  The contact resistance between two dissimilar semiconductors is determined by
the carrier transmission through their interface. Despite the ubiquitous
presence of interfaces, quantitative simulation of charge transport across such
interfaces is difficult, limiting the understanding of interfacial charge
transport. This work employs Green's functions to study the charge transport
across representative Si/Ge interfaces. For perfect interfaces, it is found
that the transmittance is small and the contact resistance is high, not only
because the mismatch of carrier pockets makes it hard to meet the momentum
conservation requirement, but also because of the incompatible symmetries of
the Bloch wave functions of the two sides. In contrast, atomic mixing at the
interface increases the carrier transmittance as the interface roughness opens
many nonspecular transmission channels, which greatly reduces the contact
resistance compared with the perfect interface. Specifically, we show that
disordered interfaces with certain symmetries create more nonspecular
transmission. The insights from our study will benefit the future design of
high-performance heterostructures with low contact resistance.
