Nowadays, achieving resonators with high quality factor (Q) in the Ultra High Frequency (UHF) range in some wireless communication applications such as filters [1], oscillators [2] and micromechanical mixer-filters [3,4] is one of the interesting subjects about micromechanical resonators. Because in all of above-mentioned applications, quality factor has a direct relationship with their performance such as insertion loss, phase noise, motional resistance and power consumption.
Among micromechanical resonators, bulk-mode resonators due to having high structural stiffness of bulk modes and lack of need to scale the resonator dimensions into the nanometer domain are developed more than flexural mode beam resonators. For a bulk mode resonator operating in a high vacuum and by locating optimal support beams at nodal points (points with zero radial displacement and lowest circumferential displacement), two extrinsic damping mechanisms such as air damping and support loss can be effectively minimized [5].
However, thermoelastic damping, which is known as the most important intrinsic dampi...