Quasi-Debye microwave loss as an intrinsic limitation of microwave performance of tunable components based on SrTiO 3 and Ba x Sr 1 − x TiO 3 ferroelectrics

A model of the quasi-Debye loss mechanism in SrTiO 3 and Ba 0.6 Sr 0.4 TiO 3 perovskite ferroelectrics at microwave frequencies is presented. The field dependence and the size of the field-induced quasi-Debye loss contribution in SrTiO 3 and Ba 0.6 Sr 0.4 TiO 3 systems have been evaluated in the simple approximation of the isotropic phonon spectra of these materials. Good agreement between experimental and simulated results for the field dependence of dielectric loss for SrTiO 3 ferroelectric material is observed for the weak dc fields [tunability n = ε ( 0 ) ∕ ε ( E ) ⪡ 2 ]. A significant feature in the field dependence of dielectric loss at microwave frequencies, a pronounced maximum, is predicted for SrTiO 3 at higher values of the bias field ( n ≅ 2 ) whereas in Ba 0.6 Sr 0.4 TiO 3 the field dependence of the loss is found to be monotonic. The influence of the quasi-Debye loss contribution on microwave performance of SrTiO 3 and Ba 0.6 Sr 0.4 TiO 3 ferroelectric materials is analyzed. It is concluded that the contribution of this mechanism is large enough to affect the performance of tunable microwave devices based on SrTiO 3 ferroelectric materials, whereas in the case of Ba 0.6 Sr 0.4 TiO 3 ferroelectrics the contribution of the quasi-Debye loss mechanism is found to be relatively small.