Unsteady Thermo-Structural Simulation of Nano-Bridge Resonators

This study provides a thermo-structural simulation to investigate the behavior of nano-bridge resonators. A three-dimensional doubly clamped bridge with a length of 10 microns, a width of 1 micron and a thickness of 300 nm vibrating in the air is simulated. A free molecular heat transfer model is used to define the heat transfer coefficient and the damping coefficient. A Finite Difference method is used to solve the transient heat transfer equation coupled with the dynamic structural equation at each time step. The study is performed for silicon. The results show the steady state amplitude variations and vibration amplitude variations by the total heat amplitude correspond to a linear system. The results also show that increasing the total heat amplitude has more significant effects on increasing the vibration amplitude rather than the steady state amplitude by a factor of 1.2. The steady state amplitude and vibration amplitude variation by the surrounding gas pressure is investigated over a range of pressures from 1 kPa to 500 kPa for a total heat amplitude of 5000 MW/m² (50 mW). The steady state amplitude and the vibration amplitude decrease by increasing the pressure due to an increase in the damping coefficient and the heat transfer coefficient. The rate of decrease is significantly higher for the vibration amplitude. This is due to the combination of increasing heat transfer coefficient, and increased damping, as the pressure increases.