A high-performance micromachined piezoresistive accelerometer, consisting of two axially stressed tiny beams combined with a central supporting cantilever, is developed for both much higher sensitivity and much broader bandwidth compared with conventional beam-mass piezoresistive accelerometers. With the pure axial-deformation scheme of the tiny beams, the developed accelerometer shows improvements in both sensitivity and resonant frequency. An analytic model is established for the pure axial-deformation condition of the tiny beams by adjusting the distance between the tiny beams and the central supporting cantilever. The specifications of the device, such as sensitivity and resonant frequency etc, are theoretically calculated. The analytic model is verified by using simulation of the finite element method (FEM), resulting in satisfactory agreement. Based on a figure of merit (the product of the sensitivity and the square of the resonant frequency), optimized design rules are obtained for the sensors of various measure-ranges from 0.25g to 25 000g. The accelerometers are fabricated by using silicon bulk micromachining technology. The formed 2.5g devices are characterized with a typical sensitivity of 106 mV/5 V/g and first mode resonant frequency of 1115 Hz. The testing results agree well with the design, thereby verifying the high performance of the proposed accelerometer. The developed sensors with the axially stressed tiny-beam scheme show obviously improved specifications, compared with previously published results.

Using the Stoney formula and its modifications, curvature-based techniques are gaining increasingly widespread application in evaluating the stress in a film on a substrate. In principle, the formula applies only when the stress is uniform throughout the film thickness. The main purpose of this paper is to extend the Stoney formula when the residual strain in the film is no longer uniform, but dependent on the z position. To achieve this goal, a general theory was introduced for the elastic deformation of an arbitrary, multilayered system. By practicing this general theory, we used a polynomial function to describe the gradient stress in a film, and contributions by different elements of the polynomial to both the curvature and the bending strain were derived. A finite element simulation for a typical film-substrate structure was then carried out, leading to the verification of the theory developed in this paper. In the discussion section, we explored the relation between the surface curvature and the bending curvature as well as the difference between the stress in the constrained planar state and that in the relaxed state. In addition, the accuracy of the simplified formula, using thin film approximation, was evaluated. Finally, a SiN x-Al MEMS structure was studied by using the formula in this paper.

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