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Infrared spectroscopy of intraband transitions in self-organized InAs/GaAs quantum
dots
S. Sauvage, P. Boucaud, F. H. Julien, J.-M. Gérard, and J.-Y. Marzin
Citation: Journal of Applied Physics 82, 3396 (1997); doi: 10.1063/1.365654
View online: http://dx.doi.org/10.1063/1.365654
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Infrared spectroscopy of intraband transitions in self-organized
InAs/GaAs quantum dots
S. Sauvage, P. Boucaud,a) and F. H. Julien
Institut d’Electronique Fondamentale, URA CNRS 22, Ba
ˆtiment 220, Universite
´Paris-Sud,
91405 Orsay, France
J.-M. Ge
´rard and J.-Y. Marzin
France Telecom, CNET Bagneux, 196 Avenue H. Ravera, 92225 Bagneux, France
~Received 19 March 1997; accepted for publication 24 June 1997!
We have investigated the midinfrared absorption between confined levels of undoped InAs/GaAs
quantum dots obtained by self-organized growth. The infrared absorption is measured by a
photoinduced infrared spectroscopy. Quantum dots with different sizes are analyzed as a function of
temperature, interband pump photon energy, intensity, and infrared polarization. We show that in
the 90–250 meV energy range the quantum dots exhibit intraband absorption between confined
levels, which are polarized along the growth axis as for usual conduction intersubband transitions in
quantum wells. Intraband absorption is observed for either selective excitation of the dots or
excitation via absorption in the wetting and GaAs layers. Based on the energy position and the
temperature dependence, the infrared resonances are attributed to intraband transitions between
confined holes and to bound-to-continuum transitions of electrons, which, respectively, shift to high
and low energy as the dot size is decreased. The reported features are found in qualitative agreement
with the theoretical predictions of Grundmann et al. @Phys. Rev. B 52, 11 969 ~1995!#.©1997
American Institute of Physics. @S0021-8979~97!03119-8#
I. INTRODUCTION
Stranski–Krastanov growth of highly mismatched semi-
conductors can lead to the spontaneous formation of islands.1
The nucleation of the pseudomorphic islands is driven by the
strain, and results in the formation of self-organized quantum
dots. These quantum dots are of particular interest since they
exhibit three-dimensional ~3D!confinement. In the case of
InAs on GaAs, the nucleation of the quantum dots starts after
the deposition of a 0.5 nm thick InAs layer. The size of the
dots can be monitored by varying the InAs coverage and the
time delay before GaAs regrowth. The growth of such het-
erostructures can be easily achieved by molecular beam ep-
itaxy and numerous reports have been published on inter-
band properties of these zero-dimension clusters.2Depending
on the growth conditions, different shapes, either pyramidal
or lens, can be obtained for the islands. Due to the inhomo-
geneous size distribution, the photoluminescence ~PL!results
from the superposition of the single narrow PL lines of indi-
vidual dots3,4 and is relatively broad ~typically, 50 meV!.
Interband lasing has been demonstrated in this deltalike-
density-of-state materials.5The intraband properties of these
atomiclike semiconductor heterostructures appear also very
promising since, unlike intersubband transitions in quantum
wells, transitions with large oscillator strength polarized ei-
ther perpendicular or in the layer plane should take place
depending on the spatial symmetry of the involved state
wave functions. Apart from the fundamental properties and
spectroscopy of the quantum dots, intraband absorption
could be used for infrared photodetection. Moreover, long
nonradiative lifetimes between excited and ground levels
have been predicted in these low-dimensional structures due
to phonon bottleneck effects.6This situation could be prom-
ising for achieving intraband stimulated emission in quantum
dots.7However, the bottleneck effect is still under debate
since the relaxation in the dots could be mediated by
Auger-like8or multiphonon relaxation processes.9
The energy position of the excited levels in quantum
dots has already been reported in the literature. Based on
resonant PL measurements, the presence of excited levels in
the conduction band of the dots has been evidenced,10 but the
reported energies were close to the phonon energy and the
presence of multiphonon relaxation processes could be at the
origin of the resonance peaks in the PL. Quantum levels of
the self-assembled dots have also been investigated by either
capacitance or far-infrared spectroscopy.11,12 In the latter
case, the islands were lens shaped and the size of the dots
was quite large ~typically, 20 nm in diameter and 7 nm in
height!. An energy spacing around 50 meV was reported
between the ground and first excited state in the conduction
band. We underline that both shape and size are important
properties for the dots since both parameters can modify the
expected interlevel spacing either in the conduction or in the
valence band. Moreover, depending on the parameters in-
cluded in the numerical modelization ~shape, strain, piezo-
electric potential,...!, different electronic structures have been
reported so far for the dots.3,13 The intraband spectroscopy,
which provides a direct measurement of the confinement en-
ergies appears, therefore, as an appropriate tool to disen-
tangle the energy structure of the dots.
In this paper, we report on intraband absorption spec-
troscopy in InAs/GaAs quantum dots. The InAs/GaAs sys-
tem has been chosen as a representative system for intraband
absorption in self-organized quantum dots. The dots investi-
gated in our work have a square base pyramidal shape before
a!Electronic mail: phill@ief.u-psud.fr
3396 J. Appl. Phys. 82 (7), 1 October 1997 0021-8979/97/82(7)/3396/6/$10.00 © 1997 American Institute of Physics
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GaAs regrowth.3When the dots are overgrown by GaAs, the
islands present a lens shape. The present islands have a typi-
cal height of 3 nm and differ from the dots reported in Refs.
11 and 12, which have a typical height of 7 nm. Both elec-
tron and holes intraband transitions are analyzed in the 90–
250 meV range as a function of the infrared polarization, the
temperature, and the interband pump energy and intensity for
quantum dots with various sizes. The intraband absorption is
observed under either resonant or nonresonant interband ex-
citation of the dots. The full width at half-maximum
~FWHM!of the absorption for bound-to-bound hole absorp-
tion is around 15 meV, a value which reflects the size distri-
bution of the dots. The dependence of the photoinduced ab-
sorption with pump intensity exhibits a saturation behavior.
From the measurement of the saturated absorption, we get an
estimate of the absorption cross section of the quantum dots.
Our results on quantum dots are interpreted using the three-
dimensional effective mass calculations of energy levels in
quantum dots reported by Grundmann et al..13 Note that, in
this work, the authors assume a pyramidal shape for the is-
lands and take into account the strain distribution and the
piezoelectric potential.
II. SAMPLES AND EXPERIMENTAL SETUP
The samples were grown by molecular beam epitaxy and
consist of 30 layers of InAs dots separated by 50 nm GaAs
barriers, the whole structure being covered by a 140 nm
GaAs cap layer. The samples are nominally undoped and
grown on ~001!GaAs oriented substrates. Because the
sample was not rotated during the growth, the distribution of
size of the quantum dots intentionally varies as a function of
the position on the wafer, which in turn, allows studying, on
the same wafer, the influence of the dot sizes. In the follow-
ing, samples A1,A
2
, and A3will correspond, respectively, to
a distribution of large, medium, and small dots. The overall
structure, dots and barriers, has been grown at 520 °C under
631026Torr As4beam equivalent pressure. The thickness
of the InAs layer below the quantum dot is 2.1 ML for
sample A1and 1.7 ML for sample A3. The nominal growth
rate for sample A1is '0.1
m
m/h. We have separately used
one sample with only ten InAs layers ~B!separated by 20 nm
GaAs barriers, which exhibits a better homogeneity of the
dots resulting in a narrower PL spectrum at low temperature.
For this particular sample, the growth rate was '0.2
m
m/h.
For infrared measurements, the samples were polished in a
multipass waveguide geometry with 45° facets in order to
enhance the absorption along the growth axis.14 The polar-
ization of the incoming infrared beam was set either in s
polarization ~parallel to the layer plane!or ppolarization
~50% of the component of the electric field along the growth
axis!. Since the density of dots is around 1010–1011 cm22,3
which is much lower than the usual doping concentration
achieved in quantum wells for observing intersubband tran-
sitions, the direct measurement of intraband absorption in
doped quantum dots is not a straightforward task. In order to
overcome this problem, we have used a double modulation
technique to enhance the sensitivity of the infrared measure-
ments. The carriers are optically generated in the quantum
dots using a chopped interband pumping and the infrared
absorption is measured in a Fourier transform infrared spec-
trometer operated in step-scan mode after lock-in detection.
FIG. 1. 5 K photoluminescence spectra of samples A1,A
2
,A
3
, and B
excited with a laser diode at 824 nm.
FIG. 2. ~a!Photoinduced infrared absorption DT/Tof sample A1vs tem-
perature. The interband excitation is provided with a 40 mW laser diode.
The curves have been offset for clarity. The absorption vanishes beyond 350
meV, which, in turn, gives the base line of each curve. ~b!Photoinduced
infrared absorption DT/Tof sample B vs temperature.
3397J. Appl. Phys., Vol. 82, No. 7, 1 October 1997 Sauvage
et al.
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Interband optical excitation was provided either by a laser
diode at 824 nm with a 40 mW output power modulated
around 90 kHz, by an argon ion laser, or by a Nd31YAG
laser. For lock-in detection purposes, a mechanical chopper
operating at 3 kHz is used for modulating the argon or YAG
laser beams. For both infrared and PL measurements, the
samples were mounted in a variable temperature He-flow
cryostat.
III. PHOTOLUMINESCENCE
The low-temperature PL of the investigated samples are
reported in Fig. 1. The PL linewidth of samples A1and A2is
relatively broad ~.100 meV!due to size fluctuations of the
dots in one layer. In the case of sample A3, besides the PL
associated with the dots, we also observe the radiative re-
combination at 1.42 eV from the InAs quantum well, which
forms the wetting layer. Due to the absence of rotation of the
sample during growth, a quantum well below the critical
thickness is deposited at the edge of the wafer. Sample A3,
which was cleaved at the limit between the two-dimensional
~2D!and 3D morphology, exhibits, therefore, PL from both
quantum dots and the quantum well. In the following, we
have based our analysis of the intraband properties of the
dots on the calculations of Ref. 13, which assumes a pyra-
midal shape of the dots. The size of the dots is referred to the
position of the PL peak. Based on these calculations, the
mean lateral size of the dots is estimated to be 9.6, 8.3, 5.5,
and 9.2 nm, respectively, for samples A1,A
2
,A
3
, and B. We
underline that these values are not indicative of a direct
structural characterization.
IV. PHOTOINDUCED INFRARED ABSORPTION
The p-polarized photoinduced infrared absorption of
sample A1as a function of the temperature is presented in
Fig. 2~a!. No resonance is observed in spolarization in the
investigated energy range. In the latter case, a monotonous
absorption, which increases at long wavelengths was ob-
served and attributed to both free carriers and substrate de-
fects ~see Fig. 3!The p-polarized infrared absorption exhib-
its a narrow absorption resonance at 115 meV with a FWHM
'15 meV and a broad absorption band with a maximum
around 190 meV. These two resonances show different tem-
perature behaviors: the broadband is maximum at low tem-
peratures and vanishes when the temperature is increased,
while the narrow line exhibits a maximum around 150 K. As
the temperature is increased, the narrow band slightly shifts
to lower energies ~'5 meV!, while the broadband shows an
opposite behavior with a '30 meV blueshift. These opposite
behaviors already indicate that these two absorption reso-
nances originate from different states, which are likely to
belong, respectively, to the valence and conduction band.
The p-polarized absorption of sample B, presented in
Fig. 2~b!, is dominated by a narrow absorption peak, which
is shifted to high energy as compared to sample A1. As al-
ready observed for the narrow peak of sample A1, the peak
for sample B shifts slightly to low energy when the tempera-
ture is increased. A careful analysis of the absorption as a
function of temperature shows that this narrow peak is su-
perimposed on a broadband, which is peaked around 150
meV and would be similar to the 190 meV peaked broad-
band of sample A1.
The influence of the dot size on the p-polarized absorp-
tion is shown in Fig. 3. Figure 3 features the photoinduced
infrared absorption spectra of samples A1,A
2
,andBata
fixed temperature of 120 K. As shown for sample A1,no
resonance is observed in spolarization for these samples in
the investigated energy range. In the case of sample B, the
infrared absorption spectrum is asymmetric with a maximum
around 150 meV and a high-energy tail, which expands up to
250 meV.15 The intensity of the photoinduced absorption of
sample A2has the same temperature behavior as the sample
B reported in Figure 2~b!.
From the calculations reported in Ref. 13, only one elec-
tron level is bound in the conduction band while four levels
are bound in the valence band, at least for the larger dots. By
analogy with the case of the intersubband transitions in quan-
tum wells, the z-polarized intraband absorption will be maxi-
mum between levels with envelope functions along the
growth direction. The hole intraband transitions are, there-
fore, expected to be dominated by ~u000&→u001&! transitions,
which exhibit a dipole moment along the growth axis. Tran-
sitions from the ground state to u100&and u010&confined
excited levels are expected to be polarized in the layer plane.
In the case of intraband transitions in the conduction band,
only transitions from the u000&bound level to the continuum-
hybridized levels of the wetting and GaAs layer are allowed.
One can observe that by analogy with quantum wells, the
magnitude of such bound-to-continuum transitions is ex-
pected to decrease when the bound level gets closer to the
barrier.16 Bound-to-continuum transitions are, therefore,
more easily evidenced when they are associated with
strongly confined bound states, which is the case for the
larger dots. From Ref. 13, the energy difference between
u000&and u001&hole levels slightly increases when the size of
the dots is decreased. To the contrary, the energy difference
between the electron level and the continuum strongly de-
creases when the size of the dots is reduced. The
u000&→u001&hole energy transition is estimated around 80
meV for a 10 nm base length, while the energy difference
FIG. 3. Photoinduced infrared absorption DT/Tof samples A1,A
2
,andBat
120Kinppolarization. The dotted curve corresponds to the infrared ab-
sorption in spolarization for sample A1. All the curves have been normal-
ized for clarity. The interband excitation is provided with a 40 mW laser
diode.
3398 J. Appl. Phys., Vol. 82, No. 7, 1 October 1997 Sauvage
et al.
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between the electron level and the GaAs conduction band is
around 150 meV for a 10 nm dot size.
Based on the preceding remarks, the identification of the
peaks is straightforward. In the case of sample A1, the
z-polarized narrow peak at 115 meV is attributed to the
u000&→u001&bound-to-bound hole transitions. The redshift
of the narrow resonance when the temperature of the sample
is increased is consistent with a depopulation of the smaller
dots in the distribution as evidenced in the PL experiments.17
This selective depopulation of small dots when the tempera-
ture is increased is illustrated in Fig. 4. The broadband ab-
sorption at 190 meV is attributed to bound-to-continuum
transitions of electrons. The blueshift of the absorption when
the temperature of the sample is increased is also consistent
with an increase of the mean dot size due to the depopulation
of smaller dots. As seen in Fig. 2, the electron resonance,
which dominates at low temperatures, vanishes when the
temperature is increased. An opposite behavior is observed
for the hole transition. These observations are also consistent
with a larger thermionic depopulation of the electron of the
dots, which are less confined than the holes. For sample B,
the mean value of the dot size is smaller than for sample A1,
the absorption peak located at 150 meV is also attributed to
the u000&→u001&hole transitions and is shifted, as expected,
to higher energy as compared to sample A1. The observation
of dominant electron transitions is less likely in this sample,
since they would occur at lower energy and with a smaller
magnitude as compared to sample A1. The slight decrease of
the broadening of the absorption of sample B when the tem-
perature is increased is also consistent with the decrease of
the inhomogeneous broadening, which corresponds to the
depopulation of the small dots.17 In the case of sample A2,
which exhibits smaller dot sizes, the absorption is mostly
attributed to bound-to-bound and bound-to-continuum hole
transitions. As the dot size is decreased, the energy of the
excited hole levels gets closer to the continuum and are ex-
pected to hybridize with the continuum states, which in turn,
explains the enhancement of the bound-to-continuum ab-
sorption. It is, therefore, concluded that the oscillator
strength of the bound-to-bound hole transitions is higher for
large dots. In the case of sample A3~not shown!, which
consists of narrow dots, no resonant absorption is observed
at low temperature since both electron and hole transitions
have weak oscillator strengths. A small resonance absorp-
tion, similar to the one reported for sample A2, was observed
at 120 K, which is not surprising since the small dots are
ionized and only the large dots of the distribution contribute
to the absorption.
The schematic energy band diagram of sample A1as
deduced from our experiments is depicted in Fig. 5. The
spectral position of the intraband absorption peaks of this
sample are in reasonable agreement with the theoretical pre-
dictions of Ref. 13, since the calculated values are, respec-
tively, 80 and 150 meV instead of 115 and 190 meV for the
u000&→u001&hole intraband transition and the electron
bound-to-continuum transition. The agreement is less satis-
fying for sample B, where the hole intraband transition is
maximum at 150 meV, whereas it is predicted in Ref. 13 to
occur around 90 meV. Our results suggest that a larger dis-
crepancy arises for the small dots. As a matter of fact, the
exact shape of the presently investigated quantum dots dif-
fers from the pyramidal shape with a 45° angle theoretically
analyzed in Ref. 13. Any changes in the geometry, strain
distribution, and piezoelectric field could, therefore, lead to
corrections on the level energies, and a discrepancy between
experimental and theoretical results is not surprising, espe-
cially for the levels that are close to the continuum.
V. RESONANT PUMPING OF THE DOTS
The preceding results are obtained for a pump energy
either close to the GaAs band gap or to the wetting layer
band-to-band energy. Depending on temperature, carriers are
created either in the barrier or in the wetting layer and, sub-
sequently, trapped in the dots. When the dots are filled, the
intraband infrared absorption can be measured. In order to
eliminate the influence of the GaAs barrier layer and the 2D
wetting layer, we have performed similar experiments using
a resonant interband pumping of the dots with a Nd31YAG
laser. In this case, the population of the quantum dots results
from a direct selective excitation of the dots. The comparison
FIG. 4. 4 K ~full line!and 120 K ~dashed line!photoluminescence of sample
A1. The curves have been xoffset to account for the band-gap variation with
temperature.
FIG. 5. Schematic band diagram featuring electron and hole intraband ab-
sorption of sample A1as deduced from infrared spectroscopy experiments.
3399J. Appl. Phys., Vol. 82, No. 7, 1 October 1997 Sauvage
et al.
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of photoinduced infrared absorption under resonant and non-
resonant interband pumping for sample B is presented in Fig.
6. The amplitude of the photoinduced absorption is similar to
the case of the resonant pumping with the YAG laser and the
nonresonant pumping with the 824 nm laser diode. The spec-
tra ~spectral position, broadening!are similar, which, in turn,
gives another signature that the p-polarized infrared absorp-
tion entirely arises from the dots. The similarity in broaden-
ing is a priori surprising, but one has to remember that the
shape fluctuation of the dots implies that for a fixed inter-
band pumping energy, the intraband transition energy is not
univocally defined. Besides, we underline that the distribu-
tion of the dot sizes gives rise to an equivalent inhomoge-
neous broadening of the PL and infrared absorption ~'10%–
15% of the energy!.
VI. DIPOLE MEASUREMENT
It is well known that at large pump intensities the ground
levels of the dots may be completely filled and that the ex-
cited levels begin to be populated. The PL can even exhibit
recombination from the excited levels.18 The dependence of
the 90 K intraband absorption of sample B as a function of
an argon pump intensity is reported in Fig. 7. At low-pump
intensity, the intraband absorption follows a square-root de-
pendence with the interband pump intensity, which is a sig-
nature of the dominance of bimolecular recombinations in
the GaAs layer. At pump intensities larger than 100 W cm22,
the intraband absorption saturates, which indicates that the
ground states of the quantum dots are completely filled. We
have separately checked that the filling of the dot levels is
also evidenced on PL spectra for these intensities. This fea-
ture is illustrated in Fig. 8, which shows a comparison of the
PL of sample B in the low- and high-pump intensity regime.
A shoulder, which corresponds to the radiative recombina-
tion of the excited levels, is clearly evidenced in the high-
pump intensity spectrum. The density of dots being close to
431010 cm22in this sample, the density of holes, which can
be trapped in the ground states is, typically, around '8
31010 cm22~two holes per dots!. From the magnitude of
intraband absorption (231024) and the ratio of the surfaces
of the exciting and probe beam, we can derive an experimen-
tal value of the absorption cross section for one layer of dots.
The absorption cross section
s
zfor light polarized along the
growth axis is found equal to
s
z'1.6310215 cm2. We can
analyze this value in terms of an equivalent quantum well.
This absorption cross section corresponds to an equivalent
dipole length '0.5 nm for an intersubband transition energy
at 160 meV assuming a 15 meV FWHM similar to the inho-
mogeneous broadening, which reflects the size distribution
of the dots. For a quantum well with infinite barriers, the
dipole moment for intersubband transitions is approximately
proportional to 0.183L, where Lis the well width. Assum-
ing that the typical thickness of the dots along the growth
axis is 3 nm and that they represent an infinite well in this
direction, we, indeed, expect a 0.54 nm dipole length. This
value is close to the experimental value. In this framework,
the effect of 3D confinement is to induce a z-polarized intra-
band transition around 160 meV in a system that exhibits a 3
nm thickness along the growth axis. We can observe that in
the case of two-dimensional system, intersubband absorption
can be homogeneously broadened with linewidths less than 5
meV, and the dipole lengths are, typically, around 2.5 nm.
VII. CONCLUSION
In summary, we have reported on the spectroscopy of
intraband transitions in self-organized quantum dots. Transi-
FIG. 6. Photoinduced infrared absorption DT/Tof sample B at 160 K under
resonant excitation with a Nd31YAG laser ~full curve!and a nonresonant
excitation provided with a laser diode at 824 nm.
FIG. 7. 90 K photoinduced intraband absorption of sample B as a function
of interband argon pump intensity. The argon laser is focused on a 250
m
m
laser spot. The full line is a guide to the eye.
FIG. 8. 4 K photoluminescence of sample B in the low ~dashed line!and
high ~full line!pump intensity regime.
3400 J. Appl. Phys., Vol. 82, No. 7, 1 October 1997 Sauvage
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tions involving both electrons and holes localized in the dots
have been observed in the midinfrared range. The transitions
have been found polarized along the growth axis of the dots
in the investigated energy range. In the InAs/GaAs system,
in-plane polarized intraband transitions with large oscillator
strengths are expected to occur at energies lower than 90
meV. The energy positions of the intraband transitions scale
with the dot size and are in satisfying agreement with the
predictions of Grundmann et al..13 The saturation of the in-
traband absorption due to the dot filling has been observed
for a pump intensity around 100 W cm22. An absorption
cross section of 1.6310215 cm2at 160 meV has been de-
duced for one dot layer plane.
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13 M. Grundmann, O. Stier, and D. Bimberg, Phys. Rev. B 52, 11 969
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14 See, for example, Quantum Well Intersubband Transitions: Physics and
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15 In the case of a thin 2D wetting layer, no intersubband absorption was
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16 B. Vinter and L. Thibeaudeau, in Intersubband Transitions in Quantum
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17 L. Brusaferri, S. Sanguinetti, E. Grilli, M. Gucci, A. K. Bignazzi, F.
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18 S. Fafard, R. Leon, D. Leonard, J. L. Merz, and P. M. Petroff, Phys. Rev.
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3401J. Appl. Phys., Vol. 82, No. 7, 1 October 1997 Sauvage
et al.
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