Upper-barrier excitons: first magnetooptical study

Transcription

1 Upper-barrier excitons: first magnetooptical study M. R. Vladimirova, A. V. Kavokin 2, S. I. Kokhanovskii, M. E. Sasin, R. P. Seisyan and V. M. Ustinov 3 Laboratory of Microelectronics 2 Sector of Quantum and Coherent Phenomena 3 Laboratory of Heteroepitaxy rseis@ffm.ioffe.rssi.ru We report on a strong experimental evidence for the upper-barrier exciton (UBE) in a Bragg-confining (In, Ga)As/GaAs superstructure. The MBE-grown structure has been designed so that to provide for the appearance of a localized exciton state with energy exceeding the band-gap of GaAs by about 3 mev. Magnetoabsorption spectra show a strong resonant feature at.548 ev, which is attributed to the UBE transition. This exciton state causes pronounced Landau oscillations in the spectra. Fitting of the spectra by the transfer matrix technique yields an oscillator strength of the UBE twice larger than that of a bulk GaAs exciton, in excellent agreement with the first principles calculation. The exciton cyclotron mass appears to be equal to the conductivity electron mass which indicates a substantial in-plane localization of the hole.. Localization at positive energies More then 6 years ago, Wigner and von Neimann [] theoretically proved a possibility of upper-barrier electron localization at some specially prepared repulsive potential. A localized state with positive energy may appear due to multiple upper-barrier reflection of the electron s de Broglie wave at different steps of the potential. In 975 Stillinger [2] proposed semiconductor superlattices as a promising object for studying the Wigner Neimann localization. For experimental observation of the upper-barrier localized states carefully designed superstructures with ideally abrupt interfaces are required. Electron states confined in a marginal potential well upper real barriers have been intensively studied during the last 4 years [3 8]. The physical reason for their existence is a substantial modification of the crystal band structure in the presence of the superlattice potential. One-dimensional minibands and minigaps are formed in this case inside former conduction and valence bands at energies both below and above real barriers. In this case any defect-like broadening of one of barrier or well layers may cause appearance of localized discrete electronic states inside minigaps. The best confinement conditions for such states are achieved if the increased barrier thickness is equal to half the electron s de Broglie wavelength and the width of each superlattice layer is equal to quarter the wavelength. These are so called Bragg confining structures. Earlier [7, 8] we have shown that the oscillator strength of upper barrier excitons (UBEs) in Bragg confining structures may exceed that in conventional quantum wells. Experimentally, exciton states formed by upper-barrier electrons and holes have been studied mainly by PLE and Raman spectroscopy [4, 6] in periodic GaAs/(Al,Ga)As structures. In the present research we dealt with the (In,Ga)As/GaAs heterosystem, which seems more suitable for studies of UBEs, since here the barrier height, i.e. energy gap in GaAs, is known exactly. Two years ago we fabricated the first sample with (In,Ga)As/GaAs superlattice surrounding a single enlarged GaAs layer [8]. In spite of the fact that a rich excitonic spectrum was observed, a direct study of the UBEs could not be realized since (i) Bragg confinement condition was not satisfied, (ii) there was no upper-barrier localized state for a hole, and (iii) there was not enough of enlarged barriers in the structure. In order to avoid these negative factors, a new structure design was realized in the MBE-grown sample investigated in this work. The sample contained periods of a superstructure consisting of a 3 nm-thick GaAs layer surrounded by periods of a 3.4/6.5 nm In. Ga.9 As/GaAs superlattice. The structure was grown on a GaAs substrate, which then was completely removed by chemical etching. This allowed us to measure directly the transmission spectra of the structure. We expected appearance of a localized direct UBE formed by an electron and a hole from the first conduction and valence minigaps, respectively, as shown in Fig.. The same figure shows calculated electron and hole envelopes in the growth direction. One can see that both wave functions are quite well localized. Note that the Bragg confinement condition is satisfied for the electron. For the heavy hole the superlattice does not act as an ideal Bragg mirror, providing however quite a good localization due to heavy effective masses in the layers. The overlap integral between the electron and hole envelopes I eh =.98.

2 ψ e II e.59 I e I hh II hh 5 Å.456 ev R = 4. mev h - ω SL LT =.3meV.544 ev 2 R = 4.3 mev h - ω UB 3 LT =.4meV 5 Å ψ hh I hh =.98 Figure : Schematic band-structure of the sample. At the top and bottom are electron (Ψ e ) and hole (Ψ hh ) envelopes for the upper-barrier states. Table : Excitonic parameters obtained experimentally Longitudinal-transverse State splitting (mev) Damping (mev) Superlattice exciton Upper-barrier exciton Experiment and discussion Light transmission was measured at liquid helium temperature in magnetic fields of up to 7 T. Figures 2 and 3 show the transmission spectrum in zero field (solid line in Fig. 2 and top curve in Fig. 3). The spectrum exhibits three resonant features associated with the ground exciton state in the system formed by electron and hole in the first superlattice minibands (), with the UBE (2), and with the transition between electron and hole in second minibands (3). One can see that the energy of the UBE transition exceeds the energy gap in GaAs by almost 3 mev. Also note that no features are seen in the spectrum at the energy of bulk GaAs exciton, which manifests a complete dominance of the artificial band structure of the supercrystal over the original crystal band structure. The broken curve in Fig. 2 shows the theoretical fitting given by the transfer matrix method. Each layer was described by a complex dielectric function having resonance terms associated with excitonic transitions and steps related to interband transitions. The best fit was obtained with the excitonic parameters listed in the Table. It is instructive to compare the experimental excitonic parameters with those calculated from the first principles. Single particle wave functions (shown in Fig. ) and energies for UBEs were calculated by the transfer matrix technique as localized solutions of one-dimensional Schroedinger equation with a superstructure potential (for more details see [7]). Then, the exciton state was calculated variationally with the simplest trial function for electron-hole in-plane relative motion f (p) = 2/π exp( p/a)/a, withabeing a variational parameter (details are given in [9]). Solving the excitonic problem in the superlattice, we used a two-parameter trial function and adapted a miniband f (p, z) =(πa 2 p a z) /2 exp[ (p 2 /a 2 p + z2 /a 2 z )/2 ] effective mass approximation, so that our 2

3 ..2 Absorption (arb. units) Transmission (arb. units) SL: hω =.2 mev, Γ=.5 mev LT - UBE: hω =.4 mev, Γ= 5 mev LT E g GaAs Figure 2: Light transmission spectrum of the structure (full curves) and the fit (broken curves). absorption spectrum is shown at the bottom. Calculated 2 3 H = Absorption (arb. units) 3 2 E g GaAs 2.9 T Figure 3: Magnetoabsorption spectra of the structure. Arrows mark excitonic transitions. The vertical full line corresponds to the energy gap in GaAs. 3

4 Table 2: Excitonic parameters calculated from the first principles Longitudinal-transverse Binding energy State splitting (mev) at zero field (mev) Superlattice exciton Upper-barrier exciton procedure consisted in generalizing the method [] to the case of the magneto-exciton. Excitonic parameters calculated in this way are shown in Table Magnetic field (T) y (mev) Upper barrier Super lattice.7 K Figure 4: Fan diagrams formed by the ground exciton state and the upper-barrier exciton. Peak energies corrected by adding the calculated binding energy are also plotted versus the free electron cyclotron energies ( ω ) in coordinates y = ω (l + /2) lines and 2. The slope of these lines yield the exciton cyclotron mass. One can see a very good agreement between the experiment and the calculation, especially having in mind the fact that layer thicknesses have not been a subject of fitting. Figures 3 and 4 show the magnetoabsorption spectra of the structure and the corresponding fan diagram, respectively. A pronounced Landau quantization is seen both for the superlattice exciton and for the UBE. Correcting the fan diagrams by adding calculated exciton binding energies to the energies of the absorption peaks we obtained true Landau fans, which allowed us to determine the reduced cyclotron masses for both excitons. We found µ =.54 m for the superlattice exciton and µ =.7 m for the upper-barrier exciton. The latter value coincides with the electron effective mass in GaAs on the electron upper-barrier localized state level. This means that the heavy-hole in-plane mass is infinite, which may be caused by the in-plane upper-barrier localization of the hole. Most probably, the localization takes place owing to monolayer fluctuations of heteroboundaries, which are essential for the upper-barrier confined state. In this case the usual selection rules for transitions between different electron and hole Landau levels are violated so that one can see in absorption the transitions from a single hole level to all electron Landau levels, which explains 4

5 the absence of hole mass contribution corresponding to their infinity. In conclusion, a direct experimental evidence for upper-barrier localized excitons in (In, Ga)As/GaAs superstructure has been obtained by use of magnetooptical spectroscopy. In excellent agreement with theoretical expectations the upper-barrier excitons show a large oscillator strength, which manifests their strong quantum confinement. This work has been supported by the Russian Foundation for Basic Research. References [] J. von Neimann and E. Wigner 929 Phys. Z [2] F. H. Stillinger and D. R. Herrick 975 Phys. Rev. A 446 [3] C. Sirtori, F. Capasso, J. Faist, D. L. Sivco, S. N. G. Chu and A. Y. Cho 992 Appl. Phys. Lett [4] M. Zahler, I. Brener, G. Lenz, J. Salzman and E. Cohen 992 Appl. Phys. Lett [5] F. Capasso, C. Sirtori, J. Faist, D. L. Sivco, S. Nee, G. Chu and A. Y. Cho 992 Nature [6] M. Zahler, E. Cohen, J. Salzman, E. Linder and L. N. Pfeiffer 993 Phys. Rev. Lett [7] M. R. Vladimirova and A. V. Kavokin 995 Phys. Solid State [8] A. V. Kavokin, M. R. Vladimirova, R. P. Seisyan, S. I. Kokhanovskii, M. E. Sasin, V. M. Ustinov, A. Yu. Egorov and A. E. Zhukov 995 in Semiconductor Heteroepitaxy: Growth, Characterization and Device Applications ed B. Gil and R. -L. Aulombard (World Scientific: Singapore) p 482 [9] A. V. Kavokin, A. I. Nesvizhskii and R. P. Seisyan 993 Sov. Phys. Semicond [] E. L. Ivchenko and A. V. Kavokin 99 Sov. Phys. Semicond