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 (110) and (100) silicon crystalline directions are used to analyze both linear and nonlinear elastic behavior of silicon with p- (N ≅ 4.19e + 18 to 1.63e + 20 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> ) and n-type (N ≅ 1.58e + 18 to 5.91e + 19 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> ) 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.