SiSn Electronic Band Structure Modelling Using Density Functional Theory for Optoelectronic Applications

Abstract

Abstract Body: Investigation of new group IV alloys to find a direct bandgap material that can emit and detect light efficiently has been pursued by Si photonics in the past decades. The integration of optoelectronics on the electronics chips enables high-speed data transfers through emitters and detectors that are compatible with Si technology 1. Although GeSn has been shown as a group IV that can achieve the above-mentioned goals by different groups 2, other alloys of group IV have not been yet fully investigated due to technical challenges such as insolubility, lattice mismatch, unavailability of proper precursor, etc. Theoretical calculations show that SixSn1-x alloys can also be a direct bandgap material like GeSn with the difference of having a larger bandgap due to high direct band edge of Si at 3.2 eV (Γ-valley)3. However, the theoretical study of this material is not well developed. The estimation of Sn concentration needed to achieve direct bandgap varies in the range of 40-60% while the experimentalist are expecting that to be in the 25% range.3 In this paper we have studied both material properties as well as electronic band structure using density functional theory (DFT) calculations. We have adopted generalized gradient approximation- Perdew–Burke–Ernzerhof (GGA-PBE) 4 with Vienna Ab-initio Simulation Package (VASP).5 The 16-atom cubic supercells of Si and Sn, as well as the unit cell, were used in this modeling in order to find the atomic configurations and energetics. The supercells were relaxed for all the atoms with a residual force of less than 5 × 10−5 eV/Å for each atom. A (4×4×4) Monkhorst−Pack mesh of k-points for a periodic 16-atom supercell was adopted to generate the Brillouin zone. We calculated the lattice constant and its formation energy for all compositions using the GGA–PBE exchange-correlation potential considering the structural relaxation of an isotropic stress for the supercell. The change in the lattice follows the Vegard’s law and a slight bowing (=0. 05 Å) is observed across the full range which is close to previously reported values 0.02-0.084 Å 3, 6 . The lattice constants of Si and α-Sn were estimated to be 5.47 and 6.65 Å, respectively. These values are in close agreement with previously reported values of 5.47Å for Si7 and 6.65–6.74 Å for α-Sn 8 using a similar modeling method of GGA–PBE. It is noteworthy that compared to other group IV binary alloys such as SiGe and GeSn, the proposed bowing parameter is slightly lower. The band structure of all compositions of SixSn1-x is calculated for both unit cell and supercell of 16 atoms. The electronic properties of the alloys are affected by the displacement of Si1-xSnx atoms; therefore, structural relaxation of the structures plays an important role in the band structure. These structures were relaxed to a high extent as stated above. Since the GGA-PBE method underestimates the bandgap of SixSn1-x alloys, different methods have been applied to bring the calculations closer to the real bandgap. In our calculations, we have included the valence band offset of SixSn1-x alloys. The valence band offset is attributed to the electronic interaction between the occupied and unoccupied orbitals of Si1-xSnx. Therefore, by considering an Sn dependent valence band offset as well as heavy, light, and split-off hole bands, the calculations are closer to the real bandgaps. More details of the material properties along with the electronic band structure calculations will be presented at the conference.