Precision Resonant Beam Strain Sensor Employing Gap-Dependent Frequency Shift

A micromechanical structure for on-chip strain sensing maps strain-induced gap changes to resonance frequency shifts while employing differential strategies to null out bias uncertainty, all towards repeatable measurement of sub-nm displacement changes that equate to sub-$-\mu\varepsilon$ strain increments. The key enabler here is the use of gap-dependent electrical stiffness to shift resonance frequencies as structural elements stretch or shrink to relieve stress. An output based on the difference frequency between two close proximity structures with unequal stress arm lengths (cf. Fig. 1) removes uncertainty on the initial gap spacing and permits a $206\ \text{Hz}/\mu\varepsilon$ scale factor. The ability to precisely measure the frequency of the high-$Q$ (∼4000) structures, down to at least 1 Hz, puts the resolution of this sensor at least $5\mathrm{n}\varepsilon$ (or 790 Pa for polysilicon). An on-chip highly sensitive strain sensing device like this will likely be instrumental to managing stress changes over the lifetime of micromechanical circuits, such as oscillators and filters.