A semiconductor structure includes a buffer layer stack comprising a plurality of III-V material layers, and the buffer layer stack includes at least one layered substructure. Each layered substructure comprises a compressive stress inducing structure between a respective first buffer layer and a respective second buffer layer positioned higher in the buffer layer stack than the respective first buffer layer. A lower surface of the respective second buffer layer has a lower Al content than an upper surface of the respective first buffer layer. An active semiconductor layer of the III-V type is provided on the buffer layer stack. The surface of the respective relaxation layers is sufficiently rough to inhibit the relaxation of the respective second buffer layer, and comprises a Root Mean Square (RMS) roughness larger than 1 nm. A method is provided for producing the semiconductor structure.