Method for fabrication of recessed electrical elements, which by choice can be recessed electrical contacts and/or junctions and/or electrical components, formed in group III-N semiconductor layers heterostructure in which layer composition is selected so, that in a buffer layer of a heterojunction, near boundary with the III-N barrier layer, a two-dimensional electron gas channel is formed, in the regions of the semiconductor layers heterostructure, in which the recessed electrical elements would be formed, recesses are formed and filled with the materials, intended for the forming of selected elements, wherein each recess of the recesses is formed using a laser irradiation and the method comprises the following steps: a) coating a top surface of the III-N semiconductor layers heterostructure, grown on a substrate, with at least one a protective layer, in order to form a blank, b) placing the blank, prepared in the step a), into a chamber, vacuumed or filled with an inert or shielding gas, the chamber having a transparent window through which the laser radiation enters the chamber, c) forming each said recess by directing through the transparent window in the chamber to the blank the focused ultrashort pulsed laser radiation, which has selected parameters to remove the protective layer and required thickness of the material in order to form the recess of required depth in the semiconductor layers of the heterostructure, d) translating the blank and focused laser beam in respect to each other in the controlled manner to the position, selected for the forming of the next recess, directing the focused laser beam similarly as in the step c) and selecting the appropriate parameters of laser irradiation to form another recess of required shape and depth and/or required number of recesses with the same or different dimensions, e) filling the recesses, formed in the step c) or d) with corresponding material layers, to form the selected electrical elements, f) removing the remaining protective layer after forming of required recessed contacts and/or junctions and/or components in the step e), g) annealing the recessed electrically conductive contacts and junctions and electrical components using the rapid thermal annealing technique to an optimal temperature in the inert gas environment until a metal to 2DEG channel contact resistance is reduced, h) forming the recessed isolating elements, required for a separation and/or isolation of the elements, formed in the step g). a) coating a top surface of the III-N semiconductor layers heterostructure, grown on a substrate, with at least one a protective layer, in order to form a blank, b) placing the blank, prepared in the step a), into a chamber, vacuumed or filled with an inert or shielding gas, the chamber having a transparent window through which the laser radiation enters the chamber, c) forming each said recess by directing through the transparent window in the chamber to the blank the focused ultrashort pulsed laser radiation, which has selected parameters to remove the protective layer and required thickness of the material in order to form the recess of required depth in the semiconductor layers of the heterostructure, d) translating the blank and focused laser beam in respect to each other in the controlled manner to the position, selected for the forming of the next recess, directing the focused laser beam similarly as in the step c) and selecting the appropriate parameters of laser irradiation to form another recess of required shape and depth and/or required number of recesses with the same or different dimensions, e) filling the recesses, formed in the step c) or d) with corresponding material layers, to form the selected electrical elements, f) removing the remaining protective layer after forming of required recessed contacts and/or junctions and/or components in the step e), g) annealing the recessed electrically conductive contacts and junctions and electrical components using the rapid thermal annealing technique to an optimal temperature in the inert gas environment until a metal to 2DEG channel contact resistance is reduced, h) forming the recessed isolating elements, required for a separation and/or isolation of the elements, formed in the step g).