Piezoresistive stress sensors for advanced semiconductor materials

In this work, the general theory of piezoresistivity both at a fixed reference temperature and at variable temperature has been presented and applied. The primary equations needed for designing test chip stress sensors on (100) and (111) silicon have been reviewed and expanded. The general piezoresistivity theory has also been applied to several alternative wafer orientations including (110), (112), and (115) silicon wafers, and general expressions for resistance changes experienced by in-plane resistors fabricated on these three types of silicon have been derived. In addition, the theory for several basic sensor rosette configurations fabricated on these alternative wafer planes have been presented.; Using symbolic algebra computations, the optimized silicon wafer orientation has been found where the most stress components can be measured in a temperature compensated manner. Also, the effects of wafer plane tilt for (100) and (111) silicon wafers on piezoresistive coefficient calibration have been studied. Piezoresistive theories for advanced semiconductor materials have also been investigated. In particular, theories have been established for 3C and 6H silicon carbide materials, which have been long proposed for high temperature microelectronic applications. The general equations for sensors fabricated on the (0001) 6H SiC wafer plane have also been derived. In addition, a strain based piezoresistive theory has been established and its relation to the stress-based sensor theory has been presented in detail. Also, the elastic constants of silicon have been measured using a simple electrical strain gage technique.; Finally, several techniques used for calibration of the piezoresistive coefficients have been investigated, and calibration fixtures for hydrostatic pressure and automated four-point bending have been designed and constructed. Furthermore, the hydrostatic pressure calibration technique has been applied to a number of test chip designs. The developed hydrostatic procedure also required the temperature coefficients of resistance (TCR) to be experimentally determined. Finally, nonlinear finite element stress analyses have been performed for various sizes of wafers under uniform pressure plate loading and various three dimensional die-on-beam structures under bending to provide appropriate stress distributions needed for wafer level and die-on-beam calibration techniques.