Tunneling Measurement of Electron-Plasmon Interaction in Degenerate Semiconductors

Abstract

The electronic proper self-energy due to electron-plasmon interactions in degenerate semiconductors has been evaluated using the random-phase approximation. This self-energy, together with elementary models of the barrier-penetration factor, is used to calculate the tunneling characteristics of rectifying metal contacts on the degenerate semiconductors. The calculations predict broad, doping-dependent resonances in $\frac{d^{2}I}{d{V}^2}$ at $\mathrm{}\left|\mathrm{eV}\right|\mathrm{}$, approximately equal to the plasmon energy $\hslash {\omega }_p$ in the semiconductor. In contrast to the analogous calculations for electron-phonon interactions, the major features of the predicted line shapes are due to quasiparticle renormalization (i.e., k dependence of the self-energy) rather than quasiparticle dispersion (i.e., $\epsilon$ dependence of the self-energy). Comparison of the model calculations with experimental data taken using indium contacts on selenium- and tellurium-doped GaAs, $2.1\times {10}^{18} {\mathrm{cm}}^{-3\mathrm{}}\le n\le 6.2\times {10}^{18} {\mathrm{cm}}^{-3\mathrm{}}$, show satisfactory agreement between the predicted and observed line shapes. The resonance structure in the experimental $\frac{d^{2}I}{d{V}^2}$ characteristics is identified independently with the plasmon energy in the GaAs electrode by correlation with the plasma minimum observed in the infrared reflectivity of the samples used in the tunneling measurements.