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.     

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.     

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.     

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.     

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 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.     

Collective behavior of interwell excitons in GaAs/AlGaAs double quantum wells

Photoluminescence spectra of interwell excitons in double GaAs/AlGaAs quantum wells (n-i-n structures) have been investigated (an interwell exciton in these systems is an electron-hole pair spatially separated by a narrow AlAs barrier). Under resonance excitation by circularly polarized light, the luminescence line of interwell excitons exhibits a significant narrowing and a drastic increase in the degree of circular polarization of photoluminescence with increasing exciton concentration. It is found that the radiative recombination rate significantly increases under these conditions. This phenomenon is observed at temperatures lower than the critical point and can be interpreted in terms of the collective behavior of interwell excitons.     

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.     

Two-photon correlations of luminescence at the Bose-Einstein condensation of dipolar excitons

Correlations of the luminescence intensity (the second-order correlation function g ⁽²⁾(τ)), where τ is the delay time between the photons detected in pairs) under the conditions of the Bose-Einstein condensation (BEC) of dipolar excitons has been studied in a temperature range of 0.45–4.2 K. Photoexcited dipolar excitons have been accumulated in a lateral trap in a GaAs/AlGaAs Schottky diode with a 25-nm wide single quantum well with an electric bias applied across the heterolayers. Two-photon correlations have been measured with the use of a two-beam intensity interferometer with a time resolution of }~0.4 ns according to the well-known classical Hanbury-Brown-Twiss scheme. The photon bunching has been observed at the onset of Bose-Einstein condensation manifested by the appearance of a narrow exciton condensate line in the luminescence spectrum at an increase in the optical pumping (the line width near the threshold is ?200 μeV). At the same time, the two-photon correlation function itself obeys the super-Poisson distribution, g ⁽²⁾(τ) > 1, at time scale τ_c ? 1 ns of the system coherence. The photon bunching is absent at a pumping level substantially below the condensation threshold. The effect of bunching also decreases at pumping significantly above the threshold, when the narrow exciton condensate line starts to dominate in the luminescence spectra, and finally disappears with the further increase in the optical excitation. In this region, the distribution of pair photon correlations is a Poisson distribution manifesting the united quantum coherent state of the exciton condensate. Under the same conditions, the first-order spatial correlation function g ⁽¹⁾(r) determined from the interference pattern of the luminescence signals from the spatially separated parts of the condensate at constant pumping remains noticeable at distances of no less than 4 μm. The discovered effect of photon bunching is very sensitive to temperature and decreases by several times with a temperature increase in the range of 0.45–4.2 K. Assuming that the luminescence of the dipolar excitons directly reflects the coherence properties of the gas of interacting excitons, the discovered photon bunching at the onset of condensation, where the fluctuations of the exciton density and, consequently, of the luminescence intensity are most significant, indicates a phase transition in the interacting Bose gas of excitons, which is an independent way of detecting the Bose-Einstein condensation of 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.     

Interface-related effects on confined excitons in GaAs/AlxGa1−xAs single quantum wells

Confined excitons in non-abrupt GaAs/Al_xGa_1−xAs single quantum wells are studied. The graded interfaces are described taking into account fluctuations in their thickness a and positioning with respect to the abrupt interface picture. Numerical results for confined (0,0),(1,1) and (0,2) excitons in GaAs/Al_0.3Ga_0.7As quantum wells show that while the interfacial fluctuations produce small changes (<0.5 meV) in the exciton binding energies, the confined exciton energies can be red- or blue-shifted as much as 25 meV for wells with mean width of 50 Å and 2 ML wide interfaces.     

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)     

Luminescence of excitons in slightly asymmetric double quantum wells

We report the first studies of exciton luminescence spectra from asymmetric double quantum wells (DQWs) of very similar width. The DQWs were of GaAs/AlGaAs and the differences in widths of the coupled wells were one or two monolayers. The coupled direct and indirect exciton states anticross with a resonance splitting of 1.33 meV. An additional luminescence line appearing at low temperatures is identified as a localized indirect exciton. Fiz. Tverd. Tela (St. Petersburg) 39, 735–739 (April 1997)     

Exciton/plasmon mixing in metal–semiconductor heterostructures

We report on the strong coupling between surface plasmons and inorganic quantum well excitons. The sample is formed by a corrugated silver film deposited on the top of a heterostructure consisting of five GaAs/GaAlAs quantum wells grown by molecular beam epitaxy. Reflectometry experiments at low temperature (77 K) evidence the formation of plasmon/heavy-hole exciton/light-hole exciton mixed states. The interaction energies, deduced by fitting the experimental data with a coupled oscillator model, amount to 22 meV for the plasmon/light-hole exciton and 21 meV for the plasmon/heavy-hole exciton. Some particularities of the plasmon–exciton coupling are also discussed and qualitatively related to the plasmon polarization.     

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.     

The optical properties of Be,Mg and Zn-diffused gallium phosphide

Interest in the Ga-site acceptors Be and Mg was stimulated by the possibility that they might produce efficient luminescence on association with O, analogous to the well-known red Zn-O luminescence in GaP but at higher transition energy. Attention was directed to diffusion doping by Be and Mg of GaP O-doped during growth because the reactivity of Be and Mg with O renders double doping during crystal growth very difficult. Structured green donor-acceptor pair spectra were observed at 1.6°K from many Be-diffused crystals, yielding an accurate measure of (E_A)_BE, 50 ± 1 meV. Moderately efficient orange-red luminescence was also observed below ∼ 100 °K from these crystals, but the intensity of this luminescence decreased rapidly to negligible levels by ∼ 200°K. This luminescence also contains sharp structure at 1.6°K, of a form characteristic of the decay of excitons bound to complex centres. Many sharp phonon replicas occur, involving local modes as well as characteristic GaP modes. One set of no-phonon lines, at least, near 2.19 eV, shows zero-field splitting, luminescence decay times and behaviour in magnetic and external strain fields characteristic of exciton decay at a centre with <100>; or <111>-type symmetry axes, containing no extra electronic particles. The exciton state is split by 2.4 meV by J-J coupling, and the axial field of the centre splits the hole states by ∼ 1.0 meV. These bound excitons are specifically characteristics of diffused GaP and appear analogous to bound excitons observed below 2.12 eV in Zn-diffused GaP. It is probable that the relevant centres contain diffusion components such as Be or Zn interstitials and improbable that O_P is involved. By contrast, weak orange bound exciton luminescence observed in Mg-diffused GaP does involve O, presumably as O_P. No analysis of the magneto-optical behaviour of this Mg-related bound exciton was possible in our crystals, so its symmetry axis was not established. It is possible that this is the Mg_Ga-O_P bound exciton. If so, the two-fold reductions in the exciton localisation energy from ∼ 0.32 eV to ∼ 0.15 eV and in the mass of the Ga-site substituent has produced dramatic changes in the form of the phonon cooperation between the Zn-O and “Mg-O” excitons. The “Mg-O” exciton luminescence is not dominant in our crystals, even at low temperature. The exciton state is again split by a local crystal field as well as by J-J coupling, but here the former splitting is predominant; 2_∈0 = 3.9 meV, Δ = 0.60 meV.     

Photoluminescence and exciton resonances over the scattered light in multiphonon spectra of resonant scattering in the CdTe/ZnTe superlattices with narrow quantum wells

Photoluminescence and Raman scattering spectra in CdTe/ZnTe heterostructures and superlattices with narrow quantum wells (4.8–9.2 Å) in a temperature range of 5–300 K have been measured. The temperature dependences of the intensity of exciton luminescence in isolated quantum wells have been studied, and the thermal activation energies associated with the effective barriers for electrons and holes have been determined. In CdTe/ZnTe heterostructures, the binding energies of an exciton with a heavy hole have been determined as functions of the quantum well width. The multiphonon Raman spectra that exhibit distinctive features, such as the weak intensity of nLO phonon lines of ZnTe (n < 8), the absence of their dependence on the number n (n > 2), and the multiple participation in scattering of acoustic LA phonons with large wave vector, have been investigated. The results have been explained based on the concept of the relaxation of hot excitons over the exciton band.     

Charge and energy transfer in double asymmetric quantum wells with quantum dots

The luminescence and luminescence excitation spectra of CdSe/ZnSe quantum dots are studied in a set of double quantum wells with the ZnSe barrier of width 14 nm, the same amount of a deposited CdSe layer forming a deep well and shallow wells with different depths. It is found that for a certain relation between the depths of shallow and deep wells in this set, conditions are realized under which the exciton channel in the luminescence excitation spectrum of a shallow well dominates in the region of kinetic exciton energies exceeding 10 longitudinal optical phonons above the bottom of the exciton band of the ZnSe barrier. A model is developed for the transfer of electrons, holes, and excitons between the electronic states of shallow and deep quantum wells separated by wide enough barriers. It is shown that the most probable process of electronic energy transfer between the states of shallow and deep quantum wells is indirect tunneling with the simultaneous excitation of a longitudinal optical phonon in the lattice. Because the probability of this process for single charge carriers considerably exceeds the exciton tunneling probability, a system of double quantum wells can be prepared in which, in the case of weak enough excitation, the states of quantum dots in shallow quantum wells will be mainly populated by excitons, which explains experimental results obtained.     

Effect of heteroboundary spreading on the properties of exciton states in Zn(Cd)Se/ZnMgSSe quantum wells

Exciton states in Zn(Cd)Se/ZnMgSSe quantum wells with different diffusion spreading of interfaces are studied by optical spectroscopy methods. It is shown that the emission spectrum of quantum wells at low temperatures is determined by free excitons and bound excitons on neutral donors. The nonlinear dependence of the stationary photoluminescence intensity on the excitation power density and the biexponential luminescence decay are explained by the neutralization of charged defects upon photoexcitation of heterostructures. With the stationary illumination on, durable (about 40 min) reversible changes in the reflection coefficient near the exciton resonances of quantum wells are observed. It is shown that, along with the shift of exciton levels, the spreading of heteroboundaries leads to three effects: an increase in the excitonphonon interaction, an increase in the energy shift between the emission lines of free and bound excitons, and a decrease in the decay time of exciton luminescence in a broad temperature range. The main reasons for these effects are discussed.     

Temperature dependent time-resolved exciton luminescence in GaAs/AlGaAs quantum wires and dots

Transient photoluminescence of GaAs/AlGaAs quantum wires and quantum dots formed by strain confinement is studied as a function of temperature. At low temperature, luminescent decay times of the wires and dots correspond to the radiative decay times of localized excitons. The radiative decay time can be either longer or shorter than that of the host quantum well, depending on the size of the wires and dots. For small wires and dots (∼ 100 nm stressor), the exciton radiative recombination rate increases due to lateral confinement. Exciton localization due to the fluctuation of quantum well thickness plays an important role in the temperature dependence of luminescent decay time and exciton transfer in quantum wire and dot structures up to at least ∼ 80 K. Lateral exciton transfer in quantum wire and dot structures formed by laterally patterning quantum wells strongly affects the dynamics of wire and dot luminescence. The relaxation time of hot excitons increases with the depth of strain confinement, but we find no convincing evidence that it is significantly slower in quasi 1-D or 0-D systems than in quantum wells.