A semiconductor heterostructure having: a substrate (SS); a buffer layer (h); a spacer layer (d, e, f); a barrier layer (b, c); and which may also include a cover layer (a) is provided. The barrier layer is doped (DS); and the barrier and spacer layers are made of one or more semiconductors having wider bandgaps than the one or more materials forming the buffer layer, the heterostructure being characterized in that: the barrier layer comprises a first barrier sublayer (c) in contact with the spacer layer, and a second barrier sublayer (b), distant from the spacer layer; and in that the second barrier sublayer has a wider bandgap than the first barrier sublayer. The invention also relates to a HEMT transistor produced using such a heterostructure and to the use of such a transistor at cryogenic temperatures.