Electronic Structure and Optical Properties of K2T

合集下载

密度函数

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。

Ni,_Cu,_Zn掺杂四方相PbTiO3力学性能、电子结构与光学性质的第一性原理研究

第53卷第2期2024年2月人㊀工㊀晶㊀体㊀学㊀报JOURNAL OF SYNTHETIC CRYSTALSVol.53㊀No.2February,2024Ni,Cu,Zn掺杂四方相PbTiO3力学性能㊁电子结构与光学性质的第一性原理研究王云杰1,2,张志远1,2,文杜林1,2,吴侦成1,2,苏㊀欣1,2(1.伊犁师范大学物理科学与技术学院,伊宁㊀835000;2.伊犁师范大学新疆凝聚态相变与微结构实验室,伊宁㊀835000)摘要:采用第一性原理研究了四方相钙钛矿PbTiO3以及Ni㊁Cu㊁Zn掺杂PbTiO3的力学性能㊁电子结构和光学性质㊂力学性能计算结果表明,Ni掺杂PbTiO3的体积模量㊁剪切模量及弹性模量在三种掺杂体系中最大㊂Ni掺杂体系德拜温度最高㊂G/B为材料的脆㊁韧性判据,Zn掺杂PbTiO3的G/B值最大,说明化学键定向性最高㊂Ni㊁Zn掺杂体系的G/B 范围为0.56<G/B<1.75,均为脆性材料,而本征PbTiO3和Cu掺杂体系G/B值小于0.56,均为韧性材料㊂通过电子结构分析,发现掺杂体系相比于本征体系带隙变窄,跃迁能量减小㊂Ni掺入使得PbTiO3费米能级处出现杂质能级,而Cu㊁Zn掺杂PbTiO3价带顶上移,费米能级进入价带,使得Cu㊁Zn掺杂PbTiO3呈现p型导电特性㊂从复介电函数㊁光学反射谱和吸收谱分析中发现,掺杂体系的静介电常数相较于本征体系有所提升㊂Ni㊁Cu㊁Zn的掺杂使得PbTiO3吸收范围扩展到红外波段,且增强了可见光波段的吸收强度,Cu掺杂PbTiO3材料的光催化特性在本征PbTiO3和三种单掺PbTiO3材料中是最好的㊂关键词:第一性原理;PbTiO3;掺杂;力学性能;电子结构;光学特性中图分类号:O561㊀㊀文献标志码:A㊀㊀文章编号:1000-985X(2024)02-0258-09 First Principles Study on Mechanical Properties,Electronic Structure and Optical Properties of Ni,Cu,Zn Doped Tetragonal PbTiO3WANG Yunjie1,2,ZHANG Zhiyuan1,2,WEN Dulin1,2,WU Zhencheng1,2,SU Xin1,2(1.School of Physical Science and Technology,Yili Normal University,Yining835000,China;2.Xinjiang Laboratory of Phase Transitions and Microstructures of Condensed Matter Physics,Yili Normal University,Yining835000,China) Abstract:The mechanical property,electronic structure,and optical properties of tetragonal perovskite PbTiO3and Ni,Cu, Zn-doped PbTiO3were studied by first principles.The mechanical property calculations show that Ni-doped PbTiO3exhibits the highest values for volume modulus,shear modulus,and elastic modulus among the three doping systems.Notably,the Ni-doped system also has the highest Debye temperature.The G/B ratio represents the material s brittleness and toughness, which is highest for Zn-doped PbTiO3,indicating the highest degree of chemical bond orientation.The G/B range for Ni and Zn-doped systems is0.56<G/B<1.75,indicating brittle materials,while the intrinsic PbTiO3and Cu-doped systems have G/B values less than0.56,indicating ductile materials.The electronic structure reveals that the doped systems have narrower band gaps and reduced transition energies compared to the intrinsic system.The introduction of Ni introduces impurity levels at the Fermi energy level in PbTiO3,while Cu and Zn doping shifts the valence band maximum upwards,causing the Fermi level to enter the valence band and resulting in p-type conductivity for Cu and Zn-doped PbTiO3.The doping of Ni,Cu and Zn expands the absorption range of PbTiO3to the infrared region and enhances the absorption intensity in the visible light range.Among the intrinsic PbTiO3and three single-doped PbTiO3materials,Cu-doped PbTiO3exhibits the best photocatalytic properties.Key words:first principle;PbTiO3;doping;mechanical property;electronic structure;optical property㊀㊀收稿日期:2023-08-02㊀㊀基金项目:伊犁师范大学科研专项提升重点项目(22XKZZ21);伊犁师范大学科研项目(2022YSZD004);伊犁师范大学大学生创新训练项目(S202110764006,YS2022G018);新疆伊犁科技计划(YZ2022Y002);新疆维吾尔自治区天山英才计划第三期(2021-2023)㊀㊀作者简介:王云杰(1999 ),男,新疆维吾尔自治区人,硕士研究生㊂E-mail:1575469121@㊀㊀通信作者:苏㊀欣,博士,副教授㊂E-mail:suxin_phy@㊀第2期王云杰等:Ni,Cu,Zn掺杂四方相PbTiO3力学性能㊁电子结构与光学性质的第一性原理研究259㊀0㊀引㊀㊀言PbTiO3(PTO)作为一种典型的钙钛矿型铁电氧化物,在居里温度(763K)以下为四方相,当处于居里温度(763K)以上时,PTO的相由四方相转变为立方相[1-2]㊂四方相PTO铁电性能较为优异,广泛应用于存储器㊁电换能器㊁微电子㊁无线通信用电介质等设备㊂此外,四方相PTO还具有较大的电光系数和较高的光折变灵敏度[3-5],因此可以用于光学传感器㊁光转换器和光调制器等[6-9]㊂除TiO2催化剂外,Ti基钙钛矿(例如CaTiO3㊁SrTiO3)还参与了自然污染物的光催化脱色和光催化水分解制氢㊂与TiO2一样,这些钙钛矿型催化剂也受到宽禁带的限制,这使得其可见光反应非常困难,光催化能力被减弱[10]㊂钙钛矿晶体结构提供了一个极好的框架,可根据特定光催化反应的要求修改带隙值,以允许可见光吸收和带边能量㊂此外,钙钛矿晶体化合物中的晶格畸变强烈影响光生载流子的分配㊂PTO由于高光催化活性,受到了广泛关注[11]㊂PTO是典型的钙钛矿型铁电氧化物,通常用于电子器件,很少用作光催化剂[12-13]㊂近年来,研究人员发现通过合理的合成方法和材料改性对PTO光催化性能进行改善㊂Hussin等和Niu 等[14-15]基于第一性原理,分别研究了La和N掺杂体系PTO的电子结构,发现La掺杂体系的带隙比本征带隙窄,N掺杂体系的PTO的费米能级进入价带顶部,使得N掺杂体系材料呈现出p型导电特性,能带结构的禁带宽度减小,对于光催化能力有一定的改善,但是关于光学性质方面并没有进行报道㊂李宏光等[16]基于第一性原理,研究了N掺杂体系的光学性质,发现光学吸收能力在可见光区域并没有较大的改善,并且Ti的氧化物进行非金属掺杂时,需要高温处理[17-18],从能量消耗的角度来说是不利的㊂综上所述,确定掺杂位置以及掺杂量成为改善PTO光催化性能的关键㊂而二价金属Ni㊁Cu㊁Zn离子更容易取代Ti4+,使O的电负性变弱,更容易改善PTO性能[19]㊂在文献调研中发现关于PTO力学性能的系统报道大多是基于本征体系[20-22],对掺杂体系的力学性能报道是罕见的,因此有必要对掺杂体系PTO光催化性能研究的同时,也对掺杂体系力学性能的改善进行系统地讨论㊂本文的主要内容是采用密度泛函理论对本征以及单掺Ni㊁Cu㊁Zn四方相PTO(PTOʒNi㊁PTOʒCu㊁PTOʒZn)的力学性能和光电性能展开系统地讨论,以期PTO能够在力学性能以及光催化方面得到更大的改善㊂1㊀理论模型与计算方法四方相PTO晶体是典型的钙钛矿结构,属于P4mm空间群[23],建立共包含40个原子的2ˑ2ˑ2超胞结构,掺杂浓度为12.5%的掺杂体系结构如图1所示,考虑到边界条件的影响,用一个Ni㊁Cu㊁Zn分别去取代超胞中的Ti原子,在超胞中有8个Ti原子的位点,根据晶体的对称性所示这8个位点为等效位点,所以不同的掺杂位置对体系没有影响㊂基于密度泛函理论的第一性原理平面波赝势方法[24-25]应用MaterialsStudio8.0[26]计算了原子各轨域的电子态密度,选择基组为广义梯度近似(general gradient approximate,GGA)下的PBE(Perdew-Burke-Ernzerhof)[27-28]交换-关联泛函,使用超软赝势(ultra-soft pseudopotential,USP)计算本征以及掺杂体系PTO 的力学性能㊁电子结构和光学性质㊂将能量㊁自洽场以及能带的收敛精度均定为5ˑ10-6eV/atom;作用于原子上的最大力为0.01eV/Å,内应力收敛精度为0.02GPa,最大位移收敛精度为5ˑ10-5Å㊂截止能为400eV,在布里渊区积分采用4ˑ4ˑ4的Monkhost-Pack型K点网格进行迭代设置[29]㊂图1㊀超晶胞掺杂模型Fig.1㊀Supercell doping model260㊀研究论文人工晶体学报㊀㊀㊀㊀㊀㊀第53卷2㊀结果与讨论2.1㊀几何结构分析表1为几何结构优化后的本征以及掺杂体系PTO超胞的晶格常数和体积的变化㊂由表1可知,本征PTO的晶格常数计算值为a=b=7.688Å,c=9.567Å,理论值为a=b=7.759Å,c=8.572Å[30],两项数据对比,晶格常数c相差约1Å,但是理论值和计算值的c/a近似,说明选用参数的可靠性㊂与本征PTO相比, Ni㊁Cu掺杂PTO的晶格常数a㊁b㊁c减小,晶胞体积减小㊂Zn掺杂PTO的晶格常数a㊁b减小,c增大,晶胞体积增大㊂表1㊀Ni㊁Cu㊁Zn掺杂的PTO超胞晶格常数㊁密度和体积Table1㊀Lattice constants,density and volume of PTO supercell doped with Ni,Cu and Zn Sample a=b/Åc/ÅVolume/Å3Density/(g㊃cm-3)c/a PTO(Experimental)7.7598.572516.0537.802 1.1 PTO(Calculated)7.6889.567565.3527.122 1.2Ni doping7.6759.396553.4507.307 1.2Cu doping7.6559.515557.6037.268 1.2Zn doping7.6639.688568.9617.127 1.22.2㊀缺陷形成能分析缺陷形成能是表征掺杂体系稳定性和原子掺入体系难易程度的物理变量㊂基于几何结构优化后的体系总能量和不同原子的化学势计算相应结构的形成能㊂各掺杂体系的形成能E f满足以下公式[31-32]:E f=E doped-E perfect-lμX+nμTi(1)式中:E doped表示各掺杂体系的总能量,E perfect表示纯PbTiO3超晶胞体系总能量,系数l㊁n分别表示掺入的原子和替代的原子数,μX表示掺入原子(X=Ni㊁Cu㊁Zn)的化学势,μTi表示被替换的Ti原子化学势㊂由于材料的缺陷形成能与其生长制备的条件有密切关系,本文计算了富氧且富铅状态下各掺杂体系的形成能㊂从表2可以看出,Ni㊁Cu㊁Zn单掺PbTiO3体系在富O(O-rich)和富Pb(Pb-rich)条件下的形成能均为负㊂这意味着在O-rich和Pb-rich条件下,Ni㊁Cu㊁Zn原子可以融入PTO中,可在实验中制造Ni㊁Cu㊁Zn单掺PbTiO3材料㊂表2㊀Ni㊁Cu㊁Zn掺杂的PTO的缺陷形成能Table2㊀Defect formation energy of PTO doped with Ni,Cu and ZnSubstitute form O-rich and Pb-rich defect formation energy/eVNi doping-14.905Cu doping-13.336Zn doping-18.6542.3㊀力学性能基于密度泛函理论,结合当前应用最普遍的有限应变方法[33],通过计算应力应变的线性得到弹性系数6个独立分量,得到6ˑ6的弹性张量矩阵㊂根据晶格点阵的空间对称性,部分分量相等,部分分量为零㊂计算所得本征以及掺杂体系PTO晶格常数变化结构的特征弹性系数矩阵元,在优化晶体结构的基础上计算出本征以及掺杂体系PTO的弹性常数C ij,如表3所示㊂同时,基于Voigt-Reuss-Hill近似[34-36]得到体积模量㊁剪切模量㊁弹性模量㊁泊松比㊁Pugh比㊁维氏硬度㊁德拜温度θD,如表4所示㊂本文B和G取Hill值,通过弹性常数分别计算下限值B V㊁G V和上限值B R㊁G R,然后求平均值得出㊂这里弹性模量可由下面公式给出[37]B=(B V+B R)/2(2)G=(G V+G R)/2(3)其中,G V=(1/15)[C11+C22+C33+3(C44+C55+C66)-2(C12+C13+C23)],B R=Δ[C11(C22+C33+C23)+C22(C33-2C13)-C33C12+C12(2C23-C12)+C13(2C12-C13)+C23(2C13-C23)]-1,㊀第2期王云杰等:Ni,Cu,Zn掺杂四方相PbTiO3力学性能㊁电子结构与光学性质的第一性原理研究261㊀G R=15{4[C11(C22+C33+C23)+C22(C33+C13)+C33C12-C12(C12+C23)-C13(C12+C13)-C23(C13+ C23)]/Δ+3[(1/C44)+(1/C55)+(1/C66)]-1,Δ=C13(C12C23-C13C22)+C23(C12C13-C11C23)+C33(C11C22-C12C12)㊂弹性模量E和泊松比分别依照下列公式(4)和(5)计算得出E=9BG/(3B+G)(4)μ=(3B-E)/(6B)(5)采用Chen-Niu模型[38],得到维氏硬度H V公式为H V=2(k2G)0.585-3(6)其中Pugh比[39]k=G/B㊂对于本征以及掺杂体系PTO的弹性常数满足Born弹性稳定性判据[30]:C11(C22+C33)ȡ2C212,C22ȡC23, C44ȡ0,C55ȡ0,说明这四种结构是力学稳定的㊂体积模量是衡量材料是否容易被压缩的标志,Ni掺杂PTO 体积模量(80.034GPa)最大,所以相较于其他三种结构更不容易被压缩㊂剪切模量可以衡量材料硬度,Ni 掺杂PTO具有最大的剪切模量,对应最大的维氏硬度10.411GPa㊂弹性模量是标志材料刚度的重要物理量,Ni掺杂PTO的弹性模量最大,所以相较于其他三种结构刚性最高㊂G/B=1.75是区分脆性材料和延展性材料分界点,G/B=0.56是区分材料韧性/脆性分界点㊂由表4可以看出,G/B的值都小于1.75,Ni㊁Zn掺杂PTO大于0.56,都是脆性材料,本征以及Cu掺杂PTO小于0.56,属于是韧性材料㊂而泊松比反映了材料在形变下体积所发生的变化,说明四种结构形变时体积变化不大,泊松比的变化规律与Pugh比的正好相反㊂众所周知,德拜温度与材料的很多物理性质,如熔点㊁弹性㊁硬度㊁比热等基本物理量密切相关㊂采用以下公式[33]求得德拜温度θD=h kB34πV a[]1/3v m(7)式中:h为普朗克常量,k B为玻尔兹曼常量,V a为原子体积,v m为平均声速,由下式求出v m=132v3t +1v31()[]-1/3(8)式中:v1与v t分别为纵波㊁横波速度,可由下面的公式求得v1=3B+4G3ρ()1/2(9)v t=Gρ()1/2(10)式(9)和(10)中,ρ为密度,已由表1给出㊂本征以及掺杂体系PTO德拜温度的计算结果见表4㊂从表4给出的结果可以看出,Ni掺杂体系的德拜温度(201.506K)最高,与它有最大的C11(196.541GPa)㊁C23(63.626GPa)㊁C66(82.707GPa),最大的体积模量(80.034GPa),最大的剪切模量(45.499GPa)和最大的弹性模量(114.752GPa)密切相关㊂由表4可知,掺杂体系的剪切模量㊁弹性模量㊁Pugh比㊁维氏硬度和德拜温度均大于本征体系㊂其中Ni 掺杂体系的体积模量要大于本征体系,Cu㊁Zn掺杂体系的小于掺杂体系,说明除Cu㊁Zn掺杂体系在抗压性低于本征体系外,在硬度和刚性等力学性能均强于本征体系㊂可见二价金属Ni㊁Cu㊁Zn的掺杂,有助于改善四方相PTO的力学性能㊂表3㊀本征以及掺杂体系PTO的弹性常数C ijTable3㊀Elastic constants C ij of PTO in intrinsic and doped systemsCompound C11/GPa C12/GPa C13/GPa C22/GPa C23/GPa C33/GPa C44/GPa C55/GPa C66/GPa PTO172.44690.23880.526217.93161.95560.58151.59247.50381.781 Ni doping196.54190.00955.858210.65263.62661.79045.25745.19982.707 Cu doping183.37769.41847.886189.35455.26166.79630.10341.91071.456 Zn doping163.76165.71541.457163.76141.45766.02635.17035.17064.722262㊀研究论文人工晶体学报㊀㊀㊀㊀㊀㊀第53卷表4㊀本征以及掺杂体系PTO的体积模量(B)㊁剪切模量(G)㊁弹性模量(E)㊁泊松比(μ)㊁Pugh比(G/B)㊁维氏硬度(H V)和德拜温度θDTable4㊀Bulk modulus(B),shear modulus(G),elastic modulus(E),Poisson ratio(μ),Pugh ratio(G/B), Vickers hardness(H V),Debye temperature(θD)of PTO in intrinsic and doped systems Compound B/GPa G/GPa E/GPaμG/B H V/GPaθD/K PTO78.43539.170100.7400.2860.4998.389188.293 Ni doping80.03445.499114.7520.2610.56810.411201.506 Cu doping75.25140.052101.7410.2750.5328.977189.392 Zn doping68.30740.606101.6710.2520.5949.880190.852 2.4㊀能带结构分析图2是本征PbTiO3以及掺杂体系的能带结构图㊂为便于分析,范围选取-5~5eV,包含费米能级,在四种体系中除Ni掺杂PbTiO3为间接带隙外,其他均为直接带隙㊂图2(a)是本征PbTiO3的能带结构图,禁带宽度为2.007eV,与实验值3.6eV相较偏低[40],所以采用剪刀算符[41]修正其带隙值(剪刀算符为1.6eV),修正后的带隙为3.607eV㊂图2(b)~(d)分别是Ni㊁Cu㊁Zn掺杂PTO的能带结构图,掺杂体系的跃迁形式所需的能量,相较于本征结构降低,并且区间处于0~1eV能带条数增多,Cu㊁Zn掺杂PbTiO3带隙值分别为1.930㊁1.936eV,价带顶有所上移,费米能级进入价带顶,使得Cu㊁Zn掺杂PbTiO3呈现出p型导电特性㊂Ni 掺杂PbTiO3价带顶到导带底的间距是1.678eV,在2eV附近出现受主能级,价带顶处出现多余的空穴载流子,这有利于电子吸收极少的能量由价带顶跃迁至受主能级,再由受主能级跃迁至导带底,或者实现受主能级之间的跃迁,从而能够大幅改善PbTiO3材料的光催化特性和导电性㊂李宏光等[16]关于N掺杂PbTiO3的研究中,能带结构出现受主能级,且价带顶下移,出现p型半导体特性,但是电子跃迁性能并不比Ni㊁Cu㊁Zn 掺杂PbTiO3更强㊂图2㊀本征PTO及三种掺杂体系的能带结构分布Fig.2㊀Band structures of intrinsic PTO and three doping systems2.5㊀态密度分析图3是本征PTO以及三种掺杂体系的总态密度图和分波态密度图㊂图3(a)是本征PTO的态密度图,㊀第2期王云杰等:Ni,Cu,Zn掺杂四方相PbTiO3力学性能㊁电子结构与光学性质的第一性原理研究263㊀Ti-3d轨道是构成导带部分的总态密度主要部分㊂价带能量处于-19~-14eV的总态密度主要由Pb-5d和O-2s轨道提供,在-8eV至费米能级的总态密度主要由O-2p以及Pb-6s轨道贡献,这与相关研究结果一致[16]㊂图3(b)~(d)分别是Ni㊁Cu㊁Zn掺杂PTO的态密度图㊂掺杂体系Pb㊁Ti和O对总态密度的贡献基本与本征态一致㊂区别在于在费米面附近,主要由O-2p及Ni㊁Cu㊁Zn的3d态之间进行杂化贡献,表现出强大的局域性㊂当Ni㊁Cu㊁Zn掺杂到PTO之后,由于掺入的Ni㊁Cu㊁Zn对总态密度贡献相对较小而不易被观察,但可以从O-2p轨道的变化进行说明,使得O-2p轨道在费米能级附近出现自由电子㊂2价金属Ni㊁Cu㊁Zn 的掺杂使得Pb㊁Ti和O之间的杂化发生变化,进而影响态密度的整体分布情况㊂掺杂体系的电子从价带顶跃迁到导带底的过程变得容易,与能带结构情况吻合㊂图3㊀本征PTO及三种掺杂体系的态密度曲线Fig.3㊀Density of states curves of intrinsic PTO and three doping systems2.6㊀光学性质分析本征以及三种掺杂体系的PTO复介电函数实部曲线和虚部曲线如图4所示,图4(a)中PTO㊁PTOʒNi㊁PTOʒCu和PTOʒZn的静态介电常数分别为2.307㊁3.305㊁3.411和4.513㊂PTOʒCu在低能区介电函数实部随着光子能量的增大而增大,并到达峰值5.714(光子能量为1.38eV),从态密度图看出这是由Cu-3d轨道向O-2p轨道的电子跃迁引起的㊂图4(b)显示PTOʒNi㊁PTOʒCu和PTOʒZn的介电函数虚部主要集中在0~10eV 的低能区,而本征PTO在虚部低能区(ɤ3eV)虚部值很小,接近零,而Ni㊁Cu㊁Zn掺杂PTO体系在虚部1.5eV左右形成新的次级主峰,PTOʒCu在低于2eV的低能区具有压倒性数值㊂可见,Ni㊁Cu㊁Zn掺杂PTO 体系光谱吸收范围扩展到红外区域,且PTOʒCu更具有优势,在可见光波段的能量吸收效果较强,说明PTOʒCu在低能区的吸收效果在三种掺杂体系中是最强的㊂图4(c)是本征以及三种掺杂体系的PTO体系的反射光谱㊂可知,本征PTO在5.77㊁7.41㊁9.74eV出现三个峰值㊂Ni㊁Cu掺杂PTO体系在可见光区域能量值大于本征PTO㊂在红外光区,Ni㊁Cu㊁Zn掺杂PTO的反射值大于本征PTO体系,PTOʒCu对可见光区域和红外光区的利用率较高,这与复介电函数图所得的结果一致㊂图4(d)是含Ni㊁Cu㊁Zn掺杂的PTO的吸收光谱㊂本征PTO只吸收紫外波段,对红外部分不吸收,本征264㊀研究论文人工晶体学报㊀㊀㊀㊀㊀㊀第53卷PTO的禁带宽度决定了Ni㊁Cu㊁Zn掺杂的PTO体系吸收主要集中在紫外波段㊂同时,掺杂使得电子跃迁变得容易,Ni㊁Cu㊁Zn掺杂的PTO体系吸收范围扩展到红外波段㊂在可见光波段,PTOʒCu吸收效果最好,并且吸收边640nm所对应的频率为1.94eV,这表明电子是从价带内跃迁到导带的,说明PTOʒCu具有潜在的光催化能力㊂在红外以及远红外波段,PTOʒZn吸收效果和PTOʒCu相近,并且比李宏光等[16]报道的N掺杂的PTO在红外远红外区域吸收效果更好㊂吸收光谱与介电㊁反射光谱的变化趋势是一致的㊂图4㊀本征PTO及三种掺杂体系的光学图谱㊂(a)复介电函数实部;(b)复介电函数虚部;(c)反射光谱;(d)吸收光谱Fig.4㊀Optical spectra of intrinsic PTO and three doping systems.(a)Real part of complex dielectric function;(b)imaginary part of complex dielectric function;(c)reflection spectra;(d)absorption spectra3㊀结㊀㊀论1)Ni掺杂PTO的体积㊁剪切和弹性模量最大,这是Ni掺杂PTO德拜温度最高的重要原因㊂体积模量的大小是衡量材料是否容易被压缩的标志,体积模量越高,材料越不容易被压缩;高剪切模量是高硬度的基本条件,最大的剪切模量使得Ni掺杂PTO有最大的维氏硬度;弹性模量是标志材料刚度的重要物理量,表明四种材料中Ni掺杂PTO的刚性最高㊂2)Zn掺杂PTO的G/B值是四种材料中最大的,说明此结构中原子间的化学键的定向性最高㊂3)Ni㊁Zn掺杂PTO的G/B大于0.56,都是脆性材料,本征以及Cu掺杂PTO的G/B小于0.56,是韧性材料㊂泊松比反映了材料在形变下体积的变化,本征以及掺杂体系的泊松比都在0.25~0.5,表明本征及掺杂体系PTO形变时体积将不会发生较大的变化㊂4)掺杂体系较于本征体系跃迁能量减小,Ni掺入PTO材料的费米能级处出现杂质能级㊂Cu㊁Zn掺杂的PTO费米能级进入价带顶,使得Cu㊁Zn掺杂PTO材料呈现出p型导电特性㊂5)Ni㊁Cu㊁Zn的掺杂使得PTO吸收范围扩展到红外波段,且增强了可见光波段的吸收强度,四种结构中PTOʒCu材料的光催化性能最好㊂参考文献[1]㊀ZHANG S J,LI F,JIANG X N,et al.Advantages and challenges of relaxor-PbTiO3ferroelectric crystals for electroacoustic transducers:a review[J].㊀第2期王云杰等:Ni,Cu,Zn掺杂四方相PbTiO3力学性能㊁电子结构与光学性质的第一性原理研究265㊀Progress in Materials Science,2015,68:1-66.[2]㊀LIU Y,NI L H,REN Z H,et al.First-principles study of structural stability and elastic property of pre-perovskite PbTiO3[J].Chinese PhysicsB,2012,21(1):016201.[3]㊀SUNTIVICH J,GASTEIGER H A,YABUUCHI N,et al.Design principles for oxygen-reduction activity on perovskite oxide catalysts for fuelcells and metal-air batteries[J].Nature Chemistry,2011,3(7):546-550.[4]㊀黄㊀建,张学伍,赵㊀程,等.钛酸铅系功能陶瓷改性的研究现状及改性陶瓷的应用现状[J].机械工程材料,2021,45(6):94-98.HUANG J,ZHANG X W,ZHAO C,et al.Research status of modification of lead titanate series functional ceramics and application of modified ceramics[J].Materials for Mechanical Engineering,2021,45(6):94-98(in Chinese).[5]㊀邓鹏星,文志勤,马㊀博,等.体积应变对立方钛酸铅电子结构和光学性质的影响[J].人工晶体学报,2022,51(1):85-91.DENG P X,WEN Z Q,MA B,et al.Effect of volume strain on electronic structure and optical properties of cubic lead titanate[J].Journal of Synthetic Crystals,2022,51(1):85-91(in Chinese).[6]㊀SCOTT J F,PAZ DE ARAUJO C A.Ferroelectric memories[J].Science,1989,246(4936):1400-1405.[7]㊀HOSSEINI S M,MOVLAROOY T,KOMPANY A.First-principle calculations of the cohesive energy and the electronic properties of PbTiO3[J].Physica B:Condensed Matter,2007,391(2):316-321.[8]㊀ZHU Z Y,WANG B,WANG H,et al.First-principle study of ferroelectricity in PbTiO3/SrTiO3superlattices[J].Solid-State Electronics,2006,50(11/12):1756-1760.[9]㊀GE F F,WU W D,WANG X M,et al.The first-principle calculation of structures and defect energies in tetragonal PbTiO3[J].Physica B:Condensed Matter,2009,404(20):3814-3818.[10]㊀CHEN X,TAN P F,ZHOU B H,et al.A green and facile strategy for preparation of novel and stable Cr-doped SrTiO3/g-C3N4hybridnanocomposites with enhanced visible light photocatalytic activity[J].Journal of Alloys and Compounds,2015,647:456-462. [11]㊀GRABOWSKA E.Selected perovskite oxides:characterization,preparation and photocatalytic properties:a review[J].Applied Catalysis B:Environmental,2016,186:97-126.[12]㊀OHNO T,TSUBOTA T,NAKAMURA Y,et al.Preparation of S,C cation-codoped SrTiO3and its photocatalytic activity under visible light[J].Applied Catalysis A:General,2005,288(1/2):74-79.[13]㊀MORET M P,DEVILLERS M A C,WÖRHOFF K,et al.Optical properties of PbTiO3,PbZr x Ti1-x O3,and PbZrO3films deposited bymetalorganic chemical vapor on SrTiO3[J].Journal of Applied Physics,2002,92(1):468-474.[14]㊀HUSSIN N H,TAIB M F M,HASSAN O H,et al.Study of geometrical and electronic structure of lanthanum doped PbTiO3and PbZrTiO3:firstprinciples calculation[C]//AIP Conference Proceedings.Ho Chi Minh,Vietnam.Author(s),2018.[15]㊀NIU P J,YAN J L,MENG D L.The effects of N-doping and oxygen vacancy on the electronic structure and conductivity of PbTiO3[J].Journalof Semiconductors,2015,36(4):043004.[16]㊀李宏光,闫金良.N掺杂位置对四方相PbTiO3电子结构和光学性能的影响[J].材料科学与工程学报,2017,35(1):14-18.LI H G,YAN J L.Electronic structures and optical properties of N-doped tetragonal PbTiO3with different doping sites[J].Journal of Materials Science and Engineering,2017,35(1):14-18(in Chinese).[17]㊀ASAHI R,MORIKAWA T,OHWAKI T,et al.Visible-light photocatalysis in nitrogen-doped titanium oxides[J].Science,2001,293(5528):269-271.[18]㊀OKUNAKA S,TOKUDOME H,ABE R.Facile water-based preparation of Rh-doped SrTiO3nanoparticles for efficient photocatalytic H2evolutionunder visible light irradiation[J].Journal of Materials Chemistry A,2015,3(28):14794-14800.[19]㊀XIN H,PANG Q,GAO D L,et al.Mn ions'site and valence in PbTiO3based on the native vacancy defects[J].Condensed Matter Physics,2021,24(2):23705.[20]㊀KUMA S,WOLDEMARIAM M M.Structural,electronic,lattice dynamic,and elastic properties of SnTiO3and PbTiO3using density functionaltheory[J].Advances in Condensed Matter Physics,2019,2019:1-12.[21]㊀HACHEMI A,HACHEMI H,FERHAT-HAMIDA A,et al.Elasticity of SrTiO3perovskite under high pressure in cubic,tetragonal andorthorhombic phases[J].Physica Scripta,2010,82(2):025602.[22]㊀LI Z,GRIMSDITCH M,FOSTER C M,et al.Dielectric and elastic properties of ferroelectric materials at elevated temperature[J].Journal ofPhysics and Chemistry of Solids,1996,57(10):1433-1438.[23]㊀SÁGHI-SZABÓG,COHEN R E,KRAKAUER H.First-principles study of piezoelectricity in tetragonal PbTiO3and PbZr1/2Ti1/2O3[J].Physical Review B,1999,59(20):12771-12776.[24]㊀PERDEW J P,WANG Y E.Accurate and simple analytic representation of the electron-gas correlation energy[J].Physical Review B,1992,45(23):13244-13249.[25]㊀SEGALL M D,LINDAN P J D,PROBERT M J,et al.First-principles simulation:ideas,illustrations and the CASTEP code[J].Journal ofPhysics:Condensed Matter,2002,14(11):2717-2744.[26]㊀CLARK S J,SEGALL M D,PICKARD C J,et al.First principles methods using CASTEP[J].Zeitschrift Für Kristallographie-Crystalline266㊀研究论文人工晶体学报㊀㊀㊀㊀㊀㊀第53卷Materials,2005,220(5/6):567-570.[27]㊀ERNZERHOF M,BURKE K,PERDEW J P.Density functional theory,the exchange hole,and the molecular bond[M]//Theoretical andComputational Chemistry.Amsterdam:Elsevier,1996:207-238.[28]㊀PERDEW J P,ERNZERHOF M,ZUPAN A,et al.Nonlocality of the density functional for exchange and correlation:physical origins andchemical consequences[J].The Journal of Chemical Physics,1998,108(4):1522-1531.[29]㊀MONKHORST H J,PACK J D.Special points for brillouin-zone integrations[J].Physical Review B,1976,13(12):5188-5192.[30]㊀TAIB M F M,YAAKOB M K,BADRUDIN F W,et al.First-principles comparative study of the electronic and optical properties of tetragonal(P4mm)ATiO3(A=Pb,Sn,Ge)[J].Integrated Ferroelectrics,2014,155(1):23-32.[31]㊀WANG Q J,WANG J B,ZHONG X L,et al.Magnetism mechanism in ZnO and ZnO doped with nonmagnetic elements X(X=Li,Mg,andAl):a first-principles study[J].Applied Physics Letters,2012,100(13):673-677.[32]㊀CHEN H,LI X C,WAN R D,et al.A DFT study on modification mechanism of(N,S)interstitial co-doped rutile TiO2[J].Chemical PhysicsLetters,2018,695:8-18.[33]㊀BOUHEMADOU A.First-principles study of structural,electronic and elastic properties of Nb4AlC3[J].Brazilian Journal of Physics,2010,40(1):52-57.[34]㊀CHEN X Q,NIU H Y,LI D Z,et al.Modeling hardness of polycrystalline materials and bulk metallic glasses[J].Intermetallics,2011,19(9):1275-1281.[35]㊀VOIGT W.Lehrbuch der kristallphysik(mit ausschluss der kristalloptik),edited by bg teubner and jw edwards,leipzig berlin[J].Ann Arbor,Mich,1928.[36]㊀REUSS A.Berechnung der fließgrenze von mischkristallen auf grund der plastizitätsbedingung für einkristalle[J].ZAMM-Journal of AppliedMathematics and Mechanics,1929,9(1):49-58.[37]㊀HILL R.The elastic behaviour of a crystalline aggregate[J].Proceedings of the Physical Society Section A,1952,65(5):349-354.[38]㊀WATT J P.Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with monoclinic symmetry[J].Journal of Applied Physics,1980,51(3):1520-1524.[39]㊀PUGH S F.XCII.Relations between the elastic moduli and the plastic properties of polycrystalline pure metals[J].The London,Edinburgh,and Dublin Philosophical Magazine and Journal of Science,1954,45(367):823-843.[40]㊀YADAV H O.Optical and electrical properties of sol-gel derived thin films of PbTiO3[J].Ceramics International,2004,30(7):1493-1498.[41]㊀高㊀妍,董海涛,张小可,等.(Al x Ga1-x)2O3结构㊁电子和光学性质的第一性原理研究[J].人工晶体学报,2023,52(9):1674-1680+1719.GAO Y,DONG H T,ZHANG X K,et al.First-principle study on structure,electronic and optical properties of(Al x Ga1-x)2O3[J].Journal of Synthetic Crystals,2023,52(9):1674-1680+1719(in Chinese).。

具有氧缺陷的SrTiO3的电子结构和光学性质的第一性原理研究

Modern Physics 现代物理, 2014, 4, 113-121Published Online September 2014 in Hans. /journal/mp/10.12677/mp.2014.45014Electronic Structures and Optical Properties of the Oxygen-Deficient SrTiO3 fromFirst-Principles CalculationQingyuan Chen, Yao He*Department of Physics, Yunnan University, KunmingEmail: *yhe@Received: Sep. 1st, 2014; revised: Sep. 8th, 2014; accepted: Sep. 15th, 2014Copyright © 2014 by authors and Hans Publishers Inc.This work is licensed under the Creative Commons Attribution International License (CC BY)./licenses/by/4.0/AbstractIn recent years, perovskite oxides attracted widely attention due to its unique structure and the chemical and physical properties. SrTiO3(hereinafter referred to STO) is a kind of typical pe-rovskite oxides. It has the characteristics of typical perovskite structure, and its high dielectric constant, low dielectric loss and good thermal stability made it easier to attract more attentions.In this paper, we investigate the electronic and optical properties of STO using LDA + U method.We found that this method predicts more accurate band gap for STO. The oxygen vacancy induced local defect state and new absorption band, which enhanced the efficiency of absorption in the visible region.KeywordsFirst-Principles Calculation, SrTiO3, Defect, Electronic Structure, Optical Properties具有氧缺陷的SrTiO3的电子结构和光学性质的第一性原理研究陈清源，何垚*云南大学物理科学技术学院，昆明*通讯作者。

CdCO3电子结构与光学属性的第一性原理研究

CdCO3电子结构与光学属性的第一性原理研究盛虹;张水利;邵婷婷;杨延宁;张富春【摘要】The crystal structure,electronic structure andoptical propertiesofCdCO3were studiedby usingthe first-principlesbased onthe density functional theory (DFT)within the generalized gradient approximation (GGA). Thetheoreticalresultsindicate that the CdCO3is anindirect bandgap semiconductor materialand thebandgapis2.59 eV, whichismainly determined by Cd 4p,O 2p orbital energy levelsat thetopofvalenceband and Cd 4p,5s orbital energy levels at thebottomofconductionband. The resultsof charge density show thatCdCO3crystalis ahybrid bond semiconductor strong in ionicity bond and weak in covalent,characterized by intensep-dhybridorbitals.The optical properties of the CdCO3in which the band-to-band transitionareat leading statusareanalyzed by the precisely calculated band structure and density of state(DOS). The results of the optical properties show that obviousthreedielectric peaks appear in energyrangefrom0 eV to15eV, andthe absorb edges are located in the ultraviolet region.The above results haveimportanttheoretical significance for us to explore the potential applications based on CdCO3materialandoffer theoretical reference topreciselymonitorand control the growth ofCdCO3material.%采用基于密度泛函理论框架的第一性原理计算方法,利用广义梯度近似方法研究了CdCO3的晶体结构、电子结构和光学属性,理论计算结果表明,CdCO3属于间接宽带隙半导体材料,带隙宽度为2.59 eV,带隙主要由价带顶的Cd4p、O 2p和导带底的Cd4p、5s轨道能级决定的.而电荷密度结果显示CdCO3晶体是一种离子性较强而共价性较弱的混合键半导体,具有强烈的p轨道与d轨道杂化分布特征.利用精确计算的能带结构和态密度分析了带间跃迁占主导地位的CdCO3材料的光学属性,光学性质的计算结果显示在0~15 eV的能量范围内出现了三个明显的介电峰,吸收带边对应于紫外波段.以上结果对于探索基于CdCO3纳米材料的潜在应用具有重要的理论指导意义,也为精确监测和控制CdCO3材料的生长提供了理论依据.【期刊名称】《电子元件与材料》【年(卷),期】2017(036)012【总页数】5页(P42-46)【关键词】碳酸镉;第一性原理;电子结构;电荷密度;光学带隙;光吸收【作者】盛虹;张水利;邵婷婷;杨延宁;张富春【作者单位】渭南师范学院数理学院,陕西渭南 714000;延安大学物理与电子信息学院,陕西延安 716000;延安大学物理与电子信息学院,陕西延安 716000;延安大学物理与电子信息学院,陕西延安 716000;延安大学物理与电子信息学院,陕西延安 716000【正文语种】中文【中图分类】O643.1近年来，形貌可控的碳酸盐纳米结构材料CdXO3 (X = C, Si, Ge, Sn, Pb)由于其特殊的形态和结构而具有新奇的光学、化学和物理特性，引起人们的广泛研究热情[1]。

六硼化钇纳米粒子超导及光吸收性能研究

第50卷第3期2021年5月内蒙古师范大学学报(自然科学版)Journal of Inner Mongolia Normal University(Natural Science Edition)Vol.50No.3May2021六硼化钇纳米粒子超导及光吸收性能研究王军】，包黎红】，潮洛蒙2（1.内蒙古师范大学物理与电子信息学院，内蒙古呼和浩特010022；2.内蒙古科技大学理学院，内蒙古包头014010）摘要：采用固相烧结法成功制备出了六硼化钇（YB&）纳米粒子，首次系统研究了该纳米粉末超导及光吸收性能.结果表明，当超导转变温度T=2.75K时由正常态转变为超导态，其临界磁场为H c2=0.18T.为进一步研究YB6纳米粒子电-声子相互作用机理，采用拉曼光谱对声子振动频率进行了测量，结合McMillan公式计算出YB6纳米粒子电-声子作用常数为A=0.63,该值远小于单晶块体YB6的1.01.为进一步解释其原因，采用高分辨透射电镜对晶体缺陷进行了详细表征.结果发现，晶体缺陷导致其声子振动频率的改变，从而降低了纳米YB6电-声子相互作用常数.光吸收结果表明YB6纳米粒子吸收谷波长为785nm,对可见光具有很强的穿透性.关键词：超导性；光吸收；YB6中图分类号：O511+.3文献标志码：A文章编号：1001—8735（2021）03—0204—06doi：10.3969/j.issn.1001—8735.2021.03.003众所周知，材料的宏观物理化学性能与微观结构密切相关[12].特别是当材料晶粒尺寸减小到纳米尺度后，纳米晶材料不仅具有亚稳态的特点，而且相比于粗晶材料展现出许多新奇的物理化学性能.与此同时,材料的纳米化会改变材料电子态密度及电-声子相互等物理量，从而会对超导及光学性能有很大的影响[34].因此，如何将纳米材料微观结构与宏观性能之间进行有效关联，将对材料新性能的发现和研究具有重要作用.在众多金属硼化物中，由于六硼化钇YB6具有第二高超导转变温度T c=&4K,故其超导性能受到广泛关注.目前关于这方面的研究主要集中于单晶YB6块体材料上[8],而对于YB6纳米离子超导性能研究未见报道.研究者们为了解释单晶块体超导机理及提高临界转变温度，系统研究了压强对YB6单晶块体晶体结构和声子振动的影响[912].结果发现，当压强从0增加至40GPa时，电子-声子相互作用常数从1.44减小到0.44.与此同时，相对应的超导转变温度也从&9K减小到1.4K,表明压强对电-声子作用具有很大影响.这项研究工作的一个重要提示是,YB6的纳米化是否会改变费米能级周围的电子态密度及电子-声子相互作用，从而展现出一些新的超导性能，这是本文的重要研究内容之一.此外，虽然YB6与LaB6具有相同立方晶体结构[13],但它是否同样具有对可见光的高穿透特性，是本论文另一个重要研究内容.目前国内外对纳米YB6超导性能及光吸收实验方面的系统研究未见报道.本文首次系统研究了YB6纳米粒子超导及光吸收性能.为进一步揭示材料微观结构与宏观性能之间的内在关联，采用高分辨透射电镜和拉曼光谱等测量手段对微观结构进行了有效表征，并对超导及光吸收机理进行探讨.收稿日期：2020-11-30基金项目：国家自然科学基金资助项目（51662034）；内蒙古自治区自然科学基金资助项目（2019LH05001）；内蒙古自治区留学人员创新创业启动基金资助项目.作者简介：王军（1992-），男，内蒙古阿拉善左旗人，在读硕士研究生，主要从事纳米稀土六硼化物光吸收及热发射性能研究.通讯作者：包黎红（1983—）,男，内蒙古兴安盟人，教授，博士，主要从事纳米金属硼化物物理性能研究,E-mail:baolihong@.第3期王军等：六硼化钇纳米粒子超导及光吸收性能研究-205-1材料与方法将无水氯化钇(YCl,纯度99.95%)和硼氢化钠(NaBH4,纯度98%)粉末在空气中按摩尔比为1：&8混合研磨10〜15min.将混合均匀的粉末放入压机中，在压强为10GPa下预压成块，将其装入石英管中进行真空烧结.反应温度为1100C,保温2h.由于固相反应后产物中有YBO s的杂相，故对烧结后产物分别使用稀盐酸，蒸馏水，无水乙醇等溶液进行多次清洗.采用场发射扫描电子显微镜(日立SU-8010)和X射线衍射仪(飞利浦PW1830,CuKa)对YB6纳米粒子的物相及形貌进行表征.采用PPMS测量仪对纳米YB6交流磁化率和临界磁场进行了测量，最低温度为1.8K.采用透射电子显微镜(FEITecnai F20S-Twin200kv)观察微观结构.拉曼散射由拉曼光谱仪(LabRamHR,波长：514.5nm,激光源:Ar+)进行测量.采用分光光度计(UH4150)在光源波长350〜2500nm范围内测量其光吸收。

First-principles calculations of electronic

First-principles calculations of electronic structure and optical properties of Boron-doped ZnO with intrinsicdefectsYen-Chun Peng,Chieh-Cheng Chen,Hsuan-Chung Wu ⇑,Jong-Hong LuDepartment of Materials Engineering,Ming Chi University of Technology,New Taipei 24301,Taiwana r t i c l e i n f o Article history:Received 11August 2014Received in revised form 27October 2014Accepted 27October 2014Available online 15November 2014Keywords:First principles B-doped ZnO Intrinsic defectElectronic structure Optical propertya b s t r a c tThis study adopted ﬁrst-principles calculations to evaluate the effects of intrinsic defects on the elec-tronic structure and optical properties of Boron-doped ZnO (BZO).Four types of defect were considered:non-defective (B Zn ),Zn vacancies (V Zn ),O vacancies (V O ),and interstitial Zn (Zn i ).Calculations of forma-tion energy illustrate that O-rich conditions tend to induce V Zn ,while O-poor conditions tend to induce V O and Zn i .With respect to electric properties,V Zn defects in BZO decrease carrier concentration as well as mobility,which consequently decreases the conductivity of BZO.The existence of V O or Zn i defects in BZO leads to n-type conductive characteristics and increases the optical band gap.The existence of Zn i defects in BZO also increases the effective mass,which decreases the mobility and conductivity of BZO.As for the optical properties,the introduction of V Zn to BZO leads to an increase in transmittance in the visible light region,but a decrease in the UV region.The introduction of intrinsic V O and Zn i defects to BZO leads to a signiﬁcant decrease in transmittance in the visible as well as UV regions.The calculated results were also compared with experimental data from the literature.Ó2014Elsevier B.V.All rights reserved.1.IntroductionZnO is an abundant,non-toxic material with a wide band gap (3.37eV)and transparent properties under visible light.ZnO has recently attracted considerable attention as an alternative for Tin-doped In 2O 3(ITO),which is currently the most common choice of transparent conductive oxide for a variety of applications [1,2].The resistivity of pure ZnO is on the order of 10À2X -cm,which is far higher than that of ITO (10À4X -cm order).A great deal of research has gone into enhancing the conductivity of ZnO through the addition of various dopants,which can mainly be divided into metals [3–5]and non-metals [6,7].B-doped ZnO (BZO)thin ﬁlm shows considerable promise for its superior photoelectric proper-ties and stability [8,9].Many groups have investigated the effects of process parameters on the electric and optical properties of BZO thin ﬁlm,with the aim of optimizing performance [7–13].Miyata et al.[7]indicated that the transmittance of BZO thin ﬁlm could be improved through the introduction of O 2gas from 0sccm to 10sccm.David et al.[10]reported that annealing temperature and atmosphere strongly affect the conductivity of BZO.Yang et al.[11]concluded that the low oxygen partial pressure during deposition increases the carrier density of oxygen vacancies,which leads to a strong decline in resistivity.However,resistivity in sam-ples produced under the high oxygen partial pressure is far higher than in samples deposited under low oxygen partial pressure,which suggests the existence of p-type carriers of Zinc vacancies in ﬁlms grown under high oxygen partial pressure.Patil et al.[12]synthesized B-doped ZnO powders using a mechanochemical method.The photoluminescence (PL)spectra at room temperature is an indication that a greater number of oxygen vacancies exist in nonmetal-doped ZnO,compared to pure ZnO.In the fabrication of BZO microrods,Yılmaz et al.[13]investigated the inﬂuence of B diffusion doping on optical emission and defect formation.PL spec-tra results revealed that the intensity of the deep level visible band emission increases with an increase in annealing time,which implies a signiﬁcant increase in the concentration of intrinsic defects.As outlined above,various process conditions inﬂuence the type and number of intrinsic defects with a subsequent inﬂuence on the electric and optical properties of BZO.Gaining a comprehensive understanding of the electric and optical characteristics of BZO would require in-depth study into the effects of intrinsic defects on the properties of BZO.First-principles calculations can provide information concerning materials at the microscopic scale to eluci-date the connection between structure and properties.It is well known that the use of conventional density functional theory/10.1016/j.optmat.2014.10.0580925-3467/Ó2014Elsevier B.V.All rights reserved.⇑Corresponding author at:Department of Materials Engineering,Ming Chi University of Technology,84Gungjuan Road,Taishan,New Taipei 24301,Taiwan.Tel.:+8862290898994675;fax:+886229084091.E-mail address:hcwu@.tw (H.-C.Wu).(DFT)leads to a considerable underestimation of the calculated band gap in ZnO [14–16].In our previous study [17],we used the DFT plus Hubbard U (DFT +U)method to avoid underestimat-ing the band gap.This approach reduced the differences in calcu-lated band gap and lattice constant to within 1%of the experimental values.The current study extended the utilization of the DFT +U method to calculate and analyze the effects of intrin-sic defects (V Zn ,V O ,and Zn i )on the formation energy,crystal struc-ture,electronic structure,and optical properties of BZO.These results clarify the connections among the fabrication process,structure,and properties of BZO,for use in determining the criteria for future material designs.2.Calculation methodsThis study considered a 2Â2Â2supercell of a Wurtzite ZnO,including 16Zn atoms and 16O atoms,as shown in Fig.1.A B-monodoping model was constructed by substituting one Zn atom (number 1site)with one B atom (B Zn model),which correspond to the B concentrations of 6.25at.%.We also considered three intrinsic defects in the B Zn structure,in which Zn vacancies(B Zn V Zn ),O vacancies (B Zn V O ),and interstitial Zn (B Zn Zn i )are repre-sented as 2,3,and 4,respectively.The V Zn ,V O ,and Zn i concentra-tions corresponds to doping levels of 6.25, 6.25,and 5.88at.%,respectively.The defect concentration could be reduced using a larger supercell for the real systems;however,this study was lim-ited with regard to computer resources.Therefore,the properties of the defects calculated from a 2Â2Â2ZnO supercell such as this could be used as qualitative analysis.1432ZnO BTable 1Formation energy and optimized structure of BZO with varying intrinsic defects.Formation energy (eV)Optimized structure O-richO-poor Zn–O (Å)B–O (Å)4V (%)ZnO –– 1.981––B Zn3.750.39 1.996 1.526À3.1B Zn V Zn 5.68 5.81 1.993 1.530À3.3B Zn V O 7.550.70 1.995 1.521À5.3B Zn Zn i10.513.662.0031.5174.74.5 eV2.15 eV3.25 eV4.68 eV4.41 eV(a)(b)(c)(d)Band structures of B-doped ZnO for (a)B Zn ,(b)B Zn V Zn ,(c)B Zn V O models.Y.-C.Peng et al./Optical Materials 39(2015)34–3935All models presented in this study were developed using CASTEP software [18].Structural optimization was performed on each model before calculating properties.The Monkhorst–Pack scheme [19]K-points grid sampling in the supercells was set at 4Â4Â2.Electron–ion interactions were modeled using the ultrasoft pseudo-potential method [20].The valence conﬁgurations of the atoms were 4s 23d 10for Zn,2s 22p 4for O,and 2s 22p 1for B.The elec-tron wave functions were expanded in plane wave with an energy cutoff of 380eV.In the structural optimization process,the change in energy,maximum force,maximum stress,and maximum displacement tolerances were set at 10À5eV/atom,0.03eV/Å,0.05GPa,and 0.001Å,respectively.The energy convergence crite-rion for the self-consistent ﬁeld was set at 10À6eV.To describe the electronic structures more accurately,we adopted the DFT +U d +U p method [21],in which the U d value for Zn-3d and the U p value for O-2p orbitals were set at 10and 7eV,respectively.The band structures,band gaps,and Zn-3d orbital locations of pure ZnO,which were used for the selection of U d and U p values,can be referenced in our previous research [17,22].3.Results and discussion 3.1.Optimized structureThe average bond lengths and volume difference ratio,as obtained from geometric optimization,are summarized in Table 1.In pure ZnO,each Zn atom is bonded to its three horizontal and one vertical oxygen neighbors.The average bond length of Zn-O is 1.981Åand optimized lattice constants are a =b =3.249Åandc =5.232Å,which are in agreement with the experimental values of a =b =3.249,c =5.206Å[23].Following the substitution of one B atom for one Zn atom (B Zn model),the Zn–O bond length is longer than that of B–O (1.526Å).This is because the B 3+radius (0.27Å)is smaller than that of Zn 2+(0.74Å)[24].Therefore,the cell volume of B Zn model shrinks,which is consistent with the experi-mental results [25].Clearly,the presence of Zn or O vacancies in BZO also leads to a shrinkage in volume.Conversely,the presence of interstitial Zn leads to a longer Zn–O length and expansion in volume.3.2.Formation energyTo examine the relative stability of BZO with intrinsic defects in neutral charge state,the defect formation energy can be expressed as follows:[26,27]E f ðD Þ¼E tot ðD ÞÀE tot ðZnO ÞþXn i l ið1Þwhere E tot (ZnO)and E tot (D )are the total energy in pure ZnO and in the defective systems,respectively.n i is the number of i atoms removed from or added to the supercell.If an atom is removed from the supercell,n i is positive,otherwise is negative.l i is the chemical potential of atom i .Formation energy depends on the growth envi-ronment during the preparation process,which can be O-rich or O-poor (Zn-rich).In thermo-dynamic equilibrium,D l Zn +D l O =D H f (ZnO),where D H f (ZnO)represents the formation enthalpy of ZnO.For the chemical potential of B,this study adopted the relation of 2D l B +3D l O 6D H f (B 2O 3)under O-rich conditions and l B =l B(bulk)under O-poor conditions,where D H f (B 2O 3)represents the(a)(b)(c)(d)V ZnV OZn iBZnOO density difference for (a)B Zn ,(b)B Zn V Zn ,(c)B Zn V O ,and (d)B Zn Zn i models.The red,orange,yellow,green,and interpretation of the references to color in this ﬁgure legend,the reader is referred to the web version 36Y.-C.Peng et al./Optical Materials 39(2015)34–39formation enthalpy of B2O3.D l i represents the chemical potential of atom i referred to as the elemental solid/gas of l i(bulk/molecule).It is well known that a defective structure with lower formation energy forms more readily and denotes an increased occurrence of defects.Table1presents a summary of the calculated formation energy of BZO with various intrinsic defects,based on the neutral charge state.With the existence of B Zn,E f(B Zn V Zn)<E f(B Zn V O)<E f (B Zn Zn i)under O-rich conditions,implying that O-rich conditions are more likely to induce the formation of V Zn,followed by V O and Zn i.Under O-poor conditions,E f(B Zn V O)<E f(B Zn Zn i)<E f (B Zn V Zn),which implies that O-poor conditions are more likely to induce the formation of V O.As a result,process conditions,such as O2gasﬂow rate and substrate temperature,largely determine the type of intrinsic defects that form in BZO during preparation. The occurrence of V O is far more likely under a low-O atmosphere, and V Zn is more likely to occur under a high-O atmosphere.For the sake of comparison,we also calculated the formation energy of a single intrinsic defect(V Zn and V O)in pure ZnO.The calculated values of E f(V Zn)and E f(V O)are3.09and4.33eV under O-rich conditions and6.58and0.84eV under O-poor conditions. Thus,we can see that the formation energy of a Zn vacancy from pure ZnO(E f(V Zn))is greater than that obtained from BZO(E f(B Zn V Zn)ÀE f(B Zn)=1.93eV under O-rich conditions and5.42eV under O-poor conditions).This demonstrates that Zn vacancies form more easily in BZO than in ZnO.These results are similar to those calculated for O vacancies,which implies that B-doping facilitates the formation of V Zn and V O.Previous studies [12]obtained similar results,indicating that a greater number of oxygen vacancies or defects exist in BZO than in pure ZnO.3.3.Electronic structureTo clarify the inﬂuence of intrinsic defects on the electronic structure of BZO,we calculated the band structure,difference in charge density,and density of states(DOS),as shown in Figs.2–4,respectively.In our previous study[17,22],the calculated band structure revealed a band gap of3.37eV in pure ZnO,which is in excellent agreement with values obtained in experiments.In the present study,we focus on the properties of BZO with intrinsic defects.Fig.2presents the band structures for BZO with various intrin-sic defect models.The Fermi level indicated by the dotted line was set to zero.Fig.2(a)shows the situation in which a Zn atom in pure ZnO is replaced by a B atom,in which the Fermi level shifts from the valence band(VB)maximum to the bottom of the conduction band(CB),resulting in a shallow donor level at the bottom of the CB.The shallow donor level at B doping causes an increase in the optical band gap to4.5eV at B concentration of6.25at.%,which is well known as the Burstein-Moss effect[28].The deﬁnitionof Fig.4.Density of states for(a)B Zn,(b)B Zn V Zn,(c)B Zn V O,and(d)B Zn Zn i models.optical band gap is from the top offor n-type semiconducting materials and the bottom of conduction band for materials.Similar tendencies were experiment-based studies[29,30].Asin the vicinity of B impurities appears atoms.The calculated Mulliken bond and B–O bonds are0.371and0.658, that a B–O bond is more covalent than Mulliken bond population represents characteristics).As shown in Fig.4(a),to the bottom of CB are the Zn-4s anda few O-2s and O-2p orbitals.The main extra electron toﬁll up the CBM.According to the results calculated regarded as an intrinsic defect under the B Zn V Zn model(Fig.2(b)),when donor levels coexist,the empty states produced trons from the B Zn donor level,resulting level as well as the formation of p-type band gap of B Zn V Zn can be narrowed to eration of conduction electrons requires energy from the Fermi level to the CB, be required in the B Zn model.Thus,in may lead to a decrease in the carrier known that mobility is related to the time.The relaxation time could not be software and was assumed as a defects in BZO.The followingeffects of the effective mass on thenear the Fermi level appear nearlyof carriers with a smaller curvature The larger effective mass is related toTherefore,V Zn defects in BZO reduce both carrier concentration as well as mobility,which consequently increases the resistivity of BZO.Fig.3(b)shows that the O atoms surrounding a Zn vacancy gain fewer electrons(green color),implying the occurrence of a number of empty states of O atoms.These empty states are O-2p orbitals near the Fermi level,as shown in Fig.4(b).V O and Zn i can be regarded as intrinsic defects in an O-poor environment.Fig.2(c)and(d)show the band structures in B Zn V O and B Zn Zn i models,in which n-type conductive characteristics appear and the optical band gap increases to4.68eV and4.41eV, respectively.One shallow donor state and one deep donor state occur in these two models.In the B Zn V O model,the deep donor level is probably the charge remaining in the oxygen vacancy (Fig.3(c));in the B Zn Zn i model,it is probably the covalence charge in the vicinity of the interstitial Zn atom(Zn i)(Fig.3(d)).Fig.4(c) and(d)show that the shallow donor level in both models origi-nated from B doping,whereas the deep donor level in the B Zn V O and B Zn Zn i models originated from the addition of V O and Zn i, respectively.The deep donor level in the B Zn V O model comprises mainly Zn and O atoms;however,in the B Zn Zn i model,it also includes B atom(B-2s and B-2p states).The shallow donor states provide conduction electrons;however,the deep donor states may contribute less to the increase in carrier concentration.Qual-itatively,the curvature of the energy band near the Fermi level in the B Zn Zn i model is smaller than that in the B Zn V O model.There-fore,Zn i defects present in BZO increase the effective mass,which may consequently decrease the mobility and conductivity of BZO.3.4.Optical propertiesThe optical properties can be described via the dielectric func-tion e(x)=e1(x)+i e2(x)[31].The imaginary part of the dielectric function e2(x)is calculated as follows:e2¼2e2pX e0Xk;v;cu ckuÁrj j u v k2d E ckÀE vkÀxÀÁð2Þwhere e is the electronic charge;X is the unit cell volume;u is the vector deﬁning the polarization of the incident electricﬁeld;x is the frequency of light;and u c k and u v k are the wave functions of the conduction and valence bands,respectively.Fig.5(a)shows the e2(x)of BZO with various intrinsic defects. In the B Zn model,a blue-shift in the intrinsic absorption edge occurred due to an enlarged optical band gap as compared with ZnO.The shallow donor levels mentioned in Section3.3resulted in an absorption peak at1.2eV.The absorption peaks in the intrin-sic defect models were as follows:B Zn V Zn(0.3eV),B Zn V O(1.5eV), and B Zn Zn i(0.9eV).These peaks resulted in enhanced absorption in the visible range.The peak of B Zn V Zn is the lowest,which can probably be attributed to the transition between occupied states and unoccupied states near the Fermi level.In the B Zn V O,and B Zn Zn i models,the absorption in the visible range may be the result of a shift from the shallow and deep donor occupied states to the unoccupied states of the conduction band.Fig.5(b)presents the transmittance of BZO under various defec-tive models.Table2presents the calculated values for average transmittance associated with each model under UV and visible light.It is should be noted that the calculated results were based on the doping levels of B(6.25at.%),V Zn(6.25at.%)V O(6.25at.%), and Zn i(5.88at.%).The average transmittance of pure ZnO is89.2 %in the visible region and65.6%in the UV region.Fig.5(b)shows that the incorporation of B into ZnO decreased transmittance in the range of800–1200nm(infrared region)and400–800nm(visible light region),but increased transmittance in the range of200–400nm(UV region),compared with pure ZnO.When V Zn was introduced to BZO,transmittance in the visible light region was Optical properties of BZO with varying intrinsic defects.(a)Imaginary dielectric function,(b)Transmittance.38increased,but transmittance in the UV region decreased,compared with BZO.When V O or Zn i was introduced to BZO,the transmit-tance of visible as well as UV light declined signiﬁcantly,which implies that transmittance could be reduced by employing a low-O environment for fabrication.This may explain why trans-mittance is enhanced by an increase in oxygen pressure during processing[7].4.ConclusionsThis study used the DFT+U method to investigate the inﬂuence of intrinsic defects on the formation energy,crystal structure,elec-tronic structure,and optical properties of BZO.Our results revealed that the formation energy of V Zn is lowest under O-rich conditions and the formation energy of V O is lowest under O-poor conditions. V Zn defects in BZO may decrease carrier concentration as well as mobility,which increases transmittance in the visible light region but decreases transmittance in the UV region.V O or Zn i defects in BZO lead to the appearance of n-type conductive characteristics, increasing the optical band gap,and decreasing transmittance in the visible light and UV regions.In addition,Zn i defects increase the effective mass,which may consequently decrease the mobility and conductivity of BZO.Conﬂict of interestsThe authors declare that there is no conﬂict of interests regard-ing the publication of this article.AcknowledgementsThis work was supported by the National Science Council in Taiwan(NSC102-2221-E-131-008),for which the authors are grateful.We also acknowledge the National Center for High-performance Computing for computer time and the use of its facilities.Reference[1]T.Minami,Semicond.Sci.Technol.20(2005)S35–S44.[2]L.Zhao,G.Shao,S.Song,X.Qin,S.Han,Rare Metals30(2011)175–182.[3]V.Bhavanasi,C.B.Singh,D.Datta,V.Singh,K.Shahi,S.Kumar,Opt.Mater.35(2013)1352–1359.[4]C.Huang,M.Wang,Z.Deng,Y.Cao,Q.Liu,Z.Huang,Y.Liu,W.Guo,Q.Huang,J.Mater.Sci.–Mater.Electron21(2010)1221–1227.[5]J.L.Zhao,X.W.Sun,H.Ryu,Y.B.Moon,Opt.Mater.33(2011)768–772.[6]L.Cao,L.P.Zhu,W.F.Chen,Z.Z.Ye,Opt.Mater.35(2013)1293–1296.[7]T.Miyata,Y.Honma,T.Minami,J.Vac.Sci.Technol.A25(2007)1193–1197.[8]X.L.Chen,B.H.Xu,J.M.Xue,Y.Zhao,C.C.Wei,J.Sun,Y.Wang,X.D.Zhang,X.H.Geng,Thin Solid Films515(2007)3753–3759.[9]D.W.Kang,J.Y.Kwon,D.J.Lee,M.K.Han,J.Electrochem.Soc.159(2012)H61–H65.[10]C.David,T.Girardeau, F.Paumier, D.Eyidi, croix,N.Papathanasiou,B.P.Tinkham,P.Gu´erin,M.Marteau,J.Phys.:Condens.Matter23(2011)334209.[11]H.Yang,X.Xu,X.Zhou,Y.Ma,J.Dong,T.Wang,J.Miao,Y.Jiang,J.Mater.Sci.47(2012)6513–6516.[12]A.B.Patil,K.R.Patil,S.K.Pardeshi,J.Solid State Chem.184(2011)3273–3279.[13]S.Yılmaz,J.Nisar,Y.Atasoy,E.McGlynn,R.Ahuja,M.Parlak,E.Bacaksız,Ceram.Int.39(2013)4609–4617.[14]L.Li,W.Wang,H.Liu,X.Liu,Q.Song,S.Ren,J.Phys.Chem.C113(2009)8460–8464.[15]X.Qu,W.Wang,S.Lv,D.Jia,Solid State Commun.151(2011)332–336.[16]G.Ji,Z.Gu,M.Lu,J.Zhou,S.Zhang,Y.Chen,Physica B405(2010)4948–4950.[17]H.C.Wu,Y.C.Peng,C.C.Chen,Opt.Mater.35(2013)509–515.[18]M.D.Segall,P.J.D.Lindan,M.J.Probert,C.J.Pickard,P.J.Hasnip,S.J.Clark,M.C.Payne,J.Phys.:Condens.Matter.14(2002)2717–2744.[19]H.J.Monkhorst,J.D.Pack,Phys.Rev.B13(1976)5188–5192.[20]D.Vanderbilt,Phys.Rev.B41(1990)7892–7895.[21]X.Ma,B.Lu,D.Li,R.Shi,C.Pan,Y.Zhu,J.Phys.Chem.C115(2011)4680–4687.[22]H.C.Wu,Y.C.Peng,T.P.Shen,Materials5(2012)2088–2100.[23]R.D.Vispute,V.Talyansky,S.Choopun,R.P.Sharma,T.Venkatesan,Appl.Phys.Lett.73(1998)348–350.[24]D.R.Lide,CRC Handbook of Chemistry and Physics,87th ed.,Taylor andFrancis,Philadelphia,2006.[25]X.G.Xu,H.L.Yang,Y.Wu,D.L.Zhang,S.Z.Wu,Appl.Phys.Lett.97(2010)232502.[26]A.Janotti, C.G.Van de Walle,Phys.Rev.B:Condens.Matter.76(2007)165202.[27]T.Guo,G.Dong,Q.Chen,X.Diao,F.Gao,J.Phys.Chem.Solids75(2014)42–47.[28]P.V.Kamat,N.M.Dimitrijevic, A.J.Nozik,J.Phys.Chem.93(1989)2873–2875.[29]L.Gao,Y.Zhang,J.M.Zhang,K.W.Xu,Appl.Surf.Sci.257(2011)2498–2502.[30]B.N.Pawar,S.R.Jadkar,M.G.Takwale,J.Phys.Chem.Solids66(2005)1779–1782.[31]R.Chowdhury,S.Adhikari,P.Rees,Physica B405(2010)4763–4767.Table2Average transmittance of BZO with varying intrinsic defects.UV region(%)Visible region(%)ZnO65.689.2B Zn91.175.6B Zn V Zn68.186.8B Zn V O52.053.2B Zn Zn i59.256.9Y.-C.Peng et al./Optical Materials39(2015)34–3939。

压力对CrSi2弹性及弹性各向异性影响的研究

压力对 CrSi2弹性及弹性各向异性影响的研究摘要：本文采用密度泛函理论计算了压力下CrSi2的声子谱、电子结构、弹性常数和弹性各向异性。

结果表明，CrSi2的晶体结构参数随着压力的增加而减小。

声子色散曲线在不同外加压力下没有出现虚频，说明它们都是动力稳定的。

弹性常数也符合Born准则，表明机械学稳定性。

CrSi2的弹性常数、体积模量、剪切模量、杨氏模量、泊松比和B/G都随压力的增加而增加，表明适当的外界压力可以加强CrSi2的延展性，从而让其在工业应用上有望成为具有良好前景的可塑性金属合金的备选材料。

热容量随着压力的增大而轻微的减小。

关键词：密度泛函理论；弹性性能；各向异性1.引言随着科技的发展，现代工业对材料的强度与延展性的要求逐步提升，过渡金属铬化物因其熔化温度高、化学稳定性良好、热导率高、优益的耐高温抗氧化的性能以及相对较低的密度，令其有望作用于高温结构[1-3]，这也是近几年的研究热点之一。

CrSi2可采用自蔓延高温合成法[4]和水冷铜模激光炉制备[5]。

CrSi2在室温下具有较低的断裂韧性，在高温(>1200℃)下强度和蠕变抗力有限，但是压力对于弹性各向异性的影响力尚不清楚[6]。

弹性性能与材料的热容量、热膨胀系数等基本性能有着密切的联系。

这些特征可以通过第一性原理[7]方法得到。

在以往的文献中，许多研究者在运用实验测量和密度泛函理论计算相互使用的方法来研究CrSi2的晶体结构、力学性能、电子结构、光学性质[6,7,8,9]。

为更好地理解压力下CrSi2 的弹性各向异性从而在高压环境中应用是极为重要的。

本文系统地研究了CrSi2在高压下的结构、声子谱、弹性性能及弹性各向异性，以期探索外界压力对CrSi2弹性性能及弹性各向异性的影响，从而开发设计出具有抗压力的高温合金材料。

2计算方法本文基于密度泛函理论中的赝势平面波的第一性原理方法，采用剑桥系列总能量包(CASTEP)代码[10-14]进行模拟计算。

ZnS宽禁带半导体毕业设计

宽禁带半导体ZnS物性的第一性原理研究摘要硫化锌（ZnS）是一种新型的II-VI族宽禁带电子过剩本征半导体材料，其禁带宽度为3.67eV,具有良好的光致发光性能和电致发光性能。

在常温下禁带宽度是3.7eV，具有光传导性好，在可见光和红外范围分散度低等优点。

ZnS和基于ZnS的合金在半导体研究领域己经得到了越来越广泛的关注。

由于它们具有较宽的直接带隙和很大的激子结合能，在光电器件中具有很好的应用前景。

本文介绍了宽禁带半导体ZnS目前国内外的研究现状及其结构性质和技术上的应用。

阐述了密度泛函理论的基本原理，对第一性原理计算的理论基础作了详细的总结，并采用密度泛函理论的广义梯度近似（GGA）下的平面波贋势法，利用Castep软件计算了闪锌矿结构ZnS晶体的电子结构和光学性质。

电子结构如闪锌矿ZnS晶体的能带结构，态密度。

光学性质如反射率，吸收光谱，复数折射率，介电函数，光电导谱和损失函数谱。

通过对其能带及结构的研究，可知闪锌矿硫化锌为直接带隙半导体，通过一系列对光学图的分析，可以对闪锌矿ZnS的进一步研究做很好的预测。

关键词ZnS;宽禁带半导体；第一性原理；闪锌矿结构-I -First-principles Research on Physical Properties of Wide Bandgap Semiconductor ZnSAbstractZinc sulfide (ZnS) is a new family of ll-VI wide band gap electronic excess in tri nsic semic on ductor material with good photolu min esce nee properties and electroluminescent properties. At room temperature band gap is 3.7 eV, and there is good optical transmission in the visible and infrared range and low dispersi on. ZnS and Zn S-based alloy in the field of semic on ductor research has bee n paid more and more atte nti on. Because of their wide direct ban dgap and large excit on binding en ergy, the photovoltaic device has a good prospect.This thesis describes the current research status and structure of nature and tech ni cal applicati ons on wide band gap semic on ductor ZnS. Described the basic principles density functional theory, make a detailed summary for the basis of first principles theoretical calculations, using the density functional theory gen eralized gradie nt approximati on (GGA) un der the pla ne wave pseudopote ntial method, calculated using Castep software sphalerite ZnS crystal structure of electronic structure and optical properties. Electronic structures, such as sphalerite ZnS crystal band structure, density of states. Optical properties such as reflecta nee, absorpti on spectra, complex refractive in dex, dielectric function, optical conductivity spectrum and the loss function spectrum. Band and the structure through its research known as zin cble nde ZnS direct band gap semic on ductor,Through a series of optical map an alysis, can make a good predicti on for further study on zin cble nde ZnS.Keywords ZnS; Wide ban dgap semic on ductor; First-pri nciples; Zin cble nde structure-2-目录摘要 (I)Abstract (II)第1章绪论 ........................................................... 1..1.1 ZnS半导体材料的研究背景 ....................................... 1.1.2 ZnS的基本性质和应用........................................... 1.1.3 ZnS材料的研究方向和进展 (3)1.4 ZnS的晶体...................................................... 4.1.4.1 ZnS晶体结构 ............................................... 4.1.4.2 ZnS的能带结构............................................. 5.1.5 ZnS的发光机理................................................. 6.1.6研究目的和主要内容.............................................. 7.2.1相关理论......................................................... 9.2.1.1密度泛函理论 (9)2.1.2交换关联函数近似........................................... 1.12.2总能量的计算 (13)2.2.1势平面波方法 (14)2.2.2结构优化 (16)2.3 CASTEP软件包功能特点........................................ 1.8第3章ZnS晶体电子结构和光学性质.................................... 1.93.1闪锌矿结构ZnS的电子结构 (19)3.1.1晶格结构 (19)3.1.2能带结构 (20)3.1.3态密度 (21)3.2闪锌矿ZnS晶体的光学性质 (24)结论 (30)致谢 (31)参考文献 (32)附录A (33)附录B (45)-ill -第1章绪论1.1 ZnS半导体材料的研究背景Si是应用最为广泛的半导体材料，现代的大规模集成电路之所以成功推广应用，关键就在于Si半导体在电子器件方面的突破。

氮化镓最高密度

氮化镓的最高密度1. 引言氮化镓（GaN）是一种重要的半导体材料，具有广泛的应用前景。

其最高密度是氮化镓作为固体的质量除以固体体积的比值，是一个重要的物理参数。

本文将探讨氮化镓的最高密度及其相关性质。

2. 氮化镓的基本介绍氮化镓是由镓原子和氮原子组成的化合物，化学式为GaN。

它具有良好的热稳定性、高电子迁移率和宽的能带隙，使其成为一种重要的半导体材料。

氮化镓的最高密度是指在固态下，氮化镓的质量除以其体积所得到的数值。

3. 氮化镓的晶体结构氮化镓晶体结构属于六方晶系，空间群为P63mc。

每个氮化镓晶胞中包含2个氮原子和2个镓原子。

氮化镓晶体具有六边形的晶格结构，其中氮原子和镓原子交替排列。

4. 氮化镓的密度计算氮化镓的密度可以通过实验测量或理论计算得到。

理论计算常用的方法包括密度泛函理论（DFT）等。

通过计算得到的氮化镓密度可以与实验测量值进行比较，以验证计算方法的准确性。

5. 氮化镓的最高密度值根据实验测量和理论计算，氮化镓的最高密度约为6.15克/立方厘米。

这个数值是在标准温度和标准压力下得到的。

氮化镓的最高密度与其晶体结构和原子间的相互作用有关。

6. 氮化镓最高密度的影响因素氮化镓的最高密度受多种因素的影响，包括晶体结构、温度和杂质等。

晶体结构的改变会导致氮化镓的密度变化。

温度的升高会使晶体膨胀，从而降低氮化镓的密度。

杂质的存在也会对氮化镓的密度产生影响。

7. 氮化镓最高密度的应用氮化镓的最高密度是其重要的物理性质之一，对于材料的应用具有重要意义。

氮化镓广泛应用于光电子器件、功率器件、射频器件和光学器件等领域。

其高密度使得氮化镓能够在小尺寸器件中发挥重要作用。

8. 氮化镓最高密度的发展趋势随着科学技术的不断进步，人们对氮化镓最高密度的研究也在不断发展。

研究人员通过改变氮化镓的晶体结构、控制杂质含量等手段，努力提高氮化镓的最高密度。

同时，新的计算方法和实验技术的应用也为研究提供了更多的可能性。

镧系掺杂ZnO的电子结构和光学性质

doi: 10.12052/gdutxb.200121镧系掺杂ZnO的电子结构和光学性质白玲玲1，林志萍1，董华锋1，吴福根2（1. 广东工业大学物理与光电工程学院广东广州 510006；2. 广东工业大学材料与能源学院广东广州 510006）摘要: 通过第一性原理计算研究了镧系元素掺杂ZnO的电子结构和光学性质。

结果表明: 单层ZnO中掺杂形成能低于体ZnO的形成能。

较Zn原子而言, 具有更大原子半径的镧系原子的引入使得掺杂后的ZnO的晶格常数变大。

镧系元素的4f电子与O的2s和Zn的3p、4s轨道电子的杂化使非磁性的ZnO在掺入单个镧系原子后呈现出一定的铁磁性。

镧系元素掺杂ZnO使体系的价带和导带之间出现了杂质能级, 这使带隙减小从而提高了ZnO的导电能力; Eu/La/Ce掺杂ZnO的光吸收谱在近红外区域出现了新的吸收峰。

随Eu/Ce-O i双缺陷的形成, 氧间隙明显地改变了ZnO的光学性质。

关键词: 镧系掺杂ZnO；电子结构；光学性质；缺陷对中图分类号: O469 文献标志码: A 文章编号: 1007–7162(2021)02–0066–07Electronic Structure and Optical Properties ofLanthanide Doping ZnOBai Ling-ling1, Lin Zhi-ping1, Dong Hua-feng1, Wu Fu-gen2(1. School of Physics and Optoelectronic Engineering, Guangdong University of Technology, Guangzhou 510006, China;2. School of Materials and Energy, Guangdong University of Technology, Guangzhou 510006, China)Abstract: The electronic structure and optical properties of lanthanide doping ZnO are investigated by first-principles calculation. The formation energy of lanthanide doping in SL(single-layer)-ZnO structure that is lower than in bulk-ZnO structure. The magnetism of ZnO will change along with single lanthanide atom doping from nonmagnetic to ferromagnetic, which roots in orbital hybridization of 4f of lanthanide, O-2p and Zn-3p and-4s.Impurities level formed in CBM (conduction-band minimum) or VBM (valence-band maximum) along with lanthanide doped will reduce the band gap and improve the conductivity of materials. For Eu/La/Ce doping ZnO, new absorbing peak will be formed in infrared regions, and Eu/Ce-O i double defects will obviously improve its optical properties.Key words: lanthanide doping ZnO; electronic structure; optical properties; defect pair由于ZnO具有宽的直接带隙和大的激子结合能，其在光电设备方面吸引了越来越多的注意力[1–4]。

纤锌矿GaN的电子结构与光学性质的第一性原理计算【毕业作品】

BI YE SHE JI（20 届）纤锌矿GaN的电子结构与光学性质的第一性原理计算摘要：半导体材料的研究是一个很大的热门的方向，它在如今各种半导体器件以及光电子器件中有着广泛的前景与用途。

本文以纤锌矿结构的GaN为研究对象对它进行特性的研究。

我们采用理论计算的方法对其进行分子动力学模拟，从而计算得出它的电子结构性质与一系列光学的性质。

其中理论计算的主要是基于量子力学基础上的理论，所以被称为第一性原理的计算。

在得到纤锌矿GaN的一系列性质以后我们还对它进行了简单的Al原子的掺杂以及特性的分析。

关键词：GaN，光电性质，第一性原理Abstract:The study of semiconductor materials is a much discussed topic,and it now has a board prospect and applications in semiconductor devices and optoelectronic devices. In this paper, GaN wurtzite structure as the research object to study the characteristic of it. We adopt the method of theoretical calculation on the molecular dynamics simulation, and calculated its electronic structure properties and a series of optical properties. This theoretical calculation is mainly based on the theory of quantum mechanics, so called the first principles calculation. After getting a series of properties of wurtzite GaN,we also have simple of Al doping and then analyze of the characteristics of Al atoms.Keywords:GaN, optical and electrical properties, first principles1．绪论1.1 引言随着人们对电子产品的需求，对于半导体材料的要求愈加的苛刻，新材料逐渐被发现研究以及应用。

Sr_(2)MoBO_(6)(B=Os、Re、W)的电子结构与光学性质的第一性原理

渊区内选取 1 000 个 k 点。自洽计算的能量收敛判据为 10 - 5 Ry / f. u. 。
为了准确地描述 d 电子的库伦关联作用,计算采用“ 旋转不变” 法对 Mo 4d 和 B 5d 轨道进行了“ + U” 计
算 [15] 。通过对一系列合理 U 值的测试( Mo:2 ~ 6 eV;B:1 ~ 4 eV) ,发现得到的主要结论是一致的。因此,选
质进行理论计算,并分析能带结构与介电函数、吸收系数之间的联系,以期得到在可见光波段具有宽光谱、强
吸收的双钙钛矿材料。
1 计算方法
本文采用 VASP 软件包 [16-17] 对 Sr2 MoBO6 ( B = Os、Re、W) 进行晶体结构优化。其中电子间的交换关联
能由广义梯度近似( GGA) 的 PBE 泛函 [18] 处理,电子与离子间的相互作用由投影缀加平面波( PAW) [19] 方法
( College of Science, Qiqihar University, Qiqihar 161000, China)
Abstract:Double perovskite oxides Sr2 MoBO6 ( B = Os,Re,W) have been predicted to be half metals with high magnetic
2 结果与讨论
2. 1 晶体结构与电子结构
Sr 2 MoBO 6 ( B = Os、 Re、 W) 的晶体结构均为立
方结构, 空间群为 Fm-3 m ( No. 225 ) , 晶格常数约
为0 . 8 nm,结构示意图如图 1 所示。三种晶体的
以发现,三种 Mo 基化合物的磁转变温度均高于室温,且 Sr2 MoWO6 和 Sr2 MoOsO6 展现出半金属性质。另外,

BiFeO3及Bi2FeCrO6的电子结构和光学特性

图５ＢＦＯ（ａ）和ＢＦＣＯ（ｂ）的复介电函数Ｆｉｇ．５ＴｈｅｄｉｅｌｅｃｔｒｉｃｆｕｎｃｔｉｏｎｏｆＢＦＯ（ａ）ａｎｄＢＦＣＯ（ｂ）
３．２光学性质图５（ａ）、（ｂ）分别给出了沿ＢＦＯ和ＢＦＣＯ的（００１）方向入射线偏振光时的介电函数随能量变化曲线。
在用ＣＡＳＴＥＰ计算时，处理计算与实验误差通常的方法是使用剪刀算符。图５（ａ）为ＢＦＯ的介电函数，剪刀因子取０．７ｅＶ（仍然是ＢＦＯ的带隙计算值１．８ｅＶ与实验值２．５ｅＶ间差值）。图５（ｂ）为ＢＦＣＯ的介电函数，关于ＢＦＣＯ带隙及光学性质试验方面没有给出实验值，在此取与ＢＦＯ相同的剪刀因子。从图５可以看出，当频率为零或很低时，介电函数随能量缓慢变化，这时介电函数的虚部为０，其中ＢＦＯ的电介电常数占（０）＝６，ＢＦＣＯ的介电常数８（０）＝６．５，比文献［４］给出的ＢａＴｉＯ，（５．１２），ＳｒＴｉＯ，（４．９８）和ＰｂＴｉＯ。（５．３４）具有更大的介电常数。随着频率增加，介电函数取复数形式（虚部不为０）占（∞）＝占，（∞）和：（叫）。虚部ｓ：（山）代表介质损耗，它是由于分子的电极化过程跟不上外场变化而引起的。从图５（ａ），（ｂ）可以看出ＢＦＯ和ＢＦＣＯ的虚部都有７个明显的特征峰，对于ＢＦＯ来说，能量大于能隙２．５ｅＶ后占：（０９）≠ｏ，其中对应Ａ（５ｅＶ）主要来自０２ｐ到Ｆｅ３ｄ的电子跃迁，Ｂ（７．２ｅＶ），Ｃ（９．１ｅＶ），Ｄ（１３．４ｅＶ），Ｅ（１５．５ｅＶ）主要来自０２ｐ到Ｂｉ６ｐ的电子跃迁，Ｆ（２６．７ｅＶ），Ｇ（２８．７ｅＶ）主要来自内电子０２ｓ到Ｂｉ６ｓ的电子跃迁Ｈ。。而ＢＦＣＯ介电常数的虚部与ＢＦＯ有明显的不同，当能量大于能隙１．７ｅＶ时，８：（∞）≠０，从分态密度图也可以看出由于ｃｒ的掺人，使Ｆｅ３ｄ电子态密度分布向低能方向移动，拐点峰Ａ（２．９ｅＶ）归结为来自０２ｐ到Ｆｅ３ｄ、Ｃｒ３ｄ的电子跃迁，特征峰Ｂ（５．１ｅＶ）、Ｃ（６．４ｅＶ）、Ｄ（７．８ｅＶ）主要来自０２ｐ到Ｂｉ６ｐ和Ｃｒ３ｄ的电子跃迁，Ｅ（１５．１ｅＶ）主要来自０２ｐ到Ｃｒ３ｄ的电子跃迁，Ｆ（２６．７ｅＶ）、Ｇ（２８．３ｅＶ）主要来自０２ｓ内电子到Ｂｉ６ｓ和Ｃｒ３ｄ的电子跃迁。上述分析表明ｃｒ的掺入对ＢＦＯ的介电函数有较大的影响。

N掺杂K2Ti6O13电子结构和光学性质的第一性原理计算

D O I :10.3969/j.i s s n .1001-5337.2023.4.087 *收稿日期:2022-06-20基金项目:山东省高等学校青创人才引育计划项目.第一作者:刘保通,男,1980-,实验师;研究方向:物理学;E -m a i l :l b a o t o n g@q f n u .e d u .c n .通信作者:路洪艳,女,1982-,博士,教授;研究方向:凝聚态理论与计算;E -m a i l :h yl u @q f n u .e d u .c n .N 掺杂K 2T i 6O 13电子结构和光学性质的第一性原理计算*刘保通①, 李牙平②, 路洪艳②(①曲阜师范大学网络信息中心;②曲阜师范大学物理工程学院,273165,山东省曲阜市) 摘要:采用第一性原理计算,对N 掺杂前后六钛酸钾(K 2T i 6O 13)的电子结构和光学性质进行了研究.结果分析表明:N 掺杂后K 2T i 6O 13的带隙值略有减小且在其禁带中引入了杂质能级,由于杂质能级的作用使得N 掺杂后的K 2T i 6O 13吸收带边红移至可见光区,并在可见光范围内吸收强度出现明显的增强.关键词:N 掺杂;电子结构;光学性质;吸收红移中图分类号:O 469 文献标识码:A 文章编号:1001-5337(2023)04-0087-040 引言目前环境污染和能源短缺日益加剧,太阳能作为一种清洁可持续的绿色能源受到人们的广泛关注.其中半导体光催化技术逐渐被应用于太阳能转化和利用中[1-3].六钛酸钾(K 2T i 6O 13)是一种优异的光催化材料[4-6],因其具有优异的物理化学性能和较低的制备成本[7-9],引起研究人员研究的热潮.然而,K 2T i 6O 13带隙值较大(3.48e V )[10],对太阳光的利用率极低.为了使K 2T i 6O 13对太阳光的响应范围增大,同时,抑制光生载流子复合,有必要对其进行一定的改性研究.大量的报道指出通过N 掺杂取代T i O 2中的O可实现T i O 2对可见光的响应[11-13],基于此,本研究通过N 掺杂取代K 2T i 6O 13中的O 对K 2T i 6O 13进行改性.本文应用第一性原理计算,研究N 掺杂前后钛酸钾电子结构和光学性质的变化,探讨N 掺杂对K 2T i 6O 13光吸收能力的影响及其改性的内在机理.1 理论模型与计算方法图1为N 掺杂前后K 2T i 6O 13(1ˑ2ˑ1)超胞结构模型.本征的K 2T i 6O 13是单斜晶系,空间群为C 2/m ,每个晶胞由2个K 2T i 6O 13分子单元组成,共有42个原子[14],原子坐标见文献[15].在N 掺杂模型中,用一个N 原子取代K 2T i 6O 13中的一个O 原子.图1 (a )K 2T i 6O 13(1ˑ2ˑ1)超胞结构 (b )N 掺杂的K 2T i 6O 13超晶胞结构本文的计算通过M a t e r i a l sS t u d i o 软件中的C a s t e p 模块完成[16].首先,对K 2T i 6O 13的超胞结构进行结构优化;其次,对K 2T i 6O 13的电子结构和光学性质进行计算并且分析.本文中电子间的交换关联能采用的是基于密度泛函理论下的广义梯度近似中的P W 91形式,平面波截断能设为340e V ,布里渊区的积分采用2ˑ3ˑ3的k 点设置.计算中考虑的各元素价电子为O :2s 22p 4,T i :3s 23p 63d 24s 2,K :3s 23p 64s 1和N :2s 22p 3.2 结果与分析2.1 几何优化结果N 掺杂前后K 2T i 6O 13超胞模型几何优化后得到的晶胞参数见表1.由表1可知,本征的K 2T i 6O 13第49卷第4期2023年10月曲阜师范大学学报J o u r n a l o f Q u f u N o r m a l U n i v e r s i t yV o l .49 N o .4O c t .2023Copyright ©博看网. All Rights Reserved.晶格基矢与实验值[10]和其他理论计算值[17]相符,这证明我们的计算方法是正确合理的.N 掺杂后的K 2T i 6O 13的晶格基矢和体积都有增加,这主要因为N 原子的半径比O 原子的半径大且T i -N 键的键长较T iO 键的键长长.表1 几何优化后N 掺杂前后K 2T i 6O 13的超晶胞参数和键长P a r a m e t e r sA v e r a g e b o n d l e n gt h /Åa /Åb /Åc /ÅV /Å3T i O T i N K 2T i 6O 13[17]15.8507.6169.2431098.6372.004N -d o pe d 15.8207.6349.2521100.1572.1042.2 电子结构在图2中可以看到N 掺杂前后K 2T i 6O 13的能带结构.据图2(a )知,K 2T i 6O 13的带隙为2.834e V ,这和已有的计算结果相符[17].与实验值3.48e V [10]相比,计算值偏小,但计算结果的相对值是有意义的,可以将其视为一种有效的近似方法从而对材料的电子结构进行分析.从图2(b)可以看出,经N 掺杂后K 2T i 6O 13带隙变为2.815e V.与本征的K 2T i 6O 13相比,它的带隙值降低了0.019e V ,这有利于其光吸收边的红移.且其价带顶附近出现了杂质能级,杂质能级与导带底的能量差为2.410e V ,因此,N 的掺杂将实现K 2T i 6O 13对可见光的吸收.此外,此杂质能级为受主能级可抑制载流子的复合,进而提高其光催化性能.图2 (a )K 2T i 6O 13和(b )N 掺杂K 2T i 6O 13的能带结构图3为N 掺杂前后K 2T i 6O 13的态密度图.由图3(a )可知,纯K 2T i 6O 13的价带和导带基本上是由O2p 和T i 3d 态组成,由此可以看出O 和T i 之间可能存在强烈的相互作用.K 离子在T i O 6八面体组成的隧道状结构处以游离态存在,T i 和O 间的强相互作用使得K 2T i 6O 13结构具有很强的稳定性[15,18,19].由图3(b )和图3(c )可知,N 掺杂后在K 2T i 6O 13价带顶附近出现的杂质能级主要由O2p ,T i 3d 和N2p 轨道杂化而成.图3 (a )K 2T i 6O 13的分态密度;(b )N 掺杂K 2T i 6O 13的分态密度;(c )部分放大的N 掺杂K 2T i 6O 13的分态密度88 曲阜师范大学学报(自然科学版) 2023年Copyright ©博看网. All Rights Reserved.2.3 光学性质由于K 2T i 6O 13带隙的计算值比实验值偏小,为了使计算结果与实验结果相近,本文使用剪刀算符对光学性质的计算结果进行了修正,修正值取K 2T i 6O 13带隙的实验值与计算值的差值0.616e V.图4为N 掺杂前后K 2T i 6O 13介电函数虚部随光子能量变化曲线图.由图4可知在高能处,N 掺杂前后K 2T i 6O 13都有一个较大的峰值,这源于价带中的电子到导带的跃迁.在低能方向K 2T i 6O 13的介电函数虚部值基本为零,而N 掺杂后K 2T i 6O 13在低能范围出现了几个峰值,这源于其杂质能级中电子的跃迁.图4 K 2T i 6O 13和N 掺杂K 2T i 6O 13的介电函数虚部随光子能量变化曲线图由图5可知,K 2T i 6O 13对光的吸收范围约在0~400n m ,这个结果与已有的实验研究结果相近[20,21],再次证明我们的计算是合理的.N 掺杂后K 2T i 6O 13吸收边略有红移,这是由于其带隙值略微减小.N 掺杂后K 2T i 6O 13在350~400n m 的吸收强度明显增加,且实现了其对可见光的吸收,这是因为带隙中的杂质能级既可降低电子跃迁所需能量,又可提高光生载流子的效率.图5 K 2T i 6O 13和N 掺杂K 2T i 6O 13的吸收光谱3 结论通过第一性原理计算了K 2T i 6O 13在N 掺杂前后的能带结构㊁态密度㊁介电函数虚部和吸收光谱.计算结果表明,K 2T i 6O 13在N 掺杂后带隙变小,并且在能带中出现了杂质能级从而实现了N 掺杂后的K 2T i 6O 13对可见光的吸收.能带中的杂质能级可以抑制光生载流子的复合,使得光催化反应的效率提高.我们的计算结果为实验上研究K 2T i 6O 13光催化性能改性提供了重要的理论依据.参考文献:[1]H EY R ,Y A N FF ,Y U H Q ,e t a l .H y d r o ge n p r o d u c -t i o n i na l i g h t -d r i v e n p h o t o e l e c t r o c h e m i c a l c e l l [J ].A p pl E n e r g,2014,113:164.[2]O S T E R L OH F E .I n o r g a n i c m a t e r i a l sa sc a t a l ys t s f o r p h o t o c h e m i c a ls p l i t t i n g of w a t e r [J ].C h e m M a t e r ,2008,20:35.[3]R A NJ ,Z HA N GJ ,Y UJ ,e t a l .E a r t h -a b u n d a n t c o c a t a -l y s t s f o r s e m i c o n d u c t o r -b a s e d p h o t o c a t a l y t i cw a t e r s pl i t -t i n g [J ].C h e mS o cR e v ,2014,43:7787.[4]HA K U T A Y ,HA Y A S H IH ,A R A IKJ .H yd r o t he r m a l s y n t h e s i s of p h o t o c a t a l y s t p o t a s s i u m h e x a t i t a n a t e n a n o w i r e su n d e r s u pe r c r i t i c a l c o n d i t i o n s [J ].M a t e rS c i ,2004,39:4977.[5]K A P U S U ZD ,K A L A Y Y E ,P A R KJ ,e ta l .S yn t h e s i s a n d c h a r a c t e r i z a t i o no f h y d r o t h e r m a l l ygr o w n p o t a s s i u m t i t a n a t en a n o w i r e s [J ].JC e r a m P r o c e s sR e s ,2015,16:291.[6]L IY ,Y U H ,Y A N G Y ,e ta l .S yn t h e s i so f p o t a s s i u m h e x a t i t a n a t ew h i s k e r sw i t hh i g ht h e r m a l s t a b i l i t y f r o m T i -b e a r i n g e l e c t r i ca r cf u r n a c e m o l t e ns l a g [J ].C e r a m I n t ,2016,42:11294.[7]L IGL ,WA N G G H ,HO N GJ M.S yn t h e s i sa n dc h a r -a c t e r i z a t i o no fK 2T i 6O 13w h i s k e r sw i t h d i a m e t e r o n n a n -o m e t e r s c a l e [J ].JM a t e r S c i ,1999,18(22):1865-1867.[8]R AM íR Z -S A L G A D OJ ,D J U R A D OE ,F A B R YPJ .E u rS y n t h e s i s o f s o d i u m t i t a n a t e c o m p o s i t e s b y s o l -ge l m e t h o df o r u s e i ng a s p o t e n t i o m e t r i c s e n s o r s [J ].C e r a m S o c ,2004,24:2477.[9]P E S C A T O R IM ,Q U O N D AM C A R L O C .S yn t h e s i s a n d c h a r a c t e r i z a t i o no fK 2T i 6O 13na n o w i r e s [J ].C h e m P h y s L e t t ,2003,376:726.[10]MOH D A S ,V I S HA LSC ,AM E E R A.C o m pa r a t i v e s t u d y o f p o t a s s i u m h e x a t i t a n a t e (K 2T i 6O 13)w h i s k e r s p r e p a r e db y s o l -ge l a n ds o l i ds t a t e r e a c t i o nr o u t e s [J ].98第4期刘保通,等:N 掺杂K 2T i 6O 13电子结构和光学性质的第一性原理计算Copyright ©博看网. All Rights Reserved.A p p l S u r f S c i,2012,258:7354-7358.[11]A S A H IR,MO R I K AWA T,OHWA K IT,e t a l.V i s i-b l e-l i g h t p h o t oc a t a l y s i s i nn i t r o g e n-d o pe dt i t a n i u m o x-i d e s[J].S c i e n c e,2001,293(5528):269-271.[12]W E NPC,J IW W,Z HO N G H,e t a l.S y n t h e s i s,c h a r-a c t e r i z a t i o na n d p h o t o-c a t a l y t i c p e r f o r m a n c eo f m e s o-p o r o u s S i-Nc o-d o p e dn a n o-s p h e r i c a l a n a t a s eT i O2w i t hh i g ht h e r m a ls t a b i l i t y[J].R s c A d v,2016,6:110741-110749.[13]N G U Y E N V H,T R A N Q B,N G U Y E N X C,e ta l.S u b m e r g e d p h o t o c a t a l y t i cm e m b r a n e r e a c t o rw i t h s u s-p e n d e da n di mm o b i l i z e d N-d o p e d T i O2u n d e rv i s i b l ei r r a d i a t i o n f o r d i c l o f e n a c r e m o v a l f r o m w a s t e w a t e r[J].P e o c e s sS a fE n v i r o n,2020,142:229-237. [14]韩培德,梁建,余愿,等.六钛酸钾纳米线的结构分析[J].稀有金属材料与工程,2005,34(1):56-59. [15]华熳煜,李益民,李夏.六钛酸钾(K2T i6O13)晶须几何构型㊁能量及电子结构的第一性原理计算[J].人工晶体学报,2011,40(6):1573-1579.[16]S E G A L L M D,L I N D A NPJD,P R O B E R T MJ,e t a l.F i r s t-p r i n c i p l e ss i m u l a t i o n:i d e a s,i l l u s t r a t i o n sa n dt h eC A S T E Pc o d e[J].JP h y sC o n d e n s M a t t e r,2002,14(11):2717-2744.[17]戚玉敏,陈恒利,金朋,等.第一性原理研究M n和C u掺杂六钛酸钾(K2T i6O13)的电子结构和光学性质[J].物理学报,2018,67(6):067101.[18]HU A M Y,L IY M,L O N GCG,e t a l.S t r u c t u r a l,e l e c-t r o n i c a n de l a s t i c p r o p e r t i e so f p o t a s s i u m h e x a t i t a n a t ec r y s t a l f r o mf i r s t-p r i n c i p l e s c a l c u l a t i o n s[J].P h y s i c aB,2012,407(14):2811-2815.[19]C HA T T E R J E E A,H I R OM I C H IH A,I WA S A K IT.F i r s t p r i n c i p l es t u d y t oc o r r e l a t e l o c a t i o na n da c t i v i t yo f r u t h e n i u mo x i d e i n c o r p o r a t e d i n a l k a l i-m e t a l h e x a t i-t a n a t e s[J].JP h y sC h e m B,2001,105(17):3463-3469.[20]D U G H,C H E N Q,HA N PD,e t a l.P o t a s s i u mt i t a n-a t e n a n o w i r e s:S t r u c t u r e,g r o w t h,a n do p t i c a l p r o p e r t i e s[J].P h y sR e vB,2003,67:035323.[21]L IJ,Z HA N G Y C,Z HA N G M.L o w t e m p e r a t u r ep r e p a r a t i o na n d o p t i c a l p r o p e r t i e so f K2T i6O13[J].M a t e rL e t t,2012,79(2):136-138.F i r s t-p r i n c i p l e s c a l c u l a t i o n s o f e l e c t r o n i c s t r u c t u r e a n do p t i c a l p r o p e r t i e s o fN-d o p e dK2T i6O13L I U B a o t o n g①,L IY a p i n g②,L U H o n g y a n②(①N e t w o r k I n f o r m a t i o nC e n t e r;②S c h o o l o f P h y s i c s a n dP h y s i c a l E n g i n e e r i n g,Q u f uN o r m a lU n i v e r s i t y,273165,Q u f u,S h a n d o n g,P R C)A b s t r a c t:T h e e l e c t r o n i c s t r u c t u r e s a n d o p t i c a l p r o p e r t i e s o f p u r eK2T i6O13a n dN-d o p e dK2T i6O13h a v e b e e nc a l c u l a t e db y t h e f i r s t-p r i n c i p l e s c a l c u l a t i o n s i n t h i s p a p e r.T h e r e s u l t s s h o wt h a tNd o p i n g i n t r o d u c e s i m p u r i t y e n e r g y l e v e l s i n t o t h e f o r b i d d e nb a n d a n d d e c r e a s e s t h e b a n d g a p.D u e t o t h e e f f e c t o f i m p u r i t y e n-e r g y l e v e l,t h e a b s o r p t i o ne d g e o fN-d o p e dK2T i6O13r e d-s h i f t s t o t h e v i s i b l e r e g i o n,a n d t h e a b s o r p t i o n i n-t e n s i t y i n c r e a s e s s i g n i f i c a n t l y i n t h e v i s i b l e r a n g e.K e y w o r d s:N-d o p i n g;e l e c t r o n i c s t r u c t u r e;o p t i c a l p r o p e r t i e s;a b s o r p t i o n r e d-s h i f t09曲阜师范大学学报(自然科学版)2023年Copyright©博看网. All Rights Reserved.。

mote2的电子结构及光学性质的理论研究

_______________________________
收稿日期：2019-10-12；修改日期：2019-11-13 基金项目：国家自然科学基金项目(11564019, 11147158)；江西省教育厅科研课题(GJJ170654) 作者简介：马睿华(1999-)，男，河南洛阳人，井冈山大学数理学院本科生(E-mail:maruihua@);
刘珊珊(1999-)，女，江西九江人，井冈山大学数理学院本科生(E-mail:liushanshan@); 辛霞(1999-)，女，山东烟台人，井冈山大学数理学院本科生(E-mail:xinxia@); 周慧颖(1998-)，女，山东潍坊人，井冈山大学数理学院本科生(E-mail:zhouhuiying@); 任梦琦(1998-)，女，山东东营人，井冈山大学数理学院本科生(E-mail:renmengqi@); *伍冬兰(1978-)，女，江西吉安人，教授，博士，主要从事分子结构与光谱研究(E-mail:wudonglan1216@).
MoTe2 的电子结构及光学性质的理论研究
马睿华，刘珊珊，辛霞，周吉安 343009)
摘要：利用密度泛函理论第一性原理方法对 MoTe2 的能带结构、能态密度和光学性质进行了理论计算，得到能带结构、态密度、光吸收谱、能量损失谱和介电函数等光学性质。结果表明：MoTe2 具有间接带隙宽度为 1.066 eV 的半导体材料，价带主要由 Mo 的 5s4p 价电子和 Te 的 5s5p 价电子起主要作用；导带由 Mo 和 Te 的 4d 价电子起
关键词：MoTe2；电子结构；光学性质；第一性原理
中图分类号：O561.3
文献标识码：A
DOI:10.3969/j.issn.1674-8085.2020.01.003

硅化镁的电子结构与热力学性质

硅化镁的电子结构与热力学性质柳福提;程晓洪;张淑华【摘要】利用密度泛函理论的赝势平面波方法对 Mg2Si 晶体的结构进行了几何优化，在优化的基础上对电子结构、弹性常数与热力学性质进行了第一性原理计算．结果得到 Mg2Si 是一种带隙为 0.2846eV 的间接带隙半导体；其导带主要以Mg 的 3p、3s 与Si 的 3p 态电子构成；弹性常量 C11= 114.39GPa、C12= 22.45GPa、C44= 42.78GPa；零温度与零压下的德拜温度为 676.4K．运用线性响应方法确定了声子色散关系，得到Mg2Si 的等容热容、德拜温度、焓、自由能、熵等热力学函数随温度变化的关系．%The electronic structure,elastic constants and thermodynamic properties of Mg2Si were calculated based on the optimized structure by using the first-principles pseudo-potential method of density functional theory.The results showed that the indirect band gap of Mg2Si was 0.2846eV;conduction band was constituted mainly by 3p,3s electrons of Mg atoms and 3p electrons of Si atom;elastic constants C11=114.39GPa,C12=22.45GPa,C44=42.78GPa;Debye temperature is 676.4K at zero pressure and zero temperature.The linear response method was applied to determine the phonon dispersion relations,and the relations of thermodynamic functions of heat capacity,Debye temperature,enthalpy,free energy,entropy with temperature were calculated.【期刊名称】《宜宾学院学报》【年(卷),期】2012(000)006【总页数】4页(P39-42)【关键词】硅化镁;电子结构;弹性常量;热力学性质【作者】柳福提;程晓洪;张淑华【作者单位】宜宾学院物理与电子工程学院,四川宜宾644000 宜宾学院计算物理四川省高校重点实验室,四川宜宾644000;宜宾学院计算物理四川省高校重点实验室,四川宜宾644000;宜宾学院实验与教学资源管理中心,四川宜宾644000【正文语种】中文【中图分类】O48金属硅化物材料具有许多优异的热学、电学及力学性能，其中硅化镁(Mg2 Si)是Mg-Si二元体系的唯一稳定化合物，它具有高熔点、高硬度、高弹性模量的特性，是一种窄带隙n型半导体材料，在光电子器件、电子器件、能源器件、激光、半导体制造、恒温控制通讯等领域有重要应用前景［1-5］.由于合金元素Mg与Si的原料资源非常丰富，地层蕴含量大，价格低廉，无毒无污染，因此，Mg2 Si作为一种新型环境半导体材料引起了广大研究工作者的极大关注.近年来，许多学者对Mg2 Si材料的各种性质进行了不少的研究，如有学者对Mg2 Si的晶格动力学［6］，能带结构和介电函数［7-10］，掺杂及光学性质［11-12］，几何结构、弹性及其热力学性质［13-14］进行了研究，这些研究结果对Mg2 Si材料的利用与设计具有重要意义，但对Mg2 Si的热容、德拜温度等热力学性质的研究却很少，故本文采用基于第一性原理的赝势平面波方法，对Mg2 Si的能带结构、弹性常量、德拜温度、热容、自由能、熵等热力学函数进行理论计算，为Mg2 Si材料的实验与设计提供预测.Mg2 Si晶体具有反萤石结构，属于面心立方晶格，空间群为 Fm3m，群号是225，晶格常数 a=0.6391nm［15］.在晶体结构中，每个Si原子位于(0，0，0)位置，配位数是8，形成边长为a的面心立方结构.Mg原子位于(0.25，0.25，0.25)位置，每个Mg原子位于Si原子组成的四面体的中心，形成边长为a/2的简立方结构，Mg2 Si晶胞结构如图1所示.本文采用基于密度泛函理论的第一性原理赝势平面波方法，理论计算全部由Material Studios 5.0软件中的量子力学模块CASTEP程序包完成.它是一个基于密度泛函理论的从头算量子力学程序，将离子势用赝势替代，把电子波函数用平面波基组展开，电子与电子相互作用的交换和相关势由局域密度近似(LDA)或广义梯度近似(GGA)进行校正，是目前公认较精确的电子结构计算的理论方法.具体参数设置如下，在几何优化与电子结构计算中：能量截断值(Ultrafine)为380eV，能量收敛度(Energy tolerance)为5.0×10-6 eV/atom，作用在每个原子上的最大力收敛精度0.01eV/Å，最大应变收敛度为0.02GPa，最大位移收敛度为5.0×10-4Å.在倒易空间布里渊中k点的设置使用Monkhorst-Pack法，选取密度为4×4×4，赝势选取超软赝势，参与赝势计算的价电子分别为Mg：2p6 3s2与Si：3s2 3p2，电子与电子之间的交换关联泛函选用广义梯度近似(GGA)中的RPBE方案.声子散射的计算中：能量截断能为900eV，自洽计算的收敛精度为1.0×10-4 eV/cell，k点选取密度为3×3×3，赝势为Hamann提出的模守恒赝势(Norm-conserving).3.1 结构优化根据Mg2 Si晶格参数的实验值，建立起相应的晶体结构，经过几何优化后，得到晶格参数为a=0.6422nm，与实验值0.6391nm［15］非常接近，误差为0.5%，在第一性原理计算可接受的范围以内，后面各种性质的计算是在此优化结构的基础上进行的，说明计算结果应该具有较好的预测性.3.2 能带结构通过对Mg2 Si能带结构的计算，得到沿布里渊区高对称点方向的能带结构如图2所示.从图2可以看出，导带的最低点在X点，价带的最高点在G点，不在同一k点处，说明Mg2 Si是间接带隙半导体.第一布里渊区中高对称k点在导带底Ec与价带顶Ev的特征能量如表1.导带在X点处取得的能量最小值为0.2846eV，而价带在G点处取得能量的最大值为0eV，所以Mg2 Si的带隙为0.2846eV，与陈茜等［2］的结果0.2994eV比较接近.能带的宽窄在能带的分析中非常重要，从表1可得到，导带底的能带宽度为(2.6761eV-0.2846eV=2.3915eV)，价带顶的能带宽度为(-2.5231eV-0eV=-2.5231eV)，即导带底能带比价带顶能带窄，意味着处于导带底能带中的电子有效质量较大，也就是说，导带底的电子有效质量大于价带顶的空穴有效质量，说明Mg2 Si是重电子，轻空穴的间接能隙半导体.图3为Mg2 Si的总态密度，通过分析得出，Mg2 Si的能带有四个区，其中价带区有三个：-42.877～-42.863 eV为最低能量段，能带宽度很小，来源于Mg的3p态电子;-8.937～-6.994 eV为次低能价带，该价带主要是Mg的3s与Si的3s 态电子的贡献;其余几条靠近费米能级的能带对应于高能价带，能量范围为-4.580～0 eV，该能带的主要贡献是Mg的3p与Si的3p态电子，Mg的3s与Si的3s态电子对该能带有少量的贡献.Mg2 Si的导带主要是Mg的3p、3s与 Si的3p态电子，Si的3s电子的贡献相对较小.3.3 弹性常数弹性在材料科学、化学、物理学及地球物理学等领域都是一个比较重要的研究对象，固态物质的状态方程、比热容、德拜温度、熔点等都与弹性相关.由弹性常数可以获得晶体各向异性特点及晶体结构的稳定性等方面的重要信息.Mg2 Si属于面心立方晶系，其弹性张量Cij有3个独立分量C11、C12及C44，通过几何优化之后计算出Mg2 Si在零温度与零压下的弹性常数与体弹模量如表2所示.根据各向同性系数可算出Mg Si的S=2 1.075，说明其各向同性较好.体弹性模量与剪切模量分别表征材料抵抗断裂与塑性形变的能力，其比值可作为延性或脆性的量度，高B/G(其临界值为1．75)值意味着物质是易延展的，低 B/G表示该材料是易碎的，计算得到Mg2 Si的B/G=1.206，说明Mg2 Si易碎.3.4 德拜温度德拜温度是物质热力学性质的一个重要物理量，利用弹性常量可以计算晶体的德拜温度.通过前面计算得到的弹性常量，运用德拜近似计算出Mg2 Si晶体的德拜温度.根据 Voigt［16］近似，剪切模量为根据Reuss［17］近似，剪切模量为从理论证明，多晶体模量刚好是Voigt和Reuss给出的算术平均值，即对于立方晶体，当p=0GPa时，体弹性模量为然后由剪切模量与体弹性模量求出压缩纵波速和横波波速vs=可得到平均声速最后由平均声速及德拜近似可求得德拜温度118.82 22.27 44.96 54.45 1.07前面各式中，ħ是普朗克常数，k是玻耳兹曼常数，NA是阿伏伽德罗常数，n是原胞中的原子数，M是原胞中分子的质量，V为原胞的体积，ρ=M/V是密度．通过以上式子的计算，得到Mg2 Si在零温度与零压下的德拜温度为θD=676．4K，德拜频率ωD=8.856 ×1013 Hz，它们直接反映晶体的热力学性质.3.5 热容、焓、自由能与熵函数计算中还运用线性响应方法确定了Mg2 Si在第一布里渊区的色散关系与声子的态密度，分别如图4、图5所示.在Mg2 Si晶体的原胞中有两个镁原子与一个硅原子，共有3支声学波与6支光学波.从图中可以看出，当波矢k趋于零时，有三支晶格振动波的频率趋于零，这三支晶格振动波即为声学波，其中有两支横波，一支纵波，其余6支即为光学波.计算结果得到Mg2 Si在G点的光学波的频率分别为7.829×1012 Hz、8.336×1012 Hz和9.408×1012 Hz.在准谐德拜近似下，利用声子态密度来探讨Mg2 Si的热力学性质，利用热容公式：可以算出Mg2 Si在给定的温度下的热容、德拜温度.在温度为0～1000K范围的等容热容、德拜温度分别如图6、图7所示.在温度为40.5K时，热容为1.264 J/mol.K，德拜温度为674.2K，与用弹性常量计算所得零温度与零压下的德拜温度(676.4)非常接近;温度为303K时热容为62.05 J/mol.K，而实验值为67.9 J/mol.K，此时的德拜温度为585.5 K，随着温度的升高，热容趋于73.6 J/mol.K，非常接近经典极限值74.8 J/mol.K，与杜隆-珀替定律一致.焓、自由能、熵函数在温度趋于0K时都趋于零，与热力学第三定律相符，它们随温度的具体变化关系如图8所示.利用基于密度泛函理论的赝势平面波方法对Mg2 Si晶体的电子结构与热力学性质进行了第一性原理计算.计算结果得到Mg2 Si是一种带隙为0.2846eV的间接带隙半导体;其导带主要以Mg的3p、3s与Si的3p态电子构成;弹性常量C11=114.39GPa、C12=22.45GPa、C44=42.78 GPa;零温度与零压下的德拜温度为676.4K;运用线性响应方法确定了声子色散关系，得到Mg2 Si在40.5K时的德拜温度为674.2K、等容热容随温度的升高趋近杜隆-珀替经典极限值74.8J/mol.K;焓、自由能、熵等热力学函数随温度变化关系与热力学第三定律一致.【相关文献】［1］姜洪义，张联盟.Mg-Si基热电化合物的研究现状［J］.材料导报，2002，16(3)：20-22. ［2］陈茜，谢泉，闫万珺，等.Mg2 Si电子结构及光学性质的第一性原理计算［J］.中国科学 G 辑，2008，38(7)：825-833.［3］ Song R B，Aizawa T，Sun JQ.SynthesisofMg2 Si1-x Snx solid solutions as thermoelectric materials by bulkmechanical alloying and hot pressingmaterials［J］.MaterSci Eng B，2007(136)：111-116.［4］臧树俊，周琦，马勤，等.金属间化合物 Mg2 Si研究进展［J］.今日铸造，2006，27(8)：866-870.［5］姜洪义，刘琼珍，张联盟，等.Mg-Si基热电材料量子化学计算［J］.计算物理，2004，21(5)：439-442.［6］ Tani J I，Kido ttice dynmics of Mg2 Si and Mg2 Ge compounds from first-principles calculations［J］.Intermetallics，2008(16)：418.［7］ Au-Yang M Y，Cohen M L.Electronic structure and optical propertiesof Mg2 Si，Mg2 Ge，and Mg2 Sn［J］.Phys Rev，1969，178(3)：1358-1364.［8］ Aymerich F，Mula G.Pseudopotential band structures of Mg2 Si，Mg2 Ge，andMg2 Sn，and of the solid solution Mg2Ge，Sn［J］.Phys Suatus solid，1970，42(2)：697-704.［9］ Corkill JL，Cohen M L.Structures and electronic properties of IIA-IV antifluorite compounds［J］.Phys Rev B，1993，48：17138-17144.［10］Imai Y，Watanabe A.Energetics of alkaline-earth metal silicides calculated using a first-principle pseudoptentialmethod［J］.Intermetallics，2002(10)：333-341.［11］闵新民，邢学玲，朱磊.Mg2 Si与掺杂系列的电子结构与热电性能研究［J］.功能材料，2004(35)：1154-1159.［12］陈茜，谢泉，杨创华.掺杂Mg2 Si电子结构及光学性质的第一性原理计算［J］.光学学报，2009，29(1)：229-235.［13］彭华，春雷，李吉超.Mg2 Si的电子结构和热电输运性质的理论研究［J］.物理学报，2010，59(6)：4123-4129.［14］刘娜娜，孙韩英，刘洪生.Mg2 Si弹性性质及热力学性质的第一性原理计算［J］.材料导报，2009(23)：278-280.［15］Owen E A，Preston G D.The atomic structure of two intermetallic compounds ［J］.Nature(London)，1924(113)：914-914.［16］VoightW.Lehrbuch der Kristallphysik［M］.Leipzig：Taubner，1996.［17］Reuss A.Berechung der fliessgrenze von mischkristallen［J］.Z Angew Math Mech，1929(9)：49-58.［18］Hill R.The elastic behavior of a crystalline aggregate［J］.Proceedings of the Royal Society of London Series A，1952，65(5)：350.。

P和As掺杂Mn_(4)Si_(7)第一性原理计算

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：１０００９８５Ｘ（２０２１）０２０２７３０５ＦｉｒｓｔＰｒｉｎｃｉｐｌｅｓＣａｌｃｕｌａｔｉｏｎｓｏｆＰａｎｄＡｓＤｏｐｅｄＭｎ４Ｓｉ７ＺＨＯＮＧＹｉ，ＺＨＡＮＧＪｉｎｍｉｎ，ＷＡＮＧＬｉ，ＨＥＴｅｎｇ，ＸＩＡＯＱｉｎｇｑｕａｎ，ＸＩＥＱｕａｎ（ＩｎｓｔｉｔｕｔｅｏｆＮｅｗＯｐｔｏｅｌｅｃｔｒｏｎｉｃＭａｔｅｒｉａｌｓａｎｄＴｅｃｈｎｏｌｏｇｙ，ＣｏｌｌｅｇｅｏｆＢｉｇＤａｔａａｎｄＩｎｆｏｒｍａｔｉｏｎＥｎｇｉｎｅｅｒｉｎｇ，ＧｕｉｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｇｕｉｙａｎｇ５５００２５，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ＴｈｅｅｌｅｃｔｒｏｎｉｃｓｔｒｕｃｔｕｒｅａｎｄｏｐｔｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆｉｎｔｒｉｎｓｉｃａｎｄＰ，ＡｓｄｏｐｅｄＭｎ４Ｓｉ７ｗｅｒｅｃａｌｃｕｌａｔｅｄｗｉｔｈｔｈｅｆｉｓｒｔｐｒｉｎｃｉｐｌｅｓｃａｌｃｕｌａｔｉｏｎｍｅｔｈｏｄ．ＴｈｅｒｅｓｕｌｔｓｈｏｗｓｔｈａｔｔｈｅｉｎｔｒｉｎｓｉｃＭｎ４Ｓｉ７ｉｓａｎｉｎｄｉｒｅｃｔｓｅｍｉｃｏｎｄｕｃｔｏｒｍａｔｅｒｉａｌｗｉｔｈａｇａｐｏｆ０．８１０ｅＶ，ｔｈｅＰｄｏｐｅｄＭｎ４Ｓｉ７ｂａｎｄｇａｐｉｎｃｒｅａｓｅｓｔｏ０．８３９ｅＶ，ａｎｄｔｈｅＡｓｄｏｐｅｄＭｎ４Ｓｉ７ｂａｎｄｇａｐｄｅｃｒｅａｓｅｓｔｏ０．７５２ｅＶ．Ｄｏｐｉｎｇｃａｕｓｅｓａｓｈｉｆｔｔｏｔｈｅｌｏｗｅｎｅｒｇｙｒｅｇｉｏｎ，ａｎｄｃａｕｓｅｓａｎｉｎｃｒｅａｓｅｏｆｔｈｅｒｅａｌｐａｒｔｏｆｄｉｅｌｅｃｔｒｉｃｆｕｎｃｔｉｏｎｎｏｔａｂｌｙｉｎｔｈｅｌｏｗｅｎｅｒｇｙｒｅｇｉｏｎａｎｄａｎｉｎｃｒｅａｓｅｏｆｔｈｅｉｍａｇｉｎａｒｙｐａｒｔｉｎａｌｍｏｓｔａｌｌｒｅｇｉｏｎ，ｉｍａｇｉｎａｒｙｐａｒｔｄｅｃｒｅａｓｅｓｔｏｚｅｒｏａｆｔｅｒ８ｅＶ．Ｂｅｓｉｄｅｓ，ｄｏｐｉｎｇｏｂｖｉｏｕｓｌｙｉｎｃｒｅａｓｅｓｔｈｅｅｘｔｉｎｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔ，ａｂｓｏｒｐｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｒｅｆｌｅｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔａｎｄｐｈｏｔｏｃｏｎｄｕｃｔｉｖｉｔｙｉｎｔｈｅｈｉｇｈｅｎｅｒｇｙｒｅｇｉｏｎ，ａｎｄｉｍｐｒｏｖｅｓｔｈｅｏｐｔｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆｔｈｅＭｎ４Ｓｉ７．Ｋｅｙｗｏｒｄｓ：ｆｉｒｓｔｐｒｉｎｃｉｐｌｅ；Ｍｎ４Ｓｉ７；ｄｏｐｉｎｇ；ｂａｎｄｓｔｒｕｃｔｕｒｅ；ｄｅｎｓｉｔｙｏｆｓｔａｔｅ；ｏｐｔｉｃａｌｐｒｏｐｅｒｔｙ收稿日期：２０２０１１２６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。

211000590_α和β-Si3N4的电子、光学及热力学性质的第一性原理计算

第４０卷　第２期原　子　与　分　子　物　理　学　报Ｖｏｌ．４０Ｎｏ．２２０２３年４月ＪＯＵＲＮＡＬＯＦＡＴＯＭＩＣＡＮＤＭＯＬＥＣＵＬＡＲＰＨＹＳＩＣＳＡｐｒ．２０２３!"#$"%&'"()*+",-.-/,0.1.-;..838556α和β－Ｓｉ３Ｎ４的电子、光学及热力学性质的第一性原理计算蒋文龙１，戴　涛１，张　帆１，张雨林１，刘正堂２，杜艺华１，刘其军１（１西南交通大学键带工程组，成都６１００３１；２西北工业大学凝固技术国家重点实验室，西安７１００７２）摘　要：基于密度泛函理论的第一性原理方法，计算了α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的晶体结构、电子结构、光学性质和声子谱，并对结果进行了理论分析计算结果表明两种相都含有较强的共价键，均为绝缘体，且α－Ｓｉ３Ｎ４的禁带宽度略大于β－Ｓｉ３Ｎ４计算获得的光学吸收系数表明α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４主要吸收紫外光，并二者的能量损失峰在２４４ｅＶ附近 α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的声子谱中均无虚频，表明二者的结构是稳定的在０～１０００Ｋ范围内，α－Ｓｉ３Ｎ４的热容约为β－Ｓｉ３Ｎ４的两倍本文的计算结果可以为Ｓｉ３Ｎ４的相关应用提供理论依据关键词：氮化硅；电子结构；光学性质；声子谱中图分类号：Ｏ４６９文献标识码：ＡＤＯＩ：2."278449:"2... ./;0"-.-/".-; (8)Ｆｉｒｓｔ－ｐｒｉｎｃｉｐｌｅｓｃａｌｃｕｌａｔｉｏｎｓｏｆｔｈｅｅｌｅｃｔｒｏｎｉｃ，ｏｐｔｉｃａｌａｎｄｔｈｅｒｍｏｄｙｎａｍｉｃｐｒｏｐｅｒｔｉｅｓｏｆα－Ｓｉ３Ｎ４ａｎｄβ－Ｓｉ３Ｎ４ＪＩＡＮＧＷｅｎＬｏｎｇ１，ＤＡＩＴａｏ１，ＺＨＡＮＧＦａｎ１，ＺＨＡＮＧＹｕＬｉｎ１，ＬＩＵＺｈｅｎｇＴａｎｇ２，ＤＵＹｉＨｕａ１，ＬＩＵＱｉＪｕｎ１（１．ＢｏｎｄａｎｄＢａｎｄＥｎｇｉｎｅｅｒｉｎｇＧｒｏｕｐ，ＳｏｕｔｈｗｅｓｔＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ６１００３１，Ｃｈｉｎａ；２．ＳｔａｔｅＫｅｙＬａｂｏｒａｔｏｒｙｏｆＳｏｌｉｄｉｆｉｃａｔｉｏｎＰｒｏｃｅｓｓｉｎｇ，ＮｏｒｔｈｗｅｓｔｅｒｎＰｏｌｙｔｅｃｈｎｉｃａｌＵｎｉｖｅｒｓｉｔｙ，Ｘｉ’ａｎ７１００７２，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｗｅｕｓｅｄｔｈｅｆｉｒｓｔ－ｐｒｉｎｃｉｐｌｅｓｍｅｔｈｏｄｂａｓｅｄｏｎｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎａｌｔｈｅｏｒｙｔｏｃａｌｃｕｌａｔｅｔｈｅｃｒｙｓｔａｌｓｔｒｕｃｔｕｒｅｓ，ｅｌｅｃｔｒｏｎｉｃｓｔｒｕｃｔｕｒｅｓ，ｏｐｔｉｃａｌｐｒｏｐｅｒｔｉｅｓａｎｄｐｈｏｎｏｎｓｐｅｃｔｒａｏｆα－Ｓｉ３Ｎ４ａｎｄβ－Ｓｉ３Ｎ４ＴｈｅｏｂｔａｉｎｅｄｒｅｓｕｌｔｓｈａｖｅｂｅｅｎｔｈｅｏｒｅｔｉｃａｌｌｙａｎａｌｙｚｅｄＴｈｅｃａｌｃｕｌａｔｅｄｒｅｓｕｌｔｓｓｈｏｗｔｈａｔｂｏｔｈｐｈａｓｅｓｃｏｎｔａｉｎｓｔｒｏｎｇｃｏｖａｌｅｎｔｂｏｎｄｓａｎｄａｒｅｉｎｓｕｌａｔｏｒｓＴｈｅｂａｎｄｇａｐｏｆα－Ｓｉ３Ｎ４ｉｓｓｌｉｇｈｔｌｙｌａｒｇｅｒｔｈａｎｔｈａｔｏｆβ－Ｓｉ３Ｎ４Ｔｈｅｃａｌｃｕｌａｔｅｄｏｐｔｉｃａｌａｂｓｏｒｐｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｓｓｈｏｗｔｈａｔα－Ｓｉ３Ｎ４ａｎｄβ－Ｓｉ３Ｎ４ｍａｉｎｌｙａｂｓｏｒｂｕｌｔｒａｖｉｏｌｅｔｌｉｇｈｔ，ａｎｄｔｈｅｉｒｅｎｅｒｇｙｌｏｓｓｐｅａｋｓａｒｅａｒｏｕｎｄ２４４ｅＶＩｎｔｈｅｐｈｏｎｏｎｓｐｅｃｔｒａ，α－Ｓｉ３Ｎ４ａｎｄβ－Ｓｉ３Ｎ４ｈａｖｅｎｏｉｍａｇｉｎａｒｙｆｒｅｑｕｅｎｃｙ，ｉｎｄｉｃａｔｉｎｇｔｈａｔｔｈｅｙａｒｅｓｔａｂｌｅＩｎｔｈｅｒａｎｇｅｏｆ０～１０００Ｋ，ｔｈｅｈｅａｔｃａｐａｃｉｔｙｏｆα－Ｓｉ３Ｎ４ｉｓａｂｏｕｔｔｗｉｃｅｔｈａｔｏｆβ－Ｓｉ３Ｎ４ＴｈｅｃａｌｃｕｌａｔｅｄｒｅｓｕｌｔｓｉｎｔｈｉｓｐａｐｅｒｗｉｌｌｐｒｏｖｉｄｅａｔｈｅｏｒｅｔｉｃａｌｂａｓｉｓｆｏｒｔｈｅｒｅｌａｔｅｄａｐｐｌｉｃａｔｉｏｎｓｏｆＳｉ３Ｎ４Ｋｅｙｗｏｒｄｓ：Ｓｉｌｉｃｏｎｎｉｔｒｉｄｅ；Ｅｌｅｃｔｒｏｎｉｃｓｔｒｕｃｔｕｒｅ；Ｏｐｔｉｃａｌｐｒｏｐｅｒｔｉｅｓ；Ｐｈｏｎｏｎｓｐｅｃｔｒｕｍ收稿日期：２０２２０３１４基金项目：国家自然科学基金（１２１４７２０８）；２０２１年国家级大学生创新创业训练计划项目（２０２１１０６１３０８６）作者简介：蒋文龙（２０００—），男，四川成都人，主要从事材料性质研究．Ｅｍａｉｌ：１６８６２６３９２＠ｑｑ．ｃｏｍ通讯作者：杜艺华．Ｅｍａｉｌ：ＮｉｋｋｙＤＹＨ＠ｍｙ．ｓｗｊｔｕ．ｅｄｕ．ｃｎ；刘其军．Ｅｍａｉｌ：ｑｉｊｕｎｌｉｕ＠ｈｏｍｅ．ｓｗｊｔｕ．ｅｄｕ．ｃｎ１　引　言氮化硅（Ｓｉ３Ｎ４）是目前应用较为广泛的陶瓷材料之一，它是一种几乎不发生高温变形的陶瓷材料，并且具有优异的高温机械性能，常常被用于制造涡轮机械器件［１］Ｓｉ３Ｎ４的硬度高，摩擦系数小，具有自润滑性能［２］，且具有良好的抗疲劳性能和耐摩擦磨损性能近年来，随着光电子技术第４０卷原　子　与　分　子　物　理　学　报　第２期的发展，氮化硅薄膜由于具有高的化学稳定性、热稳定性和良好的介电特性，被视为有广泛用途的电子材料之一此外，氮化硅还具有比较高的热导率［３］，可以用于大功率电子产品的散热材料．在ＭＯＳ电路中，Ｓｉ３Ｎ４还可以作为栅极材料提高击穿电压氮化硅常见的晶体结构有３种，分别是α、β和γ相，其中α和β相分别属于三角和六角晶系，且可以在常压下制备 α－Ｓｉ３Ｎ４的空间群为Ｐ３１ｃ，β－Ｓｉ３Ｎ４的空间群为Ｐ６３／ｍＸｕ等人［４］使用原子轨道正交线性组合方法（ＯＬＣＡＯ），研究了Ｓｉ３Ｎ４，α－ＳｉＯ２和Ｓｉ２Ｎ２Ｏ的电子结构潘洪哲等人［５］利用第一性原理计算了β－Ｓｉ３Ｎ４的能带结构和光学性质，发现β－Ｓｉ３Ｎ４的吸收系数在１００ｎｍ处存在峰值雷金桥［６］通过实验的方式研究了α－Ｓｉ３Ｎ４在高温高压（０～３０ＧＰａ）下的热力学性质然而，对α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４二者的基本性质进行对比分析的理论研究较少因此，本文使用基于密度泛函理论的第一性原理方法，对α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的Ｍｕｌｌｉｋｅ布居数、能带结构、态密度、介电函数和声子谱等进行了计算，并据此分析了它们的成键情况、电子结构、光学性质、热力学性质２　计算方法本文的计算是在ＣＡＳＴＥＰ［７］上进行的，交换关联项选取了广义梯度近似（ＧＧＡ）中的Ｐｅｒｄｅｗ－Ｂｕｒｋｅ－Ｅｒｎｚｅｒｈｏｆ（ＰＢＥ）［８，９］ α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４中参与计算的价电子均为Ｓｉ的３ｓ２３ｐ２和Ｎ的２ｓ２２ｐ３对晶胞模型进行结构优化时，采用了ＢＦＧＳ算法［１０］，截断能设置为７７０ｅＶ，自洽循环收敛精度为５０×１０－７ｅＶ／ａｔｏｍ，原子间所受的应力误差小于００２ＧＰａ，原子间最大位移收敛误差小于５０×１０－４?，体系的总能量收敛标准为５０×１０－６ｅＶ／ａｔｏｍ．赝势采用模守恒赝势，α－Ｓｉ３Ｎ４的布里渊区ｋ点网格取２×２×４，β－Ｓｉ３Ｎ４的布里渊区ｋ点网格取２×２×６图１　晶体结构：（ａ）α－Ｓｉ３Ｎ４，（ｂ）β－Ｓｉ３Ｎ４Ｆｉｇ１　Ｃｒｙｓｔａｌｓｔｒｕｃｔｕｒｅｓ：（ａ）α－Ｓｉ３Ｎ４，（ｂ）β－Ｓｉ３Ｎ４３　结果与分析３１　晶格参数α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４的晶体结构如图１所示．计算得到α－Ｓｉ３Ｎ４的晶格参数为ａ＝ｂ＝７７９４２?，ｃ＝５６５０１?，Ｖ＝２９７５６３５?３，与实验值ａ＝ｂ＝７７５２１?，ｃ＝５６１９２?，Ｖ＝２９２４４?３［１１］符合得很好，说明模型和计算方法是可信的计算得到β－Ｓｉ３Ｎ４的晶胞参数为ａ＝ｂ＝７６５３７?，ｃ＝２９１８３?，Ｖ＝１４８０５０６?３，与实验值ａ＝ｂ＝７６０８?，ｃ＝２９?，Ｖ＝１４５７４３?３［１２］相吻合３２　布居分析为了研究两种结构的化学键，本文计算了α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的Ｍｕｌｌｉｋｅｎ布居数［１３］从表１中可知，α－Ｓｉ３Ｎ４中有４种不同的Ｎ原子和２种不同的Ｓｉ原子，单个Ｎ原子平均可以得到１３８～１３９个价电子，单个Ｓｉ原子平均会失去１８３～１８６个价电子在表２中可以看到，Ｎ－Ｓｉ键的布居值在０６３ｅ～０６９ｅ之间，这表明Ｎ－Ｓｉ键为共价键由表３可知，β－Ｓｉ３Ｎ４中有２种Ｎ原子，１种Ｓｉ原子，β－Ｓｉ３Ｎ４的单个Ｎ原子平均可以得到１３９个价电子，单个Ｓｉ原子平均会失去１８５个价电子在表４中，Ｎ－Ｓｉ键的布居值为０５８ｅ，０６１ｅ，１３９ｅ的键长分别为１７４７０５?，１７３８２３?和１７４５４７?，表明电子处于成键轨道，且体现为强的共价作用３３　电子结构图２是α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４的能带结构图［１４］．第４０卷蒋文龙，等：α和β－Ｓｉ３Ｎ４的电子、光学及热力学性质的第一性原理计算第２期表１　α－Ｓｉ３Ｎ４的原子布居Ｔａｂｌｅ１　Ａｔｏｍｉｃｐｏｐｕｌａｔｉｏｎｓｏｆα－Ｓｉ３Ｎ４Ｓｐｅｃｉｅｓｓ（ｅ）ｐ（ｅ）Ｔｏｔａｌ（ｅ）Ｃｈａｒｇｅ（ｅ）Ｎ１１６５４７３６３８－１３８Ｎ２１６５４７５６３９－１３９Ｎ３１６７４７１６３８－１３８Ｎ４１６４４７４６３８－１３８Ｓｉ１０７７１３８２１４１８６Ｓｉ２０７６１４１２１７１８３表２　α－Ｓｉ３Ｎ４的键布居Ｔａｂｌｅ２　Ｂｏｎｄｐｏｐｕｌａｔｉｏｎｓｏｆα－Ｓｉ３Ｎ４ＢｏｎｄＰｏｐｕｌａｔｉｏｎ（ｅ）Ｌｅｎｇｔｈ（?）Ｎ－Ｓｉ０６８１７３０２５０６９１７３９３４０６７１７４１９７０６８１７４６３５０６７１７４８６５０６９１７４９３６０６３１７５３２２０６５１７５８９６表３　β－Ｓｉ３Ｎ４的原子布居Ｔａｂｌｅ３　Ａｔｏｍｉｃｐｏｐｕｌａｔｉｏｎｓｏｆβ－Ｓｉ３Ｎ４Ｓｐｅｃｉｅｓｓ（ｅ）ｐ（ｅ）Ｔｏｔａｌ（ｅ）Ｃｈａｒｇｅ（ｅ）Ｎ１１６４４７５６３９－１３９Ｎ２１６５４７４６３９－１３９Ｓｉ１０７６１３９２１５１８５表４　β－Ｓｉ３Ｎ４的键布居Ｔａｂｌｅ４　Ｂｏｎｄｐｏｐｕｌａｔｉｏｎｓｏｆβ－Ｓｉ３Ｎ４ＢｏｎｄＰｏｐｕｌａｔｉｏｎ（ｅ）Ｌｅｎｇｔｈ（?）Ｎ－Ｓｉ０６１１７３８２３１３９１７４５４７０５８１７４７０５从图２ａ中可以发现，α－Ｓｉ３Ｎ４的能隙Ｅｇ＝４６６５ｅＶ，与文献值４９ｅＶ［１５］相一致在图２ｂ中，β－Ｓｉ３Ｎ４的能隙Ｅｇ＝４２７８ｅＶ（文献值为４４ｅＶ［８］）由于α－Ｓｉ３Ｎ４晶胞中的原子数为β－Ｓｉ３Ｎ４的两倍，故α－Ｓｉ３Ｎ４能带明显多于β－Ｓｉ３Ｎ４．α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４价带顶部和导带底部都较为平坦，说明二者的空穴与电子的有效质量都较大此外，α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４的导带底和价带顶处于倒空间中的不同位置，所以α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４均具有间接带隙图２　能带结构：（ａ）α－Ｓｉ３Ｎ４，（ｂ）β－Ｓｉ３Ｎ４Ｆｉｇ２　Ｂａｎｄｓｔｒｕｃｔｕｒｅｓ：（ａ）α－Ｓｉ３Ｎ４，（ｂ）β－Ｓｉ３Ｎ４ α－Ｓｉ３Ｎ４的总态密度（ＴＤＯＳ）与分态密度（ＰＤＯＳ）如图３ａ所示，大致可以分为－１８２～－１３２ｅＶ，－９６ｅＶ～０ｅＶ，４４ｅＶ～１９１ｅＶ三个区域在－１８２～－１３２ｅＶ的态密度主要由Ｎ－２ｓ，Ｓｉ－３ｓ电子贡献，而－９６ｅＶ～０ｅＶ区域的态密度主要由Ｓｉ－３ｐ和Ｎ－２ｐ电子贡献在费米面附近的态密度主要由两种原子的ｐ电子贡献，而ｓ电子的贡献较小由Ｓｉ和Ｎ原子的分态密度可以看出，对导带贡献最多的是Ｓｉ－３ｐ图３ｂ中β－Ｓｉ３Ｎ４总态密度也可分为三个区域，第一区域主要由Ｎ－２ｓ轨道提供，Ｓｉ原子的ｓ和ｐ轨道的贡献不超过１５ｓｔａｔｅｓ／ｅＶ．β－Ｓｉ３Ｎ４在费米面附近的电子主要来自于Ｎ－２ｐ轨道，β－Ｓｉ３Ｎ４的导带主要由Ｓｉ的３ｐ轨道提供，而Ｎ原第４０卷原　子　与　分　子　物　理　学　报　第２期图３　α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的总态密度与分态密度Ｆｉｇ３　ＴＤＯＳｓａｎｄＰＤＯＳｓ：（ａ）α－Ｓｉ３Ｎ４，（ｂ）β－Ｓｉ３Ｎ４子贡献很少３４　光学性质复介电函数反映了介电常数与能带结构之间的关系，它是沟通带间跃迁微观物理过程与固体电子结构的桥梁，它可以反映电子的能级间跃迁和晶体的光谱信息，其在线性响应范围内可以表示为［１６］：ε（ω）＝ε１（ω）＋ｉε２（ω）（１）其中，ε１和ε２分别为复介电函数的实部和虚部介电函数的实部ε１与材料对光的反射有关，其代表处于激发态的电子由高能级向低能级跃迁时释放光子或声子的过程［１６］；介电函数的虚部ε２反映光电子从价带到导带跃迁过程中对光的吸收能量强弱，虚部越大则说明电子吸收光子的概率越高，材料对光的吸收能力也更强［１５，１６］图４表示α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的复介电函数．从图中可以看到，在能量零点时，α－Ｓｉ３Ｎ４的静态介电常数为４３０当光子能量增大到６２ｅＶ时，达到最大值７７８，光子能量为１５２ｅＶ时到达最低点复介电函数的虚部是由于材料内部极化跟不上交变电场变化引起的相位差所致，代表着材料能量损耗在４２３ｅＶ处，介电函数虚部开始出现明显的增长，这与其禁带宽度几乎一致．这是因为当入射光子的能量小于禁带宽度时，电子是禁止跃迁的；当能量高于此数值后，可发生跃迁的状态数增多，因此ε２迅速增大在图中可看出能量在９８４ｅＶ时，虚部达到最大值６８７ β－Ｓｉ３Ｎ４在能量零点的静态介电常数为４２３，当光子能量为６０８ｅＶ时达到最大值７１１虚部的最大值则是在１０４ｅＶ时达到６１９图４　α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的复介电函数Ｆｉｇ４　Ｃｏｍｐｌｅｘｄｉｅｌｅｃｔｒｉｃｆｕｎｃｔｉｏｎｓ：（ａ）α－Ｓｉ３Ｎ４，（ｂ）β－Ｓｉ３Ｎ４第４０卷蒋文龙，等：α和β－Ｓｉ３Ｎ４的电子、光学及热力学性质的第一性原理计算第２期在图５中，α－Ｓｉ３Ｎ４的反射率在０到２２２ｅＶ之间呈波浪式上升，反射率最大值出现在２２２ｅＶ处，为５６７％．可以看到，３２ｅＶ以后的反射率接近于０．在可见光范围内（１６－３ｅＶ）反射率小于１３７％ β－Ｓｉ３Ｎ４的反射率在０到２３１ｅＶ之间总体上呈现上升的趋势，反射率最大值为２３１ｅＶ处的５９２％，β－Ｓｉ３Ｎ４对可见光的反射率低于１３５％图５　α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４的反射率Ｆｉｇ５　Ｒｅｆｌｅｃｔｉｖｉｔｉｅｓ：（ａ）α－Ｓｉ３Ｎ４；（ｂ）β－Ｓｉ３Ｎ４复折射率是反映吸收性介质最主要的光学常数［１６－１９］，其表达式为：Ｎ＝ｎ－ｉｋ（２）其中实部ｎ为介质的折射率，主要由光在介质中传播速度所决定；虚部ｋ是由光在介质中传播的衰减所决定，也就是吸收系数从图６ａ中可以看出α－Ｓｉ３Ｎ４的静态折射率为２０７，在光子能量为６４４ｅＶ时达到最大折射率２８３吸收系数在４３６ｅＶ时开始有明显增长，在能量为１０７ｅＶ时，吸收系数最大为１７从图６ｂ中可以看出，β－Ｓｉ３Ｎ４的静态折射率为２０６，在能量为６７９ｅＶ时达到最大值２７２吸收系数从能量为４２３ｅＶ处开始有明显的增长，在能量为１１４ｅＶ时达到最大值１６５图７是α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４的能量损失函数，其表示电子与样品Ｓｉ３Ｎ４发生非弹性碰撞散射后的电子分布，其峰值与等离子体共振有关［２０］从图中可以看出，α－Ｓｉ３Ｎ４的能量损失的峰值在２４４ｅＶ处，峰值为１０２；β－Ｓｉ３Ｎ４的能量损失的峰值在２４３ｅＶ处，峰值比前者略高，为１１１二者的能量损失主峰的展宽相近，说明二者二次电子发射率相近图６　α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４的复折射率Ｆｉｇ６　Ｃｏｍｐｌｅｘｒｅｆｒａｃｔｉｖｅｉｎｄｅｘｅｓ：（ａ）α－Ｓｉ３Ｎ４；（ｂ）β－Ｓｉ３Ｎ４３５　声子谱及热力学性质图８是α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的声子谱．可以看到，谱线均无虚频，说明α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的结构是稳定的 α－Ｓｉ３Ｎ４的原胞中含有２８个原子，其中包括１２个Ｓｉ和１６个Ｎ原子，理论上有８４条声子谱曲线 β－Ｓｉ３Ｎ４的原胞有１４个原子，其中６个Ｓｉ和８个Ｎ原子，理论上有４２条声子谱曲线其中，α－Ｓｉ３Ｎ４的谱线中有３条声学支格波，８１条光学支格波，声学支格波反映了原胞质心的振动，而光学支格波反映的是原胞中粒子的相对振动在声子态密度图中，当频率为２５４９ＴＨｚ时，出现了最大的峰值，说明α－Ｓｉ３第４０卷原　子　与　分　子　物　理　学　报　第２期图７　α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４的损失函数Ｆｉｇ７　Ｌｏｓｓｆｕｎｃｔｉｏｎｓ：（ａ）α－Ｓｉ３Ｎ４；（ｂ）β－Ｓｉ３Ｎ４Ｎ４的晶格振动频率主要在此附近 β－Ｓｉ３Ｎ４的声子谱线中有３条声学支格波，３９条光学支格波，可以看到β－Ｓｉ３Ｎ４的晶格振动频率主要在２５５ＴＨｚ附近图９为热容与温度之间的关系热容随着温度增加而递增，曲线的斜率由大变小，渐渐趋于稳定，最终趋近于常数当温度较低时，固体的热容是由晶格热振动和电子热运共同作用，此时热容增长较快；当温度较高时，热容主要是由晶格热振动决定．同时，还可以看到α－Ｓｉ３Ｎ４热容约是β－Ｓｉ３Ｎ４的两倍４　结　论本文利用密度泛函理论计算并分析了α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４晶体的成键、电子能带结构、光学和热学性质主要得到了如下结论：（１）Ｍｕｌｌｉｋｅｎ布居数的计算结果表明，α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４内含有较强的共价键作用；（２）α－Ｓｉ３Ｎ４的理论带隙为４６６５ｅＶ，β－Ｓｉ３Ｎ４的带隙为４２７８ｅＶ，α－Ｓｉ３Ｎ４的带隙略大；（３）α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４中均发生了轨道杂化现象；（４）α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４二者的能量损失峰在２４４ｅＶ左右；（５）α－Ｓｉ３Ｎ４和β－Ｓｉ３Ｎ４的结构是稳定的；（６）β－Ｓｉ３Ｎ４热容小于α－Ｓｉ３Ｎ４图８　α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４的声子谱Ｆｉｇ８　Ｐｈｏｎｏｎｓｐｅｃｔｒａ：（ａ）α－Ｓｉ３Ｎ４；（ｂ）β－Ｓｉ３Ｎ４第４０卷蒋文龙，等：α和β－Ｓｉ３Ｎ４的电子、光学及热力学性质的第一性原理计算第２期图９　α－Ｓｉ３Ｎ４与β－Ｓｉ３Ｎ４的热容随温度的变化Ｆｉｇ９　Ｈｅａｔｃａｐａｃｉｔｉｅｓ：（ａ）α－Ｓｉ３Ｎ４；（ｂ）β－Ｓｉ３Ｎ４参考文献：［１］　ＢｅｎｃｏＬ，ＨａｆｉｎｅｒＪ，ＬｅｎｃｅｓＺ，ｅｔａｌＤｅｎｓｉｔｙｆｕｎｃｔｉｏｎａｌｓｔｕｄｙｏｆｓｔｒｕｃｔｕｒｅｓａｎｄｍｅｃｈａｎｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆＹ－ｄｏｐｅｄα－ＳｉＡｌＯＮｓ［Ｊ］ＪＥｕｒＣｅｒａｍＳｏｃ，２００８，２８：９９５［２］　ＤａｎｔｅＲＣ，ＫａｊｄａｓＣＫＡｒｅｖｉｅｗａｎｄａｆｕｎｄａｍｅｎｔａｌｔｈｅｏｒｙｏｆｓｉｌｉｃｏｎｎｉｔｒｉｄｅｔｒｉｂｏｃｈｅｍｉｓｔｒｙ［Ｊ］Ｗｅａｒ，２０１２，２８８：２７［３］　ＬｉＹＱ，ＰａｎＤ，ＺｈａｎｇＬＦ，ｅｔａｌＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＳｉＣａｎｄＳｉ３Ｎ４ｉｎｃｌｕｓｉｏｎｓｉｎｓｏｌａｒｃｅｌｌＳｉｓｃｒａｐｓａｎｄｔｈｅｉｒｍｏｔｉｏｎａｔｔｈｅＳｉ／ｓｌａｇｉｎｔｅｒｆａｃｅ［Ｊ］ＪＭａｔｅｒＲｅｓＴｅｃｈｎｏｌ，２０２２，１７：２２２０［４］　ＸｕＹＮ，ＣｈｉｎｇＷＹＥｌｅｃｔｒｏｎｉｃｓｔｒｕｃｔｕｒｅａｎｄｏｐｔｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆαａｎｄβｐｈａｓｅｓｏｆｓｉｌｉｃｏｎｎｉｔｒｉｄｅ，ｓｉｌｉｃｏｎｏｘｙｎｉｔｒｉｄｅ，ａｎｄｗｉｔｈｃｏｍｐａｒｉｓｏｎｔｏｓｉｌｉｃｏｎｄｉｏｘｉｄｅ［Ｊ］ＰｈｙｓＲｅｖＢ，１９９５，５１：１７３７９［５］　ＰａｎＨＺ，ＸｕＭ，ＺｈｕＷＪ，ｅｔａｌＦｉｒｓｔ－ｐｒｉｎｃｉｐｌｅｓｓｔｕｄｙｏｎｔｈｅｅｌｅｃｔｒｉｃａｌｓｔｒｕｃｔｕｒｅｓａｎｄｏｐｔｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆβ－Ｓｉ３Ｎ４［Ｊ］ＡｃｔａＰｈｙｓＳｉｎ，２００６，５５：３５８５（ｉｎＣｈｉｎｅｓｅ）［潘洪哲，徐明，祝文军，等 β－Ｓｉ３Ｎ４电子结构和光学性质的第一性原理研究［Ｊ］物理学报，２００６，５５：３５８５］［６］　ＬｅｉＪＱＳｔｕｄｙｏｎｐｈｙｓｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆα－ｐｈａｓｅｓｉｌｉｃｏｎｎｉｔｒｉｄｅｕｎｄｅｒｈｉｇｈｐｒｅｓｓｕｒｅ［Ｄ］Ｃｈｅｎｇｄｕ：ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，２０１９（ｉｎＣｈｉｎｅｓｅ）［雷金桥．α相氮化硅的高压物性研究［Ｄ］成都：四川师范大学，２０１９］［７］　ＳｅｇａｌｌＭＤ，ＬｉｎｄａｎＰＪＤ，ＰｒｏｂｅｒｔＭＪ，ｅｔａｌＦｉｒｓｔ－ｐｒｉｎｃｉｐｌｅｓｓｉｍｕｌａｔｉｏｎ：Ｉｄｅａｓ，ｉｌｌｕｓｔｒａｔｉｏｎｓａｎｄｔｈｅＣＡＳＴＥＰｃｏｄｅ［Ｊ］ＪＰｈｙｓ：ＣｏｎｄｅｎｓＭａｔ，２００２，１４：２７１７［８］　ＰｅｒｄｅｗＪＰ，ＢｕｒｋｅＫ，ＥｒｎｚｅｒｈｏｆＭＧｅｎｅｒａｌｉｚｅｄｇｒａｄｉｅｎｔａｐｐｒｏｘｉｍａｔｉｏｎｍａｄｅｓｉｍｐｌｅ［Ｊ］ＰｈｙｓＲｅｖＬｅｔｔ，１９９６，７７：３８６５［９］　ＫｏｈｎＷ，ＳｈａｍＬＪＳｅｌｆ－ｃｏｎｓｉｓｔｅｎｔｅｑｕａｔｉｏｎｓｉｎｃｌｕｄｉｎｇｅｘｃｈａｎｇｅａｎｄｃｏｒｒｅｌａｔｉｏｎｅｆｆｅｃｔｓ［Ｊ］ＰｈｙｓＲｅｖ，１９６５，１４０：Ａ１１３３［１０］　ＦｉｓｃｈｅｒＴＨ，ＡｌｍｌｏｆＪＧｅｎｅｒａｌ－ｍｅｔｈｏｄｓｆｏｒｇｅｏｍｅｔｒｙａｎｄｗａｖｅｆｕｎｃｔｉｏｎｏｐｔｉｍｉｚａｔｉｏｎ［Ｊ］ＪＰｈｙｓＣｈｅｍ，１９９２，９６：９７６８［１１］　ＨｕａｎｇＪＴ，ＨｕａｎｇＺＨ，ＹｉＳ，ｅｔａｌＦｅ－ｃａｔａｌｙｚｅｄｇｒｏｗｔｈｏｆｏｎｅ－ｄｉｍｅｎｓｉｏｎａｌａｌｐｈａ－Ｓｉ３Ｎ４ｎａｎｏｓｔｒｕｃｔｕｒｅｓａｎｄｔｈｅｉｒｃａｔｈｏｄｏｌｕｍｉｎｅｓｃｅｎｃｅｐｒｏｐｅｒｔｉｅｓ［Ｊ］ＳｃｉＲｅｐ，２０１３，３：３５０４［１２］　ＣｈｉｎｇＷＹ，ＸｕＹＮ，ＧａｌｅＪＤ，ｅｔａｌＡｂ－ｉｎｉｔｉｏｔｏｔａｌｅｎｅｒｇｙｃａｌｃｕｌａｔｉｏｎｏｆａｌｐｈａ－ａｎｄｂｅｔａ－ｓｉｌｉｃｏｎｎｉｔｒｉｄｅａｎｄｔｈｅｄｅｒｉｖａｔｉｏｎｏｆｅｆｆｅｃｔｉｖｅｐａｉｒｐｏｔｅｎｔｉａｌｓｗｉｔｈａｐｐｌｉｃａｔｉｏｎｔｏｌａｔｔｉｃｅｄｙｎａｍｉｃｓ［Ｊ］ＪＡｍＣｅｒａｍＳｏｃ，１９９８，８１：３１８９［１３］　ＭｕｌｌｉｋｅｎＲＳＥｌｅｃｔｒｏｎｉｃｐｏｐｕｌａｔｉｏｎａｎａｌｙｓｉｓｏｎＬＣＡＯ－ＭＯｍｏｌｅｃｕｌａｒｗａｖｅｆｕｎｃｔｉｏｎｓ［Ｊ］ＪＣｈｅｍＰｈｙｓ，１９５５，２３：１８３３［１４］　ＬｉｎＷ，ＺｈａｎｇＹＦ，ＬｉＹ，ｅｔａｌＦｉｒｓｔｐｒｉｎｃｉｐｌｅｓｔｕｄｉｅｓｏｎｔｈｅｇｅｏｍｅｔｒｙａｎｄｅｌｅｃｔｒｏｎｉｃｓｔｒｕｃｔｕｒｅｓｏｆｔｈｅＳｎＯ２（１１０）Ｓｕｒｆａｃｅ［Ｊ］ＡｃｔａＰｈｙｓ．－Ｃｈｉｍ．Ｓｉｎ，２００６，２２：７６（ｉｎＣｈｉｎｅｓｅ）［林伟，章永凡，李奕，等ＳｎＯ２（１１０）弛豫表面构型与电子结构的第一性原理研究［Ｊ］物理化学学报，２００６，２２：７６］［１５］　ＸｕＢ，ＤｏｎｇＪＪ，ＭｃＭｉｌｌａｎＰＦ，ｅｔａｌＥｑｕｉｌｉｂｒｉｕｍａｎｄｍｅｔａｓｔａｂｌｅｐｈａｓｅｔｒａｎｓｉｔｉｏｎｓｉｎｓｉｌｉｃｏｎｎｉｔｒｉｄｅａｔｈｉｇｈｐｒｅｓｓｕｒｅ：Ａｆｉｒｓｔ－ｐｒｉｎｃｉｐｌｅｓａｎｄｅｘｐｅｒｉｍｅｎｔａｌｓｔｕｄｙ［Ｊ］ＰｈｙｓＲｅｖＢ，２０１１，８１：４４［１６］　ＨｕａｎｇＫ，ＨａｎＲＱＳｏｌｉｄＳｔａｔｅＰｈｙｓｉｃｓ［Ｍ］Ｂｅｉ第４０卷原　子　与　分　子　物　理　学　报　第２期ｊｉｎｇ：ＨｉｇｈｅｒＥｄｕｃａｔｉｏｎＰｒｅｓｓ，１９９５（ｉｎＣｈｉｎｅｓｅ）［黄昆，韩汝琦固体物理学［Ｍ］北京：高等教育出版社，１９９５］［１７］　ＰａｎＨＺＦｉｒｓｔｐｒｉｎｃｉｐｌｅｓｓｔｕｄｙｏｆβ－Ｓｉ３Ｎ４ｍａｔｅｒｉａｌｓ［Ｄ］Ｃｈｅｎｇｄｕ：ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，２００６（ｉｎＣｈｉｎｅｓｅ）［潘洪哲 β相氮化硅材料的第一性原理研究［Ｄ］成都：四川师范大学，２００６］［１８］　ＳｈａｏＴＱ，ＲｅｎＴＬ，ＬｉＣＸ，ｅｔａｌＡｐｐｌｉｃａｔｉｏｎｏｆｈｉｇｈｄｉｅｌｅｃｔｒｉｃｃｏｎｓｔａｎｔｍａｔｅｒｉａｌｓｉｎｍｅｍｏｒｙｄｅｖｉｃｅｓ［Ｊ］ＲｅｓｅａｒｃｈａｎｄＰｒｏｇｒｅｓｓｏｆＳＳＥ，２００２，２２：３１２（ｉｎＣｈｉｎｅｓｅ）［绍天奇，任天令，李春晓高介电常数材料在半导体存储器件中的应用［Ｊ］固体电子学研究与进展，２００２，２２：３１２］［１９］　ＪｉａＸＹＴｈｅｓｔｒｕｃｔｕｒａｌａｎｄｏｐｔｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆＳｉＮｘｐｒｅｐａｒｅｄｂｙｒａｄｉｏｆｒｅｑｕｅｎｃｙ（ｒｆ）ｍａｇｎｅｔｒｏｎｓｐｕｔｔｅｒｉｎｇ［Ｄ］Ｂｅｉｊｉｎｇ：ＢｅｉｊｉｎｇＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，２００７（ｉｎＣｈｉｎｅｓｅ）［贾晓昀磁控溅射制备氮化硅薄膜特性研究［Ｄ］北京：北京交通大学，２００７］［２０］　ＷａｎｇＹＲ，ＺｏｕＱ，ＬｕＤＷＥｌｅｃｔｒｏｎｅｎｅｒｇｙｌｏｓｓｓｐｅｃｔｒｏｓｃｏｐｙａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｓｉｎｍａｔｅｒｉａｌｓｓｃｉｅｎｃｅ［Ｊ］Ｐｈｙｓｉｃｓ，１９９４，２３：３５０（ｉｎＣｈｉｎｅｓｅ）［王永瑞，邹骐，卢党吾电子能量损失谱学及其在材料科学中的应用［Ｊ］物理，１９９４，２３：３５０］。

Mg掺杂CdSe电子结构和光学性质的第一性原理

Mg掺杂CdSe电子结构和光学性质的第一性原理王亚超;王梅;苏希玉;李振勇;赵伟【摘要】采用基于密度泛函理论的第一性原理平面波超软赝势法,计算了纤锌矿结构Cd1-xMxSe(x=0,0.125,0.250,0.375)的电子结构和光学性质.结果表明,不同系统的价带顶都主要由Se4p态决定,其位置基本不变;导带底由Se4s态和cd5s共同决定,并且随着掺杂浓度的增加向高能区移动,结果使得带隙展宽,由此使得系统介电函数虚部的峰值和折射率实部的峰值随掺杂浓度的增大而蓝移,计算结果与实验符合.【期刊名称】《发光学报》【年(卷),期】2010(031)006【总页数】6页(P842-847)【关键词】CdSe;电子结构;光学性质;第一性原理【作者】王亚超;王梅;苏希玉;李振勇;赵伟【作者单位】曲阜师范大学物理工程学院,山东曲阜273165;曲阜师范大学物理工程学院,山东曲阜273165;河南大学特种功能材料教育部重点实验室,河南开封475004;曲阜师范大学物理工程学院,山东曲阜273165;曲阜师范大学物理工程学院,山东曲阜273165;曲阜师范大学物理工程学院,山东曲阜273165【正文语种】中文【中图分类】O471.5;O472.31 引言纤锌矿结构硒化镉 (CdSe)禁带宽度为 1.74 eV,是一种性能优良的直接带隙半导体材料[1～3]。

CdSe晶体具有宽的红外透过波段、较高的激光损伤阈值、大的非线性系数和透明波段适宜的双折射等优点。

同时,CdSe晶体的化学稳定性好、不潮解、机械强度适中、加工性能好,是应用价值很大的光学晶体,常被用于制作光敏元件、太阳能电池、激光器等。

在 CdSe中掺入Mg形成 Cd1-xMgxSe合金,人们已对其进行了较为广泛的实验研究,例如, Miotkowski等[4]用垂直梯度冷凝技术制备合金,研究了其晶格参数和光学特性;W ronkowska等[5]通过布里奇曼方法制备合金,研究了其结构和光学性质;Firszt等[6]报道了合金的光学和电学性质; Derkowska等[7]研究了合金非线性光学的性质。