Interwell excitons in GaAs/AlGaAs double quantum wells and their collective properties

Luminescence spectra of interwell excitons in GaAs/AlGaAs double quantum wells with electric-field-tilted bands (n-i-n) structures were studied. In these structures the electron and the hole in the interwell exciton are spatially separated between neighboring quantum wells by a narrow AlAs barrier. Under resonant excitation by circularly polarized light the luminescence line of the interwell excitons exhibited appreciable narrowing as their concentration increased and the degree of circular polarization of the photoluminescence increased substantially. Under resonant excitation by linearly polarized light the alignment of the interwell excitons increased as a threshold process with increasing optical pumping. By analyzing time-resolved spectra and the kinetics of the photoluminescence intensity under pulsed excitation it was established that under these conditions the rate of radiative recombination increases substantially. The observed effect occurs at below-critical temperatures and is interpreted in terms of the collective behavior of the interwell excitons. Studies of the luminescence spectra in a magnetic field showed that the collective exciton phase is dielectric and in this phase the interwell excitons retain their individual properties.     

Collective state of interwell excitons in GaAs/AlGaAs double quantum wells under pulse resonance excitation

The time evolution and kinetics of photoluminescence (PL) spectra of interwell excitons in double GaAs/AlGaAs quantum wells (n-i-n structures) have been investigated under the pulse resonance excitation of intrawell 1sHH excitons using a pulsed tunable laser. It is found that the collective exciton phase arises with a time delay relative to the exciting pulse (several nanoseconds), which is due to density and temperature relaxation to the equilibrium values. The origination of the collective phase of interwell excitons is accompanied by a strong narrowing of the corresponding photoluminescence line (the line width is about 1.1 meV), a superlinear rise in its intensity, a long time in the change of the degree of circular polarization, a displacement of the PL spectrum toward lower energies (about 1.5 meV) in accordance with the filling of the lowest state with the exciton Bose condensate, and a significant increase in the radiative decay rate of the condensed phase. The collective exciton phase arises at temperatures T<6 K and interwell exciton densities n=3×10¹⁰ cm^?2. Coherent properties of the collective phase of interwell excitons and experimental manifestations of this coherence are discussed.     

Phase diagram of the Bose condensation of interwell excitons in GaAs/AlGaAs double quantum wells

The luminescence of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructures) with large-scale fluctuations of random potential in the heteroboundary planes was studied at low temperatures down to 0.5 K. The properties of excitons whose photoexcited electron and hole are spatially separated in the neighboring quantum wells by a tunneling barrier were studied as functions of density and temperature. The studies were performed within domains about one micron in size, which played the role of macroscopic traps for interwell excitons. For this purpose, the sample surface was coated with a metal mask containing special openings (windows) of a micron size or smaller. Both photoexcitation and observation of luminescence were performed through these windows by the fiber optic technique. At low pumping powers, the interwell excitons were strongly localized because of the residual charged impurities, and the corresponding photoluminescence line was nonuniformly broadened. As the laser excitation power increased, a narrow line due to delocalized excitons arose in a threshold-like manner, after which its intensity rapidly increased with growing pumping and the line itself narrowed (to a linewidth less than 1 meV) and shifted toward lower energies (by about 0.5 meV) in accordance with the filling of the lowest exciton state in the domain. An increase in temperature was accompanied by the disappearance of the line from the spectrum in a nonactivation manner. The phenomenon observed in the experiment was attributed to Bose-Einstein condensation in a quasi-two-dimensional system of interwell excitons. In the temperature interval studied (0.5–3.6) K, the critical exciton density and temperature were determined and a phase diagram outlining the exciton condensate region was constructed.     

Exciton-exciton collisions and conversion of interwell excitons in GaAs/AlGaAs superlattices

The ratio of the densities of intra-and interwell excitons in a symmetric system of coupled quantum wells — a superlattice based on a GaAs/AlGaAs heterostructure — is investigated over a wide range of optical excitation power densities. Conversion of interwell excitons into intrawell excitons as a result of exciton-exciton collisions is observed at high exciton densities. Direct evidence for such a conversion mechanism is the square-root dependence of the interwell exciton density on the optical excitation level. The decrease in the lifetime of interwell excitons with increasing excitation density, as measured directly by time-resolved spectroscopy methods, confirms the explanation proposed for the effect. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 623–628 (25 April 1997)     

Bose condensation of interwell excitons in lateral traps: A phase diagram

The luminescence of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructures) containing large-scale random-potential fluctuations was studied. The study dealt with the properties of an exciton whose photoexcited electron and hole are spatially divided between the neighboring quantum wells under density variation and at temperatures of down to 0.5 K. We investigated domains ∼1 μm in size, which act as macroscopic exciton traps. Once the resonance laser pump power reaches a certain threshold, a very narrow delocalized exciton line appears (with a width less than 0.3 meV), which grows strongly in intensity with increasing pump power and shifts toward lower energies (by approximately 0.5 meV) in accordance with the exciton buildup in the lowest state in the domain. As the temperature increases, this spectral line disappears in a nonactivated manner. This phenomenon is assigned to Bose condensation occurring in the quasi-two-dimensional system of interwell excitons. The critical exciton density and temperature were determined within the temperature interval studied (0.5 to 3.6 K), and a phase diagram specifying the exciton condensate region was constructed. __________ Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 168–170. Original Russian Text Copyright ? 2004 by Dremin, Larionov, Timofeev.     

Bose condensation of interwell excitons in double quantum wells

The luminescence of interwell excitons in double quantum wells GaAs/AlGaAs (n-i-n heterostructures) with large-scale fluctuations of random potential in the heteroboundary planes was studied. The properties of excitons whose photoexcited electron and hole are spatially separated in the neighboring quantum wells were studied as functions of density and temperature within the domains on the scale less than one micron. For this purpose, the surfaces of the samples were coated with a metallic mask containing specially prepared holes (windows) of a micron size an less for the photoexcitation and observation of luminescence. For weak pumping (less than 50 μW), the interwell excitons are strongly localized because of small-scale fluctuations of a random potential, and the corresponding photoluminescence line is inhomogeneously broadened (up to 2.5 meV). As the resonant excitation power increases, the line due to the delocalized excitons arises in a thresholdlike manner, after which its intensity linearly increases with increasing pump power, narrows (the smallest width is 350 μeV), and undergoes a shift (of about 0.5 μeV) to lower energies, in accordance with the filling of the lowest state in the domain. With a rise in temperature, this line disappears from the spectrum (T _c ≤ 3.4 K). The observed phenomenon is attributed to Bose-Einstein condensation in a quasi-two-dimensional system of interwell excitons. In the temperature range studied (1.5–3.4 K), the critical exciton density and temperature increase almost linearly with temperature.     

Interwell excitons in GaAs superlattices

The formation of spatially indirect excitons in superlattices with narrow minibands is investigated experimentally. The interwell exciton is similar to the first Wannier–Stark localized exciton of an electrically biased superlattice. However, in the present case the localization is mediated by the Coulomb interaction of the electron and the hole without external fields.     

Interwell exciton relaxation in semimagnetic asymmetric double quantum wells

The possibility of magnetic field control of the spectral and polarization characteristics of exciton recombination is examined in Cd(Mg, Mn) Te-based asymmetric double quantum wells. At low fields, the exciton transition in a semimagnetic well is higher in energy than that in a nonmagnetic well and the interwell exciton relaxation is fast. In contrast, when the energy order of the exciton transitions reverses at high fields, unexpectedly slow relaxation of σ⁻ polarized excitons from the nonmagnetic well to the σ⁺-polarized ground state in the semimagnetic well is observed. Strong dependence of the total circular polarization degree on the heavy-light hole splitting Δ _hh-lh in the nonmagnetic well is found and attributed to the spin dependent interwell tunneling controlled by exciton spin relaxation. Such a slowing down of the relaxation allows separation of oppositely spin-polarized excitons in adjacent wells. The text was submitted by the authors in English.     

Direct and interwell excitons in magnetic nanostructures

The energies of direct and interwell excitons in superlattices based on europium and lead sulfides have been calculated. It is established that these excitons have higher oscillator strengths and binding energies due to the indirect exchange. This circumstance can be used in semiconductor devices operating on exciton transitions.     

Collective state in a bose gas of interacting interwell excitons

Experiments associated with direct observations of a collective state in a gas of interacting interwell excitons in GaAs/AlGaAs double quantum wells are discussed. The structures constitute Schottky photodiodes. In a metallic gate, circular windows of various sizes (diameters of 2 to 20 μm) are etched by means of electronic-beam lithography. Through these windows, the photoluminescence of interwell and intrawell excitons is excited and detected. A microscopic device allows the observation of the spatial structure of luminescence with a resolution of 1 μm through the windows of a sample placed in superfluid helium. Using optical interference filters, the spatial structure of the luminescence is analyzed selectively in the spectrum for interwell and intrawell excitons under the same experimental conditions. It is found that the photoluminescence of interwell excitons under certain conditions exhibits an axisymmetric spatial structure: along the perimeter of the windows through which the photoluminescence is observed, a regular ring pattern of equidistant bright spots of the luminescence of interwell excitons appears. This structure appears only above the photoexcitation power threshold and the number of equidistant bright spots in the ring increases with the pumping power. At high pumping powers, the structure of distinct periodic luminescence spots is smeared. At a fixed pumping power, the phenomenon exhibits explicit critical temperature dependence: the structure of regularly located luminescence spots is smeared at T > 4 K. Axisymmetric spatial configurations of equidistant luminescence spots are observed in windows of the diameters 2, 5, and 10 μm. For intrawell excitons, the spatial structure of luminescence is not observed under similar experimental conditions: the luminescence of intrawell excitons is spatially uniform in all the windows under investigation. The effect is a result of the collective behavior of interacting interwell excitons.     

Collective behavior of a spin-aligned gas of interwell excitons in double quantum wells

The kinetics of a spin-aligned gas of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructure) is studied. The temperature dependence of the spin relaxation time for excitons, in which a photoexcited electron and hole are spatially separated between two adjacent quantum wells, is analyzed. For this purpose, use was made of pulsed circularly polarized resonant photoexcitation of intrawell 1sHH excitons by a femtosecond frequency-controlled laser. A sharp increase in the spin-relaxation rate is observed for interwell excitons upon a change in temperature from 2 to 3.6 K. This effect is associated with indirect evidence of the coherence of the collective phase of interwell excitons at temperatures below the critical value.     

Interwell excitons in a lateral potential well in an inhomogeneous electric field

The luminescence of interwell excitons in double quantum wells based on GaAs/AlGaAs semiconductor heterostructures (n-i-n structures) in a lateral trap prepared with the use of an inhomogeneous electric field was studied at helium temperatures. A rather strong and inhomogeneous electric field occurred in the depth of the heterostructure when a current passed through the contact between the conducting tip of a tunneling microscope and the heterostructure surface to the bulk region containing a built-in gate. Because of the Stark shift of energy bands in the electric field, the photoexcited electrons and holes are spatially separated in neighboring quantum wells by a tunnel-transparent barrier and are bound into interwell quasi-two-dimensional excitons. These excitons have a dipole moment even in the ground state. Therefore, electrostatic forces in the inhomogeneous electric field cause the excitons to move in the plane of quantum wells toward the maximum field region and eventually accumulate in the lateral trap artificially prepared in such a way. The maximum trap depth achieved through the inhomogeneous electric field was 13.5 meV, and its lateral size was about 10 μm. It is shown that, in the traps prepared in this way, photoexcited interwell excitons behave with increasing concentration at sufficiently low temperatures (T=2K) in the same fashion as in the lateral traps caused by large-scale fluctuations of the random potential. At concentrations exceeding the percolation threshold, the interwell excitons condense into the lowest energy state in the trap.     

Temperature dependence of luminescence intensity under Bose condensation of interwell excitons

Photoluminescence of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructure) containing large-scale random potential fluctuations in the planes of heteroboundaries is studied. The properties of excitons, in which a photoexcited electron and a hole are spatially separated in neighboring quantum wells, were investigated upon variation of the power density of off-resonance laser excitation and temperature (1.5–4.2 K), both under lateral (in the heteroboundary plane) confinement of the excitation region to a few micrometers and without such a limitation (directly from the region of laser-induced photoexcitation focused to a spot not exceeding 30 μ. Under low pumping (with a power smaller than a microwatt), interwell excitons are strongly localized due to small-scale random potential fluctuations and the corresponding photoluminescence line is nonhomogeneously broadened to 2.5–3.0 meV. With increasing pumping power, the narrow line of delocalized excitons with a width of approximately 1 meV emerges in a threshold manner (the intensity of this line increases superlinearly near the threshold with increasing pumping). For a fixed pumping, the intensity of this line decreases linearly upon heating until it completely vanishes from the spectrum. The observed effect is attributed to Bose condensation in a quasi-two-dimensional system of interwell excitons. Within the proposed model, we show that the linear mode in the behavior of the luminescence intensity until its disappearance in the continuum of the photoluminescence spectrum upon a change in temperature is observed only for the condensed part of interwell excitons. At the same time, the luminescence of the above-the-condensate part of excitons is almost insensitive to temperature variations in the temperature range studied.     

Effects of hydrostatic pressure on intrawell and interwell excitons in a strained GaAs/GaAlAs double quantum well system

Binding energies of intrawell and interwell excitons are investigated in a GaAs/GaAlAs double quantum well system in the presence of hydrostatic pressure applied in the z-direction. Calculations have been carried out with the variational technique within the single band effective mass approximations using a two parametric trial wave function. The interband emission energy as a function of well width is calculated in the influence of pressure. The pressure dependent photoionization cross section for a charged exciton placed at the center of the quantum well is computed as a function of normalized photon energy. The dependence of the photoionization cross section on photon energy is carried out for the charged excitons. The resulting spectra are brought out for light polarized along and perpendicular to the growth direction. The results show that the charged exciton binding energy, interband emission energy and the photoionization cross section depend strongly on the well width and the hydrostatic pressure. Our results are compared with the other existing literature available.     

Temperature dependence of indirect-exciton luminescence in in-plane magnetic field

We report on a magneto-luminescence on a double quantum well subject to an in-plane magnetic field. The attention is paid to the properties of interwell excitons, which are indirect in the real space and which become indirect in the reciprocal space as well when a finite in-plane magnetic field is applied. Such indirect exciton states become optically inactive unless some relaxation mechanisms of their momentum appear. The experiment is carried out on a sample where, as reported previously, the radiative recombination of indirect excitons is possible due to their localization or via collisions with structural defects. The experimental data presented here, measured at various temperatures, favour the latter mechanism which is less sensitive to the system temperature in comparison with the former one.     

Lifetimes of bound excitons in CdSe

Lifetime measurements have been made on bound excitons in CdSe, by using the time-correlated single photon counting and a cw mode-locked dye laser. The lifetimes of the T₂ (an exciton bound to a neutral donor) and I₁ (an exciton bound to be a neutral acceptor) bound excitons have been determined to be 0.50±0.05 and 0.80±0.05 ns, respectively. These values are in good agreement with those predicted by the model of Rashba and Gurgenishvili.     

Binding energies of wannier excitons in GaAs-Ga1−xAlxAs quantum well structures

Binding energies of Wannier excitons in a quantum well structure consisting of a single slab of GaAs sandwiched between two semi-infinite slabs of Ga_1?xAl_xAs are calculated using a variational approach. Due to reduction in symmetry along the axis of growth of these quantum well structures and the presence of band discontinuities at the interfaces, the degeneracy of the valence band of GaAs is removed leading to two exciton systems, namely, the heavy hole exciton and the light hole exciton. The variations of the binding energies of these two excitons as a function of the size of the GaAs quantum wells for various values of the heights of the potential barrier are calculated and their behavior is discussed.     

Time-resolved spectra and kinetics of the exciton photoluminescence in different types of GaAs/AlAs superlattices

The temperature dependence of the recombination dynamics of excitons is investigated by time-resolved photoluminescence spectroscopy in(GaAs)_n / (AlAs)_n superlattices, where n denotes the layer thickness in monolayers, for different types of band structures. In direct-gap superlattices with a layer thickness of the order or larger than the exciton Bohr radius, the carrier dynamics is dominated by the transfer from light-hole to heavy-hole excitons. When the layer thickness becomes smaller than the exciton radius, the dynamics of free excitons is controlled by localization. vb In quasi-direct and indirect-gap superlattices, the influence of lateral potential fluctuations due to interface roughness completely governs exciton recombination.     

Exciton-plasma transition in GaAs

In this work, we study the stability of excitons at high density, i.e. we calculate the reduction of the exciton binding energy due to exciton-exciton interactions in a high-density exciton gas. We derive first the effective electron-hole interaction in the presence of free carriers and excitons. We use the static approximation. The exciton binding energy is calculated by the variational technique. The computations are specialized to GaAs. We investigate the critical density when the exciton binding disappears, which corresponds to the exciton plasma transition. We conclude that this transition occurs at higher density than the reverse plasma exciton transition, determined by the standard criteria a₀q_D =1.19 [Rogers F. J., Graboske H. C., Jr. and Harword D. J., Phys. Rev.A1, 1577 (1970)].     

Magnetopolaritons in ZnTe

From an invariant expansion, we construct the exciton Hamiltonian for the Γ₆×Γ₈ excitons in theT _d -type material ZnTe represented by an 8×8 matrix including the influences of a finite wave vector and an external magnetic field. We diagonalize the Hamiltonian matrix to obtain the exciton states. Then the excitons are coupled to the electromagnetic radiation field thus giving the polariton states. The theoretical dispersion curves are fitted to the results of two-photon Raman scattering and reflection experiments in magnetic fields up to 22 T. From this fit we deduce precise values for the eigenergies, exciton masses,g-factors, and diamagnetic shifts.