A MODEL OF VOLTAGE-DEPENDENT DIELECTRIC LOSSES FOR FERROELECTRIC MMICDEVICES

The use of high-dielectric films for microwave devices, especially pha sed-array radar systems, in the tens of GHz regime requires very low-l oss (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 BaxSr1-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 tha n 1000; and a dramatic voltage dependence of tan delta 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 mo st barium strontium titanate ceramic films the loss is extrinsic at 10 0 MHz, and the surface layer model of Neumann and Hofmann describes th e dependence of tan delta upon thickness D rather well, with tan delta increasing from 0.001 at D = 5 microns to 0.10 at 50 mn. Typical valu es at 250 nm are ca. 0.015.