Piezoresistive sensors for measurement of thermally-induced stresses in microelectronics
The general theory of conduction in a piezoresistive material subjected to temperature change is derived and the basic equations needed to design and apply test chips for thermal stress measurement are established. A general expression is obtained for the resistance changes which occur in an arbitrarily oriented 1D filamentary conductor subjected to general 3D stress states and arbitrary temperature changes. The derived formula is valid for crystals such as silicon which have cubic symmetry and diamond lattice structures. Basic equations are presented for the resistance changes experienced by stressed in-plane resistors fabricated on (100) silicon wafers. The established theory is applied to a simple two-element sensor rosette. A test chip containing this rosette configuration is designed and fabricated, and a suitable calibration system is constructed.