Process for fabricating a heterojunction field-effect transistor comprising a semiconductor structure made up of superposed layers, comprising: a) providing on a substrate layer: a buffer layer composed of a semiconductor material having a hexagonal crystal structure, namely Ga (1-x-y) Al (x) In (y) N, where x and y are comprised between 0 inclusive and 1 inclusive, the sum x+y being lower than or equal to 1; a channel layer on the buffer layer, this channel layer being composed of a material having a hexagonal crystal structure, namely Ga (1-z-w)Al (z) In (w) N, where z and w are comprised between 0 inclusive and 1 inclusive, the sum z+w being lower than or equal to 1, at least one of z and w being different from x or y, respectively; a barrier layer on this channel layer, this barrier layer being composed of a material having a hexagonal crystal structure, namely Ga (1-z'-w') Al (z') In (w') N, where z' and w' are comprised between 0 inclusive and 1 inclusive, the sum z'+w' being lower than or equal to 1, at least one of z' and w' being different from z or w, respectively; b) depositing a dielectric masking layer on the barrier layer; c) forming an opening in the dielectric masking layer and extending this opening so that the barrier layer has a reduced or zero thickness at the location of the opening; d) growing by epitaxy a semiconductor material (6, 6') having a hexagonal crystal structure, namely Ga (1-x'-y') Al (x') In (y') N, doped with germanium, where x' and y' are comprised between 0 inclusive and 1 inclusive, the sum x'+y' being lower than or equal to 1, at a sufficiently high temperature, comprised between 700°C and 1200°C, so that the material for forming the Germanium-doped Ga (1-x'-y') Al (x') In (y') N hexagonal crystal semiconductor material can migrate to a growth region defined by the opening in the masking layer by mass transport so that said step d) is selective and the Germanium-doped Ga (1-x'-y') Al (x') In (y') N hexagonal crystal semiconductor material (6, 6') has a crystal structure sufficiently defined that its side edges have an inclination relative to the vertical between 5° and 60° at the height of the masking layer and beyond,; e) depositing a source or drain contact electrode (15, 16) on the material thus deposited by epitaxy in step d); and f) depositing a gate electrode in a location outside of the growth zone. a) providing on a substrate layer: a buffer layer composed of a semiconductor material having a hexagonal crystal structure, namely Ga (1-x-y) Al (x) In (y) N, where x and y are comprised between 0 inclusive and 1 inclusive, the sum x+y being lower than or equal to 1; a channel layer on the buffer layer, this channel layer being composed of a material having a hexagonal crystal structure, namely Ga (1-z-w)Al (z) In (w) N, where z and w are comprised between 0 inclusive and 1 inclusive, the sum z+w being lower than or equal to 1, at least one of z and w being different from x or y, respectively; a barrier layer on this channel layer, this barrier layer being composed of a material having a hexagonal crystal structure, namely Ga (1-z'-w') Al (z') In (w') N, where z' and w' are comprised between 0 inclusive and 1 inclusive, the sum z'+w' being lower than or equal to 1, at least one of z' and w' being different from z or w, respectively; a buffer layer composed of a semiconductor material having a hexagonal crystal structure, namely Ga (1-x-y) Al (x) In (y) N, where x and y are comprised between 0 inclusive and 1 inclusive, the sum x+y being lower than or equal to 1; a channel layer on the buffer layer, this channel layer being composed of a material having a hexagonal crystal structure, namely Ga (1-z-w)Al (z) In (w) N, where z and w are comprised between 0 inclusive and 1 inclusive, the sum z+w being lower than or equal to 1, at least one of z and w being different from x or y, respectively; a barrier layer on this channel layer, this barrier layer being composed of a material having a hexagonal crystal structure, namely Ga (1-z'-w') Al (z') In (w') N, where z' and w' are comprised between 0 inclusive and 1 inclusive, the sum z'+w' being lower than or equal to 1, at least one of z' and w' being different from z or w, respectively; b) depositing a dielectric masking layer on the barrier layer; c) forming an opening in the dielectric masking layer and extending this opening so that the barrier layer has a reduced or zero thickness at the location of the opening; d) growing by epitaxy a semiconductor material (6, 6') having a hexagonal crystal structure, namely Ga (1-x'-y') Al (x') In (y') N, doped with germanium, where x' and y' are comprised between 0 inclusive and 1 inclusive, the sum x'+y' being lower than or equal to 1, at a sufficiently high temperature, comprised between 700°C and 1200°C, so that the material for forming the Germanium-doped Ga (1-x'-y') Al (x') In (y') N hexagonal crystal semiconductor material can migrate to a growth region defined by the opening in the masking layer by mass transport so that said step d) is selective and the Germanium-doped Ga (1-x'-y') Al (x') In (y') N hexagonal crystal semiconductor material (6, 6') has a crystal structure sufficiently defined that its side edges have an inclination relative to the vertical between 5° and 60° at the height of the masking layer and beyond,; e) depositing a source or drain contact electrode (15, 16) on the material thus deposited by epitaxy in step d); and f) depositing a gate electrode in a location outside of the growth zone.