Stress Relaxation of a Patterned Microstructure on a Diaphragm

Abstract

Stress relaxation of a patterned thin film on diaphragms of different material and thickness was investigated through experimental study and numerical simulation. The diaphragm deflections, caused by relaxation of the residual stress in a patterned thin film residing on top, were measured using a Twyman–Green laser interferometer. The first diaphragm used was a Si3N4(top)/SiO2/Si composite diaphragm and the second a 0.5-μm-thick Si3N4 membrane. Custom-written simulation software, which uses a novel numerical algorithm named Nonlinear Sequential Analysis (N-LISA), was utilized to calculate the stress distribution in the patterned thin film and the diaphragm substrate. Agreement between the model and the experimental results was satisfactory. Simulation of the system balance between a tensile-stressed circular Ti film and a stress-free Si substrate of different thickness clearly shows a transition in the substrate behavior from a pure plate to a pure membrane. Interestingly, the deflection of the Si substrate caused by the residual stress in the Ti film reaches its maximum at a certain substrate thickness where plate and membrane characteristics coexist. This study addresses some basic mechanics issues involved in modern devices dealing with thin diaphragms.