Nonlinearity reduction in silicon resonators by doping and re-orientation

In this paper, it is shown for the first time that nonlinearity in n-type doped silicon micro-resonators can be reduced by modifying the doping concentration and the resonator alignment to a different crystalline orientation. Spring hardening, a trend opposite to the commonly-observed spring softening, is demonstrated in extensional resonators fabricated on a highly Phosphorus-doped (n~5×10¹⁹ cm^-3) silicon substrate and oriented in the [100] direction. Therefore, it is hypothesized that for a specific level of doping concentration the nonlinear stiffness coefficients (k₁ and k₂) can be cancelled and the device will behave linearly for a large range of input power. It is observed that devices fabricated on an Arsenic-doped substrate with lower doping concentration (n~3×10¹⁹ cm^-3) mechanically fail before they reach bifurcation, a preliminary proof for our hypothesis.