Electronic structure of SnxGe1−x alloys for small Sn compositions: Unusual structural and electronic properties

Abstract

The full potential augmented plane wave plus local orbital method using the local density approximation within the framework of density functional theory is applied to investigate structural, electronic, and thermodynamic properties of SnxGe1−x alloys for small Sn compositions (x=0.0625, 0.125, 0.1875, and 0.25). For the structural properties, we found strong deviation from Vegard’s law for the variation in the lattice parameter, moreover, this deviation is found positive as found experimentally. This feature is in direct contrast with conventional IV-IV alloys, were the deviation of the variation in the lattice parameter from Vegard’s law is generally weak and negative. The calculated bond lengths of Sn–Ge, also show significant departures of bond lengths from the virtual crystal approximation (VCA). The calculations confirm a strong band gap reduction in Ge. For small Sn incorporation, the calculated optical band gap bowing (i.e., bowing of the direct band gap) is found strongly composition dependent. For small Sn composition (x=0.0625), we found a strong optical band gap bowing of 2.9 eV, in very good agreement with the measured values at low Sn composition of 2.8 eV of [He and Atwater, Phys. Rev. Lett. 79, 1937 (1997)] and 2.84 eV of Pérez Ladrón de Guevara et al. [Appl. Phys. Lett. 91, 161909 (2007)]. For small composition regime (0<x<0.1875) we found an optical band gap bowing of 1.9 eV again in good agreement with the measured value of 1.94 eV at room temperature. For the indirect band gap at L point, a bowing of 0.90 eV is found in agreement with the measured value of 1.23 eV. Regarding the local environment of the Sn atoms, we notice that the clustering has a strong influence on the direct band gap; the maximal (minimal) Sn-clustered configurations have the highest (lowest) band gap. From a detailed analysis of the physical origin of the optical band gap bowing, we found that the relative contribution of the three components [volume deformation (VD), charge exchange, and strain] show that the most significant effect is the structural one (relaxation and VD) due to the large mismatch of the lattice constants of Sn and Ge (∼15%). Our results show that the change from indirect to direct band gap occurs at ∼0.105 in perfect agreement with the measured value of 0.1. Our value for the critical composition is found lower than the value predicted by the VCA (∼0.20). Finally, we found that the instability of SnGe alloys is basically dominated by a strong charge transfer between Sn and Ge, leading a positive chemical energy, this instability is amplified by positive strain energy. The relatively weak negative structural energy is not enough to stabilize the SnGe alloys.