Interpretation of the Fermi Surface Warping in Narrow-Gap Semiconductors using A Simple Tight-Binding Model

Abstract

CdSnAs2 is a narrow-gap semiconductor belonging to the group of II-IV-V2 compounds with chalcopyrite structure, the closest electronic and structural analogs of the III-V compounds. Measurements of the angular dependences of the Shubnikov-de Haas (SdH) oscillation periods and electron effective masses in degenerate n-type CdSnAs2 samples have confirmed that the Fermi surface is an oblate ellipsoid of revolution around the [001] axis with eccentricity depending on electron concentration1). This ellipsoidal shape is expected on the basis of the four-level \(\mathop K\limits^ \to .\mathop P\limits^ \to\) model for chalcopyrites2), which is a generalisation of Kane’s three-band model to the case of pseudocubic semiconductors. Detailed investigations of the SdH effect as a function of the magnetic field direction in samples with electron concentrations n around 1018 cm-3, however, clearly show deviations from an ellipsoidal Fermi surface. For instance, for a sample with n = 2.7 X 1018cm-13 we observe an anisotropy of about 1.5 percent in the SdH period P when the magnetic field \(\mathop B\limits^ \to\) is rotated in the (001) plane. See Fig. 1. This angular dependence has to be attributed to warping of the Fermi surface. Note that the main anisotropy in P due to the eccentricity of the ellipsoid (\(\mathop B\limits^ \to\) in the (100) plane) is considerably larger than the warping anisotropy. Inclusion of higher-band interactions in the \(\mathop K\limits^ \to .\mathop P\limits^ \to\) model adopting the perturbation method of Lowdin3,4, as has been done in order to explain the warping of the Fermi surface of the III-V compounds HgSe and GaSb5), results in poor fits for our CdSnAs2 data even if one uses seven fitting parameters. In this paper we present a miodel to describe the geometry of the Fermi surface of CdSnAs2 including the warping. This model, which is inspired by methods described by Harrison in his book, has simplicity in common with the \(\mathop K\limits^ \to .\mathop P\limits^ \to\) model but needs no fitting parameters.