First-principles total-energy calculations of atomic and electronic structure in relaxed (formula presented)

We analyzed the atomic and electronic structures in relaxed (Formula presented) crystals using first-principles total energy calculations. First, to investigate the dependence of properties on C and Ge concentrations, uniform alloys with (Formula presented) 0.0625, 0.125, and 0.5 were examined. It was found that the total energy when C atoms are surrounded by Si atoms (Type (Formula presented) is lower than that when they are surrounded by Ge atoms (Type (Formula presented) because of the larger gain in chemical binding energy in spite of the larger distortion energy. The band gaps are reduced for (Formula presented) and 0.125 from those for (Formula presented) indicating a finite gap (semiconductor) for Type-(Formula presented) structure but no band gap for Type-(Formula presented) structure. In the semiconducting alloys of Type A, the effective masses of heavy holes become smaller. The alloy crystals with (Formula presented) have direct band gaps, and the oscillator strengths of the optical transition between the band-edge states are much larger than for (Formula presented) systems without a C atom, because of the C s-orbital component in the bottom of the conduction bands. Next, to extend these results to random alloys, five C arrangements of (Formula presented) alloys were examined. The reduction of effective hole mass does not depend on the C arrangements. Every crystal has a direct band gap with C s-orbital component at the conduction-band bottom, leading to high-optical transition as in the uniform alloy. Finally, the band structure of the alloys were systematically described based on the tight-binding expression, which speculated that the band gap of the random alloy might be larger than that of the uniform alloy.