Piezoresistance in p-type silicon revisited

Abstract

We calculate the shear piezocoefficient π44 in p-type Si with a 6x6 k·p Hamiltonian model using the Boltzmann transport equation in the relaxation-time approximation. Furthermore, we fabricate and characterize p-type silicon piezoresistors embedded in a (001) silicon substrate. We find that the relaxation-time model needs to include all scattering mechanisms in order to obtain correct temperature and acceptor density dependencies. The k·p results are compared to results obtained using a recent tight-binding (TB) model. The magnitude of the π44 piezocoefficient obtained from the TB model is a factor of 4 lower than experimental values; however, the temperature and acceptor density dependencies of the normalized values agree with experiments. The 6x6 Hamiltonian model shows good agreement between the absolute value of π44 and the temperature and acceptor density dependencies when compared to experiments. Finally, we present a fitting function of temperature and acceptor density to the 6x6 model that can be used to predict the piezoresistance effect in p-type silicon. © 2008 American Institute of Physics.