23光纤传感

Ferroelectrics,401:246–250,2010Copyright©Taylor&Francis Group,LLCISSN:0015-0193print/1563-5112onlineDOI:10.1080/00150191003677171Quantum Effect on SrRuO3/BaTiO3/SrRuO3 Ferroelectric Ultrathin Film CapacitorH.WU,1,∗Y.G.ZHAN,1AND W.Z.SHEN21Department of Applied Physics,Donghua University,Ren Min Road2999,Songjiang District,Shanghai201620,P.R.China2Laboratory of Condensed Matter Spectroscopy and Opto-Electronic Physics,Department of Physics,Shanghai Jiao Tong University,1954Hua Shan Road,Shanghai200030,P.R.ChinaWe have carried out a detailed investigation on the quantum effect onSrRuO3/BaTiO3/SrRuO3ferroelectric ultrathinfilm capacitors fully strained with aSrTiO3substrate.We employ the transversefield Ising model,taking into account theincomplete charge compensation of the realistic SrRuO3electrode and the misfit strainimposed by the SrTiO3substrate in the Hamiltonian,to quantitatively explain the ex-perimental observation in the literature.It is found that quantum mechanism under theinfluence of the incomplete charge compensation of the electrode plays an importantrole in determining the ferroelectric properties of BaTiO3ultrathinfilms between twometallic electrodes.Keywords Ferroelectric ultrathinfilm;spontaneous polarization;dielectric suscepti-bilityPACS numbers:77.84.Dy,77.80.-e,and77.55.+fI.IntroductionUltrathin ferroelectric(FE)films have attracted much attention from the scientific as well as application points of view with recent breakthroughs in fabricating high-quality oxide films[1–3].The crucial physics with an FE layer inserted between realistic electrodes is incomplete compensation of the FE polarization charge:the compensation charges will be induced with afinite extent,called the Thomas-Fermi screening lengthλ.Such an incomplete compensation of the polarization charges will induce a depolarizingfield E d in the FE layer and consequently suppress the FE polarization[4–8].Recently,Junquera and Ghosez[5]performedfirst principles calculations for a fully strained SrRuO3(SRO)/BaTiO3(BTO)/SRO heterostructure on a SrTiO3(STO)(001)sub-strate.By taking into account the depolarizingfield E d,they predicted that the polarization of the BTO thinfilm vanishes at the critical thickness of2.4nm.More recently,Kim et al. [9,10]have published a series of experimental studies of ultrathin,down to5nm,FE SRO/BTO/SRO capacitors fully strained with an STO substrate.They demonstrated the Received August23,2009;infinal form October14,2009.∗Corresponding author.E-mail:wuhua@246Quantum Effect on Ferroelectric Thin Film247 effect of E d on the FE polarization for BTOfilms with variousfilm thickness from5to30 nm and provided an upper bound of5nm for the critical thickness.Up to now,most theoretical research did not take into account the extrinsic effect, including such characteristics as thefinite screening lengthλof the electrode and the strain conditions imposed by the substrate.In the present work,we employ the transversefield Ising model(TIM)to quantitatively investigate the size effect and quantum effect on a fully strained SRO/BTO/SRO FE ultrathinfilm capacitor on an STO substrate by taking into account the depolarizingfield induced by the incomplete charge compensation at the FE-electrode interface and compressive strain induced by the substrate.II.Theoretical BackgroundThe Hamiltonian of the system can be expressed as:H=−i S x i−12i,jJ i,j S ziS zj−2i(E+E d)µS zi,(1)where the detailed explanations of the parameters ,J i,j,S i and E can be found in Ref.11.µ=2.35eÅis the effective dipolar moment of each spin that we obtained byfitting theexperimental data in Ref.9.E d=−Pε0εF(2εF/d2εF/d+εe/λ)[4,9]is the depolarizingfield due tothe incomplete charge compensation,where d is thefilm thickness,P is the polarization, and accurate values of the parametersε0,εe,εF,andλcan be found in Ref.9.Choi et al.[12]reported the enhancement of ferroelectricity in strained BTO thinfilms, in which T C is enhanced by the compressive strain via T C=θ+Aεs.Here,θ=393K is the Curie-Weiss temperature of unstrained BTO and A is a constant associated with Curie constant,electrostrictive coefficients and elastic compliances.In the present work, we not only take into account the depolarizingfield,but also the compressive misfit strain εs=(a −a0)/a0,where a0=0.4005nm[13]is the lattice constant of free-standing cubic BTO and a =0.3905nm[10]is the in-plane lattice parameter of a fully strained BTO film,resulting in the misfit strainεs being−2.5%.Byfitting the experimental results [12]of thick BTOfilms grown by pulsed laser deposition(PLD)with various strains,we obtain A=−3.2×104K and T C=1193K for30nm BTO thinfilm.We can therefore get J=6127k B K and =1850k B K,which are different from the corresponding parameters for bulk BTO[14],byfitting the experimental spontaneous polarization for d=30nm in Ref.9.Under the meanfield approximation,we obtainP=Nµ(J d P+4Nµ2E)4N2µ2 2+(J d P+4Nµ2E)2×tanh4N2µ2 2+(J d P+4Nµ2E)24Nµk B T,(2)χ(T,d)=1ε0dPdEE=0,(3)where N is the pseudospin density[15],andχ(T,d)is the dielectric susceptibility.It shouldbe noted that J d=J−8Nµ2λε0(εe d+2εFλ)is the modified nearest-neighbor pseudospin interactiondue to the effect of incomplete charge compensation.248H.Wu et al.050010001500153045T C (K )d (nm)P s (µC /c m 2) d (nm)Figure 1.(a)Thickness dependence of the spontaneous polarization P S for T =300K.The solid and dashed curves represent the theoretical results for λ=0.08nm and λ=0nm,respectively,and solid squares correspond to the experimental data reported in Ref.9.(b)Thickness dependence of the phase transition temperature T C .Dashed line represents our extrapolated thickness dependence of T C for classical case under the approximation of T C /2k B .III.Results and DiscussionFigure 1(a)shows the thickness dependence of the spontaneous polarization P S at T =300K.Our theoretical results are in good agreement with the experimental data.Note that the P S value with d =30nm is about 44µC/cm 2,which is larger than the BTO bulk value of 26µC/cm 2.This enhancement should be attributed to the compressive strain imposed by STO substrate.Since the intrinsic surface effect is neglected,the spontaneous polarization should be thickness independent for a film with an ideal electrode (λ=0nm).For a film with a realistic SRO electrode (λ=0.08nm [9]),however,the incomplete charge compensation will reduce the spontaneous polarization.Moreover,with the decrease of the film thickness,the spontaneous polarization exhibits a more and more rapid decrease with decreasing film thickness and approaches zero at a critical thickness d C (T =300K )=4.2nm.Figure 1(b)shows the thickness dependence of the transition temperature T C .By deal-ing with the Hamiltonian,we obtain the analytical T C = 2k B ArcTanh(2 /J d ),which decreases more and more rapidly with the film thickness and approaches zero at d C (T =0K)=4.17nm.The above-mentioned polarization and transition properties originate from the com-petition between the thickness dependent pseudospin interaction and quantum mechanical tunneling,and consequently,can be explained in a certain microscopic mechanism with the quantity J d /2 to scale the quantum effect (this will be discussed below),which leads to the dramatic suppression of ferroelectricity with the decrease of film thickness.For classical cases,where T C /2k B ,the thickness dependence of the transitiontemperature can be expressed as:T C ≈T C (λ=0)−8Nµ2λT C (λ=0)/ε0εe J d (dashed line in Fig.1(b)),where T C (λ=0)= 2k B ArcTanh(2 /J )=1323K is the transition temperature for BTO film with an ideal electrode.If we extrapolate this result to the low temperature region,we easilyobtain the critical thickness d C 1=2.4nm,in good agreement with the predicted data [5]through the first principles calculation.The above-mentioned relation is in accordance with that derived within the framework of the nonlinear thermodynamic theory by including the effect of the depolarizing field [16,17],where the influence of the quantum mechanismQuantum Effect on Ferroelectric Thin Film2490.81.01.21.41.6d (nm)J d /2ΩγFigure 2.Thickness dependence of the critical exponent γ(left horizontal arrow)and J d /2 (right horizontal arrow).J d /2 ,representing the competition between the thickness dependent pseudospin interaction and quantum mechanical tunneling,is used to scale the quantum effect in our calculation within the framework of the TIM.The critical thickness,at which T C =0K,corresponds to the case of J d /2 =1.was neglected.In contrast to the classical cases,T C and the critical thickness d C (T =0K )will remarkably deviate from the classical results under the role of quantum mechanism.With the consideration of quantum effect,1/χin the paraelectric phase can be ex-pressed as 1/χ∝(T −T C )γ,where the critical exponent γis important for scaling the quantum effect.We have displayed in Fig.2the critical exponent γas a function of the film thickness.With the decrease of the film thickness,γgradually deviates from the classical value 1and increases rapidly near d C .The fact that γreaches 2at d C indicates a dramatic increase of the quantum effect on the dielectric properties for SrRuO 3/BaTiO3/SrRuO 3ferroelectric ultrathin film.It should be noted that J d /2 ,which varies with the film thick-ness due to the incomplete charge compensation caused by the imperfect electrode,is used to scale the quantum effect in our calculation within the framework of the TIM.With the decrease of the film thickness,the reduction of J d /2 will cause the enhancement of quantum effect and the suppression of ferroelectricity (Fig.2).The critical thickness,at which T C =0K,corresponds to the case of J d /2 =1.With the decrease of film thickness,the quantum fluctuation gradually dominates over the decreasing polarization interaction,leading to the transition from a ferroelectric at J d /2 >1to a paraelectric at J d /2 <1.AcknowledgmentsThis work was supported by the Natural Science Foundation of China under contract No.10747114and Shanghai Educational Development Foundation under contract No.2007CG43.References1.Y .S.Kim et al.,Appl.Phys.Lett.86,102907(2005).2.C.H.Ahn,K.M.Rabe,and J.M.Triscone,Science 303,488(2004).3.H.N.Lee et al.,Nature (London)433,395(2005).4.R.R.Mehta,B.D.Silverman,and J.T.Jacobs,J.Appl.Phys.44,3379(1973).5.J.Junquera and P.Ghosez,Nature 422,506(2003).6.Igor Kornev,Huaxiang Fu,and L.Bellaiche,Phys.Rev.Lett.93,196104(2004).7.D.D.Fong et al.,Science 304,1650(2004).8.Z.Wu et al.,Phys.Rev.B 70,104108(2004).250H.Wu et al.9.D.J.Kim et al.,Phys.Rev.Lett.95,237602(2005).10.Y.S.Kim et al.,Appl.Phys.Lett.86,102907(2005).11.H.Wu and W.Z.Shen,Phys.Rev.B73,094115(2006).12.K.J.Choi,et al.,Science306,1005(2004).13.V.V.Lemanov,E.P.Smirnova,P.P.Syrnikov,and E.A.Tarakanov,Phys.Rev.B54,3151(1996).14.L.Zhang,W.Zhong,and W.Kleemann,Phys.Lett.A276,162(2000).,where a⊥=0.427nm[9]is the c-axis lattice constant and a = 15.Pseudospin density N=1a2 ·a⊥0.3905nm[9]is the in-plane lattice parameter of BTOfilm fully strained with the STO substrate.16.N.A.Pertsev,A.G.Zembilgotov,and A.K.Tagantsev,Phys.Rev.Lett.80,1988(1998).17.R.Plonka et al.,Appl.Phys.Lett.86,202908(2005).。