  We develop a generalized theory for the scattering process produced by
interface roughness on charge carriers and which is suitable for any
semiconductor heterostructure. By exploiting our experimental insights into the
three-dimensional atomic landscape obtained on Ge/GeSi heterointerfaces
obtained by atom probe tomography, we have been able to define the full set of
interface parameters relevant to the scattering potential, including both the
in-plane and axial correlation inside real diffuse interfaces. Our experimental
findings indicate a partial coherence of the interface roughness along the
growth direction within the interfaces. We show that it is necessary to include
this feature, previously neglected by theoretical models, when heterointerfaces
characterized by finite interface widths are taken into consideration.
