Multi-Objective Optimization of a Ball Grid Array Using modeFRONTIER® and COMSOL Multiphysics®

H. Strandberg[1], T. Makkonen[2], and J. Leinvuo[2]
[1]ESTECO Nordic AB, Lund, Sweden
[2]VTI Technologies Oy, Vantaa, Finland

Capacitive MEMS (Micro-Electro-Mechanical Systems) accelerometers may be directly soldered to the printed circuit board by an array of solder balls. Differences in the thermal expansion coefficients of the pertinent materials cause deformations of the accelerometer under temperature change. This may cause a relative movement of the sensing masses with respect to the sensing electrodes, resulting in a change in capacitance and a false acceleration output. A multi-objective optimization was used to find the best location of the solder balls which minimized the measurement error under varying temperature and, at the same time, maximized the expected service life due to fatigue of the solder balls. While the achieved improvement in service life was moderate, an order of magnitude improvement was achieved for the predicted measurement error.