A light-emitting diode manufacturing method including the forming of three-dimensional semiconductor elements, extending along parallel axes, made of a III-V compound, each having a lower portion and a flared upper portion inscribed within a frustum of half apical angle α. The method further comprises, for each semiconductor element, the forming of an active area covering the top of the upper portion and the forming of at least one semiconductor layer of the III-V compound covering the active area by vapor deposition at a pressure lower than 10 mPa, by using a flux of the group-III element along a direction inclined by an angle θIII and a flux of the group-V element along a direction inclined by an angle θV with respect to the vertical axis, angles θIII and θV being smaller than angle α.