Electron transport and pressure coefficients associated with theL1CandΔ1Cminima of germanium

Hall-effect and resistivity measurements have been made on n-type and ultrapure germanium. The n-type material was characterized by measuring the electron mobility ${\mu }_L$ as a function of temperature down to 100 K at atmospheric pressure. At high pressure, the band structure of germanium becomes similar to that of silicon at atmospheric pressure, making the ${\Delta }_{1C}$ minima accessible to direct electrical investigation. In this siliconlike structure, the electron mobility ${\mu }_{\Delta }$ was found to increase with temperature T from 800 ${\mathrm{cm}}^2$ ${\mathrm{V}}^{\mathrm{-}1}$ ${\mathrm{S}}^{\mathrm{-}1}$ at 300 K according to $T^{\mathrm{-}2.7}$, indicating that intervalley scattering dominates as in silicon. This contrasts with electron scattering in the $L_{1C}$ minima which is dominated by deformation potential intravalley scattering. An analysis with the values $m_t^{\mathrm{*}}$=0.288 and $m_l^{\mathrm{*}}$=1.353 gave intervalley coupling constants of 3.7×${10}^8$ and 2.9×${10}^8$ eV ${\mathrm{cm}}^{\mathrm{-}1}$ for the 430-K (LO) and 320-K (LA) phonons, respectively. Having established ${\mu }_L$ and ${\mu }_{\Delta }$, the resistivity ρ was measured as a function of pressure in ultrapure material at 300 K. It was found to increase exponentially below 25 kbar where the material was n type corresponding to ${\mathrm{dE}}_L$/dP=(4.8±0.2)×${10}^{\mathrm{-}6}$ eV ${\mathrm{bar}}^{\mathrm{-}1}$. A p- to n-type transition was observed and beyond 35 kbar, where the material was p type, the resistivity decreased exponentially corresponding to ${\mathrm{dE}}_{\Delta }$/dP=-(2.4±0.4)×${10}^{\mathrm{-}6}$ eV ${\mathrm{bar}}^{\mathrm{-}1}$. With the effective-mass values given above, best overall fit was obtained with Δ$E_{L?(\mathrm{hy}\Delta }$=0.21±0.01 eV at atmospheric pressure.