Residual stress and Young's modulus measurement of capacitive micromachined ultrasonic transducer membranes

Abstract

Membranes supported by posts are used as vibrating elements of capacitive micromachined ultrasonic transducers (CMUTs). The residual stress built up during the fabrication process determines the transducer properties such as resonance frequency, collapse voltage, and gap distance. Hence, it is important to evaluate and control the stress in thin film CMUT membranes. The residual stress in the membrane causes significant vertical displacements at the center of the membrane. The stress bends the membrane posts, and the slope at the membrane edges result in amplified displacement at the center by the radius of the membrane. By measuring the center displacement, it is possible to determine the stress provided that Young's modulus of the thin film is known accurately. Usually, in thin film structures Young's modulus differs from that of bulk materials and it depends on thin film deposition technique. In this paper, we propose a novel technique for the measurement of stress and Young's modulus of CMUT membranes. The technique depends on the measurement of membrane deflection and resonance frequency. We modeled the stress and Young's modulus dependence of membrane deflection and resonance frequency using finite element analysis. We used an atomic force microscope (AFM) to measure the membrane deflection and a laser interferometer to determine the resonance frequency of the membrane. The technique is tested on a CMUT membrane. We found that our LPCVD deposition technique yields residual stress of around 100 MPa and Young's modulus of around 300 GPa.