A semiconductor substrate is a provided and an insulating layer is formed thereon. A cavity structure is formed above the insulating layer, including a lateral growth channel and a fin seed structure arranged in the lateral growth channel. The fin seed structure provides a seed surface for growing a fin structure. One or more first semiconductor structures of a first semiconductor material and one or more second semiconductor structures of a second, different, semiconductor material are grown sequentially in the growth channel from the seed surface in an alternating way. The first semiconductor structures provide a seed surface for the second semiconductor structures and the second semiconductor structures provide a seed surface for the first semiconductor structures. The second semiconductor structures are selectively etched, thereby forming the fin structure comprising a plurality of parallel fins of the first semiconductor structures. Corresponding semiconductor structures are also included.