A model of voltage-dependent dielectric losses for ferroelectric MMIC devices

Abstract

The use of high-dielectric films for microwave devices, especially phased-array radar systems, in the tens of GHz regime requires very low-loss (0.01 to 0.1) films. Unfortunately most ferroelectrics have losses that diverge (greater than unity) in this frequency range. We develop in the present study quantitative models for dielectric loss in both SrTiO₃ and Ba_xSr_1−xTiO₃ (BST) that give dependences upon temperature, frequency, and especially voltage or field. In pure strontium titanate we find that loss is intrinsic, with quality factor “Q” greater than 1000; and a dramatic voltage dependence of tan δ is observed to fit the C^3/2(V) dependence upon capacitance predicted for three- and four-phonon anharmonicity for voltages up to 5V (E = 250 kV/cm). In most barium strontium titanate ceramic films the loss is extrinsic at 100 MHz, and the surface layer model of Neumann and Hofmann describes the dependence of tan δ upon thickness D rather well, with tan δ increasing from 0.001 at D = 5 microns to 0.10 at 50 nm. Typical values at 250 nm are ca. 0.015.