A method for manufacturing a semiconductor material including a semi-polar III-nitride layer from a starting substrate including a plurality of grooves periodically spaced apart by a distance L2, each groove including a first inclined flank having a crystallographic orientation C and a second inclined flank having a different crystallographic orientation, a first inclined flank of a groove and a second inclined flank of an adjacent groove forming a castellation , the top of the castellation being covered with a mask, the method comprising the step of: - forming first III-nitride crystals on the first inclined flanks of the grooves , the growth parameters of the III-nitride crystals being adapted to favour lateral growth of said crystals, o the growth first inducing triangular cavities formed between the substrate and two adjacent III-nitride crystals, a triangular cavity comprising a base, two walls and a vertex, the base corresponding to the substrate, a wall corresponding to a first III-nitride crystal, the other wall corresponding to said adjacent first III-nitride crystal, and the vertex corresponding to the start of the intersection between the two adjacent crystals, wherein the presence of the mask avoids parasitic growth on the surface covered with the mask, o then, inducing an overlap between the adjacent III-nitride crystals in order to form elongated cavities extending from the vertex and arranged above the triangular cavities in line with the overlapping areas between the first crystals in the meeting plane between the first crystals , at the intersection between two first adjacent overlapping crystals; - forming a two-dimensional III-nitride layer on the III-nitride crystals formed beforehand. - forming first III-nitride crystals on the first inclined flanks of the grooves , the growth parameters of the III-nitride crystals being adapted to favour lateral growth of said crystals, o the growth first inducing triangular cavities formed between the substrate and two adjacent III-nitride crystals, a triangular cavity comprising a base, two walls and a vertex, the base corresponding to the substrate, a wall corresponding to a first III-nitride crystal, the other wall corresponding to said adjacent first III-nitride crystal, and the vertex corresponding to the start of the intersection between the two adjacent crystals, wherein the presence of the mask avoids parasitic growth on the surface covered with the mask, o then, inducing an overlap between the adjacent III-nitride crystals in order to form elongated cavities extending from the vertex and arranged above the triangular cavities in line with the overlapping areas between the first crystals in the meeting plane between the first crystals , at the intersection between two first adjacent overlapping crystals; o the growth first inducing triangular cavities formed between the substrate and two adjacent III-nitride crystals, a triangular cavity comprising a base, two walls and a vertex, the base corresponding to the substrate, a wall corresponding to a first III-nitride crystal, the other wall corresponding to said adjacent first III-nitride crystal, and the vertex corresponding to the start of the intersection between the two adjacent crystals, wherein the presence of the mask avoids parasitic growth on the surface covered with the mask, o then, inducing an overlap between the adjacent III-nitride crystals in order to form elongated cavities extending from the vertex and arranged above the triangular cavities in line with the overlapping areas between the first crystals in the meeting plane between the first crystals , at the intersection between two first adjacent overlapping crystals; - forming a two-dimensional III-nitride layer on the III-nitride crystals formed beforehand. <EOS>