First-order piezoresistance coefficients in heavily doped p-type silicon crystals

Kozlovskiy, S. I.; Nedostup, V.V.; Boǐko, I. I.

doi:10.1016/j.sna.2006.03.009

Cited by 19 publications

(13 citation statements)

References 11 publications

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“…It is, however, an experimental fact that it severely underestimates the piezocoefficient 44 at high doping levels; this is very important since optimization of piezoresistive sensors for low 1 / f noise favor the use of high doping levels. 9 Recently, Kozlovskiy et al 10 carried out a detailed analytical study of piezoresistance in p-type silicon using analytical valence band models of varying complexity, derived from Pikus and Bir, 11 combined with a power law model for momentum relaxation time, as was also used in previous works. [12][13][14] Approximations to the valence band structure valid close to the top of the valence band were used in Refs.…”

Section: Introductionmentioning

confidence: 99%

Piezoresistance in p-type silicon revisited

Richter

Pedersen

Brandbyge

et al. 2008

Journal of Applied Physics

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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.

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Section: Introductionmentioning

confidence: 99%

Piezoresistance in p-type silicon revisited

Richter

Pedersen

Brandbyge

et al. 2008

Journal of Applied Physics

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“…͑3͒, only the effect of the stress xx was considered. However, if all in-plane stress components are included, we obtain a relative resistance change ⌬R / R of In p-type silicon, the piezocoefficient 44 is much larger than 11 and 12 , i.e., ͉ 11 / 44 ͉Ϸ0.8% and ͉ 12 / 44 ͉Ϸ4.3%. 1 Moreover, the maximum value of the shear stress in the chip was measured to be 3.6% of xx .…”

Section: H Discussionmentioning

confidence: 99%

“…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. [9][10][11][12] Essentially, the piezoresistance effect is a change in the resistivity tensor ͑second order͒ caused by an applied stress. 13 The effect is characterized by a fourth order piezoresistivity tensor, which, in the case of silicon due to symmetry, has three independent coefficients.…”

Section: Introductionmentioning

confidence: 99%

Four point bending setup for characterization of semiconductor piezoresistance

Richter

Arnoldus

Hansen

et al. 2008

Review of Scientific Instruments

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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%.

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“…Especially this interaction should be taken into account at high uniaxial strains when the strain induced shifts in energy of the sub-bands are comparable with energy of the SO sub-band in the unstrained state SO = 0.044 eV [17]. At high elastic strains an adequate description of the dispersion law of holes could be obtained in frame 6 × 6 model of the valence band [17][18][19].…”

Section: Dispersion Lawmentioning

confidence: 99%

“…In this case the dispersion law of holes in the v-th sub-band could be written in the following form [19] …”

Section: Dispersion Lawmentioning

confidence: 99%

Piezoresistive effect in p-type silicon classical nanowires at high uniaxial strains

Kozlovskiy

Sharan

2011

J Comput Electron

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The longitudinal piezoresistance of the p-type silicon nanowires oriented along the 100 , 110 and 111 crystallographic directions is examined at high uniaxial compressive and tensile elastic stresses ∼1 GPa. The detail research on base of the six-band model of the valence band involves quantum kinetic approach to calculation of the kinetic coefficients (conductivity, mobility) in classical nanowires with diameter that is significant higher the de Broglie wavelength of the band carriers. Two mechanisms of scattering (charged impurities and longitudinal acoustic phonons) are investigated. Qualitative agreement has been reached between calculated and known experimental data. A quantitative agreement with experiment is obtained in assumption about a formation of the stress concentration (stress raisers) in regions of nanowires that are depleted by the band carriers.

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First-order piezoresistance coefficients in heavily doped p-type silicon crystals

Cited by 19 publications

References 11 publications

Piezoresistance in p-type silicon revisited

Piezoresistance in p-type silicon revisited

Four point bending setup for characterization of semiconductor piezoresistance

Piezoresistive effect in p-type silicon classical nanowires at high uniaxial strains

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