Simplified Analytical Damping Constant Model for Design of MEMS Capacitive Accelerometer With Gold Perforated Proof-Mass Structure

Abstract

This paper describes a simplified analytical model of a damping constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> to design a MEMS capacitive accelerometer using the multi-layer metal technology. The proposed model is introduced by combining the theoretical equation with the approximate form factor obtained by the measured data. In order to create the model, we fabricated several types of MEMS capacitive accelerometers with different structure parameters such as the etching hole area, the perforated proof-mass area, and the gap. The calculation results show that by the proposed model, the damping constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> was in accord with the measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> . We also confirmed that the relative error between the measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> and the damping constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> by the proposed model could be improved to one-half of the conventional model. Moreover, the Brownian noise <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}_{\text {N}}$ </tex-math></inline-formula> calculated by the proposed model was also consistent with the measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}_{\text {N}}$ </tex-math></inline-formula> . In addition, to confirm the suitability of the proposed model for CMOS-MEMS multi-physics simulation, we performed the simulation of the ring-down characteristics of a gold perforated proof-mass differential MEMS capacitive accelerometer. The simulated results suggested that the ring-down characteristics by the proposed model coincided with those of the measured data. Therefore, we verified that the proposed model would be effective for the analysis and the design of the MEMS capacitive accelerometer with the gold perforated proof-mass.