Exciton relaxation and coupling dynamics in a GaAs/Al${}_{x}$Ga${}_{1\ensuremath{-}x}$As quantum well and quantum dot ensemble

Exciton relaxation and coupling dynamics in a GaAs/Al $_{x}$ Ga $_{1 - x}$ As quantum well and quantum dot ensemble

G. Moody, M. E. Siemens, A. D. Bristow, X. Dai, A. S. Bracker, D. Gammon, and S. T. Cundiff

Phys. Rev. B 83, 245316 – Published 27 June 2011

Abstract

Exciton inter- and intra-actions in a GaAs/AlGaAs quantum well (QW) and quantum dot (QD) ensemble are studied using optical two-dimensional Fourier transform spectroscopy. We measure population dynamics for times up to 300 ps and temperatures up to 50 K and observe biexponential decay for both QW and QD excitons, strong QW $\to$ QD relaxation, and weak QD $\to$ QW activation. The population dynamics are modeled using a system of rate equations that incorporate radiative and nonradiative decay, coupling between bright and dark exciton states, and QW $\leftrightarrow$ QD coupling. The fast decay rates are attributed to exciton-bound hole spin flips between optically active and inactive states and are similar for the QW and QDs, indicating excitons are weakly localized in the QDs. The QW $\to$ QD relaxation rate increases with temperature, and QD $\to$ QW excitation is observed at temperatures $⩾$ 35 K.

Received 16 December 2010

DOI:https://doi.org/10.1103/PhysRevB.83.245316

Authors & Affiliations

G. Moody^1,2, M. E. Siemens^1,*, A. D. Bristow^1,†, X. Dai^1,‡, A. S. Bracker³, D. Gammon³, and S. T. Cundiff^1,2,§

¹JILA, University of Colorado and National Institute of Standards and Technology, Boulder, Colorado 80309-0440, USA
²Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
³Naval Research Laboratory, Washington, District of Columbia 20375, USA

^*Present address: Department of Physics and Astronomy, University of Denver, Denver, CO 80208-6900, USA.
^†Present address: Department of Physics, West Virginia University, Morgantown, WV 26506-6315, USA.
^‡Present address: Department of Physics, Tsinghua University, 100084 Beijing, China.
^§cundiff@jila.colorado.edu

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Vol. 83, Iss. 24 — 15 June 2011

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Figure 1
Schematic diagram of the optical 2DFTS experimental setup. Notation: $f_{i}$ : lens; BS: beam splitter. Inset: energy level scheme relevant for the QW and QD heavy-hole excitons. Upon excitation by linearly polarized light, excitons are created in the $| \pm 1 〉$ bright states.Reuse & Permissions
Figure 2
QW exciton (QW), QW biexciton (QW $_{BX}$ ), QD exciton ensemble (QDs), QW $\to$ QD relaxation peak (RP), and QD $\to$ QW excitation peak (EP) are observed in the 2D amplitude spectra for increasing $T$ . The temperature is fixed at 35 K. Each spectrum is normalized to the QW peak, and the amplitudes are marked on the $T = 5$ ps color bar. The laser spectrum is represented by the solid white line on the $T$ $=$ 50 ps 2D spectrum.Reuse & Permissions
Figure 3
Biexponential decay of the integrated (a) QW and (b) QD peaks and the (c) RP and (d) EP growth with $T$ at 35 K. Temperature dependence of rates extracted from the fits are shown for the (e) QW, (f) QDs, (g) RP, and (h) EP. The open squares in (e) and (f) represent the single exponential decay rate measured at higher photon densities, converging toward the slow decay rate with increasing density. Panels (a)–(h) are plotted on a logarithmic vertical scale. The final row shows the ratio of the slow and fast exponential decay fit amplitudes for the (i) QW and (j) QDs and the exponential growth fit amplitudes for the (k) RP and (l) EP. The EP is observed for temperatures $⩾$ 35 K.Reuse & Permissions
Figure 4
Possible decay channels within and between QW and QD exciton spin states are highlighted. Transfer rates between QW and QD states are labeled as $Γ_{ij}^{+ / -}$ , where the $+$ (–) corresponds to excitation (relaxation) and $i$ ( $j$ ) corresponds to the initial (final) state. Electron/hole spin flips transfer the exciton between the $| \pm 1 〉$ and $| \pm 2 〉$ states at a rate of $Γ_{12}^{QW + / -}$ for the QW and $Γ_{12}^{QD + / -}$ for the QDs. QW/QD population decay to the ground state, through radiative and nonradiative processes, occurs at a rate of $Γ_{i 0}^{QW / QD}$ , where $i$ is either 1 or 2 depending on the exciton spin state.Reuse & Permissions
Figure 5
Measured (points) and calculated (solid lines) populations of the (a) QW, (b) QDs, (c) RP, and (d) EP obtained by solving the system of rate equations [Eqs. (1, 2, 3, 4)]. Rates used in the equations are obtained from exponential decay and growth fits to the data displayed in Fig. 3, except for $Γ_{12}^{QW / QD +}$ and $Γ_{20}^{QW / QD}$ , which are adjusted to obtain best agreement between the model and data. The calculated populations with $Γ_{20}^{QW / QD}$ (dashed line) and $Γ_{12}^{QW / QD +}$ (dashed-dotted line) equal to zero are also shown.Reuse & Permissions

Physical Review B

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Exciton relaxation and coupling dynamics in a GaAs/Al $_{x}$ Ga $_{1 - x}$ As quantum well and quantum dot ensemble

G. Moody, M. E. Siemens, A. D. Bristow, X. Dai, A. S. Bracker, D. Gammon, and S. T. Cundiff

Phys. Rev. B 83, 245316 – Published 27 June 2011

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Physical Review B

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Exciton relaxation and coupling dynamics in a GaAs/AlxGa1−xAs quantum well and quantum dot ensemble

G. Moody, M. E. Siemens, A. D. Bristow, X. Dai, A. S. Bracker, D. Gammon, and S. T. Cundiff

Phys. Rev. B 83, 245316 – Published 27 June 2011

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Exciton relaxation and coupling dynamics in a GaAs/Al $_{x}$ Ga $_{1 - x}$ As quantum well and quantum dot ensemble