Silicon Photonics: Fundamentals and Devices

4.5 Fundamental Absorption in Direct Gap

Although Si is an indirect-gap material, the purposes of introducing the section related to direct gap are quite a few. First of all, the theory is used in this chapter to develop the theory for indirect-gap semiconductors. Second, the present theory is modified in Chapter 4 for quantum structures using direct-gap material. Third, indirect- to direct-gap crossover has indeed been observed in quantum structures involving group IV materials. The present theory will be useful in such systems.

We present in this section the basic conservation laws in direct-gap materials and then proceed to obtain the expression for the absorption coefficient for direct-gap semiconductors.

4.5.1 Conservation Laws

When photons of energy greater than the fundamental band gap are incident on a semiconductor sample, electrons from the valence band absorb the photons and move to the conduction band. As a consequence, an empty state or a hole is created in the valence band. The absorption of photons thus leads to the generation of excess electron–hole pairs (EHPs). The absorption coefficient rises rapidly as the photon energy , the band gap energy. This process is shown schematically in Figure 4.3.

Figure 4.3 Fundamental absorption process in a direct-gap semiconductor (left) and in an indirect-gap semiconductor (right).

Two conditions must be fulfilled for this interband ...