Disclosed herein are (1) a light-emitting semiconductor device that uses a gallium nitride compound semiconductor (Al.sub.x Ga.sub.1-x N) in which the n-layer of n-type gallium nitride compound semiconductor (Al.sub.x Ga.sub.1-x N) is of double-layer structure including an n-layer of low carrier concentration and an n.sup.+ -layer of high carrier concentration, the former being adjacent to the i-layer of insulating gallium nitride compound semiconductor (Al.sub.x Ga.sub.1-x N); (2) a light-emitting semiconductor device of similar structure as above in which the i-layer is of double-layer structure including an i.sub.L -layer of low impurity concentration containing p-type impurities in comparatively low concentration and an i.sub.H -layer of high impurity concentration containing p-type impurities in comparatively high concentration, the former being adjacent to the n-layer; (3) a light-emitting semiconductor device having both of the above-mentioned features and (4) a method of producing a layer of an n-type gallium nitride compound semiconductor (Al.sub.x Ga.sub.1-x N) having a controlled conductivity from an organometallic compound by vapor phase epitaxy, by feeding a silicon-containing gas and other raw material gases together at a controlled mixing ratio.