Polarons in Degenerate Semiconductors

The second-order self-energies of an electron in a degenerate Fermi gas arising from polar coupling to longitudinal optic phonons and from both piezoelectric and deformation-potential coupling to (Debye) acoustic phonons are evaluated exactly and analytically. Numerical calculations of the resulting density of states for optical phonons exhibit logarithmic singularities at the Fermi energy μ and at μ+ω₀. Similar structure due to the electron's interaction with acoustical phonons is exhibited by the proper self-energy but is smoothed out in the density of states by the nonvanishing imaginary part of the self-energy. The singularities at the Fermi surface are removed by the random-phase-approximation screening of the electronphonon interaction due to mobile charge carriers. These results indicate that several proposed explanations for low-bias conductance anomalies in tunnel diodes are inapplicable.