Analytical study of temperature coefficients of bulk MEMS capacitive accelerometers operating in closed-loop mode

Abstract In this work, the temperature coefficients of capacitive accelerometers operating in closed-loop mode, namely the temperature coefficient of bias (TCB) and temperature coefficient of the scale factor (TCSF), are studied analytically. They are modeled based on the working principle of the sensor and the effects of the thermal deformation on capacitance. The modeling analysis shows that TCB is caused by a rigid displacement of the proof-mass induced by thermal deformation. As such, several methods were proposed to decrease TCB, such as soft die-attaching, middle-located anchors for movable electrodes, and flexible supporting beams. The modeling analysis also shows that variations of the capacitive gap induced by thermal deformation is a critical factor which causes TCSF. However, the temperature dependence of the stiffness of the supporting beam plays no role on TCSF because the inertial force is balanced by the electrostatic force rather than the spring force. Therefore, TCSF can be reduced significantly as long as the thermal deformation is fully suppressed, such as by soft die-attaching and middle-located anchors for fixed electrodes. In addition, the decrease in susceptibility of the electrostatic force to the variation of the gap can also decrease TCSF. Finally, the analysis on TCB and TCSF are both verified by a group of experiments on packaged accelerometers mounted on PCB circuits.