Research On The Thermal Stability Of Capacitive Microaccelerometer

As a kind of MEMS accelerometers, capacitive microaccelerometers (CMA) have been widely applied in internet of things, mobile communication, inertial navigation, and so on. The thermal stability of CMA refers to their ability of performances against environmental temperature change. It is characterized by the Bias Thermal Drift (BTD) and the Scale Factor Thermal Drift (SFTD) which represent the temperature sensitivities of bias and scale factor respectively. Thermal stability has a strong impact on the accuracy of CMA, and is one of the key factors to determine whether CMA can be applied into high-end system, such as inertial navigation system. Therefore, in order to design CMA with better thermal stability, it is significant in both theory and practice to develop the thermal stability model (especially analytical model) and investigate the critical factors affecting thermal stability thoroughly.To develop the analytical thermal stability model contains two main parts. One is to establish the analytical thermal deformation model for MEMS Die Attaching Structure (MDAS), and another one is to establish the analytical computational method for the bias and scale factor. The analytical thermal deformation model for MDAS also lays a foundation for the analytical thermal stability model of many other MEMS devices. In this paper, the analytical thermal deformation model for MDAS, as well as the analytical methods for calculating bias and scale factor, are established firstly; the analytical thermal stability model for CMA is then established, and further more the critical factors affecting thermal stability are analyzed thoroughly; finally an improving structure of CMA with much better thermal stability is proposed, and its good performances are verified by experiments.To establish the analytical thermal deformation model for MDAS, the variational principle is employed to deduce the high-order differential equations for MDAS, and the analytical solution of differential equations is then obtained. The analytical model has two advantages:first, the accurate calculation for the thermal deformation is achieved through modeling the shear deformation in MDAS as second-order shear deformation; second, the computational cost is reduced because the high-order differential equations are solved analytically based on Fourier series. With the analytical model, the factors affecting the interfacial thermal stress and the thermal deformation of the substrate are analyzed. The results show that the interfacial thermal stress is mainly affected by the elastic modulus of adhesives, and the thermal deformation of the substrate is affected both by the elastic modulus of adhesives and the substrate thickness.According to the detection principle of CMA, the analytical computational method for bias and scale factor are derived based on both Parallel Plate Capacitance Model (PPCM) and Conformal Mapping Capacitance Model (CMCM). With PPCM, the analytical formulas of bias and scale factor are obtained and the formulas allow one to carry out the analysis quantitatively and qualitatively. The method based on CMCM has higher accuracy and can be utilized to carry out the analysis quantitatively.Combing the analytical thermal deformation model for MDAS with analytical method for calculating the bias and scale factor, two analytical thermal stability models are established, named as Parallel Plate Thermal Stability Model (PPTSM) and Conformal Mapping Thermal Stability Model (CMTSM) respectively. Compared to CMTSM, PPTSM has the analytical formulas for BTD and SFTD, so can indicate the critical factors affecting thermal stability clearly. However, the accuracy of CMTSM is higher. The computational efficiency of the two analytical models are very high, so they handle the complexity and low efficiency in thermal stability analysis, which are caused by the thermal-mechanical-electrical coupling of thermal stability. By the two analytical models, the critical factors affecting the thermal stability are analyzed thoroughly. The results show that BTD is mainly caused by the thermal deformation, which has certain relationship with the fabrication errors, the location of the anchor of proof-mass, the elastic modulus of adhesives and substrate thickness. SFTD is composed of two parts. The first part is mainly determined by the temperature coefficient of elastic modulus of silicon, and the second part is caused by the thermal deformation. These two parts have opposite signs, and the absolute value of first part is lower than that of second part. The second part of SFTD is affected by the location of the anchor of the fixed comb lingers, the ratio between wide gap and narrow gap, finger width, elastic modulus of adhesives and substrate thickness.Based on the analysis results of the thermal stability, an improving structure of CMA is designed to improve the thermal stability. In the improving structure, BTD is reduced by middle-locating the anchor for proof-mass. The second part of SFTD is reduced by reducing the length of the anchor for fixed fingers in sensitive direction, and the total SFTD is passively compensated by making the two parts of SFTD cancel each other partly. Experimental samples of CMA are fabricated and tested to verify the analysis results of thermal stability and the efficacy of the improving structure. The average value of BTD is reduced from 1.85mg/℃ to 0.52mg/℃, and the average value of SFTD reduced from 162.7ppm/℃ to 50.8ppm/℃.