Semiconductor defect transition level evaluation method based on finite temperature kinetic sampling

Abstract

The application discloses a semiconductor defect transition energy level evaluation method based on limited temperature dynamics sampling, and relates to the technical field of semiconductor material calculation and performance evaluation. A supercell model containing a target point defect is constructed, and structural relaxation under the 0K limit is performed to obtain an equilibrium state structure. A first-principle molecular dynamics simulation of a canonical ensemble is performed at a working temperature, and dynamic trajectories of different charge states are collected. Configuration snapshots extracted from the trajectories are subjected to electrostatic potential alignment correction, and the dynamic correction of the valence band top characteristic energy is performed by using the local electrostatic potential difference of skeleton atoms in a defect-free reference supercell. Then, a multi-state energy difference cross matrix is constructed, and the adiabatic transition free energy between each charge state is solved. Whether an intermediate charge state system needs to be introduced to ensure the calculation accuracy is determined according to the phase space overlap degree. In combination with the dynamic vertical transition energy level and the adiabatic thermodynamic transition energy level, the defect state is determined, and the quantitative screening of the defect is realized.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor material calculation and performance evaluation technology, specifically, it relates to a method for evaluating semiconductor defect transition energy levels based on finite temperature dynamic sampling. Background Technology

[0002] Intrinsic point defects in semiconductor materials introduce defect states within the band gap, which act as recombination centers for charge carriers, thus directly determining the photoelectric conversion efficiency and device stability of the material. Therefore, accurately assessing the charge state transition energy levels of defects is a core prerequisite for screening and controlling defects in next-generation semiconductor materials.

[0003] Currently, in industrial R&D and academia, the industry standard method for predicting defect transition energy levels relies on static density functional theory calculations under the 0K limit. With the rapid development of a new generation of optoelectronic semiconductor materials with "soft lattice" properties, the inherent physical limitations of this industry standard method are becoming increasingly prominent when dealing with complex systems with strong electron-phonon coupling and significant room temperature thermal fluctuations. First, static models are difficult to reflect the thermal fluctuations of devices at actual operating temperatures. Soft lattice materials exhibit significant lattice vibrations and continuous configuration evolution such as disordered rotation of organic cations at room temperature, which can lead to dynamic fluctuations in band edges and defect energy levels. Existing static techniques are unable to capture such key physical processes that determine the transient trapping behavior of charge carriers, which can easily cause deviations in the evaluation results. Secondly, the local lattice structure reshaping caused by defects when trapping charge carriers is accompanied by significant charge-lattice coupling, resulting in high lattice relaxation energy and configuration entropy change. Due to the lack of multi-state phase space sampling capability at finite temperatures, existing technologies have difficulty in quantitatively analyzing the entropy change contribution, which can easily lead to misjudgment when determining the deep and shallow energy level characteristics of materials at service temperatures. In addition, the few traditional thermodynamic integration methods that attempt to calculate the free energy at finite temperatures have strong path dependence, and often face problems of convergence difficulties and excessive computational resource consumption when dealing with large-scale atomic rearrangements.

[0004] To address the aforementioned issues, this invention proposes a semiconductor defect transition energy level evaluation method based on finite temperature dynamic sampling. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a semiconductor defect transition energy level evaluation method based on finite-temperature kinetic sampling, which solves the problem that existing technologies are unable to accurately evaluate semiconductor defect charge state transition energy levels at finite temperatures.

[0006] The objective of this invention can be achieved through the following technical solutions: A semiconductor defect transition energy level evaluation method based on finite-temperature kinetic sampling, the method comprising: Step 1: Construct a supercell model of the semiconductor material containing the target intrinsic point defect. Under the 0K limit, perform full relaxation optimization of the cell parameters and atomic coordinates of the supercell structure of the initial charge state and at least one target charged state to obtain the equilibrium structure. Step 2: Using the equilibrium structure as the initial state, perform ab initio molecular dynamics simulations based on the operating temperature and canonical ensemble with a preset thermal equilibrium relaxation time, and collect the dynamic trajectories of the initial charge state and each target charged state. Step 3: Extract multi-frame configuration snapshots of the dynamic trajectory, and apply electrostatic potential alignment correction to the configuration snapshots of the target charged state in each frame to eliminate the finite size effect introduced by the periodic boundary conditions. By utilizing the difference between the spatial average of the local electrostatic potential of selected framework atoms in a defect-free reference supercell and the 0K limit, the valence band top characteristic energy of each frame configuration snapshot is dynamically corrected to obtain the valence band top characteristic energy at a finite temperature. Step 4: Calculate the potential energy of all targets under charged states for each frame configuration snapshot. After electrostatic potential alignment correction and dimensionless processing by dividing by thermal energy factor, construct the multi-state energy difference cross matrix, solve the dimensionless free energy difference between the charge state systems corresponding to each target charged state, and obtain the adiabatic transition free energy of each target charged state. Step 5: Calculate the phase space overlap matrix between all-charge ensembles and determine whether the overlap between adjacent charge ensembles is lower than a preset threshold. If so, an intermediate charge state ensemble with an intermediate charge value is introduced between the corresponding adjacent charge states, and its dynamic trajectory and snapshot are supplemented to re-execute the free energy calculation until the overlap between all adjacent charge state ensembles is not lower than the preset threshold, and the final adiabatic transformation free energy is output; otherwise, it is output directly. Step 6: Using the statistical average value of the instantaneous energy difference distribution between the target charge state and the initial charge state calculated under the initial charge state equilibrium trajectory, determine the dynamic vertical transition energy level at the operating temperature; using the adiabatic transition free energy, combined with the valence band top position of the semiconductor material at the operating temperature, determine the adiabatic thermodynamic transition energy level. Based on the position of the adiabatic thermodynamic transition energy level relative to the band edge of the semiconductor material, it is determined whether the defect is a dynamically activated recombination center or a dynamically passivated state at the operating temperature, thus completing the quantitative screening of defects in the semiconductor material.

[0007] As a further aspect of the present invention, the specific method for constructing the semiconductor material supercell model containing the target intrinsic point defect in step 1 is as follows: Identify the semiconductor material to be evaluated, denoted as Q; The original unit cell of semiconductor material Q is expanded in three dimensions by a predetermined integer multiple to lock the target intrinsic point defects associated with semiconductor material Q, including vacancy defects, interstitial defects and antisite defects, and to construct the semiconductor material supercell model QM associated with semiconductor material Q. The vacancy defect is defined as the absence of an atom at a lattice position, the interstitial defect is defined as the presence of an atom in the gap between lattice positions, and the antisite defect is defined as the lattice position of one intrinsic atom occupying the position of another intrinsic atom. The plane wave pseudopotential method based on density functional theory is used to perform full relaxation optimization of cell parameters and atomic coordinates in the supercell model QM of semiconductor materials under the 0K limit for the target intrinsic point defects in the initial charge state and at least one target charged state, so as to obtain the equilibrium structure GQM.

[0008] As a further aspect of the present invention, the specific method for collecting the dynamic trajectories of the initial charge state and each target charged state in step 2 is as follows: The equilibrium structure GQM was extracted as the initial state, and a preset operating temperature T was introduced. Ab initio molecular dynamics simulation was performed using a canonical ensemble based on the Nosé-Hoover thermostat. Starting from the ab initio molecular dynamics simulation, after reaching the preset thermal equilibrium stage, dynamic trajectories that meet the equilibrium phase space sampling length requirements are collected for the supercell structures of the initial charged state and at least one target charged state. The preset thermal equilibrium stage duration is 5 ps, the equilibrium phase space sampling length requirement duration is 4 ps, and the step size is set to 1 fs, where ps is picosecond and fs is femtosecond.

[0009] As a further aspect of the present invention, in step 3, the specific method for extracting multiple frame configuration snapshots of the dynamic trajectory and applying electrostatic potential alignment correction to each frame configuration snapshot is as follows: The dynamic trajectories of the supercell structure of the initial charge state and at least one target charge state are extracted independently. N frame configuration snapshots are extracted at preset time intervals to eliminate the time correlation between adjacent transient configurations, thus forming a multi-frame configuration snapshot of the initial charge state and each target charge state. Here, N is a preset integer and the preset time interval is 10fs. Dynamic electrostatic potential alignment correction is performed on any extracted frame configuration snapshot, where the correction formula is: E corr =q×(V q,far -V bulk,far ), where E corr V is the electrostatic potential alignment correction energy, q is the net charge of the initial or target charged state associated with the corresponding frame configuration snapshot, and V is the net charge of the initial or target charged state. q,farV represents the local electrostatic potential of a pre-selected framework atom furthest from the defect center in the supercell structure corresponding to the target charged state. bulk,far This represents the reference potential of a pre-selected framework atom in an ideal, defect-free, pure supercell structure in a neutral charge state. Based on electrostatic potential alignment correction energy E corr Dynamic electrostatic potential alignment correction is performed on all extracted frame configuration snapshots.

[0010] As a further aspect of the present invention, in step 3, the specific method for dynamically correcting the valence band top characteristic energy of each frame configuration snapshot to obtain the valence band top characteristic energy at a finite temperature is as follows: Obtain any s-th frame configuration snapshot from the multi-frame configuration snapshots associated with the neutral charge state with net charge q=0 of the defect-free pure supercell, where s is the counting index and 1≤s≤N; The spatially averaged local electrostatic potential of all pre-selected framework atoms within the ideal, defect-free, pure supercell structure under the s-th frame configuration snapshot is obtained by taking the spatial arithmetic mean, denoted as V. ~s bulk,ref ; The spatially averaged local electrostatic potential V ~s bulk,ref The average electrostatic potential V, calculated by spatial arithmetic averaging of the local electrostatic potentials of all pre-selected framework atoms within an ideal, defect-free, pure supercell structure optimized under static full relaxation at the 0K limit, is the same as the average electrostatic potential V. ~0K bulk,ref After interpolation, the original valence band top eigenenergy of the s-th frame configuration snapshot is dynamically corrected using the following formula: ε s VBM,corr =ε s VBM,raw -(V ~s bulk,ref -V ~0K bulk,ref ); Where, ε s VBM,corr ε represents the valence band top characteristic energy at a finite temperature in the s-th frame configuration snapshot after dynamic reconstruction correction. s VBM,raw This represents the uncorrected valence band top eigenvalue extracted directly from the configuration snapshot of frame s using first-principles calculations; Similarly, by determining the valence band peak eigenenergy at finite temperature for all frame configuration snapshots, and taking the ensemble average, the average valence band peak position at finite temperature is obtained, denoted as <ε. VBM > V,T .

[0011] As a further aspect of the present invention, in step 4, the specific method for calculating the dimensionless free energy difference between the charge states corresponding to each target charged state to obtain the adiabatic transition free energy of each target charged state is as follows: Multiple configuration snapshots are extracted from the dynamic trajectory of any target charged state j. Under non-relaxation conditions, the potential energy of these multiple configuration snapshots under all target charged states i is calculated using single-point energy from density functional theory. An electrostatic potential alignment correction is then applied, and the resulting absolute potential energy is divided by the thermal energy factor k at the current service temperature. B T is processed to be dimensionless to obtain dimensionless potential energy, which is constructed as a multi-state energy difference cross matrix. In this matrix, the target charged state j and the target charged state i independently traverse all charge state ensembles involved in the calculation. i and j are both greater than or equal to 1 and less than or equal to M, where M is the total number of target charged states. By employing the multistate Bennett acceptor ratio equation, the dimensionless free energy difference between the systems of different charge states is self-consistently solved, specifically as follows:

[0012] By iteratively converging and solving the nonlinear equations, the dimensionless free energy between the charged states of each target can be directly calculated, and then multiplied by the thermal energy factor k at the current service temperature. B T, reduce the adiabatic transformation free energy with physical dimensions to calculate, denoted as ΔF; in, Let be the dimensionless free energy of the target charged state i. =F i / k B T,k B Where F is Boltzmann's constant, T is absolute temperature, and F is... i Let i be the actual Helmholtz free energy under the target charged state i; The N j x is the total number of frame configuration snapshots extracted from the target charged state j. jn This is the nth frame configuration snapshot extracted from the target charged state j, where n is the counting index, 1≤n≤N. j K is the counting index, 1≤K≤M; The u i (x jn ) is a configuration snapshot x jn Under the target charged state i, apply electrostatic potential alignment correction and divide by the thermal energy factor k. B The dimensionless potential energy obtained after T.

[0013] As a further aspect of the present invention, in step 5, the specific method for outputting the final adiabatic transformation free energy is as follows: Extract all target charged states R, calculate the phase space overlap matrix O between the ensembles of all target charged states, and its matrix element O i,i+1 This represents the statistical distribution overlap of all frame configuration snapshots of the i-th target charged state ensemble and the (i+1)-th target charged state ensemble in the microconfiguration phase space; The minimum phase space overlap threshold between adjacent target charged state ensembles is set to 0.03. Traverse all matrix elements O i,i+1 If the overlap is greater than or equal to the minimum phase space overlap critical threshold of 0.03, the final adiabatic transformation free energy ΔF is directly output. If the overlap is less than the minimum phase space overlap threshold of 0.03, then a net charge of q is introduced between the i-th and (i+1)-th target charged states. mid =(q i +q i+1 The new intermediate charge state ensemble of q / 2 completes the intermediate state supplementation step, where q i q i+1 These are the net charge amounts of the i-th and (i+1)-th target charged states, respectively; Similarly, in ascending order of charge, the same processing is performed on all matrix elements. For all the new intermediate charge states introduced, dynamic trajectories and multi-frame configuration snapshots are obtained and incorporated into the multi-state energy difference cross matrix. The adiabatic transformation free energy solution is then re-executed, and the phase space overlap matrix O is recalculated. Repeat the above overlap verification and intermediate state supplementation steps until the overlap of all adjacent matrix elements in the phase space overlap matrix O is greater than or equal to 0.03, and output the final adiabatic transformation free energy ΔF.

[0014] As a further aspect of the present invention, in step 6, the specific method for determining the dynamic vertical transition energy level at the operating temperature using the statistical average value of the instantaneous energy difference distribution of the defect charge state calculated under the initial charge state equilibrium trajectory is as follows: Extract the dynamic trajectory of the target intrinsic point defect under the initial charge state q and mark it as the equilibrium trajectory; Calculate the instantaneous energy difference distribution of the defect charge states, statistically average its value, and output the dynamic vertical transition energy level ε at the operating temperature T. vert (q / q'), specifically:

[0015] Where, ε vert (q / q') represents the dynamic vertical transition energy level of the target intrinsic point defect from the initial charge state q to the final charge state q'; This represents the ensemble statistical average of the equilibrium trajectory based on the initial charge state q; E tot (X q ) and E tot (X q' ) represent the total energy of the initial charge state q and the unrelaxed single-point energy calculated by directly assigning the final charge state q' under the frozen lattice configuration, respectively; E corr q With E corr q' This is a finite-size electrostatic potential correction term used to eliminate periodic spurious interactions under the corresponding charge state; q'-q represents the change in charge before and after the transformation; <ε VBM > V,T is the ensemble statistical average of the valence band top characteristic energy of an ideal, defect-free, pure supercell structure at a finite temperature, used to align the calculation results with the material band edge, where the finite temperature corresponds to the operating temperature T.

[0016] As a further aspect of the present invention, in step 6, the specific method for determining the adiabatic thermodynamic transition energy level by utilizing the adiabatic transition free energy and combining it with the valence band top position of the semiconductor material at the operating temperature is as follows: Based on the steps described in step 4, the adiabatic transition free energy ΔF(q->q') from q to q' is analyzed, and the adiabatic thermodynamic transition energy level ε is determined by combining the position of the valence band top of the semiconductor material at the operating temperature T. dyn (q / q'), specifically:

[0017] Where, ε dyn (q / q') is the adiabatic thermodynamic transition energy level of the target intrinsic point defect from the initial charge state q to the final charge state q'; F(X q ) and F(X q' ) represent the Helmholtz free energies of the supercell structure of the target intrinsic point defect after finite-temperature fully dynamic lattice relaxation, under the initial charge state q and the final charge state q'.

[0018] As a further aspect of the present invention, the specific method for quantitatively screening defects in semiconductor materials in step 6 is as follows: Extracting the adiabatic thermodynamic transformation energy level ε dyn (q / q'), and calculate its energy difference with the nearest band edge; If ε dynIf (q / q') is greater than 0.15 eV from the nearest band edge at the operating temperature, then the adiabatic thermodynamic transition energy level ε is determined. dyn (q / q') is located deep within the band gap at actual temperatures; The output determines whether the current target intrinsic point defect is dynamically activated as a composite center at the operating temperature. If the adiabatic thermodynamic transformation energy level ε dyn If the difference between (q / q') dynamically drifting out of the band gap or the nearest band edge is less than or equal to 0.15 eV, it is considered dynamic passivation.

[0019] The beneficial effects of this invention are: This invention addresses the problem of insufficient sampling and difficulty in convergence of traditional integral algorithms under large-scale lattice distortion by employing a unique phase space overlap adaptive verification and intermediate state supplementation mechanism, while simultaneously solving the static energy level distortion problem. This allows the thermodynamic analysis of complex defects to be freed from the path dependence limitation of non-adiabatic evolution. Frame-by-frame dynamic electrostatic potential alignment correction eliminates local electrostatic noise and background potential drift during evolution, making first-principles defect calculations more applicable to flexible semiconductors with "soft lattice" properties. Furthermore, by using finite-temperature phase space trajectory sampling instead of traditional absolute zero-degree single-point optimization, it accurately captures the configuration entropy change and dynamic lattice relaxation energy of materials at service temperatures, providing a high-precision quantitative evaluation basis for the composition engineering optimization and defect tolerance screening of next-generation optoelectronic materials. Attached Figure Description

[0020] The invention will now be further described with reference to the accompanying drawings.

[0021] Figure 1 This is a flowchart illustrating the method described in this invention; Figure 2 This is a diagram showing the temporal evolution of potential energy and the phase space overlap matrix under each charge state trajectory in Embodiment 4 of the present invention. Figure 3 This is a diagram showing the energy level distribution of typical intrinsic point defects such as iodine interstitial Ii, iodine vacancy VI, and lead vacancy VPb in the three halide perovskite systems of methylamine lead iodine (MAPbI3), formamidinium lead iodine (FAPbI3), and cesium lead iodine (CsPbI3) under different calculation methods in Example 5 of the present invention. Figure 4 This is a histogram comparing the relaxation energies of typical defects in three halide perovskite materials in Example 5 of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and 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.

[0023] like Figure 1 As shown, this application provides a semiconductor defect transition energy level evaluation method based on finite-temperature kinetic sampling, aiming to solve the technical problem that traditional static approximation methods cannot accurately evaluate the dynamic behavior and energy level positions of defects at operating temperatures. By integrating ab initio molecular dynamics sampling, dynamic electrostatic potential alignment correction, multistate free energy calculation, and phase space overlap determination, it achieves accurate prediction of the thermodynamic transition energy levels and dynamic vertical transition energy levels of intrinsic point defects in semiconductor materials at finite temperatures, thus providing a reliable theoretical basis for quantitative defect screening and device performance optimization.

[0024] As an embodiment 1 of this application, it specifically includes: Step 1: Construct a supercell model of the semiconductor material containing the target intrinsic point defect. Under the 0K limit, perform full relaxation optimization of the cell parameters and atomic coordinates of the supercell structure of the initial charge state and at least one target charged state to obtain the equilibrium structure. Step 2: Using the equilibrium structure as the initial state, perform ab initio molecular dynamics simulations based on the operating temperature and canonical ensemble with a preset thermal equilibrium relaxation time, and collect the dynamic trajectories of the initial charge state and each target charged state. Step 3: Extract multi-frame configuration snapshots of the dynamic trajectory, and apply electrostatic potential alignment correction to the configuration snapshots of the target charged state in each frame to eliminate the finite size effect introduced by the periodic boundary conditions. By utilizing the difference between the spatial average of the local electrostatic potential of selected framework atoms in a defect-free reference supercell and the 0K limit, the valence band top characteristic energy of each frame configuration snapshot is dynamically corrected to obtain the valence band top characteristic energy at a finite temperature. Step 4: Calculate the potential energy of all targets under charged states for each frame configuration snapshot. After electrostatic potential alignment correction and dimensionless processing by dividing by thermal energy factor, construct the multi-state energy difference cross matrix, solve the dimensionless free energy difference between the charge state systems corresponding to each target charged state, and obtain the adiabatic transition free energy of each target charged state. Step 5: Calculate the phase space overlap matrix between all-charge ensembles and determine whether the overlap between adjacent charge ensembles is lower than a preset threshold. If so, an intermediate charge state ensemble with an intermediate charge value is introduced between the corresponding adjacent charge states, and its dynamic trajectory and snapshot are supplemented to re-execute the free energy calculation until the overlap between all adjacent charge state ensembles is not lower than the preset threshold, and the final adiabatic transformation free energy is output; otherwise, it is output directly. Step 6: Using the statistical average value of the instantaneous energy difference distribution between the target charge state and the initial charge state calculated under the initial charge state equilibrium trajectory, determine the dynamic vertical transition energy level at the operating temperature; using the adiabatic transition free energy, combined with the valence band top position of the semiconductor material at the operating temperature, determine the adiabatic thermodynamic transition energy level. Based on the position of the adiabatic thermodynamic transition energy level relative to the band edge of the semiconductor material, it is determined whether the defect is a dynamically activated recombination center or a dynamically passivated state at the operating temperature, thus completing the quantitative screening of defects in the semiconductor material.

[0025] Example 2

[0026] This embodiment is based on Embodiment 1, using silicon (Si), a semiconductor material widely used in power devices, as the object, to evaluate one of the most important intrinsic point defects: silicon vacancies V_Si, at an operating temperature of 300K, specifically as follows: First, a supercell model of the semiconductor material containing the target intrinsic point defect is constructed.

[0027] Specifically, the semiconductor material to be evaluated was identified as silicon.

[0028] By expanding the original diamond structure unit cell of silicon by a factor of 2 in each of the three dimensions, a silicon supercell model containing 64 atoms was constructed: a 2×2×2 supercell.

[0029] Remove a silicon atom from the silicon supercell model to construct a silicon vacancy V_Si defect.

[0030] Using the plane wave pseudopotential method based on density functional theory, we perform full relaxation optimization on supercell structures with defects in the initial charge state (q=0), a positive charge state (q=+1), and a negative charge state (q=-1) under the 0K limit.

[0031] The optimization process allows for full relaxation of the cell parameters and all atomic coordinates until the Hermann-Feynman force on each atom is less than 0.01 eV / Å, and the energy converges to 1 × 10⁻⁶. -5 eV, thus obtaining the equilibrium structure under three charge states, denoted as X, respectively. 0 X +1 X -1 .

[0032] The equilibrium structure X obtained above 0 X +1 X-1 For the initial state of each dynamic simulation, the operating temperature T = 300K is introduced.

[0033] Ab initio molecular dynamics simulations were performed using a canonical ensemble based on the Nosé-Hoover thermostat, with the thermostat time constant set to 100 fs.

[0034] Each ab initio molecular dynamics simulation first runs for 5 picoseconds (ps) to allow the system to reach thermal equilibrium. Then, dynamic trajectories are collected for the supercell structures of the initial charge state, +1 valence state, and -1 valence state, respectively, with a collection time of 4 picoseconds. The integration step size of the ab initio molecular dynamics simulation is set to 1 femtosecond (fs), so a total of 4000 configuration snapshots are collected for each charge state. From the dynamic trajectories of the three charge states collected above, configuration snapshots are extracted at fixed time intervals of 10 fs. For a 4 ps trajectory, N = 400 configuration snapshots are extracted for each charge state to form their respective ensembles. For each extracted frame of configuration snapshot, a dynamic electrostatic potential alignment correction is performed. The correction formula is: E corr =q×(V q,far -V bulk,far ).

[0035] Where q is the net charge of the charge state corresponding to the frame configuration snapshot; V q,far To select the average local electrostatic potential of the eight framework silicon atoms farthest from the defect center in the supercell structure of this frame band defect; V bulk,far To calculate the electrostatic potential alignment correction energy E for the reference potential of the eight silicon atoms at the same spatial position in an ideal, defect-free, pure silicon supercell structure. corr The total energy of the system is used to correct subsequent calculations.

[0036] Meanwhile, the valence band top characteristic energy of each frame configuration snapshot in the dynamic trajectory of a defect-free pure unit cell is dynamically corrected to obtain the valence band top position at a finite temperature.

[0037] For any s-th (1≤s≤N) frame configuration snapshot, first calculate the spatial arithmetic mean of the local electrostatic potential of all pre-selected framework silicon atoms in the ideal defect-free pure supercell structure under that snapshot, for example, the local electrostatic potential of all 64 silicon atoms in the supercell, denoted as V. ~s bulk,ref ; Then, the average electrostatic potential V of the same ideal supercell structure under the 0K limit is calculated. ~0K bulk,ref The difference.

[0038] Finally, the original valence band eigenvalues ​​are corrected using the following formula: εs VBM,corr =ε s VBM,raw -(V ~s bulk,ref -V ~0K bulk,ref ).

[0039] The ensemble average of the corrected valence band top energy across all frames yields the average valence band top position <ε at 300K. VBM > V,T .

[0040] For the three target charged states of initial charge state 0, +1 and -1, the potential energy of each frame configuration in all three charge states is calculated from their respective 400 frame configuration snapshots without structural relaxation, using the single-point energy of density functional theory.

[0041] The calculated potential energy is applied to the electrostatic potential alignment correction E. corr The resulting absolute potential energy is then divided by the thermal energy factor at the current service temperature to obtain dimensionless potential energy. This constructs a polymorphic energy cross matrix of size 3×(400+400+400)=3×1200.

[0042] Multiple configuration snapshots are extracted from the dynamic trajectory of any target charged state j. Under non-relaxation conditions, the potential energy of these multiple configuration snapshots under all target charged states i is calculated using single-point energy from density functional theory. An electrostatic potential alignment correction is then applied, and the resulting absolute potential energy is divided by the thermal energy factor k at the current service temperature. B T is processed to be dimensionless to obtain dimensionless potential energy, which is constructed as a multi-state energy difference cross matrix. In this matrix, the target charged state j and the target charged state i independently traverse all charge state ensembles involved in the calculation. i and j are both greater than or equal to 1 and less than or equal to M, where M is the total number of target charged states. The dimensionless free energy difference between systems with different charge states is solved using the Bennett acceptor ratio equation for multistate systems by solving the following set of nonlinear equations:

[0043] By iteratively converging and solving the nonlinear equations, the dimensionless free energy between the charged states of each target can be directly calculated, and then multiplied by the thermal energy factor k at the current service temperature. B T, reduce the adiabatic transformation free energy with physical dimensions to calculate, denoted as ΔF; in, The dimensionless free energy of the target charged state i =F i / kB T,k B Where F is Boltzmann's constant, T is absolute temperature, and F is... i Let i be the actual Helmholtz free energy under the target charged state i; The N j x is the total number of frame configuration snapshots extracted from the target charged state j. jn This is the nth frame configuration snapshot extracted from the target charged state j, where n is the counting index, 1≤n≤N. j K is the counting index, 1≤K≤M; The u i (x jn ) is a configuration snapshot x jn Under the target charged state i, apply electrostatic potential alignment correction and divide by the thermal energy factor k. B The dimensionless potential energy obtained after T; Through self-consistent iteration, until the change in the dimensionless free energy of the Kth target charged state is less than 1 × 10⁻⁶. -6 After convergence, the adiabatic transition free energy ΔF between the target charged states is obtained. For example, the adiabatic transition free energy ΔF (0→+1) from state 0 to state +1 is obtained.

[0044] Next, the phase space overlap matrix O between the ensembles of the +1, 0, and -1 charge states is calculated, with matrix element O... 1,2 The overlap of the distribution of the +1 valence state and the 0 valence state ensemble in the potential energy space is represented by a threshold value of 0.03 for the minimum phase space overlap.

[0045] According to calculations, O +1,0 =0.15, O 0,-1 =0.22, both greater than the threshold, indicating that the potential energy sampling between adjacent charge states overlaps sufficiently, and there is no need to insert intermediate charge states; therefore, the calculated ΔF(0→+1) and ΔF(0→-1) are directly output as the final adiabatic transformation free energy.

[0046] Then, determine the dynamic vertical transition energy level ε at the operating temperature T. vert (q / q').

[0047] Using the equilibrium dynamic trajectory of the initial charge state (q=0), the instantaneous energy difference of the system transitioning from state 0 to state +1 or -1 in each sampling configuration is calculated, and its average value is statistically analyzed. The calculation formula is as follows:

[0048] Where, ε vert (q / q') represents the dynamic vertical transition energy level of the target intrinsic point defect from the initial charge state q to the final charge state q'; This represents the ensemble statistical average of the equilibrium trajectory based on the initial charge state q; E tot (X q ) and E tot (X q' ) represent the total energy of the initial charge state q and the unrelaxed single-point energy calculated by directly assigning the final charge state q' under the frozen lattice configuration, respectively; E corr q With E corr q' This is a finite-size electrostatic potential correction term used to eliminate periodic spurious interactions under the corresponding charge state; q'-q represents the change in charge before and after the transformation; <ε VBM > V,T is the ensemble statistical average of the valence band top characteristic energy of an ideal, defect-free, pure supercell structure at a finite temperature, used to align the calculation results with the material band edge, where the finite temperature corresponds to the operating temperature T.

[0049] For example, based on the above calculations, for the transition from a state with 0 charge to a state with +1 charge, q=0, q'=+1, the calculated dynamic vertical transition energy level ε vert (q / q') is the vertical excitation energy required for an electron to be excited from the defect energy level to the conduction band or valence band.

[0050] Secondly, determine the adiabatic thermodynamic transition energy level ε. dyn (q / q'), adiabatic transformation free energy ΔF (0→+1), and the calculated finite temperature valence band top position <ε VBM > V,T The calculation formula is as follows:

[0051] Where, ε dyn (q / q') is the adiabatic thermodynamic transition energy level of the target intrinsic point defect from the initial charge state q to the final charge state q'; F(X q ) and F(X q' ) represent the Helmholtz free energies of the supercell structure of the target intrinsic point defect after finite-temperature fully dynamic lattice relaxation, under the initial charge state q and the final charge state q'.

[0052] ε is obtained by calculation using the above formula. dyn (0 / +1) and ε dyn (0 / -1); Finally, the quantitative screening of defects was completed, and the adiabatic thermodynamic transition energy level ε was analyzed and calculated.dyn (0 / +1) is the position relative to the nearest band edge of the silicon material.

[0053] If ε dyn If the distance (0 / +1) from the top of the valence band or the bottom of the conduction band is greater than 0.15 eV, then the silicon vacancy V_Si is determined to be a dynamically activated recombination center at the operating temperature of 300K, which means that it will significantly promote nonradiative recombination and is harmful to device performance.

[0054] If the energy level dynamically drifts out of the band gap or close to the nearest band edge, such as less than 0.1 eV, it is determined to be a dynamic passivation state. In this embodiment, the ε of the silicon vacancy at 300 K is... dyn (0 / +1) is located deep in the band gap and is therefore identified as a dynamically activated recombination center.

[0055] Example 3

[0056] This embodiment differs from Embodiment 2 in that the evaluation object is the nitrogen vacancy defect V_N in gallium nitride (GaN), the operating temperature is 500K, and an intermediate state replenishment mechanism is triggered in step 5, as detailed below: Due to the significant charge-state dependent local relaxations of different positively charged states, the atomic configurations of the +3 and +2 valence states of the V_N defect differ greatly at 500K, resulting in extremely low phase space overlap. After completing step 4 and constructing the overlap matrix O, the overlap O between the +3 and +2 valence states was calculated and found to be... +3,+2 It is only 0.005, far below the preset critical threshold of 0.03.

[0057] Therefore, the result in step 5 is that a new intermediate charge state needs to be introduced between the +3 valence state (q1=+3) and the +2 valence state (q2=+2).

[0058] According to the formula q_mid=(q1+q2) / 2, the net charge of the new charge state is calculated to be q_mid=(3+2) / 2=+2.5, thus introducing the +2.5 valence state.

[0059] The data of the newly added +2.5 valence state ensemble are incorporated into the original polymorphic energy difference cross matrix, and the polymorphic Bennett acceptor ratio equation is re-executed. This process is iterated, and the overlap of the new adjacent states (+3 and +2.5, +2.5 and +2) is checked again until the overlap of all adjacent matrix elements reaches 0.03 or above. The final output adiabatic transition free energy ΔF(+3→+2) has higher statistical reliability and calculation accuracy.

[0060] This embodiment effectively solves the problem of non-convergence of the multi-state Bennett acceptor ratio equation or inaccurate calculation of free energy caused by insufficient sampling by dynamically inserting intermediate charge states between charge states with insufficient phase space overlap, thereby improving the robustness and accuracy of the assessment of high charge state defect energy levels in wide bandgap semiconductors.

[0061] Example 4

[0062] This embodiment, based on the above embodiments, provides a semiconductor defect transition energy level evaluation method based on finite-temperature kinetic sampling, specifically for the quantitative evaluation of the depth characteristics of lead vacancy VPb defects in methylamine lead iodine (MAPbI3), such as... Figure 2 As shown, the execution process is as follows: Through initial model construction and static pre-optimization, a tetragonal MAPbI3 supercell model containing 96 atoms was constructed, and a lead vacancy defect was constructed by removing a central Pb atom.

[0063] Using the VASP software package, with a plane wave cutoff energy of 400 eV, full relaxation optimization was performed on the structures in the initial charge state (q=0) and charged state (q=-1) at 0 K.

[0064] Finite-temperature ab initio molecular dynamics was used for sampling, with the operating temperature set at 300K. The Nosé-Hoover thermal bath method was used in the NVT ensemble, with a time step of 1fs. Simulations of the defective supercell structures in the initial charge state and charged state were performed for 8ps respectively. The first 4ps thermal equilibrium stage was removed, and the evolution trajectory in the subsequent 4ps was retained as the phase space production trajectory.

[0065] A frame of configuration snapshot is extracted every 10 fs, and 400 frames are obtained for each state; For a snapshot of a charged state, the pre-selected framework Pb atom furthest from the defect center is located to read its 1s core energy level, and a correction is applied based on the perfect supercell to eliminate background charge drift. The single-point energies of the configuration snapshot under different charge states are cross-calculated, assembled into a dimensionless potential energy difference matrix, and input into the multi-state Bennett acceptor ratio equation solver.

[0066] The phase space overlap check and intermediate state supplementation loop are performed. The matrix elements are calculated by combining the free energy of each state. The comparison shows that the adjacent matrix elements are less than the critical threshold of 0.03, which means that an intermediate ensemble with the arithmetic mean of charge needs to be introduced between q=0 and q=-1. After self-consistency verification, six intermediate charge state ensembles of -0.25, -0.43, -0.46, -0.50, -0.625, and -0.75 were introduced in sequence. The trajectories of the new intermediate states were obtained and snapshots were extracted. The potential energy difference was recalculated and incorporated into the cross matrix to perform self-consistency iteration again until all adjacent matrix elements were greater than or equal to 0.03.

[0067] Based on the convergent overlap network, the final thermodynamic evaluation result is output analytically: The calculated adiabatic thermodynamic free energy change of lead vacancy VPb in MAPbI3 from the initial charge state to the q=-1 state is 2.099 eV. The free energy decomposition shows that inorganic framework vibration, organic cation orientation, local defect reconstruction and their coupling effects contribute a configuration entropy change term of -0.42 eV, and the total lattice adiabatic relaxation energy reaches 1.262 eV.

[0068] Based on the band edge position of the corresponding material at 300K, the adiabatic thermodynamic transition energy level is determined to be located 0.663eV above the top of the valence band. The final system output determines that the VPb defect in the MAPbI3 material is dynamically activated as a deep-level strong nonradiative recombination center under room temperature service conditions.

[0069] Example 5

[0070] This embodiment, based on the above embodiments, provides a semiconductor defect transition energy level evaluation method based on finite-temperature kinetic sampling. Specifically, it is used for the quantitative evaluation of the depth characteristics of lead vacancy VPb defects in the all-inorganic semiconductor material cesium lead-iodine (CsPbI3). Figure 3 , Figure 4 As shown, the execution process is as follows: Through initial model construction and static pre-optimization, a CsPbI3 orthogonal black phase defect supercell model containing 79 atoms was constructed. The defect supercell model was constructed by removing one Pb atom from the center position of a perfect supercell, that is, a perfect supercell with 80 atoms minus one atom to obtain a vacancy defect supercell.

[0071] In this embodiment, the density functional theory calculation parameters are kept exactly the same as those in Example 4. Static all-atom relaxation optimization is performed on the defective supercell structure with initial charge state (q=0) and charged state (q=-1) at 0K to obtain the static optimal configuration.

[0072] Finite-temperature ab initio molecular dynamics was used for sampling. The simulation running temperature was set to 300K, and an ab initio molecular dynamics simulation with a duration of 8ps was performed under a canonical ensemble based on the Nosé-Hoover thermostat to collect the equilibrium phase space evolution configuration trajectory.

[0073] Dynamic snapshot configurations are uniformly extracted from the production trajectory at 10-fs intervals. Based on the above embodiments, a physical alignment correction term E is applied to the energy of each snapshot. corr To eliminate periodic background charge drift.

[0074] The single-point energies of the configuration under different charge states are cross-calculated, and the statistical reweighted self-consistent free energy of the initial charge state and charged state trajectories is solved using the multi-state Bennett acceptor ratio method.

[0075] The phase space overlap verification and intermediate state supplementation loop as described in Example 4 are executed synchronously. After self-consistent verification and comparison, it is found that the phase space overlap of the initial charge state and the charged state trajectory has directly reached and satisfied the preset statistical convergence threshold. Therefore, the step of adding intermediate charge states is skipped.

[0076] Based on the converged kinetic reweighted network, the final thermodynamic evaluation result is analytically output: Quantitative analysis results show that, due to the lack of internal rotational freedom of inorganic cesium Cs+ ions, the Pb-I inorganic framework generates extremely strong steric constraints on the reshaping of defect structures, making the configuration entropy change of the system almost zero, and the total lattice adiabatic relaxation energy drops sharply from 1.262 eV in Example 4 to 0.011 eV. It should be noted that in the Pb-I inorganic framework, Pb and I refer to lead atom Pb and iodine atom I, respectively, and Pb-I refers to the octahedral framework formed by lead atom Pb and iodine atom I.

[0077] Based on the actual band edge position of the cesium lead-iodine material at 300K, the defect adiabatic thermodynamic transition energy level of the lead vacancy was determined to be located at -0.094eV below the top of the valence band. The final system output determined that the VPb defect in the CsPbI3 system exhibits a shallow energy level defect under room temperature service conditions, and has excellent defect tolerance characteristics.

[0078] The above evaluation results provide a reliable quantitative screening basis for introducing inorganic cations through A-site composition engineering to suppress deep-level nonradiative recombination centers in semiconductor materials.

[0079] All data in the formulas described above have been calculated with dimensions removed. Furthermore, any content not described in detail in this specification is existing technology known to those skilled in the art.

[0080] The above description is merely an example and illustration of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the invention or exceed the scope defined in the claims, all of which should fall within the protection scope of the present invention.

[0081] It should be stated that all user data collected in this application was collected with the user's consent and authorization. Furthermore, the uses of user data are legal and compliant, and the use and processing of user data comply with the relevant laws, regulations, and standards of the relevant regions.

Claims

1. A method for evaluating semiconductor defect transition energy levels based on finite-temperature kinetic sampling, characterized in that, The method includes: Step 1: Construct a supercell model of the semiconductor material containing the target intrinsic point defect. Under the 0K limit, perform full relaxation optimization of the cell parameters and atomic coordinates of the supercell structure of the initial charge state and at least one target charged state to obtain the equilibrium structure. Step 2: Using the equilibrium structure as the initial state, perform ab initio molecular dynamics simulations based on the operating temperature and canonical ensemble with a preset thermal equilibrium relaxation time, and collect the dynamic trajectories of the initial charge state and each target charged state. Step 3: Extract multi-frame configuration snapshots of the dynamic trajectory, and apply electrostatic potential alignment correction to the configuration snapshots of the target charged state in each frame to eliminate the finite size effect introduced by the periodic boundary conditions. By utilizing the difference between the spatial average of the local electrostatic potential of selected framework atoms in a defect-free reference supercell and the 0K limit, the valence band top characteristic energy of each frame configuration snapshot is dynamically corrected to obtain the valence band top characteristic energy at a finite temperature. Step 4: Calculate the potential energy of all targets under charged states for each frame configuration snapshot. After electrostatic potential alignment correction and dimensionless processing by dividing by thermal energy factor, construct the multi-state energy difference cross matrix, solve the dimensionless free energy difference between the charge state systems corresponding to each target charged state, and obtain the adiabatic transition free energy of each target charged state. Step 5: Calculate the phase space overlap matrix between all-charge ensembles and determine whether the overlap between adjacent charge ensembles is lower than a preset threshold. If so, an intermediate charge state ensemble with an intermediate charge value is introduced between the corresponding adjacent charge states, and its dynamic trajectory and snapshot are supplemented to re-execute the free energy calculation until the overlap between all adjacent charge state ensembles is not lower than the preset threshold, and the final adiabatic transformation free energy is output; otherwise, it is output directly. Step 6: Using the statistical average value of the instantaneous energy difference distribution between the target charge state and the initial charge state calculated under the initial charge state equilibrium trajectory, determine the dynamic vertical transition energy level at the operating temperature; using the adiabatic transition free energy, combined with the valence band top position of the semiconductor material at the operating temperature, determine the adiabatic thermodynamic transition energy level. Based on the position of the adiabatic thermodynamic transition energy level relative to the band edge of the semiconductor material, it is determined whether the defect is a dynamically activated recombination center or a dynamically passivated state at the operating temperature, thus completing the quantitative screening of defects in the semiconductor material.

2. The method according to claim 1, characterized in that, In step 1, the specific method for constructing the semiconductor material supercell model containing the target intrinsic point defect is as follows: Identify the semiconductor material to be evaluated, denoted as Q; The original unit cell of semiconductor material Q is expanded in three dimensions by a predetermined integer multiple to lock the target intrinsic point defects associated with semiconductor material Q, including vacancy defects, interstitial defects and antisite defects, and to construct the semiconductor material supercell model QM associated with semiconductor material Q. The vacancy defect is defined as the absence of an atom at a lattice position, the interstitial defect is defined as the presence of an atom in the gap between lattice positions, and the antisite defect is defined as the lattice position of one intrinsic atom occupying the position of another intrinsic atom. The plane wave pseudopotential method based on density functional theory is used to perform full relaxation optimization of cell parameters and atomic coordinates in the supercell model QM of semiconductor materials under the 0K limit for the target intrinsic point defects in the initial charge state and at least one target charged state, so as to obtain the equilibrium structure GQM.

3. The method according to claim 2, characterized in that, In step 2, the specific method for collecting the dynamic trajectories of the initial charge state and each target charged state is as follows: The equilibrium structure GQM was extracted as the initial state, and a preset operating temperature T was introduced. Ab initio molecular dynamics simulation was performed using a canonical ensemble based on the Nosé-Hoover thermostat. Starting from the ab initio molecular dynamics simulation, after reaching the preset thermal equilibrium stage, dynamic trajectories that meet the equilibrium phase space sampling length requirements are collected for the supercell structures of the initial charged state and at least one target charged state. The preset thermal equilibrium stage duration is 5 ps, the equilibrium phase space sampling length requirement duration is 4 ps, and the step size is set to 1 fs, where ps is picosecond and fs is femtosecond.

4. The method according to claim 3, characterized in that, In step 3, the specific method for extracting multiple frame configuration snapshots of the dynamic trajectory and applying electrostatic potential alignment correction to each frame configuration snapshot is as follows: The dynamic trajectories of the supercell structure of the initial charge state and at least one target charge state are extracted independently. N frame configuration snapshots are extracted at preset time intervals to eliminate the time correlation between adjacent transient configurations, thus forming a multi-frame configuration snapshot of the initial charge state and each target charge state. Here, N is a preset integer and the preset time interval is 10fs. Dynamic electrostatic potential alignment correction is performed on any extracted frame configuration snapshot, where the correction formula is: E corr =q×(V q,far -V bulk,far ), where E corr V is the electrostatic potential alignment correction energy, q is the net charge of the initial or target charged state associated with the corresponding frame configuration snapshot, and V is the net charge of the initial or target charged state. q,far V represents the local electrostatic potential of a pre-selected framework atom furthest from the defect center in the supercell structure corresponding to the target charged state. bulk,far This represents the reference potential of a pre-selected framework atom in an ideal, defect-free, pure supercell structure in a neutral charge state. Based on electrostatic potential alignment correction energy E corr Dynamic electrostatic potential alignment correction is performed on all extracted frame configuration snapshots.

5. The method according to claim 4, characterized in that, In step 3, the valence band top characteristic energy of each frame configuration snapshot is dynamically corrected to obtain the valence band top characteristic energy at a finite temperature. The specific method is as follows: Obtain any s-th frame configuration snapshot from the multi-frame configuration snapshots associated with the neutral charge state with net charge q=0 of the defect-free pure supercell, where s is the counting index and 1≤s≤N; The spatially averaged local electrostatic potential of all pre-selected framework atoms within the ideal, defect-free, pure supercell structure under the s-th frame configuration snapshot is obtained by taking the spatial arithmetic mean, denoted as V. ~s bulk,ref ; The spatially averaged local electrostatic potential V ~s bulk,ref The average electrostatic potential V, calculated by spatial arithmetic averaging of the local electrostatic potentials of all pre-selected framework atoms within an ideal, defect-free, pure supercell structure optimized under static full relaxation at the 0K limit, is the same as the average electrostatic potential V. ~0K bulk,ref After interpolation, the original valence band top eigenenergy of the s-th frame configuration snapshot is dynamically corrected using the following formula: ε s VBM,corr =ε s VBM,raw -(V ~s bulk,ref -V ~0K bulk,ref ); Where, ε s VBM,corr ε represents the valence band top characteristic energy at a finite temperature in the s-th frame configuration snapshot after dynamic reconstruction correction. s VBM,raw This represents the uncorrected valence band top eigenvalue extracted directly from the configuration snapshot of frame s using first-principles calculations; Similarly, by determining the valence band peak eigenenergy at finite temperature for all frame configuration snapshots, and taking the ensemble average, the average valence band peak position at finite temperature is obtained, denoted as <ε. VBM > V,T .

6. The method according to claim 5, characterized in that, In step 4, the specific method for calculating the dimensionless free energy difference between the charge states corresponding to each target's charged state, and obtaining the adiabatic transition free energy of each target's charged state, is as follows: Multiple configuration snapshots are extracted from the dynamic trajectory of any target charged state j. Under non-relaxation conditions, the potential energy of these multiple configuration snapshots under all target charged states i is calculated using single-point energy from density functional theory. An electrostatic potential alignment correction is then applied, and the resulting absolute potential energy is divided by the thermal energy factor k at the current service temperature. B T is processed to be dimensionless to obtain dimensionless potential energy, which is constructed as a multi-state energy difference cross matrix. In this matrix, the target charged state j and the target charged state i independently traverse all charge state ensembles involved in the calculation. i and j are both greater than or equal to 1 and less than or equal to M, where M is the total number of target charged states. By employing the multistate Bennett acceptor ratio equation, the dimensionless free energy difference between the systems of different charge states is self-consistently solved, specifically as follows: By iteratively converging and solving the nonlinear equations, the dimensionless free energy between the charged states of each target can be directly calculated, and then multiplied by the thermal energy factor k at the current service temperature. B T, reduce the adiabatic transformation free energy with physical dimensions to calculate, denoted as ΔF; in, Let be the dimensionless free energy of the target charged state i. =F i / k B T,k B Where F is Boltzmann's constant, T is absolute temperature, and F is... i Let i be the actual Helmholtz free energy under the target charged state i; The N j x is the total number of frame configuration snapshots extracted from the target charged state j. jn This is the nth frame configuration snapshot extracted from the target charged state j, where n is the counting index, 1≤n≤N. j K is the counting index, 1≤K≤M; The u i (x jn ) is a configuration snapshot x jn Under the target charged state i, apply electrostatic potential alignment correction and divide by the thermal energy factor k. B The dimensionless potential energy obtained after T.

7. The method according to claim 6, characterized in that, In step 5, the specific method for outputting the final adiabatic transformation free energy is as follows: Extract all target charged states R, calculate the phase space overlap matrix O between the ensembles of all target charged states, and its matrix element O i,i+1 This represents the statistical distribution overlap of all frame configuration snapshots of the i-th target charged state ensemble and the (i+1)-th target charged state ensemble in the microconfiguration phase space; The minimum phase space overlap threshold between adjacent target charged state ensembles is set to 0.

03. Traverse all matrix elements O i,i+1 If the overlap is greater than or equal to the minimum phase space overlap critical threshold of 0.03, the final adiabatic transformation free energy ΔF is directly output. If the overlap is less than the minimum phase space overlap threshold of 0.03, then a net charge of q is introduced between the i-th and (i+1)-th target charged states. mid =(q i +q i+1 The new intermediate charge state ensemble of q / 2 completes the intermediate state supplementation step, where q i q i+1 These are the net charge amounts of the i-th and (i+1)-th target charged states, respectively; Similarly, in ascending order of charge, the same processing is performed on all matrix elements. For all the new intermediate charge states introduced, dynamic trajectories and multi-frame configuration snapshots are obtained and incorporated into the multi-state energy difference cross matrix. The adiabatic transformation free energy solution is then re-executed, and the phase space overlap matrix O is recalculated. Repeat the above overlap verification and intermediate state supplementation steps until the overlap of all adjacent matrix elements in the phase space overlap matrix O is greater than or equal to 0.03, and output the final adiabatic transformation free energy ΔF.

8. The method according to claim 7, characterized in that, In step 6, the specific method for determining the dynamic vertical transition energy level at the operating temperature using the statistical average value of the instantaneous energy difference distribution of the defect charge state calculated under the initial charge state equilibrium trajectory is as follows: Extract the dynamic trajectory of the target intrinsic point defect under the initial charge state q and mark it as the equilibrium trajectory; Calculate the instantaneous energy difference distribution of the defect charge states, statistically average its value, and output the dynamic vertical transition energy level ε at the operating temperature T. vert (q / q'), specifically: Where, ε vert (q / q') represents the dynamic vertical transition energy level of the target intrinsic point defect from the initial charge state q to the final charge state q'; This represents the ensemble statistical average of the equilibrium trajectory based on the initial charge state q; E tot (X q ) and E tot (X q' ) represent the total energy of the initial charge state q and the unrelaxed single-point energy calculated by directly assigning the final charge state q' under the frozen lattice configuration, respectively; E corr q With E corr q' This is a finite-size electrostatic potential correction term used to eliminate periodic spurious interactions under the corresponding charge state; q'-q represents the change in charge before and after the transformation; <ε VBM > V,T is the ensemble statistical average of the valence band top characteristic energy of an ideal, defect-free, pure supercell structure at a finite temperature, used to align the calculation results with the material band edge, where the finite temperature corresponds to the operating temperature T.

9. The method according to claim 8, characterized in that, In step 6, the specific method for determining the adiabatic thermodynamic transition energy level by utilizing the adiabatic transition free energy and combining it with the valence band peak position of the semiconductor material at the operating temperature is as follows: Based on the steps described in step 4, the adiabatic transition free energy ΔF(q->q') from q to q' is analyzed, and the adiabatic thermodynamic transition energy level ε is determined by combining the position of the valence band top of the semiconductor material at the operating temperature T. dyn (q / q'), specifically: Where, ε dyn (q / q') is the adiabatic thermodynamic transition energy level of the target intrinsic point defect from the initial charge state q to the final charge state q'; F(X q ) and F(X q' ) represent the Helmholtz free energies of the supercell structure of the target intrinsic point defect after finite-temperature fully dynamic lattice relaxation, under the initial charge state q and the final charge state q'.

10. The method according to claim 9, characterized in that, In step 6, the specific method for quantitatively screening defects in semiconductor materials is as follows: Extracting the adiabatic thermodynamic transformation energy level ε dyn (q / q'), and calculate its energy difference with the nearest band edge; If ε dyn If (q / q') is greater than 0.15 eV from the nearest band edge at the operating temperature, then the adiabatic thermodynamic transition energy level ε is determined. dyn (q / q') is located deep within the band gap at actual temperatures; The output determines whether the current target intrinsic point defect is dynamically activated as a composite center at the operating temperature. If the adiabatic thermodynamic transformation energy level ε dyn If the difference between (q / q') dynamically drifting out of the band gap or the nearest band edge is less than or equal to 0.15 eV, it is considered dynamic passivation.

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