Permittivity and Microstructure of (Ba,Sr)TiO 3 Films: Temperature and Electric Field Response

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(100)SrRuO 31(100)Ba0 8Sr 0.2Ti0 3 1(100)SrRuO 3, (100)SrRuO 3I1 (100)SrTiO 311 (100)SrRuO 3and (100)SrTiO 31I(001)YBa 2Cu 307.• have been grown by laser ablation. There was only a small difference of the dielectric permittivity, in the temperature range 180-300K, between a bulk single crystal and an epitaxial (100)SrTiO 3 layer inserted between either high-Tc superconducting or SrRuO 3 electrodes. At T0.8,Th77K) in tunable microwave components based on low loss high-Tc superconducting films [1], b) (x=0.3-0.5,T-300K) in varactor type capacitance structures [2], and c) (x 125 K, was independent on electric field (ETcurie the substance is in paraelectric state and from (5), at E=0, follow Curie-Weiss relation e/e0= CI/(T-T0 ) (6) The difference between To and Tctrie for Bal-xSrxTiO 3 alloys is small [12]. The measured e(E) dependencies for the STO layers fitted well those extrapolated by relation (5), see curves 2 and 5 in the Fig.4a. The parameter l(T) for the STO layer may be determined from e(T) at E = 0 and the non-linearity parameter, 4, from the £(E) dependence at small E. In accordance with (5) s 2da/dE = - 61 2 (T),E (7) The r 2de/dE(E) dependence for the STO layer in the NBCO/STO/NBCO heterostructure and tangent for the curve at low E are shown on Fig.4a. The 4's determined for the STO [9] and BSTO [20] layers from the slope of the E 2ds/dE(T) curve at low E were in the range (6-10)x10 9 F 3 VIm 2. The ý for the STO and BSTO layers was hardly dependent on temperature. The estimated ý for the STO layer in the trilayers agree well with that obtained from Raman spectroscopy data on shift of the soft mode frequency in electric field for the bulk single crystal of the strontium titanate [15]. Devonshire [13] has shown, that, when ý•0, right side of the relation (2) have to include electromechanical terms which lead to piezoelectric effect and electrostriction. Because of mechanical effect, free energy of ferroelectric is decreased by a term proportional to the square of the elastic strain [22]. This strain is proportional to the square of polarisation, so electromechanical term in the expression for free energy of the ferroelectrics have to be proportional to p 4. The electromechanical coupling does not alter Curie-Weiss relation, but influence Tcurie [13,22]. The shift of Curie temperature ATcurie in electric field may be expressed as [14] ATcurie = C2 E (8)

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is dependent on coefficients rT,ý,y for the powers of the polarisation in expansion of the free energy. The C2= 1.9x 10 3 [14], for E(V/cm), was determined from plots of electrical polarisation P versus applied electric field E, measured at different temperatures. An observed essential shift (ATMax-45 K) of the maximum in the e(T) curve for the BSTO layer when -2V bias voltage was applied to the SRO electrodes relative to that in the case of Vb=0 agrees well with an estimation made on the base of the relation (8). External electric field during measurements of the curve 3 at Fig.3b was Vb/d=25xl 0 3 (V/cm). According to (8), the shift of the Curie po

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