An Improved Static Membrane Deflection Analysis for Collapse Mode CMUT Fabricated by Sacrificial Release Method

Abstract

To improve the accuracy of the static membrane deflection calculation for the collapse mode capacitive micromachined ultrasonic transducer (CMUT) fabricated by sacrificial release (SR) method. The beam theory was used and the substrate supporting force can be modeled by a coefficient to the load on the membrane. The surrounding supporting post bending can be modeled by applying the elastic support boundary conditions (ESBCs) for the peripheral part of the membrane. CMUT devices have been fabricated using the SR process to validate this analytical analysis. Young’s modulus of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {Si}_{{3}} \text {N}_{{4}}$ </tex-math></inline-formula> was derived as 200 GPa by a method using center deflections of several different radii single-layer conventional devices under 1 atm. The analytical deflection results and contact radius results for the collapse mode CMUT membranes were testified by experimental results under 1 atm and were found matching the experimental results. This showed that the analysis can provide improved results for SR fabricated CMUT devices by including the substrate supporting effect and the post bending effect.