Modeling of the disorder contribution to the band-tail parameter in semiconductor materials

In this paper, we present a quantitative and analytical formulation of the disorder contributions to the band-tail parameter model in semiconductor materials with Urbach exponential behavior, which arise from the influence of the bulk and grain boundary trap concentration and strain. We based our calculation on the Halperin-Lax model combined with a recent model that considered the tail parameter E₀ as the sum of interactive and disorder contributions. The resulting formulation converged to the Dow-Redfield model, which supports its validity. Our theory, applied to experimental data, yields bulk-defect and grain-boundary trap concentrations in good agreement with reports for mono- and polycrystalline semiconductors. Our model can describe wholly the band-tail parameter of any semiconductor.