Magneto-elastic Polarons and Superconductivity of Underdoped Cuprates HTS's

PHYSICAL REVIEW B94,241110(R)(2016)Hubbard band versus oxygen vacancy states in the correlated electron metal SrVO3S.Backes,1T.C.R¨o del,2,3F.Fortuna,2E.Frantzeskakis,2P.Le F`e vre,3F.Bertran,3M.Kobayashi,4R.Yukawa,4 T.Mitsuhashi,4M.Kitamura,4K.Horiba,4H.Kumigashira,4R.Saint-Martin,5A.Fouchet,6B.Berini,6Y.Dumont,6A.J.Kim,1F.Lechermann,7,8H.O.Jeschke,1M.J.Rozenberg,9R.Valent´ı,1,*and A.F.Santander-Syro2,†1Institut f¨u r Theoretische Physik,Goethe-Universit¨a t Frankfurt,Max-von-Laue-Strasse1,60438Frankfurt am Main,Germany 2CSNSM,Univ.Paris-Sud,CNRS/IN2P3,Universit´e Paris-Saclay,91405Orsay Cedex,France3Synchrotron SOLEIL,L’Orme des Merisiers,Saint-Aubin-BP48,91192Gif-sur-Yvette,France 4Photon Factory,Institute of Materials Structure Science,High Energy Accelerator Research Organization(KEK),1-1Oho,Tsukuba305-0801,Japan5SP2M-ICMMO-UMR-CNRS8182Universit´e Paris-Sud,Universit´e Paris-Saclay,91405Orsay Cedex,France 6GEMaC,Universit´e de Versailles St.Quentin en Y.-CNRS,Universit´e Paris-Saclay,Versailles,France7Institut f¨u r Theoretische Physik,Universit¨a t Hamburg,Jungiusstrasse9,20355Hamburg,Germany8Institut f¨u r Keramische Hochleistungswerkstoffe,TU Hamburg-Harburg,D-21073Hamburg,Germany 9Laboratoire de Physique des Solides,CNRS,Univ.Paris-Sud,Universit´e Paris-Saclay,91405Orsay Cedex,France(Received22February2016;published19December2016)We study the effect of oxygen vacancies on the electronic structure of the model strongly correlatedmetal SrVO3.By means of angle-resolved photoemission spectroscopy(ARPES)synchrotron experiments,we investigate the systematic effect of the UV dose on the measured spectra.We observe the onset of a spuriousdose-dependent prominent peak at an energy range where the lower Hubbard band has been previously reportedin this compound,raising questions on its previous interpretation.By a careful analysis of the dose-dependenteffects we succeed in disentangling the contributions coming from the oxygen vacancy states and from the lowerHubbard band.We obtain the ARPES spectrum in the limit of a negligible concentration of vacancies,wherea clear signal of a lower Hubbard band remains.We support our study by means of state-of-the-art ab initiocalculations that include correlation effects and the presence of oxygen vacancies.Our results underscore therelevance of potential spurious states affecting ARPES experiments in correlated metals,which are associatedwith the ubiquitous oxygen vacancies as extensively reported in the context of a two-dimensional electron gas atthe surface of insulating d0transition metal oxides.DOI:10.1103/PhysRevB.94.241110Introduction.A major challenge of modern physics is to understand the fascinating phenomena in strongly correlated transition metal oxides(TMOs),which emerge in the neighbor-hood of the Mott insulator state.Some preeminent examples that have gathered interest for almost30years are high temperature superconductivity,colossal magnetoresistance, heavy fermion physics,and,of course,the Mott metal-insulator transition itself[1].Significant theoretical progress was made with the introduction of dynamical meanfield theory (DMFT)and its combination with ab initio density functional methods[local density approximation(LDA)+DMFT],which allows treatment of the interactions promoting itinerancy and localization of electrons on equal footing[2–4].Among the most emblematic achievements of DMFT is the prediction of a Hubbard satellite,which separates from the conduction band of a metal.This satellite results from the partial localization of conduction electrons due to their mutual Coulomb repulsion. Early DMFT studies also showed that it is the precursor of the localized electronic states of a Mott insulator[5].Since then,these predictions promoted a large number of studies using photoemission spectroscopy,which is a technique to directly probe the presence of Hubbard bands.In this context, the TMO system SrVO3has emerged as the drosophila model system to test the predictions of strongly correlated electron *valenti@itp.uni-frankfurt.de†andres.santander@csnsm.in2p3.fr theories.In fact,SrVO3is arguably the simplest correlated metal.It is a simple cubic perovskite,with nominally one electron per V site,which occupies a threefold degenerate t2g conduction band.While the presence of a satellite in the photoemission spectra of Ni metal was already well known,in the context of correlated TMOs,the Hubbard band was originally reported in a systematic investigation of Ca1−x Sr x VO3[6],which was followed by many subsequent studies,including angle-resolved photoemission spectroscopy (ARPES)[7–9]and comparisons with theoretical predictions (see,for instance,Refs.[10–20],among others).One of the most salient features in SrVO3is the observation of a broad peak at an energy of about−1.5eV in angle integrated photoemission spectra(upper black curve in Fig.1), which is interpreted as a Hubbard satellite linked to the V t2g electrons.This feature is also seen in a large range of 3d1materials[21,22].The ratio of spectral strength between the quasiparticle(QP)state and the incoherent satellite in SrVO3is an important indicator of the magnitude of electron correlations[1,2].However,photoemission experiments using different photon energies or light brilliance have reported very dissimilar values for such a ratio[11],making the quantitative benchmarking of realistic ab initio theories for correlated electron systems difficult[6,11,18,23,24].Moreover,as shown in Fig.1,a broad peak at about the same energy is also observed in several d0TMO cubic perovskites,such as SrTiO3, KTaO3,or anatase TiO2.Nevertheless,in all these cases the feature has been clearly linked to the presence of oxygenS.BACKES et al.PHYSICAL REVIEW B94,241110(R)(2016)FIG.1.Integrated UV photoemission spectra for various per-ovskite oxides,showing a quasiparticle peak at E F and an in-gap state at energies between1and1.5eV.For SrVO3(upper black curve),a correlated-electron metal,the QP peak corresponds to the bulk conduction band,and as will be shown further,the in-gap state is a superposition of the lower Hubbard band and localized electronic states associated with oxygen vacancies.For the other d0 oxides,such as KTaO3(blue curve),anatase TiO2(green curve), or SrTiO3(red curve),the QP peak and in-gap state correspond respectively to a confined quasi-2D electron gas at the sample surface and to localized states,all formed by oxygen vacancies.The crystal orientation(normal to the samples’surface)is indicated in all cases. defects[25–32].Interestingly,recent ab initio calculations show that the spectral weight at−1.3eV in SrTiO3most likely is not of Ti t2g orbital character,but should be understood as an in-gap defect state with Ti e g character[33–36].Thus,we are confronted with the fact that at about1.5eV below the Fermi level(E F),wefind the lower Hubbard bands of d1systems as well as the in-gap states of oxygen-deficient d0systems.In view of these observations one may unavoidably wonder(and worry),despite the great success of DMFT methods,whether the putative Hubbard satellite of SrVO3might also originate from oxygen vacancy states.Moreover,one should also worry about the possibility of these extrinsic states affecting the features of the conduction band dispersion.In the present Rapid Communication we resolve these issues in a thorough manner.We present a systematic photoemission study of SrVO3,to demonstrate dramatic consequences in the spectra due to the creation of oxygen ing ARPES,we directly show that the UV or x-rays used for measurements can produce a large enhancement, of almost an order of magnitude,of the peak at−1.5eV, similar to the effect observed in d0oxide insulators[25–28,37].Despite these significant effects on the energy states around the Mott-Hubbard band,we are able to determine the bulk SrVO3photoemission spectrum in the limit of a negligible concentration of vacancies,where a clear signal of the dispersive correlated Hubbard band remains.We support the interpretation of the experimental data by means of state-of-the-art LDA+DMFT calculations on SrVO3with oxygen vacancies.Consistent with our experimental data,the calculations show that oxygen vacancies produce states(of e g symmetry)at energies near the Hubbard satellite.While our study provides definite evidence of a correlated Hubbard band in SrVO3as predicted by DMFT,it also underlines the significant effects due to oxygen vacancies,which may also affect photoemission data in other TMOs.Methods.The bulk-like relaxed,crystalline(001)oriented SrVO3thinfilms were grown by pulsed laser deposition (PLD)either at the GEMaC laboratory,then measured at the CASSIOPEE beamline of Synchrotron SOLEIL,or in a PLD chamber directly connected to the ARPES setup at beamline2A of KEK-Photon Factory(KEK-PF)[9,38,39]. To clean the surfaces in UHV prior to ARPES experiments at SOLEIL,the SrVO3thinfilms were annealed at550◦C for t=5–20min at pressures lower than2×10−8Torr.At KEK-PF,the PLD growth was performed under a pressure below10−7Torr,to obtain UHV-clean surfaces,using a Sr2V2O7target,which has excess oxygen with respect to SrVO3,thus minimizing the formation of vacancies during the growth.In all cases,the surface quality was confirmed right before ARPES measurements by low-energy electron diffraction(LEED).The thinfilms measured at KEK-PF showed a c(4×4)surface reconstruction,which does not affect the analysis and conclusions of this work.For the ARPES measurements we used linearly polarized photons in the energy range30–110eV and hemispherical electron analyzers with vertical slits at SOLEIL and horizontal slits at KEK-PF.The angular and energy resolutions were0.25◦and 15meV.The mean diameter of the incident photon beam was smaller than100μm.The UV light brilliance,measured using calibrated photodiodes,was≈5×109photons s−1μm−2at SOLEIL,and about100times smaller at KEK-PF.The samples were cooled down to T=20K before measuring.Unless specified otherwise,all data were taken at that temperature. The results were reproduced on more thanfive samples.All through this Rapid Communication,directions and planes are defined in the cubic unit cell of SrVO3.We denote [hkl]the crystallographic directions in real space, hkl the corresponding directions in reciprocal space,and(hkl)the planes orthogonal to those directions.The indices h,k,and l of hkl correspond to the reciprocal lattice vectors of the cubic unit cell of SrVO3.The Supplemental Material[40]presents further details about the sample growth and measurements.Experimental results.Figure2(a)shows the integrated photoemission spectra of SrVO3as a function of the UV dose, measured at CASSIOPEE SOLEIL under the same conditions of light brilliance of any standard ARPES experiment at a third-generation synchrotron.The measurements were done by continuously irradiating the sample with hν=33eV photons while recording the spectra as a function of irradiation time, with an accumulation time of about2min per spectrum.The blue and black curves show spectra for the lowest and highest measured doses,obtained respectively after∼2min and∼2h of irradiation.These data clearly demonstrate that the very UV or x-rays used for photoemission experiments can produce radical changes in the measured spectra of SrVO3.Note in fact that a similar effect has been observed for VO2[41].In particular,from Fig.2(a)we observe that the amplitude ofHUBBARD BAND VERSUS OXYGEN V ACANCY STATES IN THE...PHYSICAL REVIEW B94,241110(R)(2016)FIG.2.(a)Photoemission spectra of SrVO3as a function of UV dose,measured at Synchrotron SOLEIL(hν=33eV).The energy distribution curves(EDCs)were extracted from raw ARPES data around the 002point integrated along the k= 010 direction.(b)Corresponding momentum distribution curves(MDCs)integrated over50meV below E F.Peaks in the MDCs indicate the Fermi momenta.(c),(d)Same as(a),(b)for SrTiO3(hν=47eV).Thefilling of a2DEG upon UV irradiation is evidenced by the formation of QP peaks in the EDCs and MDCs at E F[inset of(c)and(d),respectively].All data were taken at20K.the in-gap state at−1.5eV,and,more significantly,the ratio of in-gap to quasiparticle(QP)amplitudes,strongly increase with increasing UV dose,going from about1:3in a pristine sample to more than2:1in a heavily irradiated sample. Importantly,note that the QP peak position remains basically dose independent,implying that the carriers created by the UV or x irradiation do not significantly dope the conduction band,and form dominantly localized states.This is confirmed in Fig.2(b),which shows that the Fermi momenta of the QP band,given by the peak positions in the momentum distribution curves(MDCs)at E F,are also dose independent. Additional data presented in the Supplemental Material further demonstrate that our measurements yield the expected3D bulk Fermi surface of SrVO3.Thus,the observed increase in intensity of the in-gap state upon UV irradiation cannot be ascribed to a change infilling of the conduction band,which could have affected the electron correlations.Instead,this unambiguously shows the light-assisted formation of localized defect states at essentially the same energy as that of the expected intrinsic lower Hubbard band—which should then resemble the in-gap peak observed at the lowest UV doses.In fact,as mentioned previously,it is well established that strong doses of UV or x-rays create a large concentration of oxygen vacancies in several d0perovskites[25–32,42]. As illustrated in Figs.2(c)and2(d)for the case of SrTiO3, the progressive doping of the surface region with oxygen vacancies,due to synchrotron UV irradiation,has two effects: the formation of a very intense in-gap state at about−1.3eV, and,in contrast to SrVO3,the simultaneous creation of a sharp QP peak at E F corresponding to a confined quasi-2D electron gas(2DEG)at the samples’surface.The effective mass of such2DEG,precisely determined by ARPES,matches the mass expected from density functional theory calcula-tions[25,26,43,44].Thus,as in SrVO3,the increase in intensityof the in-gap state observed in SrTiO3upon UV or x irradiationcannot be due to an onset or increase of electron correlations,and should be ascribed to an extrinsic effect.We therefore conclude that,in SrVO3,exposure to syn-chrotron UV or x-rays creates oxygen vacancies,which are inturn responsible for the extrinsic increase in intensity of thein-gap state evidenced by our measurements.This effect canseriously obscure the determination of the spectral function ofthis model system,thus hampering the advancement of validtheories for correlated electron systems.Thefindings described above imply that the correct ex-perimental determination of the vacancy-free photoemissionspectrum of SrVO3should(i)use samples that from thebeginning have the lowest possible concentration of oxygenvacancies,and(ii)use doses of UV or x-ray light low enoughto avoid light-induced changes in the measured spectra.Tothis end,we measured SrVO3thinfilms grown directly insitu at beamline2A of KEK-PF.As mentioned before,the growth protocol of such thinfilms minimizes the formationof vacancies,while the UV light brilliance at KEK-PF is ∼100times smaller than the one in Figs.2(a)and2(b)from measurements at SOLEIL.We checked(see the SupplementalMaterial)that under these conditions the spectra did notchange with time,even after several hours of measurements.The resulting energy-momentum ARPES map,and its secondderivative,are presented in Figs.3(a)and3(b).One clearlyobserves the dispersing QP band along with an also dispersivein-gap state of weaker intensity,corresponding to the intrinsiclower Hubbard band,as reported in previous works[7].Theintrinsic spectral function of SrVO3will then be given by such aphotoemission spectrum,which approaches the vacancy-freelimit,modulo dipole-transition matrix elements,inherent toS.BACKES et al.PHYSICAL REVIEW B94,241110(R)(2016)FIG.3.(a)Energy-momentum ARPES intensity map measured at KEK-PF with a low UV dose on a SrVO3sample prepared in situ,using a well-established protocol to minimize the formation of oxygen vacancies(see the main text and Supplemental Material).Note that due to the choice of light polarization,the heavy bands along(100)are not observed and only the contribution of the light d xy band is detected.The data were acquired at hν=88eV around ¯103.(b)Second derivative(negative values)of the map in(a).The use of second derivatives allows a better visualization of the dispersion of both the quasiparticle and Mott-Hubbard bands on the same color plot.The dispersionless feature at E F is a spurious effect of such a second derivative on the Fermi-Dirac cutoff.(c),(d)Same as(a),(b)after a strong UV irradiation dose,measured at SOLEIL(hν=33eV),typical of modern third-generation synchrotrons.The measurements were done at hν=33eV close to 002.All data were taken at20K.Note that at constant photon energy,ARPES maps out the electronic structure at a spherical surface of three-dimensional (3D)k space,which can be locally approximated to a plane for all our measurements(details in the Supplemental Material).The different choice of photon energies and k-space positions for measurements at KEK-PF[(a)and(b)]and SOLEIL[(c)and(d)]was dictated by the different geometrical configurations and constraints of the beamlines in both synchrotrons.the photoemission process,which can still modulate the intensity of the QP peak relative to the Hubbard peak.A calculation of such matrix elements requires a full one-step calculation of the photoemission process,which is beyond the scope of this work.By contrast,Figs.3(c)and3(d) show the momentum-resolved electronic structure of a sample, measured at SOLEIL,that was intensively irradiated.There, the peak at−1.5eV becomes broader,more intense,and nondispersive—all characteristic signatures of a high random concentration of oxygen vacancies.Numerical calculations.To rationalize from a microscopic point of view the influence of oxygen vacancies on the electronic structure of SrVO3,we performed charge self-consistent LDA+DMFT calculations for bulk SrVO3and var-ious relaxed oxygen-deficient SrVO3supercells.The latter are computationally demanding calculations.We shall focus here on the case of a2×2×3supercell with two oxygen vacancies located at opposite apical sites of one vanadium atom,as shown in the inset of Fig.4(b).We use such a vacancy arrangement as it is the prototypical one for d0compounds[43].For our LDA+DMFT calculations we chose values of U= 2.5eV and J=0.6eV for vanadium and included the effects of bandwidth renormalization due to dynamically screened Coulomb interactions by following the prescription suggested in Ref.[45](the LDA+DMFT unrenormalized data are shown in the Supplemental Material).In Figs.4(a)and4(c)we show, respectively,the results of the k-integrated and k-resolved spectral functions for bulk SrVO3without oxygen vacancies. Wefind the expected features of a t2g quasiparticle peak at the Fermi level and a lower Hubbard band at negative energies of the same t2g nature,in agreement with the photoemission spectra in Fig.2(a)and Figs.3(a)and3(b).The light band at E F along k 100 [Fig.4(c)]consists of two degenerate bands of d xy and d xz characters,while the heavy band along the same direction has d yz character.While comparing with the measured k-resolved spectral function[Figs.3(a)and3(b)],HUBBARD BAND VERSUS OXYGEN V ACANCY STATES IN THE...PHYSICAL REVIEW B94,241110(R)(2016)FIG.4.LDA+DMFT results for SrVO3including bandwidth renormalization effects[45].(a)k-integrated spectral function for bulk SrVO3.The V t2g orbitals show a quasiparticle peak at E F and a lower Hubbard band at−1.6eV.(b)Spectral function for the2×2×3supercell of SrVO3with two oxygen vacancies.An additional nondispersive V e g vacancy state originating from the V atom neighboring the oxygen vacancies leads to a sharp peak below the Fermi level at∼−1.0eV.The V t2g orbitals show a quasiparticle peak at E F and a lower Hubbard band at−1.8eV.(c)and(d)show the corresponding spectral functions(multiplied by a Fermi-Dirac function at20K)along the X- -X path.one should bear in mind that along -X(or -Y)the heavy d yz(or d xz)bands are silenced by dipole-transition selection rules in the experiment[25].Inclusion of bandwidth renormalization[45]renders the lower Hubbard band at an energy(−1.6eV)in reasonable agreement with experiment (−1.5eV).We adopted typical values for U and J from the literature.We did not attempt to further optimize the values to get a better quantitative agreement with the experimental data, for two reasons:First is the heavy numerical cost,and second, as we show next in the calculations with oxygen vacancies, the adopted values facilitate the distinct visualization of the contributions from the Hubbard and localized states to the incoherent peak at∼−1.5eV.The removal of oxygen atoms in the system leads to the donation of two electrons per oxygen to its surrounding. Already at the level of density functional theory(DFT)in the local density approximation(LDA)(see the Supplemental Material),wefind that most of the charge coming from the additional electrons is transferred to the3d z2orbitals of the neighboring V atom,developing into a sharp peak of e g symmetry located around−1.0eV,i.e.,at an energy close to the position of the experimentally observed oxygen vacancy states.In analogy to the experimental average over many lattice sites,note that averaging among various supercells with differentoxygen vacancy locations and concentrations(which is beyondthe scope of the present work)would result in a wider in-gape g band,as demonstrated for the case of SrTiO3(see Fig.3ofRef.[34])and for some cases in SrVO3(see the SupplementalMaterial,Fig.S7).By including electronic correlations within(bandwidth renormalized)LDA+DMFT we then see that allthe experimental observations qualitatively emerge.In fact,the conducting t2g orbitals develop a lower Hubbard bandpeaked at energies about−1.8eV[Figs.4(b)and4(d)],similarto the bulk case without oxygen vacancies.Most notably,this lower Hubbard satellite does not increase in amplitudewith the introduction of vacancies,but rather broadens.Inaddition,the oxygen vacancy defect states situated at about −1eV remain qualitatively unchanged by the correlation effects,but experience a broadening with respect to the pureLDA case.This is in agreement with the photoemission data,evidencing that the increase in intensity of the in-gap statein the oxygen-deficient SrVO3is not to be attributed to anincrease in population of the lower Hubbard satellite,butinstead to the manifestation of vacancy states of e g character.Conclusions.In summary,we performed a detailed study of the effects of oxygen vacancies in the spectroscopy of the archetypal strongly correlated electron system SrVO3.We found that oxygen vacancy states,which are created by UV or x-ray irradiation,occur at energies close to the Hubbard satellite.This dramatically affects the measured line shape of the Mott-Hubbard band and the ratio of intensities between the quasiparticle and the Mott-Hubbard peaks.By means of a systematic study under a controlled irradiation dose, using samples directly grown in situ,we were able to obtain the photoemission spectrum of the bulk SrVO3system in the limit of a negligible concentration of oxygen vacancies. Our experimental interpretation is supported by LDA+DMFT calculations,which provided further insight into the likely nature of the oxygen vacancy states.Acknowledgments.We thank Silke Biermann,Ralph Claessen,Marc Gabay,and Michael Sing for discussions. This work was supported by public grants from the French National Research Agency(ANR),project LACUNES No. ANR-13-BS04-0006-01,and the“Laboratoire d’Excellence Physique Atomes Lumi`e re Mati`e re”(LabEx PALM project ELECTROX)overseen by the ANR as part of the“Investisse-ments d’Avenir”program(reference:ANR-10-LABX-0039). 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１０００ ０５６９／２０２０／０３６（０６） １７０５ １８ＡｃｔａＰｅｔｒｏｌｏｇｉｃａＳｉｎｉｃａ　岩石学报ｄｏｉ：１０ １８６５４／１０００ ０５６９／２０２０ ０６ ０４榴辉岩中单斜辉石 石榴子石镁同位素地质温度计评述黄宏炜１　杜瑾雪１　柯珊２ＨＵＡＮＧＨｏｎｇＷｅｉ１，ＤＵＪｉｎＸｕｅ１ ａｎｄＫＥＳｈａｎ２１ 中国地质大学地球科学与资源学院，北京　１０００８３２ 中国地质大学地质过程与矿产资源国家重点实验室，北京　１０００８３１ ＳｃｈｏｏｌｏｆＥａｒｔｈＳｃｉｅｎｃｅｓａｎｄＲｅｓｏｕｒｃｅｓ，ＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＧｅｏｓｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８３，Ｃｈｉｎａ２ ＳｔａｔｅＫｅｙＬａｂｏｒａｔｏｒｙｏｆＧｅｏｌｏｇｉｃａｌＰｒｏｃｅｓｓｅｓａｎｄＭｉｎｅｒａｌＲｅｓｏｕｒｃｅｓ，ＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＧｅｏｓｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８３，Ｃｈｉｎａ２０１９ １１ １４收稿，２０２０ ０４ ０８改回ＨｕａｎｇＨＷ，ＤｕＪＸａｎｄＫｅＳ ２０２０ Ｒｅｖｉｅｗｏｎｔｈｅｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓｆｏｒｅｃｌｏｇｉｔｅｓ ＡｃｔａＰｅｔｒｏｌｏｇｉｃａＳｉｎｉｃａ，３６（６）：１７０５－１７１８，ｄｏｉ：１０ １８６５４／１０００ ０５６９／２０２０ ０６ ０４Ａｂｓｔｒａｃｔ Ｔｈｅｒｅｍａｒｋａｂｌｅｅｑｕｉｌｉｂｒｉｕｍｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｆｒａｃｔｉｏｎａｔｉｏｎｂｅｔｗｅｅｎｃｌｉｎｏｐｙｒｏｘｅｎｅａｎｄｇａｒｎｅｔｏｂｓｅｒｖｅｄｉｎｅｃｌｏｇｉｔｅｓｍａｋｅｓｉｔａｐｏｔｅｎｔｉａｌｈｉｇｈ ｐｒｅｃｉｓｉｏｎｇｅｏｔｈｅｒｍｏｍｅｔｅｒ Ｔｈｅｒｅｆｏｒｅ，ｔｈｉｓｐａｐｅｒｓｅｌｅｃｔｓ６４ｐａｉｒｓｏｆｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｄａｔａｏｆｅｃｌｏｇｉｔｅｓｉｎｔｈｅＣｈｉｎｅｓｅｓｏｕｔｈｗｅｓｔｅｒｎＴｉａｎｓｈａｎｏｒｏｇｅｎ，ｉｎｔｈｅＤａｂｉｅ ＳｕｌｕｏｒｏｇｅｎａｎｄｉｎｔｈｅＫａａｐｖａａｌｃｒａｔｏｎｉｎｔｈｅＳｏｕｔｈＡｆｒｉｃａｆｒｏｍｌｉｔｅｒａｔｕｒｅｓ Ｔｈｅｎ，ｗｅｓｃｒｅｅｎｅｄ５０ｐａｉｒｓｏｆｄａｔａｔｈａｔｒｅａｃｈｔｈｅｅｑｕｉｌｉｂｒｉｕｍｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｆｒａｃｔｉｏｎａｔｉｏｎｂｙｔｈｅδ２６ＭｇＣｐｘ δ２６ＭｇＧｒｔｄｉａｇｒａｍ Ｕｓｉｎｇｔｈｅｓｅｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｅｑｕｉｌｉｂｒｉｕｍｆｒａｃｔｉｏｎａｔｉｏｎｄａｔａ，ｗｅｃａｌｃｕｌａｔｅｄｐｅａｋｔｅｍｐｅｒａｔｕｒｅｓｏｆｅｃｌｏｇｉｔｅｓｂｙｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓｏｆＨｕａｎｇｅｔａｌ （２０１３）ｔｈｒｏｕｇｈｆｉｒｓｔ ｐｒｉｎｃｉｐｌｅｓｃａｌｃｕｌａｔｉｏｎａｎｄＷａｎｇｅｔａｌ （２０１２）ａｎｄＬｉｅｔａｌ （２０１６）ｔｈｒｏｕｇｈｅｍｐｉｒｉｃａｌｅｓｔｉｍａｔｉｏｎ，ａｎｄｃｏｍｐａｒｅｄｔｈｅｍｗｉｔｈｔｈｅｐｅａｋｔｅｍｐｅｒａｔｕｒｅｓｇｉｖｅｎｂｙｏｔｈｅｒｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓ Ｂｙａｎａｌｙｚｉｎｇｔｈｅｃａｌｃｕｌａｔｉｏｎｒｅｓｕｌｔｓ，ｉｔｉｓｆｏｕｎｄｔｈａｔｆｏｒｏｒｏｇｅｎｉｃｅｃｌｏｇｉｔｅｓ，ｔｈｅｃａｌｃｕｌａｔｉｏｎｒｅｓｕｌｔｓｏｆｔｈｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｏｆＨｕａｎｇｅｔａｌ （２０１３）ａｒｅｃｏｎｓｉｓｔｅｎｔｗｉｔｈｔｈｏｓｅｐｒｅｖｉｏｕｓｌｙｏｂｔａｉｎｅｄｂｙｔｒａｄｉｔｉｏｎａｌｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓａｎｄｐｈａｓｅｅｑｕｉｌｉｂｒｉａｍｏｄｅｌｉｎｇ，ｗｈｉｌｅｔｈｅｃａｌｃｕｌａｔｉｏｎｒｅｓｕｌｔｓｏｆｔｈｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓｏｆＷａｎｇｅｔａｌ （２０１２）ａｎｄＬｉｅｔａｌ （２０１６）ａｒｅｓｉｇｎｉｆｉｃａｎｔｌｙｌｏｗｅｒ Ｆｏｒｔｈｅｃｒａｔｏｎｅｃｌｏｇｉｔｅｓ，ｔｈｅｃａｌｃｕｌａｔｉｏｎｒｅｓｕｌｔｓｏｆａｌｌｔｈｅｔｈｒｅｅｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓａｒｅｓｉｇｎｉｆｉｃａｎｔｌｙｄｉｆｆｅｒｅｎｔｆｒｏｍｒｅｓｕｌｔｓｏｆｔｒａｄｉｔｉｏｎａｌｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓｂｙｍｏｒｅｔｈａｎ５０℃，ｗｈｉｃｈｉｓｍｏｓｔｐｒｏｂａｂｌｙｃａｕｓｅｄｂｙｒｅ ｅｑｕｉｌｉｂｒｉｕｍｏｆｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｄｕｒｉｎｇｅａｒｌｙｒｅｔｒｏｇｒａｄｅｍｅｔａｍｏｒｐｈｉｓｍａｔｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｓ Ｔｈｉｓｉｎｄｉｃａｔｅｓｔｈａｔｔｈｅｓｅｔｈｒｅｅｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓａｒｅｎｏｔａｐｐｌｉｃａｂｌｅｆｏｒｔｈｅｃｒａｔｏｎｅｃｌｏｇｉｔｅｓ Ｂａｓｅｄｏｎｔｈｅａｂｏｖｅｄａｔａ，ｔｈｅｍｅｔｈｏｄｏｆｅｍｐｉｒｉｃａｌｅｓｔｉｍａｔｉｏｎｉｓｕｓｅｄｔｏｃａｌｉｂｒａｔｅａｎｅｗｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒ，ｗｈｉｃｈｉｓΔ２６ＭｇＣｐｘ Ｇｒｔ＝１ １１×１０６／［Ｔ（Ｋ）］２（Ｒ２＝０ ９２）．Ｉｎａｄｄｉｔｉｏｎ，ｔｈｉｓｐａｐｅｒａｌｓｏｂｒｉｅｆｌｙｄｉｓｃｕｓｓｅｓａｐｐｌｉｃａｔｉｏｎｐｒｏｓｐｅｃｔｏｆｔｈｅｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓａｎｄｔｈｅｐｒｏｂｌｅｍｓｔｈａｔｓｈｏｕｌｄｂｅｐａｉｄａｔｔｅｎｔｉｏｎｔｏｄｕｒｉｎｇａｐｐｌｉｃａｔｉｏｎ Ｋｅｙｗｏｒｄｓ Ｅｃｌｏｇｉｔｅｓ；Ｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒ；Ｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅ；Ｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔ摘　要 榴辉岩中单斜辉石和石榴子石之间显著的镁同位素平衡分馏，使其成为一种具有潜力的高精度地质温度计。

第４０卷㊀第７期２０１９年７月发㊀光㊀学㊀报ＣＨＩＮＥＳＥＪＯＵＲＮＡＬＯＦＬＵＭＩＮＥＳＣＥＮＣＥＶｏｌ ４０Ｎｏ ７Ｊｕｌｙꎬ２０１９文章编号:１０００￣７０３２(２０１９)０７￣０９１５￣０７界面处理对ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴｓ器件动态特性的影响韩㊀军１ꎬ赵佳豪１ꎬ赵㊀杰１ꎬ２ꎬ邢艳辉１∗ꎬ曹㊀旭１ꎬ付㊀凯２ꎬ宋㊀亮２ꎬ邓旭光２ꎬ张宝顺２(１.北京工业大学信息学部光电子技术省部共建教育部重点实验室ꎬ北京㊀１００１２４ꎻ２.中国科学院苏州纳米技术与纳米仿生研究所纳米器件与应用重点实验室ꎬ江苏苏州㊀２１５１２３)摘要:研究不同界面处理对ＡｌＧａＮ/ＧａＮ金属￣绝缘层￣半导体(ＭＩＳ)结构的高电子迁移率晶体管(ＨＥＭＴ)器件性能的影响ꎮ采用Ｎ２和ＮＨ３等离子体对器件界面预处理ꎬ实验结果表明ꎬＮ２等离子体预处理能够减小器件的电流崩塌ꎬ通过对Ｎ２等离子体预处理的时间优化ꎬ发现预处理时间１０ｍｉｎ能够较好地提高器件的动态特性ꎬ３０ｍｉｎ时动态性能下降ꎮ进一步引入ＡｌＮ作为栅介质插入层并经过高温热退火后能够有效提高器件的动态性能ꎬ将器件的阈值回滞从４１１ｍＶ减小至１１１ｍＶꎬ动态测试表明ꎬ在９００Ｖ关态应力下ꎬ器件的电流崩塌因子从４２.０４减小至４.７６ꎮ关㊀键㊀词:电流崩塌ꎻＡｌＮ栅介质插入层ꎻ界面处理ꎻＡｌＧａＮ/ＧａＮ高电子迁移率晶体管中图分类号:ＴＮ３８６.２㊀㊀㊀文献标识码:Ａ㊀㊀㊀ＤＯＩ:１０.３７８８/ｆｇｘｂ２０１９４００７.０９１５ＩｍｐａｃｔｏｆＩｎｔｅｒｆａｃｅＴｒｅａｔｍｅｎｔｏｎＤｙｎａｍｉｃＣｈａｒａｃｔｅｒｉｓｔｉｃｏｆＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴｓＨＡＮＪｕｎ１ꎬＺＨＡＯＪｉａ￣ｈａｏ１ꎬＺＨＡＯＪｉｅ１ꎬ２ꎬＸＩＮＧＹａｎ￣ｈｕｉ１∗ꎬＣＡＯＸｕ１ꎬＦＵＫａｉ２ꎬＳＯＮＧＬｉａｎｇ２ꎬＤＥＮＧＸｕ￣ｇｕａｎｇ２ꎬＺＨＡＮＧＢａｏ￣ｓｈｕｎ２(１.ＫｅｙＬａｂｏｒａｔｏｒｙｏｆＯｐｔｏ￣ｅｌｅｃｔｒｏｎｉｃｓＴｅｃｈｎｏｌｏｇｙꎬＭｉｎｉｓｔｒｙｏｆＥｄｕｃａｔｉｏｎꎬＢｅｉｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙꎬＢｅｉｊｉｎｇ１００１２４ꎬＣｈｉｎａꎻ２.ＫｅｙＬａｂｏｒａｔｏｒｙｏｆＮａｎｏＤｅｖｉｃｅｓａｎｄＡｐｐｌｉｃａｔｉｏｎｓꎬＳｕｚｈｏｕＩｎｓｔｉｔｕｔｅｏｆＮａｎｏ￣ｔｅｃｈａｎｄＮａｎｏ￣ｂｉｏｎｉｃｓꎬＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓꎬＳｕｚｈｏｕ２１５１２３ꎬＣｈｉｎａ)∗ＣｏｒｒｅｓｐｏｎｄｉｎｇＡｕｔｈｏｒꎬＥ￣ｍａｉｌ:ｘｉｎｇｙａｎｈｕｉ＠ｂｊｕｔ.ｅｄｕ.ｃｎＡｂｓｔｒａｃｔ:ＴｈｅｅｆｆｅｃｔｓｏｆｄｉｆｆｅｒｅｎｔｋｉｎｄｓｏｆｉｎｔｅｒｆａｃｅｔｒｅａｔｍｅｎｔｏｎｔｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｏｆＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴｓｗｅｒｅｓｔｕｄｉｅｄｉｎｔｈｉｓｐａｐｅｒ.Ｎ２ａｎｄＮＨ３ｐｌａｓｍａｐｒｅｔｒｅａｔｍｅｎｔｗｅｒｅｕｓｅｄｔｏｉｍｐｒｏｖｅｔｈｅｉｎｔｅｒｆａｃｅｑｕａｌｉｔｙ.ＴｈｅｒｅｓｕｌｔｓｓｈｏｗｔｈａｔＮ２ｐｌａｓｍａｐｒｅｔｒｅａｔｍｅｎｔｃｏｕｌｄｒｅｄｕｃｅｔｈｅｃｕｒｒｅｎｔｃｏｌｌａｐｓｅｏｆｄｅｖｉｃｅｓ.ＢｙｏｐｔｉｍｉｚｉｎｇｔｈｅｔｉｍｅｏｆＮ２ｐｌａｓｍａｐｒｅｔｒｅａｔｍｅｎｔꎬｉｔｗａｓｆｏｕｎｄｔｈａｔｔｈｅｄｙｎａｍｉｃｃｈａｒａｃｔｅｒｉｓｔｉｃｏｆｄｅｖｉｃｅｓｗｉｔｈ１０ｍｉｎｔｈｅｐｒｅｔｒｅａｔｍｅｎｔｗａｓｉｍｐｒｏｖｅｄꎬｗｈｉｌｅｔｈａｔｏｆ３０ｍｉｎｗａｓｄｅｇｒａｄｅｄ.Ａｓａｇａｔｅｄｉｅｌｅｃｔｒｉｃｉｎ￣ｔｅｒｃａｌａｔｉｏｎｌａｙｅｒꎬｔｈｅａｎｎｅａｌｅｄＡｌＮｉｎｔｅｒｌａｙｅｒｃａｎｅｆｆｅｃｔｉｖｅｌｙｉｍｐｒｏｖｅｔｈｅｄｙｎａｍｉｃｃｈａｒａｃｔｅｒｉｓｔｉｃｏｆｔｈｅｄｅｖｉｃｅ.ＴｈｅＶｔｈｈｙｓｔｅｒｅｓｉｓｗａｓｄｅｃｒｅａｓｅｄｆｒｏｍ４１１ｍＶｔｏ１１１ｍＶꎬａｎｄｔｈｅｄｅｖｉｃｅｃｕｒｒｅｎｔｃｏｌｌａｐｓｅｆａｃｔｏｒｗａｓｒｅｄｕｃｅｄｆｒｏｍ４２.０４ｔｏ４.７６ａｆｔｅｒｕｎｄｅｒＯＦＦ￣ｓｔａｔｅＶＤｓｔｒｅｓｓｏｆ９００.Ｋｅｙｗｏｒｄｓ:ｃｕｒｒｅｎｔｃｏｌｌａｐｓｅꎻＡｌＮｇａｔｅｄｉｅｌｅｃｔｒｉｃｉｎｓｅｒｔｉｏｎｌａｙｅｒꎻｉｎｔｅｒｆａｃｅｔｒｅａｔｍｅｎｔꎻＡｌＧａＮ/ＧａＮｈｉｇｈｅｌｅｃｔｒｏｎｍｏｂｉｌｉｔｙｔｒａｎｓｉｓｔｏｒｓ㊀㊀收稿日期:２０１８￣０８￣２０ꎻ修订日期:２０１８￣１０￣１７㊀㊀基金项目:国家自然科学基金(６１２０４０１１ꎬ１１２０４００９ꎬ６１５７４０１１)ꎻ北京市自然科学基金(４１４２００５ꎬ４１８２０１４)ꎻ北京市教委科学研究基金(ＰＸＭ２０１８＿０１４２０４＿５０００２０)资助项目ＳｕｐｐｏｒｔｅｄｂｙＮａｔｉｏｎａｌＮａｔｕｒａｌＳｃｉｅｎｃｅＦｏｕｎｄａｔｉｏｎｏｆＣｈｉｎａ(６１２０４０１１ꎬ１１２０４００９ꎬ６１５７４０１１)ꎻＢｅｉｊｉｎｇＮａｔｕｒａｌＳｃｉｅｎｃｅＦｏｕｎｄａ￣ｔｉｏｎ(４１４２００５ꎬ４１８２０１４)ꎻＢｅｉｊｉｎｇＭｕｎｉｃｉｐａｌＥｄｕｃａｔｉｏｎＣｏｍｍｉｓｓｉｏｎＳｃｉｅｎｔｉｆｉｃＲｅｓｅａｒｃｈＦｕｎｄ(ＰＸＭ２０１８＿０１４２０４＿５０００２０)９１６㊀发㊀㊀光㊀㊀学㊀㊀报第４０卷１㊀引㊀㊀言ＧａＮ作为第三代半导体的代表ꎬ具有高禁带宽度㊁高击穿电场㊁高电子迁移率㊁以及耐酸碱等特点ꎮ以ＡｌＧａＮ和ＧａＮ异质结结构制备的高电子迁移率晶体管ꎬ由于极化效应产生的天然的高浓度㊁高迁移率的二维电子气ꎬ在功率开关器件的大功率及高频性能方面有很好的应用前景[１￣４]ꎮＭＩＳ￣ＨＥＭＴ器件可以有效地减小器件的栅极漏电ꎬ提高耐压ꎬ提高栅驱动能力ꎮ但是由于栅介质的引入ꎬ产生新的界面ꎬ界面质量给器件的应用带来新的问题ꎬ影响器件的可靠性和阈值回滞等ꎮＥｌｌｅｒ等[５]详细报道了对于ＧａＮ表面的处理过程ꎬ包括湿法化学处理[６]㊁真空退火处理[７]㊁气体氛围下退火处理[８]及离子束㊁等离子体处理[９￣１０]等ꎮＧａＮ材料表面存在含Ｏ的化合物和Ｎ空位[２ꎬ１１]ꎬ这两种缺陷态成为影响界面质量的主要因素ꎬ目前的报道中ꎬ集中于使用含Ｎ等离子体来处理器件表面[１２￣１４]ꎬ主要作用机理为去除Ｏ杂质和补充Ｎ空位ꎮＨａｓｈｉｚｕｍｅ[１５]在器件钝化作用前使用Ｎ２作为等离子体处理样品表面ꎬ得到了很高质量的钝化结果ꎬ而且界面态浓度下降ꎮＲｏｍｅｒｏ[１６]通过原位含氮气等离子体预处理ꎬ器件的电流崩塌㊁输出功率㊁增益等特性取得了非常好的效果ꎮ在本文研究中ꎬ我们对ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴ器件工艺过程中的界面处理进行优化比较ꎬ实验利用等离子体预处理研究不同气体(Ｎ２和ＮＨ３)及不同预处理时间对器件直流性能和动态特性的影响ꎬ并在该研究基础上ꎬ继续引入ＡｌＮ栅介质插入层进行界面处理ꎬ研究采用ＡｌＮ栅介质插入层进行界面处理对器件动静态特性的影响ꎮ２㊀实㊀㊀验ＡｌＧａＮ/ＧａＮＨＥＭＴ外延材料是通过金属有机物化学气相沉积技术在Ｓｉ(１１１)衬底上生长的ꎬ外延结构依次为成核层㊁ＧａＮ缓冲层和ＡｌＧａＮ势垒层ꎮ器件的制备工艺过程为:(１)界面处理过程ꎻ(２)栅介质钝化层制备ꎬ采用ＬＰＣＶＤ沉积ＳｉＮｘ作为栅介质ꎬ主要考虑其具有良好的稳定性和漏电[７]ꎬ利用ＳｉＨ２Ｃｌ２和ＮＨ３作为Ｓｉ源和Ｎ源ꎬ温度７８０ħꎻ(３)注入隔离ꎬ采用Ｆ离子进行注入隔离ꎻ(４)欧姆接触制备ꎬ利用磁中性环路放电刻蚀ＳｉＮｘ形成窗口ꎬ电子束蒸发沉积Ｔｉ/Ａｌ/Ｎｉ/Ａｕ为２０/１３０/５０/５０ｎｍꎬＮ２氛围下８５０ħ退火３０ｓ形成欧姆接触ꎻ(５)栅电极制备ꎬ利用金属热蒸发沉积Ｎｉ/Ａｕ为５０/１０ｎｍ制备栅电极ꎮ图１(ａ)显示的是ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴ器件基本结构示意图ꎬ器件栅介质层厚度为２０ｎｍꎬ器件栅长为２μｍꎬ栅宽为１００μｍꎬ栅漏距离为１６μｍꎬ栅源距离为４μｍꎮ其中对于界面处理工艺过程ꎬ设计了实验Ⅰ:采用不同预处理气体Ｎ２和ＮＨ３对ＡｌＧａＮ/ＧａＮＨＥＭＴ表面预处理ꎬ预处理时间均为５ｍｉｎꎬ实验分别设置为样品Ａ和样品Ｂꎮ在实验Ｉ基础上设计实验方案Ⅱ:选取Ｎ２作为预处理气体ꎬ研究不同预处理时间对ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴ器件的影响ꎬ设置样品Ｃ㊁Ｄ㊁Ｅ分别预处理的时间为０ꎬ１０ꎬ３０ｍｉｎꎮ上述等离子体预处理温度为３５０ħꎬ压强为２６６Ｐａ(２０００ｍｔｏｒｒ)ꎬＲＦ功率为６０ＷꎬＬＦ功率为５０ＷꎮSiN x2DEGAlGaNSiBufferSGAlN2DEGAlGaNSiN xSiBufferSGDD（a）（b）图１㊀(ａ)实验器件基本结构示意图ꎻ(ｂ)引入插入层后的器件结构示意图ꎮＦｉｇ.１㊀(ａ)Ｓｃｈｅｍａｔｉｃｏｆｄｅｖｉｃｅｓｆｏｒｄｉｆｆｅｒｅｎｔｐｒｅ￣ｔｒｅａｔｍｅｎｔ.(ｂ)Ｓｃｈｅｍａｔｉｃｏｆｄｅｖｉｃｅｓｔｒｕｃｔｕｒｅｆｏｒｓａｍｐｌｅｗｉｔｈｉｎ￣ｓｅｒｔｉｏｎｌａｙｅｒ.为进一步改善ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴ器件性能ꎬ在上述实验的基础上ꎬ设计实验Ⅲ:采取ＰＥＡＬＤ生长的ＡｌＮ作为栅介质插入层ꎬ设置样品Ｆ㊁Ｇ㊁Ｈꎬ引入ＡｌＮ插入层的器件结构示意图为图１(ｂ)ꎮ样品Ｆ作为空白对照组未引入插入层界面处理过程ꎬ样品Ｇ和样品Ｈ利用ＰＥＡＬＤ生长３ｎｍＡｌＮꎬＴＭＡｌ为Ａｌ源ꎬＮ２为Ｎ源ꎬ生长温度３００ħꎮ样品Ｈ在栅介质沉积后于Ｎ２氛围下１０００ħ退火２ｍｉｎꎮ样品栅介质ＬＰＣＶＤ￣ＳｉＮｘ１２ｎｍꎮ器件尺寸分别为:栅长２μｍꎬ栅宽１００μｍꎬ栅漏距离３０μｍꎬ栅源距离３μｍꎮ每组实验均采用安捷伦Ｂ１５０５Ａ进行测试表征ꎮ㊀第７期韩㊀军ꎬ等:界面处理对ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴｓ器件动态特性的影响９１７㊀３㊀结果与讨论３.１㊀界面预处理气体的影响图２是Ｎ２和ＮＨ３预处理器件的转移输出曲线ꎬ从图２中可以看出不同的预处理气体对器件的直流特性具有明显的影响ꎮＮ２和ＮＨ３等离子体预处理之后器件的峰值跨导分别是６４.６ｍＳ/ｍｍ和７０.７ｍＳ/ｍｍꎬ饱和电流分别为５７９.３ｍＡ/ｍｍ和５５０ｍＡ/ｍｍꎮＮ２等离子体预处理的器件跨导峰值较ＮＨ３等离子体预处理器件低ꎬ但是饱和电流有所增加ꎮ在图２中还看到ꎬ相比于Ｎ２等离子体预处理ꎬＮＨ３等离子体预处理的实验结果中存在饱和电流下降的现象ꎬ这与Ｋｉｍ[１２]报道的一致ꎬ究其原因是在ＮＨ３在较低功率下产生等离子体的同时会产生一个Ｈ＋的钝化效果ꎮ类似的钝化对于器件的ＲＦ性能会有所提升ꎬ但对器件的ＤＣ特性有退化ꎬＨａｓｈｉｚｕｍｅ[１７]和Ｒｏｍｅｒｏ[１６]的研究已经证明了这一点ꎮ为了进一步对比采用Ｎ２和ＮＨ３不同预处理气体对表面态引起的器件性能退化作用ꎬ实验对样品Ａ和样品Ｂ进行了电流崩塌的表征ꎮ图３分别显示了关态下漏极电压600500-20V GS /VI D /(m A ·m m -1)4003002001000N 2plasmaNH 3plasma（a ）-15-10-55406080200G m /(m S ·m m -1)6005002V d /VI D /(m A ·m m -1)4003002001000N 2plasma NH 3plasma（b ）461012143V -3V -5V -7V -9V80V GS -15~3V 图２㊀Ｎ２和ＮＨ３等离子体预处输出曲线理器件转移输出曲线对比ꎮ(ａ)转移曲线ꎻ(ｂ)输出曲线ꎮＦｉｇ.２㊀ＴｔｒａｎｓｆｅｒａｎｄｏｕｔｐｕｔｃｕｒｖｅｓｆｏｒｓａｍｐｌｅＡｗｉｔｈＮ２ｐｌａｓｍａａｎｄｓａｍｐｌｅＢｗｉｔｈＮＨ３ｐｌａｓｍａ.(ａ)Ｔｒａｎｓ￣ｆｅｒｃｕｒｖｅｓ.(ｂ)Ｏｕｔｐｕｔｃｕｒｖｅｓ.10080300V d /VR D y n a m i c /R O N20010100506040200N 2plasma NH 3plasmaOFF 鄄state:V GS =-15VOFF 鄄ON swtiching time:t =200滋s ON 鄄state:V GS =0V V D =1V图３㊀Ｎ２和ＮＨ３等离子体预处理器件电流崩塌对比Ｆｉｇ.３㊀ＣｕｒｒｅｎｔｃｏｌｌａｐｓｅｆｏｒｓａｍｐｌｅＡｗｉｔｈＮ２ｐｌａｓｍａａｎｄｓａｍｐｌｅＢｗｉｔｈＮＨ３ｐｌａｓｍａ１０ꎬ５０ꎬ１００ꎬ２００ꎬ３００Ｖ下的电流崩塌ꎮ从图３中可以看到在不同的漏极偏压下ꎬＮ２等离子体预处理器件的电流崩塌因子明显较ＮＨ３等离子体预处理的小ꎬＮ２等离子体预处理器件在偏压１００Ｖ时崩塌因子最大值为３５.６ꎬＮＨ３等离子体预处理器件为５７.５ꎻ在偏压３００Ｖ时ꎬＮＨ３等离子体预处理器件的崩塌因子最大值为８５.３ꎬＮ２等离子体预处理器件为１９.１ꎮ对比器件的动静态性能ꎬ采用Ｎ２等离子体预处理能够有效地提高器件的动态性能ꎮ３.２㊀界面预处理时间的影响图４给出了不同预处理时间下ꎬ器件转移输出特性对比ꎮ结果显示不同预处理时间对样品的基本电学性能影响不明显ꎬ预处理后器件的静态性能没有大的提高ꎮ采用ｐｕｌｓｅ￣ＤＣ表征器件的动态性能ꎮ器件测试脉冲是(５ｍｓꎬ３ｍｓ)ꎬ即关态偏压施加的时间是３ｍｓꎬ测试周期是５ｍｓꎬ器件关态偏压为(ＶＤ:５０ＶꎬＶＧＳ:－２０Ｖ)ꎮ图５中展示了不同时间预处理器件的直流/脉冲输出电流曲线对比ꎮ相比于静态输出电流ꎬＣ㊁Ｄ㊁Ｅ样品的脉冲输出电流都发生了明显下降ꎬ其中未经过Ｎ２等离子体预处理的样品Ｃ下降最为严重ꎬ预处理时间１０ｍｉｎ的样品Ｄ结果最好ꎬ样品Ｃ㊁Ｄ及样品Ｅ的饱和电流下降幅度分别为３０６.１ꎬ９９.１ꎬ１８４.５ｍＡ/ｍｍꎮ该结果表明利用Ｎ２等离子体预处理能够明显地减小器件界面导致的性能退化ꎮ对比预处理１０ｍｉｎ的样品Ｄ和处理３０ｍｉｎ的样品Ｅ的结果ꎬ发现长时间的预处理对器件的性能有一定的损害ꎬ主要原因是长时间的预处理导致表面有正电荷或者新的施主态的积累ꎬ使得器件动态性能下降[１８]ꎮ９１８㊀发㊀㊀光㊀㊀学㊀㊀报第４０卷V GS /V600500-15I D /（m A ·m m -1）400300200CD E 1000-20-10-505V d :10V20406080G m /（m S ·m m -1）（a ）V D /V6005004I D /（m A ·m m -1）400300200C D E100001081214V GS （b ）-14~2V 622V -2V-6V-10V 图４㊀不同预处理时间下器件转移输出特性曲线ꎮ(ａ)转移曲线ꎻ(ｂ)输出曲线ꎮＦｉｇ.４㊀Ｔｒａｎｓｆｅｒａｎｄｏｕｔｐｕｔｃｕｒｖｅｓｆｏｒｔｈｒｅｅｓａｍｐｌｅｓ.(ａ)Ｔｒａｎｓｆｅｒｃｕｒｖｅｓ.(ｂ)Ｏｕｔｐｕｔｃｕｒｖｅｓ.6005002V D /VI D /（m A ·m m -1）（a ）Pulse:(5ms,3ms)Based:(V d ,V gs )(50V,-20V)DC:V g :-14~2V step:4V V d :0~10VDCPulse40030020010000468101214166005002V D /VI D /（m A ·m m -1）（b ）Pulse:(5ms,3ms)Based:(V d ,V gs )(50V,-20V)DC:V gs :-14~2V step:4V V d :0~10VDC Pulse40030020010000468101214166005002V D /VI D /（m A ·m m -1）（c ）Pulse:(5ms,3ms)Based:(V d ,V gs )(50V,-20V)DC:V gs :-14~2V step:4V V d :0~10VDC Pulse 4003002001000046810121416600500CV D /VI D /（m A ·m m -1）（d ）400300D E200DCPulse100图５㊀直流㊁脉冲输出曲线对比ꎮ(ａ)样品Ｃꎻ(ｂ)样品Ｄꎻ(ｃ)样品Ｅꎻ(ｄ)实验样品直流/脉冲下饱和电流对比ꎮＦｉｇ.５㊀ＣｏｍｐａｒｉｓｉｏｎｏｆｐｕｌｓｅｄＩ￣Ｖｃｈａｒａｃｔｅｒｉｓｔｉｃｓ.(ａ)ＳａｍｐｌｅＣ.(ｂ)ＳａｍｐｌｅＤ.(ｃ)ＳａｍｐｌｅＥ.(ｄ)ＣｏｍｐａｒｉｓｏｎｏｆｓａｔｕｒａｔｉｏｎｏｕｔｐｕｔｃｕｒｒｅｎｔｄｅｎｓｉｔｙｂｅｔｗｅｅｎｐｕｌｓｅｄａｎｄＤＣ.３.３㊀界面栅介质插入层的影响图６展示了器件的转移输出特性对比ꎮ为了更明显地显示ꎬ将样品Ｆ㊁Ｇ的对比结果显示于图６(ａ)㊁(ｂ)ꎬ将样品Ｇ㊁Ｈ的对比结果显示于图６(ｃ)㊁(ｄ)ꎮ样品Ｆ㊁Ｇ和Ｈ阈值电压分别为－６.４６ꎬ－７.６２ꎬ－７.０４Ｖꎬ由此看出采用ＡｌＮ栅介质插入层导致了器件的阈值向负漂移ꎬ是因为引入ＡｌＮ插入层会在表面形成极化正电荷ꎬ影响阈值电压ꎮ图６中给出了样品Ｆ㊁Ｇ和Ｈ导通电阻分别为１３.８ꎬ１５.７ꎬ２０.６Ω ｍｍꎮ和样品Ｆ比较ꎬ样品Ｇ和Ｈ导通电阻增加的原因可能是引入ＡｌＮ介质插入层会造成导通电阻在一定范围内退化ꎬ从而使饱和电流下降[１９￣２０]ꎮ观察图６(ｃ)ꎬ发现样品Ｈ中ꎬ从－１５Ｖ扫到５Ｖ的正向及从５Ｖ回扫到－１５Ｖ的转移曲线回滞明显消除ꎬ而没有高温退火的样品Ｇ中回滞现象明显ꎮ图７给出了实验样品的正向阈值与负向阈值的对比ꎬ器件的阈值在回扫过程中会出现正向漂移ꎬＦ㊁Ｇ和Ｈ器件的阈值回滞ΔＶｔｈ(Ｖｔｈ负向－Ｖｔｈ正向)分别为４１１ꎬ５０６ꎬ１１１ｍＶꎮ和样品Ｆ相比ꎬ样品Ｈ的ΔＶｔｈ降低７２.９９％ꎬ可以看出采用退火后ＡｌＮ栅介质插入层界面处理的器件阈值回滞明显消除ꎬ说明由界面引起的器件性能退化得到控制ꎮ另外ꎬ未经过退火的ＡｌＮ介质插入层的界面处理的器件Ｇ㊀第７期韩㊀军ꎬ等:界面处理对ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴｓ器件动态特性的影响９１９㊀阈值回滞反而增大ꎬ这可能是ＡｌＮ材料中存在缺陷导致的ꎮ经过１０００ħ的退火过程的样品ＨꎬＡｌＮ材料存在重结晶过程ꎬ提高了ＡｌＮ材料质量ꎬ改善了界面质量ꎮ400-15V GS /VI D /（m A ·m m -1）（a ）30020010006Reference(F)AlN interlaye(G)V GS :-15~5VV D :15~-15V V D :10V-12-9-6-303２00４0６0８0Ｇm /（m S ·m m -1）400V D /VI D /（m A ·m m -1）（b ）3002001000Reference(F)AlN interlaye(G)２４６８１０R ON (F)=13.8赘·mm R ON (G)=15.7赘·mm400-15V GS /VI D /（m A ·m m -1）（c ）30020010006Anneal(H)AlN interlaye(G)V GS :15~5V V GS :15~-15V V D :10V-12-9-6-303２00４0６0８0Ｇm /（m S ·m m -1）400V D /VI D /（m A ·m m -1）（d ）3002001000AlN interlayer anneal(H)AlN interlaye(G)２４６８１０R ON (G)=15.7赘·mm R ON (G)=20.6赘·mmAlN interlayer(G)图６㊀样品转移㊁输出特性曲线对比ꎮ(ａ㊁ｂ)样品Ｆ㊁Ｇ对比ꎻ(ｃ㊁ｄ)样品Ｇ㊁Ｈ对比ꎮＦｉｇ.６㊀Ｃｏｍｐａｒｉｓｏｎｏｆｔｒａｎｓｆｅｒａｎｄｏｕｔｐｕｔｃｕｒｖｅｓｆｏｒｓａｍｐｌｅｓ.(ａꎬｂ)ＳａｍｐｌｅＦａｎｄｓａｍｐｌｅＧ.(ｃꎬｄ)ＳａｍｐｌｅＧａｎｄｓａｍｐｌｅＨ.-6.2FV t h /VGH506mV111mVV GS :-15~5V V GS :5~-15V411mV -6.0-6.4-6.6-6.8-7.0-7.2-7.4-7.6图７㊀样品Ｆ㊁Ｇ㊁Ｈ正回扫阈值回滞对比ꎮＦｉｇ.７㊀ＶｔｈｈｙｓｔｅｒｅｓｉｓｆｏｒｓａｍｐｌｅＦꎬｓａｍｐｌｅＧａｎｄｓａｍｐｌｅＨ.图８给出了样品Ｆ㊁Ｇ㊁Ｈ电流崩塌对比ꎮ对比样品Ｆ和Ｇ数据ꎬ可以看出未经过退火处理的ＡｌＮ插入层对器件的电流崩塌的改善不明显ꎬ这一结论同图７中器件阈值回滞变化相一致ꎮ对比样品Ｇ与Ｈ可以看出ꎬ器件的电流崩塌得到了很好的提高ꎬ９００Ｖ下电流崩塌因子由样品Ｇ中的４２.０４下降到样品Ｈ的４.７６ꎬ抑制效果明显ꎮ因此利用退火ＡｌＮ作为栅介质插入层进行界面处理ꎬ能够有效改善Ａｌ￣ＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴ器件界面ꎬ提高界面质量ꎬ抑制电流崩塌ꎬ提高器件可靠性ꎮQuiesent drain bias/V80R D y n a m i c /R O N40080010060402002006001000AlN interlayer anneal(H)AlN interlayer(G)Reference(F)图８㊀样品Ｆ㊁Ｇ㊁Ｈ电流崩塌对比ꎮＦｉｇ.８㊀ＣｕｒｒｅｎｔｃｏｌｌａｐｓｅｆｏｒｓａｍｐｌｅＦꎬｓａｍｐｌｅＧａｎｄｓａｍｐｌｅＨ.４㊀结㊀㊀论本文研究了ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴ器件制备过程中不同界面处理对其性能的影响ꎮ研究发现ꎬ经过Ｎ２等离子体预处理较ＮＨ３等离子体预处理能够降低器件的电流崩塌因子ꎬ提高器件的可靠性ꎬ在该研究基础上优化了Ｎ２等离子体预处理时间ꎬ实验结果显示１０ｍｉｎ等离子体预处理能９２０㊀发㊀㊀光㊀㊀学㊀㊀报第４０卷够有效地提高器件脉冲下电流ꎮ进一步引入ＡｌＮ栅介质插入层ꎬ实验发现利用ＡｌＮ插入层及退火工艺能够有效地改善ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴ器件界面质量ꎬ抑制电流崩塌ꎬ提高器件可靠性ꎬ器件的阈值回滞从４１１ｍＶ减小至１１１ｍＶꎬ实现在关态应力９００Ｖ下将器件的电流崩塌因子由４２.０４下降到４.７６ꎮ参㊀考㊀文㊀献:[１]ＺＨＡＮＧＺＬꎬＹＵＧＨꎬＺＨＡＮＧＸＤꎬｅｔａｌ..Ｓｔｕｄｉｅｓｏｎｈｉｇｈ￣ｖｏｌｔａｇｅＧａＮ￣ｏｎ￣ＳｉＭＩＳ￣ＨＥＭＴｓｕｓｉｎｇＬＰＣＶＤＳｉ３Ｎ４ａｓｇａｔｅｄｉｅｌｅｃｔｒｉｃａｎｄｐａｓｓｉｖａｔｉｏｎｌａｙｅｒ[Ｊ].ＩＥＥＥＴｒａｎｓ.ＥｌｅｃｔｒｏｎＤｅｖ.ꎬ２０１６ꎬ６３(２):７３１￣７３８.[２]ＬＩＵＳＣꎬＣＨＥＮＢＹꎬＬＩＮＹＣꎬｅｔａｌ..ＧａＮＭＩＳ￣ＨＥＭＴｓｗｉｔｈｎｉｔｒｏｇｅｎｐａｓｓｉｖａｔｉｏｎｆｏｒｐｏｗｅｒｄｅｖｉｃｅａｐｐｌｉｃａｔｉｏｎｓ[Ｊ].ＩＥＥＥＥｌｅｃｔｒｏｎＤｅｖ.Ｌｅｔｔ.ꎬ２０１４ꎬ３５(１０):１００１￣１００３.[３]ＫＥＬＥＫÇＩÖꎬＴＡŞＬＩＰＴꎬＹＵＨＢꎬｅｔａｌ..ＥｌｅｃｔｒｏｎｔｒａｎｓｐｏｒｔｐｒｏｐｅｒｔｉｅｓｉｎＡｌ０.２５Ｇａ０.７５Ｎ/ＡｌＮ/ＧａＮｈｅｔｅｒｏｓｔｒｕｃｔｕｒｅｓｗｉｔｈｄｉｆｆｅｒｅｎｔＩｎＧａＮｂａｃｋｂａｒｒｉｅｒｌａｙｅｒｓａｎｄＧａＮｃｈａｎｎｅｌｔｈｉｃｋｎｅｓｓｅｓｇｒｏｗｎｂｙＭＯＣＶＤ[Ｊ].Ｐｈｙｓ.ＳｔａｔｕｓＳｏｌｉｄｉꎬ２０１２ꎬ２０９(３):４３４￣４３８.[４]王凯ꎬ邢艳辉ꎬ韩军ꎬ等.掺Ｆｅ高阻ＧａＮ缓冲层特性及其对ＡｌＧａＮ/ＧａＮ高电子迁移率晶体管器件的影响研究[Ｊ].物理学报ꎬ２０１６ꎬ６５(１):０１６８０２￣１￣６.ＷＡＮＧＫꎬＸＩＮＧＹＨꎬＨＡＮＪꎬｅｔａｌ..ＧｒｏｗｔｈｓｏｆＦｅ￣ｄｏｐｅｄＧａＮｈｉｇｈ￣ｒｅｓｉｓｔｉｖｉｔｙｂｕｆｆｅｒｌａｙｅｒｓｆｏｒＡｌＧａＮ/ＧａＮｈｉｇｈｅｌｅｃｔｒｏｎｍｏｂｉｌｉｔｙｔｒａｎｓｉｓｔｏｒｄｅｖｉｃｅｓ[Ｊ].ＡｃｔａＰｈｙｓ.Ｓｉｎｉｃａꎬ２０１６ꎬ６５(１):０１６８０２￣１￣６.(ｉｎＣｈｉｎｅｓｅ)[５]ＥＬＬＥＲＢＳꎬＹＡＮＧＪＬꎬＮＥＭＡＮＩＣＨＲＪ.ＥｌｅｃｔｒｏｎｉｃｓｕｒｆａｃｅａｎｄｄｉｅｌｅｃｔｒｉｃｉｎｔｅｒｆａｃｅｓｔａｔｅｓｏｎＧａＮａｎｄＡｌＧａＮ[Ｊ].Ｊ.Ｖａｃ.Ｓｃｉ.Ｔｅｃｈｎｏｌ.Ａꎬ２０１３ꎬ３１(５):０５０８０７￣１￣２９.[６]ＸＩＯＮＧＣꎬＬＩＵＳＨꎬＬＩＹＨꎬｅｔａｌ..Ｈｏｔｃａｒｒｉｅｒｅｆｆｅｃｔｏｎｔｈｅｂｉｐｏｌａｒｔｒａｎｓｉｓｔｏｒｓ ｒｅｓｐｏｎｓｅｔｏｅｌｅｃｔｒｏｍａｇｎｅｔｉｃｉｎｔｅｒｆｅｒｅｎｃｅ[Ｊ].Ｍｉｃｒｏｅｌｅｃｔｒ.Ｒｅｌｉａｂｉｌ.ꎬ２０１５ꎬ５５(３￣４):５１４￣５１９.[７]ＺＨＡＮＧＺＬꎬＦＵＫꎬＤＥＮＧＸＧꎬｅｔａｌ..ＮｏｒｍａｌｌｙｏｆｆＡｌＧａＮ/ＧａＮＭＩＳ￣ｈｉｇｈ￣ｅｌｅｃｔｒｏｎｍｏｂｉｌｉｔｙｔｒａｎｓｉｓｔｏｒｓｆａｂｒｉｃａｔｅｄｂｙｕｓｉｎｇｌｏｗｐｒｅｓｓｕｒｅｃｈｅｍｉｃａｌｖａｐｏｒｄｅｐｏｓｉｔｉｏｎＳｉ３Ｎ４ｇａｔｅｄｉｅｌｅｃｔｒｉｃａｎｄｓｔａｎｄａｒｄｆｌｕｏｒｉｎｅｉｏｎｉｍｐｌａｎｔａｔｉｏｎ[Ｊ].ＩＥＥＥＥｌｅｃｔｒｏｎＤｅｖ.Ｌｅｔｔ.ꎬ２０１５ꎬ３６(１１):１１２８￣１１３１.[８]ＰＥＮＧＭＺꎬＺＨＥＮＧＹＫꎬＷＥＩＫꎬｅｔａｌ..Ｐｏｓｔ￣ｐｒｏｃｅｓｓｔｈｅｒｍａｌｔｒｅａｔｍｅｎｔｆｏｒｍｉｃｒｏｗａｖｅｐｏｗｅｒｉｍｐｒｏｖｅｍｅｎｔｏｆＡｌＧａＮ/ＧａＮＨＥＭＴｓ[Ｊ].Ｍｉｃｒｏｅｌｅｃｔｒ.Ｅｎｇ.ꎬ２０１０ꎬ８７(１２):２６３８￣２６４１.[９]ＶＡＮＫＯＧꎬＬＡＬＩＮＳＫＹ'ＴꎬＨＡŠＣ㊅ÍＫＳꎬｅｔａｌ..ＩｍｐａｃｔｏｆＳＦ６ｐｌａｓｍａｔｒｅａｔｍｅｎｔｏｎｐｅｒｆｏｒｍａｎｃｅｏｆＡｌＧａＮ/ＧａＮＨＥＭＴ[Ｊ].Ｖａｃｕｕｍꎬ２００９ꎬ８４(１):２３５￣２３７.[１０]ＭＥＹＥＲＤＪꎬＦＬＥＭＩＳＨＪＲꎬＲＥＤＷＩＮＧＪＭ.ＳＦ６/Ｏ２ｐｌａｓｍａｅｆｆｅｃｔｓｏｎｓｉｌｉｃｏｎｎｉｔｒｉｄｅｐａｓｓｉｖａｔｉｏｎｏｆＡｌＧａＮ/ＧａＮｈｉｇｈｅｌｅｃｔｒｏｎｍｏｂｉｌｉｔｙｔｒａｎｓｉｓｔｏｒｓ[Ｊ].Ａｐｐｌ.Ｐｈｙｓ.Ｌｅｔｔ.ꎬ２００６ꎬ８９(２２):２２３５２３￣１￣３.[１１]ＷＡＴＡＮＡＢＥＴꎬＴＥＲＡＭＯＴＯＡꎬＮＡＫＡＯＹꎬｅｔａｌ..Ｌｏｗ￣ｉｎｔｅｒｆａｃｅ￣ｔｒａｐ￣ｄｅｎｓｉｔｙａｎｄｈｉｇｈ￣ｂｒｅａｋｄｏｗｎ￣ｅｌｅｃｔｒｉｃ￣ｆｉｅｌｄＳｉＮＦｉｌｍｓｏｎＧａＮｆｏｒｍｅｄｂｙｐｌａｓｍａｐｒｅｔｒｅａｔｍｅｎｔｕｓｉｎｇｍｉｃｒｏｗａｖｅ￣ｅｘｃｉｔｅｄｐｌａｓｍａ￣ｅｎｈａｎｃｅｄｃｈｅｍｉｃａｌｖａｐｏｒｄｅｐｏｓｉｔｉｏｎ[Ｊ].ＩＥＥＥＴｒａｎｓ.ＥｌｅｃｔｒｏｎＤｅｖ.ꎬ２０１３ꎬ６０(６):１９１６￣１９２２.[１２]ＫＩＭＪＨꎬＣＨＯＩＨＧꎬＨＡＭＷꎬｅｔａｌ..Ｅｆｆｅｃｔｓｏｆｎｉｔｒｉｄｅ￣ｂａｓｅｄｐｌａｓｍａｐｒｅｔｒｅａｔｍｅｎｔｐｒｉｏｒｔｏＳｉＮｘＰａｓｓｉｖａｔｉｏｎｉｎＡｌＧａＮ/ＧａＮｈｉｇｈ￣ｅｌｅｃｔｒｏｎ￣ｍｏｂｉｌｉｔｙｔｒａｎｓｉｓｔｏｒｓｏｎｓｉｌｉｃｏｎｓｕｂｓｔｒａｔｅｓ[Ｊ].Ｊｐｎ.Ｊ.Ａｐｐｌ.Ｐｈｙｓ.ꎬ２０１０ꎬ４９(４Ｓ):０４ＤＦ０５. [１３]ＨＵＡＮＧＳꎬＪＩＡＮＧＱＭꎬＹＡＮＧＳꎬｅｔａｌ..ＥｆｆｅｃｔｉｖｅｐａｓｓｉｖａｔｉｏｎｏｆＡｌＧａＮ/ＧａＮＨＥＭＴｓｂｙＡＬＤ￣ｇｒｏｗｎＡｌＮｔｈｉｎｆｉｌｍ[Ｊ].ＩＥＥＥＥｌｅｃｔｒｏｎＤｅｖ.Ｌｅｔｔ.ꎬ２０１２ꎬ３３(４):５１６￣５１８.[１４]ＥＤＷＡＲＤＳＡＰꎬＭＩＴＴＥＲＥＤＥＲＪＡꎬＢＩＮＡＲＩＳＣꎬｅｔａｌ..ＩｍｐｒｏｖｅｄｒｅｌｉａｂｉｌｉｔｙｏｆＡｌＧａＮ￣ＧａＮＨＥＭＴｓｕｓｉｎｇａｎＮＨ３/ｐｌａｓ￣ｍａｔｒｅａｔｍｅｎｔｐｒｉｏｒｔｏＳｉＮｐａｓｓｉｖａｔｉｏｎ[Ｊ].ＩＥＥＥＥｌｅｃｔｒｏｎＤｅｖ.Ｌｅｔｔ.ꎬ２００５ꎬ２６(４):２２５￣２２７.[１５]ＨＡＳＨＩＺＵＭＥＴꎬＯＯＴＯＭＯＳꎬＯＹＡＭＡＳꎬｅｔａｌ..ＣｈｅｍｉｓｔｒｙａｎｄｅｌｅｃｔｒｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆｓｕｒｆａｃｅｓｏｆＧａＮａｎｄＧａＮ/ＡｌＧａＮｈｅｔｅｒｏｓｔｒｕｃｔｕｒｅｓ[Ｊ].Ｊ.Ｖａｃ.Ｓｃｉ.Ｔｅｃｈｎｏｌ.ꎬ２００１ꎬ１９(４):１６７５￣１６８１.[１６]ＲＯＭＥＲＯＭＦꎬＪＩＭÉＮＥＺＪＩＭＥＮＥＺＡꎬＭＩＧＵＥＬ￣ＳÁＮＣＨＥＺＭＩＧＵＥＬ￣ＳＡＮＣＨＥＺＪꎬｅｔａｌ..ＥｆｆｅｃｔｓｏｆＮ２ｐｌａｓｍａｐｒｅｔｒｅａｔ￣ｍｅｎｔｏｎｔｈｅＳｉＮｐａｓｓｉｖａｔｉｏｎｏｆＡｌＧａＮ/ＧａＮＨＥＭＴ[Ｊ].ＩＥＥＥＥｌｅｃｔｒｏｎＤｅｖ.Ｌｅｔｔ.ꎬ２００８ꎬ２９(３):２０９￣２１１.[１７]ＨＡＳＨＩＺＵＭＥＴꎬＯＯＴＯＭＯＳꎬＩＮＡＧＡＫＩＴꎬｅｔａｌ..ＳｕｒｆａｃｅｐａｓｓｉｖａｔｉｏｎｏｆＧａＮａｎｄＧａＮ/ＡｌＧａＮｈｅｔｅｒｏｓｔｒｕｃｔｕｒｅｓｂｙｄｉｅｌｅｃ￣ｔｒｉｃｆｉｌｍｓａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｔｏｉｎｓｕｌａｔｅｄ￣ｇａｔｅｈｅｔｅｒｏｓｔｒｕｃｔｕｒｅｔｒａｎｓｉｓｔｏｒｓ[Ｊ].Ｊ.Ｖａｃ.Ｓｃｉ.Ｔｅｃｈｎｏｌ.Ｂꎬ２００３ꎬ２１(４):１８２８￣１８３８.㊀第７期韩㊀军ꎬ等:界面处理对ＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴｓ器件动态特性的影响９２１㊀[１８]ＲＥＩＮＥＲＭꎬＬＡＧＧＥＲＰꎬＰＲＥＣＨＴＬＧꎬｅｔａｌ..Ｍｏｄｉｆｉｃａｔｉｏｎｏｆ ｎａｔｉｖｅ ｓｕｒｆａｃｅｄｏｎｏｒｓｔａｔｅｓｉｎＡｌＧａＮ/ＧａＮＭＩＳ￣ＨＥＭＴｓｂｙｆｌｕｏｒｉｎａｔｉｏｎ:ｐｅｒｓｐｅｃｔｉｖｅｆｏｒｄｅｆｅｃｔｅｎｇｉｎｅｅｒｉｎｇ[Ｃ].ＰｒｏｃｅｅｄｉｎｇｓｏｆＩＥＥＥＩｎｔｅｒｎａｔｉｏｎａｌＥｌｅｃｔｒｏｎＤｅｖｉｃｅｓＭｅｅｔｉｎｇꎬＷａｓｈ￣ｉｎｇｔｏｎꎬＤＣꎬＵＳＡꎬ２０１５:３５.５.１￣３５.５.４.[１９]ＡＣＵＲＩＯＥꎬＣＲＵＰＩＦꎬＭＡＧＮＯＮＥＰꎬｅｔａｌ..ＩｍｐａｃｔｏｆＡｌＮｌａｙｅｒｓａｎｄｗｉｃｈｅｄｂｅｔｗｅｅｎｔｈｅＧａＮａｎｄｔｈｅＡｌ２Ｏ３ｌａｙｅｒｓｏｎｔｈｅｐｅｒｆｏｒｍａｎｃｅａｎｄｒｅｌｉａｂｉｌｉｔｙｏｆｒｅｃｅｓｓｅｄＡｌＧａＮ/ＧａＮＭＯＳ￣ＨＥＭＴｓ[Ｊ].Ｍｉｃｒｏｅｌｅｃｔｒ.Ｅｎｇ.ꎬ２０１７ꎬ１７８:４２￣４７.[２０]ＨＵＡＮＧＳꎬＪＩＡＮＧＱＭꎬＹＡＮＧＳꎬｅｔａｌ..ＭｅｃｈａｎｉｓｍｏｆＰＥＡＬＤ￣ｇｒｏｗｎＡｌＮｐａｓｓｉｖａｔｉｏｎｆｏｒＡｌＧａＮ/ＧａＮＨＥＭＴｓ:ｃｏｍｐｅｎ￣ｓａｔｉｏｎｏｆｉｎｔｅｒｆａｃｅｔｒａｐｓｂｙｐｏｌａｒｉｚａｔｉｏｎｃｈａｒｇｅｓ[Ｊ].ＩＥＥＥＥｌｅｃｔｒｏｎＤｅｖ.Ｌｅｔｔ.ꎬ２０１３ꎬ３４(２):１９３￣１９５.韩军(１９６４－)ꎬ男ꎬ北京人ꎬ博士ꎬ副教授ꎬ２００８年于北京工业大学获得博士学位ꎬ主要从事半导体材料与器件方面的研究ꎮＥ￣ｍａｉｌ:ｈａｎｊｕｎ＠ｂｊｕｔ.ｅｄｕ.ｃｎ邢艳辉(１９７４－)ꎬ女ꎬ吉林德惠人ꎬ博士ꎬ副教授ꎬ２００８年于北京工业大学获得博士学位ꎬ主要从事氮化镓半导体材料的生长㊁测试分析及器件等方面的研究ꎮＥ￣ｍａｉｌ:ｘｉｎｇｙａｎｈｕｉ＠ｂｊｕｔ.ｅｄｕ.ｃｎ。

Structural and multiferroic properties of La-modified Bi Fe O 3 ceramicsS. R. Das, R. N. P. Choudhary, P. Bhattacharya, R. S. Katiyar, P. Dutta, A. Manivannan, and M. S. SeehraCitation: Journal of Applied Physics 101, 034104 (2007); doi: 10.1063/1.2432869View online: /10.1063/1.2432869View Table of Contents: /content/aip/journal/jap/101/3?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inEffect of Pr- and Nd- doping on structural, dielectric, and magnetic properties of multiferroicBi0.8La0.2Fe0.9Mn0.1O3J. Appl. Phys. 115, 134102 (2014); 10.1063/1.4870454Improved dielectric and magnetic properties of Ti modified BiCaFeO3 multiferroic ceramicsJ. Appl. Phys. 113, 023908 (2013); 10.1063/1.4774283Structural, magnetic, and optical properties of Pr and Zr codoped BiFeO3 multiferroic ceramicsJ. Appl. Phys. 112, 094102 (2012); 10.1063/1.4761968Structure and properties of La-modified Na0.5Bi0.5TiO3 at ambient and elevated temperaturesJ. Appl. Phys. 112, 054111 (2012); 10.1063/1.4751357Structural and physical properties of room temperature stable multiferroic properties of single-phase ( Bi 0.9 La 0.1 ) FeO 3 – Pb ( Fe 0.5 Nb 0.5 ) O 3 solid solution systemsJ. Appl. Phys. 105, 07D919 (2009); 10.1063/1.3072034Structural and multiferroic properties of La-modified BiFeO3ceramics S.R.Das,R.N.P.Choudhary,P.Bhattacharya,and R.S.Katiyar a͒Department of Physics,University of Puerto Rico,San Juan,PR-00931,Puerto RicoP.Dutta,A.Manivannan,and M.S.SeehraDepartment of Physics,West Virginia University,Morgantown,West Virginia26506͑Received4May2006;accepted23November2006;published online6February2007͒The coexistence of the magnetic and the electrical properties in lanthanum͑La͒-modified bismuthferrite͑Bi1−x La x FeO3,x=0.05,0.1,0.15,and0.2͒ceramics was studied and compared with those ofbismuth ferrite͑BiFeO3͒.The presence of a small secondary phase of BiFeO3͑arises due to excessBi2O3͒was removed on La substitution at the Bi site,as observed in x-ray diffraction͑XRD͒.Theeffect of La substitution on dielectric constant,loss tangent,and remnant polarization of the sampleswas studied in a wide range of temperature͑77–400K͒and frequency͑1kHz–1MHz͒.Thevariation of magnetization,coercivefield,and exchange bias with temperature͑2–300K͒and Laconcentration were investigated.These changes in the magnetic parameters with La doping alongwith those of the electron magnetic resonance parameters measured at300K and9.28GHz areunderstood in terms of increase in the magnetic anisotropy and magnetization.These results alsoshow that stabilization of crystal structure and nonuniformity in spin cycloid structure by Lasubstitution enhances the multiferroic properties of BiFeO3.©2007American Institute of Physics.͓DOI:10.1063/1.2432869͔I.INTRODUCTIONBismuth ferrite͑BiFeO3͒has recently gained consider-able importance both technologically and scientifically be-cause of the existence of both ferroelectrics and͑anti͒ferro-magnetic ordering in the same phase in the material,and also magnetoelectric coupling between the two respective order parameters͑spin and charge͒.Unfortunately,spontaneous polarization and magnetization of the material at room tem-perature are small due to large leakage current and loss tan-gent,and hence it is difficult to study the dielectric properties in the low frequency range.1,2Therefore,Krainik et al.3mea-sured the temperature dependence of dielectric constant of bismuth ferrite͑BFO͒at microwave frequencies.The low value of polarization is attributed to the presence of second-ary phases and low resistivity of BiFeO3ceramics whereas the high leakage current is attributed to the presence of Fe2+ ions.4,5In order to increase the dielectric constant,reduce the leakage current,and hence to improve the ferroelectric po-larization in BFO,some attempts have been made including a small doping at the Bi/Fe sites.There are also several reports on the synthesis of solid solution of BiFeO3with other perovskite structures͑with different concentrations͒, which has improved electrical properties of BFO.Fedulov et al.6studied the BiFeO3–PbTiO3solid solutions,and re-ported that up to78mole%of BiFeO3the structure remains rhombohedral,after which it becomes tetragonal.Ismailzade et al.7showed that in BiFeO3–BaTiO3solid solution,the structure remains rhombohedral for67mole%of BiFeO3, from67toϳ6mole%it is cubic,and below6mole%,the structure of solid solution transforms to tetragonal.There are also some reports on the ferroelectric and ferromagnetic properties of cationic substituted BiFeO3.8–10Palkar et al.9,10 reported the ferroelectric and ferromagnetic properties of La and Tb at the Bi site,and La at the Bi site and Mn at the Fe site substituted BiFeO3.Though they did not observed any improvement in the ferroelectric properties in La/Mn-substituted BiFeO3,a small enhancement of mag-netic properties was clearly observed.The͑La,Tb͒substi-tuted at the Bi site in BiFeO3ceramic showed high values of dielectric constant and magnetoelectric coupling at room temperature.Recently,Wang et al.8observed an improve-ment in the dielectric properties of BiFeO3on substituting La at the Bi site and Ga at the Fe site,and making its composite with43mole%of PbTiO3.The room temperature dielectric constant was found to be1800with low loss tangent of0.024,and T c shifted toϳ500from1103K͑BiFeO3͒.Also,a larger induced magnetization͑compared to single crystal BiFeO3͒was obtained at room temperature at much lower magneticfield,and the magnetization value increased at5K.BiFeO3has a ferroelectric Curie temperature T c Ϸ1103K and antiferromagnetic͑AF͒Neel temperature T N Ϸ643K.11Since T c and T N are significantly different,it may be argued that spin and polarization ordering must be un-coupled and driven by different modes.The AF ordering is not completely compensated because of observed weak magnetism.12Neutron diffraction studies13have shown an incommensurately modulated cycloidal spin structure with a long wavelength␭Ϸ600Å.In electron magnetic resonance ͑EMR͒studies,a low-field mode with paramagnetic-resonance-like linear relationship between energy andfield ͑h␯=g␮B H͒is observed for TϽT N with gϷ2.0͑for low La concentration͒,in addition to the highfield antiferromagnetic resonance͑AFMR͒modes,with criticalfield͑spinflip͒Ϸ18kOe.11In thinfilms of BiFeO3,the enhanced polariza-tion and magnetization have been interpreted due to epitaxiala͒Author to whom correspondence should be addressed;FAX:ϩ1-787-764-2571;electronic mail:rkatiyar@JOURNAL OF APPLIED PHYSICS101,034104͑2007͒0021-8979/2007/101͑3͒/034104/7/$23.00©2007American Institute of Physics101,034104-1constraint destroying the cycloidal ordering.14,15Magneto-electric properties of epitaxially grown La-modified BiFeO 3thin films have recently been reported by Lee et al.16and showed enhancement in the polarization and magnetization.In this paper,we report the effect of La substitution ͑5–20mole %at the Bi site ͒on structural,electrical,and magnetic properties of BiFeO 3ceramics ͓i.e.,Bi 1−x La x FeO 3͑BFOL ͔͒.II.EXPERIMENTThe high purity ͑99.9%,Alfa Aesar ͒bismuth oxide ͑Bi 2O 3͒,iron oxide ͑Fe 2O 3͒,and lanthanum oxide ͑La 2O 3͒were mixed ͑stoichiometry ͒in an agate mortar and pestle in wet medium ͑alcohol ͒to prepare BiFeO 3͑BFO ͒and Bi 1−x La x FeO 3͓x =0.05͑BFOL5͒,x =0.10͑BFOL10͒,x =0.15͑BFOL15͒,and x =0.20͑BFOL20͔͒ceramics.The slurries of the above mixtures were dried overnight in anoven at 50°C.The homogeneous mixed powders were cal-cined at different temperatures for different duration.BFO powder was calcined in two different steps;͑a ͒500°C.for 1h and ͑b ͒850°C.for 2h.The calcination temperatures/time for BFOL5/BFOL10and BFOL15/BFOL20were found to be 870°C/2h and 890°C/2h,respectively.The fine calcined powders of BFO and BFOL were used to make circular pellets of 7mm diameter and 1–2mm thickness.All the pellets were sintered at 890°C.for 4h for densifi-cation.In order to study phase formation and to carry out pre-liminary structural analysis of BFO and BFOL,x-ray diffrac-tion pattern were taken using Cu K ␣radiation ͑␭=1.5405Å͒of a Seimens D5000powder diffractometer.Dif-ferential thermal analysis of all the samples were carried out to study the phase transition behavior,using Shimatzu differ-ential thermal analyses ͑DTA ͒thermal analyser.The scan-ning electron micrographs ͑SEM ͒of the pellet samples were taken to study the grain size and size distributions.The di-electric constant and loss tangent were measured using an impedance analyzer ͑HP4294A ͒and temperature controller ͑M/s MMR Technology,Inc.͒in a wide range of frequencies ͑1kHz–1MHz ͒and temperatures ͑77–500K ͒.Ferroelec-tric polarizations were measured on poled samples using a hysteresis loop tracer ͑M/s Radiant Technology Inc.͒.The magnetization M as a function of applied field H at different temperatures ͑2–300K ͒was measured using a supercon-ducting quantum interference device ͑SQUID ͒magnetome-ter.The EMR studies of all the samples were carried out at 300K using an X -band spectrometer operating at 9.28GHz.TABLE parison of lattice parameters,and tolerance factors of ͑Bi 1−x La x ͒FeO 3ceramics.The estimated standard deviations are in the positiona ͑Å͒c ͑Å͒V ͑Å͒3t x =0.0 5.6206͑20͒13.6924͑20͒374.570.915x =0.05 5.6011͑80͒13.6472͑80͒371.010.916x =0.10 5.6019͑70͒13.6429͑70͒370.770.917x =0.15 5.5942͑48͒13.6386͑48͒369.640.919x =0.205.5879͑48͒13.6066͑48͒367.940.920FIG.1.X-ray diffraction patterns of BiFeO 3and Bi 1−x La x FeO 3͑0.05ഛx ഛ0.2͒polycrystalline ceramics.FIG.2.Differential thermal analyses ͑DTA ͒of BiFeO 3and Bi 1−x La x FeO 3͑0.05ഛx ഛ0.2͒.FIG.3.Scanning electron micrographs ͑SEM ͒of BFO,BFOL5,BFOL10,and BFOL20ceramics.III.RESULTS AND DISCUSSIONFigure 1shows the XRD pattern of BFO and BFOL ceramics.All the diffraction peaks of BFO were indexed and lattice parameters were determined in a hexagonal unit cell using a powder diffraction refinement computer program.17The La-modified BiFeO 3was also fitted with the same crys-tal structure.Though all the diffraction peaks were well iden-tified,few low intensity peaks were observed at 2␪ϳ27°–28°in case of BiFeO 3ceramic.Upon La substitution at the Bi site,the impurity phase was eliminated.The impu-rity peaks were identified,probably because of the addition of 10%extra Bi 2O 3.Peak shifts were calculated using peak fit software.Table I compares the refined least squares lattice constants of BFO and BFOL with their estimated standard deviations in parenthesis.Figure 2shows the thermograms of BFO and BFOL powders in the temperature range of 0–1200°C.Three dis-tinct features were observed ͑based on change of slopes of all the curves ͒:͑a ͒ϳ300–350°C corresponds to Neel tempera-tures of magnetic phase transition,͑b ͒800–900°C corre-sponds to the ferroelectrics Curie temperatures/phase transi-tion,and ͑c ͒950–1150°C corresponds to the heat loss at the melting points of BFO and BFOL ceramics.These observa-tions suggest that the lanthanum substitution lowered the ferroelectric phase transition temperature but increases the melting point of BFO.Figure 3shows the scanning electron micrographs of BFO and BFOL ceramics.The average grain size of all the samples is very much similar,and in the range of 2–3␮m.However,it can be noticed that with a small lanthanum con-centration ͑5–10mole %͒,the density of sample ͑i.e.,lessvoids ͒increases.In the BFOL20sample,small grains coa-lesce to form large grains,and hence different microstruc-tures of large grain size are obtained.The microstructures and absence of secondary phases on La substitution in BFO are some of the main reasons for enhanced electrical and magnetic properties of BFOL.Figures 4͑a ͒and 4͑b ͒show the variation of dielectric constant of BFOL with frequency at 300and 630K,respec-tively.It is observed that at higher temperature ͑630K ͒,the dielectric constant of the ceramic samples increases by an order of magnitude ͑with minimal changes in BFOL10and BFOL15͒.This increase is considered as due to the magnetic phase transition around that temperature.This is more evi-dent from the Fig.5.At 300K,no frequency dispersion was observed in the material ͑with an exception of BFOL5͒.However,at 630K most of the ceramic samples exhibited frequency dispersion at lower frequencies.Figures 5͑a ͒and 5͑b ͒show the temperature variation of dielectric constant at two different frequencies 100kHz and 1MHz,respectively.Because of temperature limitation of our sample holder ͑i.e.,maximum temperature=700K ͒,we could not obtain ferroelectric phase transition temperature of BFO and BFOL ͑as observed from DTA results ͒.However,a sharp increase in dielectric constant started from 500K for all the ceramics.Figures 6͑a ͒and 6͑b ͒show variation of loss tangent with temperature at 100kHz and 1MHz,respectively.At the lower frequency,the loss tangent is higher,and it decreases as a function of the frequency ͑lower frequency data are not shown here ͒.Around room temperature ͑ϳ300K ͒loss tan-gent peaks were observed for all the samples.AsevidentFIG.4.͓͑a ͒and ͑b ͔͒.Dielectric con-stant vs frequency ͑100kHz–1MHz ͒of BFO and BFOL ceramics at 300and 630K.FIG.5.͓͑a ͒and ͑b ͔͒.Dielectric con-stant vs temperature of BFO and BFOL ceramics at 100kHz and 1MHz.from our dielectric measurements,dielectric anomaly of BFOL corresponds to the magnetic phase transition tempera-tures.Both the dielectric constant and the loss tangent of all the ceramics have a signature of attaining local maxima,a characteristic for multiferroics.Figure 7shows the ferroelectric hysteresis loops mea-sured on poled samples of BFO,BFOL5,and BFOL20at 300K and at different applied fields.BFO did not give a perfect ferroelectric loop.However,on La substitution,the loop gradually changes to that of ferroelectric nature reduc-ing the leakage.Still the samples are not totally leakage free.The ferroelectric polarization of x =0.05sample,which has a better microstructure and higher dielectric constant is shown for comparison.The remnant polarization of BFOL20ce-ramic was found to be 2P r Ϸ13␮C/cm 2at an applied field of 20kV/cm.These suggest the improvement of electrical and ferroelectric properties upon lanthanum substitutions at the Bi site in BFO ceramics.Figure 8shows the magnetization M versus applied field H of BFO and BFOL at room temperature ͑BFOL5data not shown in the figure ͒.Asymmetric hysteresis loops at 300and2K were obtained from which we measured the coercivity H c ,the exchange bias H e ,the average remanence magnetiza-tion M r =͑M r ++M r −͒/2and the magnetization at 55kOe ͑de-fined as M H ͒.In Table II ,we have compared the value of these quantities for all the BFO and BFOL samples.All the samples have negative H e ͑i.e.,their loops are shifted to the negative side by exchange bias ͒.At T =2K the magnitudes of the loop parameters ͑H c ,H e ,M H ,and M r ͒increase on increasing La concentration.The enhancement of the mag-netic parameters,perhaps due to increased magnetoelectric coupling 8,18on La-modified BFO are observed here.The hysteresis loops parameters ͑at 300K ͒for the samples of BFO ͑Table II ͒are presented graphically in Fig.8͑inset ͒.The M vs H curves are nearly linear,and hence M does not have any tendency to saturate even at 55kOe.Consequently the saturation magnetization cannot be determined and only the magnetization at 55kOe,viz.,M H is listed in Table II .For 20%La in BFO,a typical loop in the low field region was observed.Similar sets of data were obtained at 2K,except the magnitudes of H e ,H c ,and M H aredifferent.FIG.6.͓͑a ͒and ͑b ͔͒.Loss tangent vs temperature of BFO and BFOL ceram-ics at 100kHz and 1MHz.FIG.7.Ferroelectric hysteresis of BFO,BFOL5,and BFOL20ceramics at different applied fields.In Fig.9͑a ͒,we plot the magnitude of the negative ex-change bias,viz.,H e of BFOL both at T =2and 300K.A similar plot for the coercivity H c and the average remanence M r is shown in Figs.9͑b ͒and 9͑c ͒,respectively,where a systematic increase in their magnitudes with La doping is observed,especially at 2K.We also measured temperature dependence of H c ,H e ,and M H ͑Fig.10͒of BFO,where H c increases with increase in temperature and H e goes through a maximum near 100K.The presence of exchange bias H e in all our samples here is most intriguing since H e usually signifies the presence of a ferromagnet/antiferromagnet ͑F/AF ͒interface in a system.19–21In the weak ferromagnet ␣-Fe 2O 3,in which Dzyloshisky-Moriya ͑DM ͒antisymmetric exchange interac-tion is considered as the source of weak ferromagnetism,we did not observe exchange bias in a separate experiment not reported here.In BFO,the conventional DM interaction is zero.11A magnetoelectric interaction ͑such as DM interac-tion ͒,which couples both to the polarization and magnetiza-tion,has been introduced to explain the cycloidal spin struc-ture and its transformation to a homogeneous AF state under an applied magnetic field.11–16,18–22Whether the observed ex-change bias can be theoretically explained by this DM inter-action still needs to be understood.The temperature dependence of the low-field ͑H =200Oe ͒susceptibility for all the samples is shown in Fig.11.The temperature dependence of ␹is quite subtle except for the pure BFO sample,which obeys Curie law at lower temperatures,perhaps due to an otherwise undetected para-magnetic impurity.Also,in the 20%La doped sample,␹is considerably lower which may be due to the different shape of its hysteresis loop ͑Fig.8͒.Figure 12shows the room temperature EMR studies of all the samples at 9.28GHz suggesting an EMR line near g Ϸ2.0for BFO,BFOL5,and BFOL10samples,which is in good agreement with the observations of Ruette et al.11The samples with 15%and 20%La doping have higher gvalues.FIG.8.Magnetic hysteresis loops of BFO and BFOL samples.The insets show the details of the loops for lower fields.TABLE II.Magnetic parameters of ͑Bi x La x ͒FeO 3͑x =0.0,0.05,0.10,0.15,and 0.20͒at room temperature.Composition H c ͑Oe ͒H e ͑Oe ͒M r ͑emu/g ͒M H ͑emu/g ͒at 55kOe⌬H ͑Oe ͒g value ͑⌬H ͒2ᐉ͑104͒/mg x =0620−3500.00380.35335 2.04 3.16x =0.05478−1800.00320.35900 2.0314.3x =0.101045−3600.00770.401050 2.0517.5x =0.152840−3250.02150.401480 2.1655.4x =0.20840−3300.07360.5518602.52304The peak-to-peak linewidth ⌬H and the line intensity I =͑⌬H ͒2ᐉ͑ᐉ=peak-to-peak height ͒of this line also increase with increase in La doping.These observed changes in the EMR and magnetic parameters with increase in La doping ͑Table II ͒are mutually consistent in the following way.The increase in H c implies increase in magnetic anisotropy,which in turn increases the EMR linewidth ⌬H and gvalues.23Since the EMR line intensity is proportional to ͑⌬H ͒2as noted above,the line intensity also increases with increase in La doping.In the doped samples,a second over-lapping line begins to emerge and shifts to lower fields with increasing La doping.Since exchange bias H e is also ob-served in the undoped BFO,it is unlikely that the source of this line is related to the presence of the exchange bias.The EMR parameters ͑Table II ͒represent values for the compos-ite line observed here since it is difficult to completely re-solve the two lines.The second line could result from any nonuniformity in the spatial magnetization of the samples such as from magnetic domains.Because of the increase of the EMR linewidth and H c with increase in La doping,both signifying increase in anisotropy,domains are more likely to be present for the larger Ladopings.FIG.9.Effect of La doping on ͑a ͒exchange bias ͑−H e ͒,͑b ͒coercivity H c ,and ͑c ͒average magnetization M r at 2and 300K.Lines joining the points are for visualaid.FIG.10.Temperature dependence of exchange bias ͑−H e ͒,coercivity ͑H c ͒,and magnetization M H at 55kOe for the BFO.Lines joining the points are for visualclarity.FIG.11.Temperature dependence of the low-field susceptibility ␹measured at H =200Oe for BFO and BFOLceramics.FIG.12.Room temperature EMR spectra of the BFO and BFOL samples measured at f =9.28GHz.The vertical line marks the calculated position for g =2.0.IV.CONCLUSIONSPure and La substituted BiFeO3ceramics were synthe-sized using solid-state reaction substitution at Bisite eliminated the small impurity phase of BiFeO3and sta-bilized the crystal structure into hexagonal symmetry.Though the dielectric properties were not enhanced by Lasubstitution,systematic increase in both the ferroelectric andferromagnetic properties were achieved.The observed in-creases in the magnetic parameters͑H c,H e,and M r͒and EMR parameters͑⌬H,g,intensity I͒with increase in Ladoping reflect corresponding increases in the magnetic aniso-tropy and magnetization.However,the observation of ex-change bias H e in this ferromagnetic-ferroelectric system ismost intriguing and requires theoretical interpretation.It ishoped that these studies will stimulate such an investigation. 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IOP P UBLISHING R EPORTS ON P ROGRESS IN P HYSICS Rep.Prog.Phys.71(2008)062501(9pp)doi:10.1088/0034-4885/71/6/062501Two gaps make a high-temperature superconductor?S H¨ufner1,2,M A Hossain1,2,A Damascelli1,2and G A Sawatzky1,21AMPEL,University of British Columbia,Vancouver,British Columbia,V6T1Z4,Canada2Department of Physics and Astronomy,University of British Columbia,Vancouver,British Columbia,V6T1Z1,CanadaReceived27February2008,infinal form2April2008Published2May2008Online at /RoPP/71/062501AbstractOne of the keys to the high-temperature superconductivity puzzle is the identification of theenergy scales associated with the emergence of a coherent condensate of superconductingelectron pairs.These might provide a measure of the pairing strength and of the coherence ofthe superfluid,and ultimately reveal the nature of the elusive pairing mechanism in thesuperconducting cuprates.To this end,a great deal of effort has been devoted to investigatingthe connection between the superconducting transition temperature T c and the normal-statepseudogap crossover temperature T∗.Here we present a review of a large body ofexperimental data which suggests a coexisting two-gap scenario,i.e.superconducting gap andpseudogap,over the whole superconducting dome.We focus on spectroscopic data fromcuprate systems characterized by T maxc ∼95K,such as Bi2Sr2CaCu2O8+δ,YBa2Cu3O7−δ,Tl2Ba2CuO6+δand HgBa2CuO4+δ,with particular emphasis on the Bi-compound which has been the most extensively studied with single-particle spectroscopies.(Somefigures in this article are in colour only in the electronic version)This article was invited by Professor L Greene.Contents1.Introduction12.Emerging phenomenology32.1.Angle-resolved photoemission42.2.Tunneling52.3.Raman scattering52.4.Inelastic neutron scattering52.5.Heat conductivity63.Outlook and conclusion6 Acknowledgments6 References71.IntroductionSince their discovery[1],the copper-oxide high-T c superconductors(HTSCs)have become one of the most investigated class of solids[2–24].However,despite the intense theoretical and experimental scrutiny,an understanding of the mechanism that leads to superconductivity is still lacking.At the very basic level,what distinguishes the cuprates from the conventional superconductors is the fact that they are doped materials,the highly atomic-like Cu 3d orbitals give rise to strong electron correlations(e.g. the undoped parent compounds are antiferromagnetic Mott–Hubbard-like insulators),and the superconducting elements are weakly-coupled two-dimensional layers(i.e.the celebrated square CuO2planes).Among the properties that are unique to this class of superconducting materials,in addition to the unprecedented high superconducting T c,the normal-state gap or pseudogap is perhaps the most noteworthy.The pseudogap wasfirst detected in the temperature dependence of the spin-lattice relaxation and Knight shift in nuclear magnetic resonance and magnetic susceptibility studies[25].The Knight shift is proportional to the density of states at the Fermi energy;a gradual depletion was observed below a crossover temperature T∗,revealing the opening of the pseudogap well above T c on the underdoped side of the HTSC phase diagram(figure1).As the estimates based on thermodynamicx (c)Tx (a)x(b)T* T cT*T cT*T cFigure1.Various scenarios for the interplay of pseudogap(blue dashed line)and superconductivity(red solid line)in thetemperature-doping phase diagram of the HTSCs.While in(a)the pseudogap merges gradually with the superconducting gap in the strongly overdoped region,in(b)and(c)the pseudogap lines intersect the superconducting dome at about optimal doping(i.e.maximum T c).In most descriptions,the pseudogap line is identified with a crossover with a characteristic temperature T∗rather than a phase transition;while at all dopings T∗>T c in(a),beyond optimal doping T∗<T c in(b)and T∗does not even exist in(c).Adapted from[12].quantities are less direct than in spectroscopy we,in the course of this review,concentrate mainly on spectroscopic results; more information on other techniques can be found in the literature[5].As established by a number of spectroscopic probes, primarily angle-resolved photoemission spectroscopy,[26,27] the pseudogap manifests itself as a suppression of the normal-state electronic density of states at E F exhibiting a momentum dependence reminiscent of a d x2−y2functional form.For hole-doped cuprates,it is largest at Fermi momenta close to the antinodal region in the Brillouin zone—i.e.around (π,0)—and vanishes along the nodal direction—i.e.the(0,0) to the(π,π)line.Note however that,strictly speaking, photoemission and tunneling probe a suppression of spectral weight in the single-particle spectral function,rather than directly of density of states;to address this distinction,which is fundamental in many-body systems and will not be further discussed here,it would be very interesting to investigate the quantitative correspondence between nuclear magnetic resonance and single-particle spectroscopy results.Also,no phase information is available for the pseudogap since,unlike the case of optimally and overdoped HTSCs[28],no phase-sensitive experiments have been reported for the underdoped regime where T∗ T c.As for the doping dependence,the pseudogap T∗is much larger than the superconducting T c in underdoped samples,it smoothly decreases upon increasing the doping,and seems to merge with T c in the overdoped regime,eventually disappearing together with superconductivity at doping levels larger than x∼0.27[5–24].In order to elaborate on the connection between pseudogap and high-T c superconductivity,or in other words between the two energy scales E pg and E sc identified by T∗and T c,respectively,let us start by recalling that in conventional superconductors the onset of superconductivity is accompanied by the opening of a gap at the chemical potential in the one-electron density of states. According to the Bardeen–Cooper–Schrieffer(BCS)theory of superconductivity[29],the gap energy provides a direct measure of the binding energy of the two electrons forming a Cooper pair(the two-particle bosonic entity that characterizes the superconducting state).It therefore came as a great surprise that a gap,i.e.the pseudogap,was observed in the HTSCs not only in the superconducting state as expected from BCS, but also well above T c.Because of these properties and the hope it might reveal the mechanism for high-temperature superconductivity,the pseudogap phenomenon has been very intensely investigated.However,no general consensus has been reached yet on its origin,its role in the onset of superconductivity itself,and not even on its evolution across the HTSC phase diagram.As discussed in three recent papers on the subject [12,15,17],and here summarized infigure1,three different phase diagrams are usually considered with respect to the pseudogap line.While Millis[15]opts for a diagram like the one infigure1(a),Cho[17]prefers a situation where the pseudogap line meets the superconducting dome at x 0.16(figures1(b)and(c));Norman et al[12]provide a comprehensive discussion of the three different possibilities. One can summarize some of the key questions surrounding the pseudogap phenomenon and its relevance to high-temperature superconductivity as follows[12,15,17]:1.Which is the correct phase diagram with respect to thepseudogap line?2.Does the pseudogap connect to the insulator quasiparticlespectrum?3.Is the pseudogap the result of some one-particle bandstructure effect?4.Or,alternatively,is it a signature of a two-particle pairinginteraction?5.Is there a true order parameter defining the existence of apseudogap phase?6.Do the pseudogap and a separate superconducting gapcoexist below T c?7.Is the pseudogap a necessary ingredient for high-T csuperconductivity?In this review we revisit some of these questions,with specific emphasis on the one-versus two-gap debate.Recently,this latter aspect of the HTSCs has been discussed in great detail by Goss Levi[30],in particular based on scanning-tunneling microscopy data from various groups[31–33].Here we expand this discussion to include the plethora of experimental results available from a wide variety of techniques.We0.050.100.150.200.250408012016050100150E n e r g y (m e V )Hole doping (x)T c (K )Figure 2.Pseudogap (E pg =2 pg )and superconducting (E sc ∼5k B T c )energy scales for a number of HTSCs with T max c ∼95K(Bi2212,Y123,Tl2201and Hg1201).The datapoints were obtained,as a function of hole doping x ,by angle-resolved photoemission spectroscopy (ARPES),tunneling (STM,SIN,SIS),Andreev reflection (AR),Raman scattering (RS)and heat conductivity (HC).On the same plot we are also including the energy r of the magnetic resonance mode measured by inelastic neutron scattering (INS),which we identify with E sc because of the striking quantitative correspondence as a function of T c .The data fall on two universal curvesgiven by E pg =E max pg (0.27−x)/0.22and E sc =E max sc [1−82.6(0.16−x)2],with E maxpg =E pg (x =0.05)=152±8meV and E maxsc =E sc (x =0.16)=42±2meV (the statistical errors refer to the fit of the selected datapoints;however,the spread of all available data would be more appropriately described by ±20and ±10meV ,respectively).show that one fundamental and robust conclusion can be drawn:the HTSC phase diagram is dominated by two energy scales,the superconducting transition temperature T c and the pseudogap crossover temperature T ∗,which converge to the very same critical point at the end of the superconducting dome.Establishing whether this phenomenology can be conclusively described in terms of a coexisting two-gap scenario,and what the precise nature of the gaps would be,will require a more definite understanding of the quantities measured by the various probes.2.Emerging phenomenologyThe literature on the HTSC superconducting gap and/or pseudogap is very extensive and still growing.In this situation it seems interesting to go over the largest number of data obtained from as many experimental techniques as possible,and look for any possible systematic behavior that could be identified.This is the primary goal of this focused review.We want to emphasize right from the start that we are not aiming at providing exact quantitative estimates of superconducting and pseudogap energy scales for any specific compound or any given doping.Rather,we want to identify the general phenomenological picture emerging from the whole body of available experimental data [5,9,13,16,18,34–72].We consider some of the most direct probes of low-energy,electronic excitations and spectral gaps,such as angle-resolved photoemission (ARPES),scanning-tunneling microscopy (STM),superconductor/insulator/normal-metal(SIN)and superconductor/insulator/superconductor (SIS)tunneling,Andreev reflection tunneling (AR)and Raman scattering (RS),as well as less conventional probes such as heat conductivity (HC)and inelastic neutron scattering (INS).The emphasis in this review is on spectroscopic data because of their more direct interpretative significance;however,these will be checked against thermodynamic/transport data whenever possible.With respect to the spectroscopic data,it is important to differentiate between single-particle probes such as ARPES and STM,which directly measure the one-electron excitation energy with respect to the chemical potential (on both side of E F in STM),and two-particle probes such as Raman and inelastic neutron scattering,which instead provide information on the particle-hole excitation energy 2 .Note that the values reported here are those for the ‘full gap’2 (associated with either E sc or E pg ),while frequently only half the gap is given for instance in the ARPES literature.In doing so one implicitly assumes that the chemical potential lies half-way between the lowest-energy single-electron removal and addition states;this might not necessarily be correct but appears to be supported by the direct comparison between ARPES and STM/Raman results.A more detailed discussion of the quantities measured by the different experiments and their interpretation is provided in the following subsections.Here we would like to point out that studies of B 2g and B 1g Raman intensity [19,40,52],heat conductivity of nodal quasiparticles [70,71]and neutron magnetic resonance energy r [42]do show remarkable agreement with superconducting or pseudogap energy scales as inferred by single-particleTable1.Pseudogap E pg and superconducting E sc energy scales (2 )as inferred,for optimally doped Bi2212(T c∼90–95K),from different techniques and experiments.Abbreviations are given in the main text,while the original references are listed.Experiment Energy meV ReferencesARPES—(π,0)peak E pg80[34,35]Tunneling—STM…70[18,36]Tunneling—SIN…85[37]Tunneling—SIS…75[38,39]Raman—B1g…65[40]Electrodynamics…80[5,41]Neutron—(π,π) r E sc40[42]Raman—B2g…45[40]Andreev…45[43]SIS—dip…40[39]probes,or with the doping dependence of T c itself.Thus they provide,in our opinion,an additional estimate of E sc and E pg energy scales.As for the choice of the specific compounds to include in our analysis,we decided to focus on those HTSCs exhibiting a similar value of the maximum superconductingtransition temperature T maxc ,as achieved at optimal doping,so that the data could be quantitatively compared without any rescaling.We have therefore selected Bi2Sr2CaCu2O8+δ(Bi2212),YBa2Cu3O7−δ(Y123),Tl2Ba2CuO6+δ(Tl2201) and HgBa2CuO4+δ(Hg1201),which have been extensivelyinvestigated and are all characterized by T maxc ∼95K[73](with particular emphasis on Bi2212,for which the most extensive set of single-particle spectroscopy data is available). It should also be noted that while Bi2212and Y123are ‘bilayer’systems,i.e.their crystal structure contains as a key structural element sets of two adjacent CuO2layers, Tl2201and Hg1201are structurally simpler single CuO2-layer materials.Therefore,this choice of compounds ensures that our conclusions are generic to all HTSCs with a similar T c, independent of the number of CuO2layers.A compilation of experimental results for the magnitude of pseudogap(E pg=2 pg)and superconducting(E sc∼5kB T c) energy scales,as a function of carrier doping x,is presented infigure2(only some representative datapoints are shown,so as not to overload thefigure;similar compilations were also obtained by a number of other authors)[5,9,13,16,42,43,52, 57,60,70,74,75].The data for these HTSCs with comparableT max c ∼95K fall on two universal curves:a straight linefor the pseudogap energy E pg=2 pg and a parabola for the superconducting energy scale E sc∼5k B T c.The two curves converge to the same x∼0.27critical point at the end of the superconducting dome,similarly to the cartoon of figure1(a).In order to summarize the situation with respect to quantitative estimates of E pg and E sc,we have listed in table1the values as determined by the different experimental techniques on optimally doped Bi2212(with T c ranging from 90to95K).While one obtains from this compilation the average values of E pg 76meV and E sc 41meV at optimal doping,the numbers do scatter considerably.Note also that these numbers differ slightly from those given in relation to the parabolic and straight lines infigure2(e.g.E maxsc= 42meV)because the latter were inferred from afitting of superconducting and pseudogap data over the whole doping range,while those in table1were deduced from results for optimally doped Bi2212only.It is also possible to plot the pseudogap E pg and superconducting E sc energy scales as estimated simultaneously in one single experiment on the very same sample.This is done infigure3for Raman,tunneling and ARPES results from Bi2212and Hg1201,which provide evidence for the presence of two energy scales,or possibly two spectral gaps as we discuss in greater detail below,coexisting over the whole superconducting dome.2.1.Angle-resolved photoemissionThe most extensive investigation of excitation gaps in HTSCs has arguably been done by ARPES[9,10,26,27,34,35,54–66,76–80].This technique provides direct access to the one-electron removal spectrum of the many-body system;it allows,for instance in the case of a BCS superconductor[29], to measure the momentum dependence of the absolute value of the pairing amplitude2 via the excitation gap observed for single-electron removal energies,again assuming E F to be located half-way in the gap[9,10].This is the same in some tunneling experiments such as STM,which however do not provide direct momentum resolution but measure on both sides of E F[18].The gap magnitude is usually inferred from the ARPES spectra from along the normal-state Fermi surface in the antinodal region,where the d-wave gap is largest;it is estimated from the shift to high-binding energy of the quasiparticle spectral weight relative to the Fermi energy.With this approach only one gap is observed below a temperature scale that smoothly evolves from the so-called pseudogap temperature T∗in the underdoped regime,to the superconducting T c on the overdoped side.We identify this gap0.050.100.150.200.25408012016050100150Energy(meV)Hole doping (x)T c(K)Figure3.Pseudogap E pg and superconducting E sc energy scales (2 )as estimated,by a number of probes and for different compounds,in one single experiment on the very same sample. These data provide direct evidence for the simultaneous presenceof two energy scales,possibly two spectral gaps,coexisting in the superconducting state.The superconducting and pseudogap lines are defined as infigure2.with the pseudogap energy scale E pg=2 pg.This is also in agreement with recent investigations of the near-nodal ARPES spectra from single and double layer Bi-cuprates[57,76,77], which further previous studies of the underdoped cuprates’Fermi arc phenomenology[78–80].From the detailed momentum dependence of the excitation gap along the Fermi surface contour,and the different temperature trends observed in the nodal and antinodal regions,these studies suggest the coexistence of two distinct spectral gap components over the whole superconducting dome:superconducting gap and pseudogap,dominating the response in the nodal and antinodal regions,respectively,which would eventually collapse to one single energy scale in the very overdoped regime.2.2.TunnelingThe HTSCs have been investigated by a wide variety of tunneling techniques[13,18,36–39,44–51],such as SIN[38,51],SIS[37–39],STM[18,36,46],intrinsic tunneling[47–50]and Andreev reflection,which is also a tunneling experiment but involves two-particle rather than single-particle tunneling(in principle,very much like SIS) [13,43,72].All these techniques,with the exception of intrinsic tunneling3,are represented here either in thefigures or table.Similarly to what was discussed for ARPES at the antinodes,there are many STM studies that report a pseudogap E pg smoothly evolving into E sc upon overdoping[18,31]. In addition,a very recent temperature-dependent study of overdoped single-layer Bi-cuprate detected two coexisting,yet clearly distinct,energy scales in a single STM experiment[32]. In particular,while the pseudogap was clearly discernible in the differential conductance exhibiting the usual large spatial modulation,the evidence for a spatially uniform superconducting gap was obtained by normalizing the low-temperature spectra by those just above T c 15K.These values have not been included infigures2and3because T c 95K;however,this study arguably provides the most direct evidence for the coexistence of two distinct excitation gaps in the HTSCs.One can regard Andreev reflection(pair creation in addition to a hole)as the inverse of a two-particle scattering experiment such as Raman or INS.A different view is also possible:SIN tunneling goes over to AR if the insulator layer gets thinner and thinner[13];thus a SIN tunneling,as also STM,should give the same result as AR.However while SIN and STM measure the pseudogap,AR appears to be sensitive to the superconducting energy scale E sc(figure2).We can only conjecture that this has to do with the tunneling mechanisms actually being different.3The most convincing tunneling results showing two coexisting gaps were actually obtained by intrinsic tunneling[47–50],in particular from Bi2Sr2CuO6+δ(Bi2201)[48].However,because this technique suffers from systematic problems[50],and one would anyway have to scale the Bi2201data because of the lower value of T c and in turn gap energy scales,these results were not included infigures2or3.Since intrinsic tunneling is in principle a clean SIS experiment which measures pair energies through Josephson tunneling, a refinement of the technique might provide an accurate estimate of both superconducting and pseudogap simultaneously,and is thus highly desirable.SIS tunneling experiments[39]find E pg/E sc 1for Bi2212at all doping levels.There are,however,some open questions concerning the interpretation of the SIS experiments. This technique,which exploits Josephson tunneling,measures pair spectra;the magnitude of E pg can readily be obtained from the most pronounced features in the spectra[39].The signal related to E sc is seen as a‘sideband’on the E pg features;it does not seem obvious why,if the E sc signal did originate from a state of paired electrons,it would not show up more explicitly.2.3.Raman scatteringLight scattering measures a two-particle excitation spectrum providing direct insight into the total energy needed to break up a two-particle bound state or remove a pair from a condensate. Raman experiments can probe both superconducting and pseudogap energy scales,if one interprets the polarization dependent scattering intensity in terms of different momentum averages of the d-wave-like gap functions:one peaked at(π,0) in B1g geometry,and thus more sensitive to the larger E pg which dominates this region of momentum space;the other at(π/2,π/2)in B2g geometry,and provides an estimate of the slope of the gap function about the nodes,(1/¯h)(d /d k)|n, which is more sensitive to the arguably steeper functional dependence of E sc out of the nodes[19,40,52,53].One should note,however,that the signal is often riding on a high background,which might result in a considerable error and data scattering.At a more fundamental level,while the experiments in the antinodal geometry allow a straightforward determination of the gap magnitude E pg,the nodal results need a numerical analysis involving a normalization of the Raman response function over the whole Brillouin zone,a procedure based on a low-energy B2g sum rule(although also the B2g peak position leads to similar conclusions)[52].This is because a B2g Raman experiment is somewhat sensitive also to the gap in the antinodal direction,where it picks up,in particular,the contribution from the larger pseudogap.2.4.Inelastic neutron scatteringInelastic neutron scattering experiments have detected the so-called q=(π,π)resonant magnetic mode in all of the T c 95K HTSCs considered here[16].This resonance is proposed by some to be a truly collective magnetic mode that, much in the same way as phonons mediate superconductivity in the conventional BCS superconductors,might constitute the bosonic excitation mediating superconductivity in the HTSCs. The total measured intensity,however,amounts to only a small portion of what is expected based on the sum rule for the magnetic scattering from a spin1/2system[8,16,24, 42,68,69];this weakness of the magnetic response should be part of the considerations in the modeling of magnetic resonance mediated high-T c superconductivity.Alternatively, its detection below T c might be a mere consequence of the onset of superconductivity and of the corresponding suppression of quasiparticle scattering.Independently of the precise interpretation,the INS data reproduced infigure2show that the magnetic resonance energy r tracks very closely, over the whole superconducting dome,the superconductingenergy scale E sc∼5k B T c(similar behavior is observed, in the underdoped regime,also for the spin-gap at the incommensurate momentum transfer(π,π±δ)[81]).Also remarkable is the correspondence between the energy of the magnetic resonance and that of the B2g Raman peak.Note that while the q=(π,π)momentum transfer observed for the magnetic resonance in INS is a key ingredient of most proposed HTSC descriptions,Raman scattering is a q=0probe.It seems that understanding the connection between Raman and INS might reveal very important clues.2.5.Heat conductivityHeat conductivity data from Y123and Tl2201fall onto the pseudogap line.This is a somewhat puzzling result because they have been measured at very low temperatures,well into the superconducting state,and should in principle provide a measure of both gaps together if these were indeed coexisting below T c.However,similarly to the B2g Raman scattering, these experiments are only sensitive to the slope of the gap function along the Fermi surface at the nodes,(1/¯h)(d /d k)|n; the gap itself is determined through an extrapolation procedure in which only one gap was assumed.The fact that the gap values,especially for Y123,come out on the high side of the pseudogap line may be an indication that an analysis with two coexisting gaps might be more appropriate.3.Outlook and conclusionThe data infigures2and3demonstrate that there are two coexisting energy scales in the HTSCs:one associated with the superconducting T c and the other,as inferred primarily from the antinodal region properties,with the pseudogap T∗. The next most critical step is that of addressing the subtle questions concerning the nature of these energy scales and the significance of the emerging two-gap phenomenology towards the development of a microscopic description of high-T c superconductivity.As for the pseudogap,which grows upon underdoping, it seems natural to seek a connection to the physics of the insulating parent compound.Indeed,it has been pointed out that this higher energy scale might smoothly evolve,upon underdoping,into the quasiparticle dispersion observed by ARPES in the undoped antiferromagnetic insulator[82,83]. At zero doping the dispersion and quasiparticle weight in the single-hole spectral function as seen by ARPES can be very well explained in terms of a self-consistent Born approximation[84],as well as in the diagrammatic quantum Monte Carlo[85]solution to the so-called t–t –t –J model.In this model,as in the experiment[82,83],the energy difference between the top of the valence band at(π/2,π/2)and the antinodal region at(π,0)is a gap due to the quasiparticle dispersion of about250±30meV.Note that this would be a single-particle gap .For the direct comparison with the pseudogap data infigure2,we would have to consider 2 ∼500meV;this,however,is much larger than the x=0 extrapolated pseudogap value of186meV found from our analysis across the phase diagram.Thus there seems to be an important disconnection between thefinite doping pseudogapand the zero-doping quasiparticle dispersion.The fact that the pseudogap measured in ARPES and SINexperiments is only half the size of the gap in SIS,STM,B1gRaman and heat conductivity measurements,points to a pairinggap.So although the origin of the pseudogap atfinite dopingremains uncertain,we are of the opinion that it most likelyreflects a pairing energy of some sort.To this end,the trend infigure2brings additional support to the picture discussed bymany authors that the reduction in the density of states at T∗isassociated with the formation of electron pairs,well above theonset of phase coherence taking place at T c(see,e.g.[86,87]).The pseudogap energy E pg=2 pg would then be the energy needed to break up a preformed pair.To conclusively addressthis point,it would be important to study very carefully thetemperature dependence of the(π,0)response below T c;anyfurther change with the onset of superconductivity,i.e.anincrease in E pg,would confirm the two-particle pairing picture,while a lack thereof would suggest a one-particle band structureeffect as a more likely interpretation of the pseudogap.The lower energy scale connected to the superconductingT c(parabolic curve infigure2and3)has already been proposedby many authors to be associated with the condensationenergy[86–89],as well as with the magnetic resonance inINS[90].One might think of it as the energy needed totake a pair of electrons out of the condensate;however,fora condensate of charged bosons,a description in terms of acollective excitation,such as a plasmon or roton,would bemore appropriate[24].The collective excitation energy wouldthen be related to the superfluid density and in turn to T c.In thissense,this excitation would truly be a two-particle process andshould not be measurable by single-particle spectroscopies.Also,if the present interpretation is correct,this excitationwould probe predominantly the charge-response of the system;however,there must be a coupling to the spin channel,so as tomake this process neutron active(yet not as intense as predictedby the sum rule for pure spin-1/2magnetic excitations,whichis consistent with the small spectral weight observed by INS).As discussed,one aspect that needs to be addressed to validatethese conjectures is the surprising correspondence betweenq=0and q=(π,π)excitations,as probed by Raman andINS,respectively.We are led to the conclusion that the coexistence of twoenergy scales is essential for high-T c superconductivity,withthe pseudogap reflecting the pairing strength and the other,always smaller than the pseudogap,the superconductingcondensation energy.This supports the proposals thatthe HTSCs cannot be considered as classical BCSsuperconductors,but rather are smoothly evolving from theBEC into the BCS regime[91–93],as carrier doping isincreased from the underdoped to the overdoped side of thephase diagram.AcknowledgmentsSH would like to thank the University of British Columbiafor its hospitality.Helpful discussions with W N Hardy,。

a r X i v :c o n d -m a t /0502117v 1 [c o n d -m a t .s u p r -c o n ] 4 F eb 2005Critical point and the nature of the pseudogap of single-layered copper oxideBi 2Sr 2−x La x CuO 6+δsuperconductorsGuo-qing Zheng 1,P.L.Kuhns 2,A.P.Reyes 2,B.Liang 3and C.T.Lin 31Department of Physics,Okayama University,Okayama 700-8530,Japan 2National High Magnetic Field Laboratory,Tallahassee,FL,USA and3Max-Planck-Institut fur Festkorperforschung,Heisenbergstr.1,D-70569Stuttgart,Germany(Dated:Phys.Rev.Lett.94,047006(2005))We apply strong magnetic fields of H =28.5∼43T to suppress superconductivity (SC)in the cuprates Bi 2Sr 2−x La x CuO 6+δ(x =0.65,0.40,0.25,0.15and 0),and investigate the low temperature (T )normal state by 63Cu nuclear spin-lattice relaxation rate (1/T 1)measurements.We find that the pseudogap (PG)phase persists deep inside the overdoped region but terminates at x ∼0.05that corresponds to the hole doping concentration of approximately 0.21.Beyond this critical point,the normal state is a Fermi liquid characterized by the T 1T =const relation.A comparison of the superconducting state with the H -induced normal state in the x =0.40(T c =32K)sample indicates that there remains substantial part of the Fermi surface even in the fully-developed PG state,which suggests that the PG and SC are coexisting matters.PACS numbers:74.25.Ha,74.25.Jb,74.25.Nf,74.72.HsIn many cases,the normal state of the high transition-temperature (T c )copper oxide (cuprate)superconduc-tors above T c deviates strongly from that described by Landau’s Fermi liquid theory [1].One of the exper-imental facts taken as evidence for such deviations is the opening of a pseudogap (PG)above T c ,a phe-nomenon of loss of density of states (DOS)[2].The pseudogap is pronounced at low doping level,in the so-called underdoped regime.The pseudogap temper-ature,T ∗,generally decreases as the carrier doping rate increases.However,it is unclear whether T ∗finally merges into the T c curve in the overdoped regime [3],or it terminates before superconductivity disappears [4,5].Different classes of theories have been put forward to explain the pseudogap phenomenon (for examples,see Ref.[6,7,8,9,10,11,12,13]).It is interesting that these theories generally also propose different mechanisms for the occurrence of superconductivity.Since the topology of the phase diagram has great impact on the mechanism of the high-T c superconductivity,it is important to clarify the doping dependence of the pseudogap.Unfortunately,the onset of superconductivity,typically at ∼100K,and the large upper critical field H c 2(∼100T)prevents in-vestigation of how the pseudogap evolves with doping.The highest static field available to date (∼30T)was only able to reduce T c to half its value at most [14,15].Even the pulsed magnetic field is not enough to suppress superconductivity completely [16].Meanwhile,from angle resolved photoemission spec-troscopy (ARPES),it was found that below T ∗the Fermi surface is progressively destroyed with lowering the tem-perature and there remains only four arcs at the Fermi surface at T =T c [17].It would be helpful to see how these arcs would evolve if the superconductivity is re-moved.But again the robust superconducting phase makes it difficult to reveal the properties of the low tem-perature pseudogap state.Here we address these two issues by using single lay-ered cuprates,Bi 2Sr 2−x La x CuO 6+δ,which have substan-tially lower T c and H c 2.We study the property of the ground state induced by the application of mag-netic fields of 28.5∼43T,by using nuclear magnetic reso-nance (NMR)technique.This system is suitable for such study for it can be tuned from the overdoped regime to the underdoped regime by replacing La for Sr,and very highly overdoped by replacing Pb for Bi [18,19].More-over,it has been long suspected that interlayer coupling could complicate the superconducting-state properties as well as the normal-state properties.The present sys-tem helps since it has only one CuO 2plane in the unit cell.This material has additional advantage in its nearly ideal two dimensional structure with the largest trans-port anisotropy (104-105)among known cuprates [20].We were able to suppress superconductivity completely in the samples of x =0.40,0.25,0.15and 0,which are in the optimally doped to overdoped regimes,by apply-ing magnetic fields of 28.5∼43T generated by the Bitter and Hybrid magnets in the National High Magnetic Field Laboratory,Tallahassee,Florida.Single crystals of Bi 2Sr 2−x La x CuO 6+δwere grown by the traveling solvent floating zone (TSFZ)method with starting materials of Bi 2O 3,SrCO 3,La 2O 3and CuO (Ref.[21]).Compositional measurement was performed by Auger electron spectroscopy with an error of ±2wt.%.The excess oxygen δresides on the Bi 2O 2block and is believed to be responsible for the carrier doping in the CuO 2plane.The amount of δof the present samples was estimated to be 0.36as described in detail in Ref.[21].24812160501001502002503001/T 1T (S e c -1K -1)T (K)FIG.1:(Color on-line)The quantity 1/T 1T plotted against T for Bi 2Sr 2−x La x CuO 6+δmeasured at a field of 28.5T applied along the c-axis.Replacing La for Sr removes holes from the CuO 2plane and increases T c .The T c of Bi 2Sr 2CuO 6.36without La-doping is found to be 8K.The maximal T c =32K was obtained for La concentration of x =0.4,which is in good agreement with that reported in Ref.[22].For NMR measurements,two or three single crys-tal platelets with the dimensions of 15×5×1mm 3were aligned along the c -axis.For all measurements,the ex-ternal field is applied along the c -axis.A standard phase-coherent pulsed NMR spectrometer was used to collect data.The NMR spectra were obtained by sweeping the magnetic field at a fixed frequency (325∼492MHz)and recording the size of the spin echo area.The full width at the half maximum (FWHM)of the 63Cu NMR line for the central transition (m =1/2←→m =−1/2transition)at T =4.2K is 1.8kOe for x =0but decreases with increasing x ,reducing to 1.0kOe for x =0.4.This is probably due to removal of modu-lation in the Bi 2O 2block that is commonly seen in Bi-based cuprates [23].The 63Cu nuclear spin-lattice re-laxation rate,1/T 1,was measured at the spectrum peak by using a single saturation pulse and fitting the recov-ery of the nuclear magnetization (M (t ))after the satura-tion pulse to the theoretical curve given by Narath [24]:M (∞)−M (t )41ω(1)where A q is the q -dependent hyperfine coupling constant [25].In conventional metals,both A q and χ(q )are basi-cally q -independent so that eq.(1)yields to a T 1T =const relation.In most high-T c cuprates,the dynamical suscep-tibility has a peak at the antiferromagnetic wave vector Q =(π,π).1/T 1T is then shown to be proportional to χQ .The increase of 1/T 1T upon decreasing temperature is generally attributed to the increase of χQ ,namely,to the development of antiferromagnetic correlations.For antiferromagnetically correlated metals,this quantity fol-lows a Curie-Weiss relation [26,27],χQ ∝1/(T +θ),so that 1/T 1T ∼1/(T +θ)before superconductivity sets in.In the x =0.65sample,this is true above T =200K,while below this temperature 1/T 1T starts to decrease,leaving a broad peak at around T ∗=200K.This is a typical pseudogap behavior seen in this NMR quantity [28].Our observation of the pseudogap in this single-layered cuprate system is consistent with that made by the ARPES measurement for a x =0.35sample [29].In-terestingly,the pseudogap persists even in the x =0.15sample which is in the overdoped regime,although with a reduced T ∗=60K.Such a low T ∗has not so far been possible to access ,since it is below T c in most materials.As noted already,in the x =0sample,however,the pseu-dogap is no more present.Instead,a T 1T =const relation holds below T =100K,which indicates that the normal state is a Fermi liquid.The result that the magnitude of 1/T 1T for x ≤0.15is enhanced over that for x ≥0.25is probably due to the increase of the transferred hyperfine coupling constant which has previously been reported in the heavily overdoped regime [30].Figure 2shows the magnetic field dependence of 1/T 1T for x =0.40under H =0,28.5T and 43T.The data for H =0were obtained by NQR (nuclear quadrupole reso-nance)measurements at the frequency of νQ ∼30.2MHz.The data for H =43T were obtained at the hybrid mag-net (outsert field of 11T and insert field of 32T)at the High Magnetic Field Laboratory.Note that below T c =32K,1/T 1T is H -dependent between 0and 28.5T,but no magnetic field dependence is observed beyond 28.5T.This indicates that the superconductivity for the x =0.40sample is suppressed by a field greater than 28.5T,which is also supported by the ac susceptibility measurement using the NMR coil.Therefore,our results for x ≤0.40characterize microscopically the low-T normal (ground)state when superconductivity is removed.In Fig.3we compare the high field (H =28.5T)data30510151/T 1T (S e c -1K -1)T (K)FIG.2:(Color on-line)Magnetic field dependence of 1/T 1T for Bi 2Sr 1.6La 0.4CuO 6+δ.The arrow indicates T c at zero mag-neticfield.5101520251/T 1T (s e c -1K -1)T (K)FIG.3:(Color on-line)Magnetic field dependence of 1/T 1T for the as-grown,overdoped sample,Bi 2Sr 2CuO 6+δ.The ar-row indicates T c at zero magnetic field.and the zero-field data for the x =0sample.In the normal state above T c (H =0)=8K,both sets of data agree well.This indicates that the Fermi liquid state in this over-doped sample is an intrinsic property;it is not an effect of high magnetic field.Note that the Fermi liquid state persists when the superconducting state is suppressed.The doping dependence of T ∗is shown in Fig.4,along with the x -dependence of T c that was determined as the zero resistance temperature and agrees well with the on-501001502002500.080.120.160.20.24T e m p e r a t u r e (K )1-xhole concentration (p )FIG.4:(Color on-line)Phase diagram obtained from NMR measurements for Bi 2Sr 2−x La x CuO 6+δ.T ∗is the tempera-ture below which the pseudogap develops,and T c is the su-perconducting transition temperature.The upper scale of the transverse axis is adopted from Ref.[22].PG and SC denote the pseudogap phase and superconducting phase,respectively.set temperature of the Meissner signal in the ac suscepti-bility measured using the NMR coil.The maximal T c is achieved at T c =32K for x opt =0.40.The results indicate that there exists a critical doping concentration p cr at which the pseudogap terminates and beyond which the ground state when the superconductivity is suppressed is a Fermi liquid.The critical point is around x =0.05which corresponds to p cr ∼0.21,according to Ando’s characterization [22](see the upper scale of the trans-verse axis of Fig.3).We mention a caveat that T ∗at zero magnetic field for the overdoped regime could be slightly higher than that we found here at high magnetic field [15],therefore p cr could be slightly higher.However,the limit for largest possible p cr is set by the x =0sample (p ∼0.22)which shows no pseudogap.Note that the p cr we found is much larger than the op-timal doping concentration (p opt ∼0.15).Therefore,our results indicate that there is no quantum phase transition taking place at the optimal doping,as opposed to the hy-pothesis that is frequently conjectured [4,31].However,if the pseudogap is associated with some sort of phase transition [11],then p cr ∼0.21may be viewed as a quan-tum critical point.But again,note that p cr is far greater than the optimum doping concentration p opt =0.15.It is interesting that many physical quantities,such as the su-perfluid density [32],show distinct change upon crossing a doping concentration that is close to the present p cr .4 Finally,thefield dependence of1/T1T below T c(H=0),as seen in Fig.2,indicates that the pseudogap is anincomplete gap;even in the fully-developed pseudogapstate,i.e.at T∼1K,there remains substantial DOS atthe Fermi level,which is lost only after superconductivitysets in.This suggests that superconductivity and pseudo-gap are coexisting matters.Below T∗,some parts of theFermi surface are lost due to the onset of the pseudogap,but other parts of the Fermi surface remain ungapped.Ifone roughly estimates the DOS from5[29]J.M.Harris et al,Phys.Rev.Lett.79,143(1997).[30]Y.Kitaoka et al,Physica(Amsterdam)C179,107(1991).[31]S.Sachdev,Science288,475(2000).[32]C.Panagopoulos et al,Phys.Rev.B67,220502(2003).[33]G.-q.Zheng et al,Phys.Rev.B70,014511(2004).[34]ughlin,G.G.Lonzarich,P.Monthoux and D.Pines,Adv.Phys.50,361(2001).。

高温超导机制
高温超导是指在相对较高的温度下（通常指液氮温度以上），材料表现出超导现象的现象。

高温超导的机制目前仍然不是完全清楚，但已经有一些理论和实验证据可以解释它。

最初被提出的是BCS理论。

这个理论是用来解释低温超导的。

根据这个理论，低温超导是由于电子之间的库仑相互作用引起的。

BCS 理论认为，超导体的电子处于一个被称为“Cooper配对”的状态。

这种配对可以减少电子之间的相互斥力，并克服了电阻。

然而，高温超导体中的配对机制与低温超导体中的不同。

目前认为，高温超导体中的超导机制主要是由电子之间的强相互作用引起的。

这种相互作用可以产生一种被称为“奇异性”的量子效应。

奇异性是一种特殊的自旋排列方式，在高温超导体中，它可以形成一种类似于Cooper配对的状态。

这种状态可以减少电子之间的相互斥力，并克服了电阻。

除了奇异性，还有其他一些理论也被用来解释高温超导的机制，如强耦合理论、自旋液体理论等。

这些理论都试图解释高温超导体中的电子之间的相互作用是如何导致超导现象的。

总的来说，高温超导机制仍然是一个活跃的研究领域。

虽然我们已经有了一些理论和实验证据，但还有很多问题需要进一步研究。

解决这些问题将有助于我们更好地理解高温超导，并为未来的应用提供更好的材料。

- 1 -。

DOI: 10.1126/science.1220854, 773 (2013);339 Science et al.Marc André Meyers ConnectionsStructural Biological Materials: Critical Mechanics-MaterialsThis copy is for your personal, non-commercial use only.clicking here.colleagues, clients, or customers by , you can order high-quality copies for your If you wish to distribute this article to othershere.following the guidelines can be obtained by Permission to republish or repurpose articles or portions of articles): May 1, 2013 (this information is current as of The following resources related to this article are available online at/content/339/6121/773.full.html version of this article at:including high-resolution figures, can be found in the online Updated information and services, /content/339/6121/773.full.html#ref-list-1, 12 of which can be accessed free:cites 51 articles This article/cgi/collection/mat_sci Materials Sciencesubject collections:This article appears in the following registered trademark of AAAS.is a Science 2013 by the American Association for the Advancement of Science; all rights reserved. The title Copyright American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the Science o n M a y 1, 2013w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o mStructural BiologicalMaterials:CriticalMechanics-Materials ConnectionsMarc AndréMeyers,1,2*Joanna McKittrick,1Po-Yu Chen3Spider silk is extraordinarily strong,mollusk shells and bone are tough,and porcupine quills and feathers resist buckling.How are these notable properties achieved?The building blocks of the materials listed above are primarily minerals and biopolymers,mostly in combination;the first weak in tension and the second weak in compression.The intricate and ingenious hierarchical structures are responsible for the outstanding performance of each material.Toughness is conferred by the presence of controlled interfacial features(friction,hydrogen bonds,chain straightening and stretching);buckling resistance can be achieved by filling a slender column with a lightweight foam.Here,we present and interpret selected examples of these and other biological materials.Structural bio-inspired materials design makes use of the biological structures by inserting synthetic materials and processes that augment the structures’capability while retaining their essential features.In this Review,we explain this idea through some unusual concepts.M aterials science is a vibrant field of in-tellectual endeavor and research.Thisfield applies physics and chemistry, melding them in the process,to the interrela-tionship between structure,properties,and perform-ance of complex materials with technological applications.Thus,materials science extends these rigorous scientific disciplines into complex ma-terials that have structures providing properties and synergies beyond those of pure and simple solids.Initially geared at synthetic materials,ma-terials science has recently extended its reach into biology,especially into the extracellular matrix, whose mechanical properties are of utmost im-portance in living organisms.Some of the semi-nal work and important contributions in this field are either presented or reviewed in(1–5).There are a number of interrelated features that define biological materials and distinguish them from their synthetic counterparts[inspired by Arzt(6)]: (i)Self-assembly.In contrast to many synthetic processes to produce materials,the structures are assembled from the bottom up,rather than from the top down.(ii)Multi-functionality.Many com-ponents serve more than one purpose.For exam-ple,feathers provide flight capability,camouflage, and insulation,whereas bones provide structural framework,promote the growth of red blood cells, and provide protection to the internal organs.(iii) Hierarchy.Different,organized scale levels(nano-to ultrascale)confer distinct and translatable prop-erties from one level to the next.We are starting to develop a systematic and quantitative understandingof this hierarchy by distinguishing the character-istic levels,developing constitutive descriptionsof each level,and linking them through appro-priate and physically based equations,enabling afull predictive understanding.(iv)Hydration.Theproperties are highly dependent on the level ofwater in the structure.There are some exceptions,such as enamel,but this rule applies to mostbiological materials and is of importance to me-chanical properties such as strength(which isdecreased by hydration)and toughness(which isincreased).(v)Mild synthesis conditions.Themajority of biological materials are fabricated atambient temperature and pressure as well as in anaqueous environment,a notable difference fromsynthetic materials fabrication.(vi)Evolution andenvironmental constraints.The limited availabil-ity of useful elements dictates the morphologyand resultant properties.The structures are notnecessarily optimized for all properties but arethe result of an evolutionary process leading tosatisfactory and robust solutions.(vii)Self-healingcapability.Whereas synthetic materials undergodamage and failure in an irreversible manner,biological materials often have the capability,due to the vascularity and cells embedded in thestructure,to reverse the effects of damage byhealing.The seven characteristics listed above arepresent in a vast number of structures.Nevertheless,the structures of biological materials can bedivided into two broad classes:(i)non-mineralized(“soft”)structures,which are composed of fibrousconstituents(collagen,keratin,elastin,chitin,lignin,and other biopolymers)that display widelyvarying mechanical properties and anisotropiesdepending on the function,and(ii)mineralized(“hard”)structures,consisting of hierarchicallyassembled composites of minerals(mainly,butnot solely,hydroxyapatite,calcium carbonate,and amorphous silica)and organic fibrous com-ponents(primarily collagen and chitin).The mechanical behavior of biological con-stituents and composites is quite diverse.Bio-minerals exhibit linear elastic stress-strain plots,whereas the biopolymer constituents are non-linear,demonstrating either a J shape or a curvewith an inflection point.Foams are characterizedby a compressive response containing a plastic orcrushing plateau in which the porosity is elim-inated.Many biological materials are compositeswith many components that are hierarchicallystructured and can have a broad variety of con-stitutive responses.Below,we present some of thestructures and functionalities of biological ma-terials with examples from current research.Here,we focus on three points:(i)How high tensilestrength is achieved(biopolymers),(ii)how hightoughness is attained(composite structures),and(iii)how bending resistance is achieved in light-weight structures(shells with an interior foam).Structures in Tension:Importance of BiopolymersThe ability to sustain tensile forces requires aspecific set of molecular and configurational con-formations.The initial work performed on exten-sion should be small,to reduce energy expenditure,whereas the material should stiffen close to thebreaking point,to resist failure.Thus,biopolymers,such as collagen and viscid(catching spiral)spidersilk,have a J-shaped stress-strain curve where mo-lecular uncoiling and unkinking occur with con-siderable deformation under low stress.This stiffening as the chains unfurl,straighten,stretch,and slide past each other can be repre-sented analytically in one,two,and three dimen-sions.Examples are constitutive equations initiallydeveloped for polymers by Ogden(7)and Arrudaand Boyce(8).An equation specifically proposedfor tissues is given by Fung(3).A simpler for-mulation is given here;the slope of the stress-strain(s-e)curve increases monotonically with strain.Thus,one considers two regimes:(i)unfurlingand straightening of polymer chainsd sd eºe nðn>1Þð1Þand(ii)stretching of the polymer chain backbonesd sd eºEð2Þwhere E is the elastic modulus of the chains.Thecombined equation,after integrating Eqs.1and2,iss=k1e n+1+H(e c)E(e–e c)(3)Here k1is a parameter,and H is the Heavisidefunction,which activates the second term at e=e c,where e c is a characteristic strain at whichcollagen fibers are fully extended.Subsequent straingradually becomes dominated by chain stretch-ing.The computational results by Gautieri et al.(9)on collagen fibrils corroborate Eq.3for n=1.This corresponds to a quadratic relation between1Department of Mechanical and Aerospace Engineering andMaterials Science and Engineering Program,University ofCalifornia,San Diego,La Jolla,CA92093,USA.2Department ofNanoengineering,University of California,San Diego,La Jolla,CA92093,USA.3Department of Materials Science and En-gineering,National Tsing Hua University,Hsinchu30013,Taiwan,Republic of China.*To whom correspondence should be addressed.E-mail:mameyers@ SCIENCE VOL33915FEBRUARY2013773o n M a y 1 , 2 0 1 3 w w w . s c i e n c e m a g . o r g D o w n l o a d e d f r o mstress and strain (s ºe 2),which has the char-acteristic J shape.Collagen is the most important structural bio-logical polymer,as it is the key component in many tissues (tendon,ligaments,skin,and bone),as well as in the extracellular matrix.The de-formation process is intimately connected to the different hierarchical levels,starting with the poly-peptides (0.5-nm diameter)to the tropocollagen molecules (1.5-nm diameter),then to the fibrils (~40-to 100-nm diameter),and finally to fibers (~1-to 10-m m diameter)and fascicles (>10-m m diameter).Molecular dynamics computations (9)of entire fibrils show the J -curve response;these computational predictions are well matched to atomic force microscopy (AFM)(10),small-angle x-ray scattering (SAXS)(11),and experiments by Fratzl et al .(12),as shown in Fig.1A.The effect of hydration is also seen and is of great impor-tance.The calculated density of collagen de-creases from 1.34to 1.19g/cm 3with hydration and is accompanied by a decrease in the Young ’s modulus from 3.26to 0.6GPa.The response of silk and spider thread is fascinating.As one of the toughest known ma-terials,silk also has high tensile strength and extensibility.It is composed of b sheet (10to 15volume %)nanocrystals [which consist of highly conserved poly-(Gly-Ala)and poly-Ala domains]embedded in a disordered matrix (13).Figure 1B shows the J -shape stress-strain curve and molecular configurations for the crystalline domains in silkworm (Bombyx mori )silk (14).Similar to collagen,the low-stress region corre-sponds to uncoiling and straightening of the pro-tein strands.This region is followed by entropic unfolding of the amorphous strands and then stiffening due to load transfer to the crystalline b sheets.Despite the high strength,the major mo-lecular interactions in the b sheets are weak hy-drogen bonds.Molecular dynamics simulations,Fig.1.Tensile stress-strain relationships in bio-polymers.(A )J -shaped curve for hydrated and dry collagen fibrils obtained from molecular dynamics (MD)simulations and AFM and SAXS studies.At low stress levels,considerable stretching occurs due to the uncrimping and unfolding of molecules;at higher stress levels,the polymer backbone stretches.Adapted from (9,12).(B )Stretching of dragline spider silk and molecular schematic of the protein fibroin.At low stress levels,entropic effects domi-nate (straightening of amorphous strands);at higher levels,the crystalline parts sustain the load.(C )Mo-lecular dynamics simulation of silk:(i)short stack and (ii)long stack of b -sheet crystals,showing that a higher pullout force is required in the short stack;for the long stack,bending stresses become im-portant.Hydrogen bonds connect b -sheet crystals.Adapted from (14).(D )Egg whelk case (bioelastomer)showing three regions:straightening of the a helices,the a helix –to –b sheet transformation,and b -sheet extension.A molecular schematic is shown.Adapted from (18).300.000.2Yield pointEntropic unfoldingMD simulationsStick slipStiffening β-crystal123456700012345670102030405050010001500200025050075010001250150017500.40.60.80.010.020.030.040.05MD wet (Gautieri et al)SAXS (Sasaki and Odajima)AFM (Aladin et al)MD dry (Gautieri et al)2520151050S t r e s s (M P a )S t r e s s(M P a )StrainABCDStrain (m/m)Length (nm)Length (nm)Stick-slip deformation (robust)"brittle" fracture (fragile)i iiP u l l -o u t f o r c e (p N )00.20.4Native state Unloading: reformation of α-helicesDomain 4: Extension andalignmentof β-sheets0.60.8ε=0ε4ε=01.0012345StrainS t r e s s (M P a )E n e r g y /v o l u m e (k c a l /m o l /n m 3)L e n g t hI I II II III IIIIVIVFDomain 3: Formation of β-sheetsfrom random coilsε3Domain 2: Extension of random coilsε2Domain 1: Unraveling of α-helicesinto random coilsε1Toughness (MD)Resilience (MD)T=-1°C T=20°C T=40°C T=60°C T=80°C15FEBRUARY 2013VOL 339SCIENCE 774REVIEWo n M a y 1, 2013w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o mshown in Fig.1C,illustrate an energy dissipative stick-slip shearing of the hydrogen bonds during failure of the b sheets (14).For a stack with a height L ≤3nm (left-hand side of Fig.1C),the shear stresses are more substantial than the flex-ure stresses,and the hydrogen bonds contribute to the high strength obtained (1.5GPa).How-ever,if the stack of b sheets is too high (right-hand side of Fig.1C),it undergoes bending with tensile separation between adjacent sheets.The nanoscale dimension of the b sheets allows for a ductile instead of brittle failure,resulting in high toughness values of silk.Thus,size affects the mechanical response considerably,changing the deformation characteristics of the weak hydro-gen bonds.This has also been demonstrated in bone (15–17),where sacrificial hydrogen bonds between mineralized collagen fibrils contribute to the excellent fracture resistance.Other biological soft materials have more complex responses,marked by discontinuities in d s /d e .This is the case for wool,whelk eggs,silks,and spider webs.Several mechanisms are responsible for this change in slope;for instance,the transition from a -to b -keratin,entropic changes with strain (such as those prevalent in rubber,where chain stretching and alignment decrease entropy),and others.The example of egg whelk is shown in Fig.1D (18).In this case,there is a specific stress at which a -keratin heli-ces transform to b sheets,with an associated change in length.Upon unloading,the reverse occurs,and the total reversible strain is,therefore,extensive.This stress-induced phase transforma-tion is similar to what occurs in shape-memory alloys.Thus,this material can experience sub-stantial reversible deformation (up to 80%)in a reversible fashion,when the stress is raised from 2to 5MPa,ensuring the survival of whelk eggs,which are continually swept by waves.These examples demonstrate the distinct properties of biopolymers that allow these ma-terials to be strong and highly extensible with distinctive molecular deformation characteristics.However,many interesting biological materials are composites of flexible biopolymers and stiff minerals.The combination of these two constit-uents leads to the creation of a tough material.Imparting Toughness:Importance of Interfaces One hallmark property of most biological com-posites is that they are tough.Toughness is defined as the amount of energy a material ab-sorbs before it fails,expressed asU ¼∫e fs d eð4Þwhere U is the energy per volume absorbed,s is the stress,e is the strain,and e f is the failure strain.Tough materials show considerable plastic deformation (or permanent damage)coupled with considerable strength.This maximizes the integral expression in Eq.4.Biological com-posite materials (for example,crystalline and noncrystalline components)have a plethora oftoughening mechanisms,many of which depend on the presence of interfaces.As a crack im-pinges on an interface or discontinuity in the material,the crack can be deflected around the interface (requiring more energy to propagate than a straight crack)or can drive through it.The strength of biopolymer fibers in tension im-pedes crack opening;bridges between micro-cracks are another mechanism.The toughening mechanisms have been divided into intrinsic (ex-isting in the material ahead of crack)and extrinsic (generated during the progression of failure)cat-egories (19).Thus,toughening is accomplished by a wide variety of stratagems.We illustrate this concept for four biological materials,shown in Fig.2.All inorganic materials contain flaws and cracks,which reduce the strength from the theo-retical value (~E /10to E /30).The maximum stress (s max )a material can sustain when a preexisting crack of length a is present is given by the Griffith equations max ¼ffiffiffiffiffiffiffiffiffiffi2g s E p a r ¼YK Icffiffiffiffiffip ap ð5Þwhere E is the Young ’s modulus,g s is the sur-face (or damage)energy,and Y is a geometric parameter.K Ic ¼Y −1ffiffiffiffiffiffiffiffiffiffi2g s E p is the fracture toughness,a materials property that expresses the ability to resist crack propagation.Abalone (Haliotis rufescens )nacre has a fracture tough-ness that is vastly superior to that of its major constituent,monolithic calcium carbonate,due to an ordered assembly consisting of mineral tiles with an approximate thickness of 0.5m m and a diameter of ~10m m (Fig.2A).Additionally,this material contains organic mesolayers (separated by ~300m m)that are thought to be seasonal growth bands.The tiles are connected by mineral bridges with ~50-nm diameter and are separated by organic layers,consisting of a chitin network and acidic proteins,which,when combined,have a similar thickness to the mineral bridge diame-ters.The Griffith fracture criterion (Eq.5)can be applied to predict the flaw size (a cr )at which the theoretical strength s th is achieved.With typical values for the fracture toughness (K Ic ),s th ,and E ,the critical flaw size is in the range of tens of nanometers.This led Gao et al .(20)to propose that at sufficiently small dimensions (less than the critical flaw size),materials become insensitive to flaws,and the theoretical strength (~E /30)should be achieved at the nanoscale.However,the strength of the material will be determined by fracture mechanisms operating at all hierar-chical levels.The central micrograph in Fig.2A shows how failure occurs by tile pullout.The interdigitated structure deflects cracks around the tiles instead of through them,thereby increasing the total length of the crack and the energy needed to fracture (increasing the toughness).Thus,we must de-termine how effectively the tiles resist pullout.Three contributions have been identified and are believed to operate synergistically (21).First,themineral bridges are thought to approach thetheoretical strength (10GPa),thereby strongly attaching the tiles together (22).Second,the tile surfaces have asperities that are produced during growth (23)and could produce frictional resist-ance and strain hardening (24).Third,energy is required for viscoelastic deformation (stretching and shearing)of the organic layer (25).One important aspect on the mechanical prop-erties is the effect of alignment of the mineral crystals.The oriented tiles in nacre result in an-isotropic properties with the strength and modulus higher in the longitudinal (parallel to the organic layers)than in the transverse direction.For a composite with a dispersed mineral m of volume fraction V m embedded in a biopolymer (bp)matrix that has a much lower strength and Young ’s modulus than the mineral,the ratio of the lon-gitudinal (L)and transverse (T)properties P (such as elastic modulus)can be expressed,in simpli-fied form,asP L P T ¼P mP bpV m ð1−V m Þð6ÞThus,the longitudinal properties are much higher than the transverse properties.This aniso-tropic response is also observed in other oriented mineralized materials,such as bone and teeth.Another tough biological material is the exo-skeleton of an arthropod.In the case of marine animals [for instance,lobsters (26,27)and crabs (28)],the exoskeleton structure consists of layers of mineralized chitin in a Bouligand arrange-ment (successive layers at the same angle to each other,resulting in a helicoidal stacking sequence and in-plane isotropy).These layers can be en-visaged as being stitched together with ductile tubules that also perform other functions,such as fluid transport and moisture regulation.The cross-ply Bouligand arrangement is effective in crack stopping;the crack cannot follow a straight path,thereby increasing the materials ’toughness.Upon being stressed,the mineral components frac-ture,but the chitin fibers can absorb the strain.Thus,the fractured region does not undergo physical separation with dispersal of fragments,and self-healing can take place (29).Figure 2B shows the structure of the lobster (Homarus americanus )exoskeleton with the Bouligand ar-rangement of the fibers.Bone is another example of a biological ma-terial that demonstrates high toughness.Skeletal mammalian bone is a composite of hydroxyapatite-type minerals,collagen and water.On a volu-metric basis,bone consists of ~33to 43volume %minerals,32to 44volume %organics,and 15to 25volume %water.The Young ’s modulus and strength increase,but the toughness decreases with increasing mineral volume fraction (30).Cortical (dense)mammalian bone has blood ves-sels extending along the long axis of the limbs.In animals larger than rats,the vessel is encased in a circumferentially laminated structure called the osteon.Primary osteons are surrounded by hypermineralized regions,whereas secondary SCIENCEVOL 33915FEBRUARY 2013775REVIEWo n M a y 1, 2013w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o m(remodeled)osteons are surrounded by a cement line (also of high mineral content)(31).In mam-malian cortical bone,the following intrinsic toughening mechanisms have been identified:molecular uncoiling and intermolecular sliding of collagen,fibrillar sliding of collagen bonds,and microcracking of the mineral matrix (19).Extrinsic mechanisms are collagen fibril bridging,uncracked ligament bridging,and crack deflec-tion and twisting (19).Rarely does a limb bone snap in two with smooth fracture surfaces;the crack is often deflected orthogonal to the crack front direction.In the case of (rehydrated)elk (Cervus elaphus )antler bone (shown in Fig.2C)(32),which has the highest toughness of any bone type by far (33),the hypermineralized re-gions around the primary osteons lead to crackdeflection,and the high amount of collagen (~60volume %)adds mechanisms of crack re-tardation and creates crack bridges behind the crack front.The toughening effect in antlers has been estimated as:crack deflection,60%;un-cracked ligament bridges,35%;and collagen as well as fibril bridging,5%(33).A particu-larly important feature in bone is that the fracture toughness increases as the crack propagates,as shown in the plot.This plot demonstrates the crack extension resistance curve,or R -curve,behavior,which is the rate of the total energy dissipated as a function of the crack size.This occurs by the activation of the extrinsic tough-ening mechanisms.In this manner,it becomes gradually more difficult to advance the crack.In human bone,the cracks are deflected and/ortwisted around the cement lines surrounding the secondary osteons and also demonstrate R -curve behavior (34).The final example illustrating how the presence of interfaces is used to retard crack propagation is the glass sea sponge (Euplectella aspergillum ).The entire structure of the V enus ’flower basket is shown in Fig.2D.Biological silica is amorphous and,within the spicules,consists of concentric layers,separated by an organic material,silicatein (35,36).The flexure strength of the spicule notably exceeds (by approximately fivefold)that of monolithic glass (37).The principal reason is the presence of interfaces,which can arrest and/or deflect the crack.Biological materials use ingenious meth-ods to retard the progression of cracks,therebyAbalone shell: NacreMineral bridgesLobsterDeer antlerChitin fibril networkHuman cortical boneMineral crystallitesPrimary osteonsSubvelvet/compact Subvelvet/cCompact Comp p actTransition zoneCancellousCollagen fibrilsDeep sea spongeSkeletonSpicules20 mm1 cmHuman cortical boneElk antlerTransverseIn-plane longitudinalASTM validASTM invalid Mesolayers ABCD0.1 mm500 nm500 nm ˜1 nm˜3 nm˜20 nmCrack extension, ⌬a (mm)T o u g h n e s s , J (k J m -2)50 nm200 nm 10 ␮m500 nm2 ␮m1 ␮m200 ␮m300 ␮m˜10 ␮m0.010.11101000.20.40.6500 00 nm50 nmFig.2.Hierarchical structures of tough biological materials demonstrating the heterogeneous interfaces that provide crack deflection.(A )Abalone nacre showing growth layers (mesolayers),mineral bridges between mineral tiles and asperities on the surface,the fibrous chitin network that forms the backbone of the inorganic layer,and an example of crack tortuosity in which the crack must travel around the tiles instead of through them [adapted from (4,21)].(B )Lobster exoskeleton showing the twisted plywood structure of the chitin (next to the shell)and the tubules that extend from the chitin layers to the animal [adapted from (27)].(C )Antler bone image showing the hard outer sheath (cortical bone)surrounding the porous bone.The collagen fibrils are highly aligned in the growth direction,with nanocrystalline minerals dispersed in and around them.The osteonal structure in a cross section of cortical bone illustrates the boundaries where cracks perpendicular to the osteons can be directed [adapted from (33)].ASTM,American Society for Testing and Mate-rials.(D )Silica sponge and the intricate scaffold of spicules.Each spicule is a circumferentially layered rod:The interfaces between the layers assist in ar-resting crack anic silicate in bridging adjacent silica layers is observed at higher magnification (red arrow)(36).15FEBRUARY 2013VOL 339SCIENCE776REVIEWo n M a y 1, 2013w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o mincreasing toughness.These methods operate at levels ranging from the nanoscale to the structur-al scale and involve interfaces to deflect cracks,bridging by ductile phases (e.g.,collagen or chitin),microcracks forming ahead of the crack,delocal-ization of damage,and others.Lightweight Structures Resistant to Bending,Torsion,and Buckling —Shells and FoamsResistance to flexural and torsional tractions with a prescribed deflection is a major attribute of many biological structures.The fundamental mechanics of elastic (recoverable)deflection,as it relates to the geometrical characteristics of beams and plates,is given by two equations:The first relates the bending moment,M ,to the curvature of the beam,d 2y /dx 2(y is the deflection)d 2y dx 2¼MEIð7Þwhere I is the area moment of inertia,which de-pends on the geometry of the cross section (I =p R 4/4,for circular sections,where R is the ra-dius).Importantly,the curvature of a solid beam,and therefore its deflection,is inversely propor-tional to the fourth power of the radius.The sec-ond equation,commonly referred to as Euler ’s buckling equation,calculates the compressive load at which global buckling of a column takes place (P cr )P cr ¼p 2EI ðkL Þ2ð8Þwhere k is a constant dependent on the column-end conditions (pinned,fixed,or free),and L is the length of the column.Resistance to buck-ing can also be accomplished by increasing I .Both Eqs.7and 8predict the principal designLongitudinal sectionToucan beak Keratin layers(i) Fibers(circumferential)Megafibrils and fibrilsBarbsBarbulesCortexCortical ridgesFoamRachisNodes(iii) Medulloidpith(ii) Fibers (longitudinal)Feather rachisPlant-Bird of ParadisePorcupine quillsNodesRebarClosed-cell foamTransverseLongitudinalCross sectionABCD5 mm 1 mm1 cm 0.1 mm5m 5 m m1c 1 c m1 mm100 ␮m500 ␮mFig.3.Low-density and stiff biological materials.The theme is a dense outer layer and a low-density core,which provides a high bending strength –to –weight ratio.(A )Giant bird of paradise plant stem showing the cellular core with porous walls.(B )Porcupine quill exhibiting the dense outer cortex surrounding a uniform,closed-cell foam.Taken from (42).(C )Toucan beak showing the porousinterior (bone)with a central void region [adapted from (43)].(D )Schematic view of the three major structural components of the feather rachis:(i)superficial layers of fibers,wound circumferentially around the rachis;(ii)the majority of the fibers extending parallel to the rachidial axis and through the depth of the cortex;and (iii)foam comprising gas-filled polyhedral structures.Taken from (45)SCIENCEVOL 33915FEBRUARY 2013777REVIEWo n M a y 1, 2013w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o m。