Atomic-resolution study of lattice distortions of buried In_xGa_1-xAs monolayers in GaAs(001)

X-ray standing wave measurements were used to study the strain in one monolayer of pseudobinary alloy In_xGa_1-xAs buried in GaAs(001) by molecular-beam epitaxy. The measured In position along the [001] direction exhibited a nearly linear dependence on the In concentration x, thus supporting the validity of macroscopic continuum elasticity theory at the one-monolayer limit. A random-cluster calculation using a valence force field was performed to explain microscopically the origin of the vertical expansion of the strained monolayer observed by the experiment. The calculated As-In-As bond angle and the positions of the first-nearest-neighbor As atoms of In suggest that the nearly linear dependence of the In height on the alloy composition is a combined result of the As-In-As bond bending and the local lattice distortion at the GaAs/In_xzGa_1-xAs interface. The calculated In-As and Ga-As bond lengths were found to depend weakly on the In concentration, consistent with an earlier calculation for the case of a thick In_xGa_1-xAs film on GaAs(001) and the available x-ray absorption fine-structure data.