A light-emitting semiconductor device 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.x2 Ga.sub.1-x2).sub.y2 In.sub.1-y2 N n.sup.+ -layer (4) of high carrier (n-type) concentration, a zinc (Zn) and Mg doped ((Al.sub.x1 Ga.sub.1-x1).sub.y2 In.sub.1-y2 N n.sup.+ -layer (5), and a Mg doped (Al.sub.x2 Ga.sub.1-x2).sub.y2 In.sub.1-y2 N n.sup.+ -layer (6). The AlN layer (2) has a 500 .ANG. thickness. The GaN n.sup.+ -layer (3) has about a 2.0 .mu.m thickness and a 2.times.10.sup.18 /cm.sup.3 electron concentration. The n.sup.+ -layer (4) has about a 2.0 .mu.m thickness and a 2.times.10.sup.18 /cm.sup.3 electron concentration. A double i-layer structure includes the emission layer (5) and the i-layer (6). The emission layer (5) has about a 0.5 .mu.m thickness, and the i-layer (6) has about a 0.5 .mu.m thickness. Parts of the emission layer (5) and the i-layer (6) are p-type regions (50, 60). Both of the p-type regions exhibit p-type conduction with a 2.times.10.sup.17 /cm.sup.3 hole concentration. The emission layer (5) and the i-layer (6), except for the p-type region, exhibit semi-insulative characteristics.