A method for calculating the band structure of superlattice materials

Abstract

The present invention discloses a method for calculating the band structure of a superlattice material, comprising the following steps: ab initio calculation of the lattice constants of the substrate and the various bulk materials that comprise the superlattice; constructing a superlattice model using the substrate lattice constants and the lattice constants of the various bulk materials that comprise the superlattice; relaxing the superlattice model; performing electron self-interaction correction using the shDFT-1 / 2 algorithm to obtain a corrected pseudopotential; and calculating the electronic band structure of the superlattice using the corrected pseudopotential. The present invention proposes an optimized shDFT-1 / 2 calculation method that achieves excellent results for covalent semiconductors such as InAs and GaSb, and superlattice materials composed of them. The shDFT-1 / 2 calculation method requires no empirical parameters and is both highly accurate and universally applicable.

Description

Technical Field

[0001] The present invention belongs to the technical field of infrared detection devices, and in particular relates to a method for calculating the energy band structure of a superlattice material. Background Art

[0002] Infrared detectors are widely used in integrated optoelectronic systems in modern high-end weaponry due to their advantages, such as long detection range, strong anti-interference capabilities, good concealment, and all-weather capability. With the growing demand for military equipment modernization and the continuous expansion of terminal applications, the demand for high-performance focal plane infrared detectors is also increasing. Focal plane detectors with ultra-large array sizes and ultra-small pixel pitches have gradually become the mainstream development direction, and at the same time, higher requirements are being placed on the performance of infrared detector materials.

[0003] Based on the material system, infrared detectors can be primarily categorized into mercury cadmium telluride (HgCdTe) and indium antimonide (InSb) interband transition photovoltaic detectors, GaAs / AlGaAs quantum well subband transition detectors, and two types of InAs / GaSb superlattice detectors. The advantage of HgCdTe lies in its high photon absorption rate and the longest carrier lifetime. However, due to the weak direct valence bond between tellurium and mercury, mercury vacancies are easily formed, making the HgCdTe structure inherently fragile, affecting the long-term stability of the device. Furthermore, the material suffers from poor uniformity, high cost, and its ultimate performance is limited by the Auger recombination mechanism. Therefore, alternatives to HgCdTe are being sought. The advantages of InSb include low cost and a simpler fabrication process, but due to its non-tunable wavelength, its application range is limited. While quantum well detectors offer good uniformity and low cost, they cannot absorb vertically incident light, require grating coupling, and require cooling to relatively low temperatures for operation, which is inconsistent with the development trend of infrared detectors. However, due to the physical separation of electrons and holes in type II superlattice materials, the effective mass of electrons is larger, which can effectively suppress Auger recombination and reduce the tunneling current in the space charge region. Therefore, this material is considered to be an alternative material that may surpass the ultimate performance of mercury cadmium telluride.

[0004] The InAs / GaSb superlattice was first proposed by Sai-Halasz and Esaki in 1977, followed by Smith and Mailhiot in 1987, who proposed applying the InAs / GaSb superlattice material system to infrared detection. After more than 30 years of development, research on the band engineering of the InAs / GaSb superlattice system and its application in infrared detection has become increasingly in-depth. The lattice constants of InAs and GaSb are very similar, with a mismatch of only 0.6%, making them easy to grow. In the InAs / GaSb superlattice, the conduction band of the InAs layer is lower than the valence band of the GaSb layer, with a band overlap of approximately 150 meV. This confines electrons to the InAs layer and holes to the GaSb layer. This physical separation of electrons and holes improves the carrier Auger recombination lifetime. Because the InAs and GaSb layers that comprise the periodic superlattice structure are both very thin, electrons and holes in adjacent layers couple to each other, expanding the energy levels in the superlattice into microbands. The superlattice's bandgap is determined by the first electron subband C1 and the first hole subband (heavy hole band HH1), corresponding to the lowest-energy electron and hole states. The effective bandgap is the energy distance between the bottom of C1 and the top of HH1. The superlattice's effective bandgap is smaller than that of the bulk InAs and GaSb materials and varies with the thickness of each layer and the type of interface. This allows the desired cutoff wavelength to be achieved by varying the relevant material parameters. The material's response band covers nearly the entire infrared region, from 3μm to 25μm, and the band structure is easily adjustable.

[0005] Currently, the theoretical design and research of superlattice infrared detection materials are mainly based on two calculation methods: the empirical tight-binding approximation method and the k·p perturbation method. A research team at Northwestern University in the United States developed the empirical tight-binding approximation method and gradually applied it to the band gap calculation of InAs / GaSb superlattice systems. This method can take into account the influence of the growth interface on the band structure, but it is difficult to calculate wave functions and light absorption coefficients with this method, which poses a significant obstacle to further calculation and analysis. Israel's SCD company mainly uses the k·p perturbation method to calculate the electronic structure of superlattice systems. However, the k·p perturbation method is only applicable to examining the band structure at high symmetry points and cannot consider defects, interfaces, and doping in the material system. At the same time, both methods are empirical methods, and their accuracy strongly depends on the selection of parameters, making them unsuitable for band gap prediction across the entire wavelength range. Therefore, for sophisticated material design, it is necessary to choose a calculation method that starts from the first principles of quantum mechanics and does not contain empirical parameters. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the prior art and provide a method for calculating the band structure of superlattice materials. The method of the present invention is used to calculate the band structure of superlattice materials with high accuracy and strong universality.

[0007] The technical solution of the present invention is implemented as follows: The present invention discloses a method for calculating the band structure of a superlattice material, comprising the following steps:

[0008] Ab initio calculation of the lattice constants of the substrate and the various bulk materials that make up the superlattice;

[0009] Constructing a superlattice model using the substrate lattice constant and the lattice constants of various bulk materials constituting the superlattice;

[0010] Relax the superlattice model;

[0011] The electron self-interaction correction is performed using the shDFT-1 / 2 algorithm to obtain the corrected pseudopotential;

[0012] The electronic band structure of the superlattice is calculated using the corrected pseudopotential.

[0013] Furthermore, the lattice constants of the substrate and the lattice constants of various bulk materials constituting the superlattice are calculated ab initio, specifically including: using a GGA algorithm to ab initio calculate the lattice constants of the substrate and the lattice constants of various bulk materials constituting the superlattice.

[0014] Furthermore, the GGA functional form is selected from one of the three types: PBEsol, AM05, and Wu-Cohen.

[0015] Furthermore, when constructing a superlattice model, the cell is expanded according to the doping or interface layer element ratio, and the corresponding different ratios of the interface layer are controlled by cell expansion, so that the interface layer of the superlattice model reaches the required ratio.

[0016] Furthermore, a superlattice model is constructed using the substrate lattice constant and the lattice constants of various bulk materials constituting the superlattice, specifically including: preliminarily constructing a superlattice unit cell, whose lattice constants in the a and b directions are set to corresponding multiples of the calculated values ​​of the substrate lattice constants; and its lattice constant in the c direction is initially set to the sum of multiples of the calculated values ​​corresponding to the various bulk materials constituting the superlattice.

[0017] Furthermore, the superlattice model is relaxed, specifically including: structural relaxation of the superlattice unit cell, wherein only the lattice constant in the c direction is allowed to change to reduce stress and lower energy, while allowing the coordinates of each atom to relax freely, and obtaining the optimized superlattice unit cell structure under the above restrictions.

[0018] Furthermore, the shDFT-1 / 2 algorithm is used to perform electron self-interaction correction to obtain a corrected pseudopotential, specifically including: using the shDFT-1 / 2 self-potential cutoff function to scan and calculate the self-potential cutoff radius, obtaining the cutoff radius when the band gap takes the maximum value, and selecting the pseudopotential corresponding to the cutoff radius as the corrected pseudopotential.

[0019] Furthermore, each element of each bulk material constituting the superlattice adopts a self-energy potential of -1 / 4 electron.

[0020] Furthermore, the shDFT-1 / 2 self-potential cutoff function is:

[0021]

[0022] Among them, r in With r out are the inner and outer diameters of the spherical shell, r is the distance between the current position and the nucleus; Θ(r) is the value of the truncation function, and n is an exponential factor.

[0023] The present invention has at least the following beneficial effects: the present invention proposes an optimized shDFT-1 / 2 calculation method, which achieves good calculation results for covalent semiconductors such as InAs and GaSb and superlattice materials composed of them. The shDFT-1 / 2 calculation method has no empirical parameters and is not only highly accurate but also highly universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0025] Figure 1 A flow chart of a method for calculating the band structure of a superlattice material provided by an embodiment of the present invention;

[0026] Figure 2 A visual illustration of the underestimation of semiconductor band gaps due to errors in electron self-interaction;

[0027] Figure 3 Schematic diagram of the spatial distribution of valence band holes in common covalent semiconductors Si and GaAs;

[0028] Figure 4 Schematic diagram of the spatial distribution of valence band holes and conduction band electrons in semiconductor Ge;

[0029] Figure 5 Schematic diagram of the semiconductor InAs band structure calculated by GGA and HSE06;

[0030] Figure 6 Schematic diagram of the band structure of semiconductors InAs and GaSb given by shDFT-1 / 2;

[0031] Figure 7Schematic diagram of the 7MLInAs–7MLGaSb–0.7MLInSb structure;

[0032] Figure 8 Schematic diagram of the energy band structure of 7MLInAs–7MLGaSb–0.7MLInSb, where (a) is the schematic diagram of the energy band structure of 7MLInAs–7MLGaSb–0.7MLInSb calculated using shGGA-1 / 4-1 / 4; (b) is the schematic diagram of the energy band structure of 7MLInAs–7MLGaSb–0.7MLInSb calculated using GGA;

[0033] Figure 9 Schematic diagram of the 14MLInAs–7MLGaSb–1.4MLInSb structure;

[0034] Figure 10 Schematic diagram of the energy band structure of 14MLInAs–7MLGaSb–1.4MLInSb, where (a) is the schematic diagram of the energy band structure of 14MLInAs–7MLGaSb–1.4MLInSb calculated using shGGA-1 / 4-1 / 4; (b) is the schematic diagram of the energy band structure of 14MLInAs–7MLGaSb–1.4MLInSb calculated using GGA. DETAILED DESCRIPTION

[0035] 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 only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0036] See also Figure 1 , an embodiment of the present invention provides a method for calculating the band structure of a superlattice material, comprising the following steps:

[0037] S1) Ab initio calculation of the lattice constants of the substrate and the various bulk materials that comprise the superlattice, specifically using the GGA (generalized gradient approximation) algorithm. Ab initio calculation of the lattice constants of each material ensures that no additional stress is introduced beyond the fixed stress caused by superlattice matching.

[0038] S2) constructing a superlattice model using the substrate lattice constant and the lattice constants of the various bulk materials that comprise the superlattice. When constructing the superlattice model, the cell is expanded based on the doping or element ratio of the interface layer. By expanding the cell, the composition of the interface layer is controlled to achieve the desired ratio in the interface layer of the superlattice model.

[0039] Constructing a superlattice model specifically includes: preliminarily constructing a superlattice unit cell, wherein the lattice constants in the a and b directions are set as corresponding multiples of the calculated values ​​of the substrate (e.g., GaSb) lattice constants as needed, and the lattice constant in the c direction is roughly taken as the sum of multiples of the calculated values ​​corresponding to the various bulk materials constituting the superlattice as needed.

[0040] S3) Relaxing the superlattice model, specifically comprising: structurally relaxing the superlattice unit cell, wherein only the lattice constant in the c direction is allowed to change to reduce stress and lower energy, while allowing the coordinates of each atom to relax freely, and obtaining the optimized superlattice unit cell structure under the above restrictions.

[0041] S4) Using the shDFT-1 / 2 (shell DFT-1 / 2) algorithm to perform electron self-interaction corrections, a modified pseudopotential is obtained. This includes: using the shDFT-1 / 2 self-potential cutoff function to scan and calculate the self-potential cutoff radius, obtaining the cutoff radius at the maximum band gap, and selecting the pseudopotential corresponding to this cutoff radius as the modified pseudopotential. The -1 / 4 electron self-potential is used for all elements in the superlattice material. This variational scan determines the shDFT-1 / 2 cutoff radius parameter to ensure uniqueness of the result.

[0042] S5) Calculate the electronic band structure of the superlattice using the corrected pseudopotential.

[0043] Aiming at the material design and computational simulation of superlattice infrared detection, the present invention proposes a new method of using shDFT-1 / 2 to perform ab initio calculation of the electronic band structure of the superlattice system, aiming to combine the universality of ab initio calculation with the accuracy of the band.

[0044] Density functional theory, the current mainstream method for first-principles calculations of semiconductor energy bands, suffers from underestimation of band gaps. For calculations of superlattice systems such as InAs / GaSb, the number of atoms in the supercell typically ranges from 100 to 500. Density functional theory can only achieve satisfactory computational speeds using its most basic local density approximation (LDA) or generalized gradient approximation (GGA). However, under the LDA / GGA approximation, the resulting electronic energy eigenvalues ​​cannot be theoretically linked to the experimental band gap. If interpreted as true electronic energy levels, the semiconductor band gap is underestimated. This problem can be addressed by improving the electron exchange energy and introducing a certain amount of Hartree-Fock exact exchange, leading to hybrid functional methods. Alternatively, quasiparticle methods from many-body physics can be employed, performing a perturbative expansion of the self-energy. For example, the well-known GW approximation can be taken to a first-order approximation, where the imaginary part of the self-energy is expressed as the product of the single-particle Green's function G and the kinetically screened Coulomb interaction W. However, the computational complexity of hybrid functional and GW approximation is 2-3 orders of magnitude higher than that of LDA / GGA, which makes it too computationally expensive to use in superlattice material design, and even difficult to achieve with current computing power.

[0045] Materials such as InAs and GaSb belong to The lattice constants of semiconductors in this system are very close, but the lattice constants calculated ab initio by LDA and GGA often deviate from experimental values. Unlike LDA, which severely underestimates the lattice constants, the lattice constants approximated by GGA depend on the specific functional form. The lattice constants predicted by the PBE functional are generally significantly overestimated, but the three GGA functional forms, PBEsol, AM05, and Wu-Cohen, can give lattice constants very close to experimental values. Therefore, this method uses one of these GGA functional forms for structural optimization and electronic structure calculations.

[0046] With a computational effort basically comparable to that of LDA and GGA, there are still some band gap correction methods. The idea behind this method is to perform self-energy correction based on LDA and GGA calculations to compensate for errors in electron self-interaction.

[0047] The method of the present invention should solve the problem that GGA underestimates the band gap of semiconductors. The reason why the band gap is underestimated can be attributed to the error of electron self-interaction. Since electrons are regarded as density distributions in the theoretical framework of density functional theory, the external equivalent potential field felt by a single electron may include a part of the electrostatic potential generated by itself. However, in physical reality, electrons are not repelled by themselves. Under the ideal single-electron approximation, that is, under the premise of being able to correctly handle exchange and correlation effects, this part of the electron self-interaction will be strictly offset by a part of the exchange energy. Since the exchange energy of LDA and GGA is not accurate, it will lead to incomplete cancellation of self-interactions, resulting in self-interaction errors. For semiconductors, the self-interaction error of valence band electrons (the self-repulsion of negative charges) will cause the valence band energy to be overestimated, but there are no electrons in the conduction band, so the valence band is mistakenly shifted up relative to the conduction band, resulting in an underestimate of the band gap, such as Figure 2 shown.

[0048] The applicant's research found that the DFT-1 / 2 and shDFT-1 / 2 algorithms can be used to correct the inaccurate exchange energy problem under the LDA and GGA approximations.

[0049] DFT-1 / 2 addresses this problem by applying a real-space energy correction to the atoms that comprise the valence band, shifting the valence band downward. Specifically, the self-energy correction is applied to the solid using the atomic calculations, assuming the self-energy of the hole localized near the atom is the same as in the atomic case. To facilitate self-consistent calculations, the corresponding atomic self-energy potential is derived: the difference between the classical potential calculated using the LDA and GGA functionals and the classical potential of the ion after half-electron deprivation. The self-energy potential is essentially a long-range Coulomb potential, which, when superimposed on a periodic solid, can lead to energy divergence. A spherical cutoff is first performed on the self-energy potential. According to the variational principle (the ground state corresponds to an energy minimum), the cutoff radius should be chosen to maximize the semiconductor's band gap, corresponding to minimizing the ground-state energy. DFT-1 / 2 performs very well on semiconductors with strong ionicity. For some covalent semiconductors, such as Si, the self-energy potential of each atom deprived of one-quarter of its electrons is used, since both bonding atoms are Si.

[0050] DFT-1 / 2 does not give the correct total energy and electronic structure at the same time, but only gives the corrected electronic band structure. Therefore, the structural relaxation and ground state energy calculations of DFT-1 / 2 rely on LDA or GGA calculations. Because the total energy calculation and the electronic structure calculation are performed separately, it provides convenient conditions for achieving efficient correction of the band gap. However, there are serious problems when DFT-1 / 2 calculates covalent semiconductors such as Ge. For example, Ge is predicted to have a direct band gap, and the band gap value is only 0.40eV. In addition, for covalent semiconductors between elemental semiconductors (diamond, Si, Ge, etc.) and ionic semiconductors (such as HfO2), there is uncertainty in the charge deprivation scheme of their self-energy potential. A large number of calculations have shown that DFT-1 / 2 has good calculation results for semiconductors with strong ionicity, but for typical covalent semiconductors such as InAs and GaSb, the accuracy of the band calculation results of DFT-1 / 2 cannot meet the requirements.

[0051] Since the valence band holes of covalent semiconductors are often not localized on a single atom, but are generally shared by two bonding atoms, such as Figure 3 As shown in Figure 2, since holes can be shared in general, the use of a spherical cutoff function may lead to overcorrection in the near-core region. Figure 4 The spatial distribution of valence band holes and conduction band electrons in semiconductor Ge is shown. For typical covalent semiconductors, there is a general rule that holes are located near the bond center, while conduction band electrons have a higher probability of appearing in the near-core region. Therefore, a spherical shell cutoff function should be introduced for covalent semiconductors:

[0052]

[0053] Among them, r in With r out are the inner and outer diameters of the spherical shell, respectively, and both need to be given by variational calculus to maximize the band gap of the semiconductor. r is the distance between the current position and the nucleus; Θ(r) is the value of the cutoff function, 1 represents no cutoff, 0 represents complete cutoff, and the intermediate value represents partial cutoff; n is an exponential factor, the larger n is, the sharper the cutoff, and in this embodiment n is fixed to 20; this formula is the definition of the shDFT-1 / 2 self-potential cutoff function. When the inner diameter is equal to zero, shDFT-1 / 2 automatically degenerates into ordinary DFT-1 / 2. The charge deprivation scheme is generally to deprive 1 / 4 of the electrons each. Only when the valence band hole completely surrounds the anion and the conduction band electrons completely belong to the cationic system, only 1 / 2 of the electrons are deprived from the anion.

[0054] shDFT-1 / 2 is a new algorithm for accurately calculating the band structure of covalent semiconductors. Its function is to correct the underestimation of the band gap by LDA or GGA and restore the correct semiconductor band gap.

[0055] Because shDFT-1 / 2 avoids unnecessary corrections in the near-core region, it no longer lowers the conduction band and provides good calculation results for covalent semiconductor materials such as Ge and GaAs.

[0056] Among superlattice infrared detection materials, the most commonly used are devices based on InAs / GaSb superlattice. Figure 5 A comparison of the InAs band structures given by the GGA and HSE06 hybrid functionals (both taking spin-orbit coupling into account) is presented. Due to a severe band gap underestimate, the conventional GGA predicts InAs to be metallic, while the HSE06 gives a direct band gap of 0.22 eV, slightly lower than the zero-temperature experimental value of 0.41 eV. Analysis of the conduction and valence bands reveals that both exhibit s- and p-state electronic characteristics, with the absence of hard electron orbitals such as 2p and strongly correlated narrow bands. Therefore, the band gap correction scheme for InAs is not suitable for DFT+U, but rather for shDFT-1 / 2. Calculations for GaSb yielded the same conclusion.

[0057] Figure 6 The band structures of the semiconductors InAs and GaSb are presented using shDFT-1 / 2. Using the PBEsol functional for structural relaxation and total energy calculations, shDFT-1 / 2 predicts that InAs has a direct band gap of 0.58 eV, only slightly higher than the experimental value. GaSb is also predicted to be a direct band gap semiconductor, with a band gap value consistent with the experimental value. This demonstrates the suitability of the shDFT-1 / 2 algorithm for electronic structure calculations of InAs and GaSb systems.

[0058] The present invention takes the InAs / GaSb superlattice system as an example, and the calculation process is as follows:

[0059] Using the GGA approximation, and selecting one of three functionals, PBEsol, AM05, or Wu-Cohen, the structure of zinc-blende GaSb was optimized to obtain the equilibrium lattice constant. In this example, the substrate used was GaSb. Because epitaxial growth was performed on a GaSb substrate, the lattice constants of InAs in the a and b directions were chosen to match those of the substrate.

[0060] An InAs / GaSb superlattice model is constructed using the lattice constant of GaSb. To achieve the desired ratio in the interface layer, the superlattice model requires appropriate cell expansion based on the doping or element ratios in the interface layer. This allows for compositional control of the interface layer at varying ratios. The lattice constant is considered the side length of the constructed model, and cell expansion is considered replicating a previous unit cell in the abc directions.

[0061] Taking 7ML InAs–7ML GaSb–0.7ML InSb as an example, there are two interface layers with a ratio of 0.35ML. When the superlattice is not expanded in the a and b directions, there are only 2 group III elements and 2 group V elements in 1ML. 0.65 Sb 0.35 For example, to achieve the desired ratio, the cell needs to be expanded once in both the a and b directions, resulting in a 2×2 supercell, followed by atomic replacement. At this point, As:Sb = 5:3 = 0.625:0.375, very close to the actual ratio of the 7ML InAs–7ML GaSb–0.7ML InSb interface layer. Therefore, the a and b directions need to be appropriately expanded according to the proportion of the interface layer or bulk material, and the lattice constants in the a and b directions are set to the corresponding multiples of the calculated value of the GaSb lattice constant (in the case of no cell expansion, the lattice constants in the a and b directions are equal to the calculated value of the lattice constant of the substrate, such as GaSb; when cell expansion is required, if the cell is expanded n times in the a or b direction, the lattice constant in the a or b direction is set to n times the calculated value of the GaSb lattice constant), and the lattice constant in the c direction is initially taken as a multiple of the calculated value corresponding to the GaSb lattice constant (the c direction is the growth direction of the material, and it will grow periodically in a period of xML InAs-yMLGaSb-0.1xML InSb. In the case of no cell expansion, the multiple should be (x+y) / 2+1. If it is not an integer, it must be doubled to become an integer through cell expansion).

[0062] The c-axis lattice constant and internal atomic coordinates of the superlattice model are fully relaxed;

[0063] shDFT-1 / 2 electronic structure calculations were performed using the following steps: The cutoff radii for bulk InAs and GaSb were determined using shDFT-1 / 2, using the -1 / 4 electron self-potential for all four elements. For InAs, four self-potential cutoff radii were scanned, both inside and outside the In and As elements, to obtain the cutoff radii at the maximum band gap and the corrected pseudopotential. For GaSb, four self-potential cutoff radii were scanned, both inside and outside the Ga and Sb elements, to obtain the cutoff radii at the maximum band gap and the corrected pseudopotential. The pseudopotential corresponding to the cutoff radius at the maximum band gap is the corrected pseudopotential.

[0064] The electronic band structure of InAs / GaSb superlattice is calculated using -1 / 4 electron corrected In, As, Ga, and Sb pseudopotentials.

[0065] Take the 7MLInAs–7MLGaSb–0.7MLInSb and 14MLInAs–7MLGaSb–1.4MLInSb systems as examples.

[0066] The 7MLInAs–7MLGaSb–0.7MLInSb superlattice model structure is as follows Figure 7 As shown, 0.7MLInSb is 0.35MLInSb formed at the two interfaces. Due to the order of material growth, two different interface layers are formed at the two interfaces, namely InAs 0.65 Sb 0.35 and Ga 0.65 In 0.35 Sb. Expand the model to a 2x2 supercell and replace the elements in similar proportions, which is actually InAs 0.625 Sb 0.375 and Ga 0.625 In 0.375 Sb.

[0067] The electronic structure of the 7MLInAs–7MLGaSb–0.7MLInSb superlattice is calculated using the shDFT-1 / 2 corrected pseudopotential and the uncorrected pseudopotential. The band structure diagram is shown in the figure below. Figure 8 As shown in the figure, the specific shDFT-1 / 2 algorithm is shGGA-1 / 4-1 / 4. Comparing the band structures of the two, shGGA-1 / 4-1 / 4 calculates a direct band gap of 293 meV, with an energy difference of 157 meV between the first heavy hole band and the first light hole band. In contrast, the band structure calculated by GGA shows an indirect band gap of only 80 meV. GGA's systematic underestimation of the band gap persists, and the band structure is no longer consistent with reality.

[0068] The structure of the 14MLInAs–7MLGaSb–1.4MLInSb superlattice model after relaxation is as follows Figure 9 As shown, there are two different interface layers, InAs and GaSb, which are the same as 7MLInAs–7MLGaSb–0.7MLInSb. 0.3 Sb 0.7 and Ga 0.3 In 0.7 The model of 14MLInAs–7MLGaSb–1.4MLInSb needs to expand the cell and change the a and b directions into a 2x1 supercell, so the actual interface layer of the model is InAs 0.25 Sb 0.75 and Ga 0.25 In 0.75 Sb.

[0069] Figure 10The band structure calculation results for 14MLInAs–7MLGaSb–1.4MLInSb are more striking when comparing the results obtained using the corrected pseudopotential of shGGA-1 / 4-1 / 4 with those obtained using the uncorrected pseudopotential. The calculation using shGGA-1 / 4-1 / 4 still shows a direct band gap of 133 meV, with an energy difference of 132 meV between the first heavy hole band and the first light hole band. However, the result calculated using GGA shows no band gap at all, and the valence band top and conduction band bottom do not overlap, significantly deviating from the actual result. In systems with smaller band gaps, the GGA calculation results are particularly poor.

[0070] In terms of computational time, shDFT-1 / 2 requires scanning the unit cell for a cutoff radius, but because the unit cell is small, this additional time is very short. Furthermore, the scan radius results can be reused, requiring only a single scan. When calculating superlattice models, uncorrected pseudopotentials are used during relaxation, so the computation times required for DFT and shDFT-1 / 2 are similar. Subsequent electronic structure calculations require only modified pseudopotentials, with other parameters remaining the same. Typically, shDFT-1 / 2 computation times are of the same order of magnitude as DFT.

[0071] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the band structure of a superlattice material, characterized in that: The steps include: Ab initio calculation of the lattice constants of the substrate and the lattice constants of the individual materials that make up the superlattice; A superlattice model is constructed using the substrate lattice constant and the lattice constants of various bulk materials constituting the superlattice, specifically comprising: preliminarily constructing a superlattice primitive cell, wherein the lattice constants in the a and b directions are set as multiples of the calculated values ​​of the substrate lattice constants; the lattice constant in the c direction is initially set as the sum of m multiples of the calculated values ​​corresponding to the various bulk materials constituting the superlattice; without cell expansion, the lattice constants in the a and b directions are equal to the calculated values ​​of the substrate lattice constants; if the interface layer of the superlattice model is to reach a corresponding proportion, the cell needs to be expanded according to the doping or interface layer element ratio when constructing the superlattice model, and the composition control of the interface layer with corresponding different proportions is achieved by cell expansion. When cell expansion is required, if the cell is expanded n times in the a or b direction, the lattice constant in the a or b direction is set to n times the calculated value of the substrate lattice constant; The c direction is the growth direction of the material. The periodic growth is performed with xMLInAs-yML GaSb-0.1xMLInSb as one cycle. Without cell expansion, the multiple m should be (x+y) / 2+1. If the multiple m is not an integer, it needs to be doubled to an integer through cell expansion. Relax the superlattice model; The electron self-interaction correction is performed using the shDFT-1 / 2 algorithm to obtain the corrected pseudopotential; The electronic band structure of the superlattice is calculated using the corrected pseudopotential.

2. The method for calculating the band structure of a superlattice material according to claim 1, wherein: The lattice constants of the substrate and the lattice constants of the various bulk materials constituting the superlattice are calculated from scratch, specifically including: using a GGA algorithm to calculate the lattice constants of the substrate and the lattice constants of the various bulk materials constituting the superlattice from scratch.

3. The method for calculating the band structure of a superlattice material according to claim 2, wherein: The GGA functional form is selected from one of the three types: PBEsol, AM05, and Wu-Cohen.

4. The method for calculating the band structure of a superlattice material according to claim 1, wherein: The superlattice model is relaxed, specifically including: structural relaxation of the superlattice unit cell, wherein only the lattice constant in the c direction is allowed to change to reduce stress and lower energy, while allowing the coordinates of each atom to relax freely, and obtaining the optimized superlattice unit cell structure under the above restrictions.

5. The method for calculating the band structure of a superlattice material according to claim 1, wherein: The shDFT-1 / 2 algorithm is used to perform electron self-interaction correction to obtain a corrected pseudopotential, specifically including: using the shDFT-1 / 2 self-potential cutoff function to scan and calculate the self-potential cutoff radius, obtaining the cutoff radius when the band gap takes the maximum value, and selecting the pseudopotential corresponding to the cutoff radius as the corrected pseudopotential.

6. The method for calculating the band structure of a superlattice material according to claim 5, wherein: The shDFT-1 / 2 self-energy potential cutoff function is: Among them, r in With r out are the inner and outer diameters of the spherical shell, r is the distance between the current position and the nucleus; Θ(r) is the value of the truncation function, and n is an exponential factor.

7. The method for calculating the band structure of a superlattice material according to claim 5, wherein: Each element of each bulk material constituting the superlattice adopts a self-energy potential of -1 / 4 electron.

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