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。
