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physica status solidi (b)

On the Influence of Disorder on Radiatively Coupled Multiple Quantum Wells

Bernd Grote, T. Stroucken, S. Haas, P. Thomas, S. W. Koch

Published Jan 1, 1998• 10 citations
Publisher

Abstract

A theoretical investigation of the effects of static disorder on the linear optical response and the degenerate four-wave-mixing signals of multiple quantum well Bragg structures is presented. It is shown that disorder leads to a finite radiative coupling strength of subradiant modes that are optically forbidden in the ideal structure. In the absorption spectrum, the subradiant modes appear as sharp resonances in the presence of barrier thickness fluctuations, whereas the disorder induced subradiant modes are inhomogeneously broadened in the presence of interface roughness. The decay of the time integrated four-wave-mixing signal at large delays is determined by the dephasing time of subradiant modes, whereas the initial fast decay is dominated by the superradiant mode. A free induction decay is observed in the presence of barrier thickness fluctuations. In contrast, even a small inhomogeneous broadening induces a photon-echo-like behavior for the subradiant modes, while the superradiant mode still exhibits a free induction decay.

DOI
10.1002/(sici)1521-3951(199801)205:1<209::aid-pssb209>3.0.co;2-#

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A theoretical investigation of the effects of static disorder on the linear optical response and the degenerate four-wave-mixing signals of multiple quantum well Bragg structures is presented. It is shown that disorder leads to a finite radiative coupling strength of subradiant modes that are optically forbidden in the ideal structure. In the absorption spectrum, the subradiant modes appear as sharp resonances in the presence of barrier thickness fluctuations, whereas the disorder induced subradiant modes are inhomogeneously broadened in the presence of interface roughness. The decay of the time integrated four-wave-mixing signal at large delays is determined by the dephasing time of subradiant modes, whereas the initial fast decay is dominated by the superradiant mode. A free induction decay is observed in the presence of barrier thickness fluctuations. In contrast, even a small inhomogeneous broadening induces a photon-echo-like behavior for the subradiant modes, while the superradiant mode still exhibits a free induction decay.
A theoretical investigation of the effects of static disorder on the linear optical response and the degenerate four-wave-mixing signals of multiple quantum well Bragg structures is presented. It is shown that disorder leads to a finite radiative coupling strength of subradiant modes that are optically forbidden in the ideal structure. In the absorption spectrum, the subradiant modes appear as sharp resonances in the presence of barrier thickness fluctuations, whereas the disorder induced subradiant modes are inhomogeneously broadened in the presence of interface roughness. The decay of the time integrated four-wave-mixing signal at large delays is determined by the dephasing time of subradiant modes, whereas the initial fast decay is dominated by the superradiant mode. A free induction decay is observed in the presence of barrier thickness fluctuations. In contrast, even a small inhomogeneous broadening induces a photon-echo-like behavior for the subradiant modes, while the superradiant mode still exhibits a free induction decay.
The influence of radiative coupling on the four-wave-mixing signals of multiple-quantum-well structures is investigated theoretically for excitation at the excitonic resonance. It is shown that amplitude and shape of the FWM signals depend strongly on the number of quantum wells N in the sample and on the periodicity of the structure. For a fixed delay time τ12, the signal amplitude of a Bragg structure increases quadratically with N due to constructive interference as long as the radiative decay rate Nγrad is small compared to the inverse delay time τ—112. For large N, if the enhanced radiative decay rate exceeds the inverse delay time, superradiant emission leads to a decrease of the observed signals with increasing N. The signals of anti-Bragg structures with an odd number of quantum wells decrease with increasing N due to destructive interference effects whereas anti-Bragg structures with an even number of quantum wells behave similarly to Bragg structures.
Time-integrated and spectrally resolved degenerate-four-wave mixing experiments at liquid helium temperature on the heavy- hole exciton resonance of a wedged (In,Ga)As/GaAs quantum well Bragg structure reveal a strong dependence of the dynamic and amplitude of the coherent nonlinear optical response in dependence on sample position. In the vicinity of the Bragg resonance the signal amplitude depends on both the rapid dephasing due to enhanced superradiant decay of the excitons and on the constructive interference of the signal amplitude in the backward Bragg reflection direction. We find that even in the presence of moderate inhomogeneous broadening of the excitonic resonance the superradiant decay dominates the excitonic nonlinearity at Bragg resonance. Our experimental results can be fairly well described by solutions based on the semiconductor Maxwell-Bloch equations taking disorder into account.
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 have performed time-integrated as well as time-resolved femtosecond degenerate four-wave-mixing measurements on inhomogeneously broadened (Zn,Cd)Se/ZnSe quantum-well structures. Potential fluctuations due to alloy disorder in the ternary wells give rise to localized quasi-zero-dimensional excitons and biexcitons. For time-integrated detection, they manifest themselves by distinct (disorder-renormalized) quantum beats. Time resolving these transients reveals a free-induction-decay-like emission nature of the biexciton in contrast to the photon-echo exciton contribution. Using a five-level scheme, containing both biexcitons and antibound two-exciton states, this striking emission-type change is explained by fluctuation and correlation effects upon the biexciton binding energy. A combination of time-resolved and time-integrated four-wave mixing is thus a powerful tool to gain information about the disorder in a given kind of quantum structure.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.