Hole band nonparabolicity and effective mass measurement in p-SiGe/Ge heterostructures

Abstract

The effective mass is one of the key parameters governing the properties of two-dimensional carrier gases. Preferred methods for its determination are measurements of the temperature dependence of Shubnikov–de Haas (SdH) oscillations and of the cyclotron resonance frequency. In both methods the Landau level transition energy is determined at finite magnetic fields, while tacitly assuming the effective mass derived therefrom to equal the zero-field effective (density of states, DOS) mass. We show that in the presence of strong band nonparabolicity as in p-Ge/SiGe heterostructures, this assumption is not always justified. In this work the temperature dependence of theoretical SdH oscillations is explicitly simulated from the calculated Landau level structure, allowing us to determine theoretical masses in exact analogy to a SdH measurement. The calculations are performed within a 6 × 6 envelope function approximation (EFA). The same method is used to calculate the zero-field DOS mass. Our analysis shows that it is the pronounced nonparabolicity of the heavy hole band, leading to a nonlinear magnetic field dependence of Landau level energies, that invalidates the assumption of equal cyclotron and DOS masses. In particular, we show that at high carrier density the DOS mass is significantly underestimated in a SdH measurement.