Elastic strain at pseudomorphic semiconductor heterojunctions studied by x-ray photoelectron diffraction: Ge/Si(001) and Si/Ge(001)

We have used x-ray photoelectron diffraction to probe strain at the lattice-mismatched semiconductor heterojunctions Ge/Si(001) and Si/Ge(001). Deposition of four-monolayer equivalents of Si on Ge(001) at {~}350 ^∘{}C causes cluster formation, whereas deposition of the same amount of Ge on Si(001) at nearly the same temperature results in more laminar growth. These findings are consistent with surface thermodynamic considerations in that Ge has a lower surface free energy than does Si. Careful measurement of the polar angle at which the forward-scattering-induced diffraction peak along [011] occurs provides an estimate of the perpendicular lattice constant a_⊥. By this means, we estimate a_⊥ to be 5.62 and 5.31 {} for the Ge/Si(001) and Si/Ge(001) interfaces, respectively. In order to obtain a more quantitative measure of the strain, we have used reliability (R) factor analysis to determine a_⊥ by comparison of experiment with single-scattering calculations. This analysis yields values of 5.75±{}0.04 and 5.38±{}0.08 {} for Ge/Si and Si/Ge, respectively. These values suggest less distortion by {~}0.1 {} in the strained overlayers than what is predicted by classical elastic theory. However, agreement with the strain predicted for the Ge/Si(001) interface by more accurate total-energy pseudopotential calculations is excellent. Finally, high-angular-resolution azimuthal scans at any polar angle are not particularly sensitive to tetragonal distortion, at least for the diamond crystal structure.