Calculation of the Dielectric Function for Highly Excited Polar Semiconductors

Electronic structure and optical properties of Zn X(X=O,S,Se,Te):A density functional study S.Zh.Karazhanov,1,2P.Ravindran,1A.Kjekshus,1H.Fjellvåg,1and B.G.Svensson3 1Centre for Material Science and Nanotechnology,Department of Chemistry,University of Oslo,P.O.Box1033Blindern,N-0315Oslo,Norway2Physical-Technical Institute,2B Mavlyanov Street,Tashkent700084,Uzbekistan3Department of Physics,University of Oslo,P.O.Box1048Blindern,N-0316Oslo,Norway͑Received5July2006;revised manuscript received15November2006;published6April2007͒Electronic band structure and optical properties of zinc monochalcogenides with zinc-blende-and wurtzite-type structures were studied using the ab initio density functional method within the local-density approxima-tion͑LDA͒,generalized-gradient approximation,and LDA+U approaches.Calculations of the optical spectrahave been performed for the energy range0–20eV,with and without including spin-orbit coupling.Reflec-tivity,absorption and extinction coefficients,and refractive index have been computed from the imaginary partof the dielectric function using the Kramers-Kronig transformations.A rigid shift of the calculated opticalspectra is found to provide a goodfirst approximation to reproduce experimental observations for almost all thezinc monochalcogenide phases considered.By inspection of the calculated and experimentally determinedband-gap values for the zinc monochalcogenide series,the band gap of ZnO with zinc-blende structure hasbeen estimated.DOI:10.1103/PhysRevB.75.155104PACS number͑s͒:71.15.Ϫm,71.22.ϩiI.INTRODUCTIONThe zinc monochalcogenides͑Zn X;X=O,S,Se,and Te͒are the prototype II-VI semiconductors.These compoundsare reported to crystallize in the zinc-blende-͑z͒and wurtzite ͑w͒-type structures.The Zn X-z phases are optically isotropic, while the Zn X-w phases are anisotropic with c as the polaraxis.Zn X phases are a primary candidate for optical devicetechnology such as visual displays,high-density opticalmemories,transparent conductors,solid-state laser devices,photodetectors,solar cells,etc.So,knowledge about opticalproperties of these materials is especially important in thedesign and analysis of Zn X-based optoelectronic devices.Optical parameters for some of the Zn X phases havewidely been studied experimentally in the past.Detailed in-formation on this subject is available for ZnO-w,1–9ZnS-w,9ZnS-z,9–11ZnSe-z,9,10and ZnTe-z,9,10,12,13and see the sys-tematized survey in Ref.14.However,there are no experi-mental data on optical properties of ZnSe-w,ZnTe-w,andZnO-z.Furthermore,there is a lack of consistency betweensome of the experimental values for the optical spectra.Thisis demonstrated in Fig.1,which displays reflectivity spectrafor ZnO-w measured at T=300K by three different groups.Dielectric-response functions were calculated using theKramers-Kronig relation.As is seen in Fig.1,intensity of theimaginary part of the dielectric function͑⑀2͒and reflectivity ͑R͒corresponding to the fundamental absorption edge of ZnO-w are higher8than those at the energy range10–15eV, while in Ref.14it is vice versa.The optical spectra in Fig.1 measured using the linearly polarized incident light for elec-tricfield͑E͒parallel͑ʈ͒and perpendicular͑Ќ͒to the c axes are somehow close to those of Ref.7using nonpolarized incident light.Using the experimental reflectivity data,a full set of op-tical spectra for ZnO has been calculated15for the wide en-ergy range0–26eV.Density functional theory16͑DFT͒in the local-density approximation17͑LDA͒has also been used to calculate optical spectra for ZnO-w͑Ref.18͒and ZnS-w ͑Ref.18͒by linear combination of atomic orbitals and for ZnS-z19and ZnSe-z19by self-consistent linear combination of Gaussian orbitals.The optical spectra of ZnO͑including excitons͒has been investigated20by solving the Bethe-Salpeter equation.Band-structure studies have been per-formed by linearized-augmented plane-wave method plus lo-cal orbitals͑LAPW+LO͒within the generalized gradient and LDA with the multiorbital mean-field Hubbard potential ͑LDA+U͒approximations.The latter approximation is found to correct not only the energy location of the Zn3d electrons and associated band parameters͑see also Refs.21 and22͒but also to improve the optical response.Despite the shortcoming of DFT in relation to underestimation of band gaps,the locations of the major peaks in the calculated en-ergy dependence of the optical spectra are found to be in good agreement with experimental data.It should be noted that the error in calculation of the band gap by DFT within LDA and generalized-gradient approxi-mation͑GGA͒is more severe in semiconductors with strong Coulomb correlation effects than in other solids.21–25This is due to the mean-field character of the Kohn-Sham equations and the poor description of the strong Coulomb correlation and exchange interaction between electrons in narrow d bands͑viz.,the potential U͒.Not only the band gap͑E g͒but also the crystal-field͑CF͒and spin-orbit͑SO͒splitting ener-gies͑⌬CF and⌬SO͒,the order of states at the top of the valence band͑VB͒,the location of the Zn3d band and its width,and the band dispersion are found21,22,26,27to be incor-rect for ZnO-w by the ab initio full potential͑FP͒and atomic-sphere-approximation͑ASA͒linear muffin-tin orbital ͑LMTO͒methods within the pure LDA͑Refs.26and27͒and by the projector-augmented wave͑PAW͒method within LDA and GGA.21,22Thesefindings were ascribed21,22to strong Coulomb correlation effects.DFT calculations within LDA plus self-interaction correction͑LDA+SIC͒and LDA +U are found21,22,26to rectify the errors related to⌬CF andPHYSICAL REVIEW B75,155104͑2007͒⌬SO ,order of states at the top VB,and width and location of the Zn 3d band,as well as effective masses.In other semi-conductors,in which the Coulomb correlation is not suffi-ciently strong,the ⌬CF and ⌬SO values derived from DFT calculations within LDA are found to be quite accurate.This was demonstrated for diamondlike group IV ,z -type group III-V ,II-VI,and I-VII semiconductors,28w -type AlN,GaN,and InN,29using the LAPW and V ASP -PAW,the w -type CdS and CdSe,27z -type ZnSe,CdTe,and HgTe,30using the ab initio LMTO-ASA,and z -and w -type ZnSe and ZnTe ͑Refs.21and 22͒as well as z -type CdTe,31using the V ASP -PAW and FP LMTO methods.Although the SO splitting at the top of VB is known to play an important role in electronic structure and chemical bonding ofsemiconductors,21,22,26,28–30,32,33there is no systematic study of the role of the SO coupling in optical properties of these materials.Several attempts have been undertaken to resolve the DFT eigenvalue problem.One such approach is the utilization of the GW approximation ͑“G”stands for one-particle Green’s function as derived from many-body perturbation theory and “W”for Coulomb screened interactions ͒.Although GW re-moves most of the problems of LDA with regard to excited-state properties,it fails to describe the semiconductors with strong Coulomb correlation effects.For example,two studies of the band gap of ZnO calculated using the GW correction underestimated E g by 1.2eV ͑Ref.34͒and overestimated it by 0.84eV.35Calculations for Zn,Cd,and Hg monochalco-genides by the GW approach showed 36that the band-gap underestimation is in the range 0.3–bination of exact-exchange ͑EXX ͒DFT calculations and the optimized-effective GW potential approach is found 37to improve the agreement with the experimental band gaps and Zn 3d en-ergy levels.Band gaps calculated within the EXX treatment are found to be in good agreement with experiment for thes -p semiconductors.38,39Excellent agreement with experi-mental data was obtained 39also for locations of energy levels of the d bands of a number of semiconductors and insulators such as Ge,GaAs,CdS,Si,ZnS,C,BN,Ne,Ar,Kr,and Xe.Another means to correct the DFT eigenvalue error is to use the screened-exchange LDA.40Compared to LDA and GW,this approximation is found to be computationally much less demanding,permitting self-consistent determination of the ground-state properties and giving more correct band gaps and optical properties.Other considered approaches for ab initio computations of optical properties involve electron-hole interaction,41partial inclusion of dynamical vertex cor-rections that neglect excitons,42and empirical energy-dependent self-energy correction according to the Kohn-Sham local-density theory of excitation.19However,the simplest method is to apply the scissor operator,43which displaces the LDA eigenvalues for the unoccupied states by a rigid energy ing the latter method,excellent agree-ment with experiments has been demonstrated for lead monochalcogenides 44and ferroelectric NaNO 2.45However,the question as to whether the rigid energy shift is generally applicable to semiconductors with strong Coulomb correla-tion effects is open.In this work,electronic structure and optical properties of the Zn X -w and -z phases have been studied in the energy range from 0to 20eV based on first-principles band-structure calculations derived from DFT within the LDA,GGA,and LDA+U .PUTATIONAL DETAILSExperimentally determined lattice parameters have been used in the present ab initio calculations ͑Table I ͒.The ideal positional parameter u for Zn X -w is calculated on the as-sumption of equal nearest-neighbor bond lengths:27u =13ͩa cͪ2+14.͑1͒The values of u for the ideal case agree well with the experi-mental values u *͑see Table I ͒.Self-consistent calculations were performed using a 10ϫ10ϫ10mesh according to the Monkhorst-Pack scheme for the Zn X -z phases and the ⌫-centered grid for the Zn X -w phases.A.Calculations byV ASPpackageOptical spectra have been studied based on the band-structure data obtained from the V ASP -PAW package,55which solves the Kohn-Sham eigenvalues in the framework of the DFT ͑Ref.16͒within LDA,17GGA,56and the simplified ro-tationally invariant LDA+U .23,24The exchange and correla-tion energies per electron have been described by the Perdew-Zunger parametrization 57of the quantum Monte Carlo results of Ceperley and Alder.58The interaction be-tween electrons and atomic cores is described by means of non-norm-conserving pseudopotentials implemented in the V ASP package.55The pseudopotentials are generated in accor-dance with the PAW ͑Refs.59and 60͒method.The use of the PAW pseudopotentials addresses the problem ofinad-FIG.1.Reflectivity spectra R ͑␻͒for ZnO-w determined experi-mentally at 300K in Refs.9and 14͑solid circles ͒,Ref.8͑open circles ͒,and Ref.7͑solid lines ͒,along with the imaginary part of the dielectric-response function ͓⑀2͑␻͔͒calculated using the Kramers-Kronig relation.The results of Ref.7͑open circles ͒are used for both E ʈc and E Ќc ,because no polarized incident light was used in the experiments.KARAZHANOV et al.PHYSICAL REVIEW B 75,155104͑2007͒equate description of the wave functions in the core region ͑common to other pseudopotential approaches61͒,and its ap-plication allows us to construct orthonormalized all-electron-like wave functions for Zn3d and4s and s and p valence electrons of the X atoms under consideration.LDA and GGA pseudopotentials have been used,and the completelyfilled semicore Zn3d shell has been considered as valence states.It is well known that DFT calculations within LDA and GGA locate the Zn3d band inappropriately close to the top-most VB,hybridizing the O p band,falsifying the band dis-persion,and reducing the band gap.Nowadays,the problem is known to be solved by using the LDA+SIC and LDA +U.21,22,26,62–64For the DFT calculations within LDA+U, explicit values of the parameters U and J are required as input.In previous papers,21,22we have estimated the values of the U and J parameters within the constrained DFT theory65and in a semiempirical way by performing the cal-culations for different values of U and forcing it to match the experimentally established66location of the Zn3d bands. Based on the results,21,22the values of the parameters U and J listed in Table I are chosen to study the optical spectra.B.Calculations by MINDLAB packageFor investigation of the role of the SO coupling in elec-tronic structure and optical properties of Zn X,DFT calcula-tions have been performed using the MINDLAB package,67 which uses the full potential linear muffin-tin orbital͑FP LMTO͒method.For the core charge density,the frozen-core approximation is used.The calculations are based on LDA with the exchange-correlation potential parametrized accord-ing to Gunnarsson-Lundquist68and V osko-Wilk-Nussair.69The base geometry in this computational method consists of a muffin-tin part and an interstitial part.The basis set is comprised of linear muffin-tin orbitals.Inside the muffin-tin spheres,the basis functions,charge density,and potential are expanded in symmetry-adapted spherical harmonic functions together with a radial function and a Fourier series in the interstitial.C.Calculation of optical propertiesFrom the DFT calculations,the imaginary part of the di-electric function⑀2͑␻͒has been derived by summing transi-tions from occupied to unoccupied states for energies much larger than those of the phonons:⑀2ij͑␻͒=Ve22␲បm2␻2͵d3k͚nnЈ͗kn͉p i͉knЈ͘ϫ͗knЈ͉p j͉kn͘f kn͑1−f knЈ͒␦͑⑀knЈ−⑀kn−ប␻͒.͑2͒Here,͑p x,p y,p z͒=p is the momentum operator,f kn the Fermi distribution,and͉kn͘the crystal wave function correspond-ing to the energy⑀kn with momentum k.Since the Zn X-w phases are optically anisotropic,components of the dielectric function corresponding to the electricfield parallel͑Eʈc͒and perpendicular͑EЌc͒to the crystallographic c axis have been considered.The Zn X-z phases are isotropic;conse-quently,only one component of the dielectric function has to be analyzed.The real part of the dielectric function⑀1͑␻͒is calculated using the Kramer-Kronig transformation.The knowledge ofTABLE I.Theoretically and experimentally͑in brackets͒determined unit-cell dimensions a and c,vol-umes V,ideal u͓calculated by Eq.͑1͔͒,and experimental u*,as well as values of the parameters U and J from Refs.21and22,were used in the present calculations.For w-type structure,a=b.For the z-type structure, a=b=c and all atoms are infixed positions.Phasea͑Å͒c͑Å͒V͑Å3͒u*uU͑eV͒J͑eV͒ZnO-w a 3.244͑3.250͒ 5.027͑5.207͒45.82͑47.62͒0.3830.38091ZnS-w b,c 3.854͑3.811͒ 6.305͑6.234͒81.11͑78.41͒0.3750.37561ZnSe-w a,d 4.043͑3.996͒ 6.703͑6.626͒94.88͑91.63͒0.3750.37181ZnTe-w e,f 4.366͑4.320͒7.176͑7.100͒118.47͑114.75͒0.3750.37371ZnO-z g 4.633͑4.620͒99.45͑98.61͒81ZnS-z h,i 5.451͑5.409͒161.99͑158.25͒91ZnSe-z a 5.743͑5.662͒189.45͑181.51͒81ZnTe-z i,j 6.187͑6.101͒236.79͑227.09͒81Reference46.b Reference18.c Reference47.d Reference48.e Reference49.f Reference50.g Reference51.h Reference52.i Reference53.j Reference54.ELECTRONIC STRUCTURE AND OPTICAL PROPERTIES…PHYSICAL REVIEW B75,155104͑2007͒both the real and imaginary parts of the dielectric tensor allows one to calculate other important optical spectra.In this paper,we present and analyze the reflectivity R ͑␻͒,the absorption coefficient ␣͑␻͒,the refractive index n ͑␻͒,and the extinction coefficient k ͑␻͒:R ͑␻͒=ͯͱ⑀͑␻͒−1ͱ⑀͑␻͒+1ͯ2,͑3͒␣͑␻͒=␻ͱ2ͱ⑀12͑␻͒+⑀22͑␻͒−2⑀1͑␻͒,͑4͒n ͑␻͒=ͱͱ⑀12͑␻͒+⑀22͑␻͒+⑀1͑␻͒2,͑5͒k ͑␻͒=ͱͱ⑀12͑␻͒+⑀22͑␻͒−⑀1͑␻͒2.͑6͒Here,⑀͑␻͒=⑀1͑␻͒+i ⑀2͑␻͒is the complex dielectric function.The calculated optical spectra yield unbroadened functions and,consequently,have more structure than the experimental ones.44,45,70,71To facilitate a comparison with the experimen-tal findings,the calculated imaginary part of the dielectric function has been broadened.The exact form of the broad-ening function is unknown.However,analysis of the avail-able experimentally measured optical spectra of Zn X shows that the broadening usually increases with increasing excita-tion energy.Also,the instrumental resolution smears out many fine features.These features have been modeled using the lifetime broadening technique by convoluting the imagi-nary part of the dielectric function with a Lorentzian with a full width at half maximum of 0.002͑ប␻͒2eV,increasing quadratically with the photon energy.The experimental reso-lution was simulated by broadening the final spectra with a Gaussian,where the full width at half maximum is equal to 0.08eV.III.RESULTS AND DISCUSSIONA.Band structureThe optical spectra are related to band dispersion and probabilities of interband optical transitions.So,it is of in-terest to analyze the electronic structure in detail.Band dis-persions for Zn X -w and Zn X -z calculated by DFT within LDA and LDA+U are presented in Fig.2.The general fea-tures of the band dispersions are in agreement with previous studies ͑see,e.g.,Refs.26,62,and 72͒.It is seen from Fig.2that the conduction-band ͑CB ͒minima for Zn X -w and Zn X -z are much more dispersive than the VB maximum,which shows that the holes are much heavier than the CB electrons in agreement with experimental data 73,74for the effective masses and calculated with FP LMTO and ͑Ref.26͒linear combination of atomic orbitals,18as well as with our findings.21,21Consequently,mobility of electrons is higher than that of holes.Furthermore,these features indicate that p electrons of X ͑that form the topmost VB states ͒are tightly bound to their atoms and make the VB holes less mobile.Hence,the contribution of the holes to the conductivity is expected to be smaller than that of CB electrons even though the concentration of the latter is smaller than that of the former.These features emphasize the predominant ionic na-ture of the chemical bonding.Another interesting feature of the band structures is that the VB maximum becomes more dispersive with increasing atomic number of X from O to Te.As noted in our previous contributions,21,22the band gaps of Zn X calculated by DFT within LDA,GGA,and LDA +U are underestimated and the question as to whether it is possible to shift the CB states rigidly was kept open.As found from the optical spectra discussed on the following sections,rigid shifts of the CB states up to the experimen-tally determined locations can provide a good first approxi-mation for the stipulation of the band gap.So,for the band dispersions in Fig.2,we have made use of this simple way for correcting the band gaps calculated by DFT.The only problem in this respect was the lack of an experimental band-gap value for ZnO-z .To solve this problem,the experi-mental and calculated ͑by DFT within LDA ͒band gaps ͑E g ͒of the Zn X series were plotted as a function of the atomic number of X .As seen from Fig.3,E g for the Zn X -w phases are very close to the corresponding values for the Zn X -z phases and the shape of the experimentaland calculated functional dependencies is in conformity.On this basis,theFIG.2.Band dispersion for ZnO-w ,ZnS-w ,ZnSe-w ,ZnTe-w ,ZnO-z ,ZnS-z ,ZnSe-z ,and ZnTe-z calculated according to LDA ͑solid lines ͒and LDA+U ͑dotted lines ͒.The Fermi level is set to zero energy.KARAZHANOV et al.PHYSICAL REVIEW B 75,155104͑2007͒band gap of ZnO-z is estimated by extrapolating the findings for Zn X -z from ZnS-z to ZnO-z .This procedure gave E g Ϸ3.3eV for ZnO-z .It is well known that not only band gaps are underesti-mated within LDA and GGA,but also band dispersions come out incorrectly,whereas location of energy levels of the Zn 3d electrons are overestimated ͑see,e.g.,Refs.20–22and 63͒.As also seen from Fig.2,calculations within the LDA+U approach somewhat correct the location of the en-ergy levels of the Zn 3d electrons.The elucidation of the eigenvalue problem and the order of states at the topmost VB from LDA,GGA,and LDA+U calculations are discussed in Refs.20–22and 26and will not be repeated here.Examination of Fig.2shows that the VB comprises three regions of bands:first a lower region consists of s bands of Zn and X ,a higher-lying region of well localized Zn 3d bands,and on top of this a broader band dispersion originat-ing from X -p states hybridized with Zn 3d states.The latter subband is more pronounced in ZnO than in the other Zn X phases considered.The hybridization is most severe accord-ing to the LDA and GGA calculations,whereas the LDA +U calculations somehow suppress this and improve the band-gap underestimation.A more detailed discussion of these aspects is found in Refs.21and 22.The SO splitting at the topmost VB is known to play an important role for the electronic structure and chemical bonding of solids.28,29,32In semiconductors with z -type struc-ture,the SO splitting energy is determined as the difference between energies of the topmost VB states with symmetry ⌫8v and ⌫7v .28,29,32In the w -type compounds,the topmost VB is split not only by SO interaction but also by CF,giving rise to three states at the Brillouin-zone center.To calculate theSO splitting energy for w -type phases,the quasicubic model of Hopfield 75is commonly used.It is well known that the SO splitting energy derived from ab initio calculations agrees well with experimental data only for some of the semiconductors.This is demonstrated,for example,for all diamondlike group IV and z -type group III-V ,II-VI,and I-VII semiconductors,28w -type AlN,GaN,and InN,29Zn X -w and -z ͑X =S,Se,and Te ͒,21,22and CdTe.31However,the errors in estimated SO and CF splitting ener-gies by LDA calculations are significant for semiconductors with strong Coulomb correlation effects,as demonstrated,e.g.,for ZnO.21,22,26For such systems,DFT calculations within LDA+U ͑Refs.21,22,and 26͒are shown to provide quite accurate values for ⌬CF and ⌬SO .Overestimation of the p -d hybridization in various variants of the DFT can also lead to the wrong spin-orbit coupling of the valence bands.76,77Systematic study of the SO coupling parameters was per-formed for zinc-blende II-VI semiconductors ͑Ref.30͒using the TB and LMTO methods,as well as for all diamondlike and zinc-blende semiconductors ͑Ref.28͒using the FLAPW method with and without the p 1/2local orbitals and the frozen-core PAW method implemented into V ASP .The cor-rections coming from the inclusion of the local p 1/2orbitals are found to be negligible for the compounds with light at-oms.Analysis of these results shows that the SO splitting energy coming from calculations using the V ASP -PAW shows good agreement with the experimental data.This result was also obtained 21recently for Zn X of wurtzite and zinc-blende structures.As demonstrated in Refs.21and 22the SO split-ting energy ͑⌬SO ͒increases when one moves from ZnO-z to ZnTe-z ,in agreement with earlier findings of Ref.28.To study the role of the SO coupling in band dispersion,the present ab initio calculations have been performed by V ASP and MINDLAB packages and spin-orbit splitting energy is found.The results are presented in Table II .Analysis of Table II shows that ͑⌬SO ͒calculated by MINDLAB is quite accurate.As expected,band dispersions calculated with and with-out the SO coupling differ little when the SO splittingenergyFIG.3.Band gaps for Zn X -w ͑circles ͒and Zn X -z ͑triangles ͒phases determined experimentally ͑filled symbols,from Refs.21and 22͒and calculated ͑open symbols ͒by DFT within LDA as a function of the atomic number of the X component of Zn X .TABLE II.Calculated SO splitting energy ͑in meV ͒using the MINDLAB package along with the previous theoretical and experi-mental findings.ZnO-z ZnS-z ZnSe-z ZnTe-z –3166432914–3166432914−34a 66a 393a 889a −34b 66b 398b 916b −37c 64c 392c 898c −33d64d 393d 897d 65e420f910fLAPW,Ref.28.b LAPW+p1/2,Ref.28.c V ASP -PAW,Ref.28.dV ASP -PAW,Ref.21.eExperiment,Ref.78.f Experiment,Ref.79.ELECTRONIC STRUCTURE AND OPTICAL PROPERTIES …PHYSICAL REVIEW B 75,155104͑2007͒is small.However,the difference increases when one moves from ZnO to ZnTe.This feature is demonstrated in Table II and Fig.4for band dispersions of ZnO-z ,ZnO-w ,ZnTe-z ,and ZnTe-w calculated by V ASP with and without including the SO coupling.As is well known ͑see,e.g.,Refs.21,26,and 27͒,without the SO coupling,the top of the VB of Zn X -w is split into a doublet and a singlet state.In the band structure,the Fermi level is located at the topmost one ͑Fig.4͒,which is the zero energy.Upon inclusion of the SO cou-pling into calculations,the doublet and singlet states are split into three twofold degenerate states called A ,B ,and C states with energies E g ͑A ͒,E g ͑B ͒,and E g ͑C ͒,respectively,80ar-ranged in order of decreasing energy,i.e.,E g ͑A ͒ϾE g ͑B ͒ϾE g ͑C ͒.The center of gravity of the A ,B ,and C states,located at ͓E g ͑A ͒−E g ͑C ͔͒/3below the topmost A state,re-mains to be nearly the same as the topmost VB,correspond-ing to the case without the SO coupling.26,27Consequently,to compare band structures calculated with and without the SO coupling,one should plot the band structure with the Fermi energy at the center of gravity of the A ,B ,and C states for the former and at the topmost VB for the latter.Hence,when the SO coupling is applied,the A and B states as well as the bottommost CB move upwards to ͓E g ͑A ͒−E g ͑C ͔͒/3in en-ergy,whereas the C state moves downwards to ͓E g ͑A ͒−E g ͑C ͔͒2/3compared to the center of gravity.Then,posi-tions of the lowest VB region calculated with and without the SO coupling remain nearly identical.B.General features of optical spectra of Zn XSince optical properties of solids are based on the band structure,the nature of the basic peaks in the optical spectracan be interpreted in terms of the interband transitions re-sponsible for the peaks.Such an interpretation is available for semiconductors with z -and w -type structures.11,14,81In order to simplify the presentation of the findings of this work,the labels E 0,E 1,and E 2of Ref.11͑from the reflec-tivity spectra ͒were retained in Table III and Fig.4.The subscript 0is ascribed to transitions occurring at ⌫,the sub-script 1to transitions at points in the ͓111͔direction,and the subscript 2to transitions at points in the ͓100͔direction ͑re-ferring to the k space for the z -type structure ͒.Assignment of the E 0,E 1,and E 2peaks to optical transitions at high-symmetry points is presented in Table III and Fig.4.The optical spectra ⑀1͑␻͒,⑀2͑␻͒,␣͑␻͒,R ͑␻͒,n ͑␻͒,and k ͑␻͒calculated by DFT within LDA,GGA,and LDA+U are displayed in Figs.5–8and compared with available experi-mental findings.14The spectral profiles are indeed very simi-lar to each other.Therefore,we shall only give a brief ac-count mainly focusing on the location of the interband optical transitions.The peak structures in Figs.5–8can be explained from the band structure discussed above.All peaks observed by experiments ͑see,e.g.,Refs.11and 14͒are reproduced by the theoretical calculations.Because of the underestimation of the optical band gaps in the DFT calculations,the locations of all the peaks in the spectral profiles are consistently shifted toward lower energies as compared with the experimentally determined spectra.Rigid shift ͑by the scissor operator ͒of the optical spectra has been applied,which somewhat removed the discrepancy between the theoretical and experimental results.In general,the cal-culated optical spectra qualitatively agree with the experi-mental data.In our theoretical calculations,the intensity of the major peaks are underestimated,while the intensity of some of the shoulders is overestimated.This result is in good agreement with previous theoretical findings ͑see,e.g.,Ref.19͒.The discrepancies are probably originating from the ne-glect of the Coulomb interaction between free electrons and holes ͑excitons ͒,overestimation of the optical matrix ele-ments,and local-field and finite-lifetime effects.Further-more,for calculations of the imaginary part of the dielectric-response function,only the optical transitions from occupied to unoccupied states with fixed k vector are considered.Moreover,the experimental resolution smears out many fine features,and,as demonstrated in Fig.1,there is inconsis-tency between the experimental data measured by the same method and at the same temperature.However,as noted in the Introduction,accounting for the excitons and Coulomb correlation effects in ab initio calculations 20by the LAPW +LO within LDA+U allowed correcting not only theenergyFIG. 4.Band dispersion for ZnO-z ,ZnO-w ,ZnTe-z ,and ZnTe-w calculated by the V ASP -PAW method within LDA account-ing for SO coupling ͑solid lines ͒and without SO coupling ͑open circles ͒.Topmost VB of the band structure without SO coupling and center of gravity of that with SO coupling are set at zero energy.Symmetry labels for some of the high-symmetry points are shown for ͑c ͒ZnTe-z and ͑d ͒ZnTe-w to be used for interpretation of the origin of some of the peaks in the optical spectra of Zn X -w and Zn X -z .TABLE III.Relation of the basic E 0,E 1,and E 2peaks in the optical spectra of Zn X to high-symmetry points ͑see Refs.11and 14͒in the Brillouin zone at which the transitions seem to occur.Peak z type w type,E ʈc w type,E Ќc E 0⌫8→⌫6⌫1→⌫1⌫6→⌫1E 1L 4,5→L 6A 5,6→A 1,3M 4→M 1E 2X 7→X 6KARAZHANOV et al.PHYSICAL REVIEW B 75,155104͑2007͒。

1.文章名：Local Grid Refinement for Low-Frequency Current Computation in 3-D HumanAnatomy Models作者：Andreas Barchanski文章出处：IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 4, APRIL 2006文章主要观点：●文章主要介绍人体模型方面，它是按照解剖学方式建立模型的。

低频人体解剖学模型.pdf2.文章名：Simulation of Slowly Varying Electromagnetic Fields in the Human Body Consideringthe Anisotropy of Muscle Tissues作者：Victor C. Motrescu（Germany）文章出处：IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 4, APRIL 2006文章主要观点：●文章主要仿真了高压输电线下方的，在50HZ电压下人的电流分布。

●人体模型是采用的1文章中的模型，肌肉等器官的电磁参数是各向异性参数。

●为了能较好的得到仿真，仿真分为两个步骤：a.输电线下方没有人体模型。

b.取第一步的仿真数据作为人体模型的边界条件进行仿真，得到人体内部电磁场分布。

注意边界条件的施加方法与种类。

●人体各器官在各频率的介电常数与导电率是在文章：[D. Andreuccetti, R. Fossi, and C.Petrucci, An internet resource for the calculation of the dielectric properties of body tissues in the frequency range 10 Hz–100 GHz. Florence, Italy: Inst. Appl. Phys., 1997.]输电线下方人体效应.pdf3. 文章名： Modeling of Induced Current Into the Human Body by Low-Frequency MagneticField From Experimental Data作者：Riccardo Scorretti文章出处：IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 5, MAY 2005文章主要观点：● 该文章主要提出了3步骤来解决50Hz 磁场对人体的影响。

第５０卷第２期２０２１年２月人　工　晶　体　学　报ＪＯＵＲＮＡＬＯＦＳＹＮＴＨＥＴＩＣＣＲＹＳＴＡＬＳＶｏｌ．５０　Ｎｏ．２Ｆｅｂｒｕａｒｙ，２０２１Ｐ和Ａｓ掺杂Ｍｎ４Ｓｉ７第一性原理计算钟　义，张晋敏，王　立，贺　腾，肖清泉，谢　泉（贵州大学大数据与信息工程学院，新型光电子材料与技术研究所，贵阳　５５００２５）摘要：采用第一性原理计算方法，对本征Ｍｎ４Ｓｉ７以及Ｐ和Ａｓ掺杂的Ｍｎ４Ｓｉ７的电子结构和光学性质进行计算解析。

计算结果表明本征Ｍｎ４Ｓｉ７是带隙值为０．８１０ｅＶ的间接带隙半导体材料，Ｐ掺杂Ｍｎ４Ｓｉ７的带隙值增大为０．８３９ｅＶ，Ａｓ掺杂Ｍｎ４Ｓｉ７的带隙值减小为０．７５２ｅＶ。

掺杂使得Ｍｎ４Ｓｉ７的能带结构和态密度向低能方向移动，同时使得介电函数的实数部分在低能区明显增大，虚数部分几乎全部区域增加且８ｅＶ以后趋向于零。

此外掺杂还增加了高能区的消光系数、吸收系数、反射系数以及光电导率，明显改善了Ｍｎ４Ｓｉ７的光学性质。

关键词：第一性原理；Ｍｎ４Ｓｉ７；掺杂；能带结构；态密度；光学性质中图分类号：Ｏ４６９ 文献标志码：Ａ 文章编号：１０００ ９８５Ｘ（２０２１）０２ ０２７３ ０５Ｆｉｒｓｔ ＰｒｉｎｃｉｐｌｅｓＣａｌｃｕｌａｔｉｏｎｓｏｆＰａｎｄＡｓＤｏｐｅｄＭｎ４Ｓｉ７ＺＨＯＮＧＹｉ，ＺＨＡＮＧＪｉｎｍｉｎ，ＷＡＮＧＬｉ，ＨＥＴｅｎｇ，ＸＩＡＯＱｉｎｇｑｕａｎ，ＸＩＥＱｕａｎ（ＩｎｓｔｉｔｕｔｅｏｆＮｅｗＯｐｔｏｅｌｅｃｔｒｏｎｉｃＭａｔｅｒｉａｌｓａｎｄＴｅｃｈｎｏｌｏｇｙ，ＣｏｌｌｅｇｅｏｆＢｉｇＤａｔａａｎｄＩｎｆｏｒｍａｔｉｏｎＥｎｇｉｎｅｅｒｉｎｇ，ＧｕｉｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｇｕｉｙａｎｇ５５００２５，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ＴｈｅｅｌｅｃｔｒｏｎｉｃｓｔｒｕｃｔｕｒｅａｎｄｏｐｔｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆｉｎｔｒｉｎｓｉｃａｎｄＰ，ＡｓｄｏｐｅｄＭｎ４Ｓｉ７ｗｅｒｅｃａｌｃｕｌａｔｅｄｗｉｔｈｔｈｅｆｉｓｒｔ ｐｒｉｎｃｉｐｌｅｓｃａｌｃｕｌａｔｉｏｎｍｅｔｈｏｄ．ＴｈｅｒｅｓｕｌｔｓｈｏｗｓｔｈａｔｔｈｅｉｎｔｒｉｎｓｉｃＭｎ４Ｓｉ７ｉｓａｎｉｎｄｉｒｅｃｔｓｅｍｉｃｏｎｄｕｃｔｏｒｍａｔｅｒｉａｌｗｉｔｈａｇａｐｏｆ０．８１０ｅＶ，ｔｈｅＰｄｏｐｅｄＭｎ４Ｓｉ７ｂａｎｄｇａｐｉｎｃｒｅａｓｅｓｔｏ０．８３９ｅＶ，ａｎｄｔｈｅＡｓｄｏｐｅｄＭｎ４Ｓｉ７ｂａｎｄｇａｐｄｅｃｒｅａｓｅｓｔｏ０．７５２ｅＶ．Ｄｏｐｉｎｇｃａｕｓｅｓａｓｈｉｆｔｔｏｔｈｅｌｏｗｅｎｅｒｇｙｒｅｇｉｏｎ，ａｎｄｃａｕｓｅｓａｎｉｎｃｒｅａｓｅｏｆｔｈｅｒｅａｌｐａｒｔｏｆｄｉｅｌｅｃｔｒｉｃｆｕｎｃｔｉｏｎｎｏｔａｂｌｙｉｎｔｈｅｌｏｗｅｎｅｒｇｙｒｅｇｉｏｎａｎｄａｎｉｎｃｒｅａｓｅｏｆｔｈｅｉｍａｇｉｎａｒｙｐａｒｔｉｎａｌｍｏｓｔａｌｌｒｅｇｉｏｎ，ｉｍａｇｉｎａｒｙｐａｒｔｄｅｃｒｅａｓｅｓｔｏｚｅｒｏａｆｔｅｒ８ｅＶ．Ｂｅｓｉｄｅｓ，ｄｏｐｉｎｇｏｂｖｉｏｕｓｌｙｉｎｃｒｅａｓｅｓｔｈｅｅｘｔｉｎｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔ，ａｂｓｏｒｐｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｒｅｆｌｅｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔａｎｄｐｈｏｔｏｃｏｎｄｕｃｔｉｖｉｔｙｉｎｔｈｅｈｉｇｈｅｎｅｒｇｙｒｅｇｉｏｎ，ａｎｄｉｍｐｒｏｖｅｓｔｈｅｏｐｔｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆｔｈｅＭｎ４Ｓｉ７．Ｋｅｙｗｏｒｄｓ：ｆｉｒｓｔ ｐｒｉｎｃｉｐｌｅ；Ｍｎ４Ｓｉ７；ｄｏｐｉｎｇ；ｂａｎｄｓｔｒｕｃｔｕｒｅ；ｄｅｎｓｉｔｙｏｆｓｔａｔｅ；ｏｐｔｉｃａｌｐｒｏｐｅｒｔｙ 收稿日期：２０２０ １１ ２６ 基金项目：国家自然科学基金（６１２６４００４）；贵州省科学技术基金（黔科合基础［２０１８］１０２８）；贵州大学研究生重点课程（贵大研［２０１５］０２６）；贵州省高层次创新型人才培养项目（黔科合人才［２０１５］４０１５）；贵州省留学回国人员科技活动择优资助项目（黔人项目资助合同［２０１８］０９） 作者简介：钟　义（１９９４—），男，湖南省人，硕士研究生。

Definition of optical constantsCASTEP can calculate the optical properties of solids that are due to electronic transitions.In general, the difference in the propagation of an electromagnetic wave through vacuum and some other material can be described by a complex refractive index, N:Eq. CASTEP 48In vacuum N is real, and equal to unity. For transparent materials it is purely real, the imaginary part being related to the absorption coefficient by:Eq. CASTEP 49The absorption coefficient indicates the fraction of energy lost by the wave when it passes through the material, so that the intensity at the distance x from the surface is I(x)=I(0)exp(-2πηx), where I(0) is the intensity of the incident light.The reflection coefficient can be obtained for the simple case of normal incidence onto a plane surface by matching both the electric and magnetic fields at the surface:Eq. CASTEP 50However, when performing calculations of optical properties it is common to evaluate the complex dielectric constant and then express other properties in terms of it. The complex dielectric constant, ε(ω), is given by:Eq. CASTEP 51and hence the relation between the real and imaginary parts of the refractive index and dielectric constant is:Eq. CASTEP 52Another frequently used quantity for expressing optical properties is the optical conductivity, σ(ω):Eq. CASTEP 53Optical conductivity is usually used to characterize metals, however CASTEP is aimed more toward the optical properties of insulators and semiconductors. The main difference between the two is that intraband transitions play important role in the IR part of the optical spectra of metals and these transitions are not considered at all in CASTEP.A further property that can be calculated from the complex dielectric constant is the energy loss function. It describes the energy lost by an electron passing through a homogeneous dielectric material and is given by:Eq. CASTEP 54Connection to experimental observablesExperimentally, the most accessible optical parameters are the absorption, η(ω), and the reflection, R(ω), coefficients. In principle, given the knowledge of both of these, the real and imaginary parts of N can be determined, through Eq. CASTEP 49and Eq. CASTEP 50. Eq. CASTEP 51 allows expression in terms of thecomplex dielectric constant. However, in practice, the experiments are more complicated than the case of normal incidence considered above. Polarization effects must be accounted for and the geometry can become quite complex (for example, transmission through multilayered films or incidence at a general angle). CASTEP supports spin-polarized calculations of optical properties for magnetic systems. Only transitions between the states with the same spin are allowed. For a more general discussion of the analysis of optical data see Palik (1985). Connection to electronic structureThe interaction of a photon with the electrons in the system is described in terms of time dependent perturbations of the ground state electronic states. Transitions between occupied and unoccupied states are caused by the electric field of the photon (the magnetic field effect is weaker by a factor of v/c). When these excitations are collective they are known as plasmons (which are most easily observed by the passing of a fast electron through the system rather than a photon, in a technique known as Electron Energy Loss Spectroscopy, described by Eq. CASTEP 54 , since transverse photons do not excite longitudinal plasmons). When the transitions are independent they are known as single particleexcitations. The spectra resulting from these excitations can be thought of as a joint density of states between the valence and conduction bands, weighted by appropriate matrix elements (introducing selection rules).Evaluation of the dielectric constantCASTEP calculates the imaginary part of the dielectric constant, which is given by:Eq. CASTEP 55where u is the vector defining the polarization of the incident electric field.This expression is similar to Fermi's Golden rule for time dependent perturbations, and ε2(ω) can be thought of as detailing the real transitions between occupied and unoccupied electronic states. Since the dielectric constant describes a causal response, the real and imaginary parts are linked by a Kramers-Kronig transform. This transform is used to obtain the real part of the dielectric function, ε1(ω).Details of the calculationEvaluation of matrix elementsThe matrix elements of the position operator that are required to describe the electronic transitions in Eq. CASTEP 55may normally be written as matrix elements of the momentum operator allowing straightforward calculation in reciprocal space. However, this depends on the use of local potentials (Read and Needs, 1991), while in CASTEP nonlocal potentials are more often used. The corrected form of the matrix elements is:Eq. CASTEP 56Ultrasoft pseudopotentials produce an additional contribution to optical matrix elements that is also included in CASTEP results. Drude correctionThe intraband contribution to the optical properties affects mainly the low energy infrared part of the spectra. It can be described sufficiently accurately via an semiempirical Drude term in the optical conductivity:Eq. CASTEP 57in terms of the plasma frequency ωP and damping parameter γD which depends on many details of the material and is usually obtained from experiment. The Drude damping parameter describes the broadening of the spectra due to effects not included in the calculation. Examples of processes that contribute to this broadening are electron-electron scattering (including Auger processes), electron-phonon scattering, and electron-defect scattering. This last contribution is usually the most important. As a result an a priori determination of the broadening would require knowledge as to the concentrations and kinds of defects present in the sample under study.PolarizationFor materials that do not display full cubic symmetry, the optical properties will display some anisotropy. This can be included in the calculations by taking the polarization of the electromagnetic field into account. As mentioned above, the unit vector u defines the polarization direction of the electric field. When evaluating the dielectric constant there are three options: polarized: requires a vector to define the direction of the electric field vector for the light at normal incidence to the crystal.∙unpolarized: requires a vector to define the direction of propagation of incident light at normal incidence to the crystal. The electric field vector is taken as an average over the plane perpendicular to this direction.∙polycrystal: no direction need be specified, the electric field vectors are taken as a fully isotropic average. Scissors operatorAs discussed below, the relative position of the conduction to valence bands is erroneous when the Kohn-Sham eigenvalues are used. In an attempt to fix this problem, inherent in DFT, we allow a rigid shift of the conduction band with respect to the valence band. This procedure of artificially increasing the band gap is know as a scissor operator.Limitations of the methodLocal field effectsThe level of approximation used here does not take any local field effects into account. These arise from the fact that the electric field experienced at a particular site in the system is screened by the polarizability of the system itself. So, the local field is different from the applied external field (that is, the photon electric field). This can have a significant effect on the spectracalculated (see the example of bulk silicon calculation below) but it is prohibitively expensive to calculate for general systems at present.Quasiparticles and the DFT bandgapIn order to calculate any spectral properties it is necessary to identify the Kohn-Sham eigenvalues with quasiparticle energies. Although there is no formal connection between the two, the similarities between the Schrödinger-like equation for the quasiparticles and the Kohn-Sham equations allow the two to be identified. For semiconductors, it has been shown computationally (by comparing GW and DFT band structures) that most of the difference between Kohn-Sham eigenvalues and the true excitation energies can be accounted for by a rigid shift of the conduction band upward with respect to the valence band (Godby et al., 1992). This is attributed to a discontinuity in the exchange-correlation potential as the system goes from (N)-electrons to (N+1)-electrons during the excitation process. There can, in some systems, be considerable dispersion of this shift across the Brillouin zone, and the scissor operator used here will be insufficient.Excitonic effectsIn connection with the absence of local field effects, excitonic effects are not treated in the present formalism. This will be of particular importance for ionic crystals (for example NaCl) where such effects are well known.Other limitations∙The nonlocal nature of the GGA exchange-correlation functionals is not taken into account when evaluating the matrix elements but it is expected that this will have a small effect on the calculated spectra.∙Phonons and their optical effects have been neglected.∙Finally, there is an intrinsic error in the matrix elements for optical transition due to the fact that pseudowavefunctions have been used (that is they deviate from the true wavefunctions in the core region). However, the selection rules will not be changed when going from pseudo- to all-electron wavefunctions.Sensitivity of optical properties to calculation parametersNumber of conduction bandsThis parameter defines the energy range covered in the calculation, and it also determines the accuracy of the Kramers-Kronigtransform. It is clear from Figure 1that ε2(ω) converges rapidly with the number of conduction bands included.Figure 1. Convergence of the dielectric function with the number of conduction bandsEnergy cutoffThe value of the energy cutoff that was used in the original SCF calculation of the ground state electron density is an important factor that determines the accuracy of the calculated optical properties. A bigger basis set provides more accurate self-consistent charge density and more variational freedom when searching for wavefunctions of unoccupied states. Figure 2showsthat while it is important to converge the calculation with respect to the planewave cutoff to obtain the correct energies for the spectral features, the shape of those features is reached rapidly.Figure 2. Convergence of the dielectric function with the cutoff energyNumber of k-points in the SCF calculationThe accuracy of the ground state electron density depends on the number of k-points used in the SCF run as well as on the basis set quality. Figure 3reveals that the optical properties converge rapidly with the number of k-points used in the SCF run, whichimplies low sensitivity to the details of the charge density. Figure 3. Convergence of the dielectric function with the number of k-points in the SCF calculationNumber of k-points for Brillouin zone integrationIt is important to use a sufficient number of k-points in the Brillouin zone when running optical matrix element calculations. The matrix element changes more rapidly within the Brillouin zone than electronic energies themselves. Therefore, one requires more k-points to integrate this property accurately than are needed for an ordinary SCF calculation. Figure 4 clearly demonstrates the importance of converging the Brillouin zone integration forthe optical properties with respect to the k-point density. Both energies and spectral features are strongly affected by the accuracy of this integration.Figure 4. Convergence of the dielectric function with the number of k-points in the optical matrix elements calculationSee Also:Theory in CASTEP。

Vol.42 2021年2月No.2 397~411［综合评述］CHEMICAL JOURNAL OF CHINESE UNIVERSITIES高等学校化学学报MXenes材料的光学特性及相关研究进展黄大朋，于浩海，张怀金（山东大学晶体材料国家重点实验室,晶体材料研究所,济南250100）摘要过渡金属碳化物、氮化物或碳氮化物(MXenes)具有丰富的元素组成和结构可调性,显示出丰富的物理化学性质和巨大的应用潜力.本文以此类材料的基本光学特性为基础,从光子发射、透明导电及储能、非线性光学、表面等离激元及拉曼增强、光热转化、光催化及光响应等光学相关领域展开分析和综述.并对此二维材料相关应用的未来发展及机遇作了简单评述,以期为进一步的研究提供参考.关键词MXenes；金属态；线性光学；非线性光学中图分类号O613；O734文献标志码A过渡金属碳化物、氮化物或碳氮化物（MXenes）材料是近几年新兴的二维（2D）材料，其丰富的元素组成和结构可调性赋予了其丰富的物理化学性质，并逐渐在2D材料家族中脱颖而出.MXenes材料的化学式为M n+1X n T x，其中M表示早期过渡金属Sc，Y，Ti，Zr，Hf，V，Nb，Ta，Cr，Mo或W，X表示碳和/或氮，通常n=1~3，T表示表面终端（主要是—OH，=O和—F），其下角x表示表面官能团的数量. 2D片层的厚度在1nm范围内，可以通过改变MXenes中的n从M2XT x到M3X2T x和M4X3T x来调控.通常MXenes是通过选择性腐蚀MAX相陶瓷的A元素而获得的，其中A是一组IIIA到VIA族元素.因此MXenes与MAX一样具有六方对称性，属于P63/mmc空间群.其中过渡金属（M）原子排列成一个近密排结构，X元素原子位于其八面体间隙位置.图1（A）~（C）描绘了211，312和413计量比的MAX相六方单胞.单胞由M6X八面体组成，如Ti6C，其与A元素层（例如Al、Si或Ge）交错分布.211，312和413MAX 相之间的区别在于分隔A层的M原子层数量不同.MAX相中M6X棱边共享的八面体基本构架与二元碳化物和氮化物MX是相同的.在312和413计量比的MAX结构中，一般有2个不同的M位点，分别是与A相邻的M（1）和不相邻的M（2）.在413结构中，还存在2个非等效的X位，X（1）和X（2）.在所有情况下，MX层彼此成对，并由充当镜像平面的A层分开，如图1（D）所示.MAX结构是各向异性的，晶格参数通常为a≈0.3nm和c≈1.3nm（211相），c≈1.8nm（312相）和c≈2.3~2.4nm（413相）［1~4］.由于其独特的晶体结构以及外层过渡金属d轨道电子的贡献，多数MXenes通常表现为金属态或窄带隙半导体属性，并且外层过渡金属对于材料的能带结构和电子特性具有决定性作用，因此2D MXenes家族丰富的结构可调性及元素组合赋予了此类材料诸多新奇特性，如半金属态、拓扑绝缘态、半导体态以及铁磁性和反铁磁性［5~7］.由于材料的光学响应与其结构和电子特性直接相关，比如带内及带间电子跃迁直接决定了材料的光学吸收及光子辐射行为，因此具有丰富可调性的MXenes材料在光学领域同样展现出极大潜力并吸引研究者在此领域展开研究和应用开发.目前，相关综述主要集中在MXenes材料制备及电化学等相关领域，而在光学及光电子器件相关领doi：10.7503/cjcu20200584收稿日期：2020-08-21.网络出版日期：2020-12-25.基金项目：国家自然科学基金(批准号:51890863,51632004)和山东省泰山学者基金资助.联系人简介：于浩海,男,博士,教授,主要从事光电功能晶体、激光技术与器件以及晶体物理方面的研究.E⁃mail:****************.cn张怀金,男,博士,教授,主要从事人工晶体生长和性能研究.E-mail:********************.cnVol.42高等学校化学学报域仍缺乏综合性概述与分析，因此本文重点考察此类二维晶体的光学特性及其相关应用，从基本光学特性出发，对其新近发现的新奇光学特性及应用展开分析和综述，主要涉及光子发射、透明导电及储能、非线性光学、表面等离激元及拉曼增强、光热转化、光催化及光响应等光学相关领域.1MXenes 材料的基本光学特征MXenes 的线性光学性质（如吸收、光致发光等）和非线性光学性质（如饱和吸收、非线性折射率等）高度依赖于其能带结构（如能带隙、直接/间接带隙、拓扑绝缘特性等），更具体地说，是依赖于线性和非线性介电函数（ε）的色散或折射率（n=εμ）的色散.Lashgari 等［8］利用全势线性缀加平面波方法（FLAPW ）和随机相位近似（RPA ）方法计算了二维Ti n +1X n MXene 化合物（Ti 2C ，Ti 2N ，Ti 3C 2和Ti 3N 2）的光学响应［复介电函数（ε）、反射、吸收和电子能量损失函数］，介电函数的虚部Im ε计算如下：Im ε[interband ]ij (ω)=h 2e 2πm 2ω2∑n∫d k ψC n k p i ψV n k ψV n k p j ψC n k δ(E C n k -E V n k -ω)(1)式中：h ，e ，m 分别为普朗克常数、电子电荷和电子有效质量；ψV n k 对应于占据的价带能级；ψC nk 代表第一布里渊区k 点上的空导带能级；E C n k 和E V nk 分别代表未占据的导带和占据的价带能态；ω是相互作用电磁波的频率.通过反向变换，可以得到相应的实部为：Re ε[interband ]ij(ω)=δij +2πP ∫0∞ω′Im εij (ω)(ω′)2-ω2(2)式中：P 为主值积分.带内跃迁的贡献分别为：Im ε[intraband ]ij (ω)=Γω2pl ,ij ω(ω2+Γ2)(3)Re ε[intraband ]ij (ω)=1-ω2pl ,ij ω(ω2+Γ2)(4)式中：ω2p =ne 2ε0m ，ω2p 表示等离子体频率；n 表示自由载流子或电子浓度；m 表示有效电子质量；Γ表示Drude 模型中的阻尼/损耗项.因此，带间和带内电子跃迁贡献的完整介电函数可以写成：ε(ω)=ε[intraband ](ω)+ε[interband ](ω)(5)单层Ti n +1X n （X=C ，N ，n =1，2）具有六方空间群对称性，其中包括三原子层Ti 2X 和五原子层Ti 3X 2.由于这种对称性，在与晶体c 轴平行（E ||x ）和垂直（E ||z ）的电场激励下，复介电函数张量只有3个非零分Fig.1Crystal structures of the 211(A),312(B),and 413(C)MAX phases and high⁃angle annular dark field TEM image,acquired along the [11-20]zone axis of Ti 3SiC 2,showing the twinned structureand the resulting characteristic “zig⁃zag ”stacking of MAX phases(D)[4]Copyright 2010,Elsevier.398No.2黄大朋等：MXenes 材料的光学特性及相关研究进展量：εxx （ω）=εyy （ω）和εzz （ω）.图2（A ）描绘了相应的介电张量.介电函数虚部Im ε的峰归属于不同带内和带间电子跃迁的直接贡献.介电函数实部Re ε可以通过Kramers -Kronig 关系获得，如图2（A ）中插图所示.利用频率依赖的复介电函数，可以计算出反射和吸收等重要的光学参数.吸光度（A ）与填充的价带到空导带能级的带间跃迁的总贡献成正比［图2（B ）］.由于特殊的合成过程，单层MXenes 的最外层过渡金属原子通常被官能团（如—F 、—O 和—OH ）钝化.最近的研究表明，表面功能化可以在很大程度上影响MXenes 的能带结构和电子特性［9~11］.MXenes 材料的独特属性（电子输运、电容等）可以通过调节表面官能团来调整.Berdiyorov ［12］通过计算模拟讨论了功能化对Ti 3C 2T 2-MXene 光学性质的影响.材料系统中频率依赖的复介电常数可以由材料的电极化率导出，即ε（ω）=ε1+ε2=1+χ（ω）（ε1与ε2分别为介电常数的实部和虚部）.如图3（A ）和（B ）所示，计算所得介电函数随官能团和光谱范围的变化而显著变化.利用介电函数还可以得出Ti 3C 2T 2的频率相关折射率n 和消光系数k ［图3（C ）和（D ）］以及吸收光谱［图3（E ）和（F ）］.在吸收光谱中可以观察到官能团之间的显著差异，特别是在低光子能量区，显示出表面官能团对于最终性质的重要影响.目前对于MXenes 材料介电函数的结论多停留在理论层面，因此下一步应该注重在实验上实现介电函数的表征和调控，尤其是单层或少层MXenes 样品，这样可以更好地指导实验设计和应用开发.Fig.2Calculated imaginary part of the dielectric function(A)(inset shows the real part)and absorptioncoefficient for Ti 3C 2⁃MXene(B)[8]The two nonzero components of the dielectric tensor εxx (ω)and εzz (ω)for electric field perpendicular(E ||x )and parallel(E ||z )to c ⁃axis are represented by the solid red and dashed blue line.Copyright 2014,Elsevier.Fig.3Real(ε1)(A)and imaginary(ε2)(B)part of dielectric function as a function of photon energyfor Ti 3C 2T 2⁃MXene;refractive index,n (C),and the extinction coefficient,k (D),as a functionof photon energy for Ti 3C 2T 2MXene and absorption spectra of Ti 3C 2T 2⁃MXene for small(E)and larger(F)range of photon energy [12]Ti 3C 2:solid⁃black curves;Ti 3C 2F 2:dashed⁃red curves;Ti 3C 2O 2:dotted⁃green curves;Ti 3C 2(OH)2:dash⁃dotted⁃bluecurves.Shaded area shows the visible range of the spectrum.Copyright 2016,American Institute of Physics.399Vol.42高等学校化学学报2MXenes 材料在光学相关领域中的研究进展2.1MXenes 材料的光发射性能及应用MXenes 材料通常具有金属态属性，以Ti 3C 2-MXene 为例，其导带与价带在布里渊区沿Γ-M 和M⁃K 方向合并，因此此能带结构使其成为原子级金属材料.使用常规湿化学刻蚀法制备的Ti 3C 2-MXene 中通常还带有表面终端，比如—F ，—O ，—OH 等.这些表面基团对其能带结构可能产生轻微的修饰作用，使其带隙打开至约0.1eV ，但仍保持较高的电导率［13］.其独特的能带结构和通常情况下的间接带隙（0~0.1eV ）特征，使其在可见光或紫外光激发下产生的带边电子-空穴对并未产生可见或红外的光子发射或者光子发射率极低［14］.这种激子相关的光致发光（PL ）在过渡金属双硫属化合物（TMDs ）中是非常典型的，但在MXenes 材料原始状态下并未实现.2019年，Zhang 等［15］通过调控Ti 3C 2-MXene 表面TiO 2的参与，在大片层Ti 3C 2-MXene 中观察到了光致发光现象并表征了其激发波长依赖特性.并且在一定的表面TiO 2修饰量下获得了可调的光发射红移现象［图4（A ）和（B ）］.另一种使MXenes 材料获得光发射能力的方法是利用量子限域效应使材料的能带隙打开和能带结构发生改变.当MXenes 材料尺寸减小到几纳米并以量子点的形态存在时［16］，其能带结构向直接带隙的转变以及带隙的打开能够允许电子辐射跃迁，在可见光和紫外光激发下可以表现出明显的、可调节的可见光发射［图4（C ）和（D ）］.MXenes 这一光学特征与其金属态能带结构形成鲜明对比，因此对MXenes 材料光发射性能的研究主要是集中在MXenes 量子点（MQDs ）状态下的光学行为.通常，MQDs 在约260，310和350nm 处可观察到3个吸收峰，这取决于其粒径和组成.光致发光谱带高度依赖于激发波长，随着激发波长从340nm 到440nm 的变化，PL 光谱相应地从400nm 到600nm 发生变化.Xue 等［16］在水热过程中通过改变温度制备了平均尺寸分别为2.9，3.7和6.2nm 的Ti 3C 2-MQDs.在320nm 波长的光激发下，最大量子产率可达9.9%.同时他们还发现，光致发光强度与溶液pH 值无关，这可能是由于—NH 基团对MQDs 高度的表面钝化所致.Niu 等［17］发现溶剂对裁剪所得Ti 3C 2-MQDs 的量子产率和荧光寿命有很大影响.在二甲基甲酰胺（DMF ）溶剂环境中所得MQDs 的量子产率最高可达10.7%.在二甲基亚砜（DMSO ）溶剂环境中所得MQDs 的荧光寿命在3种溶剂（DMF 、DMSO 和乙醇）中是最长的，为4.7ns ［图5（A ）］.鉴于DMSO溶剂Fig.4Schematic of TiO 2clusters interspersed throughout the Ti 3C 2⁃MXene flake,and the diagrams of PLtransitions at perfect Ti 3C 2⁃MXene and defective TiO 2(A),PL spectra of Ti 3C 2⁃MXene without(left)and with modification(right)at the excitation wavelengths of 405nm,532nm and 632.8nm(B)[15],schematic diagram of preparation of MXenes quantum dots(MQDs)(C)and UV⁃Vis spectra(solidline),PLE(dashed line),and PL spectra(solid line,λex =320nm)of MQD in aqueous solutions(D)[16](A,B)Copyright 2019,Elsevier.(C,D)Copyright 2017,John Wiley and sons.400No.2黄大朋等：MXenes 材料的光学特性及相关研究进展较大极性和较强氧化性的特点，此处相对较长的荧光寿命是由MQDs 较多的氧化位点和小的尺寸所致.此外，他们还发现Fe 3+在DMF 中会对MQDs 产生独特的荧光猝灭效应［图5（B ）］，而在其它两个溶剂中并不明显.在氨水溶液中通过类似的水热过程，Huang 等［18］发现制备的V 2C -MQDs 具有显著钝化的表面，其PL 量子产率高达15.9%，远高于非钝化量子点.在所获宽带发射谱基础上，借助纳秒脉冲强激发下触发的非线性散射机制，实现了红、绿、黄、蓝4色同时发射的白色激光［图5（C ）和（D ）］.Lu 等［19］通过溶剂热方法，使用油酸作为表面修饰剂制得了Ti 3C 2-MQDs ，其在紫外光激发下可以表现出白光效果，使用近红外飞秒激光激发还可以产生双光子白光发射，并且MQDs 的荧光可以在外部施加压力调节下实现冷白到暖白光的转变［图5（E ）］.另外，Ti 3C 2-MXene 与乙二胺在高压釜中于160℃反应12h 可以制备出氮掺杂的Ti 3C 2-MQDs ［20］［图5（F ）］，其光致发光量子产率可达18.7%，荧光寿命为7.06ns.所制的氮掺杂的Ti 3C 2-MQDs 在Na +，Mg 2+，Cu 2+，K +，Mn 2+，Zn 2+，Ca 2+，Al 3+，Ce 3+，Cu +和Ni 2+离子中表现出对Fe 3+的选择性荧光猝灭特性，因此可作为超灵敏Fe 3+探针，检出限可达100µmol/L.Chen 等［21］发现Ti 3C 2-MQDs 的发光强度对表面缺陷的去质子化非常敏感，增加MQDs 溶液的pH 值可显著降低MQDs 的zeta 电位、460nm 处的吸光度以及PL 发射强度和寿命.通过使用pH 不敏感的［Ru （dpp ）3］Cl 2作为发射参比，Ti 3C 2-MQDs 可以用作比率pH 传感器来定量监测细胞内pH 值.Wang 等［22］在其所制样品中发现Ti 3C 2-MQDs 的光致发光在pH 值升高至6以上后波长和强度均无明显变化，而在低pH 值（2~5）时，光致发光强度则显著降低.近来，Nb 2C -MQDs 也被开发出来，并通过S 、N 掺杂获得了19%的发光效率［23］，其在被作为荧光探针用于3D 脑组织成像时获得了较好的效果.Yang 等［24］也论证了Nb 2C -MQDs 优异的光稳定性和生物兼容性，为新型传感/成像纳米荧光团的应用研究提供了一种新的方案.另外电化学发光（ECL ）正成为一种越来越强大的生物和环境诊断分析工具.在Ti 3C 2-MQDs 中也观察到了高效的ECL行为，但其机制因溶剂不同而不同［17，25］.可见，MQDs 是当前MXenes 材料在光学领域应用的关键形态，而进一步地应用开发仍需要充分认识MQDs 的发光机理，以获得更有效的发光调控和实现发光效率提升来满足不同场合下的应用需求.Fig.5Fluorescent lifetime of s⁃MQDs(a),f⁃MQDs(b),and e⁃MQDs(c)(A),PL intensity of f⁃MQDs excited at377nm upon addition of Fe 3+ions ranging from 0to 750×10−6mol/L(B)[17],emission spectra from theV 2C MQD colloid for different pump fluences(C),plot of the calculated CIE coordinates of emissionspectra under different pumping fluence(D)[18],schematic illustration of the emission,and under theconditions of high pressure(E)[19],and fluorescence emission spectra of the prepared N⁃MQDs(160℃)at different excitation wavelengths and photographs under UV light(365nm)(inset)(F)[20](A,B)Copyright 2018,John Wiley and sons;(C,D)Copyright 2019,John Wiley and sons;(E)Copyright 2019,John Wiley and sons;(F)Copyright 2018,Royal Society of Chemistry.401Vol.42高等学校化学学报2.2MXenes 材料的线性光学传输性能及透明导电和储能应用由于费米能级附近高的电子态密度，MXenes 材料展现出不同寻常的光电子传输性能，因此在光电子应用中被寄予厚望.如前所述，MXenes 材料的电子能带结构受表面终端的影响较大，电负性较大的—O 终端相比于—F 和—OH 会产生更大的带隙.通常—O 终端半导体态的MXenes 在低能量范围（<1.5eV ）会表现出相对较小的ε2（ω）值，表明—O 终端的MXenes 可能具有较低的光学吸收.另一方面，MXenes 具有间接带隙的能带结构时，当光子能量与带隙相等时，由于带间跃迁的动量失配，光子不能被吸收，因此，激发电子跃迁需要更高的光子能量.相应地，具有间接带隙的Ti 2CO 2有可能进一步在更高光频扩展传输窗口［8，26，27］.通常金属材料或类金属材料也需要考虑能量小于1eV 的带内跃迁，因此相比于—O 终端的MXenes ，无终端及—F 和—OH 终端的MXenes 的金属态特征使得它们在低光学频率范围的光吸收会进一步增强.如图6（A ）和（B ）所示，波长1300nm （约0.95eV ）以上的增强的吸收在Ti 3C 2T x 中已被观察到［28］.在可见光谱范围，相比于原始MXenes ，—O 终端的样品表现出较强的光吸收，而氟化和羟基化表面的样品则表现出较弱的光吸收.在紫外光谱范围，所有表面终端均会导致吸收和反射的增强［12］.通常，具有较小n 的M n +1X n 由于其较低的态密度被认为光透明性更好.总体来说，二维MXenes 材料具有高的导电性和光学透明性，许多研究组已报道了宽带透射率在90%以上的MXenes 薄膜［28~32］.在Ti 3C 2-MXene 中观察到的800nm 处的吸收峰归属于固有的平面外带间跃迁［8，33，34］.Ti 3C 2-MXene 在可见光区的光学透过率被证明高于还原氧化石墨烯（rGO ）［图6（C ）］，并且大的离子相互作用增加的c 轴晶格（例如NMe 4OH ）可进一步提高光学透过率［31，32］.在玻璃、石英和聚醚酰亚胺衬底上通过旋涂制备的1.2nm Ti 3C 2-MXene 薄膜在可见光波段获得了3%的超低光衰减［28］.单层石墨烯在可见光区吸收2.3%的光，考虑到Ti 3C 2-MXene 比单层石墨烯厚3倍，因此这些实验结果表明Ti 3C 2-MXene 具有更高的透光率.由于MXenes 具有高的导电性和光学透明性，因此被广泛用作透明导电电极.如图6（D ）所示，Halim 等［31］用磁控溅射法在蓝宝石衬底上直接沉积了MAX 相Ti 3AlC 2，使用HF 或NH 4HF 2水溶液从MAX Fig.6UV⁃Vis⁃NIR linear optical attenuation of spin⁃coated Ti 3C 2⁃MXene films as a function of depositionthickness(A),calculated imaginary(top)and real(bottom)dielectric dispersion based on the experi⁃mental results of (A)(B)[28],absorbance of Ti 3C 2⁃MXene features low optical attenuation at 550nmcompared to reduced graphene oxide(rGO)(C)[32],transmittance spectra and visual images(on right)for Ti 3AlC 2(I),Ti 3C 2⁃MXene(II),and Ti 3C 2⁃MXene⁃IC(III)films of 15nm nominal thickness(D)[31],schematic diagram of the complementary inverter consisting of p⁃FET[WSe 2/Ti 2C(OH)x F y ]andn⁃FET[MoS 2/Ti 2C(OH)x F y ]devices(E)[35]and Ti 3C 2⁃MXene/n⁃Si heterostructure(F)[37](A,B)Copyright 2016,John Wiley and sons.(C)Copyright 2016,John Wiley and sons.(D)Copyright 2014,American Chemical Society.(E)Copyright 2016,John Wiley and sons.(F)Copyright 2017,John Wiley and sons.402No.2黄大朋等：MXenes 材料的光学特性及相关研究进展前驱体中提取出Al 原子后，原位制备了Ti 3C 2-MXene 膜.用NH 4HF 2蚀刻制备的19nm 厚的Ti 3C 2-MXene 薄膜在可见到红外范围内可透过约90%的光，并在100K 下显示金属导电性.Hantanasirisakul 等［32］使用喷涂方法在玻璃和柔性基底上制备了厚度为5~70nm 的均匀MXene 薄膜.该薄膜具有可调的电阻（R s ）（0.5~8kΩ/sq ）和光学透过率（40%~90%），且易于制作.其确定的品质因数（FoM e =σDC /σOPT ）在0.5~0.7之间.四甲基氢氧化铵在水溶液中的电化学插层/脱层可进一步优化透光率.值得注意的是，Dillon 等［28］通过溶液处理的旋涂方法可获得高导电性（∼6500S/cm ）MXene 薄膜，同时每纳米厚度可见光透过大于97%.因此，实验上MXene 也被用作WSe 2和MoS 2场效应晶体管的电极［图6（E ）］［35］.Ti 2C -MXene 的载流子浓度通过霍尔测量确定为3.5×1014cm -2，电导为0.026S ，显示高电导性.通过Kelvin 探针力显微镜测试，Ti 2C -MXene 的功函数为4.98eV.Ti 2C -MXene 与Cr 在真空中的接触电阻估计为0.243Ω·mm ，甚至低于石墨烯-Cr 连接的报道值［36］.另外，Zhai 等［37］研究了垂直范德华异质结Ti 3C 2-MXene/n -Si （Ti 3C 2-MXene 功函数为4.37eV ）的光电特性，如图6（F ）所示，Ti 3C 2-MXene 不仅作为透明电极，而且有助于光诱导载流子的分离和输运.并且退火、温度、光照和外加电压对Ti 3C 2-MXene/n -Si 肖特基异质结性能均有影响，通过优化获得了响应速度和恢复速度都很高的自驱动垂直结光电探测器.最近，Chen 等［38］制备了一种仿生透明的Ti 3C 2-MXene 薄膜电极并将其与静电纺丝TiO 2薄膜复合获得了一种半透明式紫外光电探测器，电极和构建的探测器均表现出优异的柔性特征，可以承受1000次的弯曲循环.这项工作提供了一种构建柔性透明器件的新思路和选择.另外，Zhou 等［39］将透明导电的Ti 3C 2-MXene 与银纳米线复合，发现经过热处理后可以获得最优的光学和电学性能，薄层电阻为18.3Ω/sq ，透过率为52.3%.此复合结构在X 波段表现出较高的电磁屏蔽效率（32dB ），同时能够保持较强的界面附着力和较好的柔韧性.另外，MXenes 材料兼具优异的电化学性能［30，40，41］，因此也是透明超级电容器（SCs ）的理想候选材料.如前所述，通过旋涂纳米片溶液然后真空退火制备的Ti 3C 2-MXene 不会遇到渗透问题［29］.如图7所示，由于没有金属或金属网集电器，该装置具有高度透明性.在三电极装置中，透过率（T ）为98%的样品的CV 曲线严重偏离准矩形，而T 较低（如T =40%）的电极可以很好地保持宽的氧化还原峰对.因此，测量的面电容和速率容量可由薄膜厚度控制.例如，T =98%的样品在10mV/s 条件下面电容为0.13mF/cm 2，接近PEDOT ：PSS 薄膜［42］，但高于基于石墨烯量子点透明导电极［43］；将薄膜厚度增加到60nm （T =40%）时，10mV/s 条件下面电容为3.4mF/cm 2.结合品质因子（FoMc ）和光电导率（σop ），Ti 3C 2-MXene 薄膜的透明超级电容器电极的体容量（C V ）为676F/cm 3，明显高于其它透明超级电容器电极，如多壁碳纳米管［44］、石墨烯［45］及PEDOT ：PSS ［42］.最近，Qin 等［46］开发了一种全溶液处理的MXene 基半透明柔性光伏超级电容器，该器件将柔性有机光伏组件与透明Ti 3C 2-Mxene 超级电容器集成，其中光生伏打部分的电极也由Ti 3C 2-MXene 充当，有机离子凝胶作为垂直方向上的电解质.Ti 3C 2-MXene 充当透明电极的光生伏打组件的能量转换效率为13.6%，Ti 3C 2-MXene 超级电容器组件的体电容可达502F/cm 3.最终柔性集成的光伏超级电容器平均透过率可达33.5%，并获得高达88%的存储效率.此策略为基于Fig.7Schematic demonstration of Ti 3C 2T x MXene⁃based transparent,flexible solid⁃state supercapacitorand comparison of volumetric capacitance of Ti 3C 2T x to other transparent film systems(A)andmeasured areal capacitance of various Ti 3C 2T x films(B)[30]Copyright 2017,John Wiley and sons.403404Vol.42高等学校化学学报MXenes的高性能全溶液处理工艺柔性光伏超级电容器的制造提供了一条简单的途径，这对于实现柔性和可打印电子产品的未来技术非常重要.除Ti3C2-MXene外，其它MXenes材料［47~49］，如V2C-MXene、Ti2C-MXene等也相继被开发，并展现出一定竞争力.MXenes的光电性能以及优异的体积电容和样机性能表明，其在柔性触摸屏、显示器、有机太阳能电池、透明储能器件、可穿戴电子设备等领域均有巨大的应用前景.但是目前所制备的MXenes材料薄膜及其器件的稳定性、可重复性等仍需被优化.倘若MXenes材料的稳定性问题被有效解决，那么相比于其它先进材料（如C60、碳纳米管、石墨烯等），由于其独特的可调表面和过渡金属元素，MXenes无疑将带来更多的新机遇.2.3MXenes材料的非线性光学性能及应用非线性光学效应是指在强场激光辐照下，强的振荡电场诱导介质发生极化，该极化不但会随外加光场的频率振荡，而且会产生高次谐波振荡，甚至会有直流电场分量.为了定量地描述非线性光学效应，宏观极化在光的电场作用下可以展开成泰勒级数［50］：P=ε0χ（1）E+ε0χ（2）E2+ε0χ（3）E3+ (6)式中：ε0为自由空间的介电常数；χ（i）项是第i阶的电极化率.电场中的二次项产生二阶非线性光学效应，其强度用二阶非线性光学极化率χ（2）来描述.重要的二阶效应有线性电光效应（Pockels效应）、二次谐波产生、和频和差频产生以及光整流.这些二阶效应只在对称破缺的非中心对称结构中表现出来.用三阶非线性光学极化率项χ（3）描述的效应有四波混频过程，例如三次谐波产生、二次电光效应、强度相关的折射率（非线性光学折射）和吸收（非线性吸收）.三阶以外的更高阶非线性过程通常太弱，缺少实际应用价值.两个重要的非线性吸收过程可用χ（3）的虚部量化，具有实际意义，分别是：（1）饱和吸收，其中χ（3）带有负号项；（2）双光子吸收，它描述了在较高强度下的更高吸收，因此χ（3）带有正号项.目前对MXenes非线性光学性质的研究主要集中在三阶非线性光学效应，主要是对饱和吸收的研究.使用聚焦准直激光束可实现一个简单的高强度条件，用于表征材料中的非线性光学折射或吸收.一种非常合适的方法是Z扫描法，如图8（A）和（B）所示，MXenes样品沿光轴（Z）并穿过激光束焦点的平移使得样品在不同位置经历了不同的光强度.在开孔和闭孔条件下连续测量的透射比作为激光强度的函数，可以分别揭示样品的非线性光学吸收和折射响应信息［51~54］.研究发现，在给定波长下，Ti3C2-MXene有效非线性吸收系数随脉冲能量的变化呈下降趋势［图8（C）］，表明在低脉冲能量下，单光子可饱和吸收过程占主导地位.然而，随着脉冲能量的增加，也会发生双光子吸收过程［53］.饱和吸收可以用一个简单的二能级模型来描述，当基态和激发态电子占居数达到平衡且入射场可以从吸收介质中去耦合时，说明吸收介质不能吸收更多的光子.在实验上，它表现为随着辐照强度的增加，介质的透射率逐渐增加.Ti3CN-MXene被用作可饱和吸收体，调制深度为1.7%，分别用于1.55µm和1.88µm的超快锁模和调Q操作［55］.多用途喷墨打印的MXenes利用其高透明性和宽频带的可饱和吸收特性，与各种激光谐振器集成［图8（D）~（F）］，实现了从近红外到中红外的超快激光产生，脉冲持续时间短至100fs［56］.最近，基于MXenes的可饱和吸收材料的应用已经扩展到固态和陶瓷激光器［57~59］.除了超快激光产生［53，55，56，58，60］外，MXenes也可以与反饱和吸收特性的C60［61，62］结合以实现非交互传输的光子二极管［图8（G）］［54］.另外，通过利用其优良的光学克尔效应（也是从强度依赖的折射率中获得），Ti3C2T x纳米片基于色散的全光开关已经被证明［63］［图8（H）］.利用其优异的三阶非线性光学特性，在全光纤装置中获得了四波混频，其转换效率为-59dB，调制速度为10GHz［64］.最近，Lu等［19］使用近红外飞秒脉冲激光（800nm）也发现了Ti3C2-MXene量子点的双光子吸收行为及宽带的白光荧光发射现象.He等［65］在Nb2C-MXene中也获得了宽带的非线性光学响应，并且发现了其有趣的非线性吸收响应的反演特性，即在近红外范围内Nb2C-MXene的非线性吸收过程存在饱和吸收向双光子吸收的转变，这一特点有望在微纳光开关器件中获得进一步开发和应用.同时，Zhang等［66］也发现V2C-MXene可以表现出优异的稳定性和较强的调制深度（近50%），利用其优异的饱和吸收特性，在Er掺杂光纤激光器中成功获得第206阶。

MaterialsStudio软件在《硅材料科学与技术》教学中的应用《硅材料科学与技术》是材料学院相关专业的重要专业课，在学习半导体物理、晶体物理、固体物理等课程的基础上，学习半导体硅材料的基本性质、制备工艺、结构和性能等方面的知识。

在教学过程中，如果能形象生动地展开教学活动，直观地解释相关的物理概念、现象、过程、结构及状态等。

因此，在学习基础理论的同时，采用Materials Studio计算模拟软件对半导体硅材料进行模拟计算，培养学生的自主创新和动手动脑能力。

为后续课程的学习、技能的培养和将来的研究工作打下基础。

1 Visualizer可视化分子建模界面结合《硅材料科学与技术》教学环节的设计1.1 简介Materials studio材料计算模拟软件是美国Accelrys 公司为材料科学领域开发的一款科学计算模拟软件，用于帮助科研工作者解决当今材料科学中的一些重要问题。

因此《硅材料科学与技术》中的物理及化学性质，所涵盖的知识点及概念可以利用Materials Studio 软件建模并计算，功能强大，操作简单直观。

在此基础上也能进行位错及缺欠的构建；构建超晶胞；计算弹性模量；电子光谱与介电常数；红外、拉曼光谱；声子谱及声子态密度；电子结构及密度的可视化等等。

1.2 硅单晶胞的导入及超胞的建立Materials Studio/Visualizer程序包内建了很多常用的晶体结构，包括半导体硅材料的晶体结构。

通过Visualizer 模块中的File-〉Import-〉Structure-〉semiconductors->Si.msi功能导入程序内建的硅单晶结构，并三维可视化。

在此晶体结构基础上进行超晶胞拓展。

其操作为Visualizer 模块中的File-〉Build-〉Symmetry-〉Supercell，在弹出的Supercell对话框中的Supercell range： A： B： C：空白处填入想要生成的超晶胞维度，接着再按下Create Supercell 按钮就可生成硅的超晶胞。

湖南铁路科技职业技术学院毕业设计（论文）铁路货车脱轨原因分析及对策目录刖H (4)一、中国铁路货车简介 (5)二、铁路货车脱轨的机理和种类 (5)1.货车脱轨的主要原因分析 (5)2.货车脱轨的种类分析 (6)3.车辆脱轨临界状态的评定指标 (7)三、铁路货车脱轨案例 (9)1.国内铁路货车脱轨典型案例 (9)2.国外铁路货车脱轨典型案例 (10)四、铁路货车转向架 (10)1.货车转向架概述 (10)2.轮轨关系分析 (11)五、防止货车脱轨的措施及建议 (12)1.合理控制货车空车速度 (12)2.特殊区段采用钢轨侧面涂油 (12)3.建立车辆部门严格检修制度 (12)4.加强线路招治，提高修理标准 (14)5.空、重车辆的混编 (14)6.列车部门加强列车的平稳操纵 (15)7.阴阳轨的设胃及缩小轨距 (15)后语 (16)参考文献 (17)摘要：车辆脱轨大多数情况是多种因素综介作用的结果。

重量的差异是空重车最根本的差异，而它对车辆最直接的影响是造成摇枕下弹簧的静挠度的差异。

空重车辆载重的不同导致弹簧挠度的差异，造成了同一车辆在空车和重载时运行性能的不同。

从转向架的角度来考虑，评定抗脱轨安全性的指标主要有脱轨系数和轮重减载率两项指标，脱轨系数临界值越高，脱轨的可能性越小;根据GB 5599-1985规定，轮重的减载(AP)与线路状态如轨距、高低、水平有关，车辆的状况有关，减载越大，越容易脱轨。

通过分析货车空车车辆在直线线路上的动态性能、线路状态、车辆编组、环境温度等因素对货车脱轨的影响，得出合理结论，提出防止货车脱轨的措施。

关键词：货车脱轨影响因素预防措施Abstract：Vehicle derailment in most cases is the result of a variety of factors of dielectric function.Weight differences is the most fundamental empty heavy truck,and it is the most direct impact of vehicle swing bolster spring under the static deflection difference.Entity heavy traffic load of the differences in spring deflection,caused the same vehicle in empty and different overloaded running performance.To consider from the Angle of the bogie,evaluation index of resisting derailment safety. Mainly include the derailment coefficient and wheel weight lightening rate two indicators,derailment coefficient threshold is higher,the smaller the possibility of derailment.According to the stipulations of GB 5599-1985,wheel weight lightening(AP)and gauge,height,horizontal line state,i.e.,the status of the vehicle,the greater the lightening,the more easily derailed.By analyzing the truck unloaded vehicle on a straight line,line state, vehicle dynamic performance organization,the influence of environment temperature on the wagon derailment,reasonably come to the conclusion, puts forward the measures to prevent wagon derailment.Keywords：Wagon derailment influence factor prevention measures刖言随着大规模的提速，货物列车中空车在直线区段的脱轨事故频繁发生。