A light-emitting semiconductor device (10) consecutively includes a sapphire substrate (1), an AlN buffer layer (2), a silicon (Si) doped GaN n.sup.+ -layer (3) of high carrier (n-type) concentration, a Si-doped (Al.sub.x3 Ga.sub.1-x3).sub.y3 In.sub.1-y3 N n.sup.+ -layer (4) of high carrier (n-type) concentration, a zinc (Zn) and Si-doped (Al.sub.x2 Ga.sub.1-x2).sub.y2 In.sub.1-y2 N emission layer (5), and a Mg-doped (Al.sub.x1 Ga.sub.1-x1).sub.y1 In.sub.1-y1 N p-layer (6). The AlN layer (2)--is 500 .ANG. in thickness. The GaN N.sup.+ -layer (3) is about 2.0 .mu.m in thickness and has an electron concentration of about 2.times.10.sup.18 /cm.sup.3. The n.sup.+ -layer (4) is about 2.0 .mu.m in thickness and has an electron concentration of about 2.times.10.sup.18 /cn.sup.3. The emission layer (5) is about 0.5 .mu.m in thickness. The p-layer 6 is about 1.0 .mu.m in thickness and has a hole concentration of about 2.times.10.sup.17 /cm.sup.3. Nickel electrodes (7, 8) are connected to the p-layer (6) and n.sup.+ -layer (4), respectively. A groove (9) electrically insulates the electrodes (7, 8) from each other. The composition ration of Al, Ga, and In in each of the layers (4, 5, 6) is selected to meet the lattice constant of GaN in the n.sup.+ -layer (3). The LED (10) is designed to improve luminous intensity and to obtain a purer blue color.