Jacob Richter

Piezoresistance in p-type silicon revisited

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 ...

Four point bending setup for characterization of semiconductor piezoresistance.

We present a four point bending setup suitable for high precision characterization of piezoresistance in semiconductors. The compact setup has a total size of 635 cm(3). Thermal stability is ensured by an aluminum housing wherein the actual four point bending fixture is located. The four point bending fixture is manufactured in polyetheretherketon and a dedicated silicon chip with embedded piezoresistors fits in the fixture. The fixture is actuated by a microstepper actuator and a high sensitivity force sensor measures the applied force on the fixture and chip. The setup includes heaters embedded in the housing and controlled by a thermocouple feedback loop to ensure characterization at different temperature settings. We present three-dimensional finite element modeling simulations of the fixture and discuss the possible contributions to the uncertainty of the piezoresistance characterization. As a proof of concept, we show measurements of the piezocoefficient pi(44) in p-type silicon at three different doping concentrations in the temperature range from T=30 degrees C to T=80 degrees C. The extracted piezocoefficients are determined with an uncertainty of 1.8%.

Engineering piezoresistivity using biaxially strained silicon

We calculate the shear piezocoefficient of p-type silicon with grown-in biaxial strain using a 6×6 k⋅p method. We find a significant increase in the value of the shear piezocoefficient for compressive grown-in biaxial strain, while tensile strain decreases the piezocoefficient. The dependence of the piezocoefficient on temperature and dopant density is altered qualitatively for strained silicon. In particular, we find that a vanishing temperature coefficient may result for silicon with grown-in biaxial tensile strain. These results suggest that strained silicon may be used to engineer the piezoresistivity to enhance the performance of piezoresistive stress sensors.