Electronic and optical properties of strained Ge/Si superlattices

We present a comprehensive theoretical study of short-period (Ge${)}_{\mathit{n}}$/(Si${)}_{\mathit{m}}$ strained-layer superlattices (SLS’s) on Si and Ge [001] substrates, and the ‘‘free-standing’’ case, based on ab initio calculations. In order to compensate for the error in the excitation energies inherent to the local-density approximation, we add ad hoc potentials on the atomic sites. With this correction the calculated transition energies compare favorably with quasiparticle calculations and experiment. Special emphasis is placed on the orthorhombic nature of the SLS’s with both n and m even, as reflected in both the energy-band structure and the dielectric response ${\mathit{varepsilon}}_2$(ω), which is different for all three polarizations along the main axes. The effects of various substrates is examined for the occurring interband transitions, and in some cases reduced to a simple deformation-potential ansatz. A similar approach is taken for the splitting of the top of the valence band due to the internal uniaxial strain, which obeys a simple Vegard-type law; it is shown that confinement effects are negligible up to the values considered, i.e., n+m=12. The SLS’s with a period of n+m=10 and sufficiently large strain in the Si layers have a direct gap; the transition from the top of the valence band to the lowest zone-folded conduction band at k=0, however, is only dipole allowed for special cases, such as the superlattices with n,m odd, i.e., for systems with no inversion symmetry. The (Ge${)}_5$/(Si${)}_5$ SLS is predicted to be a good candidate for optoelectronic devices. A reversal of the two lowest folded conduction states (dipole allowed and forbidden, respectively) is obtained when going from the n=4 to the n=6 case. Recent experiments on 10-monolayer SLS’s are discussed in the light of our results.