| Silicon micromechanical resonators have the potential to replace quartz crystal oscillators in many frequency reference applications. Quality factor, Q, is a measure of how resonators lose energy and impacts the equivalent electrical resistance, which is important for designing oscillator circuits with these resonators, of the mechanical resonator. However, the different ways that resonators can lose energy (e.g., air damping, substrate loss, surface dissipation, thermoelastic dissipation (TED)) are not well understood. This work focuses on the investigation of thermoelastic dissipation, an energy loss mechanism whereby mechanical energy stored in the resonator is irrecoverably transferred to the thermal domain. In thermoelastic dissipation, strain gradients lead to temperature gradients in the resonator. If these temperature gradients are allowed to relax via heat flow, the mechanical energy is irrecoverable and TED has occurred. The underlying physics of TED was first formalized by Clarence Zener in the 1930s for simple structures. This work addresses the impact of more complex geometries on TED and the need for a general analysis technique for arbitrary structures.; Silicon micromechanical resonators were fabricated in a single wafer vacuum encapsulation at pressures < 1 Pa. Novel resonator geometries have been investigated that reduce the impact of TED, while at the same time verifying the validity of novel finite element simulations that predict TED-limited Q. These resonators employ slots designed in the beams that disrupt the heat flow across the beam, altering the process of thermoelastic dissipation. An increase of Q of up to 4X (10,000 to 40,000) was seen with this method. As a result, we are now able to engineer the TED-limited Q for micromechanical resonant beams, by decoupling the impact of TED from the characteristic length across a resonant beam. |
