Free-electron density effects on the exciton dynamics in coupled quantum wells A. Herna ´ ndez-Cabrera and P. Aceituno Departamento de Fı ´sica Ba ´sica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain Received 16 December 1999; revised manuscript received 10 February 2000 We have studied the alterations produced by the free-electron density on the dipole moment generated by the exciton oscillations in an asymmetric coupled quantum-well system. This physical situation is possible for the case of carrier injection, when the electron concentration is greater than the hole concentration, and free electrons and excitons coexist. Excitons are directly created by hole-assisted electron resonant tunneling, where doped layers supply electrons and holes. Many-body interaction and elastic scattering strongly influence the coherent dynamics of excitons, leading to time-dependent modifications of the resonant energy levels and of the level-splitting energies. As a consequence, nonperiodic charge oscillations and nonlinear regimes appear for electron densities higher than 10 10 cm -2 . Beyond electron densities of 10 11 cm -2 the exciton generation can be inhibited, leading to tunneling collapse. I. INTRODUCTION Semiconductor quantum wells have shown many new op- tical and electronic properties playing a key role in many electronic devices. 1,2 Recently, GaAs/Ga x Al 1 -x As semicon- ductor coupled quantum wells have been used to observe tunneling charge oscillation in solids. 3 In such an experi- ment, the superposition of both symmetric and antisymmet- ric quantum-well eigenstates in the conduction band leads to coherent tunneling between both wells, and thus to an electron-hole pair with a time-dependent separation. Then a time-varying excitonic dipole moment in the quantum-well region is obtained, allowing the emission of electromagnetic radiation at the oscillation frequency. There is also a great interest in other related phenomena as spatially coherent quantum-well QW excitons, with an in-plane momentum k ex  0, due to their capability of radi- ating in the perpendicular direction to the QW and its pos- sible application in vertical planar microcavities. Until now, resonant optical pumping was needed to create such excitons efficiently. In a recent experiment and theory, Cao et al. 4 have shown the possibility of the direct creation of electri- cally pumped QW excitons with k ex  0. In a previous paper 5 we analyzed the exciton binding energy in asymmet- ric coupled quantum wells ACQW’s. In the direct genera- tion of excitons, electrons tunnel from an n-type material through a barrier to the left quantum well LQW. Owing to the structure ends in a p-type material Fig. 1, we assume that holes diffuse thermally into the right quantum well RQW and the process is assisted by the electron-hole Cou- lomb interaction, and a two-particle process is obtained. Then, and under resonant conditions between two adjacent wells with different widths, electrons in the excitonic state can tunnel back and forth from one well to the other. As commented before, the generated time-dependent dipole can radiate terahertz electromagnetic waves before radiative re- combination. Such a dipole moment is determined by the interwell electron density imbalance. The oscillation period,  T =2   /  T , is determined by the level splitting energy  T for ACQW’s. Here  T =  2 +(2 T ) 2 , where T is the tunnel- ing matrix element and  is the splitting for uncoupled wells. The resonance  =0 and  T =2 T , the minimum splitting energy is usually achieved by applying an electric field per- pendicular to DQW layers. In order to clarify the meaning of mentioned parameters, we sketched in Fig. 2 two pairs of energy levels in the vicinity of the resonances  =0, indi- cated by arrows for free electrons and for electrons in the exitonic state, respectively. Curves correspond to an ACQW configured by a 8-nm LQW and 6-nm RQW, separated by a 3-nm barrier, and subjected to different electric fields. The resonant photoexcitation has been widely studied, from both the theoretical 6–11 and the experimental point of view. 2,12,13 While the concentrations of the two types of car- riers forming excitons are equal in photoexcitation, the case of direct created excitons is essentially different because we can deal with two very different concentrations of electrons and holes. The different doping of electrodes causes this pe- culiarity. We stress here that, in the usual experimental con- ditions, donor concentration is greater than acceptor concen- tration 10 18 and 10 16 cm -3 , respectively. 4 The excess of injected electrons will remain in the free-electron energy level without forming excitons and interacting not only be- tween themselves but also with electrons trapped in excitons. FIG. 1. Asymmetric double quantum well under the excitonic electron resonant condition in the absence of free-electron density effects. PHYSICAL REVIEW B 15 JUNE 2000-I VOLUME 61, NUMBER 23 PRB 61 0163-1829/2000/6123/158737/$15.00 15 873 ©2000 The American Physical Society