Piezoresistance of silicon and strained Si0.9Ge0.1

Journal of Applied Physics

Pedersen

Brandbyge

et al. 2008

Self Cite

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.

Section: Introductionmentioning

confidence: 99%

Piezoresistance in p-type silicon revisited

Journal of Applied Physics

Pedersen

Brandbyge

et al. 2008

Self Cite

“…5,6 Smith experimentally determined the three piezoresistance coefficients of lightly doped silicon. The piezoresistance coefficients for more heavily doped silicon were later experimentally determined by other research groups, 2,3 and still, today, the piezoresistance coefficients of silicon and other materials are topics of interest in both academia 4,7,8 and industry. The continued academic interest is partly due to the scarcity of reliable measurements and partly due to a discrepancy between theoretical models and available measurements especially for p-type silicon.…”

Section: Introductionmentioning

confidence: 99%

“…8,[15][16][17][18][19] In Refs. 16 and 18 an optical method is used to measure the deflection and curvature of the chip.…”

Section: Introductionmentioning

confidence: 99%

“…The main focus is to characterize the piezoresistivity of p-type silicon and other related semiconductor materials, e.g., Si under tensile strain 19 and compressively strained SiGe. 8 In this paper, we present measurements of the piezocoefficient 44 in p-type silicon with several different doping concentrations in the temperature range T = 30-80°C as an example of use of the setup. Boron doped silicon is the preferred piezoresistive material in commercial micro electromechanical systems ͑MEMS͒ due to the large piezocoefficient 44 ration, these piezocoefficients result in a high sensitivity of the MEMS device, since the effective longitudinal and transverse piezocoefficients are large and almost matched in magnitude but of opposite sign.…”

Section: Introductionmentioning

confidence: 99%

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Four point bending setup for characterization of semiconductor piezoresistance

Review of Scientific Instruments

Arnoldus

Hansen

et al. 2008

Self Cite

We present a four point bending setup suitable for high precision characterization of piezoresistance in semiconductors. The compact setup has a total size of 635cm3. 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 π44 in p-type silicon at three different doping concentrations in the temperature range from T=30°CtoT=80°C. The extracted piezocoefficients are determined with an uncertainty of 1.8%.

“…6,7 However, use of silicon with grown-in biaxial strain for piezoresistive sensing purposes, where higher accuracy is needed since piezoresistance is the primary effect, has not yet received much attention, and only few experimental results exist. 8 In this paper we study theoretically the piezoresistivity of p-type silicon with grown-in biaxial strain by calculating the change in transport properties of the material in response to a small additional shear stress.…”

mentioning

confidence: 99%

Engineering piezoresistivity using biaxially strained silicon

Pedersen

Applied Physics Letters

Brandbyge

et al. 2008

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.