The structural properties of pseudomorphic Si/Ge(001) heterostructures are investigated using a newly developed model in which the interface is viewed as a perturbation with respect to an infinite periodic system (the virtual crystal). The use of density-functional perturbation theory allows us to treat composition profiles of virtually any complexity at a negligible numerical cost and with an accuracy which is very close to that of state-of-the-art self-consistent calculations. We find that-at variance with recent measurements from x-ray photoelectron diffraction and ion scattering experiments-the macroscopic theory of elasticity accurately predicts the interplanar spacings of the heterostructure starting already at 2-3 planes away from the interface whereas a sizeable overstrain occurs in the region close to the interface. We suggest that the discrepancy between our findings and the experimental results could be due to atomic interdiffusion across the interface which would affect the composition of nominally pure Si (Ge) slabs, thus reducing the stress acting on the epilayer.
