A semiconductor structure comprising: - a silicon base wafer; - on top of said silicon based wafer, a buffer layer stack comprising a plurality of layers which are all comprising AlGaN material, wherein AlGaN refers to a composition comprising Al, Ga and N in any stoichiometric/compositional ratio, which composition may vary, said buffer layer stack comprising at least two layered substructures, each said layered substructure comprising a respective first buffer layer (40;40'), a respective second buffer layer (41;41') and a compressive stress inducing structure (5;5') between said respective first buffer layer (40;40') and said respective second buffer layer (41;41') positioned higher in said buffer layer stack than said respective first buffer layer (40;40'), a lower surface of said respective second buffer layer (41;41') having a lower Al content than an upper surface of said respective first buffer layer (40;40'); - an active semiconductor layer of III-V type provided on said buffer layer stack; - wherein each said compressive stress inducing layered structure (5;5') comprises a pseudomorphic planarization layer (6;6') near its lower surface and a relaxation layer near its upper surface, the Al content of a lower surface of said planarization layer (6;6') being lower than or equal to the Al content of said upper surface of said respective first buffer layer (40;40') and the Al content of an upper surface of said planarization layer (6;6') being lower than the Al content of a lower surface of said relaxation layer (8;8'), and the Al content of an upper surface of said relaxation layer (8;8') been higher than the Al content of said respective second buffer layer (41;41'); said respective second buffer layers (41;41') having been grown pseudomorphically on top of said respective relaxation layers (8;8') to thereby build up compressive stress in said respective second buffer layers (41;41'); and - the surface of said respective relaxation layers (8;8') comprises a Root Mean Square roughness larger than 1 nm, such that said roughness inhibits the relaxation of said compressive stress in said respective second buffer layers (41;41'). - a silicon base wafer; - on top of said silicon based wafer, a buffer layer stack comprising a plurality of layers which are all comprising AlGaN material, wherein AlGaN refers to a composition comprising Al, Ga and N in any stoichiometric/compositional ratio, which composition may vary, said buffer layer stack comprising at least two layered substructures, each said layered substructure comprising a respective first buffer layer (40;40'), a respective second buffer layer (41;41') and a compressive stress inducing structure (5;5') between said respective first buffer layer (40;40') and said respective second buffer layer (41;41') positioned higher in said buffer layer stack than said respective first buffer layer (40;40'), a lower surface of said respective second buffer layer (41;41') having a lower Al content than an upper surface of said respective first buffer layer (40;40'); - an active semiconductor layer of III-V type provided on said buffer layer stack; - wherein each said compressive stress inducing layered structure (5;5') comprises a pseudomorphic planarization layer (6;6') near its lower surface and a relaxation layer near its upper surface, the Al content of a lower surface of said planarization layer (6;6') being lower than or equal to the Al content of said upper surface of said respective first buffer layer (40;40') and the Al content of an upper surface of said planarization layer (6;6') being lower than the Al content of a lower surface of said relaxation layer (8;8'), and the Al content of an upper surface of said relaxation layer (8;8') been higher than the Al content of said respective second buffer layer (41;41'); said respective second buffer layers (41;41') having been grown pseudomorphically on top of said respective relaxation layers (8;8') to thereby build up compressive stress in said respective second buffer layers (41;41'); and - the surface of said respective relaxation layers (8;8') comprises a Root Mean Square roughness larger than 1 nm, such that said roughness inhibits the relaxation of said compressive stress in said respective second buffer layers (41;41').