Calculations of the time taken for excitons to form in GaAs quantum wells

The time taken for excitons to form has been calculated by solving the Boltzmann equation for an 80 Angstrom GaAs quantum well. Our results show that longitudinal acoustic phonon emission is the most important relaxation mechanism for exciton formation from free-electron-hole pairs at low lattice temperatures. The time taken for excitons to form is found to depend on the excitation conditions: the excitation density, the electron-hole plasma temperature and the lattice temperature, and is approximately proportional to 1+k(B) T-eh/E-b (where T-eh is the electron-hole plasma temperature and Eb is the exciton binding energy) at a fixed lattice temperature. For the excitation conditions used by Kumar et al (Kumar R, Vengurlekar A S, Prabhu S S, Shah J and Pfeiffer L N 1996 Phys. Rev. B 54 4891), the calculated time is 108 ps, which is of the same order of magnitude as the experimentally deduced one of 50 Qs. We find that the approximation in which the wave-vector component q(z) of the LA phonon is taken as zero can lead to underestimation of the rate of exciton formation. A longer time of 150 ps for the exciton formation can be obtained using this approximation.