A method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window

Abstract

This invention relates to the field of semiconductor material computation methods, and discloses a method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window. The method includes applying displacement perturbations to the defect configurations of AgBiS2 to generate a set of candidate geometric configurations, obtaining the defect ground state formation energy, and extracting thermodynamic transition energy levels and non-radiative trapping barriers to integrate them into barrier reference data. A polygonal phase diagram constraint boundary is defined within a multi-dimensional optimization parameter space to generate a feasible region for tracking the initial state. The grid point set is traversed to decouple high-temperature defect freezing and low-temperature carrier rearrangement, obtaining a room-temperature self-consistent Fermi level. The concentration of dangerous charge states is evaluated using the barrier reference data, and a dynamic penalty factor based on a safe concentration threshold is introduced to construct a modified objective function. The modified objective function is iteratively optimized to obtain a parameter set, thereby establishing a process control window. This invention can maximize the free electron concentration while suppressing deep-level recombination centers, outputting macroscopic fabrication process parameters.

Description

Technical Field

[0001] This invention relates to the field of semiconductor material calculation methods, specifically a method for calculating the doping characteristics of n-type AgBiS2 material under a narrow chemical potential window. Background Technology

[0002] Narrow-bandgap semiconductor AgBiS2 shows promise in optoelectronic devices, but deep-level defects generated during fabrication can easily form nonradiative recombination centers, limiting n-type doping efficiency. Currently, conventional static structural relaxation calculations for theoretically evaluating the doping characteristics of this material tend to get stuck in local minima when dealing with complex defect configurations, failing to accurately obtain the true ground-state structure of the defects. Due to the bias in the ground-state energy calculations, it is difficult to accurately analyze the dynamic recombination behavior of deep-level defects in multiphonon emission states, resulting in the inability to effectively identify the nonradiative recombination centers that limit n-type doping efficiency at the fundamental electronic structure level.

[0003] Meanwhile, existing calculation methods typically rely on a single-temperature thermodynamic equilibrium assumption when deriving Fermi levels, neglecting the high-temperature defect freezing and low-temperature carrier rearrangement phenomena that occur during actual cooling of materials. This single-temperature model can cause errors in electron configuration calculations, making it impossible to accurately output the total freezing concentration of different defects and the room-temperature rearrangement concentration of each charge state. Consequently, it leads to a lack of reliable data support for assessing the concentration of defects in dangerous charge states.

[0004] Furthermore, conventional computational models struggle to effectively bridge the gap between fundamental theory and macroscopic fabrication processes within the extremely narrow chemical potential window of AgBiS2. Lacking an optimization mechanism that combines microscopic calculations with macroscopic device tolerance, current technologies cannot simultaneously maximize free electron concentration while strictly constraining the formation of dangerous recombination centers. This makes it difficult to precisely pinpoint the optimal set of thermodynamic parameters, which in turn cannot be reversed to specific feed ratios, annealing temperatures, and sulfur vapor partial pressures. Consequently, they cannot directly provide a clear process control window for the actual fabrication of n-type AgBiS2 materials. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for calculating the doping characteristics of n-type AgBiS2 materials within a narrow chemical potential window. This method solves the problem that deep-level defects in narrow-bandgap semiconductor AgBiS2 materials easily form non-radiative recombination centers during preparation, limiting n-type doping efficiency and device photoelectric conversion performance. Furthermore, this invention addresses the difficulty of conventional theoretical calculations in accurately defining and outputting the range of process control parameters for suppressing dangerous defect concentrations within a narrow chemical potential window.

[0006] To achieve the above objectives, the present invention provides a method for calculating the doping characteristics of n-type AgBiS2 materials within a narrow chemical potential window, comprising: A set of candidate geometric configurations is generated by applying displacement perturbation to the defect configurations in the narrow bandgap semiconductor AgBiS2 system, and the defect ground state formation energy corresponding to the target charge state is obtained by using the set of candidate geometric configurations; Thermodynamic transition energy levels of deep-level defects are extracted based on the defect ground state formation energy, and non-radiative electron trapping barriers and hole trapping barriers are extracted based on the thermodynamic transition energy levels, and integrated into barrier benchmark data. Define a multidimensional optimization parameter space, delineate a polygonal phase diagram constraint boundary within the multidimensional optimization parameter space, and generate a discrete grid point set inside the polygonal phase diagram constraint boundary as the starting feasible region for tracing. Traverse and track the discrete grid point set within the initial feasible region to obtain the total freezing concentration of different defects, and obtain the room temperature self-consistent Fermi level based on the total freezing concentration. The concentration of dangerous charge states was assessed by combining barrier baseline data and room temperature self-consistent Fermi level data, and a modified objective function was constructed based on the comparison results of dangerous charge state concentration and safe concentration threshold. The modified objective function is iteratively optimized to obtain a set of parameters that satisfy the convergence condition. Based on the parameter set, the doping characteristics of the n-type AgBiS2 material are determined and a corresponding process control window is established.

[0007] This invention generates a set of configurations through displacement perturbation and extracts the trapping barrier, reflecting the nonradiative recombination mechanism of carriers in multiphonon emission states. It decouples the high-temperature defect freezing process from the room-temperature carrier rearrangement process, constructs an objective function by combining phase diagram boundary constraints and a dynamic penalty factor, and achieves a self-consistent solution for the Fermi level in a multidimensional parameter space. This process links the electronic structure of microscopic defects with macroscopic process conditions, enabling the optimization of n-type doping parameters while suppressing the concentration of deep-level recombination centers.

[0008] Furthermore, applying displacement perturbations to the defect configurations within the narrow-bandgap semiconductor AgBiS2 system generates a set of candidate geometric configurations. The specific steps for obtaining the defect ground state formation energy corresponding to the target charge state using this set of candidate geometric configurations include: An intrinsic AgBiS2 primitive cell is constructed and expanded according to periodic boundary conditions to generate an intrinsic supercell; target atoms are removed or added within the intrinsic supercell to construct defect centers containing vacancies, interstitials or antisites, forming a defect-containing supercell. Within a defective supercell, the atoms of the first and second coordination layers surrounding the defect center are defined as neighboring atomic domains. Systematic displacement perturbations are applied to the atoms in the neighboring atomic domains along different crystallographic directions. The systematic displacement perturbations are discretized and gridded according to the set amplitude step size and lattice symmetry rules, splitting and expanding the single initial structure to generate a set of candidate geometric configurations composed of multiple different initial distortion states. Pre-relaxation calculations are performed on the candidate geometry set to obtain the ground state structure with the lowest global energy. Static electronic structure calculations are then performed on the ground state structure, and the electrostatic energy shift caused by long-range Coulomb interactions is compensated using an extended finite-size dielectric correction scheme to obtain the defect ground state formation energy corresponding to the target charge state. By applying displacement perturbations to the nearest-neighbor atomic domains and extending the initial distortion state, the structural relaxation is prevented from falling into local minima, ensuring that the obtained ground state structure has the lowest global energy characteristic.

[0009] Furthermore, the extended finite-size dielectric correction scheme is based on the long-range electrostatic energy offset introduced by the periodic lattice composed of point charges under an anisotropic dielectric background and the total macroscopic potential energy alignment correction term, and extracts the finite-size dielectric correction. The total macroscopic potential energy alignment correction term is determined based on the product of the charge state value of the defect and the macroscopic electrostatic potential alignment difference between the supercell containing the target charge state defect and the intrinsically defect-free supercell at a position far from the defect center. The defect ground state formation energy is obtained by combining the total system energy of the supercell containing the target charge state defect, the total system energy of the intrinsically defect-free supercell, the total chemical potential change due to atomic exchange, the electron chemical potential change corresponding to the charge exchange between the defect and the electron system, and the addition and subtraction of finite-size dielectric correction. A finite-size dielectric correction scheme is used to address the periodic boundary conditions of charged defects, eliminating the electrostatic interaction offset caused by the finite supercell size.

[0010] Furthermore, the extraction of thermodynamic transition energy levels for deep-level defects based on the defect ground state formation energy specifically includes: setting the values ​​of the charge states undergoing mutual transformation and the values ​​of adjacent charge states for the deep-level defect; calculating the energy difference between the defect ground state formation energy corresponding to the charge state value and the defect ground state formation energy corresponding to the adjacent charge state value, with the Fermi level set to 0; calculating the total charge transferred when adjacent different charge states undergo mutual transformation; and using the ratio of the energy difference to the total charge as the thermodynamic transition energy level. Establishing an energy benchmark for the mutual transformation between different charge states provides thermodynamic boundary conditions for analyzing the electron capture and emission processes of deep-level defects.

[0011] Furthermore, the extraction of non-radiative electron trapping barriers and hole trapping barriers based on thermodynamic transition energy levels specifically includes: obtaining two equilibrium lattice configurations corresponding to the charge states of the thermodynamic transition energy levels, extracting the structural evolution path along the geometric evolution trajectory of the two equilibrium lattice configurations, and integrating the displacement of each atom and the corresponding atomic mass on the structural evolution path to calculate the mass-weighted displacement. A one-dimensional configuration coordinate diagram is constructed using mass-weighted displacement as the abscissa and the total system energy, including the ground-state supercell containing the target charge state defect, as the ordinate. This diagram is then used to analyze the lattice adiabatic potential energy surface, extracting the non-radiative electron and hole trapping barriers for charge carriers in multiphonon emission states. Furthermore, by using the mass-weighted displacement to construct the one-dimensional configuration coordinate diagram, the multidimensional lattice relaxation process is reduced in dimension, allowing for the analysis of the lattice adiabatic potential energy surface crossing behavior of charge carriers in multiphonon emission states, and the extraction of the non-radiative trapping barriers.

[0012] Furthermore, the establishment of a multidimensional optimization parameter space and the delineation of polygonal phase diagram constraint boundaries within this space include: constructing a multidimensional optimization parameter space by treating the silver chemical potential, sulfur chemical potential, and annealing temperature as three independent variables; delineating polygonal phase diagram constraint boundaries within the multidimensional optimization parameter space using the host phase stability condition and the secondary competing phase repulsion condition; the host phase stability condition includes the thermodynamic equilibrium relationship between the sum of the chemical potentials of the elements constituting AgBiS2 and the formation enthalpy of the AgBiS2 host phase, and the sum of the chemical potentials of the elements includes the silver chemical potential, the bismuth chemical potential, and twice the sulfur chemical potential; The energy required to form a single chemical unit of the secondary competing phase under a given chemical potential is obtained by calculating the sum of the products of the chemical potentials of the elements contained in the secondary competing phase and the number of atoms of each element. The energy of the secondary competing phase is then constrained to not exceed its formation enthalpy, and an inequality constraint is constructed as a repulsion condition for the secondary competing phase. By introducing phase stability and repulsion conditions, the thermodynamically legal region for the synthesis of AgBiS2 materials is defined, preventing the optimization of process parameters from deviating from the physical boundaries of material growth.

[0013] Furthermore, the discrete grid point set within the initial feasible region is traversed and tracked to obtain the total freezing concentration of different defects. Based on the total freezing concentration, a room-temperature self-consistent Fermi level is obtained. The concentration of dangerous charge states is evaluated by combining the barrier reference data and the room-temperature self-consistent Fermi level. The specific implementation process of constructing the modified objective function based on the comparison results of the concentration of dangerous charge states and the safe concentration threshold is as follows: High-temperature defect freezing simulation within the decoupled feedback loop is performed to obtain the total freezing concentration of different defects; based on the total freezing concentration, low-temperature carrier rearrangement is performed to obtain the room-temperature self-consistent Fermi level; combined with barrier reference data, the relative energy level shift between the room-temperature self-consistent Fermi level and the deep energy level transition level is monitored, and the concentration of dangerous charge states is evaluated using the relative energy level shift. When the concentration of dangerous charge states exceeds the safe concentration threshold, a dynamic penalty factor is introduced into the initial objective function which is guided by maximizing the concentration of n-type free electrons to construct a modified objective function; wherein, defect charge states whose electron trapping barrier extracted under the multiphonon emission model is less than the set barrier determination threshold are defined as having dangerous charge states. The safe concentration threshold is determined by progressively increasing the recombination center concentration in a device-level computer-aided design simulation model, extracting the defect concentration value that causes a decrease in device photoelectric conversion efficiency exceeding 5%. The high-temperature equilibrium process is decoupled from the room-temperature rearrangement process, reflecting the physical state of defect freezing during material cooling. A dynamic penalty factor is used to establish a relationship between the barrier data extracted from microscopic calculations and the concentration threshold tolerated by the macroscopic device, guiding the optimization algorithm to avoid regions with high recombination center concentrations.

[0014] Furthermore, the ratio of the statistical weighting factor of the hazardous charge state to the total statistical weighting factor of all possible charge states of a single defect type within the bandgap is calculated to obtain the room temperature statistical weighting ratio. The total freezing concentration of the corresponding defect is multiplied by the room temperature statistical weighting ratio of the hazardous charge state to obtain the hazardous charge state concentration. When the hazardous charge state concentration does not exceed the safe concentration threshold, the dynamic penalty factor is set to 0. Based on the statistical allocation normalization principle, the concentration weights of each charge state at room temperature are allocated to ensure that the assessment of the hazardous charge state concentration conforms to the thermodynamic statistical distribution law.

[0015] Furthermore, obtaining the set of parameters that make the modified objective function satisfy the convergence condition and determining the doping characteristics of the n-type AgBiS2 material specifically includes: monitoring the magnitude of the gradient norm of the modified objective function in multiple consecutive iterations, determining that the algorithm process has converged when the gradient norm is less than the tolerance setting value, and analyzing the set of parameters that make the modified objective function obtain the global minimum value. The doping characteristics of n-type AgBiS2 materials, excluding the activation probability of deep-level recombination centers, were established using a parameter set. The gradient norm was used as a convergence criterion to locate the optimal point in the multidimensional parameter space that maximizes the free electron concentration while suppressing dangerous defects.

[0016] Furthermore, analyzing the parameter set that enables the objective function to reach its global minimum and establishing the corresponding process control window specifically includes: representing the parameter set as a spatial vector group containing the optimal silver chemical potential, optimal sulfur chemical potential, and optimal annealing temperature; extracting the room-temperature self-consistent Fermi level, free electron concentration, and rearrangement concentration distribution of various defects corresponding to the parameter set; converting the optimal sulfur chemical potential into the optimal sulfur vapor partial pressure using an ideal gas thermodynamic model; and outputting the optimal process parameters including the optimal annealing temperature, optimal sulfur vapor partial pressure, and silver to bismuth feed ratio to establish the process control window. Transforming the optimal chemical potential data into experimentally operable annealing temperature and sulfur vapor partial pressure parameters opens up a path for theoretical calculations to guide material preparation.

[0017] Furthermore, the calculation of mass-weighted displacement includes: calculating the displacement difference of all atoms in the lattice at the nodes of the structural evolution path relative to the initial equilibrium state position, summing the square of the product of the displacement difference and the corresponding atomic mass of each atom, taking the square root, and extracting the coordinate change in a single dimension as the abscissa of the one-dimensional configuration coordinate diagram; and fitting the lattice adiabatic potential energy surface corresponding to different charge states in the one-dimensional configuration coordinate diagram using a parabolic function. The equilibrium energy is calculated by subtracting the energy at the lowest point of the parabola corresponding to the initial charge state from the energy at the spatial intersection of the lattice adiabatic potential energy surface. The calculated energy difference serves as the corresponding non-radiative electron or hole trapping barrier. Integrating atomic displacement differences with mass reflects the physical characteristics of lattice vibration modes in structural evolution, ensuring the physical equivalence of function fitting in the one-dimensional configuration coordinate diagram.

[0018] Furthermore, a high-temperature charge-neutral equation is established, which includes the free electron concentration dependent on the high-temperature Fermi level, the hole concentration dependent on the high-temperature Fermi level, the total net charge concentration contributed by all types of defects in all possible charge states, and the concentration of introduced exogenous donor doping. The high-temperature Fermi level is obtained by solving the equation. Based on the high-temperature Fermi level, the concentration distribution terms of the corresponding defects in all possible charge states are determined. The total frozen concentration is obtained by iterating through and summing the concentration distribution terms corresponding to all possible charge states. The concentration distribution term is derived by multiplying the lattice site density that the corresponding defect may occupy in the crystal unit cell, the electronic state degeneracy factor corresponding to the charge state, and the thermodynamic distribution probability term derived from Boltzmann statistics. A closed-loop high-temperature charge neutrality condition is constructed to achieve a self-consistent analysis of charged defects and carrier concentration under high-temperature thermal equilibrium.

[0019] Furthermore, the process of obtaining a room-temperature self-consistent Fermi level by performing a low-temperature carrier rearrangement solution based on the total freezing concentration includes: establishing a room-temperature charge-neutral equation that includes the free electron concentration dependent on the room-temperature self-consistent Fermi level, the hole concentration dependent on the room-temperature self-consistent Fermi level, the total net charge concentration contributed by the defect system at room temperature determined based on the total freezing concentration, and the concentration of introduced exogenous donor doping, and solving it to obtain the room-temperature self-consistent Fermi level. The ratio of the statistical weighting factor for the corresponding charge state at room temperature to the total statistical weighting factor obtained by summing all possible charge states of the defect is calculated to obtain the statistical partition normalization ratio. The total frozen concentration is multiplied by the statistical partition normalization ratio to obtain the rearrangement concentration distribution of the defect in the corresponding charge state at the self-consistent Fermi level at room temperature. By fixing the total defect concentration and allowing electron redistribution within the band gap, the carrier rearrangement behavior after the material is cooled to room temperature is simulated, improving the accuracy of Fermi level assessment.

[0020] Furthermore, the dynamic penalty factor is extracted by multiplying the penalty intensity multiplier coefficient with a non-negative activation triggering composite term constructed based on an exponential deviation model. The non-negative activation triggering composite term is selected and output by the maximum value between 0 and the result of subtracting 1 from the exponential term. The exponential term is obtained by dividing the difference between the dangerous charge state concentration and the safe concentration threshold by the penalty sensitivity control hyperparameter. A modified objective function is established by constructing a summation term containing a negative free electron concentration bias benchmark term representing the initial goal of maximizing the optimization and the dynamic penalty factor. A triggering term is constructed using a deviation model to guide the objective function to generate a gradient change when the dangerous charge state concentration exceeds the threshold, thereby achieving the rejection of dangerous doping parameters.

[0021] Furthermore, the gradient norm is equal to the Euclidean norm of the multidimensional gradient vector, which is the square root of the sum of the squares of the partial derivatives of each component. The partial derivatives include the partial derivatives of the modified objective function with respect to the silver chemical potential, the partial derivatives of the modified objective function with respect to the sulfur chemical potential, and the partial derivatives of the modified objective function with respect to the annealing temperature. The tolerance setting is obtained by reading the electron step energy convergence standard value from the underlying quantum chemical calculation environment, performing a square root operation on the electron step energy convergence standard value to obtain the baseline accuracy, and then calculating the tolerance setting value by combining it with the grid spacing. By comprehensively considering the partial derivatives of the multidimensional parameters and combining them with the underlying calculation accuracy, the tolerance is established to ensure the numerical stability of the optimization process and the objectivity of the stopping conditions.

[0022] Furthermore, the formula for calculating the optimal sulfur vapor partial pressure is based on the total sulfur chemical potential under a specified combination of temperature and pressure; the total sulfur chemical potential includes the standard chemical potential of sulfur at the optimal annealing temperature under standard atmospheric pressure, and the sum of the chemical potential correction term due to pressure deviation at the optimal annealing temperature; the chemical potential correction term is determined based on the product of half, Boltzmann constant, optimal annealing temperature, and the natural logarithm of the relative pressure ratio. The relative pressure ratio is the ratio of the optimal sulfur vapor partial pressure to the standard atmospheric pressure. The optimal sulfur vapor partial pressure is calculated by replacing the total sulfur chemical potential with the optimal sulfur chemical potential. A gas thermodynamic model is used to map the deviation of the chemical potential into changes in macroscopic gas pressure, achieving the dimensional conversion between thermodynamic state variables.

[0023] This invention provides a method for calculating the doping characteristics of n-type AgBiS2 materials within a narrow chemical potential window. It offers the following advantages: 1. This invention generates a set of candidate geometric configurations by applying a systematic displacement perturbation to the defect configuration in the narrow bandgap semiconductor AgBiS2 system to obtain the defect ground state formation energy, and extracts the nonradiative trapping barrier by combining thermodynamic transition energy levels. This overcomes the problem that conventional static relaxation calculations are prone to getting trapped in local minima. It can accurately analyze the dynamic recombination behavior of deep-level defects in the multiphonon emission state, effectively identify the nonradiative recombination center that limits the n-type doping efficiency from the basic electronic structure level, and improve the reliability of defect attribute definition and doping characteristic evaluation.

[0024] 2. This invention derives a room-temperature self-consistent Fermi level by executing a decoupled high-temperature defect freezing simulation and low-temperature carrier rearrangement solution loop, combined with the obtained barrier reference data. This objectively reflects the change in defect distribution state of semiconductor materials during actual cooling, eliminates the electron configuration calculation bias caused by a single temperature model, and accurately outputs the total freezing concentration of defects and the room-temperature rearrangement concentration of each charge state, providing data support for accurately assessing and suppressing the concentration of dangerous charge state defects.

[0025] 3. This invention generates a discrete grid point set in a multidimensional parameter space constrained by phase diagram boundaries and introduces a dynamic penalty factor based on a safe concentration threshold to iteratively optimize the modified objective function. This achieves the integration of basic theoretical calculations and macroscopic preparation processes. While pursuing the maximization of free electron concentration, it constrains the generation of dangerous recombination centers. It can accurately lock the optimal parameter set within a narrow chemical potential window, and then reversely convert it into specific feed ratios, annealing temperatures, and sulfur vapor partial pressures. This directly provides a clear process control window for the actual preparation of n-type AgBiS2 materials. Attached Figure Description

[0026] Figure 1 This is a structural diagram of the calculation system for the doping characteristics of n-type AgBiS2 material under a narrow chemical potential window according to the present invention. Figure 2 The main flowchart of the calculation method for the doping characteristics of n-type AgBiS2 material under a narrow chemical potential window of the present invention is shown below. Figure 3 This is a flowchart illustrating the ground state configuration construction and formation energy calculation of the present invention; Figure 4This is a flowchart of the transition level analysis and barrier reference extraction of the present invention; Figure 5 This is a flowchart of the multidimensional optimization space definition and feasible region initialization process of the present invention; Figure 6 This is a flowchart of the algorithm convergence determination and optimal parameter analysis of the present invention; Figure 7 This is a one-dimensional configuration coordinate diagram of sulfur vacancies according to an embodiment of the present invention; Figure 8 This is an intrinsic defect formation energy spectrum calculated and output under optimal chemical potential conditions according to an embodiment of the present invention. Detailed Implementation

[0027] The technical solutions in 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.

[0028] See attached document Figure 1 This invention provides a calculation system for the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window, including: an energy calculation module, a parameter extraction module, a boundary initialization module, a decoupling solution module, and a parameter output module.

[0029] The energy calculation module is used to apply displacement perturbation to the defect configuration in the narrow bandgap semiconductor AgBiS2 system to generate a set of candidate geometric configurations. It performs pre-relaxation calculation on the generated set of candidate geometric configurations to obtain the ground state structure with the lowest global energy, and performs static electronic structure calculation on the obtained ground state structure. It uses the extended Freysoldt-Neugebauer-Vande Walle (finite size dielectric) correction scheme to compensate for the electrostatic energy shift caused by long-range Coulomb interaction, and outputs the defect ground state formation energy corresponding to the target charge state.

[0030] The energy calculation module receives the defect ground state formation energy corresponding to the target charge state. The parameter extraction module is used to extract the thermodynamic transition energy levels between adjacent charge states for deep-level defects based on the defect ground state formation energy corresponding to the target charge state. Based on the equilibrium configuration structure evolution path of the extracted thermodynamic transition energy levels, a one-dimensional configuration coordinate diagram is constructed to analyze the lattice adiabatic potential energy surface. By analyzing the lattice adiabatic potential energy surface, the non-radiative electron trapping barrier and hole trapping barrier of charge carriers in the multiphonon emission state are extracted. The non-radiative electron trapping barrier and hole trapping barrier are integrated and the barrier reference data is output.

[0031] The boundary initialization module is used to set up a multidimensional optimization parameter space with silver chemical potential, sulfur chemical potential and annealing temperature as reference coordinates. It uses the stability condition of the main phase and the repulsion condition of the secondary competing phase to delineate the polygonal phase diagram constraint boundary, and generates a discrete grid point set inside the delineated polygonal phase diagram constraint boundary, and outputs the initial feasible region for tracing.

[0032] The system receives the barrier reference data output by the parameter extraction module and the tracking start feasible region output by the boundary initialization module. The decoupled solution module traverses the discrete grid point set within the tracking start feasible region. It obtains the total freezing concentration of different defects by performing a high-temperature defect freezing simulation within the decoupled feedback loop. Based on the obtained total freezing concentration, the computational environment is switched to the device operating temperature to perform a low-temperature carrier rearrangement solution. The room temperature self-consistent Fermi level is obtained based on the solution results. The relative energy level shift between the room temperature self-consistent Fermi level and the deep energy level transition level is monitored and obtained in conjunction with the barrier reference data. The relative energy level shift is used to evaluate the concentration of dangerous charge states. When the concentration of dangerous charge states exceeds the safe concentration threshold, a dynamic penalty factor is introduced into the initial objective function, which is guided by maximizing the concentration of n-type free electrons, to construct a modified objective function. The dynamic penalty factor occupies a weight in the modified objective function, thereby forcing the optimization path to deflect in the opposite direction. The modified objective function is then output.

[0033] The algorithm receives the corrected objective function output by the decoupled solution module. The parameter output module monitors the magnitude of the gradient norm of the corrected objective function within multiple consecutive iterations. When the gradient norm is less than the tolerance setting, the algorithm is determined to have converged. The algorithm analyzes the set of parameters that makes the corrected objective function achieve the global minimum. Based on the parameter set, the algorithm determines the doping characteristics of n-type AgBiS2 material that excludes the activation probability of deep-level recombination centers under a narrow chemical potential window and establishes the corresponding process control window, outputting the optimal process parameters.

[0034] See attached document Figure 2 This invention provides a method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window, comprising the following steps: S10. Ground State Configuration Construction and Formation Energy Calculation. The energy calculation module applies displacement perturbation to the defect configuration in the narrow bandgap semiconductor AgBiS2 system to generate a set of candidate geometric configurations. It performs pre-relaxation calculation on the generated set of candidate geometric configurations to obtain the ground state structure with the lowest global energy. Then, it performs static electronic structure calculation on the obtained ground state structure and uses the extended finite size dielectric correction scheme to compensate for the electrostatic energy shift caused by long-range Coulomb interactions to obtain the defect ground state formation energy corresponding to the target charge state. S20. Transition Level Analysis and Barrier Reference Extraction. The defect ground state formation energy corresponding to the target charge state output by the energy calculation module is received. Based on the defect ground state formation energy corresponding to the target charge state, the parameter extraction module extracts the thermodynamic transition energy levels between adjacent charge states for deep-level defects. Based on the equilibrium configuration structure evolution path of the extracted thermodynamic transition energy levels corresponding to the charge states, a one-dimensional configuration coordinate diagram is constructed to analyze the lattice adiabatic potential energy surface. By analyzing the lattice adiabatic potential energy surface, the non-radiative electron trapping barrier and hole trapping barrier of charge carriers in the multiphonon emission state are extracted. The non-radiative electron trapping barrier and hole trapping barrier are integrated into barrier reference data. S30. Multidimensional Optimization Space Delineation and Feasible Region Initialization. The boundary initialization module sets up a multidimensional optimization parameter space with silver chemical potential, sulfur chemical potential, and annealing temperature as reference coordinates. It delineates the polygonal phase diagram constraint boundary using the main phase stability condition and the secondary competing phase repulsion condition, and generates a discrete grid point set inside the delineated polygonal phase diagram constraint boundary. The discrete grid point set is then output as the starting feasible region for tracing. S40. Dual-Temperature Decoupling Solution and Dynamic Penalty Execution. The module receives barrier reference data from the parameter extraction module and the tracking initial feasible region from the boundary initialization module. The decoupling solution module traverses the discrete grid point set within the tracking initial feasible region. It obtains the total freezing concentration of different defects by performing a high-temperature defect freezing simulation within the decoupling feedback loop. Based on the obtained total freezing concentration, the computational environment is switched to the device operating temperature to perform a low-temperature carrier rearrangement solution. The room-temperature self-consistent Fermi level is obtained based on the solution results. The relative energy level shift between the room-temperature self-consistent Fermi level and the deep energy level transition level is monitored using the barrier reference data. The relative energy level shift is used to assess the concentration of dangerous charge states. When the concentration of dangerous charge states exceeds the safe concentration threshold, a dynamic penalty factor is introduced into the initial objective function, which is oriented towards maximizing the concentration of n-type free electrons, to construct a modified objective function. This allows the dynamic penalty factor to occupy a weight in the modified objective function, thereby forcing the optimization path to deflect in the opposite direction. The modified objective function is then output. S50. Algorithm Convergence Judgment and Control Window Output. The module receives the corrected objective function from the decoupled solution module. The parameter output module monitors the gradient norm of the corrected objective function over multiple consecutive iterations. When the gradient norm is less than the tolerance setting, the algorithm is deemed to have converged. The module analyzes the set of parameters that makes the corrected objective function achieve its global minimum. Based on the parameter set, the module determines the doping characteristics of n-type AgBiS2 material that excludes the activation probability of deep-level recombination centers within a narrow chemical potential window and establishes the corresponding process control window.

[0035] See attached document Figure 3 For step S10, ground state configuration construction and formation energy calculation, the energy calculation module establishes the underlying thermodynamic data foundation through the following sub-steps.

[0036] S11. Construction of Defective Supercells and Application of Systematic Displacement Perturbation. The energy calculation module establishes intrinsic AgBiS2 primitive cells and expands them according to periodic boundary conditions to generate intrinsic supercells, reducing the physical coupling between adjacent primitive cells. Target atoms are removed or added within the expanded intrinsic supercells to construct defect centers containing vacancies, interstitials, or antisites, forming defective supercells. Due to the differences in ionic radii and lone pair electron effects of its constituent elements, the narrow-bandgap semiconductor AgBiS2 exhibits strong local polarization characteristics. The introduction of defect centers easily induces local lattice distortion, making conventional geometry optimization processes prone to falling into metastable states corresponding to local energy minima.

[0037] The energy calculation module delineates the first and second coordination layer atoms surrounding the defect center as nearest-neighbor atomic domains and applies systematic displacement perturbations to the atoms within these domains along different crystallographic directions. To ensure the completeness of the candidate geometry set sampling, the amplitude of the systematic displacement perturbation is set between 10% and 30% of the local average bond length. The standard for determining the systematic displacement perturbation value is based on the structural tolerance judgment in the pre-calculation stage, i.e., extracting the maximum effective displacement amplitude within the limit deformation range that will not cause the collapse of the lattice topology. The systematic displacement perturbation is discretized and meshed according to the set amplitude step size and lattice symmetry rules, splitting and expanding the single initial structure to generate a candidate geometry set composed of multiple different initial distortion states.

[0038] S12. Concurrent Pre-relaxation Calculation and Global Ground State Filtering. The energy calculation module uses density functional theory to concurrently perform geometric pre-relaxation calculations on all configurations in the candidate geometric configuration set. In the geometric pre-relaxation calculation, the atomic coordinates are continuously updated by calculating the force gradients experienced by the atoms until the forces experienced by all atoms in the configuration are less than a set force convergence threshold. In conventional calculations, the force convergence threshold is usually set between 0.01 eV / Å and 0.05 eV / Å. This range is determined by conducting convergence pre-tests on the energy force gradients of the intrinsic system. The force convergence threshold is set according to the current system's required level of energy calculation accuracy; the higher the required accuracy, the closer the force convergence threshold is to 0.01 eV / Å. For the specific matrix diagonalization solution and force field convergence process of structural relaxation in density functional theory, those skilled in the art can use plane wave basis set expansion combined with exchange-correlated functionals for solution. The principle of iterative optimization using computer clusters is a well-known technique in this field and will not be elaborated here.

[0039] After structural relaxation, the energy calculation module extracts the total system energy of the ground state supercell containing the target charge state defect in all relaxed configurations and selects the configuration with the lowest total system energy. This configuration is then identified as the ground state structure with the lowest global energy, thus completing the operation of obtaining the ground state structure with the lowest global energy. This reduces the interference of local metastable states at the physical level.

[0040] S13. Static electronic structure calculation and finite-size dielectric correction are performed. The energy calculation module performs static electronic structure calculations on the acquired ground-state structure, specifically by introducing it into a hybrid functional (e.g., the HSE06 hybrid density functional) for static electronic structure calculation. In the static electronic structure calculation, since the hybrid density functional (e.g., the HSE06 hybrid density functional) introduces precise exchange interaction, the energy calculation module iteratively adjusts the precise exchange mixing ratio parameter in the hybrid functional to align the output macroscopic bandgap value with the experimental macroscopic bandgap of 1.18 eV for AgBiS2 material, thereby reducing the electronic structure error caused by the standard functional's often underestimated bandgap. For the specific self-consistent field iterative solution of the static electronic structure calculation in density functional theory, those skilled in the art can configure the Brillouin zone K-point grid cutoff energy and perform charge density self-consistent cycling. The extraction of static band information is a well-known technique in this field and will not be elaborated here.

[0041] Under the constraint of periodic supercell boundary conditions, charged defects will engage in long-range Coulomb interactions with their spatially infinitely cyclically arranged mirror charges, causing a spurious shift in the calculated total energy of the ground-state supercell containing the target-charged defect. To address this, the energy calculation module utilizes an extended finite-size dielectric correction scheme to compensate for the electrostatic energy shift caused by long-range Coulomb interactions. Specifically, based on the derivation principle of this correction scheme, the energy calculation module extracts the finite-size dielectric correction using the following formula: ; in, This represents the finite-size dielectric correction output by the extended finite-size dielectric correction scheme, used to offset the system energy error caused by long-range Coulomb interactions; It represents the long-range electrostatic energy shift introduced by a periodic lattice composed of point charges under an anisotropic dielectric background. This represents the total macroscopic potential energy alignment correction term used to compensate for short-range electrostatic potential differences; The numerical value of the charge state carried by the defect represents the number of electrons gained or lost, and is usually taken as an integer. This represents the macroscopic electrostatic potential alignment difference between the supercell containing the target charge state defect and the intrinsic supercell at a location far from the defect center.

[0042] During the calculation, due to the difference in dielectric constant of the AgBiS2 lattice structure in different crystal directions, the energy calculation module not only loads the three-dimensional anisotropic dielectric shielding tensor to replace the scalar dielectric constant to compensate for the anisotropic dielectric background and calculate the long-range electrostatic energy offset, but also extracts the distribution information of macroscopic electrostatic potential around the defect and electrostatic potential at the corresponding position of the intrinsic supercell to fit in order to extract the macroscopic electrostatic potential alignment difference. Then, it integrates the long-range electrostatic energy offset and the macroscopic potential energy alignment correction term to obtain the finite-size dielectric correction.

[0043] S14. Defect Ground State Formation Energy Extraction. Combining the total system energy of the supercell containing the target charge state defect obtained from quantum mechanical calculations and the finite-size dielectric correction, the energy calculation module establishes and calculates the defect ground state formation energy corresponding to the target charge state according to the following relationship. This physical quantity characterizes the energy cost required for the spontaneous formation of this charge state defect in the lattice under a given chemical environment and electron chemical potential: ; in, This represents the defect ground state formation energy corresponding to the target charge state; This represents the total energy of the system containing the ground-state supercell with the target charge state defect; This represents the total energy of the intrinsically defect-free supercell. This indicates the introduction or removal during the construction of a defective supercell. The number of atoms in a supercell, where adding atoms to a supercell takes a negative value and removing atoms takes a positive value; Indicates correspondence The absolute chemical potential of atomoids is limited by the enthalpy of formation of the host phase of the corresponding element and the specific abundance of the reaction environment. This represents the total change in chemical potential caused by atomic exchange, used to measure the energy cost of material exchange when constructing defects; This term represents the change in electron chemical potential corresponding to the exchange of charge between the defect and the electronic system. The numerical value of the charge state carried by the defect represents the number of electrons gained or lost, and is usually taken as an integer. The Fermi level represents the energy level relative to the top of the valence band, reflecting the chemical potential of an electron in the system. Its value ranges continuously from 0 to the band gap of the material, which is 1.18 eV. This indicates the finite-size dielectric correction output by the extended finite-size dielectric correction scheme.

[0044] The defect ground state formation energy extraction formula provides a basic energy scale for the target parameter variables output in the calculation formula, serving as the basis for subsequent thermodynamic equation solving and environmental evolution simulation. The energy calculation module outputs the defect ground state formation energy corresponding to the target charge state and then passes it to subsequent processing steps.

[0045] See attached document Figure 4For step S20, transition level analysis and barrier benchmark extraction, the parameter extraction module receives the defect ground state formation energy corresponding to the target charge state output by the energy calculation module, and performs physical quantitative analysis to establish a nonradiative recombination evaluation index for deep-level defects. The parameter extraction module establishes and outputs barrier benchmark data through the following sub-steps: S21. Thermodynamic Transition Energy Level Extraction. Based on the input defect ground state formation energy data corresponding to the target charge state, the parameter extraction module extracts the energy nodes where deep-level defects (e.g., sulfur vacancies) readily induce nonradiative recombination in the material system, specifically targeting deep-level defect types. From a thermodynamic perspective, when the Fermi level is at the target location, the energy cost required for the defect to be in two adjacent charge states is equal. The Fermi level that results in equal formation energies is defined as a thermodynamic transition energy level. The parameter extraction module extracts the thermodynamic transition energy level using the following relationship: ; in, Indicates the numerical value of deep-level defects in charge states numerical values ​​of adjacent charge states The thermodynamic transition energy levels that occur between these levels characterize the energy positions where the energy is in intergenerational equilibrium when a defect absorbs or releases electrons. This indicates that when the Fermi level... When set to 0, the charge state value is The corresponding defect ground state formation energy; This indicates that when the Fermi level... When set to 0, the values ​​of adjacent charge states are The corresponding defect ground state formation energy; The numerical value of the charge state is The corresponding defect ground state formation energy and the value of the adjacent charge state are: The energy difference between the corresponding defect ground state formation energies; It represents the total amount of charge transferred when adjacent different charge states undergo mutual transformation; This indicates that the valence band top of the material is used as the zero-point reference position for energy calculation.

[0046] S22. Equilibrium Configuration Structural Evolution Path and Mass-Weighted Displacement Analysis. After extracting the thermodynamic transition energy levels, the parameter extraction module begins to quantify the structural relaxation degree of the lattice during the charge state transition process. The parameter extraction module obtains two equilibrium lattice configurations corresponding to the charge states of the thermodynamic transition energy levels and extracts the structural evolution path along the geometric evolution trajectory of the two equilibrium lattice configurations. For the reaction path interpolation and transition state search of the lattice structure between equilibrium configurations of different charge states, those skilled in the art can configure a micro-motion elastic band algorithm to detect energy barrier paths. Its configuration interpolation and force convergence methods are well-known technologies in the field and will not be elaborated here.

[0047] By analyzing the structural evolution path, the parameter extraction module integrates the displacement of each atom along the path with the corresponding atomic mass to calculate the mass-weighted displacement. Mass-weighted displacement The specific calculation principle is as follows: The displacement difference between the coordinates of all atoms in the lattice at the nodes of the structural evolution path and their initial equilibrium positions is calculated. The square root of the sum of the squares of these displacement differences and the products of the corresponding atomic masses of each atom is then used to obtain the coordinate change in a single dimension. (Mass-weighted displacement) The multidimensional lattice atomic displacements are reduced in dimension and quantized into a single coordinate parameter, which is used as the abscissa to characterize the degree of relaxation of deep-level defect lattice.

[0048] S23. Construction of one-dimensional configuration coordinate diagram and extraction of potential barrier benchmark. The parameter extraction module uses mass-weighted displacement... A one-dimensional configuration coordinate diagram is constructed with the x-axis representing the total energy of the system in the ground-state supercell containing the target charge-state defect, and the y-axis representing the total energy of the system. The parameter extraction module fits the lattice adiabatic potential energy surface corresponding to different charge states on the one-dimensional configuration coordinate diagram using a parabolic function. The fitting process for the lattice adiabatic potential energy surface is based on the simple harmonic oscillator approximation principle, which assumes that the lattice vibrations of the defect near the equilibrium configuration exhibit harmonic oscillator characteristics, causing the total energy of the system in the ground-state supercell containing the target charge-state defect to change as a quadratic function with lattice distortion.

[0049] For the force analysis and parabolic function fitting calculation of a harmonic oscillator with a lattice structure near its equilibrium point, those skilled in the art can configure the least squares method for function curvature optimization. The adiabatic potential energy surface fitting is a well-known technique in this field and will not be elaborated upon here. To ensure the accuracy of physical extrapolation, a threshold for the decision coefficient of the parabolic function fitting is used. If the threshold for the determination coefficient is not reached, the parameter extraction module will automatically increase the sampling point density on the structural evolution path if the value is set to be greater than 0.99.

[0050] By combining the spatial intersections of the lattice adiabatic potential energy surfaces corresponding to different charge states and the semiconductor band edge energy positions, the parameter extraction module analyzes the nonradiative trapping dynamics of charge carriers in the multiphonon emission state. The semiconductor band edge energy positions can be obtained by performing standard density functional theory static band structure calculations on a defect-free intrinsic supercell. The parameter extraction module extracts the nonradiative electron trapping barrier of charge carriers in the multiphonon emission state from the relative height of the intersections of the lattice adiabatic potential energy surfaces. With Hole Capture Barrier Non-radiative electron trapping barrier With Hole Capture Barrier The physical logic for extraction is as follows: subtract the energy at the spatial intersection of the adiabatic potential energy surface of the lattice from the energy at the lowest point of the parabola corresponding to the initial charge state of the capture (i.e., the equilibrium energy). The calculated energy difference is the corresponding non-radiative electron capture barrier. Or capture the stronghold through a hole .

[0051] Non-radiative electron trapping barrier Characterizing the activation energy of local lattice distortion that needs to be overcome to trap conduction band electrons at defect centers; hole trapping barrier. The activation energy that needs to be overcome to trap valence band holes at the defect center is characterized. After completing the extraction calculation, the parameter extraction module extracts the non-radiative electron trapping barrier. With Hole Capture Barrier The potential barrier reference data is integrated and output as a static constraint library, providing a basic basis for subsequent evaluation of the degree of charge state activation caused by deep-level recombination centers.

[0052] See attached document Figure 5 For step S30, which involves defining the multidimensional optimization space and initializing the feasible region, the boundary initialization module performs phase space constraint setting and discretization operations to provide a physically self-consistent parameter search range for subsequent global optimization calculations. The boundary initialization module establishes and outputs the initial feasible region for tracking through the following sub-steps.

[0053] S31. Definition of the Multidimensional Optimization Parameter Space. The boundary initialization module sets the core control variables required for subsequent optimization calculations, forming the multidimensional optimization parameter space. This space consists of three independent variables: the silver chemical potential, etc. Chemical potential of sulfur and annealing temperature In one embodiment, the bismuth chemical potential It is not an independent variable; its value is limited by the thermodynamic equilibrium conditions of the main phase AgBiS2.

[0054] S32. Boundary Construction of Stable Main Phase and Exclusive Competing Phases. In the physical synthesis of materials, the elemental abundance of the growth atmosphere (e.g., silver-rich or sulfur-poor environment) is directly determined by the chemical potential of each element. To ensure that the calculated physical boundary conditions are consistent with the actual material synthesis process, i.e., to guarantee that the main phase AgBiS2 can exist stably without decomposition or the formation of other impurity phases, the boundary initialization module introduces a thermodynamic equilibrium law to constrain the multidimensional optimization parameter space.

[0055] First, the stability condition of the main phase requires that the sum of the chemical potentials of the elements composing AgBiS2 satisfy the following equation: ; in, The chemical potential of silver; The chemical potential of bismuth; The chemical potential of sulfur; This refers to the enthalpy of formation of the AgBiS2 main phase. For the specific calculation, those skilled in the art can use the energy calculation module to perform first-principles total energy calculation on the intrinsically defect-free supercell and then subtract the total energy of each constituent element. The calculation method is a well-known technology in this field and will not be elaborated here.

[0056] Secondly, the competitive phase repulsion condition requires that, under any given combination of chemical potentials, the formation energy of any potential secondary competing phase is not negative, i.e., the condition for spontaneous precipitation is not met. For the Ag-Bi-S ternary system, potential secondary competing phases include, but are not limited to, binary or ternary compounds such as Ag₂S, Bi₂S₃, and AgBi₃S₅. The competitive phase repulsion condition is constrained by a series of inequalities, and its general form is as follows: ; in, This refers to a secondary competing phase that forms a chemical unit under a given chemical potential. Energy; These represent secondary competition phases. The number of atoms of elements A, B, and C (corresponding to Ag, Bi, and S in this system) in the chemical formula; The chemical potential of element A is represented as the chemical potential of silver in this embodiment. ; The chemical potential of element B is expressed as the chemical potential of bismuth in this embodiment. ; The chemical potential of element C is the chemical potential of sulfur in this embodiment. ; For this secondary competition phase The enthalpy of formation is also obtained in advance through first-principles calculations; This is the index for the secondary competing phase, used to traverse all preset potential competing phases.

[0057] Furthermore, the upper limit of the chemical potential of each element is limited by the energy of its elemental phase, i.e., it satisfies... , , The reference boundary for the single-element phase is defined. A chemical potential of 0 indicates that the element is in an enrichment-limited state. By comprehensively solving the above equations and inequalities, a closed polygonal region is analytically obtained on a two-dimensional plane with the chemical potentials of silver and sulfur as coordinate axes; this is the polygonal phase diagram constraint boundary. Any point inside the polygonal phase diagram constraint boundary represents the chemical potential environment in which the AgBiS2 main phase can exist stably. The process of solving this linear constraint set using numerical calculation methods to obtain the stable phase diagram is a well-known technique in this field and will not be elaborated upon here.

[0058] S33. Discretization of the initial feasible region's mesh. Since subsequent optimization algorithms require systematic iterative searches within the parameter space, the boundary initialization module discretizes the interior of the continuous polygonal phase diagram constraint boundary determined in step S32. This process involves uniformly dividing the interior of the polygonal phase diagram constraint boundary with a fixed step size, generating a series of discrete chemical potential coordinate points. In a specific embodiment, this step size can be set to 0.05 eV. The selection of the step size is a trade-off between computational accuracy and computational cost. In an optional implementation, its value can be set between 0.01 eV and 0.1 eV. A smaller step size can improve the precision of the optimization but increases the computational load.

[0059] Discrete chemical potential coordinates, combined with a set annealing temperature range, constitute a discrete grid point set. In one specific implementation, the annealing temperature range is set based on the actual synthesis process window and phase transition temperature of AgBiS2 material, for example, between 400K and 700K. This discrete grid point set is defined as the initial feasible region for tracing and is passed as output data to the subsequent decoupled solution module, providing it with an initial, physically valid set of search points.

[0060] For step S40, the dual-temperature decoupling solution and dynamic penalty execution, the decoupling solution module receives the potential barrier reference data output by the parameter extraction module and the tracking initial feasible region output by the boundary initialization module. The decoupling solution module traverses the discrete grid point set within the tracking initial feasible region and targets the silver chemical potential of the target. Chemical potential of sulfur and annealing temperature The following sub-steps are combined to output the modified objective function: S41. High-Temperature Defect Freezing Simulation. The high-temperature defect freezing simulation is based on a two-temperature decoupling model. The physical basis of the two-temperature decoupling model is that during the high-temperature annealing stage, the atomic diffusion process is active, and the defect concentration can reach thermodynamic equilibrium; however, during the subsequent rapid cooling process, the atomic diffusion process is suppressed, so the total number of defects is fixed, i.e., in a frozen state. The decoupling solution module first simulates the freezing process at the annealing temperature. Thermodynamic equilibrium state at high temperatures. To determine the thermodynamic equilibrium state, the charge neutrality equation at high temperatures is established and solved to determine the high-temperature Fermi level. The high-temperature charge neutrality equation can be expressed as: ; in, This indicates dependence on the high-temperature Fermi level. The concentration of free electrons; This indicates dependence on the high-temperature Fermi level. Hole concentration; This represents the Fermi level of the system under high-temperature annealing conditions. This represents the total net charge concentration contributed by all types of defects in all possible charge states. This represents the summation of all predefined defect types within the material system; This represents the summation of all possible charge states of a single defect type within the band gap; The numerical value of the charge state carried by the defect represents the number of electrons gained or lost, and is usually taken as an integer. Describing defects in a high-temperature thermodynamic equilibrium state In charge state numerical The concentration; This indicates the concentration of introduced exogenous donor doping.

[0061] Due to the intrinsic self-compensation effect of the AgBiS2 system, introducing constant exogenous donor doping is a physical prerequisite for breaking the self-compensation limitation and stimulating n-type conductivity. In a specific embodiment, to effectively control the carrier concentration, the exogenous donor doping concentration is... The set value can be configured to 1.0 × 10. 22 cm -3 To ensure that a sufficient concentration of dopant is provided to satisfy the charge-neutral condition for transfer.

[0062] For the iterative calculation process of solving nonlinear equations to extract the self-consistent Fermi level of the system, those skilled in the art can use the Newton-Raphson numerical optimization algorithm combined with the edge density of states integral model. Its numerical solution mechanism under the Fermi-Dirac statistical framework is a well-known technology in this field and will not be elaborated here.

[0063] Furthermore, in obtaining the high-temperature Fermi level Subsequently, the decoupled solution module obtains the total freezing concentration of different defects by performing a high-temperature defect freezing simulation within the decoupled feedback loop. Total freeze concentration This represents the defects of the target type under high-temperature annealing conditions. The sum of concentrations across all possible charge states. Calculate the total frozen concentration. The specific relationship is as follows: ; in, Indicates defects Total frozen concentration; This represents summing up all possible charge states of a defect of this target type. Indicates defects The density of lattice sites that may occupy a crystal unit cell lattice; Represents the numerical value of charge state The corresponding electronic state degeneracy factor; This represents a composite term of thermodynamic distribution probability derived from Boltzmann statistics; This indicates that at a given silver chemical potential Chemical potential of sulfur and high temperature Fermi level Defect ground state formation energy; Represents the Boltzmann constant; This indicates the specified annealing temperature within the optimization space.

[0064] S42. Low-temperature carrier rearrangement and room-temperature self-consistent Fermi level solution. Another part of the mechanism of the two-temperature decoupling model lies in the fact that when the material is cooled to the device operating temperature (e.g., room temperature 300K), although the total freeze concentration... The system remains frozen and unchanged, but electron exchange between the defect levels and the conduction band remains active, and carriers within the system will rearrange to achieve a new charge balance. This is based on the obtained total frozen concentration. The decoupled solution module switches the computing environment to the device operating temperature to perform low-temperature carrier rearrangement solutions, and obtains the room-temperature self-consistent Fermi level based on the solution results. .

[0065] The core of solving the low-temperature carrier rearrangement problem lies in establishing and solving the charge-neutral equation at room temperature. The specific form of the room-temperature charge-neutral equation is: ; in, This indicates a reliance on a room-temperature self-consistent Fermi level. The concentration of free electrons; This indicates a reliance on a room-temperature self-consistent Fermi level. Hole concentration; This represents the self-consistent Fermi level of the system at room temperature; This represents the total net charge concentration contributed by the defective system at room temperature; This indicates the total concentration at room temperature is defects In charge state numerical The rearrangement concentration distribution; This indicates the concentration of introduced exogenous donor doping.

[0066] In the above room-temperature charge-neutral equation, the concentration of free electrons depends on the room-temperature self-consistent Fermi level. With hole concentration Based on the statistical distribution model, they are respectively expressed as follows: ; ; in, This represents the effective density of states in the conduction band; This represents the effective density of states in the valence band; Indicates the position of the bottom energy level of the conduction band; Indicates the position of the top energy level in the valence band; This represents the composite term of carrier distribution probability derived based on the Fermi-Dirac nondegenerate approximation; Represents the Boltzmann constant; This indicates the absolute room temperature corresponding to the device's operating temperature.

[0067] Regarding the room-temperature rearrangement concentration distribution, due to the limited total number of defects, the specific concentration of each charge state is determined based on the Boltzmann distribution probability at the room-temperature self-consistent Fermi level. In the redistribution process, to reduce the coupling of a single formula, a statistical weighting factor is introduced to decompose the allocation formula. The specific calculation relationship is as follows: ; ; in, Represents the numerical value of charge state at room temperature Statistical weighting factors; Represents the numerical value of charge state The corresponding electronic state degeneracy factor; This represents the thermodynamic probability composite term of the target charge state derived from the Boltzmann distribution; This indicates a self-consistent Fermi level at room temperature. Defect ground state formation energy; Represents the Boltzmann constant; This indicates the absolute room temperature corresponding to the device's operating temperature. This indicates a self-consistent Fermi level at room temperature. Lower defects In charge state numerical The rearrangement concentration distribution; Defects representing target types Total frozen concentration; This represents the summation of all possible charge states of the defect; Represents any charge state during the traversal and summation process. Statistical weighting factors; Represents the numerical value of charge state Compared to the statistical partitioning normalized proportional term for all possible charge states.

[0068] For the process of finding the root value of the nonlinear iterative solution of the room temperature charge neutral equation, those skilled in the art can use a numerical program that combines the bisection method with tolerance threshold determination. The numerical convergence control in the multidimensional parameter space is a well-known technology in the field and will not be elaborated here.

[0069] S43. Deep-level activation monitoring and dynamic joint penalty execution. The core mechanism of this step is to transform the kinetic bottleneck of carrier recombination into a constraint within a thermodynamic optimization framework. This leads to the acquisition of a room-temperature self-consistent Fermi level. Subsequently, the decoupled solution module combines the relative energy level shift between the room-temperature self-consistent Fermi level and the deep level transition energy level obtained from the barrier reference data monitoring, and uses the relative energy level shift to assess the concentration of dangerous charge states. The physical criterion for defining a dangerous charge state is the electron trapping barrier extracted under a multiphonon emission model. The voltage level is below a set barrier threshold; in one specific embodiment, this safety barrier threshold is set to 0.2 eV. The physical basis for setting the barrier threshold is the lattice thermal excitation energy at room temperature. Several times the order of magnitude, meaning the barrier is in a range that room temperature thermal fluctuations can easily cross. For example, the electron capture barrier of the sulfur vacancy deep-level defect of the target in AgBiS2 is about 180 meV, which is within this high-risk capture range.

[0070] The decoupled solution module, based on the system's macroscopic environment and microscopic bandgap shift, accurately extracts the concentration of dangerous charge states by introducing statistical weighting factors and using the following decomposed partitioning formula. : ; ; ; in, The statistical weighting factor representing the dangerous charge state; The electronic state degeneracy factor represents the electronic state corresponding to the dangerous charge state; The composite term representing the room-temperature thermodynamic distribution probability of the dangerous charge state; This represents the defect ground state formation energy of the dangerous charge state under the current system self-consistent parameters; Represents the Boltzmann constant; This indicates the absolute room temperature corresponding to the device's operating temperature. Represents the numerical value of the charge state within the system. Statistical weighting factors; Represents the numerical value of charge state The corresponding electronic state degeneracy factor; Represents the numerical value of charge state The room temperature thermodynamic distribution probability composite term; Represents the numerical value of charge state Defect ground state formation energy under the current system self-consistent parameters; This indicates the concentration of dangerous charge states in the deep energy level activation state; Defects representing target types Total frozen concentration; This represents the summation of all possible charge states of a single defect type within the band gap; This represents the room-temperature statistical weighting of the dangerous charge state relative to all coexisting charge states in the system.

[0071] When the concentration of dangerous charge state Exceeding the safe concentration threshold This indicates that the material generated under the current process parameters contains a risk of inducing non-radiative recombination defects. Safety concentration threshold. The specific value is determined through device-level technical computer-aided design (TCAD) simulation. The specific method is as follows: gradually increase the recombination center concentration in the simulation model, and extract the defect concentration value at the critical point where the device's photoelectric conversion efficiency decreases by more than 5%. For device-level photoelectric conversion efficiency simulation, those skilled in the art can use conventional TCAD software to perform defect concentration scanning. The critical point extraction mechanism is a well-known technology in this field and will not be elaborated here.

[0072] To avoid such defects in parameter combinations during the optimization process at the algorithmic level, a dynamic penalty factor needs to be introduced into the initial objective function, which is guided by maximizing the concentration of n-type free electrons, to construct a modified objective function. To facilitate numerical optimization search, the decoupled solution module transforms the maximization problem into a minimization architecture by taking the inversion, thus enabling algorithmic optimization. This involves constructing a system containing a dynamic penalty factor. Corrected objective function mapped to negative bias free electron concentration The correlation is as follows: ; ; in, This represents the introduced dynamic penalty factor; This represents the penalty intensity multiplier, used to control the magnitude of the numerical jump caused by penalty intervention; This represents a non-negative activation triggering compound term constructed based on the exponential deviation model, used to ensure that the penalty is blocked when the optimization node is within the safe domain; A scaling parameter representing the degree of linear deviation from the safe concentration threshold; This represents the penalty sensitivity control hyperparameter, used to constrain the steepness of the penalty value; This indicates the concentration of the extracted hazardous charge state; This indicates the defined safe concentration threshold; This represents the modified objective function that minimizes the output. This represents the negative free electron concentration bias benchmark term that represents the original goal of maximizing the optimization.

[0073] For the hyperparameters of the above algorithm, the penalty intensity multiplier coefficient The value of is determined by performing an initial optimization trial without penalty, extracting the order of magnitude of the maximum spatial gradient of the free electron concentration throughout the feasible region as . The magnitude benchmark is used to ensure that the penalty term, once triggered, can effectively cover the original downhill gradient; the penalty sensitivity control hyperparameter... The value is set based on the process's tolerable concentration safety tolerance. In one optional embodiment, The value is configured to be 10. The value is configured to be 2.

[0074] Based on the modified objective function The design logic, when the concentration of dangerous charge states The concentration did not exceed the safe concentration threshold. When the non-negative activation triggers the composite term to output 0, the dynamic penalty factor is reduced. If the objective function is completely equivalent to the negative free electron concentration term, the system will slide normally along the direction of increasing electron concentration. And when the concentration of dangerous charge state Exceeding the safe concentration threshold At that time, dynamic penalty factor It increases exponentially in a positive direction, thus leading to the correction of the objective function. The calculation results show a positive penalty peak, causing the dynamic penalty factor to gain weight in the modified objective function, thus forcing the optimization path to deflect in the opposite direction. The final modified objective function will then be... Output and transmit to the parameter output module for evaluation of the optimal path.

[0075] See attached document Figure 6 For step S50, algorithm convergence determination and control window output, the modified objective function output by the decoupled solution module is received. The parameter output module performs convergence determination and parameter output operations through the following sub-steps: S51. Numerical Gradient Calculation and Search Path Update. While the decoupled solution module traverses and tracks the discrete grid point set within the initial feasible region, the parameter output module synchronously executes the numerical optimization search algorithm and utilizes the central difference method to calculate the silver chemical potential at each set of search nodes. Chemical potential of sulfur and annealing temperature Calculate the corrected objective function The partial derivatives with respect to each independent variable are used to construct the modified objective function. The local gradient vector in the multidimensional optimization parameter space is used to update the silver chemical potential within the iteration cycle based on the direction of the local gradient vector. Chemical potential of sulfur and annealing temperature The step direction. For the step size selection and coordinate update process of numerical optimization in multidimensional parameter space, those skilled in the art can configure Hessian matrix approximation or line search strategies for iteration. The numerical optimization principle is a well-known technology in this field and will not be elaborated here.

[0076] S52. Iterative convergence evaluation and determination. The parameter output module monitors and corrects the objective function. In continuous The magnitude of the gradient norm within the nth iteration period, where... This represents the preset threshold for determining the number of iterations. Gradient norm. Used to measure the corrected objective function The degree of flatness at the current parameter point. The gradient norm is extracted using the following relationship. : ; in, The partial derivative operator is used to represent partial derivatives. This indicates the modified objective function; Indicates the chemical potential of silver; Represents the chemical potential of sulfur; Indicates the annealing temperature; This represents the partial derivative of the modified objective function with respect to the chemical potential of silver; This represents the partial derivative of the modified objective function with respect to the chemical potential of sulfur; This represents the partial derivative of the modified objective function with respect to the annealing temperature; It represents the sum of the squares of the partial derivatives of each component; The Euclidean norm, or gradient norm, represents the multidimensional gradient vector. .

[0077] The parameter output module will calculate the gradient norm. Compared with the preset tolerance setting value Perform real-time comparisons. Tolerance setting. This is the square root of the self-consistent field energy convergence accuracy of the energy calculation module. Tolerance setting value. The baseline accuracy is obtained by reading the convergence standard value of the electron step energy in the underlying quantum chemistry computing environment, performing a square root operation on it, and then calculating it in conjunction with the grid spacing. In one embodiment, the tolerance setting value is... The value range is set to 1.0 × 10. -6 Up to 1.0×10 -4 between.

[0078] When the objective function is modified In continuous The algorithm is considered converged and the iteration terminates when the gradient norm in the next iteration is less than the tolerance threshold. (Iteration count threshold) The method for obtaining this is as follows: Pre-testing and evaluation are performed by extracting the trough smoothness features of the objective function within the multi-dimensional optimization space to balance computational time and convergence reliability. In a specific embodiment, the iteration count threshold is used to determine the threshold. The value range is set to 5 to 10 times. Using this standard to determine the convergence of the algorithm process can effectively avoid premature misjudgment caused by local numerical oscillations.

[0079] S53. Global Extremum Point Analysis and Doping Characterization. After the algorithm converges, the parameter output module analyzes and corrects the objective function. The set of parameters for obtaining the global minimum. To correspond with the coordinate system of the multidimensional optimization parameter space, the parameter set is specifically represented as a set of spatial vectors. It contains the optimal silver chemical potential that optimizes the objective function. Optimal sulfur chemical potential and optimal annealing temperature Based on the parameter set, the parameter output module determines the doping characteristics of n-type AgBiS2 materials that exclude the activation probability of deep-level recombination centers within a narrow chemical potential window and establishes the corresponding process control window.

[0080] Specifically, the parameter output module extracts the room-temperature self-consistent Fermi level corresponding to the parameter set. Free electron concentration And the rearrangement concentration distribution of various defects. Due to the modification of the objective function The guiding role of the penalty term in the output doping characteristics represents the theoretically achievable maximum concentration of n-type free electrons. At the same time, it eliminates the possibility of deep-level recombination centers being in dangerous charge states from a microscopic physical perspective, thus providing a deterministic boundary control window for the actual physical doping and thermal treatment processes of materials.

[0081] S54. Process Control Window Establishment and Physical Parameter Output. The parameter output module maps chemical potential coordinates to experimentally controllable physical variables to establish the corresponding process control window. For the chemical potential of sulfur... The parameter output module uses an ideal gas thermodynamic model to convert it into sulfur vapor partial pressure. The transformation logic follows the following relation: ; in, Represents the Boltzmann constant; This represents the optimal annealing temperature from the set of parameters that yield the global minimum. Indicates the partial pressure of sulfur vapor; This represents standard atmospheric pressure, with a value of 101325 Pa. Indicated at standard atmospheric pressure Below, the temperature is The standard chemical potential of sulfur at that time; This represents the relative pressure ratio of sulfur vapor partial pressure to standard atmospheric pressure. The natural logarithm of the relative pressure ratio; This indicates the optimal annealing temperature. The chemical potential correction term is due to pressure deviation; This represents the total sulfur chemical potential under the target temperature and pressure combination. The parameter output module will output the optimal sulfur chemical potential obtained from the analysis. Substitute into the relation and replace The optimal sulfur vapor partial pressure is obtained by inverse calculation. .

[0082] Standard chemical potential of sulfur The determination method is as follows: by extracting the standard enthalpy of formation of gaseous sulfur molecules and the entropy increase function with temperature from the thermodynamic database, linear interpolation calculation is performed using the Gibbs free energy definition.

[0083] The parameter output module ultimately outputs the optimal annealing temperature. Optimal sulfur vapor partial pressure And the optimal process parameters for the silver-to-bismuth feed ratio. The logic for determining the silver-to-bismuth feed ratio is as follows: the parameter output module is based on the optimal silver chemical potential in the parameter set. Matching with the corresponding bismuth chemical potential, combined with the optimal annealing temperature The elemental stoichiometry of the lower bulk phase is used to extract the concentration distribution of component defects such as silver vacancies and bismuth antisites under thermodynamic equilibrium, and then the concentration difference of micro-defects is converted into a macro-feed correction ratio that deviates from the ideal stoichiometry. The optimal process parameters define the experimental parameter range for preparing n-type AgBiS2 materials, providing a physical parameter basis for thermal field regulation and partial pressure compensation during film formation. For the specific interpolation algorithm for extrapolating the standard chemical potential using thermodynamic data tables, those skilled in the art can use polynomial fitting or the Schomatter equation for solution. The thermodynamic parameter conversion is a well-known technique in this field and will not be elaborated here.

[0084] Specific application examples: By setting an intrinsically defect-free supercell, sulfur-containing vacancies are constructed by removing sulfur atoms from target lattice sites. The defective supercell is used. A systematic displacement perturbation with an amplitude of 15% of the local average bond length is applied to the coordinates of neighboring atoms within the defective supercell to generate a set of candidate geometries. Pre-relaxation calculations are performed on the set of candidate geometries, and the atomic coordinates are iteratively updated using the conjugate gradient algorithm. The ground state structure with the lowest global energy where the force gradient converges to 0.02 eV / Å is extracted to eliminate the interference of local metastable states.

[0085] Static electronic structure calculations were performed using the HSE06 hybrid density functional. Electronic structure information was obtained by configuring the Brillouin zone K-point grid cutoff energy and performing a self-consistent charge density loop. A three-dimensional anisotropic dielectric tensor and electrostatic potential alignment term were introduced, and finite-size dielectric correction (i.e., subtracting the electrostatic energy interaction shift of charged defects caused by periodic boundary conditions) was performed using an extended finite-size dielectric correction scheme to obtain finite-size dielectric correction, accurately outputting the numerical values ​​of sulfur vacancies in charge states. , as well as The defect ground state formation energy corresponding to the target charge state at time.

[0086] Based on the defect ground state formation energy corresponding to the target charge state of the sulfur vacancy, the thermodynamic transition energy levels of deep-level defects under different charge states are analyzed. The relative displacement difference of coordinates when adjacent charge states are in equilibrium lattice configuration is calculated, and this difference is combined with atomic mass to obtain the mass-weighted displacement after dimension reduction quantization. .

[0087] In a one-dimensional configuration coordinate diagram, the lattice adiabatic potential energy surface corresponding to different charge states is fitted using a parabolic function based on the simple harmonic oscillator approximation. For example... Figure 7 As shown, its horizontal axis represents the mass-weighted displacement corresponding to the geometric deformation. (amu) 1 / 2The vertical axis represents the total energy (eV) of the system calculated using quantum mechanics and after applying an extended finite-size dielectric correction scheme. The nonradiative electron trapping barrier in the multiphonon emission state is determined and extracted by extracting the energy difference between the energy crossover point and the relative equilibrium state. With Hole Capture Barrier Barrier to capture non-radiative electrons With Hole Capture Barrier Integrate into barrier baseline data.

[0088] Using the enthalpy of formation of the main phase AgBiS2, combined with pre-calculated enthalpy data of secondary competing phases such as Ag2S, Bi2S3, elemental Ag, and elemental S within the system, a rigorous set of linear constraints for thermodynamic phase space equations and inequalities is constructed. On a multidimensional optimization parameter space with silver chemical potential, sulfur chemical potential, and annealing temperature as reference coordinates, a polygonal phase diagram constraint boundary that ensures the stable existence of the main phase is analytically obtained. Inside the defined polygonal phase diagram constraint boundary, a uniform grid discretization process is performed with a coordinate step size of 0.05 eV, generating a series of discrete chemical potential coordinate points. These coordinate points are combined with the annealing temperature range to form a discrete grid point set, which is then output as the initial feasible region for tracing.

[0089] Receive and track the initial feasible region and potential barrier baseline data, and establish a dual-temperature decoupled model for the discrete grid point set within the feasible region. Configure a high-temperature annealing simulation environment and use the Newton-Raphson numerical optimization algorithm to solve for all intrinsic defect types (such as sulfur vacancies). Silver gap Reverse position defect The high-temperature charge-neutral equation (etc.) is used to obtain the high-temperature Fermi level of the system. The total freezing concentration of various defects at this time was extracted based on the Boltzmann statistical distribution. .

[0090] The calculation parameters were switched to the device operating temperature of 300K at room temperature. A cryogenic carrier rearrangement solution was performed for the total defect concentration after freezing, and the room-temperature self-consistent Fermi level was iteratively calculated. With free electron concentration A dynamic penalty factor is introduced into the initial objective function, which is guided by maximizing the concentration of n-type free electrons. When the combination of chemical potentials corresponding to the evaluation node causes the Fermi level to transition across a deeper level, the concentration of dangerous charge states increases. Exceeding the safe concentration threshold At that time, dynamic penalty factor When triggered and a positive energy barrier is applied, the optimization path is forced to deflect in the opposite direction, and a corrected objective function is output. .

[0091] Continuous monitoring during calculation The corrected objective function in the next iteration period gradient norm Size. When the gradient norm in the multidimensional parameter space Less than the tolerance setting value At that time, the algorithm process is considered convergent. Analysis allows for the correction of the objective function. The set of parameters that yields the global minimum includes the optimal silver chemical potential. Optimal sulfur chemical potential and optimal annealing temperature The algorithm then utilizes an ideal gas thermodynamic model to output the optimal sulfur chemical potential. The reverse conversion yields the optimal sulfur vapor partial pressure for guiding experimental film-forming annealing. : Finally, combining the optimal silver chemical potential The material doping characteristics that exclude the activation probability of deep-level recombination centers under a narrow chemical potential window are determined, and the optimal process parameters are output.

[0092] See attached document Figure 8 The horizontal axis in the figure represents the room-temperature self-consistent Fermi level within the bandgap. (eV) Position. In the figure, the dark gray bottom layer represents the valence band region (VBM) (0 is the top boundary of the valence band), and the light gray bottom layer represents the conduction band region (CBM) (1.18eV is the bottom boundary of the conduction band). The vertical axis represents the defect ground state formation energy at the corresponding Fermi level. (eV). The major intrinsic point defects within the system are marked by black dashed lines that provide compensation. (Subject), black dotted line (The benefactor) and the bold black solid lines representing different energy envelope paths. (Complex defect). The gray-filled dots in the figure precisely reveal the thermodynamic transition energy levels at which sulfur vacancies undergo charge state transformation. The vertical black dotted line in the figure directly indicates the room-temperature self-consistent Fermi level output by the algorithm. A safe location.

[0093] based on Figure 7 Data analysis and extraction indicate that the sulfur vacancy system consists of donor states ( Towards deep-level composite centers ( During the evolution, the energy crossover point of the adiabatic potential energy surface is extremely close to the lowest point of the ground state equilibrium configuration. Quantitative calculations show that the nonradiative electron trapping barrier in this process... Extremely low, falling within the range of room-temperature microscopic lattice thermal excitation. Once macroscopic processes cause the Fermi level to be pushed up and cross this thermodynamic transition level, the activated neutral sulfur vacancies will act as strong traps to rapidly capture free electrons in the conduction band, resulting in a precipitous drop in carrier lifetime.

[0094] Figure 8 The physical evolution characteristics of the spectrum verified the effectiveness and core mechanism of the algorithm of this invention. In traditional single-objective process optimization, the pursuit of high electron concentration often leads to the chemical potential entering the extremely sulfur-depleted region, causing the self-consistent Fermi level to inevitably shift to the conduction band bottom and cross thermodynamic transition levels. (Right now Figure 8 The gray-filled dots (at which position) trigger catastrophic nonradiative recombination. The algorithm of this invention introduces a dynamic penalty factor. The optimal thermodynamic equilibrium point was precisely found in the multidimensional phase space. Under the optimal chemical potential conditions output by the algorithm (such as...), Figure 8 As shown in reality: on the one hand, it effectively raised the parasitic compensatory recipient ( On the one hand, the algorithm determines the formation energy of the room-temperature self-consistent Fermi level through underlying charge state constraint game. (Right now Figure 8 The vertical black dotted line (located in the middle) was successfully anchored in the absolutely safe zone immediately before the dangerous deep-level transition point.

[0095] This mechanism completely avoids the dead zone of material evolution into deep-level traps, eliminating the contradiction between macroscopic doping concentration and microscopic trap states at the first-principles level. The optimal sulfur vapor partial pressure and other process control parameters output in the end physically ensure that the prepared n-type AgBiS2 material can simultaneously possess high free electron concentration and excellent carrier survival lifetime, thereby enhancing the material's photoelectric conversion potential.

Claims

1. A method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window, characterized in that, Includes the following steps: A set of candidate geometric configurations is generated by applying displacement perturbation to the defect configurations in the narrow bandgap semiconductor AgBiS2 system, and the defect ground state formation energy corresponding to the target charge state is obtained using the set of candidate geometric configurations; Based on the ground state formation energy of the defect, the thermodynamic transition energy level of the deep energy level defect is extracted. Based on the thermodynamic transition energy level, the non-radiative electron trapping barrier and hole trapping barrier are extracted and integrated into barrier reference data. A multidimensional optimization parameter space is defined, and a polygonal phase diagram constraint boundary is delineated within the multidimensional optimization parameter space. A discrete grid point set is generated inside the polygonal phase diagram constraint boundary as the initial feasible region for tracing. Traverse the discrete grid point set within the initial feasible domain of the tracking, perform high-temperature defect freezing simulation in the decoupled feedback loop to obtain the total freezing concentration of different defects, and perform low-temperature carrier rearrangement solution based on the total freezing concentration to obtain the room temperature self-consistent Fermi level. By combining the aforementioned barrier reference data, the relative energy level shift between the room-temperature self-consistent Fermi level and the deep energy level transition level is monitored, and the concentration of dangerous charge states is assessed using the relative energy level shift. When the concentration of dangerous charge states exceeds the safe concentration threshold, a dynamic penalty factor is introduced into the initial objective function, which is guided by maximizing the concentration of n-type free electrons, to construct a modified objective function; The modified objective function is iteratively optimized to obtain a set of parameters that satisfy the convergence condition. Based on the set of parameters, the doping characteristics of the n-type AgBiS2 material are determined and a corresponding process control window is established.

2. The method for calculating the doping characteristics of n-type AgBiS2 material under a narrow chemical potential window according to claim 1, characterized in that, The specific steps for obtaining the defect ground state formation energy corresponding to the target charge state using the candidate geometric configuration set include: Intrinsic AgBiS2 primitives were established and expanded according to periodic boundary conditions to generate intrinsic supercells; By removing or adding target atoms within the intrinsic supercell, defect centers containing vacancies, interstitials, or antisites are constructed, forming a defective supercell. Within the defective supercell, the atoms of the first coordination layer and the second coordination layer surrounding the defect center are defined as neighboring atomic domains, and systematic displacement perturbations are applied to the atoms in the neighboring atomic domains along different crystallographic directions; The systematic displacement perturbation is discretized and gridded according to the set amplitude step size and lattice symmetry rules, splitting and expanding the single initial structure to generate the candidate geometric configuration set composed of multiple different initial distortion states. Pre-relaxation calculations are performed on the candidate geometric configuration set to obtain the ground state structure with the lowest global energy. Static electronic structure calculations are then performed on the ground state structure, and the electrostatic energy shift caused by long-range Coulomb interactions is compensated using an extended finite-size dielectric correction scheme to obtain the defect ground state formation energy corresponding to the target charge state.

3. The method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window according to claim 2, characterized in that, The extended finite-size dielectric correction scheme is based on the long-range electrostatic energy shift introduced by the periodic lattice composed of point charges under an anisotropic dielectric background and the total macroscopic potential energy alignment correction term, and extracts the finite-size dielectric correction. The total macroscopic potential energy alignment correction term is determined based on the product of the charge state value of the defect and the macroscopic electrostatic potential alignment difference between the supercell containing the target charge state defect and the intrinsically defect-free supercell at a position far from the defect center. The defect ground state formation energy is obtained by combining the total system energy of the supercell containing the target charge state defect ground state, the total system energy of the intrinsically defect-free supercell, the total chemical potential change due to atomic exchange, the electronic chemical potential change corresponding to the exchange charge between the defect and the electronic system, and the addition and subtraction combination of the finite size dielectric correction.

4. The method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window according to claim 1, characterized in that, The specific methods for extracting thermodynamic transition energy levels of deep-level defects based on the aforementioned defect ground state formation energy include: Values ​​for charge states that undergo mutual transformation and values ​​for adjacent charge states are set for deep-level defects; With the Fermi level set to 0, calculate the energy difference between the defect ground state formation energy corresponding to the charge state value and the defect ground state formation energy corresponding to the adjacent charge state value; Calculate the total amount of charge transferred when adjacent different charge states transition into each other; The ratio of the energy difference to the total charge is taken as the thermodynamic transition energy level.

5. The method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window according to claim 1, characterized in that, The specific steps for extracting the nonradiative electron trapping barrier and hole trapping barrier based on the aforementioned thermodynamic transition energy levels include: Two equilibrium lattice configurations corresponding to the charge states of the thermodynamic transition energy level are obtained, and the structural evolution path is extracted along the geometric evolution trajectory of the two equilibrium lattice configurations. By integrating the displacement of each atom along the structural evolution path with the corresponding atomic mass, the mass-weighted displacement is calculated. Using the mass-weighted displacement as the abscissa and the total system energy including the ground state supercell of the target charge state defect as the ordinate, a one-dimensional configuration coordinate diagram is constructed. The lattice adiabatic potential energy surface is analyzed using the one-dimensional configuration coordinate diagram. The non-radiative electron trapping barrier and the hole trapping barrier of charge carriers in the multiphonon emission state are extracted by analyzing the lattice adiabatic potential energy surface.

6. The method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window according to claim 1, characterized in that, Define a multidimensional optimization parameter space, and delineate polygonal phase diagram constraint boundaries within the multidimensional optimization parameter space, specifically including: The silver chemical potential, sulfur chemical potential, and annealing temperature are used as three independent variables to construct the multidimensional optimization parameter space. The polygonal phase diagram constraint boundary is defined in the multidimensional optimization parameter space using the main phase stability condition and the secondary competing phase repulsion condition. The stability condition of the main phase includes the thermodynamic equilibrium relationship between the sum of the chemical potentials of each element constituting AgBiS2 and the formation enthalpy of the AgBiS2 main phase. The sum of the chemical potentials of each element includes the chemical potential of silver, the chemical potential of bismuth, and twice the chemical potential of sulfur. The energy required to form a secondary competing phase of one chemical formula unit is obtained by summing the product of the chemical potential of each element contained in the chemical formula of the secondary competing phase and the number of atoms of each corresponding atom. The energy of the secondary competing phase is limited to not exceeding the formation enthalpy of the secondary competing phase, and an inequality constraint relationship is constructed as the repulsion condition of the secondary competing phase.

7. The method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window according to claim 1, characterized in that, Dangerous charge states are defective charge states in which the electron trapping barrier extracted under the multiphonon emission model is less than the set barrier determination threshold. The safe concentration threshold is determined by gradually increasing the concentration of recombination centers in the device-level computer-aided design simulation model, and extracting the defect concentration value that causes the device's photoelectric conversion efficiency to decrease by more than 5%.

8. The method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window according to claim 7, characterized in that, Extract the room-temperature statistical weighting ratio of the dangerous charge state relative to all coexisting charge states in the narrow bandgap semiconductor AgBiS2 system; The concentration of the hazardous charge state is obtained by multiplying the total freezing concentration of the corresponding defect by the room temperature statistical weighting term of the hazardous charge state. When the concentration of the dangerous charge state does not exceed the safe concentration threshold, the dynamic penalty factor is set to 0.

9. The method for calculating the doping characteristics of n-type AgBiS2 materials under a narrow chemical potential window according to claim 1, characterized in that, Obtaining the set of parameters that makes the modified objective function satisfy the convergence condition, and determining the doping characteristics of the n-type AgBiS2 material specifically includes: The algorithm is determined to have converged when the gradient norm of the modified objective function is less than the tolerance setting value during multiple consecutive iterations. The set of parameters that makes the modified objective function obtain the global minimum is then analyzed. The doping characteristics of n-type AgBiS2 materials, excluding the activation probability of deep-level recombination centers, were established using the aforementioned parameter set.

10. The method for calculating the doping characteristics of n-type AgBiS2 material under a narrow chemical potential window according to claim 9, characterized in that, The process involves analyzing the set of parameters that minimizes the objective function and establishing a corresponding process control window, specifically including: The parameter set is represented as a spatial vector group containing the optimal silver chemical potential, the optimal sulfur chemical potential, and the optimal annealing temperature. Extract the room temperature self-consistent Fermi level, free electron concentration, and rearrangement concentration distribution of various defects corresponding to the parameter set; The optimal sulfur chemical potential is converted into the optimal sulfur vapor partial pressure using an ideal gas thermodynamic model. The output includes the optimal process parameters, including the optimal annealing temperature, the optimal sulfur vapor partial pressure, and the silver to bismuth feed ratio, and establishes the process control window.

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