  The interfacial structure of SrZr$_{x}$Ti$_{1-x}$O$_3$ films grown on
semiconducting Ge substrates are investigated by synchrotron X-ray diffraction
and first-principles density functional theory. By systematically tuning Zr
content x, the effects of bonding at the interface and epitaxial strain on the
physical structure of the film can be distinguished. The interfacial perovskite
layers are found to be polarized as a result of cation-anion ionic
displacements perpendicular to the perovskite/semiconductor interface. We find
a correlation between the observed buckling and valence band offsets at the
SrZr$_{x}$Ti$_{1-x}$O$_3$/Ge interface. The theoretical valence band offsets
for the polar structures are in agreement with reported X-ray photoelectron
spectroscopy measurements. These results have important implications for the
integration of functional oxide materials with established semiconductor based
technologies.
