Phonon Energies in Germanium from Phonon-Assisted Tunneling

Abstract

The line shapes of the peaks in the bias dependence of the second derivative of the phonon-assisted tunnel current with respect to voltage were measured for Sb-doped germanium tunnel junctions between 4.2 and 1.15°K. The antimony concentration was 5×${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The phonon energies at the point $L$ in the Brillouin zone, determined to an accuracy of ±0.1%, are $E\left(\mathrm{TA}\right)=7.766\mathrm{}$, $E\left(\mathrm{LA}\right)=27.58\mathrm{}$, $E\left(\mathrm{LO}\right)=30.62\mathrm{}$, and $E\left(\mathrm{TO}\right)=36.15\mathrm{}$ in meV. This accuracy verifies the assumptions made in determining the pressure dependence of these phonon energies previously reported by the author. The major contribution to the line shapes is $\mathrm{kT}$ broadening. Minor contributions arise from a small bias dependence of the tunnel current per energy interval and from the phonon dispersion near $L$. Approximate values for the curvatures of the phonon spectrum at $L$ were determined. A lower limit of 1.6×${10}^{-11\mathrm{}}$ sec was found for the lifetimes of these phonons. From double phonon emission processes the energy of the optic phonon at $\Gamma$ was found to be 37.3±0.2 meV.