Method for calculating diffusion coefficient of interstitial defect in 4H-SiC based on charge transformation and entropy change

Abstract

The invention relates to a 4H-SiC interstitial defect diffusion coefficient calculation method based on charge transformation and entropy change, which comprises the following steps: firstly, searching defect configuration by adopting an enhanced sampling method, and calculating defect formation energy based on zero point energy contribution; secondly, determining a reaction path through a free energy surface in a defect migration process, and calculating a defect migration barrier; then, quantifying an effective potential barrier (activation energy) of defect migration based on charge transformation and an atom migration potential barrier; further, the migration entropy is solved by adopting methods such as free energy difference and vibration entropy calculation; and finally quantifying the diffusion coefficient of the gap defect in the 4H-SiC based on a macroscopic diffusion coefficient equation. According to the method, the dynamic migration capability of the defect can be rapidly quantified, and reference is provided for selection of the annealing temperature and the annealing time in an experiment.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor technology, and in particular to a method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge conversion and entropy change. Background Art

[0002] 4H-SiC is a core material for power electronic devices, widely used in quantum physics, nuclear energy, and aerospace. During single crystal growth, device fabrication, and subsequent service life, 4H-SiC often contains high concentrations of point defects (such as vacancies, interstitials, and antisites), significantly impacting material performance.

[0003] Interstitial defects are usually highly mobile and are important media for defect recovery and regulation. During the single crystal growth process, carbon vacancies are highly abundant, but they are also the main killer of carrier lifetimes, significantly affecting device performance. In order to improve the quality of SiC crystals as device materials, two different methods are usually used to reduce carbon vacancies: near-surface ion implantation and high-temperature annealing, thermal oxidation of epitaxial silicon terminals, and medium-temperature annealing under carbon-rich thermodynamic equilibrium conditions. The essence of these methods is to migrate interstitial defects with good mobility into the interior of the crystal through thermal activation. During device preparation, the surface SiC is oxidized to a SiO2 layer, and excess carbon interstitials may also remain at the interface, forming interface traps while increasing the interface state density, affecting device performance and reliability. In addition, 4H-SiC devices serving in radiation environments are usually prone to the accumulation of interstitial-vacancy pair defects, leading to material expansion and amorphization. The self-healing and recovery of radiation damage also mainly depend on the diffusion behavior of interstitial defects.

[0004] Chinese patent application publication number CN112836344A discloses a method for calculating the diffusion behavior of interstitial atoms in high-entropy alloys. By quantitatively calculating the site occupancy preferences of alloying elements and the diffusion paths of atoms in high-entropy alloys, this method solves the problem of difficult description of interstitial atomic diffusion behavior in existing technologies, enabling accurate description of interstitial atoms in high-entropy alloys and research on their diffusion processes. However, this method does not comprehensively consider the effects of charge transitions and entropy changes, and suffers from the drawbacks of multiple factors and high costs.

[0005] In summary, interstitial defects play a crucial role in the defect evolution of 4H-SiC. However, due to the lack of diffusion coefficients, selecting appropriate experimental conditions for defect manipulation is often difficult. The coexistence of multiple defects, as well as temperature and Fermi level dependence, add significant cost and uncertainty to experimentally determining the diffusion coefficient. Therefore, a theoretical model that can rapidly predict interstitial kinetic diffusion behavior is urgently needed. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change, so as to solve or partially solve the problem of unclear and difficult control of the kinetic diffusion behavior of interstitial defects in 4H-SiC.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] The present invention provides a method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change, comprising the following steps:

[0009] The most stable interstitial sites in 4H-SiC were selected as target sites, the configurations of the low potential energy regions of enhanced sampling dynamics were extracted for structural optimization, and the formation energy of the target sites was calculated based on the zero-point energy contribution.

[0010] Calculate the migration barrier based on the interstitial migration path;

[0011] Based on the formation energy and the migration barrier, searching for charge conversion and atomic migration barriers to quantify all possible ways of defect migration and their effective barriers, and screening to obtain the lowest effective barrier at each Fermi level;

[0012] Calculating a migration entropy change during the migration process based on the gap migration path;

[0013] An attempt frequency is obtained, and a diffusion coefficient is calculated based on the migration entropy change and the effective potential barrier.

[0014] As a preferred technical solution, the formation energy of the target site can be calculated using the following formula:

[0015] E f (q) = E tot (q)-E tot (bulk)+ZPE tot (q)-ZPE tot (bulk)-∑ i n i (μi+E i )+q(ε VBM +E F )+Δ q

[0016] Among them, E tot (q) is the defect state energy at charge state q, in eV; E tot (bulk) is the energy of a perfect supercell of the same size, in eV; ZPE tot (q) and ZPE tot (bulk) are the zero-point vibrational energies of the charge state q defect and the perfect supercell, in eV; ni is the number of interstitial atoms; μ i is the difference between the energy of an element in its chemical environment and the energy of its pure phase; E i is the atomic energy in pure phase, in eV; ε VBM is the valence band top energy; E F is the Fermi level relative to the valence band top; Δ q is the effective size correction term.

[0017] As a preferred technical solution, the process of calculating the migration barrier based on the interstitial migration path includes the following steps:

[0018] According to the results of enhanced sampling molecular dynamics process, the key frames of the migration process are extracted to obtain the migration mode and basic path of carbon gaps;

[0019] The migration barrier is calculated until the residual force is less than the threshold, and the configuration and migration barrier of the transition state are obtained.

[0020] As a preferred technical solution, NEB and CI-NEB methods are used to calculate the migration barrier.

[0021] As a preferred technical solution, the process of obtaining the lowest effective barrier at each Fermi level includes the following steps:

[0022] For charge state 0, for all Fermi levels, subtract the ground state formation energy from the corresponding formation energy to obtain the charge transition energy, and repeat this operation for all charge states;

[0023] For charge state 0, based on the charge transition energy and the migration barrier, the effective barrier of charge state 0 is obtained, and this operation is repeated for all charge states;

[0024] For all Fermi levels, the charge state with the lowest effective barrier and its effective barrier are screened out as the defect migration activation energy.

[0025] As a preferred technical solution, the calculation process of the migration entropy change in the migration process includes the following two methods:

[0026] (1) Calculate the difference between the vibrational entropy contributions of the ground state and the transition state (excluding one frequency in the ground state migration direction when calculating the vibrational entropy),

[0027] (2) The difference in free energy barriers at different temperatures, then divided by the temperature.

[0028] As a preferred technical solution, the diffusion coefficient is calculated using the following formula:

[0029]

[0030] Where D is the diffusion coefficient, in m 2 / s; z is the structure factor; a is the interstitial atomic migration distance, in m; Γ0 is the trial frequency; ΔS is the migration entropy change; k B is the Boltzmann constant; E b,EFE (E F ) is the effective potential barrier in eV.

[0031] As a preferred technical solution,

[0032] The process of extracting the configuration of the enhanced sampling dynamic low energy region and performing structural optimization includes:

[0033] Using enhanced sampling molecular dynamics and the NVT ensemble, we calculated the free energy surface of carbon interstitials, derived defect morphologies, and performed structural optimization. As a preferred technical solution, we screened the most stable interstitial sites in 4H-SiC as target sites. Candidate interstitial sites included carbon tetrahedral sites, silicon tetrahedral sites, hexahedral sites, carbon-silicon isocoordinated sites, carbon cleavage interstitials, and silicon cleavage interstitials.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] Fully and comprehensively consider the effects of charge transition and entropy change: In calculating the diffusion coefficient of 4H-SiC intermediate defects, the present invention searches for charge transition and atomic migration barriers to quantify all possible defect migration modes and their effective barriers, screening to obtain the lowest effective barrier at each Fermi level, taking into account the effect of charge transition on the diffusion coefficient. Furthermore, based on the interstitial migration path, the migration entropy change during the migration process is calculated, taking into account the effect of entropy change on the diffusion coefficient. By incorporating the effects of charge transition and entropy change into the accurate calculation of the kinetic diffusion coefficient and comprehensively considering factors such as charge state and Fermi level, the experimental problems of multiple factors and high costs are avoided, achieving rapid calculation of the interstitial kinetic coefficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of the calculation process of the interstitial defect diffusion coefficient in 4H-SiC in the embodiment;

[0037] Figure 2 Figure 3 is a diffusion coefficient diagram of carbon interstitial migration from the h-site to the adjacent h-site in the embodiment (part of the Fermi level diffusion coefficient overlaps and is blocked). DETAILED DESCRIPTION

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0039] In view of the problems existing in the above-mentioned prior art, this embodiment provides a method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change, aiming to solve the problem of unclear kinetic diffusion behavior of interstitial defects in 4H-SiC and difficulty in regulation. Figure 1 , the method comprises the following steps:

[0040] Step S1, screen the most stable interstitial sites in 4H-SiC, determine the most stable ground state configuration, extract the configuration of the enhanced sampling dynamics low energy region for structural optimization, and finally calculate the formation energy based on the zero-point energy contribution.

[0041] The sites considered include carbon tetrahedral sites, silicon tetrahedral sites, hexahedral sites, carbon-silicon isocoordinate sites, carbon cleavage gaps, and silicon cleavage gaps. The ground state configuration is determined by combining enhanced sampling with first-principles calculations, molecular dynamics, and machine learning. The contribution of zero-point energy is considered in the calculation of formation energies.

[0042] Step S2, determining the migration mode and basic migration path of the interstitial migration, and then calculating the reaction barrier based on the migration path.

[0043] The fundamental method for determining migration pathways is a combination of enhanced sampling with first-principles calculations, molecular dynamics, and machine learning. Methods for calculating reaction barriers include Nudged Elastic Band (NEB) and Climbing Image Nudged Elastic Band (CI-NEB).

[0044] Step S3, based on the above two steps, quantify all possible ways of defect migration and their effective barriers based on charge conversion and atomic migration barriers, and screen out the lowest effective barrier (activation energy) at each Fermi level.

[0045] The charge transfer energy is obtained by dividing the excited state formation energy by the ground state formation energy, and the effective barrier is obtained by adding the charge transfer energy and the migration barrier. The lowest effective barrier at each Fermi level determines the migration mode of the gap.

[0046] Step S4: calculating the migration entropy of the migration process based on the gap migration path.

[0047] Among them, the calculation of transfer entropy includes two methods: (a) solving the difference in free energy barriers at different temperatures; (b) solving the difference in entropy contributions between the ground state and the transition state.

[0048] Step S5: determine the trial frequency and calculate the diffusion coefficient according to the macroscopic diffusion coefficient equation.

[0049] The trial frequency is obtained by the ratio of the product of the ground state frequency and the product of the transition state frequency.

[0050] The calculation process is explained below using the calculation of the diffusion kinetic coefficient of the hexagonal (h) carbon interstitial in 4H-SiC as an example.

[0051] (1) The carbon interstitial formation energy of h-sites was calculated: the amount of carbon tetrahedral sites, silicon tetrahedral sites, hexahedral sites, carbon cleavage interstitial sites, silicon cleavage interstitial sites and other sites were compared, and it was determined that the carbon cleavage interstitial site in 4H-SiC is the most energy-favorable occupied site for carbon interstitial. The free energy surface of carbon interstitial was calculated by enhanced sampling first-principles molecular dynamics method and NVT ensemble, and the defect morphology was preliminarily determined. Then the structure was optimized. Subsequently, the zero-point energy of the ground state of the perfect supercell and the defect supercell was calculated, and the formation energy was calculated based on the zero-point energy correction.

[0052] The calculation formula of formation energy is as follows:

[0053] E f (q) = E tot (q)-E tot (bulk)+ZPE tot (q)-ZPE tot (bulk)-∑ i n i (μi+E i )+q(ε VBM +E F )+Δ q

[0054] Where, E tot (q) is the defect state energy at charge state q, in eV; E tot (bulk) is the energy of a perfect supercell of the same size, in eV; ZPE tot (q) and ZPE tot (bulk) is the zero-point vibrational energy of the charge state q defect and the perfect supercell, eV; n i is the number of interstitial atoms; μ i is the difference between the energy of an element in its chemical environment and the energy of its pure phase; E i is the atomic energy in the pure phase, eV; ε VBM is the valence band top energy; E F is the Fermi level relative to the valence band top; Δ qis the effective size correction term.

[0055] (2) Calculation of the migration barrier for the carbon interstitial migration process at the h-site: Based on the results of the enhanced sampling molecular dynamics process, the key frames of the migration process were extracted to identify the migration mode and basic path of the carbon interstitial. The migration barrier was then calculated using a combination of NEB and CI-NEB until the residual force was less than 0.03 eV / Å, obtaining the transition state configuration and migration barrier. The migration barriers for the 2+, 1+, 0, 1-, and 2- charge states were 1.20, 0.99, 0.58, 0.96, and 1.31 eV, respectively.

[0056] (3) Calculation of the activation energy for interstitial carbon migration from an h-site to an adjacent h-site: For charge state 0, subtract the ground state formation energy from its formation energy at all Fermi levels to obtain the charge transition energy, and repeat this operation for all charge states. For charge state 0, add the charge transition energy to the migration barrier to obtain the effective barrier for the 0 charge state, and repeat this operation for all charge states. For all Fermi levels, select the charge state with the lowest effective barrier and its effective barrier as the defect migration activation energy. At Fermi levels of 0.8, 1.6, 2.4, and 3.2 eV, the activation energies for interstitial carbon migration from an h-site to an adjacent site are 1.20, 0.58, 0.58, and 1.22 eV, respectively.

[0057] (4) Calculate the migration entropy of the carbon interstitial migration from the h site to the adjacent h site: solve it by the difference between the entropy contribution of the ground state and the transition state. The migration entropy changes are 4.070k for the 2+, 1+, 0, 1- and 2- charge states, respectively. B , 1.025k B , 0.730k B , 2.174k B , 1.464k B .

[0058] (5) Calculate the diffusion coefficient of the carbon interstitial migration from the h site to the adjacent h site: the trial frequency is obtained by the ratio of the product of the ground state frequency and the product of the transition state frequency; the macroscopic diffusion coefficient is solved by the following formula, and the coefficient obtained is as follows Figure 2 shown.

[0059]

[0060] Where D is the diffusion coefficient, m 2 / s; z is the structure factor; a is the interstitial atomic migration distance, m; ΔS is the entropy change; Γ0 is the trial frequency; k B is the Boltzmann constant; E b,EFE (E F ) is the effective potential barrier, eV.

[0061] In summary, this method first uses an enhanced sampling method to locate defect configurations and calculates defect formation energies based on zero-point energy contributions. Second, the free energy surface of the defect migration process is used to identify reaction pathways and calculate the defect migration barrier. The effective barrier (activation energy) to defect migration is then quantified based on charge transition and atomic migration barriers. Furthermore, the migration entropy is calculated using methods such as free energy difference and vibrational entropy calculations. Finally, the diffusion coefficient of interstitial defects in 4H-SiC is quantified based on the macroscopic diffusion coefficient equation. By incorporating the effects of charge transition and entropy change into the accurate calculation of the kinetic diffusion coefficient, and comprehensively considering factors such as charge state, Fermi level, defect concentration, and temperature, this method avoids the experimental challenges of multiple factors and high costs. This method provides a paradigm for the rapid prediction of interstitial kinetic coefficients, allows for rapid quantification of defect kinetic migration capabilities, and provides a reference for the selection of annealing temperature and time in experiments.

[0062] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change, characterized in that: The steps include: The most stable interstitial sites in 4H-SiC were selected as target sites, the configurations of the low potential energy regions of enhanced sampling dynamics were extracted for structural optimization, and the formation energy of the target sites was calculated based on the zero-point energy contribution. Calculate the migration barrier based on the interstitial migration path; Based on the formation energy and the migration barrier, searching for charge conversion and atomic migration barriers to quantify all possible ways of defect migration and their effective barriers, and screening to obtain the lowest effective barrier at each Fermi level; Calculating a migration entropy change during the migration process based on the gap migration path; An attempt frequency is obtained, and a diffusion coefficient is calculated based on the migration entropy change and the effective potential barrier.

2. The method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change according to claim 1, characterized in that: The process of extracting the configuration of the enhanced sampling dynamic low energy region and performing structural optimization includes: Based on the enhanced sampling molecular dynamics method and NVT ensemble, the free energy surface of the carbon interstitial was calculated, the defect morphology was obtained, and the structure was optimized.

3. The method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change according to claim 1, characterized in that: In the process of screening the most stable interstitial sites in 4H-SiC as target sites, the candidate interstitial sites include carbon tetrahedral site, silicon tetrahedral site, hexahedral site, carbon-silicon isocoordinated site, carbon cleavage interstitial site and silicon cleavage interstitial site.

4. The method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change according to claim 1, characterized in that: The target site formation energy can be calculated using the following formula: E f (q)=E tot (q)-E tot (bulk)+ZPE tot (q)-ZPE tot (bulk)-∑ i n i (μ i +E i )+q(ε VBM +E F )+Δ q Among them, E tot (q) is the defect state energy at charge state q, in eV; E tot (bulk) is the energy of a perfect supercell of the same size, in eV; ZPE tot (q) and ZPE tot (bulk) are the zero-point vibrational energies of the charge state q defect and the perfect supercell, in eV; n i is the number of interstitial atoms; μ i is the difference between the energy of an element in its chemical environment and the energy of its pure phase; E i is the atomic energy in pure phase, in eV; ε VBM is the energy of the valence band top; E F is the Fermi level relative to the valence band top; Δ q is the effective size correction term.

5. The method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change according to claim 1, characterized in that: The process of calculating the migration barrier based on the interstitial migration path includes the following steps: According to the results of enhanced sampling molecular dynamics process, the key frames of the migration process are extracted to obtain the migration mode and basic path of carbon gaps; The migration barrier is calculated until the residual force is less than the threshold, and the configuration and migration barrier of the transition state are obtained.

6. The method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change according to claim 5, characterized in that: The migration barriers were calculated using the NEB and CI-NEB methods.

7. The method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change according to claim 1, characterized in that: The process of obtaining the lowest effective barrier at each Fermi level includes the following steps: For charge state 0, for all Fermi levels, subtract the ground state formation energy from the corresponding formation energy to obtain the charge transition energy, and repeat this operation for all charge states; For charge state 0, based on the charge transition energy and the migration barrier, the effective barrier of charge state 0 is obtained, and this operation is repeated for all charge states; For all Fermi levels, the charge state with the lowest effective barrier and its effective barrier are screened out as the defect migration activation energy.

8. The method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change according to claim 1, characterized in that: The calculation process of the migration entropy change in the migration process includes the following two methods: (1) Calculate the difference between the vibrational entropy contributions of the ground state and the transition state (excluding one frequency in the ground state migration direction when calculating the vibrational entropy), (2) The difference in free energy barriers at different temperatures, then divided by the temperature.

9. The method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change according to claim 1, characterized in that: The diffusion coefficient is calculated using the following formula: Where D is the diffusion coefficient, in m 2 / s; z is the structure factor; a is the interstitial atomic migration distance, in m; Γ0 is the trial frequency; ΔS is the migration entropy change; k B is the Boltzmann constant; E b,EFE (E F ) is the effective potential barrier in eV.

10. The method for calculating the diffusion coefficient of interstitial defects in 4H-SiC based on charge transition and entropy change according to claim 1, characterized in that: Enhanced sampling dynamics is a combination of first principles, molecular dynamics, and machine learning methods to determine the ground state structure and transition state pathways.

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