Silicon Photonics: Fundamentals and Devices

4.12 Excitonic and Impurity Absorption

In this section, a few of the special cases of absorption, other than the band-to-band transitions discussed in Section 4.11, will be considered.

4.12.1 Excitons

The discussion in Section 3 neglects any interaction between an electron in the conduction band and a hole in the valence band. In reality, particularly at low temperatures, the Coulombic interaction between an electron and a hole may modify some physical properties like absorption or recombination. When this interaction is considered, it may be thought that an electron rotates around the heavier hole. The complex is known as an exciton, and the electron–hole pair gives rise to hydrogen-like bound states which are described by envelope functions. We shall consider that the envelope function is not confined within a few unit cells, but extends over a larger distance. This type of exciton, the Mott–Wannier excitons, plays an important role in most semiconductors.

The excitons obey the following effective-mass Schrödinger equation:

(4.157)

Here m_e and m_h are the electron and hole masses, respectively; |r_e-r_h| is the separation between an electron and a hole; and is the exciton wavefunction. Using the following transformations,

(4.158)

where lowercase symbols represent the separation and ...