Analysis of piezoresistance in p-type silicon for mechanical sensors

Typical p-type silicon mechanical sensors are designed to operate under temperature range from similar to173 K to similar to373 K and subjected to stress less than similar to100 MPa. The operation range is mainly restricted by the electrical and mechanical properties of silicon. The authors have derived an approximate piezoresistance equation valid for typical operation range of the p-type silicon mechanical sensors, from valence band model of Bir and Pikus taking into account the spin-orbit interaction. The piezoresistance in p-type silicon was analyzed based on hole transfer and conduction mass shift due to stress. These mechanisms were originally introduced by Suzuki et al. to interpret piezoresistance in p-type silicon, based on the valence band equation in the vicinity of k = 0. Under the typical operation range for p-type silicon mechanical sensors, holes are located where the value of k is relatively large, i.e., off k = 0 and degenerate band split due to stress is incomplete. Compared to previous literature, the hole behavior in the valence band was much improved and is compatible with the typical operation range for p-type silicon mechanical sensors. The shear piezoresistance coefficient pi(44) was calculated as a function of temperature (173 K to 373 K) and impurity concentration (10(18) cm(-3) to 10(21) cm(-3)).