Dynamical properties of trions and excitons in modulation doped CdTe/CdMgZnTe quantum wells

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  • Dynamical properties of trions and excitons in modulation doped CdTe/CdMgZnTe quantum wells

    D. Brinkmanna,*, J. Kudrnaa, E. Vanagasa, P. Gilliota, R. Levya, A. Arnoultb,J. Cibertb, S. Tatarenkob

    aInstitut de Physique et de Chimie des Materiaux de Strasbourg, Groupe d'Optique Non Lineaire et d'Optoelectronique,

    (UMR 7504 CNRS-ULP-EPCM), 23, rue du Lss, B.P. 20 CR, F-67037 Strasbourg Cedex, FrancebLaboratoire de Spectrometrie Physique, (UMR 55 88 UJF Grenoble I CNRS) B.P. 87, F-38402 Saint-Martin-d'Heres Cedex, France


    We report on the population and phase relaxation of neutral excitons (X) and positively charged excitons (X1), called trions, in p

    modulation doped CdTe/CdMgZnTe multiple quantum wells. Time-resolved photoluminescence (PL) measurements which investigate

    the population dynamics show that trions and excitons are in thermal equilibrium with each other and allow to determine the lifetimes of

    trions and excitons. The coherent dephasing of both quasiparticles is studied by degenerate four-wave mixing (FWM). The slower dephasing

    of trions compared with excitons is interpreted in terms of trion and hole localization. Under excitation with spectrally broad femtosecond

    laser pulses, the FWM traces show modulations due to quantum beats between the trion and exciton transitions. q 1998 Elsevier Science S.A.All rights reserved.

    Keywords: Trions; Excitons; Modulation doped quantum wells; CdTe; Time-resolved photoluminescence; Four-wave mixing

    1. Introduction

    Optical spectra of semiconductors close to the band gap

    are predominantly determined by bound complexes of elec-

    trons and holes. In addition to excitons and biexcitons, most

    recently negatively and positively charged excitons have

    been of considerable interest. These so-called trions consist

    respectively of two electrons bound to a hole (X2) or of two

    holes bound to an electron (X1). Although the existence of

    trions was predicted some 40 years ago by Lampert [1], their

    observation in bulk semiconductors remained impossible

    due to the rather small binding energy of the additional

    carrier. Only the drastic enhancement of this binding energy

    in two dimensional structures [2] has allowed observing

    both kinds of trions in electron or hole gases in IIVI-

    [3,4] and IIIV- [58] semiconductor quantum wells


    Extensive studies have been published on the binding

    energy of trions, on their polarization dependence in

    magnetic elds and on their behaviour at different carrier

    densities. The aim of this work is to investigate the popula-

    tion relaxation of trions on the one hand and their coherent

    dephasing on the other in comparison with the respective

    relaxation processes of neutral excitons. Therefore we

    carried out time-resolved photoluminescence (PL) and

    degenerate four-wave mixing (FWM) experiments in p

    modulation doped CdTe/CdMgZnTe multiple QWs. In

    these samples positive trions have recently been unambigu-

    ously identied by magneto-optical measurements [4].

    2. Sample

    The considered sample was grown on a Cd0.88Zn0.12Te

    substrate by molecular beam epitaxy and contains 5 CdTe

    QWs of 8 nm thickness enclosed between

    Cd0.69Mg0.23Zn0.08Te barriers. At a distance of 50 nm on

    both sides of each QW the barriers are p-doped with

    3 1017cm23 nitrogen acceptors providing hole densitiesof several 1010cm22 in each QW [4]. This hole density

    ensures comparable oscillator strength for the exciton and

    the trion resonances. The low temperature (5 K) absorption

    (solid curve in the inset of Fig. 4) and PL (Fig. 1) spectra

    show a doublet structure with the trion line at 2.7 meV

    below the heavy-hole 1s exciton line.

    To reduce the hole density in the QWs we can photocre-

    ate electron-hole pairs in the doped barriers by exciting the

    sample above the optical gap of the barriers with a cw He-

    Ne laser. The electrostatic potential induced by the posi-

    tively charged holes attracts the electrons into the QWs

    Thin Solid Films 336 (1998) 286290

    0040-6090/98/$ - see front matter q 1998 Elsevier Science S.A. All rights reserved.

    PII S0040-6090(98)01246-2

    * Corresponding author; e-mail: brinkman@gonlo.u-strasbg.fr.

  • where they recombine and decrease the density of the hole

    gas. In contrast, the holes created in the barriers are repelled

    so that their transfer into the QWs is strongly inhibited. As a

    result the system is found in a steady state characterized by

    an enhanced exciton oscillator strength and a reduced

    number of trion transitions.

    3. Time-resolved photoluminescence

    In the time-resolved PL experiment the QWs are excited

    by 1.7 ps pulses stemming from a self-mode-locked Ti:Sap-

    phire laser with a repetition rate of 82 MHz. Its photon

    energy is tuned to about 20 meV above the exciton line,

    i.e. far below the optical gap of the barriers. This prevents

    the photoneutralization of the hole gas by electrons excited

    in the barriers. We estimate the density of photocreated

    electron-hole pairs to about 1010 cm22 per pulse and per

    QW. The decay of the PL signal after excitation is detected

    by a combination of a spectrometer and a Photonetics

    synchroscan streak camera. Using a spectral resolution of

    about 0.5 meV we obtain a time resolution of about 10 ps.

    The sample is kept in a helium bath cryostat at 5 K.

    The inset of Fig. 2 displays the time evolution of the

    luminescence for the maximum hole density detected at

    the photon energies of the exciton and of the trion reso-

    nances. For both transitions we nd exponential decays

    with an identical decay time t . We infer that the long-livinghole gas gives rise to thermal equilibrium between the trion

    and the exciton populations. The common decay rate t21

    can thus be expressed as a weighted mean value of the

    radiative decay rates t21x of the exciton and t21x1 of the

    trion [9] as

    t21 1 1 RRtX 1 tx1


    where R Ix=Ix1 is the integrated PL intensity ratio of exci-tons and trions. We suppose that t21x and t

    21x1 do not depend

    on the density of the hole gas. To control the parameter R we

    vary the density of the hole gas as explained above by

    changing the excitation intensity of the He-Ne laser. The

    small continuous contribution to PL due to the excitation by

    the He-Ne laser is subtracted from the total PL signal. Fig. 1

    shows the time-integrated PL spectra for maximum and

    minimum hole densities obtained without excitation by

    the He-Ne laser and with an excitation intensity of about 3

    mW cm22, respectively. The corresponding intensity ratios

    are R 0:29 and R 0:03. In the inset of the same gurewe compare the two PL decays detected at the trion photon

    energy for the two different hole densities. We clearly

    observe a faster decay for the higher hole density, i.e. for

    the smaller R.

    The evolution of t21 for different intensity ratios R isdisplayed in Fig. 2. The t with relation (1) is in good

    agreement with the experimental data. It yields the exciton

    and trion lifetime tx 550 ps and tx1 80 ps. The excitonlifetime is in good agreement with values recently reported

    for CdTe/CdMgTe QWs [10]. To interpret the factor

  • tx=tx2 < 4. The fact that we nd a larger ratio tx=tx1 < 7indicates an increase of the oscillator strength of trions

    compared with that of excitons.

    4. Degenerate four-wave mixing

    Our degenerate FWM experiment is performed in the

    two-beam self-diffraction conguration [11]. The sample

    is excited by two subsequent laser pulses of 80 fs-duration

    emitted by a tuneable self-mode-locked Ti:Sapphire laser.

    The self-diffracted FWM signal is dispersed in a spectro-

    meter and detected as a function of the delay time t betweenboth pulses by a photomultiplier and a lock-in amplier. The

    laser pulses have a spectral width of about 20 meV so that

    the exciton and the trion resonances can be simultaneously

    and coherently excited. The central photon energy of the

    laser is tuned to 12 meV below the exciton line. To inhibit

    the excitation of continuum states and to favour the trion

    resonance compared to that of the exciton. The sample

    temperature is kept at 5 K.

    Fig. 3 depicts the time-integrated FWM signal as a func-

    tion of the delay for different detection photon energies. The

    two bold curves correspond to the energies of the exciton

    and the trion transition, respectively. The total density of

    photocreated quasiparticles (excitons and trions) per laser

    pulse is estimated to 1:5 1010 cm22 so that the density oftrions lies almost one order of magnitude below the concen-

    tration of the hole gas.

    The FWM traces show an exponential decay, which is

    modulated by pronounced oscillations. We nd decay

    times TDX 1:0 ps for the exciton and TDX1 1:1 psfor the trion. Due to the inhomogeneous broadening of the

    resonances the dephasing times T2 are related to the decay

    times by T2 4TD [11] and the homogeneous linewidthsare given by Gh = 2TD

    . Despite the relatively high

    hole density in the QWs, the value we nd for the exciton

    GhX 0:32 meV is comparable to values obtained for freeexcitons in `empty' CdTe [12]. Moreover, it is smaller than

    homogeneous linewidths reported for excitons embedded in

    a gas of free carriers of corresponding densities in GaAs

    QWs [13]. However the most surprising fact is the compar-

    able dephasing of trions and excitons: GhX1 0:29 meV.One would expect charged quasiparticles like trions to be

    subjected to strong Coulomb interactions with each other

    and with the hole gas and thus to suffer a faster phase


    These results point to an interpretation in terms of loca-

    lization of holes and trions strongly diminishing their scat-

    D. Brinkmann et al. / Thin Solid Films 336 (1998) 286290288

    Fig. 3. Degenerate FWM traces for different detection photon energies (a)

    1624 meV, (b) 1625.2 meV, (c) 1626 meV, (d) 1627 meV, (e) 1627.9 meV,

    (f) 1629 meV. The bold curves correspond to the trion (X1) and the exciton

    (X) transition energies.

    Fig. 4. FWM traces detected at the photon energy of the exciton for two

    different hole densities, i.e. with (dashed line: low hole density) and without

    (solid line: high hole density) excitation of the sample by the cw He-Ne

    laser. The inset shows the corresponding absorption spectra.

  • tering efciencies. We presume that the holes are trapped in

    the uctuations of the electrostatic potential induced by the

    remote dopants and thus consider the trions as excitons

    bound to these immobilized holes. In a picosecond FWM

    experiment which will be described elsewhere [19], both

    resonances are excited independently to study the dephasing

    of trions and excitons as a function of their densities. This

    experiment demonstrates that the triontrion interaction is

    much weaker than the excitonexciton interaction and thus

    conrms our interpretation. A carrier localization in poten-

    tial uctuations has been used in n modulation doped struc-

    tures to explain the existence of exciton resonances at

    carrier densities of as high as 1011 cm22 [14].

    We proceed now to the discussion of the oscillations,

    which superpose the decay of the FWM signal. These oscil-

    lations have a period of TB 1:5 ps. The correspondingenergy difference DE h=T 2:8 meV agrees very wellwith the XX1-splitting of 2.7 meV so that the modulations

    could be attributed to quantum beats or polarization inter-

    ferences [15,16] between the two resonances. The latter

    occurs whenever two or more independent transitions emit

    at slightly different frequencies whereas `true' quantum

    beats are due to the quantum mechanical superposition of

    states when several transitions share a common level. To

    distinguish between both phenomena, one has to carefully

    analyze the spectrally resolved FWM signal. According to

    the calculations of Erland et al. [16] a phase shift of p isexpected in the oscillations for polarization interferences

    when the detection energy is tuned through a single reso-

    nance. Additionally, in this case the modulation should be

    almost extinguished at the photon energies of the contribut-

    ing transitions.

    In our measurements, the oscillations are much more

    pronounced at the photon energy of the X- and X1-lines

    than between the resonances. Moreover, only a small

    phase shift can be detected for different photon energies.

    We therefore, interpret the modulations to be mainly due

    to quantum beats with a certain contribution of polarization

    interferences. If the quantum beats occur between two levels

    which are inhomogeneously broadened, polarization inter-

    ferences can be observed between non-correlated transitions

    situated on the opposite edges of the two peaks. Moreover, a

    similar behaviour has been observed in spectrally resolved

    FWM for the coherent interaction of free and donor bound

    excitons [17,18]. In fact, if at least one localized hole lies

    within the coherence volume of the free exciton, the trion

    and the exciton states form a three level system with the

    non-excited crystal as common ground state. In this case the

    modulation could be solely attributed to quantum beats. In

    contrast, at low enough hole densities the mean distance

    between holes is larger than the free exciton Bohr radius

    so that three-level systems and isolated free-exciton two-

    level systems can co-exist in the QWs. This leads to a

    mixture of quantum beats and polarization interferences.

    To prove that the observed oscillations originate from

    beatings between the exciton and the trion transitions and

    that no other resonances are involved we performed FWM

    experiments at a reduced hole concentration. As in the PL

    measurements we excite the sample with a He-Ne laser to

    decrease the density of the hole gas. The absorption spectra

    at maximum hole density and under excitation by the He-Ne

    are shown in the inset of Fig. 4 as solid and dashed lines,

    respectively. One clearly recognizes the strong enhance-

    ment of the exciton transition at the lower hole density.

    Fig. 4 displays the corresponding FWM traces detected at

    the photon energy of the exciton transition. The pronounced

    modulation of the solid curve registered for the largest hole

    density disappears almost completely when the trion transi-

    tion is strongly inhibited (dashed curve). This is a clear

    indication for the beatings to be due to the coherent excita-

    tion of trions and excitons.

    In addition, at the lower hole concentration (dashed

    curve), we observe an increase of the exciton dephasing

    time pointing to a diminution of the exciton-hole scattering

    efciency. Finally, the enhancement of the exciton oscillator

    strength results in an enhanced excitonexciton correlation

    accounting for the increase of the FWM signal at negative

    delay times.

    5. Conclusion

    In summary, we performed time-resolved photolumines-

    cence and degenerate four-wave mixing to study the radia-

    tive decay and the coherent dephasing of trions and excitons

    in modulation doped CdTe/CdMgZnTe QWs. We observed

    that the radiative decay of trions is about seven times faster

    than that of excitons. We obtained trion dephasing times

    comparable with those of the excitons pointing to a locali-

    zation of trions and holes in the uctuations of the potential

    induced by the remote dopants. The FWM traces...


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