Analysis of the effects of thermo-mechanical stress on the frequency shift of MEMS resonators

Recently, Micromechanical silicon resonant accelerometer (MSRA) has been widely applied to inertial navigation system, attitude stabilization of weapon, and geological exploration, due to its high sensitivity, strong stability and large dynamic range. However, the temperature-dependent factors, like the changes in Young's modulus of monocrystalline silicon, thermal residual stress, and the thermo-mechanical stress induced by the thermal mismatch of different materials, can lead to the frequency shift of MSRA. Therefore, it is of great importance to improve the temperature stability of MSRA. In this paper, we systematically investigated the frequency drift laws of MSRA within the temperature range of 0 to 50 °C by the finite element simulations. Because of the CTE mismatch of different materials, the silicon resonant beam in MSRA bends downward or upward, and consequently, the induced thermo-mechanical stress in the silicon resonant beam can cause the rigidity variations, leading to the frequency drift of MSRA. Furthermore, the influences of changes in the structure parameters and material characteristics of package on the frequency drift of MSRA were analyzed. In comparison to the thickness and CTE of die-attach adhesive, the influences of the silicon substrate thickness and the Young's modulus of die-attach adhesive are much more significant. This paper can provide the design principles for the MSRA package design, which are conducive to diminish the influences of temperature variations.