A layer structure for a normally-off transistor has an electron-supply layer made of a group-III-nitride material, a back-barrier layer made of a group-III-nitride material, a channel layer between the electron-supply layer and the back-barrier layer, made of a group-III-nitride material having a band-gap energy that is lower than the band-gap energies of the other layer mentioned. The material of the back-barrier layer is of p-type conductivity, while the material of the electron-supply layer and the material of the channel layer are not of p-type conductivity, the band-gap energy of the electron-supply layer is smaller than the band-gap energy of the back-barrier layer. In absence of an external voltage a lower conduction-band-edge of the third group-III-nitride material in the channel layer is higher in energy than a Fermi level of the material in the channel layer.