The invention relates to the manufacture of an LED device, including: growing nanowire semiconductors (16) on a first electrode (14) produced on an insulating surface (10, 12), and encapsulating the latter in the planarization layer (18); forming, on the planarization layer (18), a second electrode (20) having contact take-up areas (22); forming LEDs (24) by: releasing a band of the first electrode around each take-up area (22), comprising: forming a mask for defining said bands on the second electrode (20); chemically etching the planarization layer, said etching being abutted so as to preserve the planarization layer; chemically etching the thus-released portion of the nanowires; and chemically etching the remaining planarization layer; and forming a trench (28) along each of said bands up to the insulating surface (10, 12); and placing the LEDs (24) in series by connecting the take-up areas (22) and the bands of the first electrode.