Barut-Girardello coherent states for sp(N,C) and multimode Schrodinger cat states

letters to nature8.Leznoff,C.C.&Lever,A.B.P.(eds)Phthalocyanines:Properties and Applications(VCH,New York,1989).9.Wang,L.S.,Ding,C.F.,Wang,X.B.&Barlow,S.E.Photodetachment photoelectron spectroscopy ofmultiply charged anions using electrospray ionization.Rev.Sci.Instrum.70,1957±1966(1999). 10.Berkowitz,J.Photoelectron spectroscopy of phthalocyanine vapors.J.Chem.Phys.70,2819±2828(1979).11.Brown,C.J.Crystal structure of b-copper phthalocyanine.J.Chem.Soc.A2488±2493(1968).12.Rosa,A.&Baerends,E.J.Metal-macrocycle interaction in phthalocyanines:density functionalcalculations of ground and excited states.Inorg.Chem.33,584±595(1994).13.PC Spartan Plus5.1(Wavefunction,Inc.,Von Carman Ave.,Irvine,California92612,USA).14.Stewart,J.J.Optimization of parameters for semiempirical methods II:put.Chem.10;221±264(1989);MOPAC:A semiempirical molecular orbital put.Aided Mol.Design4;1±105(1990).15.D'Haennens,I.J.in Encyclopedia of Physics(eds Lerner,R.G.&Trigg,G.L.)1251±1253(VCH,NewYork,1991).16.Hodgson,P.E.,Gadioli,E.&Erba,E.G.Introductory Nuclear Physics(Clarendon,Oxford,1997).17.Scheller,M.K.&Cederbaum,L.S.A construction principle for stable multiply charged molecularanions in the gas phase.Chem.Phys.Lett.216,141±146(1993).18.Weikert,H.-G.&Cederbaum,L.S.Free doubly negative tetrahalides.J.Chem.Phys.99,8877±8891(1993).19.Boldyrev,A.I.,Gutowski,M.&Simons,J.Small multiply charged anions as building blocks inchemistry.Acc.Chem.Res.29,497±502(1996).20.Vekey,K.Multiply charged ions.Mass Spectrom.Rev.14,195±225(1995).21.Brechignac,C.,Cahuzac,P.,Kebaili,N.&Leygnier,J.Temperature effects in the Coulombic®ssion ofstrontium clusters.Phys.Rev.Lett.81,4612±4615(1998).22.Schroder,D.,Harvey,J.N.&Schwarz,H.Long-lived,multiply charged diatomic TiF n+ions(n=1±3).J.Phys.Chem.A102,3639±3642(1998).Acknowledgements.We thank R.S.Disselkamp for discussions and K.Ferris for help in the theoretical calculations.This work was supported by the US Department of Energy,Of®ce of Basic Energy Sciences, Chemical Sciences Division and is conducted at the Paci®c Northwest National Laboratory,operated for the US Department of Energy by Battelle Memorial Institute.L.-S.W.is an Alfred P.Sloan research fellow.Correspondence and requests for materials should be addressed to L.-S.W.(e-mail:ls.wang@).Dual modes of thecarbon cycle since theLast Glacial MaximumH.Jesse Smith*,H.Fischer*²,M.Wahlen*,D.Mastroianni* &B.Deck**Scripps Institution of Oceanography,University of California San Diego,La Jolla,California92093-0220,USA ......................................................................................................................... The most conspicuous feature of the record of past climate contained in polar ice is the rapid warming which occurs after long intervals of gradual cooling.During the last four transitions from glacial to interglacial conditions,over which such abrupt warmings occur,ice records indicate that the CO2concentration of the atmosphere increased by roughly80to100parts per million by volume(refs1±4).But the causes of the atmospheric CO2 concentration increases are unclear.Here we present the stable-carbon-isotope composition(d13CO2)of CO2extracted from air trapped in ice at Taylor Dome,Antarctica,from the Last Glacial Maximum to the onset of Holocene times.The global carbon cycle is shown to have operated in two distinct primary modes on the timescale of thousands of years,one when climate was changing relatively slowly and another when warming was rapid,each with a characteristic average stable-carbon-isotope composition of the net CO2exchanged by the atmosphere with the land and oceans. d13CO2increased between16.5and9thousand years ago by slightly more than would be estimated to be caused by the physical effects of a58C rise in global average sea surface temperature driving a CO2ef¯ux from the ocean,but our data do not allow speci®c causes to be constrained.Carbon dioxide in the atmosphere causes a radiative forcing second only to water vapour,and so may be a central agent in climate change.Polar ice cores contain a detailed record of climate-²Present address:Alfred-Wegener-Institute for Polar and Marine Research,Columbusstrasss,D-27515 Bremerhaven,Germany.related variables which extends more than400,000years into the past4,and are especially valuable for studying variations of atmos-pheric CO2as they contain an effectively direct record,unlike atmospheric proxies such as marine carbonates or preserved organic material5which may also re¯ect biological effects.Ice cores from Antarctica,such as those of Taylor Dome and Vostok, are the best sources for palaeoatmospheric CO2measurements because they contain only small amounts of the kinds of chemical impurities,such as carbonate dust or organic acids,that may lead to contamination by in situ CO2production2,6±8.Taylor Dome ice has the additional advantage that the entire554-m-long core is from above the depth at which air trapped in bubbles in the ice forms gas±ice clathrates.This feature is important because,as we have found,the accuracy of d13CO2measurements performed on bubble-free ice may be affected by the presence of clathrates.(d13C is de®ned in Methods.)We have measured the CO2concentration and d13CO2 of air trapped in ice from Taylor Dome,Antarctica,across the last glacial termination in order to develop a time series for the carbon-isotope composition of atmospheric CO2and to constrain the mechanisms of carbon cycling between the main sources and sinks of atmospheric CO2.The atmospheric CO2concentration data3,9(Fig.1)form a record comparable to that from Byrd and Vostok1,2.The salient features include a low but variable concentration of atmospheric CO2 between27.1and18.0kyr BP(thousand years before present, where``present''is de®ned as AD1950),when it varied between 186and201parts per million by volume(p.p.m.v.);a rise,at a fairly constant rate,from190p.p.m.v.at17.0kyr BP to an early Holocene local maximum of268p.p.m.v.at10.6kyr BP,punctuated by a shallow minimum at16.1kyr BP and a drop of8p.p.m.v.between 14and13kyr BP which may be related to the Antarctic Cold Reversal3;an8p.p.m.v.decrease,from268p.p.m.v.at10.6kyr BP to260p.p.m.v.at9.1kyr BP,followed by a rise to the pre-industrial level of about280p.p.m.v.(as discussed in detail by IndermuÈhle et al.9).These data can be combined with the carbon-isotope composition of the CO2to give a better picture of how the carbon cycle operated during this time.The main features of the carbon-isotope record shown in Fig.1 include a0.5½drop in d13CO2between18.0and16.5kyr BP,and the subsequent increase of0.7½,from-7.0½to-6.3½, between16.5and9.1kyr BP,which is interrupted by two local d13CO2minima at approximately13and10kyr BP.The minimum-to-maximum d13CO2increase began1,000to2,000years after CO2began to rise,and continued to rise for,3,000years after the CO2concentration maximum at10.6kyr BP,which we interpret as a consequence of the bimodality of carbon cycling(discussed below)rather than a decoupling of CO2concentrations from carbon-isotope compositions.Furthermore,there appears to have been an extended local minimum in d13CO2between13.4and 12.3kyr BP that accompanied the Younger Dryas10but was not concurrent with the CO2concentration drop at14kyr BP.The 0.16½difference between the average d13CO2values of the Last Glacial Maximum(LGM)and Holocene(see Fig.2legend for an explanation of these groupings)is similar to the increase of 0:1960:18½estimated by Leuenberger et al.11to have occurred between the period20±40kyr BP and the early Holocene.These data show,however,that there was a signi®cant drop in d13CO2 between the end of the LGM and the beginning of the transition, and that the subsequent rise into the early Holocene was much larger than the difference between average values for the LGM and Holocene.Moreover,inferences about the carbon cycle drawn from the comparison of the LGM and Holocene averages may be misleading because there was signi®cant variability within each of those periods,and the averages depend strongly on the interval chosen to calculate them.Finally,the variability of d13CO2before17.5kyr BP and after10.3kyr BP,0.33½and 0.37½,respectively,is about half of the magnitude of theletters to natureincrease that occurs during the transition,indicating that carbon cycling also varied considerably over shorter timescales.The atmospheric portion of the carbon cycle is extremely dynamic;,20%of the CO 2in the atmosphere is exchanged with the ocean and terrestrial biosphere every year (ref.12),so the atmosphere responds very quickly to changes in CO 2cycling between these three reservoirs.The exchange of carbon can affect the isotopic composition of atmospheric CO 2for two reasons.First,the reservoirs have different carbon-isotope compositions (the d 13CO 2of the ocean is close to 0½,the terrestrial biosphere has a d 13CO 2of approximately -25½and that of pre-industrial atmos-phere was approximately -6.5½;ref.13).Second,each ¯ux of CO 2between the atmosphere and either the ocean or the terrestrial biosphere is accompanied by a different carbon-isotope fractiona-tion,resulting in isotopically unique values of d 13CO 2for each transfer.Consequently,variations in the carbon-isotope composi-tion of atmospheric CO 2can be caused by a net ¯ux of carbon between reservoirs,or by a change in the isotopic fractionation associated with a particular atmospheric ¯ux.It also follows from this that the carbon-isotope composition of the net atmospheric CO 2exchanged,d 13CO 2(ex),is a function of the relative strengths of processes which transfer CO 2into and out of the atmosphere,so different d 13CO 2(ex)values indicate different balances of processes.When a unique balance of processes persists over thousands of years,as indicated by a unique d 13CO 2(ex),we refer to it as a `mode'of the carbon cycle.In order to examine more closely the implications of the time series shown in Fig.1,it is advantageous to consider the three data groups (LGM,transition and Holocene)individually.Doing so inFig.2reveals a relationship between the concentration of atmos-pheric CO 2and its carbon-isotope composition during each of these intervals.(Figure 2is a mixing diagram,where the inverse CO 2concentration is plotted against d 13CO 2,so that addition or removal of CO 2with a given d 13C would appear as a nearly straight line with the y -intercept approximately equal to the isotopic composition of the net CO 2added to,or subtracted from,the atmosphere.)The coherent trends displayed by these groups show that the carbon cycle has operated in two distinct modes over the past 27kyr,one during the Holocene,and possibly the LGM as well,when the average d 13C of net CO 2exchanged was approximately -10½,and another during the transition,when the average d 13C of net CO 2exchanged was approximately -5½.In other words,during the period of relatively stable,slowly changing climate of the Holocene,the carbon of the net exchanged atmospheric CO 2was isotopically lighter than the average atmospheric value (that is,d d 13CO 2/dCO 2was negative).In contrast,during the period of rapidly changing climate of the transition the net exchanged CO 2was isotopically heavier (d d 13CO 2/dCO 2was positive).Therefore,these data suggest that the carbon cycle has operated in two primary modes over the past 27kyr,one when climate is changing only slowly and another when rapid warming occurs,and that although there are clearly other processes which have affected atmospheric CO 2over the past 27kyr,as is evident from the scatter in the data shown in Fig.2,those transient variations did not overwhelm the longer-term trends.Many schemes have been advanced to account for the magnitude of the rise in the concentration of atmospheric CO 2during deglaciations (see,for example,Broecker 14for a critical review),although none seem to be uniquely suf®cient.Two factors which must be included in any analysis of the glacial±interglacial increase in atmospheric CO 2content,however,are a rise in sea surface temperature (SST)and a decrease in ocean salinity (S).In the range of SST,atmospheric CO 2concentration and salinity appropriate for this study,changes in SST affect both atmospheric p CO 2and d 13CO 2,by approximately 4.2%per 8C (ref.15)and 0.11±0.13½per 8C (ref.16),respectively,while changes in salinity alter p CO 2by 10p.p.m.v.per ½S without affecting its d 13C (ref.17).Measurements per-formed on tropical corals show that SST increased by 5±68CfromFigure 1d 13CO 2and CO 2-concentration trends.The data are based on measurements of air trapped in ice from Taylor Dome,Antarctica,and are plotted against air age.Upper curve,d 13CO 2values (®lled circles)within envelopes of 1j and 2j uncertainty (indicated as dotted and solid lines,respectively;see the Methods section for details).Lower curve,CO 2concentration data shown as open circles were measured in our laboratory at SIO 3,while the solid line shown in the Holocene (for comparison)is the higher-resolution record of Indermu hle et al.9.The age axis is divided into three intervals,called ``LGM'',``transition'',and ``Holocene''on the basis of CO 2concentrations and generally accepted ages for these periods.The LGM group includes all of the points with air ages between 27.1and 18.0kyr BP ,the youngest being the last with a CO 2concentration below the highest value of the older samples.The transition group includes the points with ages between 17.0and 10.6kyr BP ,where the local CO 2maximum which we use to de®ne the start of the Holocene occurs.The Holocene group includes all the points with ages between 10.1and 1.3kyr BP (the youngest sample measured for d 13CO 2).The boundaries between the LGM and the transition,and between the transition and the Holocene,chosen here to fall at 17.5and 10.3kyr BP ,respectively,are shown as vertical dashedlines.[CO 2] (p.p.m.)1/[CO 2] (p.p.m.-1)δ13C O 2 (‰)Figure 2Mixing diagram for Taylor Dome samples:1/[CO 2]is plotted against d 13CO 2.The data are divided into three groups,as described in the ®gure:the LGM group (open triangles,6d 13CO 2points),the transition group (®lled circles,15d 13CO 2points),and the Holocene group (open squares,10d 13CO 2points).The y -intercept of the regression line through each of the three groups of data,along with the corresponding 1j uncertainty for each value,indicates the d 13C of the CO 2exchanged by the atmosphere,d 13CO 2(ex),and is shown on the ®gure.letters to naturethe last peak-glacial period to the early Holocene18,signi®cantly more than the earlier estimate of1±28C by CLIMAP19,while the change in ocean salinity,estimated from sea level change20,was approximately-1.4½.Assuming a global average D SST(sea surface temperature change)of58C,the combined effects of temperature and salinity changes should have resulted in increases in the concentration and d13CO2of roughly30p.p.m.v.and0.6½, respectively.If this were true,then all other processes which caused variations in atmospheric CO2must together have increased its concentration by,50p.p.m.v.and its d13CO2by only0.1½.A 28C global average D SST,on the other hand,would have caused no signi®cant change in the concentration of atmospheric CO2and increased d13CO2by roughly0.2½,leaving unexplained an approximately80p.p.m.concentration increase and a0.5½d13CO2increase.Adding these changes to the0.3½whole-ocean d13CO2increase which is thought to have accompanied deglaciation21,the expected increase in atmospheric d13CO2would be between0.9½and0.6½,depending on whether a D SST of5or 28C is assumed.The observed increase of0.7½would seem to imply,then,that it is not necessary to invoke a large decrease in surface ocean productivity(which would lower atmospheric d13CO2 to values more negative than are observed)to explain the d13CO2 increase during the transition.What does become necessary,then,is to explain the0.5½drop seen between18and16.5kyr BP.In the broadest sense,the atmospheric d13CO2record presented here points to the ocean as the predominant source of atmospheric CO2during the transition.This interpretation follows from two observations.First,even if a change in average global SST alone had caused the increase in d13CO2,a realistic D SST would have resulted in an increase of atmospheric CO2concentration of less than half of what is observed,so there must have been other sources of CO2 during that time.Second,because d13CO2was increasing at a rate equal to or greater than that which rising SST alone would have caused,the additional net CO2¯ux must have had a d13CO2equal to, or greater than,that of the coexisting atmosphere,eliminating the terrestrial biosphere as a possible source.The most likely explana-tion for this is an enhanced¯ux from the ocean(with a d13C close to that of the atmosphere)which transferred CO2into the atmosphere at a rate greater than the concurrent uptake of isotopically light CO2 by an expanding terrestrial biosphere.Unfortunately,the con-straints imposed by these data are insuf®cient to allow the identi-®cation of a speci®c cause for the increased¯ux of CO2from the ocean to the atmosphere.A better understanding of the carbon cycle depends not only on better models,but on additional experimental constraints on the carbon system,particularly more precise data about changes in SST,the size and composition of the terrestrial biosphere,the growth of coral reefs during periods of sea level rise, marine productivity and the chemical composition of the oceans.M ......................................................................................................................... MethodsAll samples were taken from Taylor Dome,Antarctica(7708489S,1588439E, elevation2,374m),drilled in1993/94.The methods used for determining the CO2concentration of air trapped in ice and the measurement of its carbon-isotope composition are described in detail elsewhere22,23.CO2concentration measurements have an internal precision of63p.p.m.v.(2j)and are calculated by comparison to three standards of precisely known compositions which are run with every sample.The Craig-corrected24carbon-isotope measurements, performed on our VG Prism II isotope ratio mass spectrometer,have a1j precision of60.075½,based on numerous analyses of the CO2separated from an atmospheric air standard exposed to uncrushed ice,in order to simulate the conditions of a sample run and to check for fractionation during extraction. d13CO2is reported in normal d notation as the per mil difference between the isotopic composition of the sample and standard VPDB carbon, 13C=12C sample= 13C=12C VPDB21 31;000 .The d13CO2values reported here have been corrected for the gravitational separation of gases of different masses in the®rn,and for the presence of N2O (which results in isobaric interferences with CO2during mass spectrometry).Gravitational separation in the®rn25,26was determined by using the values of d15N2of air trapped in Taylor Dome ice from Sucher27,following the approach of Sowers and Bender28.The gravitational correction for d13CO2is,0.005½per m.C-isotope data are corrected for the presence of N2O on the basis of calibrations performed in our laboratory on CO2±N2O mixtures.The N2O concentrations of atmospheric air used for this correction,adapted from Leuenberger and Siegenthaler29,are linear interpolations of the following concentrations and dates:275p.p.b.(0±9.25yr BP),200p.p.b.(16.1±27.2kyr BP).The N2O correction is,0.001½per p.p.b.of N2O.The total1j uncertainty in the reported d13CO2of a single sample,including uncertainties in the gravitational and N2O corrections,is0.085½.Duplicate analyses of samples with air ages of2.19and17.2kyr BP have a1j uncertainty of0.060½and a triplicate analysis of the sample with an air age of27.4kyr BP has a1j uncertainty of0.049½.The depth±age scale and air age±ice age differences were calculated using a combination of¯ow modelling,correlating variations in the d18O of the ice with the well-dated GISP2,and matching atmospheric CH4concentrations and d18O of O2with variations seen in GISP230.Received8October1998;accepted7June1999.1.Barnola,J.M.,Raynaud,D.,Korotkevich,Y.S.&Lorius,C.Vostok ice core provides160,000-yearrecord of atmospheric CO2.Nature329,408±414(1987).2.Neftel,A.,Oeschger,H.,Staffelbach,T.&Stauffer,B.CO2record in the Byrd ice core50,000±5,000years BP.Nature331,609±611(1988).3.Fischer,H.,Wahlen,M.,Smith,H.J.,Mastroianni,D.&Deck,B.Ice core records of atmospheric CO2around the last three glacial terminations.Science283,1712±1714(1999).4.Petit,J.R.et al.Climate and atmospheric history of the past420,000years from the Vostok ice core,Antarctica.Nature399,429±436(1999).5.Marino,B.,McElroy,M.B.,Salawitch,R.J.&Spaulding,W.G.Glacial-to-interglacial variations in thecarbon isotopic composition of atmospheric CO2.Nature357,461±466(1992).6.Anklin,M.,Barnola,J.-M.,Schwander,J.,Stauffer,B.&Raynaud,D.Processes affecting the CO2concentrations measured in Greenland ice.Tellus B47,461±470(1995).7.Delmas,R.J.A natural artefact in Greenland ice core CO2measurements.Tellus B45,391±396(1993).8.Barnola,J.M.et al.CO2evolution during the last millennium as recorded by Antarctic and Greenlandice.Tellus B47,264±272(1995).9.IndermuÈhle,A.et al.Holocene carbon-cycle dynamics based on CO2trapped in ice at Taylor Dome,Antarctica.Nature398,121±126(1999).10.Fairbanks,R.G.The age and origin of the``Younger Dryas Climate Event''in Greenland ice cores.Paleoceanography5,937±948(1990).11.Leuenberger,M.,Siegenthaler,U.&Langway,C.C.Carbon isotope composition of atmospheric CO2during the last ice age from an Antarctic ice core.Nature357,488±490(1992).12.Tans,P.P.,Berry,J.A.&Keeling,R.F.Oceanic13C/12C observations:a new window on ocean CO2uptake.Glob.Biogeochem.Cycles7,353±368(1993).13.Friedli,H.,Lotscher,H.,Oeschger,H.,Siegenthaler,U.&Stauffer,B.Ice core record of the13C/12C ofatmospheric CO2in the past two centuries.Nature324,237±238(1986).14.Broecker,W.S.&Henderson,G.M.The sequence of events surrounding T ermination II and theirimplications for the cause of glacial-interglacial CO2changes.Paleoceanography13,352±364(1998).15.Takahashi,T.,Olafsson,J.,Goddard,J.G.,Chipman,D.W.&Sutherland,S.C.Seasonal variation ofCO2and nutrients in the high-latitude surface oceans:a comparative study.Glob.Biogeochem.Cycles 7,843±878(1993).16.Mook,W.G.,Bommerson,J.C.&Staverman,W.H.Carbon isotope fractionation between dissolvedbicarbonate and gaseous carbon dioxide.Earth Planet.Sci.Lett.22,169±176(1974).17.Weiss,R.F.Carbon dioxide in water and seawater:the solubility of a non-ideal gas.Mar.Chem.2,203±215(1974).18.Guilderson,T.P.,Fairbanks,R.G.&Rubenstone,J.L.Tropical temperature variations since20,000years ago:modulating interhemispheric climate change.Science263,663±665(1994).19.CLIMAP Project Members Seasonal Reconstructions of the Earth's Surface at the Last Glacial Maximum(Map and Chart Ser.,MC-36,Geol.Soc.Am.,Boulder,1981).20.Fairbanks,R.G.A17,000-year glacio-eustatic sea level recordÐin¯uence of glacial melting rates onthe Younger Dryas Event and deep-ocean circulation.Nature342,637±642(1989).21.Duplessy,J.C.et al.Deepwater source variations during the last climatic cycle and their impact on theglobal deepwater circulation.Paleoceanography3,343±360(1988).22.Wahlen,M.,Allen,D.&Deck,B.Initial measurements of CO2concentrations(1530to1940AD)in airoccluded in the GISP2ice core from central Greenland.Geophys.Res.Lett.18,1457±1460(1991).23.Smith,H.J.,Wahlen,M.,Mastroianni,D.&Taylor,K.C.The CO2concentration of air trapped inGISP2ice from the LGM-Holocene transition.Geophys.Res.Lett.24,1±4(1997).24.Craig,H.Isotopic standards for carbon and oxygen and correction factors for mass-spectrometricanalysis of carbon dioxide.Geochim.Cosmochim.Acta12,133±149(1957).25.Craig,H.,Horibe,Y.&Sowers,T.Gravitational separation of gases and isotopes in polar ice caps.Science242,1675±1678(1988).26.Schwander,J.The Environmental Record in Glaciers and Ice Sheets(eds Oeschger,H.and Langway,C.C.)53±67(Wiley and Sons,New York,1989).27.Sucher,C.Trapped Gases in the Taylor Dome Ice Core:Implications for East Antarctic Climate Change.Thesis,Univ.Rhode Island(1997).28.Sowers,T.&Bender,M.Elemental and isotopic composition of occluded O2and N2in polar ice.J.Geophys.Res.94,5137±5150(1989).29.Leuenberger,M.&Siegenthaler,U.Ice-age atmospheric concentration of nitrous oxide from anAntarctic ice core.Nature360,449±451(1988).30.Steig,E.J.et al.Synchronous climate changes in Antarctica and the North Atlantic.Science282,92±95(1998).Acknowledgements.We thank G.Hargreaves and J.Fitzpatrick for help obtaining samples,and E.Steig and E.Brook for sharing their depth-age scales.This work was supported by the NSF and the Director's of®ce at the Scripps Institution of Oceanography.Correspondence and requests for materials should be addressed to H.J.S.(e-mail:hjsmith@).。

1/4波片quarter-wave plateCG矢量耦合系数Clebsch-Gordan vector coupling coefficient; 简称“CG[矢耦]系数”。

X射线摄谱仪X-ray spectrographX射线衍射X-ray diffractionX射线衍射仪X-ray diffractometer[玻耳兹曼]H定理[Boltzmann] H-theorem[玻耳兹曼]H函数[Boltzmann] H-function[彻]体力body force[冲]击波shock wave[冲]击波前shock front[狄拉克]δ函数[Dirac] δ-function[第二类]拉格朗日方程Lagrange equation[电]极化强度[electric] polarization[反射]镜mirror[光]谱线spectral line[光]谱仪spectrometer[光]照度illuminance[光学]测角计[optical] goniometer[核]同质异能素[nuclear] isomer[化学]平衡常量[chemical] equilibrium constant[基]元电荷elementary charge[激光]散斑speckle[吉布斯]相律[Gibbs] phase rule[可]变形体deformable body[克劳修斯-]克拉珀龙方程[Clausius-] Clapeyron equation[量子]态[quantum] state[麦克斯韦-]玻耳兹曼分布[Maxwell-]Boltzmann distribution[麦克斯韦-]玻耳兹曼统计法[Maxwell-]Boltzmann statistics[普适]气体常量[universal] gas constant[气]泡室bubble chamber[热]对流[heat] convection[热力学]过程[thermodynamic] process[热力学]力[thermodynamic] force[热力学]流[thermodynamic] flux[热力学]循环[thermodynamic] cycle[事件]间隔interval of events[微观粒子]全同性原理identity principle [of microparticles][物]态参量state parameter, state property[相]互作用interaction[相]互作用绘景interaction picture[相]互作用能interaction energy[旋光]糖量计saccharimeter[指]北极north pole, N pole[指]南极south pole, S pole[主]光轴[principal] optical axis[转动]瞬心instantaneous centre [of rotation][转动]瞬轴instantaneous axis [of rotation]t 分布student's t distributiont 检验student's t testＫ俘获K-captureＳ矩阵S-matrixＷＫＢ近似WKB approximationＸ射线X-rayΓ空间Γ-spaceα粒子α-particleα射线α-rayα衰变α-decayβ射线β-rayβ衰变β-decayγ矩阵γ-matrixγ射线γ-rayγ衰变γ-decayλ相变λ-transitionμ空间μ-spaceχ 分布chi square distributionχ 检验chi square test阿贝不变量Abbe invariant阿贝成象原理Abbe principle of image formation阿贝折射计Abbe refractometer阿贝正弦条件Abbe sine condition阿伏伽德罗常量Avogadro constant阿伏伽德罗定律Avogadro law阿基米德原理Archimedes principle阿特伍德机Atwood machine艾里斑Airy disk爱因斯坦-斯莫卢霍夫斯基理论Einstein-Smoluchowski theory 爱因斯坦场方程Einstein field equation爱因斯坦等效原理Einstein equivalence principle爱因斯坦关系Einstein relation爱因斯坦求和约定Einstein summation convention爱因斯坦同步Einstein synchronization爱因斯坦系数Einstein coefficient安[培]匝数ampere-turns安培[分子电流]假说Ampere hypothesis安培定律Ampere law安培环路定理Ampere circuital theorem安培计ammeter安培力Ampere force安培天平Ampere balance昂萨格倒易关系Onsager reciprocal relation凹面光栅concave grating凹面镜concave mirror凹透镜concave lens奥温电桥Owen bridge巴比涅补偿器Babinet compensator巴耳末系Balmer series白光white light摆pendulum板极plate伴线satellite line半波片halfwave plate半波损失half-wave loss半波天线half-wave antenna半导体semiconductor半导体激光器semiconductor laser半衰期half life period半透[明]膜semi-transparent film半影penumbra半周期带half-period zone傍轴近似paraxial approximation傍轴区paraxial region傍轴条件paraxial condition薄膜干涉film interference薄膜光学film optics薄透镜thin lens保守力conservative force保守系conservative system饱和saturation饱和磁化强度saturation magnetization本底background本体瞬心迹polhode本影umbra本征函数eigenfunction本征频率eigenfrequency本征矢[量] eigenvector本征振荡eigen oscillation本征振动eigenvibration本征值eigenvalue本征值方程eigenvalue equation比长仪comparator比荷specific charge; 又称“荷质比(charge-mass ratio)”。

Band structures and band offsets of high K dielectrics on SiJ.Robertson *Engineering Department,Cambridge University,Trumpington Street,Cambridge CB21PZ,UKAbstractVarious high dielectric constant oxides will be used as insulator in ferroelectric memories,dynamic random access memories,and as the gate dielectric material in future complementary metal oxide semiconductor (CMOS)technology.These oxides which have moderately wide bandgaps provide a good test of our understanding of Schottky barrier heights and band offsets at semiconductor interfaces.Metal induced gap states (MIGS)are found to give a good description of these interfaces.The electronic structure and band offsets of these oxides are calculated.It is found that Ta 2O 5and SrTiO 3have small or vanishing conduction band offsets on 2O 3,Y 2O 3,ZrO 2,HfO 2,Al 2O 3and silicates like ZrSiO 4have offsets over 1.4eV for both electrons and holes,making them better gate dielectrics.#2002Elsevier Science B.V .All rights reserved.Keywords:Band structures;Band offsets;Dielectric constant oxides1.IntroductionThe closed shell transition metal (TM)oxides like SrTiO 3have been extensively studied for their ferro-electric properties,phase transitions and soft modes [1].They are now of great technological importance for electronic devices such as dynamic random access memories (DRAMs),ferroelectric non-volatile mem-ories (FeRAMs),and as alternative gate oxides in future complementary metal oxide semiconductor (CMOS)transistors [2±4].This requires them to be considered in terms of their electronic properties,by treating them as wide bandgap semiconductors [5].This paper reviews the band structures of these oxides,and then considers important electronic prop-erties such as their band offsets and Schottky barrier heights (SBHs).It turns out that the oxides have intermediate bandgaps and so they provide a goodtest of our present models of Schottky barriers and band offsets.2.Band structuresThe simplest band structures are those of the cubic ABO 3perovskites such as SrTiO 3or BaTiO 3.The bandgap is direct at G (Fig.1)[6].The valence band consists mainly of the 2p states of the O 2Àions,and the conduction band of the Ti 4 3d (t 2g )states [7].The Sr s and p states lie higher in the conduction band.However,the bonding is 60±70%ionic,and so there is signi®cant mixing of Ti d states in the valence band.The bands of the Pb perovskites differ in that Pb is divalent and it retains its 6s electrons [8].The ®lled Pb s states form an additional valence band at about À7eV as in PbTiO 3(Fig.2)[6,9].There is also some Pb s admixture in the upper valence band.The empty Pb 6p states now lie near the lowest conduction band.When Zr replaces Ti in SrTiO 3(or BaTiO 3),the bandgap increases strongly by 2eV,because itisApplied Surface Science 190(2002)2±10*Tel.: 44-1223-33-2689;fax: 44-1223-33-2662.E-mail address:jr@ (J.Robertson).0169-4332/02/$±see front matter #2002Elsevier Science B.V .All rights reserved.PII:S 0169-4332(01)00832-7controlled by the energy of the Zr d states.In contrast,in PZT,the Pb 6p states form the conduction band minimum,so the gap barely increases from 3.3to 3.7eV [10].It is recognised that the resonant covalence of Ti-d/O-p states is the origin of ferroelectricity in SrTiO 3type perovskites [11].In Pb perovskites,there is additional resonant covalence between Pb s and O p states which increases the ferroelectric polarity.SrBi 2Ta 2O 9is a layered crystal built from perovs-kite blocks separated by Bi 2O 2layers.It turns out that the Bi s and p states form the highest valence band and lowest conduction bands,respectively,while the ferro-electric response originates mainly from the TaO 3perovskite blocks [12].There is therefore an interest-ing separation of the functionality onto the Ta and Bi sub-lattices.Cubic ZrO 2has the ¯uorite structure.It has a simple band structure,as shown in Fig.3.The O p states form the valence band with a maximum at X [13].The conduction band minimum is at G ,and consists of Zr d states.The Zr d x 2Ày 2and d z 2states lie below the d xy states.The Zr s state lies midway between these at G ,but it disperses rapidly upwards.2.1.Models of Schottky barriers and semiconductor heterojunctionsThe band line-up of two semiconductors is deter-mined,like the SBH of a semiconductor on a metal,by charge transfer across the interface and the presence of any dipole layer at the interface.The charge transfer is that between the metal and the interface states of the semiconductor (Fig.4)[14].The charge transfertendsFig.1.Band structure of BaTiO 3calculated by pseudo-potential method [6].J.Robertson /Applied Surface Science 190(2002)2±103to align the Fermi level E F of the metal to the energy level of the interface states.The SBH for electrons f n between a semiconductor S and a metal M is f n S F M ÀF S F S Àw S(1)Here,F M is the work function of the metal,F S the energy of the semiconductor interface states,w S the semiconductor's electron af®nity (EA)and S the Schottky pinning parameter.S is given by [15]S11 e 2N d =ee 0(2)where e is the electronic charge,e 0the permittivity of free space,N the areal density of the interface states and d their decay length in the semiconductor.The dimensionless pinning factor S describes if the barrieris `pinned'or not.S varies between the limits S 1for unpinned Schottky barriers,and S 0for `Bardeen'barriers pinned by a high density of interface states in which the SBH is f n F S Àw S .There are numerous models of the origins of inter-face states,both intrinsic and extrinsic.In the intrinsic model originating from Bardeen and Heine,a semi-in®nite semiconductor in contact with a metal pos-sesses intrinsic states which are now called metal-induced gap states (MIGS)by Tersoff [14].F S is then the charge neutrality level (CNL)of the interface states,de®ned as the energy above which the states are empty for a neutral surface [16±18].On the other hand,the extrinsic models stress that the metal can react with the semiconductor [19].Brillson correlated the heat of reaction with S .This reaction maycreateFig.2.Band structure of PbTiO 3calculated by pseudo-potential method [6].4J.Robertson /Applied Surface Science 190(2002)2±10interface defects such as vacancies,whose gap states can pin the metal Fermi level,as noted by Spicer [20]and Dow [21].These models were supported by theobservation that pinning occurs even for monolayer coverage of metal,before the MIGS could be estab-lished.It is now believed that,overall,the intrinsic model gives a better description of Schottky barriers,because intrinsic states have a larger pinning dipole,N d ,than surface defects.The pinning parameter S has been in¯uential in our empirical understanding of Schottky barriers.Some years ago,Kurtin et al.[22]noted that S seemed to vary sharply with the ionicity of semi-conductor (Fig.5),from near 0for low ionicity semiconductors like Si and GaAs to 1for higher ionicity solids like SiO 2,SrTiO 3and KTaO 3.S is a dimensionless slope of barrier height to metal work function,S@f n @F M(3)Fig.3.Band structure of ZrO 2calculated by pseudo-potential method[6].Fig.4.Schematic diagram of SBHs.J.Robertson /Applied Surface Science 190(2002)2±105However,Louie [23]and Schluter [24]noted that Kurtin [22]had actually correlated the barrier heights to S H :S H@f n @X(4)which is the slope of barrier height to the Pauling electronegativity of the metal,and not the dimension-less S in (4).The work function and electronegativity vary roughly as [25,26]:F M 2:27X M 0:34(5)Thus,S H 2:27S ,and the Schottky limit should be S H 2:27.The data rarely reach this limit and Schluter [24]observed that S had a better correlation with the dielectric constant of the semiconductor e 0.Empiri-cally,Mo Ènch [14,27]found that S varied with e I as S11 0:1 e I À1 2(6)Certain materials are key tests of Schottky barriermodels.Diamond and xenon [14,28]have zero ioni-city but small e I ,and so their large S values show that S depends on e not on ionicity.This is tested by plotting log 1= S À1 against log e I À1 as in Fig.6.The wide gap oxides provide another key test,because they have intermediate e I values.SrTiO 3and KTaO 3were taken as high ionicity solids in the original Kurtin plot,with S H $1.However,this wasbefore data was actually known.When data [29]became available for SrTiO 3,showing S lying between 0.25and 0.4(Fig.6),it was clear that S is much lower.SrTiO 3falls well on the trend in Fig.3.The reason for this is that the SBHs depend on e I .e I is controlled by the states closest to the bandgap [5].In SrTiO 3,these are the moderately ionic Ti±O states of Ti±O bonds,not the highly ionic Sr±O states which lie well away from the gap and provide a much smaller contribution to e I .This can be seen in the partial density of states (DOS)of SrTiO 3in Fig.6.Thus,SrTiO 3and KTaO 3were misplaced in Fig.5as highly ionic solids.A lesser point is that the moderate value of S of SrTiO 3clearly correlates with e I ,and not with the low frequency dielectric constant e 0,which has a very large value for ferroelectrics and would give S %0from (6).SrTiO 3also serves as an evidence against the defect model,in that the barrier lies some way into the gap,not at the conduction band edge where the O vacancy states lie and would cause pinning.In sum-mary,the MIGS model of Schottky barriers holds for a wide range of solids of various ionicity and dielectric constants [5].The band alignment between two semiconductors is controlled by charge transfer and interface dipoles,just as Schottky barriers [30].For no dipoles,the Schottky limit,the conduction band offset isgivenFig.5.Schottky barrier pinning factor S H in the (incorrect)model of Kurtin etal.Fig. 6.Log±log plot of 1= S À1 vs.e I À1for various semiconductors and insulators to verify the MIGS model of Schottky barrier pinning factor S .6J.Robertson /Applied Surface Science 190(2002)2±10by the difference in their electron af®nities,the `elec-tron af®nity rule'.A similar idea was that for no charge transfer,the band line-ups are derived by placing each semiconductor's band on an absolute energy scale such as those of the free atom energy levels [31].Tersoff [16]showed that the band offset between two semiconductors a and b is controlled by interface dipoles as in the Schottky barrier,and so the conduc-tion band offset is given by f n w a ÀF CNL ;a À w b ÀF CNL ;bS F CNL ;a ÀF CNL ;b(7)The offsets are now described by aligning the CNLs of each semiconductor,modi®ed by the S factor.For simple semiconductors like Si,e I is large,and so S is small and the third term was negligible in the original formulation,but it is retained here for wide gap oxides.For strong pinning,the alignment is just given by the alignment of the two CNLs.The CNL energy below the vacuum level is a measure of the mean electronegativity of the semiconductor,in the same way that the work function of a metal is propor-tional to the metal's electronegativity.Thus,Eq.(7)says that the band alignment is the difference in electronegativity screened by the S factor.A wide ranging quantitative comparison found that the CNL models gives a good description of the band offsets [30].The CNL is the branch point of the semiconductor interface states.It is the integral of the Green's func-tion of the band structure,taken over the Brillouin zone [17],G E ZBZ N E H d H EE ÀE H0(8)Cardona and Christensen later provided a quicker method using a sum over special points of the Bril-louin zone [5,32].G E X i 1E ÀE i (9)2.2.Application to oxidesThe band alignments for the various wide gapoxides in contact with metal or silicon are found by calculating their CNLs and S parameters.The S factors are found from (6)using the experimental values of e Iand are shown in Table 1.The CNLs were found by calculating the oxide band structures by the tight-binding method [5,6,8,33].The tight-binding para-meters are found by ®tting to existing band structures [9,10,34],photoemission spectra and optical data [2,35±37].The CNLs for the various oxides are given in Table 1,together with the experimental values of their bandgaps and electron af®nities [2,38].SrTiO 3is an important oxide for future DRAM capacitor dielectrics.SrTiO 3is also the most studied system and the best test of our calculations.Fig.7compares the predicted SBHs of SrTiO 3on various metals with the experimental values [30,39±43].The experimental data are quite scattered but are quite consistent with S !1and our calculated value of 0.28.This shows that SrTiO 3is a key oxide in the tests of Schottky barrier models.The calculated barrier height for SrTiO 3on Pt is 0.9eV ,which is close to the 0.8eV found by photoemission by Copel et al.[43].However we cannot account for the much larger S value found by Shimizu et al.[42].BaTiO 3has similar band offsets to SrTiO 3.PbTi x Zr 1Àx O 3or PZT is an important ferroelectric for non-volatile memories,optical memories and other applications.The predicted barrier height for Pt onTable 1Calculated values for various oxides of their CNL and conduction band (CB)offset with Si aGap (eV)EA (eV)CNL (eV)e I S CB offset (eV)SiO 290.9 2.250.86 3.5b Si 3N 4 5.3 2.1 4.10.51 2.4b Ta 2O 5 4.4 3.3 3.3 4.840.40.3BaTiO 3 3.3 3.9 2.6 6.10.28À0.1BaZrO 3 5.3 2.6 3.740.530.8TiO 2 3.05 3.9 2.27.80.180.05ZrO 2 5.8 2.5 3.6 4.80.41 1.4HfO 26 2.5 3.740.53 1.5Al 2O 38.81c 5.5 3.40.63 2.8Y 2O 362c 2.4 4.40.46 2.3La 2O 36c 2c 2.440.53 2.3ZrSiO 46.5 2.4 3.6 3.80.56 1.5SrBi 2Ta 2O 94.13.53.35.30.4aExperimental values [36,37]of the bandgap,EA [2,38],dielectric constant e I [37]are also given.In Eqs.(2)and (5),F S is the energy of the CNL below the vacuum level,in this table,it is its energy above the valence band.bExperimental values.cEstimated values.J.Robertson /Applied Surface Science 190(2002)2±107PZT (Pb 0.55Zr 0.45O 3)is 1.45eV ,which is close to the 1.5eV measured by Dey et al.[44].The electron barrier of Pt on PZT is larger than that on BST because its CNL lies lower in the gap.This is because of the different band structure of PZT,in which the Pb 6s and 6p states form the band edges and this tends to lower the CNL.The larger value of the hole barrier than the electron barrier means that PZT thin ®lms can have predominantly electron injection,even though bulk PZT tends to be p-type.SrBi 2Ta 2O 9(SBT)is an important ferroelectric for non-volatile memories [2,45].It does not suffer from the loss of switchable polarisation (fatigue)when used with Pt electrodes,which is a problem for PZT.Note that more recent optical data ®nd that the bandgap of SBT is 4.1eV [2].The Schottky barrier of Pt is predicted to be 1.2eV ,which is essentially the same as that found by photoemission [46].There is an important need for high dielectric constant oxides to act as gate oxides instead of silicon dioxide [3,4].This is because the SiO 2layer is now so thin (2nm),that it no longer acts as a good insulator because of direct tunnelling across it.The solution is to replace SiO 2with a thicker layer of a medium k oxide,with the same equivalent capacitance or `equivalence oxide thickness't ox .The oxides must also satisfy certain other conditions,including chemi-cal stability in contact with Si [47].This rules out Ti and Ta which both react with Si to form SiO 2.The other key requirement is that they act as barriers toboth electrons and holes [5,32].This requires that both their valence and conduction band offsets be over 1eV .There is presently considerable effort to identify the most effective oxide,from a choice of ZrO 2,HfO 2,La 2O 3,Y 2O 3,Al 2O 3and the silicates ZrSiO 4and HfSiO 4.The calculated CB band offsets with Si are given in Table 1and summarised in Fig.8.They are compared in Table 2with recent experimental values [48±53],which is seen to be in good agreement.The important feature of Ta 2O 5and SrTiO 3is that both of them have CB offsets on Si under 1eV ,in fact 0in the case of SrTiO 3.This prediction was recently con®rmed by photoemission data of Chambers et al.[48].This means that SrTiO 3or BST cannot be a good gate oxide.The calculated CB offset for Ta 2O 5is only 0.36eV for Ta 2O 5on Si.This is consistent with recent photoemission data of Miyazaki and Hirose [49].Data for Ta 2O 5gate FETS also showed only a small elec-tron barrier [50].The CB offsets for BST and Ta 2O 5and BST are small or negligible because the bandgap is quite small and the band offsets are so asymmetric.To increasetheparison of calculated and observed SBHs of SrTiO 3on variousmetals.Fig.8.Predicted band offsets of various oxides on Si.Table 2Comparison of calculated and experimental values [48±53]of conduction band offsets on SiCalculatedExperiment References Ta 2O 50.350Miyazaki SrTiO 3À0.1<0.1Chambers ZrO 2 1.4 1.4Miyazaki 2.0Houssa Al 2O 32.82.8Ludeke8J.Robertson /Applied Surface Science 190(2002)2±10CB offset,we must either increase the bandgap or lower the CNL.The gap can be increased by raising the TM d levels,by using4d or5d metals instead of3d metals or using group IIIB metals instead of group IV. We should use zirconates,not titanates.The gap of BaZrO3is2eV wider than BaTiO3.Its offset is0.8eV.A better strategy is to lower the CNL.The CNL is lowered if the metal valence is lowered from4to3. Indeed,in Y2O3and La2O3,the CNL is much lower in the bandgap.Y2O3and La2O3are the oxides with largest CB offsets for reasonable dielectric constants. ZrO2has a bandgap of5.8eV,which is slightly wider than BaZrO3,and it also has a lower metal/ oxygen stoichiometry.This gives a larger CB offset for ZrO2(1.4eV)than BaZrO3,and indeed one which is just high enough.HfO2is similar.The calculated CB offset of1.4eV for ZrO2compares with an experi-mental value of1.4eV from photoemission[51]and a value of2eV by internal photoemission[52].This CB offset is large enough for devices.Zirconium silicate ZrSiO4and hafnium silicate HfSiO4are glassy oxides with bandgaps of $6.5eV.ZrSiO4consists of chains of alternate edge-sharing ZrO4and SiO2tetrahedra,with addi-tional Zr±O bonds between the chains,leading to an overall six-fold Zr coordination.We estimate the bandgap of ZrSiO4to be6.5eV.The calculated CB offsets are1.5eV,slightly more than ZrO2.Al2O3has a bandgap of8eV close to SiO2but with a higher k($9).Its calculated CB offset is2.8eV, which compares exactly with that measured by Ludeke et al.[53].Overall,the agreement between the calculated and subsequent experimental values for CB offsets in Table2is surprisingly good.References[1]M.E.Lines,X.Glass,Ferroelectrics,Oxford UniversityPress,Oxford,1990.[2]J.F.Scott,Ferroelectrics Rev.1(1998)1.[3]G.D.Wilk,R.M.Wallace,J.M.Anthony,J.Appl.Phys.89(2001)5243.[4]A.I.Kingon,J.P.Maria,S.K.Streiffer,Nature406(2000)1032.[5]J.Robertson,J.Vac.Sci.Technol.B18(2000)1785.[6]P.W.Peacock,J.Robertson,Unpublished work.[7]L.F.Mattheis,Phys.Rev.B6(1972)4718.[8]J.Robertson,W.L.Warren,B.A.Tuttle,D.Dimos,D.M.Smyth,Appl.Phys.Lett.63(1993)1519.[9]R.D.King-Smith,D.Vanderbilt,Phys.Rev.B49(1994)5828.[10]J.Robertson,W.L.Warren,B.A.Tuttle,J.Appl.Phys.77(1995)3975.[11]R.E.Cohen,Nature358(1992)136.[12]J.Robertson,C.W.Chen,W.L.Warren,C.D.Gutleben,Appl.Phys.Lett.69(1996)1704.[13]R.H.French,S.J.Glass,F.S.Ohuchi,Y.N.Xu,W.Y.Ching,Phys.Rev.B49(1994)5133.[14]W.MoÈnch,Phys.Rev.Lett.58(1987)1260.[15]W.MoÈnch,Surf.Sci.300(1994)928.[16]A.W.Cowley,S.M.Sze,J.Appl.Phys.36(1965)3212.[17]C.Tejedor,F.Flores,E.Louis,J.Phys.C10(1977)2163.[18]J.Tersoff,Phys.Rev.Lett.52(1984)465.[19]J.Tersoff,Phys.Rev.B30(1984)4874;J.Tersoff,Phys.Rev.B32(1985)6989.[20]L.J.Brillson,Surf.Sci.300(1994)909.[21]W.E.Spicer,T.Kendelewicz,N.Newman,K.K.Chin,I.Lindau,Surf.Sci.168(1986)240.[22]R.E.Allen,O.F.Sankey,J.D.Dow,Surf.Sci.168(1986)376.[23]S.Kurtin,T.C.McGill,C.A.Mead,Phys.Rev.Lett.30(1969)1433.[24]S.G.Louie,J.R.Chelikowsky,M.L.Cohen,Phys.Rev.B15(1977)2154.[25]M.Schluter,Phys.Rev.B17(1978)5044;M.Schluter,Thin Solid Films93(1982)3.[26]W.Gordy,W.J.O.Thomas,Phys.Rev.24(1956)439.[27]H.B.Michaelson,J.Appl.Phys.48(1977)4729.[28]W.MoÈnch,Phys.Rev.Lett.58(1986)1260.[29]W.MoÈnch,Europhys.Lett.27(1994)479.[30]R.C.Neville,C.A.Mead,J.Appl.Phys.43(1972)4657.[31]W.A.Harrison,J.Vac.Sci.Technol.14(1977)1016.[32]M.Cardona,N.E.Christensen,Phys.Rev.B35(1987)6182.[33]E.T.Yu,J.O.McCaldin,T.C.McGill,Solid State Phys.46(1992)1.[34]J.Robertson,C.W.Chen,Appl.Phys.Lett.74(1999)1168.[35]G.M.Rignanese,X.Gonze,A.Pasquarello,Phys.Rev.B63(2001)104305.[36]R.H.French,J.Am.Ceram.Soc.73(1990)477.[37]E.D.Palik,Handbook of Optical Properties of Solids,V ol.1±3,Academic Press,New York,1985.[38]W.Schmickler,J.W.Schultze,in:J.M.O'Bockris(Ed.),Modern Aspects of Electrochemistry,V ol.17,Plenum Press, London,1986.[39]G.W.Dietz,W.Antpohler,M.Klee,R.Waser,J.Appl.Phys.78(1995)6113.[40]H.Hasegawa,T.Nishino,J.Appl.Phys.69(1991)1501.[41]K.Abe,S.Komatsu,Jpn.J.Appl.Phys.31(1992)2985.[42]T.Shimizu,N.Gotoh,N.Shinozaki,H.Okushi,App.Surf.Sci.117(1997)400;()T.Shimizu,N.Gotoh,N.Shinozaki,H.Okushi,Mat.Res.Soc.Symp.Proc.(2000).[43]M.Copel,P.R.Duncombe,D.A.Neumayer,T.M.Shaw,R.M.Tromp,Appl.Phys.Lett.70(1997)3227.[44]S.K.Dey,J.J.Lee,P.Alluri,Jpn.J.Appl.Phys.34(1995)3134.[45]C.A.Paz de Araujo,J.D.Cuchiaro,L.D.McMillan,M.C.Scott,J.F.Scott,Nature374(1995)627.[46]C.D.Gutleben,Appl.Phys.Lett.71(1997)3444.[47]H.J.Hubbard,D.G.Schlom,J.Mater.Res.11(1996)2757.J.Robertson/Applied Surface Science190(2002)2±109[48]S.A.Chambers,Y.Liang,Z.Yu,R.Dropad,J.Ramdani,K.Eisenbeiser,Appl.Phys.Lett.77(2000)1662.[49]S.Miyazaki,Appl.Surface Science(2002)``these proceed-ings''.[50]S.Miyazaki,M.Narasaki,M.Ogasawara,M.Hirose,Microelec.Eng.59(2001)373.[51]A.Chatterjee,et al.,IEDM Tech Digest,1998,p.777.[52]M.Houssa,M.Tuominen,M.Nailli,V.Afansev, A.Stesmans,J.Appl.Phys.87(2000)8615.[53]R.Ludeke,M.T.Cuberes,E.Cartier,Appl.Phys.Lett.76(2000)2886;D.J.Maria,J.Appl.Phys.45(1974)5454.10J.Robertson/Applied Surface Science190(2002)2±10。

24.755 23.917 23.654 23.565 23.333 23.194 22.929 22.864 22.864 22.864 22.490 22.345 22.333 21.757 21.543 21.543 20.833 20.761 20.614 19.966 19.795 19.547 19.352 18.571 18.571 18.038 17.983 17.983 17.949 17.689 17.689 17.689 17.436 17.313 17.215 16.417 16.238 16.179 16.008 16.008 15.766 15.575 15.518 15.389 15.389 15.389 15.333 15.333 15.280 15.280 15.265 15.253 15.251 15.202
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