Nonlinearity of Degenerately Doped Flexural Mode Silicon Micromechanical Resonators

In this paper, we present an experimental study of nonlinearities in degenerately doped flexural-mode silicon MEMS resonators. Two geometries (single and double-anchored) and two wafer orientations (<;100> and <;111>) are used to analyze the elastic effects of p-type (1.31 × 10
¹⁶
to 1.61 × 10
¹⁵
cm
^-3)
and n-type (1.264 × 10
¹⁵
to 2.64 × 10
¹⁴
cm
^-3
) degenerately doped double-ended tuning forks. We employ closed-loop frequency sweeps to characterize the amplitude-frequency response of each system. Experimental results show that geometric nonlinearities and electrostatic nonlinearities dominate material and crystalline orientation-dependent nonlinearities in the flexural mode. These results present an initial exploration into characterizing nonlinear mechanical behavior of resonators operating in lower frequency bending modes.