Optical Properties and Band Structures of Strained Ge:C

Abstract

Abstract Body: Dilute germanium carbides (Ge:C) are promising optical materials for active silicon photonics since they can be grown directly on Si at temperatures compatible with post-metal CMOS fabrication. Although Ge and diamond-lattice C both have an indirect bandgap, substitution of ~1% C into Ge creates a direct bandgap suitable for lasers and modulators. However, there is disagreement in the literature about whether C creates a true direct bandgap or merely a pseudo-direct bandgap in which symmetry prevents optical emission even at Gamma (k=0). In this work, we studied the effects of strain and defects on the optical properties of Ge:C using ab initio techniques. We find Ge:C is similar to other highly mismatched alloys such as GaAs1-xNx in many ways, but it also presents several curious differences. The Vienna Ab initio Simulation Package (VASP) was used to model 128 atom supercells of Ge:C with different periodicities, as well as 128 atom supercells with a single Ge vacancy. The use of HSE06 hybrid functionals provided good agreement with experiment in both the direct and indirect bandgaps in unstrained Ge. To study whether periodic boundary conditions artificially affected the results, supercell lattice vectors were varied; the center of each supercell might align with the face, edge, or vertex of the next supercell. This changed the spacing between C atoms in different directions, mimicking a random alloy at a far lower computational cost than doubling the supercell sizes. Other groups have reported that the new conduction band edge created by C is dominated by indirect (L) states. We found instead that the conduction band splits into two bands, E- and E+, that are similar to each other (consistent with band anticrossing, BAC) but retain a predominantly Ge Γ character. The optical transitions in Ge:C are comparable with those of the direct bandgap transition (Γ) in Ge. Spectral weights after band unfolding show comparable or more weight at Γ than L for both E+ and E- states. We also ran a few validation jobs with spin-orbit coupling, compressive strain, or harder Ge potentials, and these all showed similar results. In particular, the band-to-band optical transition strength in Ge:C is within a factor of 2 of that in Ge, and it is comparable with common III-V materials currently used for lasers. We found that the pressure dependence of the band structure can be highly misleading when trying to interpret band identities. In particular, the E- band shifts with strain almost identically with the Ge CB L valley, but this is pure coincidence. Instead, the slow shift with strain comes from a carbon “defect” state near EVB+0.79 eV that varies relatively slowly, more or less tracking the vacuum level rather than the conduction band edge, unlike traditional impurity states. Because the C “defect” state is so close to the native Ge direct bandgap (0.80 eV), the splitting in bands is very strong, driving the direct bandgap more than 0.2 meV below the indirect L valley. This agrees with the deep state model of Hjalmarson and Dow and BAC models near Γ. However, BAC fails to explain the bands away from k=0, and it also does not explain the appearance of a third CB state between the E+ and E- bands. In summary, these results strongly support the development of Ge:C as a strongly optically active material for silicon photonics, with a strongly direct bandgap and optical transitions comparable with III-V materials. Furthermore, these strain results offer a route to test the computational models against experiments, using a diamond anvil cell. These tests are currently underway.