Theory of fundamental microwave absorption in sapphire (α-Al2O3)

Abstract

An accurate model for intrinsic dielectric loss in sapphire (α-Al2O3) is presented. The proposed model is based on a theory of electromagnetic field absorption governed by multiphonon relaxation processes influenced by a finite lifetime of thermal phonons. Expressions for anisotropic sapphire dielectric loss tangent are derived utilizing sapphire dielectric function given in terms of the quasiharmonic approximation. The frequency-dependent two- and three-phonon damping constants of each fundamental transverse optical mode were determined numerically employing the accurate anharmonic coefficient computations based on sapphire lattice-dynamical data. The results of the dielectric loss tangent calculations in microwave and millimeter-wave regions are presented. The developed sapphire dielectric loss model offers excellent agreement between the experimental and calculated magnitudes of the tan δ components and also accurately reproduces their frequency and temperature dependencies.

Main Source of Microwave Loss in Transition‐Metal‐Doped Ba(Zn1/3Ta2/3)O3 and Ba(Zn1/3Nb2/3)O3 at Cryogenic Temperatures

“…(a) and are significant below 100 K and dominant below 50 K. The value of the loss tangent measured at the large field of 5 × 10 4 G apparently have thus quenched the loss component from electron paramagnetic resonance and our results do not give additional insight into the mechanism of this component of loss. Earlier researchers have concluded that losses arise from mechanisms such as free carrier and polaron absorption, anharmonic‐phonon absorption, and precession of electric dipoles in polar molecules . The peak observed in the loss tangent at ~100 K in some of the samples appears to be similar to that typically attributed to polaron conduction …”

“…To date, researchers have identified a number of mechanisms that can cause microwave loss in dielectrics, including free carrier and polaron absorption, EPR, anharmonic‐phonons, and precession of electric dipoles in polar molecules …”

Origin of dielectric loss in Ba(Co1/3Nb2/3)O3 microwave ceramics

“…Dielectric loss consists of intrinsic and extrinsic components. Since single phonon absorption processes does not satisfy the energy and momentum requirements, the intrinsic loss for practical dielectrics, including Ba(Co 1/3 Nb 2/3 )O 3 , was previously ascribed to two, three, and higher order phonon absorption processes . To mix the frequencies, non‐linear components involving the anharmonic component of phonon modes are involved and these processes form the lower limit of the loss tangent, i.e., the loss tangent of an “ideal” crystal .…”

Invited Article: Dielectric material characterization techniques and designs of high-Q resonators for applications from micro to millimeter-waves frequencies applicable at room and cryogenic temperatures

“…A one layer cylindrical sapphire Bragg resonator with Q-factor of 230 000 was achieved at 9.7 GHz 14 (Figures 16 and 17). This is higher than a Whispering Gallery mode resonator at room temperature at the same frequency (Q WGH ∼ 200 000, Q WGE ∼ 100 000) 83,84,[96][97][98][99][100] and equivalent to a single spherical Bragg resonator. 20 However, the machining and assembly are much easier in the spherical case.…”