A method for simulating phonon-assisted photoluminescence spectroscopy

Abstract

The present invention provides a method for simulating phonon-assisted photoluminescence spectrum, which relates to the technical field of simulation technology of semiconductor materials, and is specifically applicable to solid materials, and comprises the following steps: constructing a unit cell model containing defects, defining four states of ABCD, and calculating phonon basis vectors corresponding to different phonon modes of the configuration state A of the ground state system at the same time; obtaining the total energy of each state through hybrid density functional self-consistent calculation, constructing a configuration diagram and ZPL energy; extracting the total energy, phonon basis vectors and atomic mass, obtaining Huang Kun factor and spectral data through calculation, and importing them into drawing software to obtain a photoluminescence spectrum. The calculation method of the present invention realizes accurate simulation calculation of the phonon-assisted photoluminescence properties of solid materials.

Description

Technical Field

[0001] The invention relates to the technical field of simulation technology of semiconductor materials, and in particular to a method for simulating phonon-assisted photoluminescence spectrum. Background Art

[0002] Semiconductor devices actually prepared often have defect structures. Point defects with optical and magnetic activity are an important material basis for the development of a new generation of optical quantum devices such as single-photon sources and quantum bits. By measuring their photoluminescence spectra, the related properties of the system excitation energy and the interaction between electrons and lattice vibrations can be obtained. Among them, the existence of impurity centers provides localized electronic states for optical transitions, and the corresponding radiative recombination process can be regulated by defect engineering, providing theoretical support for the construction of single-photon sources. The experimental photoluminescence spectrum often contains multiple physical processes, including intrinsic recombination luminescence, exciton recombination luminescence, and phonon-assisted luminescence. Under the same excitation wavelength, responses are generated in different bands, reflecting the different resonant energies of different physical processes. The physical process corresponding to phonon-assisted luminescence is: radiative recombination occurs at point defects, energy is transferred to lattice vibrations, and multiple quantized phonon modes are generated, which is reflected in the photoluminescence spectrum as a phonon-assisted luminescence peak group with lower energy than the defect luminescence peak. Since this process is one of the basic physical processes of quantum relay, accurately simulating and evaluating the phonon-assisted photoluminescence properties of materials is of great significance for the development of optical quantum devices.

[0003] The current theoretical methods for calculating photoluminescence spectra have certain limitations for calculating the photoluminescence properties of solid materials: first, most of the current mature photoluminescence calculation modules are based on molecular systems and simulated based on the transition of localized orbitals, but the valence band electron distribution of solid materials is mostly delocalized; second, the calculation module obtains the intrinsic luminescence peak, and cannot predict the photoluminescence phenomenon below the intrinsic luminescence peak energy, and there is a big difference between the physical process of intrinsic luminescence and the theory of defect-related phonon-assisted photoluminescence; third, the electronic properties of solids are often predicted using density functional theory, but the electronic properties calculated by density functional theory are ground-state electronic properties, and it is still difficult to predict the excited-state properties of solids. Therefore, it is urgent to develop a calculation method for simulating the phonon-assisted photoluminescence properties of solid materials, aiming to simulate and evaluate the photoluminescence properties of different materials and different types of defects based on the electronic properties and phonon properties calculated by first-principles. Summary of the invention

[0004] The problem solved by the present invention is how to obtain a more accurate calculation method for simulating the phonon-assisted photoluminescence properties of solid materials.

[0005] To solve the above problems, the present invention provides a method for simulating phonon-assisted photoluminescence spectroscopy, which is applicable to solid materials and comprises the following steps:

[0006] Step S1: constructing a lattice model of an orthogonal structure, and optimizing the atomic positions in the lattice model so that the atoms are in an initial state;

[0007] Step S2: constructing defects in the lattice model to obtain a unit cell model containing the defects, and obtaining a ground state system configuration state A after structural optimization;

[0008] Step S3: rearrange the electron distribution of the ground state system configuration state A, consider the spin, transfer the electron of a single K point from the top of the valence band to the bottom of the conduction band at the corresponding position, extract the ground state electron population, at this time the system is in the excited state system configuration state D, perform structural optimization on the excited state system configuration state D, obtain the excited state system configuration state C, the system transitions from the excited state system configuration state C to the ground state, obtains the ground state system configuration state B, and returns to the ground state system configuration state A after structural relaxation; at the same time, calculate the phonon basis vectors corresponding to different phonon modes of the ground state system configuration state A;

[0009] Step S4: Obtain the total energy of the ground state system configuration state A, the ground state system configuration state B, the excited state system configuration state C and the excited state system configuration state D through self-consistent calculation of hybrid density functional theory, and construct the configuration diagram and ZPL energy E ZPL ;

[0010] Step S5: extract the total energy, phonon basis vector and atomic mass in the above steps, obtain the Huang-Kun factor and spectrum data by calculation, import them into the drawing software, and obtain the photoluminescence spectrum.

[0011] Furthermore, in step S1, the optimizing the atomic positions in the lattice model so that the atoms are in an initial state includes:

[0012] The plane wave approximation is used to optimize the atomic positions in the lattice model so that the force on each atom is less than

[0013] Furthermore, in step S3, the algorithm for calculating the phonon basis vectors corresponding to different phonon modes of the ground state system configuration state A is a hybrid density functional method.

[0014] Furthermore, in step S3, the scope of consideration for calculating different phonon modes includes: considering the phonon modes of all atoms in the lattice model; or in phonon modes with lower energy eigenvalues, considering atoms farther away from the defect position as fixed atoms through an external input action radius range.

[0015] Furthermore, in step S5, the definition of the Huang Kun factor is:

[0016]

[0017] in, To reduce Planck's constant, the phonon mode eigenenergy is ω λ , the change in the phonon canonical coordinates ΔQ λ The following relations are satisfied:

[0018]

[0019] The excited state atomic position is R e,α , the ground state atomic position is R g,α , the phonon basis vector is u λ , m α Represents the mass of atom α.

[0020] Furthermore, in step S5, the spectral data takes into account the Gaussian broadening caused by temperature, and the spectral function of the electroacoustic coupling effect is:

[0021]

[0022] σ is the broadening parameter, S λ For the Huang Kun factor, is the reduced Planck constant, ω λ is the frequency corresponding to the phonon mode λ, then the photoluminescence spectrum distribution of the system is:

[0023]

[0024] Among them, E ZPL is the zero phonon line position, which is the energy difference between the ground state system configuration state A and the excited state system configuration state C; is the energy of the incident photon; the spectrum generation factor g is:

[0025] g(t)=e S(t)-S(0) ;

[0026]

[0027] Furthermore, in step S2, the defects are constructed in the lattice model using self-developed defect property simulation software.

[0028] Furthermore, in step S3 and step S4, the computing software is VASP.

[0029] Furthermore, in step S5, the drawing software is one of Origin, Gnuplot, and Matplotlib.

[0030] The advantage of the method for simulating phonon-assisted photoluminescence spectrum described in the present invention over the prior art is that, by constructing defects in the lattice model, the configuration coordinate model in the Franck-Condon principle is used to assume that the total potential energy of the system changes with the configuration coordinates, and the excited state and ground state of the same system have different configuration curves and different potential potential energy minimum points, and the configuration does not change during the electronic excitation and emission process, which is represented in the configuration diagram as the system vertically transitioning from the ground state potential energy surface to the excited state potential energy surface, thereby defining the ground state system configuration states A, B and the excited state system configuration states C and D, and through the cyclic process in step S3, the excitation energy of the electron is transferred to the phonon mode of the ion with the corresponding intrinsic energy by electron-phonon scattering, and then the equilibrium positions of each configuration, as well as the electronic properties such as the total energy, are calculated, and the phonon mode of the ground state is calculated and solved to obtain the phonon-assisted photoluminescence spectrum of the system. The calculation method described in the present invention realizes the accurate simulation calculation of the phonon-assisted photoluminescence properties of solid materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flow chart of a method for simulating phonon-assisted photoluminescence spectroscopy in an embodiment of the present invention;

[0032] Figure 2 Schematic diagram of the configuration coordinates and optical transition-relaxation process in an embodiment of the present invention, in which the positions of the four state points ABCD are marked;

[0033] Figure 3 Schematic diagram of the defect structure of gallium nitride in which Ca replaces N in an embodiment of the present invention;

[0034] Figure 4 It is an interface for setting the photoluminescence spectrum calculation module of the self-developed software in the embodiment of the present invention;

[0035] Figure 5 FIG. 4 is a photoluminescence spectrum of a gallium nitride structure in which Ca replaces N in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention uses the first principles to simulate the properties of phonon-assisted photoluminescence in solid materials, and uses the Franck-Condon principle, the main principle for calculating phonon-assisted photoluminescence spectra at present. The configuration coordinate model based on this principle assumes that the total potential energy of the system changes with the configuration coordinates, and the excited state and the ground state of the same system have different configuration curves, and each state has a different potential energy minimum point. The Franck-Condon principle believes that the configuration does not change during the electron excitation and emission process, which is represented in the configuration diagram as a vertical transition of the system from the ground state potential energy surface to the excited state potential energy surface.

[0037] Based on the above principles, in order to make the above objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0038] It should be noted that in the description of the embodiments of the present application, the description of the term "some specific embodiments" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same implementation or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0039] The embodiment of the present invention provides a method for simulating phonon-assisted photoluminescence spectroscopy, which is applicable to solid materials and includes the following steps:

[0040] Step S1: constructing a lattice model of an orthogonal structure, and optimizing the atomic positions in the lattice model so that the atoms are in an initial state;

[0041] Step S2: construct defects in the lattice model to obtain a unit cell model containing defects, and after structural optimization, obtain a ground state system configuration state A;

[0042] Step S3: rearrange the electron distribution of the ground state system configuration state A, consider the spin, transfer the electron of a single K point from the top of the valence band to the bottom of the conduction band at the corresponding position, extract the ground state electron population, at this time the system is in the excited state system configuration state D, perform structural optimization on the excited state system configuration state D, obtain the excited state system configuration state C, the system transitions from the excited state system configuration state C to the ground state, obtains the ground state system configuration state B, and returns to the ground state system configuration state A after structural relaxation; at the same time, calculate the phonon basis vectors corresponding to different phonon modes of the ground state system configuration state A;

[0043] Step S4: Obtain the total energy of the ground state system configuration state A, the ground state system configuration state B, the excited state system configuration state C and the excited state system configuration state D through self-consistent calculation of hybrid density functional theory, and construct a configuration diagram and ZPL energy;

[0044] Step S5: extract the total energy, phonon basis vector and atomic mass in the above steps, obtain the Huang-Kun factor and spectrum data by calculation, import them into the drawing software, and obtain the photoluminescence spectrum.

[0045] A method for simulating phonon-assisted photoluminescence spectrum described in an embodiment of the present invention constructs defects in a lattice model, and uses the configuration coordinate model in the Franck-Condon principle to assume that the total potential energy of the system changes with the configuration coordinates. The excited state and the ground state of the same system have different configuration curves and different potential potential energy minimum points, and the configuration does not change during electron excitation and emission. In the configuration diagram, it is represented as a vertical transition of the system from the ground state potential energy surface to the excited state potential energy surface, so the ground state system configuration states A, B and the excited state system configuration states C and D are defined. Through the cyclic process in step S3, the excitation energy of the electron is transferred to the phonon mode of the ion with the corresponding intrinsic energy by electron-phonon scattering, and then the equilibrium position of each configuration, as well as the electronic properties such as the total energy, are calculated, and the phonon mode of the ground state is calculated and solved to obtain the phonon-assisted photoluminescence spectrum of the system. The calculation method described in the embodiment of the present invention realizes the accurate simulation calculation of the phonon-assisted photoluminescence properties of solid materials.

[0046] In some specific embodiments, in step S1, optimizing the atomic positions in the lattice model so that the atoms are in an initial state includes:

[0047] The plane wave approximation is used to optimize the atomic positions in the lattice model so that the force on each atom is less than

[0048] Therefore, the atomic positions in the lattice model are optimized so that the force on each atom is maintained within a lower range, which is beneficial to the state balance of the lattice model system.

[0049] In some specific embodiments, in step S3, the algorithm for calculating the phonon basis vectors corresponding to different phonon modes of the ground state system configuration state A is a hybrid density functional method.

[0050] In some specific embodiments, in step S3, the consideration range for calculating different phonon modes includes: considering the phonon modes of all atoms in the lattice model; or in phonon modes with lower energy eigenvalues, considering atoms farther away from the defect position as fixed atoms through an external input action radius range.

[0051] As a result, the number of finite displacement degrees of freedom that need to be considered is reduced, speeding up the calculation of phonon modes.

[0052] In some specific embodiments, in step S5, the definition of Huang Kun factor is:

[0053]

[0054] in, To reduce Planck's constant, the phonon mode eigenenergy is ω λ , the change in the phonon canonical coordinates ΔQλ The following relations are satisfied:

[0055]

[0056] The excited state atomic position is R e,α , the ground state atomic position is R g,α , the phonon basis vector is u λ , m α Represents the mass of atom α.

[0057] Therefore, the Huang-Kun factor is accurately calculated according to the different situations, realizing the calculation of energy in the phonon mode.

[0058] In some specific embodiments, in step S5, the spectral data takes into account the Gaussian broadening formed by temperature, and the spectral function of the electroacoustic coupling effect is:

[0059]

[0060] σ is the broadening parameter, S λ For the Huang Kun factor, is the reduced Planck constant, ω λ is the frequency corresponding to the phonon mode λ, then the photoluminescence spectrum distribution of the system is:

[0061]

[0062] Among them, E ZPL is the zero phonon line position, which is the energy difference between the ground state system configuration state A and the excited state system configuration state C; is the energy of the incident photon; the spectrum generation factor g is:

[0063] g(t)=e S(t)-S(0) ;

[0064]

[0065] Thus, spectral data such as spectral distribution are obtained to provide input parameters for generating phonon-assisted photoluminescence spectra.

[0066] In some specific embodiments, in step S2, defects are constructed in the lattice model using self-developed defect property simulation software.

[0067] Therefore, the use of this software has streamlined the detailed calculation steps of defect structure design, defect electronic property calculation, defect formation energy calculation and defect macroscopic property prediction, realizing automatic modeling of defect structure and cross-scale integrated calculation of properties.

[0068] In some specific embodiments, in step S3 and step S4, the computing software is VASP.

[0069] Therefore, VASP is used to realize electronic structure calculation and quantum mechanics-molecular dynamics simulation, calculate the electronic properties such as the equilibrium position of each shape and total energy, and realize auxiliary calculation of phonon modes.

[0070] In some specific embodiments, in step S5, the drawing software includes one of Origin, Gnuplot, and Matplotlib. Thus, a variety of drawing software can be used to generate phonon-assisted photoluminescence spectra, and a wide range of options are available.

[0071] Example 1

[0072] The method for simulating phonon-assisted photoluminescence spectrum described in this embodiment includes the following contents:

[0073] The method of the present invention is used to calculate the photoluminescence spectrum of the C-substituted N system in GaN using VASP as the solver. Specifically, the lattice model in this embodiment is as follows: Figure 3 As shown. After structural optimization, the lattice constants of xyz are: In the lattice model, the defect is constructed. When optimizing the defect structure, the cutoff energy is 400eV and the k-point grid is 1×1×1. When constructing the excited state system configuration states C and D, the spin is set to open and the electron population is fixed. When constructing the phonon mode, the algorithm is selected as the hybrid density functional method considering symmetry, and after entering the defect position, the atoms are selected to be fixed according to the distance from the defect position. The cutoff distance set here is Distance to defect location The atoms other than the atoms are considered as fixed atoms. The embodiment of the present invention visualizes the above setting process, and the setting interface is as follows Figure 4 As shown. The options in the attached figure are: Defect structure import box: import defect structure data file; From type: elements can be automatically identified according to the import box; Number of self-consistent ion steps: set the maximum number of optimized ion steps for the structure optimization step; Self-consistent algorithm: set the electron self-consistent method, which is not selectable by default; Structure relaxation algorithm: set the structure optimization method, which is not selectable by default; System spin state: set the spin switch, which is fixed to on by default; Force convergence criterion: when the force on the atom is a value, it is judged that the structure optimization has completed convergence; Defect freezing range: set the distance threshold of the defect position, atoms outside the threshold are fixed, and atoms within the threshold can vibrate; Excited electron state: set the spin of the excited electron to up or down, single choice.

[0074] The Huang-Kun factor distribution and photoluminescence spectrum obtained are as follows: Figure 5 The horizontal axis of the attached figure is in meV, which is the energy difference between the incident photon energy and the zero-phonon line. The vertical axis is the luminous intensity, and the value is only relative.

[0075] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A method for simulating phonon-assisted photoluminescence spectroscopy, applicable to solid materials, characterized in that: The steps include: Step S1: constructing a lattice model of an orthogonal structure, optimizing the atomic positions in the lattice model, and making the atoms in the initial state, specifically comprising: optimizing the atomic positions in the lattice model using plane wave approximation, making the force on each atom less than Step S2: constructing defects in the lattice model to obtain a unit cell model containing the defects, and obtaining a ground state system configuration state A after structural optimization; Step S3: rearrange the electron distribution of the ground state system configuration state A, consider the spin, transfer the electron of a single K point from the top of the valence band to the bottom of the conduction band at the corresponding position, extract the ground state electron population, at this time the system is in the excited state system configuration state D, perform structural optimization on the excited state system configuration state D, obtain the excited state system configuration state C, the system transitions from the excited state of the excited state system configuration state C to the ground state, obtains the ground state system configuration state B, and returns to the ground state system configuration state A after structural relaxation; at the same time, calculate the phonon basis vectors corresponding to different phonon modes of the ground state system configuration state A; wherein the consideration range for calculating different phonon modes includes: considering the phonon modes of all atoms in the lattice model; or in the phonon mode with a lower energy eigenvalue, the atoms far away from the defect position are regarded as fixed atoms by externally inputting the action radius range; Step S4: Obtain the total energy of the ground state system configuration state A, the ground state system configuration state B, the excited state system configuration state C and the excited state system configuration state D through hybrid density functional self-consistent calculation, and construct the configuration diagram and ZPL energy; Step S5: extract the total energy, phonon basis vector and atomic mass in the above steps, obtain the Huang-Kun factor and spectrum data by calculation, import them into the drawing software, and obtain the photoluminescence spectrum; wherein the definition formula of the Huang-Kun factor is: in, is the reduced Planck constant, the change in the phonon canonical coordinates ΔQ λ The following relations are satisfied: The excited state atomic position is R e,α , the ground state atomic position is R g, α, phonon basis vector is u λ , m α represents the mass of atom α; The spectral data takes into account the Gaussian broadening caused by temperature, and the spectral function of the electroacoustic coupling effect is: Among them, σ is the broadening parameter, S λ is the Huang Kun factor, ω λ is the frequency corresponding to the phonon mode λ, then the photoluminescence spectrum distribution of the system is: Among them, E ZPL is the zero phonon line position, which is the energy difference between the ground state system configuration state A and the excited state system configuration state C; is the energy of the incident photon; the spectrum generation factor g is: g(t)=e S(t)-S(0) ; 2. The method for simulating phonon-assisted photoluminescence spectroscopy according to claim 1, characterized in that: In step S3 and step S4, the computing software is VASP.

3. The method for simulating phonon-assisted photoluminescence spectroscopy according to claim 1, characterized in that: In step S5, the drawing software is one of Origin, Gnuplot, and Matplotlib.

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