Quantitative Simulation Method and System for Deep-Level Transient Spectra of Irradiated Semiconductors

Abstract

This invention discloses a quantitative simulation method and system for the deep-level transient spectrum of irradiated semiconductors, belonging to the field of semiconductor irradiation technology. The method includes: acquiring the property parameters of the semiconductor and its irradiation defects; determining the defect types and inter-defect reaction paths in the annealing simulation based on the defect property parameters; using the semiconductor property parameters and the irradiation-induced PKA energy spectrum as input conditions, simulating the spatial distribution of initial point defects using the MC method; using the spatial distribution of initial point defects as initial conditions, and the defect property parameters and inter-defect reaction paths as input, simulating the types and concentrations of surviving defects after annealing using the OKMC method; using the property parameters and concentrations of surviving defects as input, solving the defect rate equation based on SRH theory, and substituting it into the theoretical formula for the DLTS output signal to obtain the quantitatively simulated DLTS. This invention can quantitatively simulate the DLTS of irradiated semiconductors and provide the micro-defect types and their specific proportions corresponding to different DLTS peaks.

Description

Technical Field

[0001] This invention relates to the field of semiconductor irradiation technology, and more specifically to a quantitative simulation method and system for the transient spectrum of deep energy levels in irradiated semiconductors. Background Technology

[0002] When semiconductor devices operate in environments with high-energy radiation, such as those from space or nuclear energy sources, they are exposed to high-energy particles. This often leads to the displacement of lattice atoms within the semiconductor, creating initial point defects (self-interstitials and vacancies). These point defects interact in complex ways with impurities present in the semiconductor and evolve over a long period, giving rise to different types of complex defects. The fundamental properties of these different types of defects generally differ significantly, and their impact on semiconductor device performance varies. Some defects do not affect semiconductor device performance; some scatter charge carriers, causing changes in electrical properties such as carrier mobility; and some introduce defect energy levels into the semiconductor bandgap, capturing and emitting charge carriers (electrons and holes) through these defect energy levels, leading to performance degradation or even permanent failure of the semiconductor device. Therefore, identifying the types of defects in irradiated semiconductors and clarifying the types of defects that severely affect semiconductor device performance is of great significance for understanding the performance degradation mechanisms of semiconductor devices and for radiation-hardening design.

[0003] Deep-level transient spectroscopy (DLTS), as one of the most commonly used and powerful experimental methods for studying defect properties, has greatly aided in the identification of deep-level defects in semiconductors. It detects important deep-level defect properties such as defect concentration, carrier trapping cross-section, and defect energy level location by measuring the change in capacitance of pn or Schottky junctions under reverse bias at different temperatures. However, it cannot correlate different measured DLTS peaks with specific microscopic defects, nor can it determine the specific defect type, composition, or structure. In contrast, theoretical simulation methods at the atomic scale, represented by density functional theory (DFT), can provide specific types, compositions, and structures of defects at the atomic level. Therefore, theoretical simulations of DLTS are urgently needed to further clarify the specific types of microscopic defects in irradiated semiconductors.

[0004] However, the simulation methods discussed in the relevant literature only rely on the defect energy levels and carrier trapping cross sections obtained from DFT calculations to qualitatively simulate DLTS. They can only give the peak position of the defect in DLTS, but cannot quantitatively give the peak intensity corresponding to each defect and its proportion in the DLTS peak. As a result, when identifying defects, only the defect energy level can be referenced, but the defect concentration cannot be referenced, which makes the defect identification very prone to deviation.

[0005] In related technologies, invention patent CN106528493B discloses a numerical simulation method for effectively separating DLTS test signals. This method effectively separates several mutually coupled deep-level defects by numerically simulating the DLTS signal of a compound semiconductor Schottky barrier. However, this method uses theoretical calculations to fit the DLTS experiment to achieve the purpose of separating coupled deep-level defects in the deep-level transient spectrum, rather than theoretically simulating DLTS. Furthermore, although this method can also separate several deep-level defects corresponding to the DLTS signal, it can only give the energy level difference of the separated deep-level defects, but cannot give the specific type of the corresponding microscopic defects.

[0006] Therefore, how to quantitatively simulate irradiated semiconductor DLTS and clearly identify the micro-defect types corresponding to DLTS signals is an urgent problem to be solved. Summary of the Invention

[0007] The technical problem to be solved by this invention is how to quantitatively simulate irradiated semiconductor DLTS and give the micro-defect type corresponding to the irradiated semiconductor DLTS signal.

[0008] The present invention solves the above-mentioned technical problems through the following technical means:

[0009] On one hand, this invention proposes a quantitative simulation method for the transient spectrum of deep energy levels in irradiated semiconductors, the method comprising:

[0010] Obtain the property parameters of semiconductors and their irradiation defect property parameters;

[0011] Based on the irradiation defect property parameters, the defect types and reaction paths between defects are determined in the annealing simulation;

[0012] Using the semiconductor's property parameters and the primary knock-on atom (PKA) energy spectrum induced by irradiation as input conditions, the spatial distribution of initial point defects was simulated using the Monte Carlo (MC) method.

[0013] Using the spatial distribution of the initial point defects as the initial condition, and the irradiation defect property parameters and the reaction paths between the defects as inputs, the object kinetic Monte Carlo (OKMC) method is used to simulate and obtain the type and concentration information of surviving defects after annealing.

[0014] Using the property parameters and concentration information of the surviving defects as input, the defect rate equation based on the Shockey-Read-Hall (SRH) theory is solved to obtain the deep-level defect concentration occupied by carriers at different times.

[0015] By substituting the concentration of deep-level defects occupied by charge carriers at different times into the theoretical formula of the DLTS output signal, a quantitatively simulated DLTS can be obtained.

[0016] This invention first obtains the basic properties of irradiation defects, then uses the MC and OKMC methods to simulate defect annealing and obtain the concentration of surviving defects after annealing. Next, it calculates and solves the defect rate equation based on SRH theory, and substitutes the solution into the theoretical formula of DLTS output signal to quantitatively simulate DLTS. This method can give the micro-defect types corresponding to different DLTS signals, the relative intensity of DLTS signals with different defects, and the proportion of different defects in the coupled DLTS signals.

[0017] Furthermore, the irradiation defect property parameters include defect formation energy, migration energy, energy level position, carrier trapping cross section, and binding energy. The determination of defect types and reaction paths between defects in the annealing simulation based on these irradiation defect property parameters includes:

[0018] Based on the aforementioned irradiation defect property parameters, the defect types in the annealing simulation are determined to include all intrinsic point defects and defect clusters with binding energy greater than 1.0 eV.

[0019] Based on the criterion that the difference between the defect formation energy before and after the reaction is greater than 1.0 eV, the reaction pathway between defects is determined.

[0020] Furthermore, the mathematical form of the defect rate equation based on SRH theory is as follows:

[0021]

[0022] Where t is time; A deep-level defect X that carries a charge of j-1 or j+1 due to being occupied by electrons or holes; For a given temperature T, at time t, the deep-level defect occupied by electrons or holes. The concentration; Let T be the thermal velocity of electrons or holes at temperature T. For cascaded charged defects X j The cross section that traps electrons or holes at temperature T; n e / h The concentration of electrons or holes; (t,T) represents the deep-level defect X occupied by electrons or holes at time t, at temperature T. j Concentration of N;C / V (T) represents the effective density of states at temperature T, either at the bottom of the conduction band or the top of the valence band. For charged deep-level defects at temperature T The activation energy for emitting electrons or holes to the bottom of the conduction band / top of the valence band; k B is the Boltzmann constant.

[0023] Furthermore, using the property parameters and concentration information of the surviving defects as input, the defect rate equation based on SRH theory is solved to obtain the deep-level defect concentration occupied by carriers at different times, including:

[0024] (a) Based on the type and concentration information of the surviving defects, construct a list of deep-level defects to be simulated and determine the temperature range for simulating DLTS, wherein the defects in the list of deep-level defects to be simulated are defects that survive after annealing and contribute defect energy levels to the band gap.

[0025] (b) Calculate the thermal velocity of charge carriers at different temperatures within the stated temperature range. And the effective density of states N at the bottom of the conduction band or the top of the valence band of a semiconductor C / V (T);

[0026] (c) Read a defect level from the list of deep-level defect levels to be simulated, and input the carrier trapping cross section and the activation energy of carrier emission at different temperatures for the defect level;

[0027] (d) Using the concentration information as the initial concentration of deep-level defects occupied by carriers, and setting the initial concentration of deep-level defects not occupied by carriers, the open-source differential equation solver lsoda is used to solve the defect rate equations based on SRH theory corresponding to the defect energy levels read in at different temperatures within the temperature range from low temperature to high temperature, so as to obtain the concentration of deep-level defects occupied by carriers at different times at different temperatures.

[0028] Repeat steps (c) and (d) until all the defect rate equations based on SRH theory corresponding to all defect levels in the list of deep-level defect energy levels to be simulated are solved.

[0029] Furthermore, the thermal motion velocity of charge carriers at different temperatures within the stated temperature range. The calculation formula is:

[0030]

[0031] The effective state density N at the bottom of the semiconductor conduction band or the top of the valence band C / V The formula for calculating (T) is:

[0032]

[0033] in, denoted as ρ, where ρ is the effective mass of an electron or hole; h is Planck's constant.

[0034] Furthermore, the theoretical formula for the DLTS output signal is:

[0035] or

[0036]

[0037] Where, ΔC ± (T) represents the capacitance at different temperatures when the deep level defect is a minority carrier trap or a majority carrier trap; C0 represents the junction capacitance when there is no deep level defect. These represent the deep-level defect concentrations occupied by charge carriers at two different times, t1 and t2, at different temperatures; for the pn junction, N... dop The doping concentration is for the shallowly doped side; for a Schottky junction, N dop This represents the doping concentration on one side of the semiconductor.

[0038] Furthermore, this invention also proposes a quantitative simulation system for the transient spectrum of deep energy levels in irradiated semiconductors, the system comprising:

[0039] The acquisition module is used to acquire the property parameters of semiconductors and their irradiation defect property parameters.

[0040] The determination module is used to determine the defect type and reaction path between defects in the annealing simulation based on the irradiation defect property parameters;

[0041] The first simulation module is used to simulate the spatial distribution of initial point defects using the semiconductor's property parameters and the PKA energy spectrum caused by irradiation as input conditions and the MC method.

[0042] The second simulation module is used to simulate and obtain the type and concentration information of surviving defects after annealing using the spatial distribution of the initial point defects as the initial condition, the irradiation defect property parameters and the reaction path between the defects as input, and the OKMC method.

[0043] The solution module is used to solve the defect rate equation based on SRH theory, taking the property parameters and concentration information of the surviving defects as input, to obtain the deep level defect concentration occupied by carriers at different times.

[0044] The quantitative simulation module is used to substitute the concentration of deep-level defects occupied by charge carriers at different times into the theoretical formula of the DLTS output signal to obtain a quantitatively simulated DLTS.

[0045] Furthermore, the determining module includes:

[0046] The type determination unit is used to determine the defect type in the annealing simulation based on the irradiation defect property parameters, including all intrinsic point defects and defect clusters with binding energy greater than 1.0 eV;

[0047] The reaction path determination unit is used to determine the reaction path between defects based on the criterion that the difference between the defect formation energy before and after the reaction is greater than 1.0 eV.

[0048] Furthermore, the mathematical form of the defect rate equation based on SRH theory is as follows:

[0049]

[0050] Where t is time; A deep-level defect X that carries a charge of j-1 or j+1 due to being occupied by electrons or holes; For a given temperature T, at time t, the deep-level defect occupied by electrons or holes. The concentration; Let T be the thermal velocity of electrons or holes at temperature T. For cascaded charged defects X j The cross section that traps electrons or holes at temperature T; n e / h The concentration of electrons or holes; Let X be the deep-level defect occupied by electrons or holes at time t at temperature T. j Concentration of N; C / V (T) represents the effective density of states at temperature T, either at the bottom of the conduction band or the top of the valence band. For charged deep-level defects at temperature T The activation energy for emitting electrons or holes to the bottom of the conduction band / top of the valence band; k B is the Boltzmann constant.

[0051] Furthermore, the theoretical formula for the DLTS output signal is:

[0052] or

[0053]

[0054] Where, ΔC ± (T) represents the capacitance at different temperatures when the deep level defect is a minority carrier trap or a majority carrier trap; C0 represents the junction capacitance when there is no deep level defect. These represent the deep-level defect concentrations occupied by charge carriers at two different times, t1 and t2, at different temperatures; for the pn junction, N... dop The doping concentration is for the shallowly doped side; for a Schottky junction, N dop This represents the doping concentration on one side of the semiconductor.

[0055] The advantages of this invention are:

[0056] (1) This invention first obtains the basic properties of irradiation defects, then uses the MC and OKMC methods to simulate defect annealing, obtains the concentration of surviving defects after annealing, then calculates the defect rate equation based on SRH theory, and substitutes the solution into the theoretical formula of DLTS output signal to quantitatively simulate DLTS; this method can give the micro-defect type corresponding to different DLTS signals, the relative intensity of DLTS signals of different defects, and the proportion of different defects in the coupled DLTS signal.

[0057] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0058] Figure 1 This is a flowchart illustrating the quantitative simulation method for the transient spectrum of irradiated semiconductor deep energy levels according to the first embodiment of the present invention.

[0059] Figure 2 This is a diagram showing the defect types and reaction pathways between defects in silicon irradiated by sub-irradiation in this invention.

[0060] Figure 3 This is the PKA integrated energy spectrum of silicon irradiated by sub-irradiation in an embodiment of the present invention;

[0061] Figure 4 This is a spatial distribution diagram of the initial point defects generated by silicon irradiation in an embodiment of the present invention;

[0062] Figure 5 This is a graph showing the change in the concentration of different defect types in neutron-irradiated silicon over time during annealing at 350K according to an embodiment of the present invention.

[0063] Figure 6 This is a graph showing the change in the concentration of VO occupied by electrons over time during voltage reverse bias, as simulated in an embodiment of the present invention.

[0064] Figure 7 This is a comparison between the deep-level transient spectrum of neutron-irradiated silicon after annealing at 350K, obtained through quantitative simulation in an embodiment of the present invention, and the experimental spectrum.

[0065] Figure 8 This is a schematic diagram of the structure of the quantitative simulation system for the transient spectrum of irradiated semiconductor deep energy levels in the second embodiment of the present invention.

[0066] Explanation of symbols in the diagram:

[0067] I represents a silicon self-interstitial defect. n V represents a silicon self-interstitial defect cluster (composed of n silicon self-interstitials), and V represents a silicon vacancy defect.n I represents a silicon vacancy defect cluster (composed of n silicon vacancies). n V m The term represents a silicon self-interstitial-silicon vacancy defect cluster (composed of n silicon self-interstitials and m silicon vacancies); P, C, and O represent substituted phosphorus, carbon, and oxygen atoms, respectively; PI represents a phosphorus-silicon self-interstitial pair defect; PV represents a phosphorus-silicon vacancy pair defect; CI represents a carbon-silicon self-interstitial pair defect; and C represents a silicon self-interstitial pair defect. n I m The denoting symbol represents a carbon-silicon self-interstitial defect cluster (composed of n carbon atoms and m silicon self-interstitials), CV represents a carbon-silicon vacancy pair defect, OI represents an oxygen-silicon interstitial pair defect, and VO represents a silicon vacancy-oxygen pair defect. (= / -) represents the transition between the two defect charge states of -2 and -1, and (- / 0) represents the transition between the two charge states of -1 and 0 (the transition of charge states also represents a defect energy level). Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] like Figure 1 As shown, the first embodiment of the present invention proposes a quantitative simulation method for the transient spectrum of deep energy levels in irradiated semiconductors, the method comprising the following steps:

[0070] S10. Obtain the property parameters of the semiconductor and its irradiation defect property parameters.

[0071] It should be noted that the semiconductors mentioned in this embodiment include, but are not limited to, germanium, gallium nitride, silicon carbide, silicon, etc.

[0072] It should be understood that those skilled in the art can obtain different semiconductor property parameters and their irradiation defect property parameters when using this method, depending on the type of semiconductor.

[0073] This embodiment uses Si as an example. Methods for obtaining the property parameters of Si and the types of defects in neutron-irradiated Si, along with their irradiation defect properties, include DFT theoretical calculations, experimental measurements, and querying semiconductor databases. The main property parameters of Si include its band gap, effective density of states in the conduction / valence bands, dielectric constant, and displacement threshold energy. The main irradiation defect properties include defect formation energy, migration energy, energy level position, trapping cross-section, and binding energy.

[0074] It should be noted that the band gap, effective density of states in the conduction / valence band, and defect energy level and carrier trapping cross section in the Si property parameters need to be obtained as temperature-dependent parameters.

[0075] S20. Based on the irradiation defect property parameters, determine the defect types and reaction paths between defects in the annealing simulation.

[0076] Furthermore, the defect types in the annealing simulation should include all intrinsic point defects and defect clusters with binding energies greater than 1.0 eV. The basic criterion for determining the reaction pathways between defects is that the difference between the defect formation energy before and after the reaction is greater than 1.0 eV.

[0077] In this embodiment, the defect type and the reaction path between defects are determined by the defect property parameters as follows: Figure 2 As shown.

[0078] S30. Using the semiconductor's property parameters and the PKA energy spectrum caused by irradiation as input conditions, the spatial distribution of the initial point defect is obtained by MC method simulation.

[0079] Furthermore, in this embodiment, using the Si property parameters and the PKA energy spectrum of primary ex-situ atoms caused by neutron irradiation of Si as input conditions, the initial spatial distribution of different cascaded internal point defects generated by irradiation is calculated using the MC method based on the two-body collision approximation.

[0080] In this embodiment, the PKA energy spectrum of neutron-irradiated Si is as follows: Figure 3 As shown. The spatial distribution of an initial point defect within a typical cascade, simulated using the MC method, is as follows. Figure 4 As shown.

[0081] S40. Using the spatial distribution of the initial point defect as the initial condition, and the irradiation defect property parameters and the reaction path between the defects as inputs, the OKMC method is used to simulate and obtain the type and concentration information of the surviving defects after annealing.

[0082] Furthermore, in this embodiment, the spatial distribution of initial point defects in different cascades is used as the initial condition, and the property parameters of Si, the property parameters of irradiated defects in Si, and the reaction paths between defects are used as inputs. The OKMC method is used to simulate and obtain the type and concentration of surviving defects after annealing.

[0083] In this embodiment, the changes in the concentration of different defect types over time during the 350K annealing process are as follows: Figure 5 As shown in the figure, the types of surviving defects include vacancy-oxygen pair defects (VO), double vacancy defects (V2), triple vacancy defect clusters (V3), oxygen-silicon self-interstitial pair defects (OI), and carbon-silicon self-interstitial pair defects (CI).

[0084] S50. Using the property parameters and concentration information of the surviving defects as input, solve the defect rate equation based on SRH theory to obtain the deep level defect concentration occupied by carriers at different times.

[0085] S60. Substitute the concentration of deep-level defects occupied by charge carriers at different times into the theoretical formula of the DLTS output signal to obtain a quantitatively simulated DLTS.

[0086] This embodiment first obtains the basic property parameters of irradiation defects, then uses the MC and OKMC methods to simulate defect annealing and obtain the concentration of surviving defects after annealing. Next, it calculates and solves the defect rate equation based on SRH theory, and substitutes the solution into the theoretical formula of DLTS output signal to quantitatively simulate DLTS. This method can give the micro-defect type corresponding to different DLTS signals, the relative intensity of DLTS signals of different defects, and the proportion of different defects in the coupled DLTS signal.

[0087] In one embodiment, the general form of the defect rate equation based on SRH theory is:

[0088]

[0089] Where t is time; A deep-level defect X that carries a charge of j-1 or j+1 due to being occupied by electrons or holes; For a given temperature T, at time t, the deep-level defect occupied by electrons or holes. The concentration; Let T be the thermal velocity of electrons or holes at temperature T. For cascaded charged defects X j The cross section that traps electrons or holes at temperature T; n e / h The concentration of electrons or holes; Let X be the deep-level defect occupied by electrons or holes at time t at temperature T. j Concentration of N; C / V (T) represents the effective density of states at temperature T, either at the bottom of the conduction band or the top of the valence band. For charged deep-level defects at temperature T The activation energy for emitting electrons or holes to the bottom of the conduction band / top of the valence band; k B is the Boltzmann constant.

[0090] During DLTS measurements, the reverse bias voltage causes carriers to be ejected from the pn junction or Schottky junction. Carrier trapping within the junction is negligible. Therefore, when simulating DLTS, the carrier trapping term (first term) in the above equation can be ignored, and only carrier emission (second term) is considered. Thus, the defect rate equation can be written in the following form:

[0091]

[0092] The purpose of using this rate equation in this embodiment is as follows: First, the rate equation is based on SRH theory, which has been widely verified over the decades since its inception, ensuring the accuracy of the defect rate equation. Second, the most difficult element to determine in the theoretical formula for the output signal of DLTS is the concentration of deep-level defects occupied by charge carriers, and this defect rate equation can provide its value, making theoretical simulation of DLTS possible. In addition, the equation is essentially a differential equation with a relatively simple form, and the solution method for such simple differential equations is already very mature and has many solvers, making it easy and efficient to solve.

[0093] In one embodiment, step S50 includes the following steps:

[0094] (a) Based on the type and concentration information of the surviving defects, construct a list of deep-level defects to be simulated and determine the temperature range for simulating DLTS, wherein the defects in the list of deep-level defects to be simulated are defects that survive after annealing and contribute defect energy levels in the band gap.

[0095] Furthermore, the defects in the deep-level defect list for quantitative DLTS simulation must be both defects that survive annealing and those that contribute defect energy levels within the band gap. The temperature range for DLTS simulation can be determined based on the temperature range of experimental DLTS. Theoretically, the closer the temperature intervals are, the better, to reduce simulation errors. However, closer intervals result in lower computational efficiency. It is recommended that the temperature intervals be between 1 and 10 K during simulation.

[0096] (b) Calculate the thermal velocity of charge carriers at different temperatures within the stated temperature range. And the effective density of states N at the bottom of the conduction band or the top of the valence band of a semiconductor C / V (T).

[0097] (c) Read a defect level from the list of deep-level defect levels to be simulated, and input the carrier trapping cross section and the activation energy of carrier emission at different temperatures of the defect level.

[0098] (d) Using the concentration information as the initial concentration of deep-level defects occupied by charge carriers, and setting the initial concentration of deep-level defects not occupied by charge carriers, the open-source differential equation solver lsoda is used to solve the defect rate equations based on SRH theory corresponding to the defect energy levels read in at different temperatures within the temperature range from low temperature to high temperature, so as to obtain the concentration of deep-level defects occupied by charge carriers at different times at different temperatures.

[0099] Repeat steps (c) and (d) until all the defect rate equations based on SRH theory corresponding to all defect levels in the list of deep-level defect energy levels to be simulated are solved.

[0100] It should be noted that the purpose of solving the defect rate equation based on SRH theory in this embodiment is to obtain the concentration of deep-level defects occupied by charge carriers at different times and temperatures.

[0101] Taking Si as an example, the solution process of the defect rate equation based on SRH theory is as follows:

[0102] (a) According to Figure 5 The survival defect types and their energy level information are shown. The list of deep energy level defects in neutron-irradiated Si is determined as {CI(- / 0), VO(- / 0), V2(= / -), V2(- / 0), V3(= / -), V3(- / 0)}, with the temperature range and interval set to [0K, 300K, 5K], that is, the temperature range is 0 to 300K and the interval is 5K.

[0103] (b) Calculate the thermal velocity of charge carriers at different temperatures within the stated temperature range. And the effective density of states N at the bottom of the conduction band or the top of the valence band of a semiconductor C / V (T).

[0104] (c) Read a defect level from the list of deep-level defect levels to be simulated, and input the carrier trapping cross section and the activation energy of carrier emission at different temperatures for the defect level.

[0105] It should be noted that, for the Si material in this embodiment, its band gap is only 1.12 eV, which is relatively small. Therefore, the temperature range of DLTS is also relatively narrow (generally 0 to 300 K). Within this temperature range, the defect trapping cross section... and defect emission activation energy They hardly change with temperature. Therefore, for this embodiment, they are all approximately taken as values ​​at 0K. However, for wide bandgap semiconductors such as gallium nitride and silicon carbide (the bandgap of gallium nitride and silicon carbide is about 3.5 eV), the temperature range of DLTS is very wide (the lowest temperature is 0K, and the highest temperature generally reaches 600K or even higher). It is necessary to consider the effect of temperature on the defect trapping cross section and the defect emission activation energy. In this case, it is necessary to use DFT to calculate their values ​​at different temperatures.

[0106] (d) Using the concentration of deep-level defects after annealing as the initial concentration of deep-level defects occupied by charge carriers, 0m -3As the initial concentration of deep-level defects not occupied by charge carriers, the open-source differential equation solver lsoda is used to solve the rate equations corresponding to the defect energy levels read in at different temperatures within the temperature range, from low temperature to high temperature, to obtain the concentration of deep-level defects occupied by charge carriers at different times at different temperatures, until the defect rate equations at all temperatures within the temperature range are solved.

[0107] (e) Repeat steps (c) and (d) until all rate equations in the list of deep-level defect energy levels to be simulated have been solved. Figure 6 The calculated values ​​for a typical deep-level defect VO are given, where the energy level is occupied by electrons (i.e., VO). - The relationship between concentration and time.

[0108] In one embodiment, the thermal velocity of charge carriers at different temperatures within the temperature range The calculation formula is:

[0109]

[0110] The effective state density N at the bottom of the semiconductor conduction band or the top of the valence band C / V The formula for calculating (T) is:

[0111]

[0112] in, denoted as ρ, where ρ is the effective mass of an electron or hole; h is Planck's constant.

[0113] In one embodiment, the theoretical formula for the DLTS output signal is:

[0114] or

[0115]

[0116] Where, ΔC ± (T) represents the junction capacitance at different temperatures when the deep level defect is a minority carrier trap or a majority carrier trap. C0 represents the junction capacitance when there is no deep level defect. These represent the deep-level defect concentrations occupied by charge carriers at two different times, t1 and t2, at different temperatures. For a pn junction, N... dop The doping concentration is for the shallowly doped side; for a Schottky junction, N dop This represents the doping concentration on one side of the semiconductor.

[0117] In this embodiment, the experimental rate window is 232s. -1 Set t1 and t2 to 2.08 × 10⁻⁶ respectively. -4 s and 2.08×10 - 3s, such as Figure 6 As shown. Substituting the deep-level defect concentrations occupied by charge carriers at two different times, t1 and t2, at different temperatures into the above formula, the quantitative simulated DLTS output signal at different temperatures can be obtained, as shown. Figure 7 As shown. (Through) Figure 7 It can be determined that the micro-defect types corresponding to different DLTS signals and their proportion in the coupled DLTS signals.

[0118] It's important to note that DLTS measures semiconductor PN junctions or Schottky junctions, and its output signal is directly related to the junction capacitance. Specifically, semiconductor defects introduce defect energy levels within the semiconductor band gap. Electrons and holes (free carriers) can occupy or be emitted from these energy levels. During DLTS measurements, a reverse bias voltage is applied to the PN junction or Schottky junction, superimposed with a periodically varying forward pulse voltage. When the voltage is reverse biased, defects ionize, and electrons or holes are emitted from the defect energy levels. When forward biased, electrons or holes re-occupy the defect energy levels. The capture and emission of electrons or holes cause changes in the junction capacitance. DLTS measures the capacitance at two different times when the voltage is reverse biased, outputting the capacitance difference between these two moments. By continuously changing the measurement temperature, a spectrum showing the capacitance difference as a function of temperature at both moments is output.

[0119] Furthermore, the derivation process of the theoretical formula for the DLTS output signal is as follows:

[0120] The junction capacitance of a semiconductor can be approximated by the capacitance of a parallel-plate capacitor, satisfying the following formula:

[0121]

[0122] Where C is the junction capacitance, ε is the semiconductor dielectric constant, A is the junction area, and d is the width of the junction barrier region.

[0123] When there are no deep-level defects in the junction, the width of the barrier region under reverse voltage bias can generally be expressed as follows:

[0124]

[0125] Where q is a unit charge, V R For reverse bias voltage, V D For the contact potential difference, N dop Let be the impurity concentration on the shallowly doped side of the junction. Thus, the junction capacitance in this case can be expressed by the following formula:

[0126]

[0127] When there are deep-level defects in the junction, applying a reverse bias will cause electrons or holes to be emitted from the defect levels, thereby changing the width of the depletion region. The width of the depletion region at this time should be:

[0128]

[0129] where d ± are the widths of the depletion region when the deep-level defect is a minority carrier trap or a majority carrier trap, respectively. is the concentration of deep-level defects occupied by free carriers at time t after applying a reverse bias at a measurement temperature of T. The corresponding junction capacitances are respectively expressed as:

[0130]

[0131] Furthermore, it can be expressed in terms of C0 as:

[0132]

[0133] Thus, the output signal of DLTS, that is, the difference ΔC ± (t, T) between C ± (t, T) at two different times t1 and t2 (t1 < t2) at different temperatures, or can be respectively expressed as:

[0134] or

[0135]

[0136] Generally speaking, compared with the doping concentration, the concentration of deep-level defects is relatively low, and the ratio of the concentration of deep-level defects occupied by carriers to the doping concentration in the formula is a small quantity. Using the Taylor formula and taking the first-order approximation, the above output signal of DLTS can be approximately expressed as:

[0137] or

[0138]

[0139] It can be seen that the output signal of DLTS only depends on the difference in the concentration of deep-level defects occupied by carriers at two different times t1 and t2, the junction capacitance C0 (or not relevant) without deep-level defects, and the doping concentration N dop is related. Among them, N dop and C0 are generally determined for a specific semiconductor junction. N dopThe values ​​can be obtained experimentally, and C0 can be calculated using the above formula (or does not need to be determined). t1 and t2 can also be determined by the set rate window. Therefore, by substituting the deep-level defect concentrations occupied by charge carriers at two different times, t1 and t2, at different temperatures into the above formula, the quantitative simulated DLTS output signal at different temperatures can be obtained.

[0140] It is worth mentioning that, due to N dop The C0 value is generally fixed for a specific semiconductor junction. The output signal of DLTS is actually proportional to the difference in deep level defect concentration occupied by charge carriers at two different times, t1 and t2. Therefore, by calculating the deep level defect concentration occupied by charge carriers at two different temperatures at t1 and t2, a quantitative simulation of the relative DLTS signal can be obtained.

[0141] Existing methods and techniques can only qualitatively simulate DLTS based on defect energy levels and carrier trapping cross sections obtained from DFT calculations, providing peak positions for specific micro-defects. However, it is difficult to clearly identify the micro-defect types corresponding to the complex and coupled DLTS signals in irradiated semiconductors. This embodiment employs a multi-scale simulation method. First, atomic-scale methods such as DFT are used to obtain the basic properties of irradiated defects. Then, MC and OKMC methods are used to simulate defect annealing, obtaining the concentration of surviving defects after annealing. Next, the defect rate equation based on SRH theory is calculated to quantitatively simulate DLTS. This embodiment's method can provide the micro-defect types corresponding to different DLTS signals, the relative intensities of DLTS signals from different defects, and the proportion of different defects in the coupled DLTS signals.

[0142] In addition, such as Figure 8 As shown, the second embodiment of the present invention proposes a quantitative simulation system for the transient spectrum of deep energy levels in an irradiated semiconductor, the system comprising:

[0143] Acquisition module 10 is used to acquire the property parameters of semiconductors and their irradiation defect property parameters;

[0144] The determination module 20 is used to determine the defect type and reaction path between defects in the annealing simulation based on the irradiation defect property parameters.

[0145] The first simulation module 30 is used to simulate the spatial distribution of the initial point defect using the semiconductor's property parameters and the PKA energy spectrum caused by irradiation as input conditions and the MC method.

[0146] The second simulation module 40 is used to simulate and obtain the type and concentration information of surviving defects after annealing using the spatial distribution of the initial point defects as the initial condition, the irradiation defect property parameters and the reaction path between the defects as input, and the OKMC method.

[0147] The solution module 50 is used to solve the defect rate equation based on SRH theory, taking the property parameters and concentration information of the surviving defects as input, to obtain the deep level defect concentration occupied by carriers at different times.

[0148] The quantitative simulation module 60 is used to substitute the concentration of deep-level defects occupied by charge carriers at different times into the theoretical formula of the DLTS output signal to obtain a quantitatively simulated DLTS.

[0149] In one embodiment, the determining module 20 includes:

[0150] The type determination unit is used to determine the defect type in the annealing simulation based on the irradiation defect property parameters, including all intrinsic point defects and defect clusters with binding energy greater than 1.0 eV;

[0151] The reaction path determination unit is used to determine the reaction path between defects based on the criterion that the difference between the defect formation energy before and after the reaction is greater than 1.0 eV.

[0152] In one embodiment, the mathematical form of the defect rate equation based on SRH theory is:

[0153]

[0154] Where t is time; A deep-level defect X that carries a charge of j-1 or j+1 due to being occupied by electrons or holes; For a given temperature T, at time t, the deep-level defect occupied by electrons or holes. The concentration; Let T be the thermal velocity of electrons or holes at temperature T. For cascaded charged defects X j The cross section that traps electrons or holes at temperature T; n e / h The concentration of electrons or holes; Let X be the deep-level defect occupied by electrons or holes at time t at temperature T. j Concentration of N; C / V (T) represents the effective density of states at temperature T, either at the bottom of the conduction band or the top of the valence band. For charged deep-level defects at temperature T The activation energy for emitting electrons or holes to the bottom of the conduction band / top of the valence band; k B is the Boltzmann constant.

[0155] In one embodiment, the solving module 50 is specifically used to perform the following steps:

[0156] (a) Based on the type and concentration information of the surviving defects, construct a list of deep-level defects to be simulated and determine the temperature range for simulating DLTS, wherein the defects in the list of deep-level defects to be simulated are defects that survive after annealing and contribute defect energy levels to the band gap.

[0157] (b) Calculate the thermal velocity of charge carriers at different temperatures within the stated temperature range. And the effective density of states N at the bottom of the conduction band or the top of the valence band of a semiconductor C / V (T).

[0158] (c) Read a defect level from the list of deep-level defect levels to be simulated, and input the carrier trapping cross section and the activation energy of carrier emission at different temperatures of the defect level.

[0159] (d) Using the concentration information as the initial concentration of deep-level defects occupied by charge carriers, and setting the initial concentration of deep-level defects not occupied by charge carriers, the open-source differential equation solver lsoda is used to solve the defect rate equations based on SRH theory corresponding to the defect energy levels read in at different temperatures within the temperature range from low temperature to high temperature, so as to obtain the concentration of deep-level defects occupied by charge carriers at different times at different temperatures.

[0160] Repeat steps (c) and (d) until all the defect rate equations based on SRH theory corresponding to all defect levels in the list of deep-level defect energy levels to be simulated are solved.

[0161] In one embodiment, the theoretical formula for the DLTS output signal is:

[0162] or

[0163]

[0164] Where, ΔC ± (T) represents the junction capacitance at different temperatures when the deep level defect is a minority carrier trap or a majority carrier trap. C0 represents the junction capacitance when there is no deep level defect. These represent the deep-level defect concentrations occupied by charge carriers at two different times, t1 and t2, at different temperatures. For a pn junction, N... dop The doping concentration is for the shallowly doped side; for a Schottky junction, N dopThis refers to the doping concentration on one side of the semiconductor. Existing methods and techniques can only qualitatively simulate DLTS based on defect energy levels and carrier trapping cross-sections obtained from DFT calculations, giving the peak positions of specific micro-defects. It is difficult to determine the micro-defect types corresponding to the complex and coupled DLTS signals in irradiated semiconductors. This embodiment employs a multi-scale simulation method. First, atomic-scale methods such as DFT are used to obtain the basic properties of irradiated defects. Then, MC and OKMC methods are used to simulate defect annealing to obtain the concentration of surviving defects after annealing. Next, the defect rate equation based on SRH theory is calculated to quantitatively simulate DLTS. The method in this embodiment can provide the micro-defect types corresponding to different DLTS signals, the relative intensities of DLTS signals for different defects, and the proportion of different defects in the coupled DLTS signals.

[0165] It should be noted that other embodiments or implementation methods of the quantitative simulation system for the transient spectrum of irradiated semiconductor deep energy levels described in this invention can refer to the above-described method embodiments, and will not be repeated here.

[0166] It should be noted that the logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0167] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0168] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0169] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0170] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A quantitative simulation method for the transient spectrum of deep energy levels in an irradiated semiconductor, characterized in that, The method includes: Obtain the property parameters of semiconductors and their irradiation defect property parameters; Based on the irradiation defect property parameters, the defect types and reaction paths between defects are determined in the annealing simulation; Using the semiconductor's property parameters and the PKA energy spectrum caused by irradiation as input conditions, the spatial distribution of initial point defects is obtained by MC method simulation; Using the spatial distribution of the initial point defects as the initial condition, and the irradiation defect property parameters and the reaction paths between the defects as inputs, the OKMC method is used to simulate and obtain the type and concentration information of surviving defects after annealing. Using the property parameters and concentration information of the surviving defects as input, the defect rate equation based on SRH theory is solved to obtain the deep level defect concentration occupied by carriers at different times, including: (a) constructing a list of deep level defect energy levels to be simulated according to the type and concentration information of the surviving defects, and determining the temperature range for simulating DLTS, wherein the defects in the list of deep level defect energy levels to be simulated are defects that survive after annealing and contribute defect energy levels in the band gap; (b) Calculate the thermal velocity of charge carriers at different temperatures within the stated temperature range. And the effective density of states N at the bottom of the conduction band or the top of the valence band of a semiconductor C / V (T); where the thermal velocity of charge carriers at different temperatures within the temperature range. The calculation formula is: The effective state density N at the bottom of the semiconductor conduction band or the top of the valence band C / V The formula for calculating (T) is: in, The effective mass of an electron or hole; h is Planck's constant; (c) Read a defect level from the list of deep-level defect levels to be simulated, and input the carrier trapping cross section and the activation energy of carrier emission at different temperatures for the defect level; (d) Using the concentration information as the initial concentration of deep-level defects occupied by charge carriers, and setting the initial concentration of deep-level defects not occupied by charge carriers, the open-source differential equation solver lsoda is used to solve the defect rate equation based on SRH theory corresponding to the defect energy levels read in at different temperatures within the temperature range, from low temperature to high temperature, to obtain the concentration of deep-level defects occupied by charge carriers at different times at different temperatures; wherein, the mathematical form of the defect rate equation based on SRH theory is: Where t is time; A deep-level defect X that carries a charge of j-1 or j+1 due to being occupied by electrons or holes; For a given temperature T, at time t, the deep-level defect occupied by electrons or holes. The concentration; Let T be the thermal velocity of electrons or holes at temperature T. X, a cascaded charged defect j The cross section that traps electrons or holes at temperature T; n e / h The concentration of electrons or holes; N Xj (t,T) represents the deep-level defect X occupied by electrons or holes at time t, at temperature T. j Concentration of N; C / V (T) represents the effective density of states at temperature T, either at the bottom of the conduction band or the top of the valence band. For charged deep-level defects at temperature T The activation energy for emitting electrons or holes to the bottom of the conduction band / top of the valence band; k B Boltzmann's constant; Repeat steps (c) and (d) until all the defect rate equations based on SRH theory corresponding to all defect levels in the list of deep-level defect energy levels to be simulated are solved. By substituting the concentration of deep-level defects occupied by charge carriers at different times into the theoretical formula of the DLTS output signal, a quantitatively simulated DLTS can be obtained.

2. The quantitative simulation method for the transient spectrum of deep energy levels of an irradiated semiconductor as described in claim 1, characterized in that, The irradiation defect property parameters include defect formation energy, migration energy, energy level position, carrier trapping cross section, and binding energy. Determining the defect type and reaction pathways between defects in the annealing simulation based on these irradiation defect property parameters includes: Based on the aforementioned irradiation defect property parameters, the defect types in the annealing simulation are determined to include all intrinsic point defects and defect clusters with binding energy greater than 1.0 eV. Based on the criterion that the difference between the defect formation energy before and after the reaction is greater than 1.0 eV, the reaction pathway between defects is determined.

3. The quantitative simulation method for the transient spectrum of deep energy levels of an irradiated semiconductor as described in claim 1, characterized in that, The theoretical formula for the DLTS output signal is: Where, ΔC ± (T) represents the junction capacitance at different temperatures when the deep level defect is a minority carrier trap or a majority carrier trap; C0 represents the junction capacitance without deep level defects. These represent the deep-level defect concentrations occupied by charge carriers at two different times, t1 and t2, at different temperatures; for the pn junction, N... dop The doping concentration is for the shallowly doped side; for a Schottky junction, N dop This represents the doping concentration on one side of the semiconductor.

4. A quantitative simulation system for the transient spectrum of deep energy levels in an irradiated semiconductor, characterized in that, The system includes: The acquisition module is used to acquire the property parameters of semiconductors and their irradiation defect property parameters. The determination module is used to determine the defect type and reaction path between defects in the annealing simulation based on the irradiation defect property parameters; The first simulation module is used to simulate the spatial distribution of initial point defects using the semiconductor's property parameters and the PKA energy spectrum caused by irradiation as input conditions and the MC method. The second simulation module is used to simulate and obtain the type and concentration information of surviving defects after annealing using the spatial distribution of the initial point defects as the initial condition, the irradiation defect property parameters and the reaction path between the defects as input, and the OKMC method. The solution module is used to solve the defect rate equation based on SRH theory with the property parameters and concentration information of the surviving defects as input, and to obtain the deep level defect concentration occupied by carriers at different times. Specifically, it includes: (a) constructing a list of deep level defect energy levels to be simulated according to the type and concentration information of the surviving defects, and determining the temperature range for simulating DLTS, wherein the defects in the list of deep level defect energy levels to be simulated are defects that survive after annealing and contribute defect energy levels in the band gap; (b) Calculate the thermal velocity of charge carriers at different temperatures within the stated temperature range. And the effective density of states N at the bottom of the conduction band or the top of the valence band of a semiconductor C / V (T); where the thermal velocity of charge carriers at different temperatures within the temperature range. The calculation formula is: The effective state density N at the bottom of the semiconductor conduction band or the top of the valence band C / V The formula for calculating (T) is: in, The effective mass of an electron or hole; h is Planck's constant; (c) Read a defect level from the list of deep-level defect levels to be simulated, and input the carrier trapping cross section and the activation energy of carrier emission at different temperatures for the defect level; (d) Using the concentration information as the initial concentration of deep-level defects occupied by charge carriers, and setting the initial concentration of deep-level defects not occupied by charge carriers, the open-source differential equation solver lsoda is used to solve the defect rate equation based on SRH theory corresponding to the defect energy levels read in at different temperatures within the temperature range, from low temperature to high temperature, to obtain the concentration of deep-level defects occupied by charge carriers at different times at different temperatures; wherein, the mathematical form of the defect rate equation based on SRH theory is: Where t is time; A deep-level defect X that carries a charge of j-1 or j+1 due to being occupied by electrons or holes; For a given temperature T, at time t, the deep-level defect occupied by electrons or holes. The concentration; Let T be the thermal velocity of electrons or holes at temperature T. For cascaded charged defects X j The cross section that traps electrons or holes at temperature T; n e / h The concentration of electrons or holes; Let X be the deep-level defect occupied by electrons or holes at time t at temperature T. j Concentration of N; C / V (T) represents the effective density of states at temperature T, either at the bottom of the conduction band or the top of the valence band. For charged deep-level defects at temperature T The activation energy for emitting electrons or holes to the bottom of the conduction band / top of the valence band; k B Boltzmann's constant; Repeat steps (c) and (d) until all the defect rate equations based on SRH theory corresponding to all defect levels in the list of deep-level defect energy levels to be simulated are solved. The quantitative simulation module is used to substitute the concentration of deep-level defects occupied by charge carriers at different times into the theoretical formula of the DLTS output signal to obtain a quantitatively simulated DLTS.

5. The quantitative simulation system for the transient spectrum of deep energy levels of irradiated semiconductors as described in claim 4, characterized in that, The determining module includes: The type determination unit is used to determine the defect type in the annealing simulation based on the irradiation defect property parameters, including all intrinsic point defects and defect clusters with binding energy greater than 1.0 eV; The reaction path determination unit is used to determine the reaction path between defects based on the criterion that the difference between the defect formation energy before and after the reaction is greater than 1.0 eV.

6. The quantitative simulation system for the transient spectrum of deep energy levels of irradiated semiconductors as described in claim 4, characterized in that, The theoretical formula for the DLTS output signal is: Where, ΔC ± (T) represents the junction capacitance at different temperatures when the deep level defect is a minority carrier trap or a majority carrier trap; C0 represents the junction capacitance without deep level defects. These represent the deep-level defect concentrations occupied by charge carriers at two different times, t1 and t2, at different temperatures; for the pn junction, N... dop The doping concentration is for the shallowly doped side; for a Schottky junction, N dop This represents the doping concentration on one side of the semiconductor.

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