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RELATION BETWEEN HOMOGENEOUS LINEWIDTH AND RADIATIVE LIFETIME OF EXCITONS IN QUANTUM WELLS

A. Honold, Lothar Schultheis, J. Kühl, C. W. Tu

Published Jul 18, 1988• 1 citation
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Abstract

At low excitation intensities the transmission and luminescence spectra of high quality direct gap semiconductor quantum wells are dominated by exciton transitions. The dynamics of these excitons is characterized by different relaxation times like the phase coherence time T2 and the recombination lifetime τ. The recombination lifetime of such two-dimensional (2D) excitons as well as its variation with the quantum well thickness L2 and the temperature T has been studied extensively by means of time-resolved photolumiaescence.1 On the other hand much less information is available for the phase coherence time T2 and the corresponding homogeneous linewidth Γh of these excitons because of the more complicated methods needed to measure it.2 The phase coherence time T2 is sensitive to all interactions of the excitons and, therefore, phase relaxation normally appears on a much shorter time scale than recombination.

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At low excitation intensities the transmission and luminescence spectra of high quality direct gap semiconductor quantum wells are dominated by exciton transitions. The dynamics of these excitons is characterized by different relaxation times like the phase coherence time T2 and the recombination lifetime τ. The recombination lifetime of such two-dimensional (2D) excitons as well as its variation with the quantum well thickness L2 and the temperature T has been studied extensively by means of time-resolved photolumiaescence.1 On the other hand much less information is available for the phase coherence time T2 and the corresponding homogeneous linewidth Γh of these excitons because of the more complicated methods needed to measure it.2 The phase coherence time T2 is sensitive to all interactions of the excitons and, therefore, phase relaxation normally appears on a much shorter time scale than recombination.
The theoretically predicted rapid superradiant decay of coherent 2D excitons on a time scale of approximately 10 ps [1] is expected to be strongly enhanced in multiple QW (MQW) Bragg structures consisting of N identical QWs separated by (Ga,Al)As barriers the thickness of which was adjusted so that the QWs had a distance d equal to one half of the heavy-hole exciton resonance wavelength λ in the medium [2]. This enhancement originates from efficient radiative coupling of excitons excited in different wells via the exchange of transverse photons. Recently we have published [3] degenerate-four-wave-mixing experiments with fs optical pulses on GaAs QW Bragg structures which demonstrate that the radiative lifetime in high-quality GaAs single QWs (SQW) is approximately 5 ps and decreases to less than 2 ps in Bragg samples with N=10. These studies revealed that radiative recombination provides the dominant contribution to the homogenous linewidth of the 2D exciton in high-quality samples and exceeds nonradiative contributions caused by scattering with sample imperfections in contrast to previous assumptions.
We report time-resolved photoluminescence (TRPL) measurements of the radiative lifetime (τr) at 1.8K of resonantly excited heavy-hole excitons in a 27nm GaAs single quantum well as a function of exciton density. By the use of AlAs interface smoothing layers [1], the sample exhibits very little inhomogeneous broadening (≈0.15meV). The exciton centre of mass motion is therefore not significantly restricted by localisation in well width fluctuation islands. However, measurements of the exciton homogeneous linewidth (Γ h ) using time-resolved degenerate four wave mixing in the self-diffraction configuration (Fig.1) [2], additionally show that the sample imperfection scattering contribution to the Γ h of these delocalised excitons is also small (0.2meV). Thus, as indicated by the dependence of Γ h on exciton density (N x ), even at moderate exciton densities, exciton-exciton scattering is the dominant dephasing interaction within the photocreated exciton ensemble.
Resonant photoexcitation of a predominantly homogeneously broadened exciton line in a GaAs quantum well results in a nonexponential time-resolved photoluminescence decay transient due to the decrease in the exciton-exciton scattering contribution to the homogeneous linewidth, ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{h}}$, as the exciton population decays. This result confirms the theoretically predicted relationship between the exciton radiative recombination lifetime and the homogenous linewidth (and coherence area) of the exciton state.
Correlated electron-hole pairs, or excitons, in semiconductor nanostructures have been studied extensively over the past few decades. The optical response of excitons is complicated due to inhomogeneous broadening, presence of multiple states, and exciton-exciton interactions. In this work we bring new perspectives to exciton physics in semiconductor quantum wells (QWs) through two-dimensional coherent spectroscopy (2DCS).\nThe effect of QW growth direction on the optical properties of excitons is explored by studying (110)-oriented GaAs QWs. The homogeneous and inhomogeneous linewidths of the heavy-hole exciton resonance are measured. By probing the optical nonlinear response for polarization along the in-plane crystal axes [1-10] and [001], we measure different homogeneous linewidths for the two orthogonal directions. This difference is found to be due to anisotropic excitation-induced dephasing, caused by a crystal-axis-dependent absorption coefficient. The extrapolated zero-excitation density homogeneous linewidth exhibits an activation-like temperature dependence.\nSpectral diffusion of excitons in (001)-oriented QWs has been studied. We show that the spectral diffusion characteristics depend strongly on the sample temperature. Spectral diffusion is generally assumed to follow the strong-redistribution approximation, partly because of lack of any evidence to the contrary. We find that this assumption is violated at low sample temperatures for excitons in QWs; high-energy excitons preferentially relax due to a negligible phonon population at low temperatures. The frequency-frequency correlation function is measured through a numerical fitting procedure to quantify spectral diffusion for sample temperatures >20>20>20 K.\nExciton-exciton interactions affect the light-matter interactions in QWs significantly. We present an intuitive and simple model for these interactions by treating excitons as interacting bosons. We show that the polarization-dependent exciton dephasing rate in GaAs quantum wells is due to the bosonic character of excitons. We fit slices from simulated spectra to those from the experimentally measured spectra and show that interference between two different quantum mechanical pathways results in a slower dephasing rate for co-circular and co-linear polarization of optical excitation pulses. This interference does not exist for cross-linearly polarized excitation pulses resulting in a faster dephasing rate. Additionally, we were able to separately quantify inter- and intra-mode interactions between excitons through exciton-density-dependent measurements.
We resonantly excite the n=2 excitons at 8 K in 13 nm and 17.5 nm GaAs quantum wells using 0.5 ps pulses from a Ti-Sapphire laser and perform four wave mixing (FWM) measurements. The exciton dephasing time is deduced by fitting the FWM spectra to a numerical solution of the optical Bloch equations for the excitonic resonance. The finite pulse width and presence of small inhomogeneous broadening are taken into account. The homogeneous linewidth thus obtained at different low excitation intensities has a linear dependence on the intensity. The zero intensity intercept is essentially governed by the n=2 exciton lifetime due to intersubband relaxation, the pure transverse dephasing contribution being relatively less important. We deduce the exciton lifetime to be 0.9 ps and 2.6 ps for the 13 nm and 17.5 nm QWs, respectively.