Piezoresistance in Silicon at Uniaxial Compressive Stresses up to 3 GPa

Abstract

The room-temperature longitudinal piezoresistance of n-type and p-type crystalline silicon along selected crystal axes is investigated under uniaxial compressive stresses up to 3 GPa. While the conductance (G) of n-type silicon eventually saturates at ≈ 45% of its zero-stress value (G(0)) in accordance with the charge transfer model, in p-type material G/G(0) increases above a predicted limit of ≈ 4.5 without any significant saturation, even at 3 GPa. Calculation of G/G(0) using ab initio density functional theory reveals that neither G nor the mobility, when properly averaged over the hole distribution, saturate at stresses lower than 3 GPa. The lack of saturation has important consequences for strained-silicon technologies.

Piezoresistance in silicon and its nanostructures

“…As a result the π-coefficients can be significantly different when measured in compression or in tension. For example, recent measurements of the π-coefficients in compression 9,21,22 are up to a factor of 2 larger than Smith's values in p-type material and almost half of the values obtained by Smith for n-type material. Full band ab initio calculations from large compressive stress to large tensile stress support these experimental conclusions 23 .…”

“…In the simplest band-edge models, the PZR was predicted to saturate at high stress much like the n-type case 16 whereas solutions of the Boltzmann equation using the full band structure predict a much weaker, or even an absence of saturation, at least up to 4 GPa 17 . Recent experimental results along with ab initio band structure calculations demonstrate that the latter interpretation is probably correct 9 . The details of the longitudinal PZR along the <110> and the <111> crystal directions are of interest, both to engineers exploiting strained Silicon technology to increase the hole mobility 16 , but also because these are the most common orientations of Silicon nanowires where the largest PZR is claimed 18 .…”

“…This anti-crossing is extremely important for the PZR since the effective mass of holes in states near the anti-crossing is significantly different from either that of the heavy or the light holes. As the stress increases the anti-crossing moves out to higher wavevectors and into the tail of the hole distribution 9 . Below stresses of approximately 3 GPa there is still a non-negligible population of holes near this band anti-crossing and this results in very little drop off in the resistance change with applied stress in this range (see Fig.…”

Piezoresistance of nano-scale silicon up to 2 GPa in tension

“…These predictions and related experimental works 14,15 are usually carried out on 2 dimensional inversion layers of holes and electrons in MOSFETs, and is expected to be lower than for bulk volumetric transport. In a recent study, 16 a strain induced enhancement of $R 0 /R above theoretical expectations, up to 6.5, without any sign of saturation, was demonstrated on p-type bulk Si wafer under compressive stresses up to 3 GPa.…”

Hidden orbital polarization in diamond, silicon, germanium, gallium arsenide and layered materials

“…(Details on the exchange interactions between orbital moments can be found in, for example, refs 23,24) To illustrate the idea that the current-induced hidden orbital polarization can play a more important role than the hidden spin polarization, we looked into the current-driven antiferromagnetism of silicon under a 2% uniaxial compressive strain along the [001] direction, achievable in real experiments. 25,26 (Because silicon has many point group symmetries, an electric current in silicon does not generate site-dependent magnetization; however, a strain can result in current-induced magnetization by breaking some symmetries. 20 ) Although silicon may not be the best material for antiferromagnetic information technology applications, it is one of the simplest and most well-known materials, a good candidate for supporting our hypothesis.…”