Stress determination of micromembranes using laser vibrometry

A laser vibrometry based dynamic technique for biaxial residual stress determination in micromembranes is reported. Layered, low pressure chemical vapor deposition (LPCVD) grown, rectangular shaped micromernbranes are ultrasonically excited. The resulting micrornembrane displacement, as a function of frequency and position, is recorded to yield resonance frequencies and associated vibrational mode numbers. The stress is determined from this infom~ation. Vibrations forced from ultrasonic pressure (-25 Pa) resulted in peak displacements of tens of nanometers at resonance. For the sample set studied the (3,1 ) mode resonance peak displayed the least damping in atmospheric testing and was used to establish stress levels 10g N/n~2. A trend for this stress showing an overall decrease by -40% as a result of them~omechanical cycling was identified. INTRODUCIVON The emergence of micrornembrane-based architectures has resulted in a need for accurate analysis of membrane stress characteristics. Micromembranes are increasingly being used for diverse applications such as x-ray lithography masks [1-4] and microwave transmission lines. Examples of membrane-based microwave components include switches, very highQ inductors, Ka-band power dividers, and filters operating from 15 GIIz to 250 GHz [59]. In order to successfully implement these structures in non-laboratory environments, it is important to investigate the residual biaxial stress build-up during fabrication, and the subsequent evolution of the stress with thermomechanical cycling. This knowledge is critical if one is to resolve and correct for stress-related failure mechanisms. Electronic components using membrane technology are increasingly being envisaged for miniaturization of future space flight hardware, here too, mechanical property dependence on structural vibrations and thermal cycling is crucial for reliable implementation. Previous work on membrane stress characterization includes both theoretical and experimental methods. Analytical and finite element stress analysis of homogeneous, rectangular and circular membranes [10,1 1 ] can predict the biaxial stress and Young’s modulus of membranes. Studies of stress and’ Young’s modulus by static (load versus deflection) measurement methods have also been reported [1 1,12]. In addition, dynamic techniques have been used where the resonant frequencies of vibrating membranes are used (as elaborated below) for determining stress [1,1 3]. A new dynamic technique for membrane stress determination utilizing laser vibrometry is described in the present report. Specifically, a tightly focused laser spot is used for interrogating the driven (vibrating) membrane surface while extracting displacement and velocity spot measurements from an interferometric analysis of the retro-reflection. I“he technique allows a comprehensive characterization of vibrating micromembranes and can