Piezoresistance in p-type silicon revisited

Abstract

We calculate the shear piezocoefficient π44 in p-type Si with a 6×6 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 6×6 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 6×6 model that can be used to predict the piezoresistance effect in p-type silicon.