Characteristics of polysilicon resonant microbeams

Abstract

Polysilicon resonant microbeams can be used as strain-sensitive elements to replace conventional silicon piezoresistors in precision sensor applications, such as pressure sensors and accelerometers. These elements are combined with conventional silicon diaphragms or flexures with a proof mass to convert pressure or acceleration directly into a frequency output. Vacuum-enclosed resonant microbeam elements 200 or 400 μm long, 45 μm wide and 1.8 μm thick have been fabricated using LPCVD mechanical-grade polysilicon at the University of Wisconsin. Q-values determined using gain/phase analysis are typically over 25 000. Lower Q-values are primarily the result of residual gas in the cavity. Closed-loop operation from −60 to 180°C using piezoresistive sensor and electrostatic drive has been achieved with automatic gain control (AGC) to prevent overdrive. The characteristic resonance frequencies of the beams have been measured, with 550 kHz, 1.2, 2.2 and 5.2 MHz being typical of the frequencies of the one-dimensional bending modes for the 200 μm length. These measurements of the multiple resonance frequencies of a single beam provide a means of testing mathematical models of the dynamic behavior as well as determining the residual beam stress. The one-dimensional (1D) differential equation of motion of a doubly clamped single-span beam with an axial load can be solved analytically for lateral natural frequencies and mode shapes. These 1D solutions have been verified by 3D finite-element methods. In addition, the finite-element models are used to identify both lateral and torsional modes. The closed-form solutions agree closely with the numerical results and the experimental data.