Piezoresistance in p-type silicon revisited

Abstract

We calculate the shear piezocoefficient 44 in p-type Si with a 6 ϫ 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 ͑001͒ 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 ͑TB͒ model. The magnitude of the 44 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 ϫ 6 Hamiltonian model shows good agreement between the absolute value of 44 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 ϫ 6 model that can be used to predict the piezoresistance effect in p-type silicon.

Piezoresistivity of thin film semiconductors with application to thin film silicon solar cells

“…Band structure calculations with the k Á p method [34] have shown that there is a strong decrease of effective conductivity mass with compressive stress which is in good agreement with the observation that the longitudinal gauge factor is positive. The effective mass is however just a part of the picture and to have a more complete explanation of piezoresistivity in p-type silicon, scattering mechanisms must be taken into account [35].…”

Thermal-Performance Instability in Piezoresistive Sensors: Inducement and Improvement

“…The dependence of piezoresistive coefficient on temperature and doping concentration is firstly reported by Kanda with the help of theoretical work and detailed experiments [38]. In the model of Kanda, the coefficient can be calculated by multiplying a piezoresistive factor, P(N A ,T) , with the piezoresistive coefficient at the temperature of 300 K. Then, a more particularly useful fitting function of piezoresistive factor for π 44 is proposed by Richter as [50,51]: $Pfalse(N_{\mathrm{A}},\mathrm{normal\Theta }false)={\mathrm{\Theta }}^{-\vartheta }{\left[1+{\left(\frac{N_{\mathrm{A}}}{N_b}\right)}^{\tau }{\mathrm{\Theta }}^{-\upsilon }+{\left(\frac{N_{\mathrm{A}}}{N_c}\right)}^{\lambda }{\mathrm{\Theta }}^{-\eta }\right]}^{-1}$ where N A is the doping concentration, Θ = T / T 0 and T 0 = 300 K. Other symbols in Equation (11) are the fitting items which can be found in [51], and the fitting results are shown in Figure 6 together with normalized piezocoefficient values calculated using the 6 × 6 k·p Hamiltonian model. P ( N A , Θ ) is larger at lower doping concentration, giving rise to a higher measurement sensitivity.…”

“…Fitted piezoresistive factor for π 44 as a function of doping concentration and temperature; Reprinted from [51], with permission of AIP Publishing.…”

On the Feasibility of a New Approach for Developing a Piezoresistive 3D Stress Sensing Rosette

“…Also, they presented analytical and experimental studies for the firstand second-order piezoresistive coefficients in both p-type and n-type silicon [17]- [21]. Other theoretical modeling of the piezoresistive effect was introduced by Kozlovsky et al [22], Toriyama et al [23] and Richter et al [24]. Temperature coefficient of resistance in silicon was studied by Bullis et al [25] and Norton et al [26].…”