Piezoresistance ofn-Type Magnesium Stannide

Abstract

The piezoresistance tensor components for $n$-type ${\mathrm{Mg}}_2$Sn have been measured from 50-300°K. The piezoresistance effect in ${\mathrm{Mg}}_2$Sn is larger than the piezoresistance effect in germanium or silicon. From these measurements and the elastic constants reported by Davis et al, the elastoresistance tensor components were obtained and found to satisfy the conditions $m_{11}=-2\mathrm{}{m}_{12}$, $m_{11}$ large, and $m_{44}$ small, in the temperature range 50-200°K. These relationships confirm that $n$-type ${\mathrm{Mg}}_2$Sn is a many-valley semiconductor with constant-energy ellipsoids in the $〈100〉$ directions. The fact that $m_{11}$ and $m_{12}$ were both linear in the temperature range 60-175°K indicates that intervalley scattering is unimportant in the extrinsic temperature region. The small value of the volume coefficient, $\frac{1}{3}(m_{11}+2\mathrm{}{m}_{12})$, indicates that carrier mobility in $n$-type ${\mathrm{Mg}}_2$Sn is relatively insensitive to changes in sample volume. The deformation potential was determined from a combination of these piezoresistance results and Umeda's magnetoresistance data, and was found to satisfy the relation ${\Xi }_u={{\Xi }_u}^0(1+\alpha T)$, where ${{\Xi }_u}^0=10.1\mathrm{}$ eV and $\alpha =\left[\right(-4.3\mathrm{}\pm 0.6)\times {10}^{-4\mathrm{}}]°$ ${\mathrm{K}}^{-1\mathrm{}}$. High-stress piezo-resistance measurements yielded a deformation potential of ${\Xi }_u=18\mathrm{}$ eV and mobility anistropy of $K=2.65\mathrm{}$ at 77.4°K. Umeda obtained $K=3.51\mathrm{}$. A possible qualitative explanation of these differences can be given in terms of a change with stress of the position of the donor levels with respect to the conduction band.