Silicon Photonics: Fundamentals and Devices

6.2 Basic Theory of Light Emission

Light emission in a semiconductor occurs due to the creation and recombination of excess electron– hole pairs (EHPs). The pairs are created by photon absorption, by the injection of carriers in a forward-biased p–n junction, or by bombardment of the material by energetic particles. The recombination process is illustrated by considering a direct-gap semiconductor, the energy (E) – wave vector (k) (E–k) diagram of which is shown in Figure 4.3a. An excess electron in the conduction band jumps to the valence band to occupy an empty state there, and thereby the excess energy is liberated in the form of a photon. Two conditions must be satisfied in this recombination process. The first, the energy conservation, requires that

(6.1)

where E_e and E_h denote, respectively, the electron and hole energies and is the energy of the emitted photon. The second condition to be fulfilled is the conservation of (crystal) momentum, which is expressed as

(6.2)

It has been shown in Chapter 4 that the wave vector of the photon, k_photon, is small compared with the wave vectors for both electrons and holes, k_e and k_h, leading to the condition for momentum conservation