Electronic structure calculations on composite channels, consisting of indium arsenide grown on the technologically relevant (001), (011) and (112)-orientated silicon surfaces are reported. The calculations are performed with NEMO 3-D, where atoms are represented explicitly in the sp3d5s* tight-binding model. The Valence Force Field (VFF) method is employed to minimize the strain. NEMO 3-D enables the calculation of localized states in the quantum well (QW) and their dispersion in the quantum well plane. From this dispersion, the bandgap, its direct or indirect in character, and the associated effective masses of the valence and conduction band can be determined. Such composite bandstructure calculations are demonstrated here for the first time. The numerical results presented here can then be included in empirical device models to estimate device performance. Pure InAs QWs create a direct bandgap material, with a relatively small gap and effective masses of about one order of magnitude smaller than for pure Si QW of equivalent thickness. Si, on the other hand, has a larger bandgap, superior thermal and mechanical properties, and a heavily invested industry. Thus heteroepitaxy of both components is expected to yield a highly optimized overall system. For samples grown along the (001) direction, Si is a direct bandgap material, and deposition of an InAs 3nm layer reduces substantially the hole effective mass and slightly the electronic mass, decreasing the magnitude of the gap. Along the (011) and (112)-growth direction, Si QWs are indirect bandgap material, and deposition of a few InAs layers suffies to make the new material a direct-bandgap heterostructure, decreasing significantly the electronic effective mass. (011) and (112) are the experimentally most relevant growth directions since they prevent heterointerface dipoles.