Limitations of Drude model in determining plasma properties for multivalley semiconductors: a case study with Ge1-xSnx alloy

Classical Drude model has long been employed to study the plasma behavior of metals. The model has also been used for semiconductors to obtain the expressions for plasma frequency and carrier-induced changes in refractive index and absorption in terms of effective mass, transport relaxation time, and mobility of the carriers. However, these expressions remain invalid for semiconductors in which carriers occupy different valleys, as in strained SiGe alloys, GeSn alloys, and even in GaAs or InP under high electric field. We modify Drude equations for occupancy of two valleys by electrons and show deviations from standard textbook expressions. The conditions for recovering known expressions are then established. To illustrate, we consider unstrained GeSn alloys over the range 0 < x < 0.2 in which L and Γ conduction band valleys cross positions at x = 0.08 resulting in a crossover from indirect to direct nature of the band gap. A comparison is made between the present values with values obtained previously.