Study on the influence of residual stress on the mechanical characteristics of free-standing Si-membranes processed by deep reactive ion etching

Abstract

The mechanical behavior of free-standing Si-membranes (diaphragms) fabricated by deep reactive ion etching (DRIE) was studied in order to emphasis the magnitude of process-induced stress and/or strain distribution in both square and circular diaphragms. For this purpose, 25 μm thick circular and square diaphragms with 4 mm diameter (or side-size) were fabricated using silicon-on-insulator wafer. The thickness and surface homogeneities of the DRIE processed Si-diaphragms were analyzed by SEM and AFM, respectively. Micro-Raman spectroscopy studies revealed a non-uniform distribution of compressive stresses throughout the diaphragm surface. Using the synchrotron based Laue diffraction measurements, the residual stress values were quantitatively estimated as 19.88 and −22.83 MPa for the unloaded circular and square diaphragms, respectively. The pressure vs. displacement experiments were conducted using the bulge testing method and these studies yielded maximum mid-point deflection values of 25 and 30 μm for the circular and square diaphragms, respectively against applied pressure of 25 kPa. Based on the deflection characteristics, the average residual stress and equivalent biaxial modulus were estimated by means of standard analytical equations. Using the finite element analysis, the mid-point deflection characteristics of the diaphragms were simulated through considering the residual stresses as input parameters and the results are compared with that of those obtained by the experimental and analytical methods. The residual stress information such as those inferred in this study would help in tuning the resonant frequency of Si-diaphragms towards sensor/actuator applications.