At an n--n hetero-interface in a GaN-based or ZnSe-based multilayered semiconductor laser and light-emitting diode, an excessive voltage drop causing the operating voltage to increased is reduced, thereby lengthening the service life of the device. A single or plurality of n-type intermediate layers are provided in the n--n hetero-interface region where the excessive voltage drop develops. The excessive voltage drop developing at the n--n hetero-interface is decreased by setting the energy value at the edge of the conduction band of each intermediate layer to a mid-value between the energy values at the edges of the conduction bands of the n-type compound semiconductors adjoining both sides of the intermediate layer. The configuration of a GaN-based MQW laser including the intermediate layer formed on sapphire substrate is shown. The relationship between the lattice constant of an intermediate layer necessary for obtaining an intermediate layer excellent in crystallinity suitable for the above object and the lattice constants of compound semiconductors adjoining both sides of the intermediate layer is described.