A semiconductor substrate, comprising a first semiconductor material, is provided and an insulating layer is formed thereon; an opening is formed in the insulating layer. Thereby, a seed surface of the substrate is exposed. The opening has sidewalls and a bottom and the bottom corresponds to the seed surface of the substrate. A cavity structure is formed above the insulating layer, including the opening and a lateral growth channel extending laterally over the substrate. A matching array is grown on the seed surface of the substrate, including at least a first semiconductor matching structure comprising a second semiconductor material and a second semiconductor matching structure comprising a third semiconductor material. The compound semiconductor structure comprising a fourth semiconductor material is grown on a seed surface of the second matching structure. The first through fourth semiconductor materials are different from each other. Corresponding semiconductor structures are also included.