Strongly buckled square micromachined membranes

The buckling of compressively prestressed square membranes with built-in ed ges is investigated experimentally and analyzed theoretically. The buckling depends weakly on Poisson's ratio and essentially is a function of the red uced prestrain, <(epsilon)over bar>(0) = epsilon(0)a(2)/h(2) where epsilon( 0) is the physical prestrain, a is the width, and h is the thickness of the membrane. As <(epsilon)over bar>(0) becomes increasingly negative, the mem brane undergoes two symmetry breaking buckling transitions.' Beyond the fir st transition occurring at <(epsilon)over bar>(cr1), the buckling profile h as all the reflection and rotation symmetries of a square. The reflection s ymmetries are lost through a second instability transition at <(epsilon)ove r bar>(cr3). The bifurcation points, <(epsilon)over bar>(cr1) and <(epsilon )over bar>(cr2). and-buckling profiles were calculated using analytical ene rgy minimization and nonlinear finite-element simulation. Both methods:agre e. The buckling of micromachined plasma-enhanced chemical vapor deposition silicon nitride membranes on a silicon wafer is interpreted in terms of the theoretical results. Good matching between measured and calculated bucklin g profiles is found. The extracted strain values are consistent irrespectiv e of the size and buckling mode of the membranes. From the average strain a cross:the wafer epsilon(0) = -3.50 x 10(-4) and complementary wafer curvatu re measurements, a Young's modulus of 130 GPa is deduced. Methods for the s traightforward extraction of epsilon(0) from experimental center deflection s of buckled square membranes are described. [443].