Nonlinearity of Degenerately Doped Bulk-Mode Silicon MEMS Resonators

Abstract

We present an experimental study of conservative nonlinearities in bulk acoustic mode (bulk-mode) silicon MEMS resonators with degenerate doping. Three types of bulk acoustic mode resonators oriented in $\langle 110\rangle $ and $\langle 100\rangle $ silicon crystalline directions are used to analyze both linear and nonlinear elastic behavior of silicon with p- ( $N \cong 4.19e+18$ to $1.63e+20$ cm $^{-3}$ ) and n-type ( $N \cong 1.58e+18$ to $5.91e+19$ cm $^{-3}$ ) doping. For accurate characterization of the amplitude-dependent nonlinear stiffness constant, we employ two methods: amplitude-frequency response and ringdown measurement. Experimental results show that the nonlinear behavior of these resonators is dominated by material-dependent mechanical nonlinearities and strongly depends on the doping type and crystal orientation. These results are useful for understanding the material-induced nonlinear properties of doped silicon and design of MEMS resonators with desired dynamic behavior, and may provide a new avenue for tailoring resonator response characteristics. [2015-0301]