Urbach tails in indium arsenide studied using nonequilibrium Green's functions

The analysis presented in this paper results in new formulas for the Urbach tail parameter, which are supposed to be valid for III-V compounds. They were derived based on numerical simulations performed with the nonequilibrium Green's function method applied to the multiband k <middle dot> p Hamiltonian of bulk material. The influence of static and dynamic disorders on the band tailing process was examined in relation to the scatterings of free carriers with longitudinal-optical (LO) phonons and ionized impurities. In this case, the disorder potentials just add to the unperturbed potential, which results in a perturbed density of states (DOS). The latter takes on exponential shape as a result of the superposition of sidebands, produced by the potential of the LO phonons. The Urbach parameter, which is the exponent of the perturbed DOS, is then proportional to the logarithm of the perturbation. This results in a modest temperature dependence of this parameter, which was observed for various III-V compounds. Moreover, the absolute values of the Urbach parameter, predicted by the present "scattering" approach, remain in reasonable agreement with experimental data reported in the literature. The range of doping densities studied extends to heavy ones; therefore, the results of this paper are crucial for addressing a current challenge in the semiconductor industry, namely the reduction of the subthreshold swing in tunneling field-effect transistors, which are considered potential future solutions for efficient, low-power logic switches.