Dispersion and loss of ferroelectric Ba0.5Sr0.5TiO3 thin films up to 110 GHz

Abstract

The frequency dependence of the complex permittivity (ε∗=ε′-jε″) of Ba0.5Sr0.5TiO3 0.3-μm-thick film is measured up to 110 GHz by using interdigitated capacitors and coplanar waveguides. It is shown that the temperature dependence (from 77 to 373 K) of microwave losses, measured at 20 GHz, is described by a tan(δ)-(ε′)3/2 law. This result indicates distributed electromagnetic wave interactions with the local soft-phonon modes. This conclusion is further confirmed by the satisfactorily fit of the frequency dependence of the complex permittivity by a Cole–Cole function with an exponent β=0.6 and a characteristic time τ=0.21 ps.