A computationally practical approach to simulating complex surface-micromachined structures with fabrication non-idealities

Abstract

The objective of this work was to develop methods which would allow the electromechanical analysis of a Microelectromechanical System (MEMS) structure with the level of complexity of a practical, high-volume manufacturable sensor while avoiding computationally impractical models. Two methods were developed. One was a simple analysis method in which the ideal structure was assumed. This allowed prediction of the stability and the effects of structure misalignment on a surface-micromachined ac,:elerometer. However, the simple method is limited bccause the actual structure has fabrication induced non-idealities, such as warpage, which can cause the simple method to be significantly in error. The second method discarded the ideal structure assumption and analyzed the non-ideal structure via a self-consistent analysis. This method is based on the calculation of an intermediate look-up table from which the electrostatic forces are obtained directly from the position of the moving mass, greatly reducing computation time and memory requirements in comparison to a standard self-consistent electromechanical analysis scheme. Using this lumped-model self-consistent scheme, we analyzed an Analog Devices, Inc. ADXL50 accelerometer including fabrication non-idealities (warpage, overetching, residual stress, etc.). For this structure the lumped-model self-consistent analysis method reduced the required number of electrostatic analysis discretization panels by a factor of about 100. Computation times were typically 5-7 hours instead of a predicted time of more than a month for a standard self-consistent electromechanical analysis scheme. Further, memory requirements for the standard method would have significant,ly exceeded practical limitations. The electromechanical resonant frequency was measured for several ADXL50 accelerometers and compared to t,he simulat,ion results showing good agreement.