Exciton formation assisted by LO phonons in quantum wells

Kinetics of exciton formation involving LO phonons is investigated in quantum wells. Considering the formation of an exciton from a free excited electron-hole pair due to LO-phonon emission, an expression is derived for the rate of formation of an exciton as a function of carrier densities, temperature, and wave vector ${\mathbf{K}}_{\Vert }$ of the center of mass of excitons in quantum wells, and the formation time of an exciton is also calculated. The theory is applied to GaAs quantum wells, in which it is found that the exciton formation dominantly occurs at ${\mathbf{K}}_{\Vert }\ne 0.$