Temperature Dependence of the Piezoresistance of High-Purity Silicon and Germanium

Abstract

The change of resistance in uniaxial compression has been measured for a number of single-crystal specimens of high-re-resistivity $n$- and $p$-type germanium and silicon over the ranges 5\ifmmode^\circ\else\textdegree\fi{} to 350\ifmmode^\circ\else\textdegree\fi{}K (Ge) and 20\ifmmode^\circ\else\textdegree\fi{} to 350\ifmmode^\circ\else\textdegree\fi{}K (Si). For $n$-type material in the orientations giving the large effect---[110] for $n$-Ge and [100] for $n$-Si---the piezoresistance is, as predicted by theory, linear in ${T}^{\ensuremath{-}1}$ over most of the temperature range and with a small intercept. It is rather insensitive to impurity scattering. The departure from linearity in ${T}^{\ensuremath{-}1}$ due to the onset of intervalley scattering near room temperature is estimated theoretically; it appears to be just barely detectable for $n$-Ge. The small piezoresistance of [100]-oriented $n$-Ge varies little with temperature over most of the extrinsic range, again in accordance with theory. For $p$-Ge the results suggest that ideally pure material would show a piezo-resistance dominated by a ${T}^{\ensuremath{-}1}$ term for both [110] and [100] orientations. It is shown that this is to be expected theoretically, although the mechanism of piezoresistance for a degenerate band is more complicated than for a many-valley model. However, the results for $p$-type material are, as they should be, much more sensitive to impurity scattering, even the sign of the effect varying with the purity for [100] specimens. For $p$-Si no simple temperature dependence is found, presumably because the spin-orbit splitting of the bands is comparable with $\mathrm{kT}$. At temperatures low enough to condense most of the carriers onto impurity centers, the piezoresistance departs from linearity in ${T}^{\ensuremath{-}1}$ and varies from specimen to specimen. This behavior appears not to be due to impurity scattering; it may be caused in part by inhomogeneities. Surface conduction effects have been observed, but can be eliminated by etching. Neither Hall nor piezoresistance measurements reveal any detectable variation of the ionization energy of donors with strain. No departure of the piezoresistance from linearity in the applied stress has been observed.