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We investigate the electronic and optical properties of free-standing and epitaxially strained ${\mathrm{Si}}_{1\ensuremath{-}y}{\mathrm{C}}_{y}$ alloys. We first determine the microscopic atomic structure of the alloys using the semi-grand-canonical Monte Carlo method and empirical interatomic potentials. For the calculation of the electronic and optical properties of the alloys we employ a supercell geometry and an empirical tight-binding model, which was fitted to reproduce the relevant band structures obtained from first-principles calculations. Our approach allows for a thorough investigation of C alloying and strain effects on the band gap, the band offsets, the effective masses of the upper valence and lowest conduction bands, and the optical properties. Our results are in very good agreement with experiment.

The piezo-optical properties of Ge, for pressure along the [001] and [111] directions, are calculated with the use of a realistic empirical tight-binding model. The real and imaginary part of components ${P}_{11}(\ensuremath{\omega})$, ${P}_{12}(\ensuremath{\omega})$, and ${P}_{44}(\ensuremath{\omega})$ of the linear piezo-optical tensor for Ge are evaluated. The main structures in ${P}_{\mathrm{ij}}$ are located around the ${E}_{1}$ and ${E}_{2}$ critical points. Deformation potential constants ${D}_{1}^{1}$, ${D}_{1}^{5}$, ${D}_{3}^{3}$, and ${D}_{3}^{5}$, for the ${E}_{1}\ensuremath{-}{(E}_{1}+{\ensuremath{\Delta}}_{1})$ transitions are also evaluated. The theoretically obtained results are in good agreement with existing experimental values.