CN109543211B - Conductivity calculation method under single-layer graphene intrinsic defects - Google Patents
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Abstract
The invention discloses a conductivity calculation method under an intrinsic defect of single-layer graphene. By using the method, the change of the structure and the electronic characteristic of the perfect graphene unit cell structure after the intrinsic defect occurs can be calculated, and the change condition of the conductivity of the perfect graphene unit cell structure can be further obtained. Firstly, establishing a unit cell configuration model of each type of intrinsic defect of single-layer graphene; then, obtaining a unit cell constant with the most stable defect structure by utilizing a first sexual principle; and theoretically analyzing and deducing the conductivity change condition of the graphene after the intrinsic defect occurs by comparing the unit cell structures, the static conditions and the energy state density of the complete perfect unit cell and the complete defect unit cell. The method expands experimental measurement based on a strict theoretical analysis means, and is suitable for analyzing the influence of the graphene defects on the conductivity of the graphene.
Description
Technical Field
The invention relates to the technical field of graphene conductivity calculation, in particular to a conductivity calculation method under an intrinsic defect of single-layer graphene.
Background
According to a report of the journal of Nature in 2005, graphene is a zero-bandgap semiconductor material with a special energy band structure, and a conduction band and a valence band are intersected at one point, namely the dispersion relation of carrier energy and wave vector in the vicinity of the point is linear. The surprising result of this derivation is that near this point the mass of the carriers is zero and can travel distances on the order of microns without being scattered. The current carrier in the graphene can be an electron or a hole, and the intrinsic current carrier mobility can reach 10 under an ideal state 5 cm 2 V -1 s -1 A rank. The mobility is almost independent of temperature, and the effective speed of the current carrier reaches 10 6 m/s. Due to the unique crystal structure and excellent electrical properties of graphene, graphene is widely and inexhaustibly applied in aerospace science and technology. However, all things are twosided, and space environments have various influences on devices and materials working in space due to the particularity of the space environments, such as large temperature difference, various ionizing radiations and electromagnetic radiations, neutral radiations, micrometeors, track fragments, high/ultrahigh vacuum and the like. Graphene is no exception, and its good conductivity also changes in the space environment due to various space environment effects. The most important influences are ionizing radiation, spatial gamma ray radiation, ultraviolet radiation, various high-energy particle radiation and the like, which can affect the conductivity of the graphene to various properties. Such as ultraviolet radiation, which is one of the more important factors in the near-day space environment. All ultraviolet radiation with wavelength shorter than 300 nm has a great effect although only accounting for about 1% of the total solar radiation energy. The ultraviolet photons can destroy carbon-carbon bonds of graphene, so that chemical structure change is caused, energy state density and charge density are changed, and conductivity of graphene is further influenced. The space irradiation environment mainly comes from the earth radiation zone, the solar cosmic rays, the Galaxy cosmic rays and the likeAre divided into electrons, protons, a few heavy ions and gamma rays, which constitute the radiation environment on the spacecraft orbit. The high-energy particles bombard the unit cell structure of the graphene to generate displacement defects, vacancy defects, adsorption defects and the like, so that the characteristics of the electron energy state distribution and the like of the graphene are changed, and the conductivity of the graphene is influenced. Also gamma rays can break the bonds of graphene, thereby affecting its conductivity.
At present, the conductivity of graphene is usually obtained by adopting an experimental detection method, however, the number of intrinsic defects is originally extremely small, and with the continuous improvement of a graphene growth process, the number of intrinsic defects is less and less, and exceeds the experimental measurement limit; therefore, a new method needs to be adopted to study the conductivity change caused by the intrinsic defect of the single-layer graphene.
Disclosure of Invention
In view of the above, the invention provides a method for calculating the conductivity under the intrinsic defect of the single-layer graphene, which utilizes the first principle calculation theory to calculate the change of the structure and the electronic characteristics after the defect occurs in the perfect graphene unit cell structure, so as to obtain the conductivity change condition.
The method for calculating the conductivity of the single-layer graphene intrinsic defects comprises the following steps:
Further, in the step 4, the electron energy state densities of the two complete unit cells are respectively integrated within a range of positive and negative 3 KT of the Fermi surface to obtain a unit cell beta 0 And unit cell beta 1 Where K is the boltzmann constant and T is the kelvin temperature.
Further, in the step 1, aiming at each type of intrinsic defect unit cell structure model, firstly fixing non-defect atoms, and performing position relaxation on the rest atoms of the unit cell to obtain the most stable configuration; then all atoms in the most stable configuration are fixed, and the whole unit cell structure is subjected to relaxation once more, so that the total system energy of the corresponding intrinsic defect unit cell is obtained.
Further, in the step 4, the complete unit cell β is calculated 1 And beta 0 When the electron energy state density distribution information is obtained, the fold structure of the graphene is taken as a nonlinear factor to be introduced into the first linear principle calculation.
Has the advantages that: the method disclosed by the invention starts from a real physical process and a basic physical principle, and analyzes the influence rule of the intrinsic defects of the graphene on the conductivity of the graphene in detail. Compared with experimental measurement, the method has no influence of experimental measurement errors. Meanwhile, the influence of different types and numbers of intrinsic defects of the graphene on the conductivity of the graphene can be analyzed by changing different calculation inputs, and the measurement efficiency is higher compared with that of an experiment. Most importantly, theoretical calculation analysis can break through the limitation of experimental measurement accuracy. Therefore, the conductivity of the graphene is analyzed more accurately, more accurately and more effectively by the method. The method can provide reliable technical support for the research on the change of the electrical properties of graphene and graphene-based functional materials, devices and aerospace loads in a radiation environment.
Drawings
Fig. 1 is a TEM image of a point defect and a calculated atomic arrangement structure diagram.
FIG. 2 is a TEM image of a single hole defect and a calculated atomic arrangement structure diagram.
FIG. 3 is a TEM photograph of three kinds of multiple hole defects that have been observed and a structural view of the atomic arrangement thereof.
Fig. 4 illustrates three exemplary out-of-plane carbon atom induced defects.
FIG. 5 is a schematic diagram of the computing software VASP and the super computer group used for computing in the embodiment of the present invention.
FIG. 6 is a schematic diagram of a material Studio interface of a business simulation application software for constructing a VASP calculation input structure file according to an embodiment of the present invention.
Fig. 7 shows a perfect unit cell structure and various intrinsic defect structures of graphene constructed in the embodiment of the present invention.
FIG. 8 shows a perfect unit cell structure beta of graphene constructed in an embodiment of the present invention 0 With various intrinsic defect structures alpha 1 ～α 4 The relative system with optimized unit cell constant can always be obtained.
FIG. 9 shows β calculated in the example of the present invention 1 And beta 0 Energy state density distribution versus integrated energy state density.
FIG. 10 is a flow chart of method steps of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a method for calculating the conductivity of a single-layer graphene intrinsic defect, which is characterized in that according to a first principle theory, a structure model is established for the graphene intrinsic defect by combining a commercial calculation program VASP, and the change of the structure and the electronic characteristic of the graphene intrinsic defect is calculated and analyzed.
The first principle is one of the important powerful and indispensable means in the early stage, peak stage and future of graphene research. The unique structure and electronic characteristics of graphene are brought by the structural characteristics of the graphene in a nanometer scale, and the first principle is that the macroscopic properties of substances are deduced from the crystal structure without any fitting parameter factors. In order to analyze the influence of radiation damage and defects on the conductivity of graphene, the crystal conductivity is analyzed from the solid physical point of view from the basic concept of material conductivity. As described above, the excellent conductivity of graphene is mainly formed by ballistic transport of electrons near the dirac point in the energy band, the conduction band is low and the valence band top coincides at the dirac point, the energy band has metallic characteristics, and the characteristics of the conductivity can be analyzed by the theory of metal electron theory in solid science. The method can be directly applied to the design, development, failure analysis and other aspects of graphene-related space materials and devices.
The method for acquiring the conductivity change of the single-layer graphene when the intrinsic defect occurs comprises the following steps:
The method comprises the steps of calculating the change of the structure and the electronic characteristics under the intrinsic defect of the single-layer graphene by utilizing a first principle, so as to obtain the conductivity change under the intrinsic defect of the single-layer graphene; in the embodiment, the software VASP is directly used for calculating the first principle, and the software has the advantages of high calculation precision, visualized input and output and convenient operation; however, the present invention is not limited to this software, and may be any software as long as it can construct a cell based on the first principle and realize calculation of the structure and electronic characteristics of the cell.
In the VASP: describing the interaction between basic particles such as ions and atoms by adopting a pseudopotential, namely describing the interaction between the particles by adopting a plane wave amplification projection algorithm; the exchange interaction between charged particles is described by a generalized gradient approximation. The set Monkhorst-Pack grid size is gradually changed while different calculation steps are performed. During plane wave vector calculation, the initial range of the truncation energy adopted by the invention is 200-700 millielectron volts, and the optimal truncation energy value obtained through optimization is 360 millielectron volts. The use of such truncation can achieve the computational accuracy requirement at an approximation.
And 2, establishing a unit cell structure model of the intrinsic defect of the graphene and determining a unit cell constant of the unit cell structure of the defect.
At room temperature, the unit cell constant of perfect single-layer graphene is a known quantity, but in order to keep the uniformity of simulation calculation, the unit cell constant of perfect single-layer graphene at room temperature needs to be determined by calculation: under the above calculation setting, a hexagonal honeycomb model of graphene is constructed by using VASP, and the energy of the cell system corresponding to different cell constants is calculated, and the lowest point of the energy is taken as the most probable cell constant. Based on the cell constants, subsequent calculations were performed.
Secondly, a unit cell structure model of the intrinsic defects of the graphene needs to be constructed. A number of known experiments and theories have determined that various types of intrinsic defects of graphene are: point defects, single hole defects, multiple hole defects, line defects, and out-of-plane carbon atom induced defects.
Wherein, the point defect: the point defect of graphene is formed due to the rotation of a C — C bond, and thus the defect is formed without causing the introduction or removal of carbon atoms in the graphene molecule and without generating carbon atoms having dangling bonds. The formation energy of such defects is about 5eV. Point defects may be generated by electron beam bombardment or rapid cooling in a high temperature environment. Fig. 1 is a TEM image of a point defect and a calculated atomic arrangement structure diagram.
Single hole defect: if one carbon atom is lost in the carbon six-membered ring arranged in series, a single hole defect is formed on the graphene. FIG. 2 is a TEM image of a single hole defect and a calculated atomic arrangement structure diagram. It is clear that the loss of one carbon atom necessarily results in the breaking of the three covalent bonds to which it is originally attached, with the result that three dangling bonds are formed.
Multiple hole defects: based on the single hole defect, if one more carbon atom is lost, multiple hole defects are generated, and fig. 3 shows TEM photographs of three types of multiple hole defects that have been observed and their atomic arrangement structures. It will be appreciated that multiple hole defects can be further complicated by the continued loss of carbon atoms in the graphene lamellae if external energy is present to enable the loss of carbon atoms (e.g., high energy electron beam bombardment).
Line defects: in the process of preparing graphene by using a chemical vapor deposition method, the graphene starts to grow at different positions on the metal surface, so that the graphene growing at different positions has different two-dimensional spatial trends due to the growth randomness, when the graphene grows to a certain size, cross fusion starts to occur, and a defect starts to appear due to the difference of initial crystal orientation in the fusion process, and the defect usually presents a linear shape. Typically produced during graphene growth.
Out-of-plane carbon atoms introduce defects: the lost carbon atoms generated during the formation of the single-hole and multiple-hole defects are not necessarily completely separated from the graphene, and many times, the carbon atoms form delocalized atoms after being separated from the original carbon six-membered ring and migrate on the surface of the graphene. When it migrates to a certain position of graphene, a new bond is formed. Such defects will destroy the original planar structure of the region to form a three-dimensional structure. FIG. 4 is a diagram of three exemplary out-of-plane carbon atom introduction defects, a-c showing the spatial arrangement of such defects, and d-e being the introduction positions of the corresponding missing carbon atoms. In practical experiments, defects introduced by the out-of-plane carbon atoms are difficult to capture through various microscopic techniques (SPM, TEM) because the out-of-plane carbon atoms have very fast migration speed or high formation energy, and no observation report about the defects introduced by the out-of-plane carbon atoms is seen at present.
Respectively constructing unit cell structure models under various intrinsic defects according to the intrinsic defects, and constructing unit cells corresponding to the defect unit cell structure models; then, calculating the system total energy of various intrinsic defect unit cells by utilizing a first principle; the lowest system always corresponds to the most stable crystal structure of intrinsic defects, i.e., the most likely model of the crystal structure of intrinsic defects. The method comprises the following specific steps:
perfect cell structure beta of graphene constructed in materialas Studio 0 And intrinsic defect cell structure alpha i (i =1,2,3,4.. Said). The result is output as a structural input file POSCAR calculated for VASP, where β is first registered 0 And (4) relaxing to obtain a unit cell structure constant of perfect graphene. Second pair of unit cells alpha i (i =1,2,3,4.) a unit cell α is obtained in the output file OUTCAR of the VASP by performing a structural relaxation i The system of (2) is always possible. Wherein the lowest energy value is selected as the real unit cell constant of each defect structure, and the most stable intrinsic defect unit cell structure alpha is obtained 0 。
In the step (3), the step (B),establishing a complete single-layer graphene intrinsic defect cell beta 1 . Sequentially aligning beta by VASP according to a calculation flow 1 And beta 0 And performing structure optimization, static calculation and system energy state density calculation.
Specifically, a complete graphene intrinsic defect unit cell is constructed according to the obtained unit cell constant information of the graphene defect structure. Then, the cell beta is completed 1 And completing cell beta 0 Performing VASP calculation to obtain complete unit cell beta 1 And completing cell beta 0 The charge distribution information and the electron energy state density distribution information of (1):
in the VASP output file of the structure calculation, the CONTCAR file is again used as the structure input file, all atoms of the unit cell are fixed, and a self-consistent static calculation is performed on the whole system, so that the charge distribution information of the whole system can be obtained.
At this time, the files CHG and CHGCAR representing the charge distribution information in the previous calculation result are used as input files of VASP, and the whole system is subjected to one-time self-consistent calculation, so that the electron energy state density distribution information of the system is obtained and reflected in the DOSCAR of the VASP output file.
And 4, analyzing the complete unit cell beta and the complete unit cell beta by combining the VASP calculation result 0 Change in conductivity of (1).
Specifically, firstly, to beta 1 And beta 2 Is analyzed for electron energy state density. The integrated energy state density of the system energy state density near the fermi surface needs to be made as input data for the theoretical derivation described below.
The method comprises the following specific steps: the conductivity according to the aforementioned analytical system employs metal electron theory:
when a constant electric field E is applied to the metal, a stable current density j is actually established in a time of the order of femtoseconds, obeying ohm's law:
j＝σE
where σ is the conductivity.
The nature of the steady current reflects that, under constant external field, the electrons reach a new steady state statistical distribution, which can also be described by a distribution function f (k) similar to that at equilibrium, and once the distribution function f (k) is determined, the current density can be directly calculated.
It is well known that in simple electronic theory, the main physical basis for explaining ohm's law is:
(i) Electrons are accelerated under the action of an electric field E;
(ii) Electrons lose directional motion due to collision
For (i), it can be shown by band theory that under the action of E, all electronic state changes obey:
where k is an electron wave vector, t is time, E is an applied electric field, q is a basic charge amount, and h is a Boltzmann constant.
Whereas for (ii) the electrons, assuming a certain collision free time τ, completely lose the directional motion obtained in the electric field once subjected to a collision. In order to quantitatively research the theory of electron motion, a differential equation, boltzmann equation, with respect to an electron transport distribution function is introduced. The boltzmann equation is established from an examination of how the electron transport distribution function varies over time, and the variation of the electron transport distribution function has two sources:
"Drift" of statistical distribution in k-space caused by ambient conditions "
ii, collision, the electrons continuously jump from one state k to another state k' due to vibration of the cell atoms or the presence of impurities, and the change of the electron state is called scattering. Assuming that the final and initial states of the collision can be simplified as b and a, the boltzmann equation can be simplified as:
wherein f is 0 Is the fermi function at equilibrium, f = f (k), τ is a parameter introduced, called relaxation time. Using the fundamental relation of energy bands:
the final current density formula is:
the above equation is expressed in terms of components:
finally, the conductivity is obtained:
notably, the above formula appears
It is shown that the contribution of the integral comes mainly from E = E F Nearby, i.e. the conductivity is mainly determined by the fermi surface E = E F The situation of the vicinity. Assuming that the metal conduction band electrons can be basically used with a single effective mass m * The following steps are described:
by unfolding the integral, ignoring higher order terms, the metal conductivity can be written as:
wherein σ 0 Representative tensor σ αβ The scalar value of (d). Intrinsic defect of graphene for its electron mobility (relaxation time) tau (E) F ) And electron effective mass m * Has substantially no influence on the system conductivity sigma 0 The influence of (b) is attributed to the electron density n. Note that n in this case is the number density of valence electrons near the fermi surface of the system. For a perfect unit cell or a defective unit cell structure of graphene, the electron distribution function of the whole system is unchanged, so the calculation result of the electron energy state density is combined to beta 1 And beta 0 And integrating the electron energy state density near the Fermi surface and comparing to obtain the conductivity change condition of the system. Wherein K is Boltzmann constant, T is Kelvin, and the conductivity characteristics of the crystal can be well reflected by the electron energy state density within plus or minus 3 KT of the Fermi surface.
In calculating the complete cell beta 1 And beta 0 When the electron energy state density distribution information is obtained, the fold structure of the graphene is taken as a nonlinear factor and introduced into the first linear principle calculation, namely, a spin-orbit coupling value is opened in an input file INCAR calculated by VASP; thus, the calculation result is more accurate.
The method provides a theoretical analysis scheme for the influence of the intrinsic defects of the graphene on the conductivity of the graphene, and makes up for the defects of experimental measurement limits.
The result of the method can also be used as a theoretical basis to further research the influence rule of the graphene extrinsic defects on the conductivity of the graphene extrinsic defects.
The following description is made with reference to specific examples:
FIG. 5 shows a first exemplary full-quantum computing commercial software VASP, whose version is vasp.5.3.5, used in the computing of the present invention, and the super computer group used in the computing of Shanghai super computing center. The pseudopotential used was PAW-GGA.
The lattice constant of single layer graphene is known, but in order to ensure the consistency of the present study, the perfect lattice constant of single layer graphene was calculated using the first principles of performance calculation tool VASP, whose unit cell was first constructed in the commercial application software materials Studio, fig. 6.
The structure information is used as input, a structure input file POSCAR of VASP is written, the cell basis vector length of the single-layer graphene is calculated to be a =0.247nm through lattice relaxation, and the cell basis vector length of the single-layer graphene is measured to be 0.246nm under room temperature (300K) through experiments. Therefore, the adopted calculation tool is verified to be more matched with the actual situation.
When intrinsic defects occur in the single layer perfect graphene unit cell, five defects have been discussed previously, namely point defects common, single hole defects, multiple hole defects, line defects and out-of-plane carbon atom introduction defects. According to analysis, the defects of line defects and defects introduced by out-of-plane carbon atoms belong to process defects generated in the growth process of graphene, and the defects can be avoided along with the continuous progress of the graphene growth process. Then cell construction is required for several other types of defects: a single vacancy defect, a double vacancy defect, a stone-wales defect and a 555-777 defect as shown in FIG. 7, which are respectively the perfect unit cell beta of graphene 0 Graphene different type structural defect unit cell alpha i (i =1,2,3,4). Derivation of beta by commercial application software materials Studio 0 And alpha i (i =1,2,3,4) in POSCAR. Substituting VASP to carry out lattice relaxation to obtain the most stable structure of each type of cell and the lowest cell energy of the system corresponding to the most stable structure, and comparing the most stable structure with the lowest cell energy, as shown in FIG. 8. Therefore, the single-vacancy defect is the most likely intrinsic defect formed by graphene, and the system energy is the lowest relative to the rest defect structures, namely the energy required by external disturbance is the smallest. Therefore, the single-vacancy defect of the graphene is selected as the defect structure unit cell beta calculated next 1 。
According to the calculation result, the cell beta of the single-layer graphene perfect structure is subjected to 0 And single vacancy intrinsic defect cell beta 1 And (5) carrying out system energy state density calculation.
Before calculating the system energy state density, the system needs to be aligned with beta 0 And beta 1 A static calculation of structural relaxation and self-consistency is performed. The static self-consistent calculation is to fix the position of each atom, perform continuous self-iterative calculation on the whole system from the most basic Schrodinger equation, and finally obtain the most reliable configuration of the whole system within the set precision range.
Previous analyses showed that for beta 0 Of conductivity scalar value σ thereof 0 The calculation formula is as follows:
after the generation of the single-vacancy defects, the electron mobility (relaxation time) and the electron effective mass of the valence electrons of the whole system are not changed, so that the influence factors on the conductivity of the system are attributed to the electron density n. And n is the number density of valence electrons near the fermi surface of the system.
In the result of the static calculation of the previous step, the unit cell beta is obtained 0 And beta 1 The self-consistent charge density of (b) is embodied in the output files CHGCAR and CHG of VASP, and then for β 0 And beta 1 Energy state density calculations were performed. At this time, when the input file INCAR is set, ICHAGR =2 in the input file is changed to ICHAGR =11, which represents that the already calculated input files CHGCAR and CHG are used, and at this time, the calculation accuracy of KPOINTS is further increased, and the coordinates of atoms are still fixed. Calculates to obtain beta 0 And beta 1 The distribution of the energy state density and the integrated energy state density of (a) are shown in fig. 9.
By accumulating integrated density of states around the fermi level
Then carrying out weighted average comparison to obtain the single-vacancy defect unit cell beta 1 Perfect crystal cell beta compared with a control group 0 The integrated energy state density reduction was 3%. Before and after the adsorptionIn other words, the electron distribution function of the whole system is unchanged, so the number density n of valence electrons near the fermi surface of the system, namely the reduction of the conductivity of the system is also 3%, which is more consistent with the experimental measurement result that the electron transport performance of the graphene vacancy defect is reduced by about 5% reported in the literature.
Establishing a lattice configuration model of a graphene intrinsic defect structure; determining the most stable lattice constant of a defect structure by utilizing first-nature principle calculation software VASP; establishing a computational cell of a first principle according to the obtained lattice structure defect model; calculating the unit cell structure, static state and energy state density of the unit cell by using first principle calculation software VASP; and theoretically analyzing and deducing the conductivity change condition of the graphene after the intrinsic defects appear according to the calculation result. The method is high in innovation, experimental measurement is expanded based on a strict theoretical analysis means, and the method is suitable for analyzing the influence of the graphene defects on the conductivity of the graphene defects, and is particularly suitable for the case that the intrinsic defect types of the graphene are difficult to determine in experiments. On the basis of the invention, the influence rule of various graphene defects on the conductivity of the graphene is continuously researched and systematically established, and the graphene has great application value in the application evaluation of materials and devices based on graphene in the aerospace radiation environment.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A method for calculating conductivity of a single-layer graphene intrinsic defect is characterized by comprising the following steps:
step 1, constructing different types of intrinsic defect unit cell structure models, and calculating the total system energy of each type of intrinsic defect unit cell by utilizing a first principle, wherein the intrinsic defect unit cell corresponding to the minimum system energy is the most stable intrinsic defect unit cell structure;
step 2, establishing a complete unit cell beta of the most stable intrinsic defect unit cell structure determined in the step 1 1 (ii) a Simultaneously establishing a single layerComplete unit cell beta of perfect unit cell structure of graphene 0 As a control;
step 3, utilizing the first principle to calculate the complete unit cell beta respectively 1 And completing cell beta 0 Charge density distribution information and electron energy state density distribution information of (a);
step 4, two complete unit cells beta 1 、β 0 The electron energy state density is respectively subjected to integral processing, and the conductivity variation of the single-layer graphene after the intrinsic defect occurs is calculated according to the variation value of the electron energy state density integral of the two complete unit cells.
2. The method for calculating conductivity under intrinsic defect of single-layer graphene as claimed in claim 1, wherein in the step 4, the electron energy state densities of two complete cells are respectively integrated within plus or minus 3 KT ranges of Fermi surface to obtain cell beta 0 And unit cell beta 1 K is a boltzmann constant, and T is a temperature in kelvin.
3. The method for calculating the conductivity of the single-layer graphene intrinsic defect of claim 1, wherein in the step 1, for each type of intrinsic defect unit cell structure model, non-defect atoms are fixed firstly, and the rest other atoms of the unit cell are subjected to position relaxation to obtain the most stable configuration; then all atoms with the most stable configuration are fixed, and the whole crystal cell structure is relaxed once again to obtain the total system energy of the corresponding intrinsic defect crystal cell.
4. Method for calculating the electrical conductivity under a single-layer graphene intrinsic defect according to claim 1 or 2, wherein in step 4, the complete unit cell β is calculated 1 And beta 0 When the electron energy state density distribution information is obtained, the fold structure of the graphene is taken as a nonlinear factor to be introduced into the first linear principle calculation.
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