or j+1 by capturing electrons / holes, is the charged defect X in the cascade j Cross section for capturing electrons / holes, N CV is the conduction band / valence band effective state density, Charged defect The activation energy of emitting electrons / holes to the bottom of the conduction band / top of the valence band, For the charged defects at different times The concentration of is the average electron / hole density in the effective cascade at time t, Defect X is charged at different times j The concentration, k B is the Boltzmann constant and T is the temperature.

[0145] The average electron / hole density in the effective cascade at time t is defined as the difference between the average potential energy in the cascade and the potential energy at infinity, then The calculation formula is as follows:

[0146]

[0147] in, is the electron / hole density before irradiation, E peb(t) is the potential energy barrier of electrons / holes when the defects in the cascade capture carriers at time t;

[0148]

[0149] Where q is the unit charge (including the sign, the q values ​​corresponding to the electron and hole cases are opposite to each other), and are the average potential in the effective cascade and the potential at infinity at time t obtained by solving the Poisson equation.

[0150] In one embodiment, the average potential in the effective cascade at time t and the potential at infinity are and By solving the Poisson equation, the steps are as follows:

[0151] (1) An effective polarization region model is proposed. This model assumes that when the defect captures carriers, polarization will occur near the cascade to form two spherically symmetrical regions with opposite charges. One is the effective cascade region where the deep energy level defect is located, and the other is the carrier depletion region surrounding the effective cascade region. Based on this model, taking infinity as the potential energy zero point and solving the Poisson equation, the potential calculation formula can be obtained:

[0152]

[0153] Among them, ε is the semiconductor dielectric constant; r0 is the effective radius of the effective cascade where the defect is located; Q1 is the concentration of the net charge in the depletion layer surrounding the effective cascade region, which is approximated as the semiconductor donor / acceptor concentration; Q0(t) is the concentration of the net charge in the effective cascade region at time t, which has the following form:

[0154]

[0155] Where C0 is the concentration of the fixed charge existing before capture; r1(t) is the radius of the entire spherical region including the effective cascade region and the depletion region at time t, which can be determined by charge conservation as follows:

[0156]

[0157] From this, we can get and The calculation formulas are:

[0158]

[0159]

[0160] In one embodiment, the dynamics simulation module 40 includes:

[0161] An input unit, used to take the radius of the effective cascade where the defect to be simulated is located, the average defect concentration in the cascade, and the parameter list as inputs of the improved rate equation based on the SRH theory;

[0162] The first solving unit is used to iteratively solve the average electron / hole density in the effective cascade at time t using a bisection method Obtaining an average electron density in the effective cascade of the defect to be simulated, for solving the improved rate equation based on the SRH theory;

[0163] The second solving unit is used to use the open source differential equation solver lsoda to iteratively solve the improved rate equation based on the SRH theory to obtain the concentration of charged defects at the next moment;

[0164] The loop execution unit is used to repeatedly execute the steps of the first solution unit and the second solution unit until the improved rate equation based on the SRH theory reaches equilibrium, the concentration of charged defects and their corresponding electron density remain unchanged, the self-consistent solution is completed, and the electrostatic potential energy barrier, the carrier density in the cascade, and the defect charge state transition ratio at any time are obtained.

[0165] It should be noted that other embodiments or implementation methods of the device for simulating carrier capture dynamics in an irradiated semiconductor of the present invention can refer to the above-mentioned method embodiments, which will not be repeated here.

[0166] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0167] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0168] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for simulating carrier capture dynamics in an irradiated semiconductor, characterized in that: The method comprises: Obtain a list of defect reaction events and parameters in the semiconductor required for annealing; Based on the defect reaction event and the parameter list, calculating the spatial distribution of cascade defects after annealing; Based on the spatial distribution of the cascade defects after annealing, obtaining the radius of the effective cascade where the defect to be simulated is located and the average concentration of defects in the cascade; Taking the radius of the effective cascade where the defect to be simulated is located and the average defect concentration in the cascade, as well as the parameter list as input, solving the improved rate equation based on SRH theory to obtain the kinetic behavior of defect-captured carriers, including: a), taking the radius of the effective cascade where the defect to be simulated is located, the average concentration of defects in the cascade, and the parameter list as inputs of the improved rate equation based on SRH theory; b) Using the bisection method to iteratively solve the average electron / hole density in the effective cascade at time t Obtaining an average electron density in the effective cascade of the defect to be simulated, for solving the improved rate equation based on the SRH theory; c) using the open source differential equation solver lsoda to iteratively solve the improved rate equation based on SRH theory to obtain the concentration of charged defects at the next moment; Repeat steps b) to c) until the improved rate equation based on the SRH theory reaches equilibrium, the concentration of charged defects and their corresponding electron density remain unchanged, the self-consistent solution is completed, and the electrostatic potential barrier, the carrier density in the cascade, and the defect charge state transition ratio at any time are obtained; The improved rate equation based on SRH theory is: in, is the thermal motion rate of electrons / holes, X j is a defect X with charge j, is a defect X that carries a charge j-1 or j+1 by capturing electrons / holes, is the charged defect X in the cascade j Cross section for capturing electrons / holes, N C / V is the conduction band / valence band effective state density, Charged defect The activation energy of emitting electrons / holes to the bottom of the conduction band / top of the valence band, For the charged defects at different times The concentration of is the average electron / hole density in the effective cascade at time t, Defect X is charged at different times j The concentration, k B is the Boltzmann constant and T is the temperature.

2. The method for simulating carrier capture dynamics in an irradiated semiconductor according to claim 1, characterized in that: The step of obtaining a list of defect reaction events and parameters in a semiconductor required for annealing includes: With reference to the theoretical calculation and experimental measurement results of DFT and molecular dynamics methods, the defect reaction events and the parameter list in the semiconductor required for annealing are obtained, wherein the defect reaction events include all defect types in the semiconductor and reaction paths between defects, and the parameter list includes semiconductor material parameters and semiconductor defect parameters.

3. The method for simulating carrier capture dynamics in an irradiated semiconductor according to claim 1, characterized in that: The calculating, based on the defect reaction event and the parameter list, to obtain the spatial distribution of the cascade defects after annealing comprises: Taking the primary dislocated atomic energy spectrum caused by neutrons as input conditions and the parameter list as input parameters, a Monte Carlo method based on two-body collision approximation is used to calculate the spatial distribution of initial cascade defects; The initial cascade defect spatial distribution is used as an initial condition, the defect reaction event and the parameter list are used as input, and the solid dynamics Monte Carlo method is used to calculate the cascade defect spatial distribution after annealing.

4. The method for simulating carrier capture dynamics in an irradiated semiconductor according to claim 1, characterized in that: The obtaining, based on the spatial distribution of the cascade defects after annealing, the radius of the effective cascade where the defect to be simulated is located and the average concentration of defects in the cascade comprises: Using the spatial distribution of the cascade defects after annealing, a radial distribution of defects to be simulated in a specific semiconductor under neutron irradiation is obtained; The radial distribution of the defect is fitted using an exponential function, and the exponential function is: N(r)=N0exp(-r / λ) Among them, N0 and λ are the defect number present factor and attenuation length respectively; Approximating the exponential function and the set truncation by using a step function, obtaining the radius of the effective cascade where the defect to be simulated is located and the average number of defects in the cascade; The effective cascade is regarded as a sphere, the volume of the effective cascade is calculated using a sphere volume calculation formula, and the average defect concentration in the cascade is obtained by dividing the average number of defects in the cascade by the volume of the effective cascade.

5. The method for simulating carrier capture dynamics in an irradiated semiconductor according to claim 1, characterized in that: The average electron / hole density in the effective cascade at time t The calculation formula is as follows: in, is the electron / hole density before irradiation, E peb (t) is the potential energy barrier of electrons / holes when the defects in the cascade capture carriers at time t; Where q is the unit charge, and are the average potential in the effective cascade and the potential at infinity at time t obtained by solving the Poisson equation.

6. The method for simulating carrier capture dynamics in an irradiated semiconductor according to claim 5, characterized in that: The steps for calculating the average potential in the effective cascade and the potential at infinity at time t include: Constructing an effective polarization region model, in which when the defect captures carriers, polarization occurs near the cascade to form two spherically symmetrical regions with opposite charges, one spherically symmetrical region is the effective cascade region where the deep energy level defect is located, and the other spherically symmetrical region is the carrier depletion region surrounding the effective cascade region; Based on the effective polarization region model, taking infinity as the potential energy zero point, the Poisson equation is solved to obtain the average potential in the effective cascade at time t and the potential at infinity.

7. The method for simulating carrier capture dynamics in an irradiated semiconductor according to claim 6, characterized in that: The formula of the effective polarization area model is as follows: Among them, ε is the semiconductor dielectric constant; r0 is the effective radius of the effective cascade where the defect is located; Q1 is the concentration of net charge in the depletion layer surrounding the effective cascade region, which is approximated as the semiconductor donor / acceptor concentration; Q0(t) is the concentration of net charge in the effective cascade region at time t; r1(t) is the radius of the entire spherical region including the effective cascade region and the depletion region at time t.

8. A device for simulating carrier capture dynamics in irradiated semiconductors, characterized in that: The device comprises: An acquisition module, used for acquiring a list of defect reaction events and parameters in a semiconductor required for annealing; A defect space calculation module, used to calculate the cascade defect space distribution after annealing based on the defect reaction event and the parameter list; A defect characteristic calculation module, used to obtain the radius of the effective cascade where the defect to be simulated is located and the average defect concentration in the cascade based on the spatial distribution of the cascade defects after annealing; The kinetic simulation module is used to solve the improved rate equation based on SRH theory by taking the radius of the effective cascade where the defect to be simulated is located, the average defect concentration in the cascade, and the parameter list as input to obtain the kinetic behavior of defect-captured carriers, specifically including: a), taking the radius of the effective cascade where the defect to be simulated is located, the average concentration of defects in the cascade, and the parameter list as inputs of the improved rate equation based on SRH theory; b) Using the bisection method to iteratively solve the average electron / hole density in the effective cascade at time t Obtaining an average electron density in the effective cascade of the defect to be simulated, for solving the improved rate equation based on the SRH theory; c) using the open source differential equation solver lsoda to iteratively solve the improved rate equation based on SRH theory to obtain the concentration of charged defects at the next moment; Repeat steps b) to c) until the improved rate equation based on the SRH theory reaches equilibrium, the concentration of charged defects and their corresponding electron density remain unchanged, the self-consistent solution is completed, and the electrostatic potential barrier, the carrier density in the cascade, and the defect charge state transition ratio at any time are obtained; The improved rate equation based on SRH theory is: in, is the thermal motion rate of electrons / holes, X j is a defect X with charge j, is a defect X that carries a charge j-1 or j+1 by capturing electrons / holes, is the charged defect X in the cascade j Cross section for capturing electrons / holes, N CV is the conduction band / valence band effective state density, Charged defect The activation energy of emitting electrons / holes to the bottom of the conduction band / top of the valence band, For the charged defects at different times The concentration of is the average electron / hole density in the effective cascade at time t, Defect X is charged at different times j The concentration, k B is the Boltzmann constant and T is the temperature.

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