Fluctuation corrections to Lifshitz tails in disordered systems

Area of Science:

• Condensed Matter Physics
• Materials Science
• Semiconductor Physics

Background:

• Quenched disorder in semiconductors creates localized electronic states near the band edge.
• These states result in an exponential tail in the density of states.
• For high impurity densities, this tail follows a universal Lifshitz form driven by potential fluctuations.

Purpose of the Study:

• To derive analytical expressions and numerical values for the Lifshitz tail in a parabolic conduction band.
• To determine the exact fluctuation prefactor of the Lifshitz tail.
• To provide a revised result for the disorder band tail in two-dimensional systems.

Main Methods:

• Utilized a replica field integral approach to analyze the electronic states.
• Identified the instanton profile for the leading exponential scaling of the Lifshitz tail.
• Employed the Gel'fand-Yaglom formalism to compute the determinant of the fluctuation operator, avoiding full spectral calculations.

Main Results:

• Derived analytical expressions for the Lifshitz tail, including its exact fluctuation prefactor.
• Obtained numerical values for the Lifshitz tail in a parabolic conduction band.
• Presented a revised calculation for the disorder band tail in two dimensions.

Conclusions:

• The study successfully characterizes the Lifshitz tail in disordered semiconductors.
• The replica field integral and Gel'fand-Yaglom formalism provide a robust framework for analyzing disorder effects.
• The findings offer a more precise understanding of electronic states at the band edge in disordered materials.