  High-doping induced Urbach tails and band gap narrowing play a significant
role in determining the performance of tunneling devices and optoelectronic
devices such as tunnel field-effect transistors (TFETs), Esaki diodes and
light-emitting diodes. In this work, Urbach tails and band gap narrowing values
are calculated explicitly for GaAs, InAs, GaSb and GaN as well as ultra-thin
bodies and nanowires of the same. Electrons are solved in the non-equilibrium
Green's function method in multi-band atomistic tight binding. Scattering on
polar optical phonons and charged impurities is solved in the self-consistent
Born approximation. The corresponding nonlocal scattering self-energies as well
as their numerically efficient formulations are introduced for ultra-thin
bodies and nanowires. Predicted Urbach band tails and conduction band gap
narrowing agree well with experimental literature for a range of temperatures
and doping concentrations. Polynomial fits of the Urbach tail and band gap
narrowing as a function of doping are tabulated for quick reference.
