Modelling and investigation of the mechanical and electrical characteristics of the silicon 3D-boss microprobe for force and deflection measurements

Abstract

The three-dimensional (3D) microprobe is based on a silicon boss-membrane with piezo-resistive Wheatstone bridge transducers which enable the measurement of the deflections of the probing sphere and, simultaneously, the forces in all three dimensions. An analytical model for the calculation of the mechanical characteristics of the 3D microprobe is presented. It uses analytical expressions for the stiffness, taking into account not only the bending of the membrane, but also its stretching. The model describes the deformations of the membranes if the probe pin is deflected, and also the linear and nonlinear mechanical characteristics of the 3D microprobe. A numerical model for the approximate calculation of the linear and nonlinear electrical characteristics of the 3D microprobe was also developed. The computational technique and results on the calculation of the optimal location of the piezo-resistors on the 3D microprobe producing the maximal sensitivity are presented. The methods and the results for the estimation of the doping concentration, the doping depth of the piezoresistors, the Hooge constant describing the main noise contribution of the resistors for low frequencies and the threshold sensitivity of the 3D microprobe are presented. A comparison and an analysis of the experimental and theoretical results of the 3D microprobe investigation are carried out. These results can be used for the development and optimization of piezoresistive 3D microprobes, cantilever sensors and a large variety of other MEMS.