This chapter presents the basic theory and characteristics of stimulated emission and optical amplification gain in semiconductors. The former is the mostimportant principlethat enablessemiconductorlaserstobeimplemented, and the latter is the most important parameter for analysis of the laser performances. First, stimulated emission in semiconductors is explained, and then quantum theory analysis and statistic analysis using the density matrix of the optical amplification gain are given. Stimulated emission and optical gain in semiconductor quantum well structures will be presented in the next chapter | 3 Stimulated Emission and Optical Gain in Semiconductors This chapter presents the basic theory and characteristics of stimulated emission and optical amplification gain in semiconductors. The former is the most important principle that enables semiconductor lasers to be implemented and the latter is the most important parameter for analysis of the laser performances. First stimulated emission in semiconductors is explained and then quantum theory analysis and statistic analysis using the density matrix of the optical amplification gain are given. Stimulated emission and optical gain in semiconductor quantum well structures will be presented in the next chapter. BAND STRUCTURE OF SEMICONDUCTORS AND STIMULATED EMISSION Band Structure of Direct-Transition Bandgap Semiconductors Semiconductor lasers utilize the interband optical transitions of carriers in a semiconductor having a direct-transition bandgap. As is well known in the electron theory of solids 1 the wave function of an electron of wave vector k momentum hk in an ideal semiconductor crystal can be written as a Bloch function hA r exp ik r uk r where uk r is a periodic function with the periodicity of the crystal lattice and uk r is normalized in a unit volume. The electron states form a band structure consisting of continuous energy levels in the band. Figure shows the band structure of GaAs 2 a representative semiconductor laser Copyright 2004 Marcel Dekker Inc. K iii ----------4-------- 100 Electron wave number Figure Band structure of the III-V semiconductor GaAs having a bandgap of direct transition type 2 . material. The figure shows the electron energy E dependent on k within the first Brillouin zone the dependences on k along the 111 and 100 directions with good symmetry in the k space are shown in the left and right halves respectively. Crystals of III-V compound semiconductors such as GaAs are of the zinc blende structure and their valence and conduction bands originate from .
