Silicon Photonics: Fundamentals and Devices

4.6 Fundamental Absorption in Indirect Gap

The conduction band minima and valence band maxima occur at the center of the Brillouin zone in direct-gap semiconductors. Therefore, the optical absorption process is indicated by a vertical line in Figure 4.3, to indicate that photons provide negligible momentum to the electrons. This happens in most of the III–V and II–VI compound semiconductors and their alloys.

The most important material for microelectronics, Si, is not, however, a direct-gap semiconductor. Therefore, a photon cannot directly lift an electron to the conduction band. In order to conserve crystal momentum or wave vector, it is necessary that some momentum-conserving agency should participate in the absorption process. At present, we shall assume that phonons, that is, quantized lattice vibrations, act as such momentum-conserving agents. The transition is indicated in Figure 4.3. The photon brings an electron in the valence band to an intermediate state, by the process of which there is negligible change of momentum. The electron then has its momentum changed by an amount q = k₀, by colliding with a phonon, and comes to one of the six degenerate conduction band valleys. The wave vector conservation then takes the form

(4.72)

where q is the phonon wave vector. We have used the same symbol q for the phonon wave vector in this chapter. The energy conservation is now expressed ...