Picosecond time evolution of free electron-hole pairs into excitons in GaAs quantum wells Rajesh Kumar, A. S. Vengurlekar, and S. S. Prabhu* Tata Institute of Fundamental Research, Bombay 400005, India Jagdeep Shah AT&T Bell Laboratories, Holmdel, New Jersey 07733 L. N. Pfeiffer AT&T Bell Laboratories, Murray Hill, New Jersey 07974 Received 15 January 1996 We measure picosecond time resolved luminescence spectra in GaAs quantum wells using frequency up- conversion luminescence spectroscopy. A careful line-shape analysis of the spectra is performed to separate the free exciton and free carrier related luminescence. From the time evolution of the free carrier luminescence, we deduce the characteristic time constant  f  for the bimolecular process of exciton formation by free electron- hole pairs. For an estimated initial carrier density of 410 10 cm -2 ,  f is found to be 50 ps. S0163-18299608031-9 I. INTRODUCTION The dynamics of exciton formation in GaAs quantum wells QWs has been a subject of considerable interest in recent years. 1–4 Since the excitons formed by the electrons and holes near their band edges are expected to have a large wave vector ( K  ), they do not couple to photons. 1 The exci- tons have to relax to sufficiently small K  values at low tem- peratures before they can undergo radiative decay. Thus, de- termination of the exciton formation time from the time evolution of the exciton photoluminescence PL is generally not possible. A direct measurement of the exciton formation dynamics, however, can be made for those material systems for which the exciton-LO phonon coupling leads to excitonic transitions from large K  vectors to the photonlike polariton branch via emission of one or more numbers of LO phonons. If the time evolution of the luminescence due to such LO phonon assisted Stokes sidebands can be measured, it can provide direct information on the free exciton formation and exciton energy relaxation dynamics. These sidebands can be easily seen in materials like CdS and CdSe. The exciton formation time in CdSe was recently deduced to be about 7–10 ps using the time evolution of the luminescence due to 2LO phonon Stokes side band of the free exciton. 5 Since such sidebands are not very prominent in GaAs or GaAs QWs, the exciton formation time in GaAs QWs has been deduced indirectly by various ways. Damen et al. 1 ob- served that the homogeneous linewidth  L of the exciton PL initially decays rapidly in less than 20 ps for an excitation density n 0 of 210 10 cm -2 . A time constant of 20 ps for the decay of the e - h pair density due to exciton formation was then deduced on the basis of the expected linear depen- dence of  L on the carrier density. 6 Blom et al. 2 studied very narrow QWs in which the time for exciton relaxation from large K  to K  0 states was expected to be small. The exciton formation time then was believed to be approximately given by the exciton luminescence rise time, measured to be about 25–40 ps for n 0 =510 10 cm -2 . Deveaud et al. 3 deduced an exciton formation time of the order of 200 ps for n 0 10 11 cm -2 by relating it to the time of survival of the high energy exponential tail of the time resolved exciton luminescence. Recently, Robart et al. 4 argued that the rapid initial decay of the exciton homogeneous linewidth, observed by them to take place in less than 10 ps for n 0 =710 10 cm -2 , in fact is related to the fast approach towards thermodynamical equi- librium between the free carriers and the excitons. It was suggested that the above time of about 10 ps should be taken as the free exciton formation time, although the free carrier luminescence was found to survive for a few hundred psecs. On the theoretical side, Thilagam and Singh 7 calculated the transition rate for a free e - h pair at the band edge to an excitonic state by acoustic phonon emission via deformation potential coupling. They obtained a time constant of a few 100s of psecs for this exciton formation process, the exact value of the time constant depending upon the QW width, taken to be in the range of 2.5–20 nm. Since many aspects of the exciton formation dynamics in GaAs QWs are still not fully clarified, it should be of interest to study the time resolved PL in GaAs QWs in more detail. A detailed modeling of the PL spectral line shapes to isolate the exciton and free carrier related PL energy distributions as a function of time has not been reported so far. In this paper, we report our measurements of picosecond time resolved PL spectra in high quality GaAs QWs using the frequency up- conversion UC technique. To separate the exciton and free carrier related luminescence spectra, we carry out a line- shape analysis of the spectra, corrected for the instrument spectral response. Relating the time evolution of the energy integrated intensity of the PL due to free e - h pairs to the time dependence of the free carrier density, we deduce the time constant  f , which determines the effective rate of bi- molecular formation of excitons from free e - h pairs. For an PHYSICAL REVIEW B 15 AUGUST 1996-I VOLUME 54, NUMBER 7 54 0163-1829/96/547/48917/$10.00 4891 © 1996 The American Physical Society