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

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

aInstitut de Physique et de Chimie des MateÂriaux de Strasbourg, Groupe d'Optique Non LineÂaire et d'OptoeÂlectronique,

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

Abstract

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 II±VI-

[3,4] and III±V- [5±8] semiconductor quantum wells

(QWs).

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 identi®ed 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 densities

of 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) 286±290

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-living

hole 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 t21

x1 of the

trion [9] as

t21 � 1 1 R

RtX 1 tx1

(1)

where R � Ix=Ix1 is the integrated PL intensity ratio of exci-

tons and trions. We suppose that t21x and t21

x1 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 ®gure

we 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 is

displayed 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 exciton

lifetime is in good agreement with values recently reported

for CdTe/CdMgTe QWs [10]. To interpret the factor <7

between the exciton and the trion decay times we can

compare our result with decay times obtained by Yoon et

al. [9] for excitons and negative trions in undoped mixed-

type-I-type-II GaAs/AlAs QWs. These authors found a ratio

D. Brinkmann et al. / Thin Solid Films 336 (1998) 286±290 287

Fig. 1. Time-integrated PL spectra under picosecond excitation at a photon

energy of 1651 meV. The dashed line shows the spectrum when the sample

is simultaneously excited by a cw He±Ne laser in order to reduce the hole

density. The solid line corresponds to the maximum hole density obtained

without excitation He±Ne laser. The corresponding time-resolved PL

signals are displayed in the inset.

Fig. 2. PL decay rate t21 as a function of R, the integrated PL intensity ratio

of excitons and trions. The curve shows a ®t by Eq. (1). The inset depicts the

PL decays detected at the photon energy of the trion (X1) and the exciton

(X) resonances at maximum hole density. The curves have been shifted

vertically for clarity.

tx=tx2 < 4. The fact that we ®nd a larger ratio tx=tx1 < 7

indicates 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 con®guration [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 between

both pulses by a photomultiplier and a lock-in ampli®er. 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 of

trions 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 TD�X� � 1:0 ps for the exciton and TD�X1� � 1:1 ps

for 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 linewidths

are given by Gh � É= 2TD

ÿ �. Despite the relatively high

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

Gh�X� � 0:32 meV is comparable to values obtained for free

excitons 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: Gh�X1� � 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

relaxation.

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) 286±290288

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 ef®ciencies. 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 trion±trion interaction is

much weaker than the exciton±exciton interaction and thus

con®rms 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 corresponding

energy difference DE � h=T � 2:8 meV agrees very well

with the X±X1-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 is

expected 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

ef®ciency. Finally, the enhancement of the exciton oscillator

strength results in an enhanced exciton±exciton 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 showed

modulations due to quantum beats between the trion and

exciton transitions.

Acknowledgements

We are grateful to B. HoÈnerlage for many fruitful discus-

sions and for a critical reading of the manuscript. The work

was supported by grants of the French MENRT. We are

indebted to Photonetics for lending us the synchroscan

streak camera.

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