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Capture, relaxation and recombination in quantum dots
Citation for published version (APA):Sreenivasan, D. (2008). Capture, relaxation and recombination in quantum dots. Technische UniversiteitEindhoven. https://doi.org/10.6100/IR633152
DOI:10.6100/IR633152
Document status and date:Published: 01/01/2008
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Capture, relaxation and recombination in
quantum dots
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven, op gezag van de
Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een
commissie aangewezen door het College voor
Promoties in het openbaar te verdedigen op
woensdag 19 maart 2008 om 16.00 uur
door
Dilna Sreenivasan
geboren te Alavil, India
Dit proefschrift is goedgekeurd door de promotoren:
prof.dr. P.M. Koenraad
en
prof.dr. H.W.M. Salemink
Copromotor:
dr. J.E.M. Haverkort
The work described in this thesis is carried out at the COBRA Inter-University Research
Institute within the Department of Applied Physics of the Eindhoven University of
Technology. The financial assistance for the research was provided by the Freeband Impulse
Program as well as by the NRC photonics project of NWO.
CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN
Sreenivasan, Dilna
Capture, relaxation and recombination in quantum dots / by Dilna Sreenivasan. – Eindhoven:
Technische Universiteit Eindhoven, 2008. - Proefschrift
ISBN 978-90-386-1220-1
NUR 926
Subject headings: III-V semiconductors / quantum dots / time resolved reflectivity /
photoluminescence / carrier dynamics / carrier diffusion / carrier recombination
Trefwoorden: 3-5 verbindingen / quantumputstructuren / fotoluminescentie / optische
meetmethoden
Printed by Ridderprint Offsetdrukkerij B.V., Delft, The Netherlands
Cover design: Dilna Sreenivasan, Robert Kanters and Simone Vinke
© 2008, D. Sreenivasan, Eindhoven, The Netherlands
Dedicated to my parents, my sister and
my beloved husband Vinit
Table of contents
1 Introduction..................................................................................................................................................1
1.1 Historical development ....................................................................................................................1 1.2 Size quantization in quantum dots ...................................................................................................2 1.3 Quantum dots: Fabrication and trends............................................................................................4 1.4 Prospects of QDs in all-optical switches .........................................................................................7 1.5 Scope of the thesis..........................................................................................................................10
2 Carrier dynamics in semiconductor quantum dots.................................................................................13
2.1 Introduction ...................................................................................................................................13 2.2 Carrier cooling and relaxation in the barrier ...............................................................................15 2.3 Ambipolar diffusion through the GaAs barrier and the wetting layer ...........................................16 2.4 Carrier capture from the wetting layer into the QDs ....................................................................18 2.5 Relaxation of carriers into the QD ground state ...........................................................................23 2.6 Low temperature grown semiconductor structures........................................................................28 2.7 Time Resolved Differential Reflectivity – Experiment ...................................................................35
3 Anomalous temperature dependence of the carrier capture time into InAs/GaAs quantum dots
grown on a quantum wire array ...............................................................................................................41
3.1 Introduction ...................................................................................................................................42 3.2 Carrier transport towards the QD plane .......................................................................................42 3.3 Experimental technique and sample details...................................................................................44 3.4 Results and discussion ...................................................................................................................46 3.5 Conclusions....................................................................................................................................54
4 Anomalous radiative lifetime in quantum rods .......................................................................................55
4.1 Introduction ...................................................................................................................................56 4.2 Electromagnetic coupling in a quantum dot array: theory............................................................57 4.3 Experimental details ......................................................................................................................61 4.4 Results and discussion ...................................................................................................................64 4.5 Conclusions....................................................................................................................................69
5 Photoluminescence from low temperature grown InAs/GaAs quantum dots.......................................73
5.1 Introduction ...................................................................................................................................74 5.2 Sample and experimental details ...................................................................................................74 5.3 Results and discussion ...................................................................................................................76 5.4 Conclusions....................................................................................................................................80
6 Time Resolved Differential Reflectivity from low temperature grown quantum dots........................81
6.1 Introduction ...................................................................................................................................82 6.2 Sample and experimental details ...................................................................................................82 6.3 Results and discussion ...................................................................................................................83 6.4 Conclusions....................................................................................................................................88
References ............................................................................................................................................................91
Summary ............................................................................................................................................................101
List of publications ............................................................................................................................................105
Acknowledgements ............................................................................................................................................107
About the author................................................................................................................................................111
1
Introduction
1.1 Historical development
Ever since the discovery of semiconductor properties of PbS by T.J. Seebeck in 1821,
semiconductor physics and technology has become an integral part of development of modern
technology. Initially, research was concentrated on the bulk properties of different
semiconductor materials. The most important early results were obtained in elemental
semiconductors like Silicon and Germanium. The Schottky contact was proposed by W.
Schottky in 1938 and current rectification was first demonstrated in 1941 by R.S. Ohl. This
development resulted in the demonstration of the first transistor by W. Shockley, J. Bardeen
and W. Brattain in 1947. Although GaAs was first fabricated by V.M. Goldschmidt in 1929
[1], Heinrich Welker pioneered the fabrication of III-V compound semiconductors in 1952
and thus paved the way for a new generation of direct bandgap semiconductors in which the
bandgap can be tuned by the material composition. In 1963, Herbert Kroemer proposed the
double heterostructure as an efficient device for current injection into a laser. Alferov et al.
proposed the idea of using an AlGaAs-GaAs double heterostructure as an active region for
carrier injection [2,3] demonstrating pulsed operation of double-heterostructure laser in 1968.
This development lead to the demonstration of the first continuous semiconductor diode laser
operating at room temperature by Alferov et al. in 1970. In 2000, Zhores I. Alferov and
Herbert Kroemer shared the Nobel prize for developing semiconductor heterostructure used in
high-speed transistors and opto- electronic devices [4].
In 1970, L. Esaki and R. Tsu [5,6] proposed the fabrication of an artificial
semiconductor superlattice by alternating thin semiconductor layers of nanometer thickness,
with alternating bandgaps. They predicted the formation of minigaps in the band structure at
Chapter 1
2
wavevectors k corresponding to the superlattice period, SL
k Lπ= . In 1974, R. Dingle
observed for the first time size quantization of energy levels in quantum wells [7]. Since then,
immense efforts have been made to improve the growth techniques such as Molecular Beam
Epitaxy (MBE) and Metal Organic Vapour Phase Epitaxy (MOVPE) which enabled the study
of semiconductor structures in which the smallest dimensions approach a single atomic layer
as well as semiconductor structures with ultra high purity. Progressive size quantization in 1,
2 and 3 directions has been achieved leading to the successful growth of 2-dimensional, 1-
dimensional and finally the zero-dimensional structures. This progress in epitaxial growth
techniques currently allows the growth of quantum wells, superlattices, quantum wires, and
quantum dots on a routine basis. Nowadays, size quantization in low-dimensional structures
has been turned into a basic property of all low-dimensional structures [4]. Semiconductor
quantum dots, which provide the ultimate nanostructure, are currently fabricated and studied
by many groups. The idea of size quantization in semiconductor structures has paved the way
for development of more compact, efficient, cost effective and faster devices. In this Chapter,
a quick overview of semiconductor properties is given along with some insight into the band
structure modification due to the size quantization. A brief introduction about the growth
technique of the QDs is also provided. Emphasis is given on the III-V compound
semiconductor structures as they are the most common material used in the opto-electronic
devices industry as well as the basic material studied in this thesis.
1.2 Size quantization in quantum dots
Based on the “de Broglie’s” theory of matter waves, electrons of momentum p are
associated with a “de Broglie” wavelength λ defined as:
*
h h
p m vλ = = (1.1)
where h is Planck’s constant and *m is the effective mass of the charge carrier. The effective
masses follow the dispersion relations ( )
( ) ( )2
2 2*
1 1 c v
e h
d E k
dkm=
with k as the wave vector,
( )*e hm as the electron (hole) effective mass and ( ) ( )c vE k as the conduction (valence) band
energy. When the dimensions of the semiconductor structure approaches the de Broglie
wavelength, the motion of carriers is restricted in that direction leading to size quantization
effects. Due to the small effective mass of electrons in a semiconductor ( *00.067em m= in
Introduction
3
GaAs where 0m is the free electron mass), the “de Broglie” wavelength is comparatively
large and therefore a clear size quantization is already achieved when the smallest dimension
of the structure is ~10 nm.
In a semiconductor crystal lattice, the envelope wavefunction approximation is used to
describe size quantization in a quantum well (QW), quantum wire (QWR) or quantum dot
(QD). The electron envelope wavefunction ( )rψ in a low-dimensional semiconductor
structure can be calculated with the Schrödinger equation ( ) ( )H r E rψ ψ= in which the
Hamiltonian H is given by:
( )
22
*2 e
H V rm
= − ∇ +
(1.2)
in which ( )V r is the confinement potential of the QW, QWR or QD which is assumed to be
infinitely deep for the moment. For any direction i in space in which a confinement potential
is present with thickness iL , the electron confinement energy iE reads:
2 2 2
2*2i
iie
nE
Lm
π=
(1.3)
in which in is an integer labeling the different confined energy levels within the structure. If
there is no confinement potential in direction j , the solution of the Schrödinger equation is
simply a parabolic dispersion relation given by:
2 2
*2
jj
e
kE
m=
(1.4)
where jk is the wave vector. For a cubic quantum dot with sides , ,i j kL L L , this approach thus
yield:
22 2 2 2
2 2 2*2
ji kijk
i j ke
nn nE
L L Lm
π = + +
(1.5)
The size quantization effects arising from the restriction of motion causes a change in the
density of states. The density of states (DOS) for a bulk, QW and QWR material, defined as
the number of states per energy per unit volume, surface or length respectively is given as:
1 02
12
1( ) , ( ) , ( )bulk QW QWRE E E E E
Eρ ρ ρ∝ ∝ ∝ (1.6)
Chapter 1
4
showing that the functional dependence of the DOS on energy fundamentally changes due to
size quantization. Finally in the QDs, energy is quantized in all three dimensions, and the
DOS becomes a series of delta functions as given below:
( )( )QD n
n
E E Eρ δ= −∑ (1.7)
The characteristic DOS spectra of all the systems are summarized below in Fig. 1.1.
Bulk3D
Quantum well
2D
Quantum wire
1D
Quantum dot
0D
Density of states
En
erg
y Ec
Ev
Bulk3D
Quantum well
2D
Quantum wire
1D
Quantum dot
0D
Density of states
En
erg
y Ec
Ev
Fig. 1.1: Density of states modification under different degrees of confinement.
From Fig. 1.1, it is immediately obvious that the density of states in a QD is fundamentally
different from all other structures since it features, in principle, a very small linewidth. The
discrete density of states in a QD, which is shown to provide an enhanced optical nonlinearity
and thus a very low saturation energy [8,9], makes the QDs an ideal structure for applications
in opto-electronic device applications.
1.3 Quantum dots: Fabrication and trends
Initial methods for fabricating semiconductor QDs were based on patterning two-
dimensional QW structures using lithographic techniques followed by etching of e.g. micro-
pillars [10,11]. These and other artificial patterning methods all had drawbacks like crystal
damage, contamination, and excessive non-radiative recombination at the side-walls [12].
With the use of advanced crystal growth techniques like MBE and MOVPE, self assembled
growth of QDs emerged as a novel way to grow high quality nanostructures. The Stranski-
Krastanow (SK) growth mode, which was originally proposed by the authors for dislocation-
free island formation in heteroepitaxial ionic crystals using energy minimization [13], is now
Introduction
5
used as an almost standard growth technique for QDs. When the SK InAs islands on GaAs are
again covered with GaAs, they act as almost perfect QDs with size quantization in all
directions, as was first proposed by Tabuchi et al. [14]. Nowadays, this growth technique is
generally referred to as self organized QD island formation.
Fig. 1.2: Bandgap energy versus lattice constant for III-V semiconductors.
The driving force behind the SK growth mode of self assembled QDs is the lattice
mismatch between the semiconductor materials chosen for the growth. Fig. 1.2 shows the
band gap energy v/s lattice constant of the most common III-V semiconductors. The lattice
mismatch between InAs and GaAs is 7% [15]. When a thin InAs layer is grown on top of a
GaAs layer, the InAs layer adjusts its lattice constant to match with the underlying GaAs
layer, thus forming a strained two dimensional wetting layer. When the thickness of the InAs
layer is further increased, (> 1.7 monolayer) the accumulated strain is relieved by the
formation of nanometer sized InAs islands as shown schematically in Fig. 1.3.
QDs with small lateral dimension of the order of 15-30 nm have been realized in the
InAs/GaAs material system. Uniformity of the size distribution has been achieved by varying
the growth temperature and by reducing the growth rate, for example by introducing growth
interrupts. By choosing appropriate material systems the optical emission wavelength can be
varied from the visible range in InAlAs/AlGaAs [16] to near infrared emission up to about 1.9
mµ in InAs/InP [17]. A red shift of the emission wavelength of InAs/GaAs QDs can also be
achieved by introducing Antimony during growth, realizing a 1.55 mµ emission wavelength
[18].
Chapter 1
6
First layer of InAs over GaAs
InAs
GaAs
First layer of InAs over GaAs
InAs
GaAs
Substrate
Wetting LayerQDs
Strain relaxation
Substrate
Wetting LayerQDsQDsQDs
Strain relaxation
Capping Capping
Fig. 1.3: Step-by-step schematic representation of Stranski-Krastanow island formation due
to lattice mismatch.
Introduction
7
In addition, the QD bandgap can be tuned by using a strain reducing layer while keeping the
shape and size of the QDs constant. Strain engineering allowed tuning of the bandgap of
InAs/GaAs QDs from 1000 nm to 1350 nm [19].
Highly uniform InAs/GaAs QDs with a PL linewidth of only 20 meV at 4 K have been
grown by the leveling and rebuilding technique in which short period InAs/GaAs superlattice
layers are introduced between the QD and the capping layer [20]. An important direction in
QD growth is the creation of both microscopically and macroscopically ordered QD
structures, for instance QD clusters. van Lippen et al. successfully grew ordered InAs QD
molecules by strain engineering of the InGaAs superlattice template on GaAs (311)B
substrate [21]. QDs with various laterally ordered patterns have been successfully grown by
combining patterned substrates and self organized anisotropic stain engineering [22-24].
1.4 Prospects of QDs in all-optical switches
The demand for faster telecommunication is increasing day by day. For long distance
connections, conventional electric cables have already been replaced by optical fiber for more
than a decade. Presently, optical fiber connections are fast approaching the end-user. The
actual switching of the data from one fiber transmission system into another one is presently
performed electronically. However, these electronic switching nodes are reaching their limit
to cope with the ever increasing amount of internet traffic needed to be transferred with larger
and larger speed. The congestion of internet traffic at the switching nodes is called the
switching bottleneck. All-optical switching provides an answer to this switching bottleneck.
Extremely fast compact all-optical switches are required with a very low switching energy to
relieve this switching bottleneck. In particular, a very low switching energy is important since
the switching of a 10 Tbit/s data stream with an all-optical switch, featuring an already very
low switching energy of 1 pJ, still requires 10 W of average optical power. Such a power
requirement presently still needs a mainframe laser which does not fit on an electronic circuit
board.
The performance of many optical devices can be improved by the introduction of QDs
into the semiconductor matrix. Some examples are light emitting devices, photodetectors,
optical modulators and optical memories based on QDs. For most device applications, a
narrow emission width, a small amount of inhomogeneous broadening and a reduction of the
non-radiative recombination are desired. Stranski-Krastanow grown self-assembled QDs are
close to an ideal choice which satisfies most of these conditions, with the exception of the still
Chapter 1
8
too large amount of inhomogeneous broadening. Besides these applications, colloidal QDs
also are ideal to be used in biology and medicine as dye and biological markers. For the
future, we envisage that more uniform QDs will become available with a reduced amount of
inhomogeneous broadening. Once such uniform QDs would become available, the threshold
current density of a QD laser, which is currently already lower than in a bulk or QW laser, as
shown in Fig. 1.4, will be further decreased up to the limit of a threshold-less laser in which
every emitted photon can be directly coupled into the cavity mode.
Fig. 1.4: Worldwide progress on the reported threshold current density for bulk, QW and QD
lasers, achieved by different groups [25].
In optical telecommunication systems, in addition to QD lasers, QDs are expected to
find application in optical modulators and all-optical switches. For the latter application, it is
of crucial importance that the presence of one electron-hole pair in the ground energy level of
the QD can completely bleach the absorption whereas two electron-hole pairs already provide
gain in a QD. The large sensitivity of the optical absorption on the QD occupation makes QDs
a very promising object for all-optical switching. In particular, semiconductor QDs provide a
very promising solution for reducing the required switching energy.
The main problem with all-optical switching in QDs is that while the “turn-on” time
can be made ultrafast by using a femtosecond switching pulse, the “turn-off” time is
determined by the radiative recombination time which is as long as a nanosecond. Although
there have been some demonstrations [26,27] of both a fast turn-on and a fast turn-off time in
Introduction
9
Mach-Zehnder switches, in these concepts the pump-excited carrier concentration depend on
the bit-pattern history of the optical switching pulses, which makes such a concept useless for
switching a high bit-rate data stream.
It is not yet possible to significantly increase the radiative recombination rate by
introducing a QD-emitter inside a Photonic bandgap cavity and utilizing the Purcell effect
[28-31]. Low-temperature growth has, however, demonstrated that the carrier recombination
time in both bulk GaAs and GaAs/AlGaAs quantum wells can be reduced to below 1 ps by
increasing the non-radiative recombination rate. It has been shown by several groups that LT
grown GaAs features an ultrafast carrier recombination time [32-35]. Mikulics et al. [36]
recently demonstrated a LT-GaAs based metal-semiconductor-metal (MSM) photodetector
with a photoresponse of 0.9 ps. A 220 fs carrier relaxation time has also been observed
recently in a LT-GaAs detector [37]. Many groups have already demonstrated ultrafast all-
optical switching using LT grown QW structures. LT-grown QD structures which are
investigated in Chapter 5 and 6 of this thesis may allow to significantly reduce the required
switching energy, but have not yet been realized. Large absorption optical non-linearity and a
fast 0.7-0.9 ps response time has been demonstrated in LT grown GaAs/AlAs multiple QW by
Tsuyoshi et al. [38]. The same group also showed that Beryllium doping induces an even
faster response (0.25 ps), since Beryllium acceptors increase the number of positively charged
arsenic anti-site defects. which are responsible for ultrafast electron trapping [39].
Takahashi et al. [40] integrated low-temperature grown Be doped InGaAs/InAlAs
multiple QWs into an all-optical switch and realized a switching speed of 300 fs (Fig. 1.5).
These authors also cleverly employed the spin polarization properties of a compressively
strained QW to increase the on-off ratio up to 40 dB. A right hand circularly polarized pump
creates spin-up and spin-down electrons at a ratio 1:3 and thus a spin dependent exciton
saturation. Thus a linearly polarized probe signal which traverses the QWs, changes to an
elliptical polarization due to a different amount of saturation of its left-handed and right-
handed circularly polarized components, when the pump is on. With the pump off, the probe
signal remains linearly polarized. The on-off ratio could be improved by using a polarizing
beam splitter which only reflects the pump-induced signal polarized perpendicular to the
original probe beam polarization to the photodetector. This strongly reduces the off-state
signal, thereby improving the on-off ratio.
Chapter 1
10
Fig. 1.5: Ultrafast all-optical switching with on-off ratios up to 40 dB by Takahashi et al.
[40]. The inset shows the 300 fs switched output pulse. (From Takahashi et al.)
1.5 Scope of the thesis
The gain dynamics and the optical nonlinearities in the QD based devices are
dependent on the carrier dynamics within the QDs [12]. There is room for further
improvement of the performance of the QD based devices when the carrier capture and
relaxation dynamics into a QD are better understood. At present, a few different carrier
relaxation mechanisms have been proposed which are all capable in explaining the carrier
capture and relaxation experiments on a specific set of QD samples. This implies that the
influence of the detailed QD properties on the relevant carrier capture and relaxation
mechanisms deserves further research. In this thesis, the influence of the barrier material on
the capture dynamics is investigated. From the experimental point of view, time resolved
reflectivity technique was chosen to investigate the carrier capture and relaxation dynamics,
which provides several advantages over the commonly used PL technique.
It is usually assumed that the QDs are independent when they are separated far enough
to avoid a tunneling coupling. In this thesis, it is shown that the excited QDs have a
significantly modified dielectric constant which causes strong light diffraction around an
excited QD. The strong light diffraction around excited QDs is shown to give rise to a hitherto
Introduction
11
ignored electromagnetic interaction between distant QDs which strongly modifies the
radiative lifetime. A proper account of the interaction between the electromagnetic field and
the QDs is, therefore, of prime importance for a proper understanding of QD-based all-optical
switching devices.
Prasanth et al. have shown that an extremely small switching energy of 6 fJ is required
for all-optical switching in an InAs/InP QD based Mach-Zehnder Interferometric switch [41].
This implies that a very low switching energy can in principle be obtained in QDs. Thus a
combination of large all-optical nonlinearity in QDs and the ultrafast carrier trapping already
observed in LT grown InGaAs/InAlAs QWs provides a clear route for the a future ultrafast
and low power all-optical switch based on low-temperature grown QDs. In the thesis, a study
of LT grown InAs/GaAs QDs is presented for this purpose.
2
Carrier dynamics in
semiconductor
quantum dots
2.1 Introduction
The picosecond and femtosecond carrier dynamics in semiconductor quantum dots are
a key issue in understanding their behavior. The carrier dynamics are influenced by both the
scattering between the photo-generated carriers and the available phonon modes within the
semiconductor crystal, as well as by the scattering between photo-generated carriers among
themselves such as electron-electron, electron-hole scattering and Auger scattering. In
addition, the carrier dynamics are also influenced by the carrier trapping at free surfaces,
interfaces and the defects present within the semiconductor crystal.
When the idea of low dimensional and in particular, zero-dimensional structures was
introduced, strong enhancements in the zero-dimensional density of states and thus also in the
optical transition matrix elements were predicted. Initial experiments performed on the 0D
structures showed, on the contrary, a low luminescence quality compared to bulk structures
and also a comparatively slow carrier relaxation time. Benisty et al. put forward the idea of a
phonon bottleneck [42]. In a typical semiconducting system, the electrons and holes lose
energy through longitudinal optical (LO) phonon emission. The LO phonons are practically
non-dispersive, in other words are highly monochromatic (~36 meV in GaAs, ~30 meV in
InAs QDs). The energy quantization in 0D structures leads to a stringent condition for energy
and momentum conservation. Due to the lack of the availability of suitable final energy states,
Chapter 2
14
it was predicted that the carrier relaxation probability through LO phonon scattering is largely
reduced in QD structures, which is known as the phonon bottleneck. Acoustic phonon
scattering is also reduced as a result of the conservation of both energy and momentum
between discrete energy levels within a QD (The LA phonon energy is 3 meV when the
wavelength of the acoustic phonon is of approximately the QD diameter). More recent results
showed that carriers within a QD relax much faster than that predicted by the presence of the
phonon bottleneck. In fact, a large number of physical mechanisms have been discussed in
literature, including polaron effects [43,44], additional scattering mechanisms such as Auger
scattering with carriers in the wetting layer [45,46], level broadening, and (multi-) excitonic
levels within a QD [47], all of which tend to partially circumvent the predicted phonon
bottleneck.
Ex
cita
tion i
nto
bar
rier
Thermalization
and diffusion Capture into WL and QD
Recombination
from QDs
Relaxation
Rec
om
bin
atio
n f
rom
th
e bar
rier
Barrier WL QD Barrier
Growth direction
Ex
cita
tion i
nto
bar
rier
Thermalization
and diffusion Capture into WL and QD
Recombination
from QDs
Relaxation
Rec
om
bin
atio
n f
rom
th
e bar
rier
Barrier WL QD Barrier
Growth direction
Fig. 2.1: Overview of the carrier capture and relaxation dynamics into a QD.
In a typical InAs/GaAs QD sample, embedded in a bulk GaAs barrier layer, both the
carrier transport through the bulk GaAs layer towards the QDs and the carrier relaxation along
Carrier dynamics in semiconductor QDs
15
the quantized energy levels within the QD has to be taken into consideration. In this thesis,
the carrier dynamics are studied using CW photoluminescence (PL) and time resolved
differential reflectivity (TRDR). In both the cases, the excitation energy is well above the QD
energy levels within the GaAs barrier layer continuum. In such a case, the carrier dynamics
from the initial excitation position and energy level within the barrier towards the QD ground-
state can be subdivided into five major steps listed below, which are schematically shown in
Fig. 2.1.
1. Carrier cooling and relaxation within the GaAs barrier layer.
2. Ambipolar diffusion in the GaAs barrier towards the QDs.
3. Carrier capture from the GaAs barrier continuum into the wetting layer (WL) continuum
and subsequently from the WL into the QDs.
4. Carrier relaxation between the discrete energy levels within the QDs.
5. Radiative and non-radiative excitonic recombination in the QDs.
2.2 Carrier cooling and relaxation in the barrier
Ultrashort pulse excitation above the GaAs-barrier bandgap initially leads to the
creation of electron-hole pairs (dipole moments) with well defined phase relationship with the
electromagnetic field. Already in the GaAs barrier layer, the coherent nature of the
polarization with the electromagnetic excitation is quickly destroyed, by the scattering of the
photo-generated carriers among themselves or with the phonon bath, which is referred to as
carrier dephasing. The carrier dephasing occurs in a < 100 fs time scale, but is strongly
dependent on the carrier density in the barrier layer. When excitons are directly photo-
generated at the GaAs bandgap, the dephasing time is somewhat larger, but is still of the order
of a few picoseconds [48]. In the case of pump excitation within the GaAs barrier and probe
detection in resonance with the QD ground state as used in the TRDR experiments reported in
this thesis, the coherent regime is virtually undetectable. This is because of the fast dephasing
occuring due to carrier scattering in the wetting layer and in the barrier as well as due to the
carrier capture and relaxation into the QDs. The dephasing is assumed to be complete due to
the large difference between the pump frequency and the probe detection frequency.
In a similar, or a somewhat larger time window, the excited carrier energy distribution
is still determined by the laser excitation energy and is thus a non-thermal carrier distribution
which cannot be defined by temperature. The electrons and holes thermalise by carrier-carrier
scattering in a few hundred femtoseconds. In this time range, the non-thermal distribution will
Chapter 2
16
relax towards a Fermi-Dirac distribution which can be characterized by a carrier temperature
which is higher, or sometimes even much higher than the lattice temperature. The thermalised
carriers subsequently cool down towards the lattice temperature by optical and acoustic
phonon emission. The initial carrier cooling by optical phonon emission occurs on a sub-
picosecond time-scale until the carriers reach the threshold for optical phonon emission, i.e.
their excess energy becomes less than the LO-phonon energy. In a true bulk layer, the final
relaxation towards the lattice temperature by acoustic phonon emission is a slow process
which may take a few hundred picoseconds. In a QD sample, carrier capture from the barrier
into the WL will start as soon as the excess energy in the barrier is less than one optical
phonon energy. The capture time into the WL will be determined by the wavefunction overlap
of the barrier states and the WL states as well as by the binding energy of the highest confined
energy level within the wetting layer [49]. Siegert et al. [50] recently measured the PL-
risetime in the WL of both undoped, p-doped and n-doped QD samples and found a capture
time into the WL of 2 ps for all three samples they investigated. In the wetting layer, the
carrier distribution will be also nonthermal initially, but it will follow the same sequence as
described above for the barrier layer.
2.3 Ambipolar diffusion through the GaAs barrier and the
wetting layer
When photon excitation energy used for pumping is higher than the barrier band gap,
the electron-hole pairs are excited into the barrier layer continuum. A very small part of the
carriers will recombine in the barrier layer itself while the majority diffuse through the barrier
layer till they reach a free surface, a recombination centre or the wetting layer in which they
can subsequently be captured. For an undoped bulk barrier layer charge neutrality will be
maintained after optical excitation, as an equal number of electrons and holes are optically
excited and any deviation from charge neutrality will quickly disappear through dielectric
relaxation. Thus, the diffusion process should be treated as ambipolar diffusion. The
ambipolar diffusion is a combined effect of both electron and hole diffusion. The ambipolar
diffusion coefficient aD is given by [51,52]:
1 1 1 1
2a e hD D D
= +
(2.1)
where ( )e hD is the electron (hole) diffusion coefficient. The ambipolar diffusion coefficient
can thus be expressed as:
Carrier dynamics in semiconductor QDs
17
( )( )2e h B
ae h
k TD
e
µ µ
µ µ=
+ (2.2)
where ( )e hµ is the electron (hole) mobility, Bk is the Boltzmann constant, T is the
temperature and e is the electron (hole) charge. The temperature dependence of aD is mainly
determined by the temperature dependence of the hole mobility, attaining a maximum at
around 80 K. Optical measurements of the ambipolar diffusion coefficient of photo-excited
electron-hole pairs were performed by Hillmer et al. [53] both in bulk GaAs and in quantum
wells, as shown in the Fig. 2.2. The ambipolar diffusion length follows directly from the
ambipolar diffusion constant and is defined as:
aL D τ= (2.3)
where τ is the bulk carrier lifetime or carrier residence time in the barrier layer.
Fig. 2.2: Temperature dependence of diffusivity in bulk GaAs (upper curve) and in quantum
wells of different thicknesses (from Hillmer et al. [53]).
Due to the random separation between the excitation position within the GaAs barrier
and position of the QDs in which the carrier is finally captured, each carrier experiences a
different diffusion length. Therefore an effective diffusion time has to be considered for an
ensemble of QDs. The carrier capture process into the QD actually takes place when there is
sufficient overlap between the wavefunctions in the barrier state and the QD envelope
wavefunction. The volume around each QD in which these wavefunctions sufficiently
overlap, will be referred to as “capture volume” in this thesis. The capture area s around a
Chapter 2
18
single QD where capture is efficient can be expressed in terms of the single dot temporal
capture cross section σ and the capture rate Γc as [54]:
/ cs σ= Γ (2.4)
Then capture volume is / cv dσ= Γ with d as the width of the QD envelope function in the
growth direction. When the carrier has reached the capture volume around the dots, the
carriers have a probability to be captured into the QD excited states, which will be discussed
in the next section.
2.4 Carrier capture from the wetting layer into the QDs
When the carriers in the wetting layer reach the capture volume of the dots, the
energetic carriers lose part of their energy through different mechanisms like emission of LO
phonons (Section 2.4.1) or Auger scattering (Section 2.4.2) and are subsequently captured
into the discrete energy states of the QD. In many articles, the reported carrier capture time is
actually a combination of a diffusion time within the GaAs barrier, the capture time into the
WL and the actual capture time into the QDs. It should be noted that only carrier capture
measurements performed in a separate confinement structure in which the diffusion time is
known, or measurements in which the capture time into the wetting layer has been subtracted,
yield a meaningful capture time into the QDs. Sosnowski et al. [55] has reported a capture
time of 2.8 ps from a well-defined separate confinement barrier into the InAs/GaAs QDs at
low excitation, while Siegert et al. [50] has reported a capture time of 4 ps, which is the
difference between the measured PL risetime into the WL and the measured PL risetime into
the highest QD excited state of an undoped QD.
2.4.1 Carrier capture by LO phonon emission
k
fLOω
k
fLOω
Fig. 2.3: Electron capture from the WL into the QD excited state by LO phonon emission.
Carrier dynamics in semiconductor QDs
19
The probability of carrier capture from a 2D wetting layer into the QD through single
LO phonon emission is given by Fermi’s Golden Rule as [56,57]:
( ) ( )22
( ) ph f iw k f H k E Eπ
δ= × −
(2.5)
where k
is the carrier wave vector of the initial state in the 2D wetting layer and f represents
the final state in the QD as represented in Fig. 2.3. The δ -function accounts for energy
conservation, in which fE and iE are the energies of the final and initial state of the
combined electron-phonon system. phH is the Hamiltonian for the carrier-phonon interaction,
which can be expressed as:
( )emission absorptionph q q
q
H H H= +∑ (2.6)
in which ,emission absorptionq qH H are the operators for phonon emission and absorption at
phonon wavevector q
. These operators can be expressed in terms of the creation and
annihilation operators, †
qa and qa for phonons of wavevector q
, as:
†.
q
emission iq rph qH C e a−= (2.7)
.q
absorption iq rqphH C e a= (2.8)
For the electron LO phonon interaction (Fröhlich interaction), the coupling coefficient qC can
be expressed as:
2
2
202
LOq
r
eC
q
ω
ε ε=
Ω
(2.9)
in which LOω is the LO phonon energy, e is the electron charge, 0ε is the vacuum
permittivity, rε the relative permittivity and Ω is a normalization volume. The process of
carrier capture through single LO phonon emission creates an additional phonon of wave
vector q
implying:
1f in n= + (2.10)
with ( ),i fn the number of LO phonons in the (initial) final state. So taking the average over
the phonon distribution and working out the Hamiltonian, the capture probability ( )w k
can be
re-written as:
Chapter 2
20
( )( ) ( )2 2.2
0
2( ) 1
2LO fiq r
LOQDkrq
ew k n f e k
q
π ωδ ε ε ω
ε ε− = + × − − Ω ∑
(2.11)
in which kε and fQDε are now the carrier energies in 2D wetting layer and in the final QD
state f , respectively. The average phonon occupation n is the Bose-Einstein distribution,
given by:
1/e 1LO Bk Tn ω − = −
(2.12)
The total carrier capture rate captureΓ from the 2D wetting layer into one particular QD state,
which is assumed to be initially empty, can be obtained by a summation over the entire
electron distribution at energy kε :
( ) ( )capture kk
w k f εΓ =∑
(2.13)
in which ( )kf ε is the Fermi-Dirac distribution. The final expression for the capture rate
reads:
( )( ) ( ) ( )2 2.
20
2 11
2LO f iq r
capture LOQDk kr qk
en f f e k
q
π ωε δ ε ε ω
ε ε− Γ = + − − Ω ∑ ∑
(2.14)
In this expression, the temperature dependence of the phonon emission induced carrier
capture rate is given by the average phonon occupation number as well as by the carrier
temperature in the wetting layer, which is expressed by the Fermi-Dirac distribution as given
below:
( ) ( )( )1k
T f nεΓ +∼ (2.15)
This expression shows that as temperature increases, the relaxation time decreases,
which is generally also observed experimentally. The Fermi-Dirac distribution in the wetting
layer and thus also the carrier temperature in the wetting layer will not be in equilibrium with
the lattice, but we assume that it will be determined by the scattering rates into and out of the
wetting layer. The carrier capture can also take place through multiphonon processes which
may involve more than one LO phonon [50] or LO and LA phonons [58] thereby satisfying
the energy conservation requirement. A schematic representation of the (multiple) phonon
emission aided capture of electrons into the excited QD state is shown in Fig. 2.4.
Carrier dynamics in semiconductor QDs
21
LO phonon LO + LA
phonon
(a) (b)
LO phonon LO + LA
phonon
LO + LA
phonon
(a) (b)
Fig. 2.4: Capture from the barrier layer to the WL and into QD by (multiple) phonon
emission. a) emission of a single LO phonon b) LO + LA phonon emission.
For interpreting the experimental results, it is important to note that in the case of
phonon mediated capture process, the carrier capture and relaxation times are independent of
the carrier density. Magnusdottir et al. [56] obtained a calculated single phonon mediated
capture time of around 0.2-0.3 ps whereas the 2-phonon mediated capture time is found to be
slightly longer for capture into the same QD state (12.5 ps).
2.4.2 Carrier capture by the Auger scattering process
f
f
sk
( )
i
c sk
f
f
sk
( )
i
c sk
Fig. 2.5: Carrier capture through Auger scattering between two electrons () or two holes
(), initially confined within the WL.
Highly energetic carriers can also lose their energy through the Auger scattering
process, in which carrier-carrier scattering transfers one carrier to a lower energy while the
Chapter 2
22
other gets scattered to a higher energy state, preferably to a continuum. Auger scattering is
more important when the density of excited carriers is high. Similarly to the phonon
bottleneck, Auger scattering will also not be energetically allowed when both carriers have to
scatter between discrete energy levels within the QD. Carrier capture through the Auger
mechanism is however possible when both carriers are initially within the 2D wetting layer
and one of the carriers is captured within a discrete QD level, while the other carrier is
scattered upwards into the WL or into the barrier layer continuum. This Auger scattering
mechanism becomes more important at high carrier densities within the WL [59].
As with the LO phonon capture, the rate of Auger scattering aided capture can be
determined from Fermi’s golden rule with the difference that, we now have to consider two
particle states. The Auger scattering induced capture probability of a carrier from a bulk (WL)
state into a QD state is given by [45,46,60]:
( )22, ,f i i
QD s coul c s f iw f k V k k E Eπ
δ= −
(2.16)
in which ick and i
sk denote the initial state of the two carriers and , fQD sf k denote the states of
the final carrier captured ( )c into the QD and the scattered carrier ( )s respectively, coulV is
the Coulomb scattering potential and fE and iE denote the energies of the final and the
initial state, respectively. If ( )s cr is the initial position of the scattered (captured) electron then
the Coulomb scattering potential is given by:
2
04Coulr c s
eV
r rπε ε=
− (2.17)
From the transition probability, the capture rate can be expressed as:
( ) ( ) ( ), ,
1i i fs c s
i i fc s s
k k kk k k
w f f fε ε ε Γ = − ∑ (2.18)
From this expression, it is clear that for an empty QD ( )1 1fsk
f ε − ∼ , the Auger rate
shows a quadratic dependence on the initial carrier density in the WL, thus making 2inΓ ∝ .
The Auger induced capture time can thus be expressed as [45]:
2
1c
iCnτ = (2.19)
Carrier dynamics in semiconductor QDs
23
where C is the Auger coefficient and in is the initial carrier density injected into the wetting
layer. The Auger induced carrier capture becomes thus increasingly important at higher
carrier densities. The Auger coefficient for carrier capture into a QD has been calculated by
different authors [45,46,60]. They generally find that the Auger induced capture rate is
maximized for small energy difference scattering, i.e. for capture into the highest energy level
inside the QD. They also observe that Auger induced capture is more efficient for electrons
than for holes.
As an example of the capture processes discussed above, the measurements of
Ohnesorge et al. [61] are presented (Fig. 2.6), in which the authors have separated phonon and
Auger assisted capture and relaxation using the excitation density as a parameter. The
processes are considered to be phonon assisted for low excitation density (< 4 W cm-2
) and
Auger assisted for high excitation density (> 4 W cm-2
). From the graphs it is clear that
phonon assisted capture is independent of carrier density whereas Auger scattering decreases
the PL rise time for increasing excitation density. The temperature dependence of the phonon
assisted capture follows from Eq. (2.15), and thus becomes faster at increasing temperature
while Auger scattering induced capture, which is experimentally observed at high excitation,
is found to be temperature independent.
Phonon
Auger
Phonon
Auger
Phonon
Auger
Phonon
Auger
Fig. 2.6: Excitation density and temperature dependence of the Auger and phonon mediated
capture and relaxation process (from Ohnesorge et al. [61]).
2.5 Relaxation of carriers into the QD ground state
The carriers which are initially captured into the excited energy levels of a QD should
finally relax down to the ground state. The discrete energy levels within a QD makes phonon
Chapter 2
24
relaxation impossible from an energy conservation point of view, which is referred to as the
phonon bottleneck. Different theories have been put forward to explain the experimentally
observed fast relaxation rates that circumvent the phonon bottleneck. The relaxation through
phonon emission and Auger scattering are considered as the major mechanisms, where the
phonon emission induced relaxation involves the emission of multiple phonons or should be
treated in a polaron picture to circumvent the phonon bottleneck. Other relaxation
mechanisms such as relaxation through a continuum background or fast hole relaxation
through a hole “continuum” of broadened hole levels, followed by electron relaxation by
electron-hole scattering are alternative explanations for the observed relaxation times.
2.5.1 Relaxation by phonon emission or polaron emission
As seen in the case of capture, multiphonon emission is possible when single phonon
emission becomes energetically impossible. A schematic representation of single and
multiphonon relaxation is presented in Fig. 2.7. The lattice temperature dependence for single
phonon emission has been calculated in Eq. (2.15). The n-phonon-induced carrier relaxation
and carrier emission processes between two states 1,2 can be more generally expressed as
[56]:
/ 1s
12
11 ( 1)
ii B
nE k Tphonon emis ion
i
eτ
∆ −− Γ = + − ∏ (2.20)
/
12
11
ii B
nE k Tphonon absorption
i
eτ
−∆− Γ = − ∏ (2.21)
in which in and iE∆ are the number and the energy of the emitted optical or acoustic
phonons and 12τ is the scattering rate at T=0.
It again follows that the phonon relaxation time decreases as temperature increases. It
has been observed that even when the energy separation is not equal to a single LO phonon
energy the relaxation is fast. De Giorgi et al. observed for a QD with a level spacing of 60
meV that, 12τ = 6.2 ps for a 2LO phonon emission process [59]. The results of most authors
are in accordance with the calculated result, but usually fit with single-phonon (n=1) induced
relaxation. Different authors however obtain different values for the phonon energy E∆ .
Notably, Ohnesorge et al. obtained 2.7E meV∆ = , which is closer to LA phonon energy
[61].
Carrier dynamics in semiconductor QDs
25
Fig. 2.7: a) Single LO phonon relaxation b) Multiple phonon relaxation
Even though multiphonon relaxation mechanism can serve as an efficient relaxation
mechanism, rigorous energy requirement nevertheless exists and cannot explain the relaxation
occurring in system which does not satisfy them. Recently the carrier relaxation dynamics
involving LO phonons have been described in terms of polaron relaxation. In this model,
electrons (or excitons) confined within a QD are strongly coupled to the confined phonon
modes and form quasi particle states, called polarons [62-64]. The polaron relaxes by a
continuous exchange of energy between the coupled electron and phonon modes in a manner
similar to Rabi oscillations [43]. In the case of polaron decay, the phonon bottleneck is
removed since the polaron decay time is determined by the short lifetime of the LO phonon
component of the polaron, which amounts several picoseconds [43,44]. Other polaron
relaxation channels have been identified such as polaron decay to LO+LA, TO+LA or 2LA
phonons. It has been experimentally shown by Zibik et al. [44] that the polaron model relaxes
the energy conservation requirement by about several tens of meV leading to efficient
relaxation between the confined QD states.
2.5.2 Auger scattering induced relaxation
Carrier relaxation from the first excited p-level towards the ground state s-level is also
possible through the Auger mechanism in the following scenario. When two carriers have
been captured in the QD p-state, one carrier can relax down to the s-state by the Auger
scattering mechanism when the other carrier has final state within the wetting layer, as shown
in Fig. 2.8a. Ferreira and Bastard [57] have first calculated the carrier relaxation times inside a
QD due to Auger scattering. Obviously, this scattering mechanism will only be effective at a
higher injected carrier density, since it requires two electrons captured into an excited state
within the QD. But once a QD contains two electrons, the Auger scattering induced relaxation
rate has been calculated to be very efficient and even sub-picosecond [57], basically because
LO + LA phonon
(a) (b)
LO phonon
Chapter 2
26
two electrons confined into the tiny space of a single QD correspond to a high carrier density.
Recently, improved calculations on the p→s relaxation in realistic self assembled QDs model,
have been performed by Narvaez et al. [47] who found relaxation time between 1 and 7 ps,
depending on the QD size. Siegert et al. [50] recently performed detailed measurements on
the p→s relaxation rate and found total PL risetimes for the QD s-state between 5-6 ps (actual
p→s relaxation time are estimated to be subpicosecond) for doped QDs which they attribute
to Auger scattering and PL risetimes of 12 ps (actual p→s relaxation time estimated to be 2-3
ps) for undoped QDs which they attribute to polaron scattering.
Auger scattering can also take place between an electron and a hole captured into the
same QD (Fig. 2.8b). In this case, the Auger process scatters the electron into the QD ground
state and hole gets excited into the wetting layer valence band. Ferreira and Bastard [57]
claims that the capture of a single electron-hole pair within a QD is already enough for fast
relaxation of one of the two carriers to the QD ground-state by intradot electron-hole Auger
scattering.
(a) (b)
Fig. 2.8: a) Relaxation to the QD ground state by Auger scattering between two confined
carriers of the same type. b) Relaxation to the QD ground state by Auger scattering between
an electron and a hole in the same QD-level, leading to relaxation of the electron and
excitation of the hole into the wetting layer.
Carrier dynamics in semiconductor QDs
27
2.5.3 Continuum relaxation
Photoluminescence excitation spectra from a single QD shows a continuum
background, in addition to the sharp lines depicting the quantized energy levels of the QD.
This continuum background is sometimes interpreted as due to the low energy tail of the WL
or the barrier states extending into the QDs [65,66]. A better interpretation for the continuum
background are the crossed transitions between confined electron states within the QD and the
WL valence band or between the confined hole states within the QD and the WL conduction
band [67]. It is believed that this background also provides a carrier relaxation channel when
the continuum background is coupled to the discrete QD states by acoustic phonon scattering
[67] or Auger scattering. Bogaart et al. [68] have experimentally shown that the continuum
relaxation channel can bypass the excited QD states, allowing direct relaxation to the QD
ground state with the emission of a single LO phonon in the last step.
2.5.4 Fast hole relaxation
Sosnowski et al. [55] has first observed a clear two-step carrier relaxation process at
low excitation density when only a single electron-hole pair is captured into the excited QD
state and the electronic level separation does not satisfy phonon relaxation route. They
proposed a different carrier relaxation mechanism based on a fast initial relaxation of the hole
towards the QD ground state. Since the confined hole states are more closely spaced than the
electron states due to their larger effective mass, and taking into account lifetime broadening
/lifetime relaxationE h τ∆ = , the QD hole levels are supposed to form a continuum which
allows for fast hole relaxation through phonon emission [47]. The electrons can also
subsequently lose their energy by electron-hole scattering and relax to the QD ground state. In
this scattering process, energy constraints are easily satisfied due to the broadening of the QD
hole levels. As an example, Sosnowski et al. [55] observed a hole relaxation time of 0.6 ps
and an electron relaxation time of 5.2 ps when carriers are injected into the QD excited state.
Urayama et al. [69] also observed an initial fast relaxation of 0.7 ps which they attribute to
fast hole relaxation, followed by a slower 6 ps relaxation due to electron relaxation by
electron-hole scattering. The two-step carrier relaxation process has been observed only by a
few authors, but in these measurements, the QDs have been inserted in a separate confinement
structure to reduce the carrier diffusion time, which might have hidden the two-step relaxation
process to other authors. It should be mentioned that this mechanism is actually identical to
the Auger scattering induced relaxation model mentioned in Section 2.5.2, with the difference
that the Auger scattering takes place between electrons and holes in this case.
Chapter 2
28
(1)
(2)
(2)
Phonon
(1)
(2)
(2)
(1)
(2)
(2)
Phonon
Fig. 2.9: Step (1) - Fast hole relaxation into the ground state by phonon emission.
Step (2) - Electron-hole scattering leading to the electron relaxation into the ground state.
From the above discussion it is clear that many different mechanisms have been
proposed to explain the experimentally observed capture and relaxation time. It is concluded
that the capture and relaxation mechanisms seem to be highly dependent on the detailed QD
properties which seem to have been “uncontrolled” when regarding the large spread in
experimental results obtained up till now. In this thesis, it will be shown that part of the
confusion is probably caused by the fact that the carrier diffusion time in the barrier is often
not controlled. Anyway, it is presently difficult to arrive at a unified picture for the carrier
capture and relaxation mechanism.
2.6 Low temperature grown semiconductor structures
In mid 1980’s, the growth of GaAs at a reduced temperature using the MBE technique
started gaining interest both from an application and a research point of view. Low
temperature (LT) GaAs was initially investigated to reduce the sidegating or backgating
problems observed in GaAs Field Effect Transistor (FET) circuit technology in an effort to
exploit the high carrier mobility in GaAs for fast FET’s [70]. At the same time LT-GaAs was
investigated for ultrafast Metal-Semiconductor-Metal (MSM) [71] photodetectors for utilizing
the ultrafast carrier life time in LT-GaAs (~1 ps) [35], which is three orders of magnitude
smaller than the ~1 ns recombination time in GaAs [72]. Since LT growth can also be
employed for growing QWs and QDs, it is possible to combine the ultrafast response times
Carrier dynamics in semiconductor QDs
29
obtainable in LT growth with the enhanced optical nonlinearity and very low optical
saturation intensity observed in QWs and QDs due to the modification of their density of
states. Okuno et al. [38] has shown that LT GaAs/AlAs multiple quantum wells (MQWs)
have larger nonlinearity compared to bulk GaAs and a response time as low as 0.8 ps. Since
then, very fast, sub-picosecond, temporal response has been demonstrated in a variety of LT-
grown MQWs of InGaAs/InAlAs, GaAs/AlAs, and InGaAs/GaAs [38,40,73-75].
Since the switching speed can be reduced to sub-picosecond or even to the
femtosecond scale, all-optical switching is considered as a potential successor of electronic
switching in optical telecommunication field. As mentioned in Section 1.4, a significant
reduction of the required switching energy, while maintaining a femtosecond response is
highly required for all optical switching to become competitive. QDs are expected to
significantly reduce the required switching energy compared to bulk and QWs, since the
saturation density required for bleaching the QD ground state corresponds to only two
electron-hole pairs per dot. Prasanth et al. [41] have demonstrated a switching energy as low
as 6 fJ for InAs/InP quantum dots incorporated in a Mach-Zehnder Interferometric switch. A
very low saturation density of 13 fJ/µm2 has also been observed for InAs quantum dots under
resonant excitation by Nakamura and co-workers [8,9]. LT-QDs are expected to combine an
ultrafast response time with the very low switching energies already reported by Prasanth et
al. [41] and Nakamura et al. [8,9]. A switch with LT-QDs as active medium is thus an ideal
candidate for ultrafast all-optical switches in the optical communications. In this thesis, low-
temperature grown QDs are investigated for combining the ultrafast life time achieved during
LT growth with the low carrier density needed for absorption saturation in QDs as a potential
material for ultra-fast switches.
The growth temperatures for MBE grown LT-GaAs is usually around 200 °C which is
well below the normal growth temperature (530-600 °C) of high quality GaAs [76]. MBE
growth of GaAs is always performed in an excess Arsenic environment. However, at a very
low growth temperature of around 200 °C, the as-grown material is highly nonstochiometric
with an excess Arsenic concentration of around 1-2%. The excess Arsenic is incorporated into
the as-grown LT-GaAs as point defects, predominantly as AsGa anti-sites [35,77]. However,
after annealing, the excess Arsenic will cluster into As-precipitates. There are different
models explaining the electrical properties of the LT-GaAs, both annealed and as-grown,
based on anti-site defects or the Arsenic precipitate formation. The defect model ignores
possible Arsenic precipitates and assumes that the material is compensated by isolated arsenic
Chapter 2
30
anti-sites. The model based on arsenic precipitates assumes Schottky barrier like behavior
with depletion regions around the precipitate [78] and is discussed later.
The concentration of Arsenic anti-site related defects in un-annealed LT-GaAs is a
function of the growth temperature and can be varied between 5x1018
cm-3
and a few times
1020
cm-3
, and has been found to (steeply) increase with decreasing growth temperature of the
LT-GaAs [79]. The AsGa anti-sites are double donors with energy levels close to the middle of
the GaAs bandgap, existing in both the neutral and the positively ionized state. The activation
energy of the anti-site defects is around 0.71 eV with a level broadening of 0.1 eV. The
neutral AsGa0 can be positively ionized by acceptors in the form of Gallium vacancies, VGa,
which are native acceptors in LT-GaAs, or by Beryllium acceptors which can be intentionally
incorporated. The typical concentrations are 1020
cm-3
for AsGa0 and 10
19 cm
-3 for AsGa
+ at a
growth temperature of 200 °C [80].
(1)
(2)
0
GaAsGaAs+
(1): Trapping from the barrier
(2): Direct recombination
(3): Trapping of carriers in the QD
(3)
(1)
(2)
0
GaAsGaAs+0
GaAsGaAs+
(1): Trapping from the barrier
(2): Direct recombination
(3): Trapping of carriers in the QD
(3)
Fig. 2.10: Trapping of carriers initially confined within the QD into the to AsGa anti-site
defects within the surrounding LT-GaAs barrier.
The ionized AsGa+ level acts as an electron trap with a trapping coefficient of 2.75x10
-8
cm3/s [81]. Neutral AsGa
0 acts as a hole trapping center with a hole trapping coefficient of
Carrier dynamics in semiconductor QDs
31
3.3x10-11
cm3/s, making the hole capture cross section three orders of magnitude smaller than
the electron capture cross section. Thus, while the electron trapping time in LT-GaAs grown
at 250 °C has been measured by different experimental techniques to be in the 300 fs region
and as short as 100 fs in LT-GaAs grown at 200 °C, the hole trapping is a much slower
process which has been measured to be of the order of 2 ps in LT-GaAs grown at 270 °C [82].
The hole trapping process is a first possible mechanism which can result in a long time tail in
a time-resolved differential reflectivity experiment which is sensitive to both the electron
trapping dynamics and the hole trapping dynamics.
It has been realized that the electron trapping efficiency critically depends on the
concentration of ionized AsGa which is determined by the acceptor concentration. In undoped
LT-GaAs, the acceptor concentration is determined by the concentration of Gallium
vacancies, VGa, with a reported density of at least three times lower than the total AsGa
density, so that only a small percentage of the total number of anti-site defects take part in the
electron trapping process [82]. If the majority of the neutral AsGa could be ionized, the defect
density needed for an ultra-fast response can be significantly lowered. A method to increase
the ionized impurity concentration is to dope the material with acceptor impurities. Beryllium
can readily act as an acceptor and is easily incorporated up to high concentrations into the
GaAs matrix during MBE growth. Beryllium doping leads to ionization of AsGa0 to AsGa
+
thereby enhancing the electron trapping probability, which leads to a faster response of the
system. Haiml et al. [33] has shown that an increasing Be concentration decreases the initial
electron trapping time in LT-GaAs from 12 ps in the absence of Be doping, down to 2 ps at a
Be concentration of 3x1019
cm-3
. However, Krotkus et al. [34] reported exactly the opposite
effect. They reported that the electron trapping time is monotonously increasing with Be
concentration in as-grown LT GaAs up to a Be-concentration of 1019
cm-3
. Only for samples
with a very high Be-doping concentration (> 1019
cm-3
), the electron trapping times sharply
decrease, reaching an ultra-fast 100 fs response time. According to Krotkus et al. [83], the
intermediate increase of the electron trapping time with Be concentration is due to a filling of
the Ga-vacancy positions within the lattice by Be. Finally, it has been proposed [39] that Be-
doping may also lead to the formation of Be-AsGa+ complexes which can act as a trapping
center for both electrons and holes. When the electrons and holes are trapped in the same real
space, the recombination is of course much faster.
As reported by Siegner et al. [80], the final step in the recombination sequence of the
excited carriers, is the recombination of the trapped electrons and the trapped holes. Since the
wavefunctions of carriers trapped in spatially separated point defects will not generally
Chapter 2
32
overlap, the recombination of the trapped carriers is a slow process, often resulting in a long-
time tail to the initially fast time behavior due to fast electron trapping in AsGa+. The slow
recombination times can sometimes lead to an induced absorption from AsGa0 to the CB since
this transition has a large cross-section. Siegner has demonstrated that the initial decay time in
a pump-probe transmission experiment becomes faster at a lower growth temperature due to
an increase of the number of AsGa+ trapping centers, while the long-time tail actually becomes
slower at lower growth temperature. This surprising effect has been attributed due to the fact
that at a very low growth temperature of 250 °C, both electrons and holes are trapped in
charged and neutral anti-site defects. The final recombination of the electrons and holes is
slow in such a situation, due to the spatial separation of the anti-site defects, resulting in a
reduced wavefunction overlap between trapped electrons and trapped holes. However, at a
somewhat higher growth temperature (350 °C), the number of anti-site defects is lower and
the holes will only be partially trapped into neutral AsGa0. As a result, the final recombination
at 350 °C is a faster process due to the better wavefunction overlap between trapped electrons
and free holes in the valence band. A second possible mechanism for a long-time tail in the
time-resolved differential reflectivity experiment is the recombination of trapped carriers.
Finally, it should be noted that the electron trapping process is not necessarily a linear
process. After the fast trapping of the electrons in the anti-site defects AsGa+
+ e-→AsGa
0, the
population of electrons in the trap states builds up as the final carrier recombination is a slow
process. The positively ionized AsGa+ point defects get saturated at high carrier density
leading to the slowing down of the electron trapping into the anti-site defect levels. The
saturation of the traps is a third possible mechanism for a long time tail [80], which in this
case, is only expected at a high excitation density and a low trap density.
A next point is the sensitivity of the TRDR pump-probe technique to the several
possible transitions in LT-GaAs. In most experiments reported in literature, the pump and the
probe laser wavelengths were identical and tuned slightly above the GaAs bandgap. In that
case, the main source of excited carriers as well as the source of the induced probe
transmission is the transition between the conduction band (CB) and the valence band (VB)
along with AsGa0
to CB transitions. For bulk GaAs, the electron photoionization cross section
from AsGa0 to the CB is 10
-16 cm
-2 at 1060 nm while the hole photoionization cross section
from AsGa+ to the VB to is 3x10
-17 cm
-2 at 1060 nm [81]. Keeping in mind that the
concentration of neutral AsGa0 is approximately 10 times larger than the concentration of
ionized AsGa+
[80], the hole photoionization can be neglected. In the experimental setup used
in the Thesis, the pump is tuned above the GaAs bandgap and the probe is tuned into
Carrier dynamics in semiconductor QDs
33
resonance with the QD ground-state transition. The pump is thus expected to mainly excite
the VB to CB interband transition along with some photo-ionization of neutral AsGa0. In turn,
the probe pulse is expected to mainly probe the quantum dot interband VB to CB transition,
with a possible (unwanted) contribution due to the bleaching of the AsGa0 to CB transition.
The objective of the experiments is of course to measure the saturation time of the interband
VB to CB transition and not the saturation of the AsGa0 to CB transition. In LT-GaAs with a
high density of anti-site defects, the probe absorption due to the AsGa0-CB transition is
difficult to saturate by the pump, leading to weak absorption modulation on this (unwanted)
transition. A further increase of the neutral AsGa concentration by lowering the growth
temperature further increases the probability of re-absorption of AsGa0 to the CB, but also
reduces possible saturation effects on this transition.
The relative importance of saturation of the AsGa0 to CB transition can be reduced
when the saturation intensity of the interband VB to CB transitions is reduced. The saturation
intensity on the interband transition can be decreased by employing QD structures [38,39,84].
Due to their modified density of states, the pump-excited carriers already completely fill the
QD ground-states at very low pump excitation density. The ultra-fast carrier recombination is
taken care of by the LT growth which introduces AsGa+ trap centers in the bulk GaAs barrier
and possibly also inside the QD. Sercel [85] has shown theoretically that carrier tunneling out
of the QD into a defect center can be very efficient and results, in principle, in an ultrafast
recombination time. The carrier recombination times in LT-grown QWs and QDs can be
further decreased by Be doping which is expected to create more AsGa+ states leading to a
faster electron trapping.
Next, the model based on the Arsenic precipitates is discussed briefly. Both
overgrowth of a LT-GaAs layer by GaAs at a normal growth temperature and post-growth
annealing of the sample (> 600 °C) leads to nucleation of Arsenic into Arsenic precipitates.
The precipitates can have an average separation in the range of 30-90 nm with diameters
varying from about 7-20 nm depending upon the annealing temperature and the amount of
excess arsenic incorporated [78,86]. These As-clusters are metallic and are surrounded by
buried Schottky barriers. When the depletion regions of the Arsenic precipitates are
overlapping (see Fig. 2.11a), LT GaAs becomes semi-insulating in nature, thus providing a
high resistivity material. Moreover, the interface between the As-cluster and the surrounding
semiconductor might act as an additional trapping surface in addition to the remaining anti-
site defects which have not yet clustered into an Arsenic precipitate. Since the density of the
As precipitates is much smaller than the density of the remaining anti-site defects, the fast
Chapter 2
34
carrier recombination time in annealed LT-GaAs is usually attributed to the remaining anti-
site defects, while the high resistivity is attributed to overlapping Schottky barriers. The
annealing temperature and the annealing time of the material are important factors in
determining whether the point defects or the Schottky barrier approach is to be used. The
transition temperature where the precipitates start to play a dominant role is around 600 °C.
Fig. 2.11: The figure shows the depletion region around As precipitates with d as the
separation between the precipitates. a) Overlapping depletion regions ( ddepletion > d). b) Non-
overlapping depletion regions (ddepletion<d). (From Melloch et al. [78])
In annealed LT-GaAs, the carrier recombination time is reported to be as short as a
few hundreds of femtoseconds [76]. van Driel et al. [87] have reported that due to annealing
at around 600 °C, LT-GaAs remains crystalline with ~1% excess arsenic, existing both in the
form of precipitates and also as point defects with a minimum density of 1018
cm-3
[88,89].
Beard et al. [35] proposed that the annealing process leads to a reduction of the lattice strain
due to the cluster formation of the excess Arsenic, resulting in an increase of the carrier
mobility. The static mobility of the unannealed LT-GaAs is between 1 and 3 cm2
V-1
s-1
compared to mobility measured at 300 K in regular GaAs (~7000 cm2
V-1
s-1
). This value is
found to increase with annealing time and annealing temperature. The annealing process also
leads to an increased separation between the clusters and thus a lower density of anti-site
defects, resulting in a longer carrier lifetime.
Carrier dynamics in semiconductor QDs
35
2.7 Time Resolved Differential Reflectivity – Experiment
Carrier dynamics in semiconductor QDs is commonly studied by time-resolved
photoluminescence (TR-PL). The disadvantage of this technique is that it is mainly useful for
materials with a high PL efficiency. When one wants to measure the carrier dynamics as a
function of temperature and up to room temperature which is most relevant for device
applications, the decreasing sensitivity of the PL-efficiency with increasing lattice
temperature makes the TR-PL technique less attractive. At a higher lattice temperature, when
the PL efficiency is low, measurements based on optical absorption such as time-resolved
transmittance and time-resolved reflectivity are most effective. Transmission experiments in
which the probe laser is tuned into resonance with the QD transition are however not possible
due to complete absorption of the probe laser in the GaAs substrate. Although etching of the
back side of the sample can be used to increase the transmitted probe signal, transmission
measurements are less attractive due to the fragility of an etched sample. In this Thesis,
reflectivity measurements which are non-destructive are chosen, since they do not require
etching of the sample.
OPOMode locked Ti –
Sapphire laser
M
M
L4L3
Sample
M
B S
Lock – in
Amplifier
Reference
Signal
Variable delay
C
M
M
L1 L2
M
M
OPO
Balanced
detector
λ = 700-980 nm
λ = 1030-1330 nm
λ = 700-980 nm
λ = 1030-1330 nm
BS -Beam Splitter
C -Chopper
L -Lens
M -Mirror
L1 = 6 cm
L2 = 6 cm
L3 = 16 cm
L4 = 8 cm
OPOMode locked Ti –
Sapphire laser
M
M
L4L3
Sample
M
B S
Lock – in
Amplifier
Reference
Signal
Variable delay
C
M
M
L1 L2
M
M
OPO
Balanced
detector
λ = 700-980 nmλ = 700-980 nm
λ = 1030-1330 nmλ = 1030-1330 nm
λ = 700-980 nmλ = 700-980 nm
λ = 1030-1330 nmλ = 1030-1330 nm
BS -Beam Splitter
C -Chopper
L -Lens
M -Mirror
L1 = 6 cm
L2 = 6 cm
L3 = 16 cm
L4 = 8 cm
Fig. 2.12: Schematic of the time resolved differential reflectivity (TRDR) experimental setup.
The carrier dynamics studied in the Thesis makes use of the time resolved differential
reflectivity technique (TRDR) in the non-resonant excitation mode. In other words, the pump
Chapter 2
36
laser and the probe laser are mutually synchronized and tuned to two different wavelengths.
The pump pulse creates electron-hole pairs in the GaAs barrier layer and the probe pulse
monitors the occupation of the quantum dots. The carrier dynamics are obtained by measuring
the pump induced change of the reflected probe signal as a function of the time delay between
the pump pulse and the probe pulse. The schematic of the experimental setup is given in Fig.
2.12. The output from a mode locked Ti: Sapphire laser with 76 MHz repetition rate is used as
the pump and is tunable in the range 700-1000 nm. The output of an Optical Parametric
Oscillator (OPO), pumped synchronously by the Ti: Sapphire laser, is used as the probe beam.
The probe is tunable in the 1030-1330 nm wavelength range with a KTP crystal and between
1350-1600 nm by using a CTA crystal. The pump wavelength is tuned into the GaAs barrier
region, thus creating a sufficient number of carriers for obtaining significant state-filling in all
QDs. The probe laser has a pulse width of 2.5 ps and is tuned to be in resonance with the QD
ground state. A continuous variation of the time delay between the pump pulse and the probe
pulse is obtained by passing the pump beam through a variable delay line. The pump beam is
mechanically chopped at a frequency of 3 kHz and is focused on the QD sample which is kept
in a flow cryostat. The cryostat enables TRDR measurement in the temperature range between
5 K and 290 K. For reducing the sensitivity of the detection system to the intensity noise of
the OPO probe laser, the probe beam is split into two. The first half is focused onto the
sample. The reflected probe beam from the sample is collected using the same focusing lens
and is detected using a balanced detector. The other half of the probe beam is used as a
reference for the balanced detector. The balanced detector is used to cancel out the probe laser
intensity noise down to -50 dB. The pump beam has an approximate focused spot size of 50
mµ on the sample and the probe beam a spot size of 30 mµ . This ensures that the probe
beam completely spatially overlaps with the pump beam. Finally, a lock-in amplifier is
connected to the balanced detector to measure the pump modulated part of the probe signal,
0
0 0
totR R R
R R
∆ −= with R and 0R as the reflected probe signals with and without pump.
2.7.1 The differential reflectivity: theoretical approach
In the experiment, the probe beam is reflected at the air-GaAs interface, at the QD-
plane and also at the back surface of the sample as schematically illustrated in Fig. 2.13. The
total reflected probe signal is the result of superposition of the reflected electric fields at each
of these interfaces [90,91].
22 2 2z zik L ik D
tot tot s QD bR r r Ar e Br e M= = + + + (2.22)
Carrier dynamics in semiconductor QDs
37
where , ,s QD br r r are the coefficients of the reflected electric fields at the surface, the QD layer
and the back surface respectively. M is the sum of all the higher order reflections in the QD
sample and L and D are the thickness of the capping layer and the total sample thickness
respectively. Since the first order reflection coefficient from the QD layer is already very
small, multiple reflections can be safely neglected. Since the back surface reflection has a
time delay of at least 13 ps with respect to the surface reflection, it also does not contribute to
the superposition and it is usually out of focus in the experimental setup.
rs rQD rb
L
D
rs rQD rbrs rQD rb
L
D
Fig. 2.13: Schematic representation of the different contributions to the total reflectivity of the
QD sample. The interference between sr and QDr is the dominant contribution to the TRDR
signal.
Thus the total reflectivity can be expressed as:
22 ki
tot s QDr r Ar e φ= + (2.23)
2k kLφ = is the phase difference between sr and QDr due to the capping layer. By neglecting
the term 2
kiQDAr e φ , which is small since 1QDr , Eq. (2.23) can be re-written as:
Chapter 2
38
2 2 * *( )k ki itot s s QD s QDr r Ar r e Ar r eφ φ= + + (2.24)
In Chapter 4, it is shown that the reflection coefficient of a layer of QDs is expressed as:
0
( )cQD
c
ir
iω ω
Γ − Γ= −
− + Γ (2.25)
in which cΓ is the radiative emission rate of a layer of radiatively coupled QDs and Γ is the
dephasing rate of the ground-state exciton, including a correction which is explained in
Chapter 4 and 0ω is the exciton resonance frequency, corrected with a depolarization shift. In
Chapter 4 it is shown that ( )cΓ − Γ is dependent on the spatial separation between resonant
(nearly identical) QDs. The total reflectivity near the resonant transition energy 0ω of the
QD can thus be re-written as:
( )
( )( ) ( )
( )( )0 0
0 0
2 2 *2 22 2
( ) k kc ci itot s s c s c
c c
i ir r Ar e Ar eφ φω ω ω ωω
ω ω ω ω
−Γ + − Γ − −= − Γ − Γ − Γ − Γ
− + Γ − + Γ
(2.26)
Eq. (2.26) can be further simplified by re-arranging terms and separating out the surface
reflectivity according to:
( ) ( ) ( )tot s QDR R Rω ω ω= + (2.27)
yielding:
( ) ( )
( )0
0
2 22 2
( ) ( ) 2 ( ) c k ktot s s c
c
cos sinr r Ar
φ ω ω φω ω ω
ω ω
Γ − − = − Γ − Γ − + Γ (2.28)
Eq. (2.28) provides an expression for the intensity of the reflected probe signal from a layer of
QDs, showing that the reflected probe signal can be expressed as a product of radiative decay
rate ( ) cωΓ = Γ − Γ and a line shape factor ( )L ω [91]. Thus the QD reflectivity is expressed
as:
( ) ( ) ( )QDR Lω ω ω= Γ (2.29)
In the TRDR experimental technique used for observing carrier dynamics studied in
the thesis, the pump pulse has a photon energy much above the GaAs bandgap. The probe
photon energy window is tuned to be in resonance with the QD exciton ground state. Due to
the large detuning, the probe is not sensitive to pump induced changes of the refractive index
of the GaAs barrier layer, which will be therefore ignored in the treatment of the reflectivity.
In addition, it is assumed that the pump-induced reflectivity of the GaAs-air interface is only
Carrier dynamics in semiconductor QDs
39
visible in the vicinity of the GaAs bandgap and not in the spectral region of the QD ground-
state exciton. It is thus assumed that the probe only responds to the refractive index change in
the QD-layer due to the pump induced carrier occupation. The differential reflectivity
0totR R R∆ = − of the probe beam with and without pump P can therefore be written as:
[ ]( ) ( ) ( )tot s QDR R RP P
ω ω ω∂ ∂
= +∂ ∂
(2.30)
Since the probe is not sensitive to the GaAs refractive index change, ( ) 0SRP
ω∂
=∂
. The
pump induced differential reflectivity thus becomes:
( ) ( )
( ) ( ) ( ) ( )tot QD
LR R L
P P P
ω ωω ω ω ω
∂ ∂ ∂Γ ∂ ∂Γ = = Γ +
∂ ∂ ∂ ∂Γ ∂Γ (2.31)
and thus
( )
( ) ( ) ( )tot
LR L
ωω ω ω
∂ ∆ = ∆Γ Γ +
∂Γ (2.32)
This is the TRDR signal that is detected for any probe frequency ω and which is measured as
a function of pump-probe delay in an actual TRDR measurement as shown in Fig. 2.14.
The carriers generated by the pump beam in the GaAs barrier diffuse to the QDs and
are subsequently captured into the QDs thereby bleaching the QD transition. The subsequent
change of reflectivity in the probe is monitored as a time-resolved differential reflectivity
(TRDR) signal. TRDR signal shown in Fig. 2.14 can be written as:
( ) ( ) ( )exp expdecay rise
R t ttR τ τ∆ − −−∼ (2.33)
where ( )rise decayτ denotes the rise-time (decay time) of the TRDR signal. The rise-time riseτ
is determined by the carrier diffusion through the barrier layer, the carrier capture and the
subsequent carrier relaxation within the QDs. The exciton recombination time, decayτ ,
indicates the exciton recombination from the QDs which can be either radiative or non-
radiative. Since the TRDR signal is sensitive to the occupation of the QDs by either electrons
or holes, this implies that the TRDR signal is expected to be sensitive to the dynamics of Ne +
Nh, in which Ne and Nh are the carrier occupation numbers for the electron and hole levels in
the QD.
Chapter 2
40
0 500 1000 1500 2000
7.0
7.5
8.0
8.5
9.0
TR
DR
sig
na
l (a
rb.
un
its)
Delay (ps)
Barrier WL QD Barrier
Pump
Probe
(1)
(1)
(2)
(1)(2)
Growth direction
0 500 1000 1500 2000
7.0
7.5
8.0
8.5
9.0
TR
DR
sig
na
l (a
rb.
un
its)
Delay (ps)
Barrier WL QD Barrier
Pump
Probe
(1)
(1)
(2)
(1)(2)
Growth direction
Fig. 2.14: An example of a TRDR signal (right) showing the pump induced reflectivity
changes. The rising part (1) is governed by the carrier diffusion, carrier capture and carrier
relaxation into the QDs and the trailing part (2) is governed by the radiative exciton lifetime
in the QDs.
3
Anomalous temperature
dependence of the carrier
capture time into InAs/GaAs
quantum dots grown on a
quantum wire array
Abstract
In this chapter, the carrier capture dynamics into arrays of quantum dots (QDs) grown
on top of a 16 period quantum wire (QWR) superlattice is studied. The QWR superlattice
template is grown in order to limit carrier diffusion length within the lower barrier. Time
resolved differential reflectivity reveals an anomalous increase of the capture time between 40
K and 100 K, both at high (2.3 kW cm-2
) and at low (203 W cm-2
) excitation density.
Photoluminescence data indicate carrier re-emission out of the QWRs into the QDs in this
temperature range. At low temperature, the rise-time decreases from 28 ps at low excitation
density down to 5 ps at high excitation density. However, at room temperature, the rise-time
is nearly independent of the excitation density. The data is interpreted by taking into
consideration the diffusion of the photo-generated carriers within the GaAs barrier before
getting captured into the QDs. The diffusion limited capture of carriers become faster when
the carriers are generated close to the QDs, the probability of which is higher at high
excitation density. The anomalous temperature dependence is interpreted as due to the
temperature dependence of the effective carrier diffusion length modified by re-emission of
carriers from the QWR superlattice into the QDs.
Chapter 3
42
3.1 Introduction
In most quantum dot (QD) devices, carriers are injected into the barrier region from
where they are captured and subsequently undergo relaxation towards the QD ground state.
The performance of these devices critically depends on the efficient capture and relaxation of
the carriers, triggering a large amount of interest [44,50,57,59,68,92,93]. In the case of
quantum dots, a slowing down of carrier relaxation due to the phonon bottleneck has been
predicted [42], but experimental observations mostly reported efficient relaxation towards the
QD ground-state. There have been several models to explain the observed capture and
relaxation times, the most prominent being the multiphonon relaxation [61,94], polaron
relaxation [43,44] and Auger relaxation [57,61,92]. Other mechanisms were also proposed,
like fast hole relaxation followed by electron relaxation due to electron-hole scattering [55]
and also continuum relaxation [68,93]. However, there is a general disagreement on the
relative importance of the mechanisms predicted.
The observed rise time of the QD photoluminescence (PL) is usually interpreted as
due to the combined carrier capture into the QDs followed by carrier relaxation within the
QDs without considering the carrier diffusion within the barrier towards the capture volumes
surrounding each of the QDs. The carrier capture into quantum wells (QWs) has been studied
previously [49] by introducing a thin confinement heterostructure around the QWs to control
the carrier transport time towards the QWs, but such a separate confinement has been omitted
in many subsequent experiments. Sun et al. recently showed that the PL rise time at low
excitation density is strongly influenced by diffusion [95]. It is well known that the diffusion
coefficient in GaAs is temperature dependent [53]. It has also been shown that the diffusion
length in GaAs/(Al,Ga)As QWs is strongly temperature dependent [96]. This implies that the
measured carrier capture time as a function of temperature might be influenced by the
temperature dependence of the carrier transport time towards the QDs. In this Chapter, the
carrier capture and relaxation into QD-arrays grown on top of a quantum wire (QWR)
superlattice template is studied as a function of excitation density and temperature.
3.2 Carrier transport towards the QD plane
During optical excitation, the carriers are created not only in the GaAs capping layer
above the QDs, but also in the QWR superlattice and the buffer layer below the QDs, since
the absorption coefficient of GaAs is approximately 104 cm
-1. The GaAs layers act as a huge
reservoir for photo-excited carriers. The photo-excited carriers subsequently diffuse by
Anomalous temperature dependence
43
ambipolar diffusion towards a small capture volume defined in and around the QDs where
sufficient overlap between the wavefunctions of the barrier-states and QD states exists. The
carriers inside this volume are captured into the QDs and undergo relaxation to the ground
state through phonon or Auger scattering. Due to the large QD aerial density, carrier diffusion
in the QD plane has negligible effect in limiting carrier capture process compared to the
vertical diffusion within the GaAs barrier layer.
As discussed in Section 2.3, the carrier diffusion time from the actual photo-excitation
position in the bulk GaAs barrier layer towards the QD-plane, which are separated by a
distance L , is given by 2
a
L
Dτ = with aD as the ambipolar diffusion coefficient defined as
( )( )2e h Ba
e h
k TD
e
µ µ
µ µ=
+. The temperature dependence of the ambipolar diffusion
coefficient is mainly determined by the temperature dependence of the hole mobility,
implying that the ambipolar diffusion coefficient is maximum around 80 K as shown in
Chapter 2. Based on bulk GaAs parameters at 80 K [53], 150aD = cm2/s and 1L mµ≈ at
80 K, a minimum carrier diffusion time of 66τ = ps is obtained, showing that the carrier
capture dynamics are expected to be dominated by carrier diffusion. At 4 K, the ambipolar
diffusion coefficient for the photo-excited carrier density is not well known, but a rough
estimate yields a carrier diffusion time of a few hundred picoseconds. This estimate also
assumes that there is no carrier localization and that all the carriers which are photo-excited in
the epilayers are able to reach the QD layer. Here it should also be noted that the carriers can
also be photo-generated in the semi-insulating buffer layer, but these carriers may get trapped
in non-radiative traps present in the substrate. At low temperature, carrier localization at
potential minima or carrier traps in the GaAs barrier may also slow down the diffusion [53].
The large strain fields present around the vicinity of the QDs, the possible dislocations present
in the capping layer directly above the QDs might also trap away photo-generated carriers
and/or slow down the carrier diffusion. A next complication is the Schottky barrier formed at
the air-semiconductor interface, which creates a built-in electric field that makes it difficult to
estimate the carrier mobility and thus also the carrier diffusion time in the capping layer.
Finally, all the carriers generated in the capping layer need not be captured by the QDs when
they reach the QD plane. They can also be transmitted through the QD plane into the lower
barrier layer. All these sample details which affect the carrier transport towards the QDs are
usually not controlled in detail and will vary from sample to sample and also between
different growth teams. These factors are one of the possible sources for the lack of
Chapter 3
44
consistency between carrier capture and relaxation experiments performed by different
groups.
Diffusion through the barrier layer from the actual excitation position towards the QD
plane can thus be a major factor which determines the observed TRDR rise-time. For the
sample studied in the thesis, a QWR superlattice (SL) is inserted below the QD-arrays in
order to limit the carrier diffusion length in the lower barrier. The QWR SL will act as a
carrier sink at least at low temperature where the QWR SL will capture away carriers which
are excited in the lower GaAs barrier layer, thus limiting the carrier diffusion length to the
100 nm thickness of the capping layer only. This provides a good platform for studying the
carrier capture and relaxation dynamics in the QDs. It will however be shown that carrier
diffusion within the barrier layers and the SL template is still strongly influencing the carrier
capture time.
3.3 Experimental technique and sample details
The sample consists of InAs/GaAs QDs grown on a GaAs (100) substrate using the
MBE technique [97]. First, a buffer layer of 200 nm thickness is grown at 580 ºC. On top of
the buffer layer, 2.3 nm In0.41GA0.59As is deposited at 540 °C, which is capped by a 0.7 nm
GaAs layer leading to the formation of QDs, which are slightly elongated in the [1-10]
direction. The QD layer is subsequently annealed for 2 minutes at 580 °C, leading to a further
elongation of the QDs in the [1-10] direction and finally results in the formation of a QWR
along [1-10]. A GaAs separator layer of 12.3 nm thickness is subsequently grown at 580 °C.
Thereafter the process of the QWR formation is repeated to finally obtain 16 periods. The
stack of 16 QWR layers is referred to as the QWR superlattice (SL) which serves as a
template for the formation of the QD-arrays. A 2.3 nm In0.41Ga0.59As layer was subsequently
deposited at 540 °C to form QDs which order into QD-arrays (Fig. 3.1). The QDs can reduce
their amount of strain when they spatially order on top of an Indium rich QWR. The sample is
finally capped with a 100 nm thick GaAs top layer.
First, the sample as well as the carrier transport from the QWR template towards the
QD-arrays was characterized by temperature dependent PL. Subsequently the carrier
dynamics was studied by using the Time Resolved Differential Reflectivity (TRDR)
technique. The PL is performed using a frequency doubled Nd:YAG laser operating at 532
nm (2.33 eV) as the excitation source. The resulting luminescence is collected using a
monochromator and a cooled InGaAs array detector. For the investigation of the carrier
Anomalous temperature dependence
45
capture and relaxation time, TRDR experiments are performed as a function of excitation
density and temperature. The pump source is a mode-locked Ti:Sapphire laser tuned to 1.67
eV, which is well above the GaAs bandgap and the probe is a synchronously pumped Optical
Parametric Oscillator (OPO) tuned to 1.14 eV, in resonance with the QD ground state energy
levels. The reflected probe is recorded as a function of delay between pump and probe pulses
by using an optical delay line. The reflected probe signal is monitored by a balanced detector
and a lock-in amplifier in order to be able to detect pump-induced reflectivity changes down
to 10-6
. The TRDR signal has an initial rising part which indicates the capture and relaxation
of carriers into the QDs, followed by an exponential decay due to the recombination of the
carriers in the QDs.
QWR SL template
QD array
QWR SL template
QD array
(a) (b)
GaAs substrate/buffer
layer
GaAs separator layer
InGaAs QWR16
layers of QWR
SL template GaAs capping layer
InAs QDs
GaAs substrate/buffer
layer
GaAs separator layer
InGaAs QWR16
layers of QWR
SL template GaAs capping layer
InAs QDs
InGaAs QWR16
layers of QWR
SL template GaAs capping layer
InAs QDs
(c)
Fig. 3.1: (a) Atomic force microscopy image of ordered quantum dot arrays formed by self-
organized anisotropic strain engineering. Scan size: 1 x 1 µm (From Mano et al. [97]). (b)
Three dimesional view of the sample structure showing the QD arrays on top of QWR SL
template. (c) Cross sectional schematic view of the QD arrays on QWR SL template.
Chapter 3
46
3.4 Results and discussion
Photoluminescence (PL) spectra of the QD-arrays and the QWR superlattice were first
recorded at 5 K at an excitation density of 490 W cm-2
. As observed in Fig. 3.2, the PL-peak
of the QD-array is centered at 1.19 eV and PL-peak from the QWRs is centered at 1.38 eV. At
5 K, the QWR superlattice emission has a twin peak structure at 1.36 eV and 1.38 eV. The
twin peaks in the QWR superlattice template reflects the size distribution of the QWRs, most
probably due to small size variation between different layers of the superlattice template. The
splitting between the QD-array peak and each of the QWR peaks amount to 176 meV and 194
meV, respectively.
1.0 1.2 1.40
PL
in
ten
sit
y (
arb
.un
its)
Energy (eV)
194 meV
176 meV
QD
QWR
5K
Fig. 3.2: Low temperature photoluminescence (5 K) from the QD-arrays at 1.19 eV as well as
from the QWRs at 1.36 and 1.38 eV.
In order to study the carrier emission out of the QWR template into the QD-arrays, the
PL was investigated as a function of sample temperature. It can be observed that the twin
peaks of the QWR SL template merge into a single peak above 50 K, indicating carrier re-
distribution between different non-identical layers of the QWR superlattice in the sample.
When the temperature is further increased from 40 K to 90 K, the intensity of the QWR PL-
peak decreases, accompanied by an increase in the intensity of the PL-peak of the QD-arrays,
as shown in Fig. 3.3. The increase in PL from the QDs and the subsequent decrease in PL
from the QWRs indicate carrier re-emission out of the QWR superlattice, followed by carrier
diffusion and finally re-capture into the QD-arrays. For temperatures above 90 K, the PL
Anomalous temperature dependence
47
intensity of the QD-arrays also starts to decrease due to carrier re-emission out of the QD-
arrays at high temperature.
1.1 1.2 1.3 1.4
0
2000
4000
6000
40 50 60 70 80 90
PL p
eak
inte
nsi
ty (
arb
. units
)
Temperature (K)
QD peak
QWR peak
65 K
PL
in
ten
sit
y (
arb
.un
its
)
Energy (eV)
47 K
57 K
77 K80 K
82 K
87 K
90 K
47 K
90 K
Fig. 3.3: Temperature dependent photoluminescence spectra of the QD-arrays near 1.19 eV
and the QWR superlattice template near 1.37 eV, showing the relative decrease of the PL
intensity of QWRs and the related increase of the intensity of the QD-arrays with rising
temperature. The inset shows the temperature dependence of the PL peak intensities of the
QDs and the QWRs.
The carrier capture and relaxation dynamics are further investigated as a function of
temperature for two different excitation densities using the TRDR technique. As a first step,
TRDR measurements were performed as a function of the excitation density at 5 K. The
amplitude of the TRDR signal shows a linear behavior below 0.3 kW/cm2 excitation density,
though there is no clear saturation regime observed up to the highest available excitation
density (2.2 kW/cm2), as shown in Fig. 3.4. The sample shows a similar behavior at room
temperature (Inset of Fig. 3.6). In Fig. 3.5, the observed TRDR rise-time is presented as a
function of the excitation density. At a low excitation density of 30 W/cm2, the TRDR rise-
time is nearly constant with a “plateau” value of 26 ps. With increasing excitation density, the
rise-time decreases to a value of 5 ps at approximately 1.5 kW/cm2. For a higher pump
excitation, a further increase of the excitation density does not affect the rise-time anymore,
which attains a constant value. At room temperature the rise-time seems to be independent of
Chapter 3
48
the excitation density with a value of ~ 5 ps which is close to the “plateau” value at high
excitation at 5 K (Fig. 3.6).
500 1000 1500 2000 2500
0 100 200 300 400 500 6000
PL p
eak inte
nsity (
arb
.un
its)
Excitation power density (W/cm2)
TR
DR
sig
na
l am
plit
ud
e (
arb
. u
nits)
Excitation power density (W/cm2)
PL at 5 K
Fig. 3.4: The dependence of the TRDR amplitude on pump excitation density at 5 K. The
graph shows a linear behavior up to 300 W/cm2, but not a clear plateau related to saturation,
indicating that complete filling of the QD is still not reached. The inset shows the PL
amplitude versus excitation density, also indicating a deviation from the linear dependence
above 300 W/cm2.
Auger scattering assisted capture and relaxation mechanism are expected to become
faster with increasing excitation density as mentioned in Section 2.4 (Chapter 2). Phonon
emission assisted capture and relaxation is expected to be independent of the excitation
density and is expected to be dominant at low excitation density. From the rise-time
dependence on the excitation density, it can be understood that the low excitation density
regime (< 50 W/cm2) can be explained by phonon emission assisted capture. For higher
excitation density, the Auger process starts to dominate. However, this straightforward
interpretation cannot explain why the TRDR rise-time reaches a second plateau value of ~ 5
ps at high excitation densities (> 1.5 kW/cm2). Auger scattering induced relaxation is not
expected to saturate at higher carrier density. A few authors [92] have “loosely” interpreted
the saturation behavior as being due to state-filling and thus saturation of the carrier
occupation within the QD. However, such an interpretation requires a very quick initial carrier
Anomalous temperature dependence
49
relaxation time followed by a slowing down of the relaxation as a function of the pump-probe
delay. In other words, such an explanation requires a non-exponential rise of the TRDR
signal, which is contrary to the experimental observations presented in this Chapter.
100 1000
5
10
15
20
25
30
TR
DR
ris
e-t
ime
(p
s)
Exitation power density (W/cm2)
Fig. 3.5: TRDR rise-time versus pump excitation density at 5 K.
0 500 1000 1500 2000 2500
1
2
3
4
5
0 500 1000 1500 2000 25000
TR
DR
sig
na
l a
mp
litu
de
(a
rb.
un
its
)
Excitation power density (W/cm2)
TR
DR
ris
e-t
ime (
ps)
Exitation power density (W/cm2)
Fig. 3.6: TRDR-rise time versus excitation density at room temperature showing only a weak
dependence on excitation. The inset shows the variation of the TRDR amplitude with
excitation density, indicating a plateau around 1000 W/cm2.
Chapter 3
50
0 100
8
0
1.0
1.2
1.4
TR
DR
Sig
nal
am
pli
tud
e
2.2 kW cm-2
203 W cm-2
TR
DR
Sig
nal (a
rb.
un
its)
Delay (ps)
5K
Fig. 3.7: The TRDR time trace at 5 K for two excitation densities showing the initial fast rise
and the slowing down of the signal at low pump excitation density.
In order to understand the rise-time behavior, the TRDR time-traces at 5 K for
different excitation densities are compared in detail as shown in Fig. 3.7. The time-traces
show a fast initial rise for all the excitation densities studied. At low excitation density, the
fast initial rise is followed by a slower increase of the TRDR signal, which is not observed at
high excitation density (Fig. 3.7). The initial fast rise observed at all excitation densities is due
to the capture of carriers initially excited very close to the capture volume defined around the
QDs. The further slowing down at larger pump-probe delay can be due to carrier diffusion
from the initial excitation position towards the QD capture volume. At low excitation density
the diffusion has a more pronounced effect, as less number of carriers are initially photo-
generated very close to, or within, the capture volume of the QDs. For example, at 5 K and
low excitation density, the number of photo-generated carriers in the GaAs barrier is around
2.9x1016
cm-3
, i.e., less than one electron-hole pair per capture volume of an individual QD.
Thus carriers which are photo-generated further away in the barrier layer have to diffuse a
larger distance to reach the QDs in which they will be finally captured, leading to the
observed slowing down of the TRDR signal after the fast initial rise. At high excitation
density, the average distance between the initially photo-generated carriers and the QD
capture volume is much smaller since more carriers are created near the capture volume.
Carrier diffusion is thus not required at high excitation density, implying that the rise of the
Anomalous temperature dependence
51
TRDR signal remains fast. The single exponential nature of the TRDR rise signal also
indicates that the carrier diffusion, capture and relaxation cannot be separated within the
present experiment.
The plateau for rise-time at low excitation density can be understood in the context of
diffusion. At 5 K all carriers excited below the QD-layer are captured by the QWR SL.
Carriers photo-excited in the capping layer will diffuse to the QD-layer where they are
partially captured and partially transmitted allowing them to diffuse and be captured into the
QWR-SL also. Thus, at low temperature, the SL template act as a carrier sink reducing the
probability of having more than one electron-hole pair in the QD capture volume. Thus the
plateau of the rise-time at around 26 ps as observed at low excitation in Fig. 3.5 can be
explained, since carrier capture into the QWR SL is limiting the availability of the carriers
which can be captured into QDs. The observed 26 ps rise-time can thus be explained by a
large diffusion length of the carriers which manage to diffuse towards the capture volume of
the QDs.
However, as excitation density increases, the excited carriers on the average have to
diffuse over a smaller distance from their excitation position to reach the QDs. In this regime,
the capture time is expected to decrease for increasing excitation density. A similar behavior
has also been observed by Sun et al. [95]. The second plateau at high excitation density can
also be interpreted by taking into consideration the diffusion of the carriers through the barrier
layer towards the QDs. As mentioned in Chapter 2, when carriers are photoexcited in the
GaAs barrier region, they need to diffuse to the capture volume surrounding the QDs, before
they can be captured. At high pump excitation density, the average distance between the
position of the nearest excited carrier in the GaAs barrier and the QDs is small, implying that
the diffusion time towards the QD is not important for the nearest excited carrier in the
barrier. A further increase of the excitation density will not further decrease the separation
between the nearest carrier and the QD. The carrier capture time is thus expected to be
excitation independent, giving a steady value for rise-time.
To get a more thorough understanding about the carrier transport towards the QDs and
the subsequent carrier capture into the QDs, the TRDR rise-time is studied as a function of
temperature. The rise-time behavior shows a very interesting feature with respect to the
temperature at both high and low excitation densities. Between 50 and 100 K, the rise-time
becomes slower, attaining a maximum value of 43 ps at low excitation and ~20 ps at high
excitation, as shown in Fig. 3.8. It is interesting to note that this is the same temperature
Chapter 3
52
region in which the carrier re-distribution from the QWRs to the QDs is taking place. The
graph of the TRDR amplitude versus temperature shows a similar behavior as the temperature
dependence of the TRDR rise-time. The TRDR amplitude first increases between 70 K and
150 K and subsequently decreases with further increase of the temperature. However, the
detailed temperature dependence of the TRDR rise-time and the TRDR amplitude is markedly
different and will be explained below.
0 50 100 150 200 250 300
5
10
15
20
25
30
35
40
45
TR
DR
ris
e t
ime
(p
s)
Temperature (K)
203 W cm-2
2.2 kW cm-2
0 50 100 150 200 250 300
5
10
15
20
25
30
35
40
45
TR
DR
ris
e t
ime
(p
s)
Temperature (K)
203 W cm-2
2.2 kW cm-2
Fig. 3.8: Temperature dependence of the TRDR rise-time at low excitation density (203
W/cm2), and at high excitation density (2.2 kW/cm
2).
The TRDR amplitude, as defined in Fig. 3.7, is a measure of the occupation of the
QD-arrays and is plotted as a function of temperature in Fig. 3.9. The strong correlation of the
TRDR amplitude and the PL intensity with respect to temperature clearly indicates a re-
distribution of the carriers from the QWR template to the QD-arrays at both excitation
densities. The temperature dependence of the rise time can be explained by carrier re-
emission out of the QWR-SL and diffusion towards the QD capture volume. As temperature
increases the QWR starts re-emitting the trapped carriers, thereby increasing the effective
diffusion length from which carriers can finally reach the QD-layer. This results in the
slowing down of the capture time as more and more carriers initially excited within QWR-SL
or the buffer layer start to migrate to the QD capture volumes, reaching a maximum
occupation at a larger time delay. As the temperature increases further, the SL template is no
Anomalous temperature dependence
53
longer able to trap the carriers for an extended amount of time, causing all the carriers in the
buffer layer to diffuse to the QD region. The effective carrier diffusion length is thus much
larger than at low temperature. Due to the fact that the QWR-SL is not a “sink” for photo-
excited carriers anymore, the carrier density in the barrier above the QDs is much larger, up to
the level that there are always more than one electron-hole pair within all capture volumes of
the QDs, leading to immediate capture into the QDs thereby showing a faster rise-time. This
accounts for the decrease of the rise-time as the temperature is increased beyond 100 K,
where the influence of carrier diffusion starts to decline. Finally as the temperature
approaches 290 K the diffusion is reduced to a minimum leading to a fast rise-time even at
low excitation densities. As seen in Fig 3.6, the rise-time does not have any pronounced
dependence on the excitation density at room temperature.
0 50 100 150 200 250 3000.0
1.5
0 50 100 150 200 250 3000
5
TR
DR
am
plit
ud
e (
arb
.units)
Temperature (K)
203 W cm-2
2.2 kW cm-2
Fig. 3.9: Amplitudes of the TRDR time-traces versus temperature for a pump excitation
density of 203 W/cm2 and 2.2 kW/cm
2.
It should be noted that the observed temperature and excitation density dependence is
usually interpreted due to the temperature dependence and excitation density dependence of
the phonon and Auger carrier capture and relaxation mechanism itself [42-
44,50,55,57,59,61,68,92-94]. In this Chapter, it is shown that the observed TRDR risetime
behavior can also be explained by the diffusion mechanism. The well-known temperature
dependence and excitation density dependence of the phonon and Auger carrier capture and
Chapter 3
54
relaxation rates are not included in the interpretation. The main conclusion is that one can
only deduce the phonon and Auger induced carrier capture and relaxation rates in an
experiment in which the carrier diffusion process, and thus the carrier density in the GaAs-
barrier near the QD-plane, is completely experimentally controlled. In some experiments
reported in literature [50,61], the authors reported the PL-lifetime in the barrier, the WL, the
QD excited levels and the QD ground-state, thus allowing to eliminate the diffusion time. It
should however be noted that even in these very carefully designed experiments, the carrier
density in the barrier above the QDs will substantially vary by the diffusion process, thus
hampering a straightforward interpretation of the experimental results without controlling the
diffusion process in detail.
3.5 Conclusions
In conclusion, it is shown that both the temperature and excitation power dependence
of rise-time can be interpreted by taking into account the diffusion of carriers towards QD-
arrays. The detailed shape of TRDR time-trace at low and high excitation density can also be
explained by the diffusion picture. It is shown that the carrier capture into and carrier re-
emission out of the SL template is a limiting factor which determines the effective carrier
diffusion length and thus determine the observed anomalous temperature as well as the
excitation density dependence of the TRDR rise-time. At very high excitation density, the
carrier capture time becomes independent of the diffusion time when the average number of
carriers in the GaAs barrier layer, within a so-called “capture volume” surrounding each QD,
exceeds unity. The data shows that an experimental study which allows for a precise control
of the diffusion dynamics in the QD barrier is needed, in order to accurately measure the
capture and relaxation time into the QDs.
4
Anomalous radiative lifetime
in quantum rods
Abstract
It is well known that spontaneous emission lifetime of an emitter can be changed by
inserting the emitter into a nanocavity, making use of the Purcell effect. The radiative decay
rate in nanostructures like carbon nanotubes, quantum dots etc can also be modified by
electromagnetic field interaction in the absence of an external cavity. This fact has been often
ignored in experimental observations. In this Chapter, the lifetime modification in a
InAs/GaAs Quantum Rod (QR) ensemble due to interaction of these rod like antennas with
the probe electromagnetic field is investigated.
A resonant exciton lifetime is observed in the QRs by using the time-resolved
differential reflectivity (TRDR) technique. At low excitation density, the decay time of the
TRDR signal shows a clear excitonic type of behavior. At increased excitation, a resonant
radiative lifetime develops, which seems to be dependent on the excited QD density being
resonant with the probe laser spectrum. The resonance behavior is interpreted as a result of
the electromagnetic coupling between the excited QDs resonant with the probe laser.
Chapter 4
56
4.1 Introduction
The radiative lifetime of confined electron-hole pairs in a quantum dot is usually
described in an exciton picture [98,99]. As a consequence, the wavelength dependence of the
exciton lifetime is believed to vary only weakly as a function of the electron-hole
wavefunction overlap. Such an approach however assumes that the permittivity of the
quantum dot medium is unaffected due to the excitation of a quantum dot. For properly
interpreting the reflectivity lifetime, it should be taken into account that the excitation of an
electron-hole pair into a semiconductor quantum dot strongly changes the local permittivity of
the quantum dot medium near the exciton resonance. The local permittivity can be modeled
[100] with a Lorentzian contribution and is expressed as:
0 hom
( ) 1QD
QD h
w
i
ωε ω ε
ω ω
= + − + Γ (4.1)
in which QDω is the phenomenological parameter [101] proportional to the QD oscillator
strength, 1w = ± is the QD ground-state population with 1w = + for the inverted case, hε
is the dielectric function of the barrier material and homΓ is the exciton dephasing rate in the
QD, which at low temperature, is only limited by the radiative decay rate ~ 1 ns-1
. At
resonance, the QD permittivity has a calculated value [102,103] of
0( )QD h QD dephasingε ω ε ω τ= = 104-10
5, which is much larger than the permittivity of the GaAs
host medium ( )11hε = . The large contrast of the local permittivity within an excited QD is
much larger than currently achieved in any artificially manufactured nanocavity. Due to the
large permittivity, the local wavelength of the light within an excited QD, 0QD
λε
( )0 1 mλ µ∼ , is smaller than the diameter of the QD, which is of the order of 20 nm. In
combination with the huge permittivity contrast, light confinement within a QD might even
become possible, implying that an excited QD is already a nanocavity itself [102,103]. For the
results presented in this chapter, it is not important whether a QD is able to act as a nanocavity
or not. It is however important to realize that an excited QD will strongly modify an incoming
electromagnetic plane wave probe in a reflection experiment due to dipole scattering. In other
words, an excited QD generates strong local electromagnetic fields in its vicinity and these
local electromagnetic fields will also couple with other excited QDs. Thus due to the strong
light diffraction, the initially isolated QDs are collectively coupled by the electromagnetic
field. The picture of coupled QDs in which the excitation is hopping from QD to QD, strongly
resembles the polariton picture in a bulk semiconductor.
Anomalous radiative lifetime
57
In the polariton picture, the excited QDs are expected to show a collective response to
the electromagnetic field. Such a collective response of all QDs which are resonant with the
external electromagnetic field will of course change the reflection lifetime of an isolated
quantum dot into the lifetime of an ensemble of radiatively coupled quantum dots.
4.2 Electromagnetic coupling in a quantum dot array: theory
In this section a simple classical description [104] is used to derive an expression for
the spontaneous emission rate 0Γ in a regular 2-dimensional array of quantum dots, which
will be used as a model representing a single layer of self-assembled QDs. A quantum
electrodynamical version of a part of this theory has been published by Slepyan et al. [105].
Consider a spherical QD with radius QDR in the presence of a plane wave external field
( )0( ) i t krE E e ωω − −= . Here ω is the frequency of the probe laser and
2k
c
π ω
λ= = is the
wave number with λ and c as the wavelength and the velocity of light in the vacuum
respectively. The QD radius QDR is assumed to be much smaller than the wavelength of the
light. In this situation the dipole approximation is valid and the electromagnetic response of a
QD can be described by the well-known Clausius-Mossotti equation for the polarizability
[106,107]:
3( )2
QD hQD
QD h
Rε ε
α ωε ε
−=
+ (4.2)
Actually, this equation is a zero-order approximation with respect to the parameter QDkR . A
more rigorous consideration [104] for the polarizability gives the equation:
35/2 3 3
( )22 2 ( ) 1 ( )3
QD hQD
QD h QDh h
Ri kR i k
ε ε αα ω
ε ε ε ε α
−= ≈
+ + − (4.3)
which is also well known, and has been applied in near-field optics. By substituting Eq. (4.1)
into Eq. (4.2) and subsequently substituting Eq. (4.2) into Eq. (4.3), the polarizability of a
single spherical QD can be expressed as
( )
( )
0
3
30 hom
3
233 9
3
QD QD
QDh QD QD
QD QD
R w
wi i k R w
R w
i
ωα ω
ωω ω ε ω
ω
ω ω
=− + + Γ −
=− + Γ
(4.4)
Chapter 4
58
In Eq. (4.4) a modified radiative emission rate Γ and a modified transition frequency 0ω ,
which is different from 0ω by the depolarization shift [105,108] is introduced, and is written
as:
0 01
3 QDwω ω ω− = − (4.5)
hom 0wΓ = Γ − Γ (4.6)
In Eq. (4.6) 0Γ is the radiative decay rate of a spherical QD embedded in a medium with
permittivity hε . For obtaining an expression for 0Γ , a correction is applied to the radiative
emission rate for a two-level atom in vacuum with the permittivity of the host medium taken
into account, by substituting 0 0/ , /h hc c ε µ µ ε→ → , thus yielding:
20 3
0
2 | |
3
hk
ε µΓ =
(4.7)
with 0µ as the transition dipole matrix element. Using this definition for 0Γ , QDω can be
written as (See Appendix A):
20
4| |QD
h QDV
πω µ
ε=
(4.8)
in which QDV is the volume of the QD.
4.2.1 The reflection coefficient of a layer of QDs
For obtaining the reflection coefficient of a layer of QDs, the effective index method is
used, in which the QD layer is replaced by a continuous thin quantum well (QW) layer with
the same average index of refraction as the QD layer. Slepyan et al. [101] have shown that
such a layer of QDs can be replaced by a thin dielectric layer, provided that the proper
electromagnetic boundary conditions are applied which were derived in their paper.
Anomalous radiative lifetime
59
X
Y
Z
hε
hε
QDd
QDd
QDR
QDε
X
Y
Z
hε
hε
QDd
QDd
QDR
QDε
X
Y
Z
X
Y
Z
hε
hε
QDd
QDd
QDR
QDε
Fig. 4.1: Schematic of a single layer of identical QDs which are ordered in a 2-dimensional
array with a mutual separation “ QDd ” between adjacent QDs.
By applying the electromagnetic boundary conditions, an expression for the
reflectivity for a QW layer is obtained, which can be expressed as [109]:
( )1
iR
iω
Λ=
− Λ (4.9)
provided that the following expression for ( )ωΛ is used [91,101]:
2
2( ) ( )
h
QD
k
d
π εω α ωΛ = (4.10)
in which QDd is the distance between the QDs in the square QD lattice (Fig. 4.1). Substitution
of Eq. (4.4) and Eq. (4.10) into Eq. (4.9) gives the reflectivity of the lattice of spherical QDs,
which can be rewritten as
0
0 0
( )( )
[ ( ) ]
QD
QD
iwB dR
i wB dω
ω ω
Γ=
− + Γ − Γ (4.11)
where, ( )QDB d is a superradiance factor expressed as:
2
3( )
( )QD
h QD
B dkd
π
ε= (4.12)
Chapter 4
60
A simplified version of Eq. (4.11) was first obtained by Slepyan et al. [101] in a paper
in which the electromagnetic boundary conditions for treating a QD layer as an effective
quantum well were derived. Here the dephasing rate homΓ , which has been ignored in
[101],has also been accounted for. Consequently, the assumption ( ) 1QDB d >> for the
superradiance factor is eliminated, which is equivalent to / 0.14QD vacuumd λ << for the host
dielectric function of 12.5hε = ; 2 / vacuumk π λ= . Since the average distance between the
QDs in the sample is about 50 nm, for 1 mvacuumλ µ= the condition for the validity of the
electromagnetic boundary conditions, / 0.14QD vacuumd λ << remains valid. However,
nonhomogeneous broadening due to the QD size distribution drastically changes the situation.
For a given frequency range (defined by the probe pulse spectral linewidth) ( )QD QDd d ω=
near the maximum of the nonhomogeneous PL spectrum, the quantity ( ) 0.1QDB d ≈ .
The imaginary part of the pole of Eq. (4.11) yields the decay rate of the probe
reflectivity signal of an array of coupled QDs which is given by
00 hom 0 2
3( ) ( )
( )coupled
QDh QD
wwB d w
kd
π
ε
ΓΓ = Γ − Γ = Γ − Γ − (4.13)
From this expression, it is obvious that the decay rate of the reflection signal increases for a
closely spaced array of QDs and returns towards the uncoupled value for large QDd . Thus a
closely spaced array of QDs tends to collectively respond to an external electromagnetic field,
thus increasing the lifetime. This theory also predicts a difference in the decay rate for an
inverted QD ground state ( )1w = + and an empty QD ground state ( )1w = − .
It should be emphasized that this expression for the decay rate of the probe
reflectivity, which decays as a function of real time t is not identical to the TRDR lifetime
which decays as a function of the pump-probe delay τ . In Appendix B, a preliminary method
to obtain the TRDR-lifetime from Eq. (4.13) is provided. Another major problem with the
present status of the theory is that it assumes an ordered array of identical QDs. In practice,
both the spatial position of the QDs and the transition energies of the ground-state excitons
are random. An improved theory for an inhomogeneous array of the QDs is currently under
preparation.
Anomalous radiative lifetime
61
4.3 Experimental details
(a) (b)(a) (b)
GaAs capping layer
InAs QRs
GaAs buffer layer
GaAs capping layer
InAs QRs
GaAs buffer layer
(c)
Fig. 4.2: (a) Cross-sectional image of the columnar (In,Ga)As QRs formed by eight stacked 2
nm GaAs/1ML InAs layers on top of a 2 ML InAs seed and overgrown by 5 nm In0.2Ga0.8As on
GaAs (100) substrate. (b) Image on an enlarged scale. The arrows indicate growth direction
(From He et al. [110]). (c) The Schematic cross-sectional view of the QR structure.
The reflectivity lifetime of columnar quantum rods is investigated by means of Time
Resolved Differential Reflectivity (TRDR). The columnar quantum rods (QRs) are grown by
Chapter 4
62
Molecular Beam Epitaxy using a “leveling and rebuilding” technique [110]. This growth
technique provides a route for the creation of height controlled columnar (In,Ga)As QRs.
First, a seed QD is grown by depositing 2 monolayers (ML) of InAs. Subsequently, 2 nm
GaAs and 1 ML InAs layers are deposited on top of the seed QD, followed by a 90 s growth
interrupt. This procedure was repeated 4 or 8 times, resulting in 4 or 8 GaAs/InAs layers on
top of the seed QD. This growth recipe produces columnar (In,Ga)As QRs which are both
uniform in composition and shape in the growth direction, and whose height is directly
determined by the number of stacked GaAs/InAs layers. The structural properties of the QRs
were investigated by cross-sectional scanning tunneling microscopy. The cross sectional STM
measurements were performed on (110) cleavage planes in ultrahigh vacuum in constant
current mode. Figures 4.2a and 4.2b show the cross-sectional STM images of the columnar
(In,Ga)As QRs with four or eight stacked GaAs/InAs layers overgrown by 5 nm In0.2Ga0.8As.
A schematic view of QR sample structure is presented in Fig. 4.2c.
The quantum rods were subsequently characterized by low-temperature
photoluminescence spectroscopy. The PL was excited by the 532 nm line of a frequency
doubled Nd:YAG laser with excitation power density of 256 W/cm2, dispersed by a single
monochromator, and detected by a cooled InGaAs array detector. The samples were cooled
down to 5 K in an optical flow cryostat. The columnar QRs show excellent PL with a width of
60 meV (FWHM), confirming their optical quality (Fig. 4.3a).
The excitation power dependent photoluminescence measurements show a clear 13
meV blue shift (Fig. 4.3b), which points towards a typical quantum wire type of behavior
[111,112]. Due to the elongated height in the growth direction, the level spacing within a QR
is expected to be much narrower than in a QD. As a consequence, the excited QR levels
which become populated at increased excitation density will tend to continuously shift the
photoluminescence spectrum towards higher energy due to bandfilling [111,112]. The
observation of a continuous blue shift is thus a clear indication that the columnar quantum
dots indeed behave as QRs.
Anomalous radiative lifetime
63
1.0 1.1 1.2 1.30
10000
20000
30000
Energy (eV)
PL
In
ten
sity (
arb
. u
nits)
4.9 W/cm2
49 W/cm2
98 W/cm2
245 W/cm2
490 W/cm2QRs, 5K
0 200 400
1.145
1.150
1.155
Excitation density (W/cm2)
PL
pea
k e
ner
gy (
eV
)
Blue shift
(a) (b)
1.0 1.1 1.2 1.30
10000
20000
30000
Energy (eV)
PL
In
ten
sity (
arb
. u
nits)
4.9 W/cm2
49 W/cm2
98 W/cm2
245 W/cm2
490 W/cm2QRs, 5K
0 200 400
1.145
1.150
1.155
Excitation density (W/cm2)
PL
pea
k e
ner
gy (
eV
)
Blue shift
1.0 1.1 1.2 1.30
10000
20000
30000
Energy (eV)
PL
In
ten
sity (
arb
. u
nits)
4.9 W/cm2
49 W/cm2
98 W/cm2
245 W/cm2
490 W/cm2QRs, 5K
0 200 400
1.145
1.150
1.155
Excitation density (W/cm2)
PL
pea
k e
ner
gy (
eV
)
Blue shift
(a) (b)
Fig.4.3: (a) Photoluminescence spectrum of 4 period InAs/GaAs QRs for different excitation
densities. (b) The PL peak energy with respect to excitation density is showing a blue shift of
the peak energy due to bandfilling.
Time resolved differential reflectivity (TRDR) measurements are subsequently
performed using picosecond pulses from a synchronously mode-locked Ti:sapphire laser as
the pump source. The pump laser has been tuned above the GaAs bandgap (1.548-1.674 eV).
The differential reflectivity is monitored by picosecond pulses from an Optical Parametric
Oscillator (OPO) which is synchronously pumped by a second mode-locked Ti:sapphire laser.
Both pulse trains are synchronized with a timing-jitter of < 2 ps using a Coherent synchrolock
system. The OPO pulses are tuned into resonance with the quantum rods (1.05-1.2 eV). The
reflected beam from the quantum rod sample is monitored by a balanced detector for
suppressing laser noise. In order to detect the differential reflectivity, the pump laser is
mechanically chopped (2.7 kHz) and the reflected probe beam is measured by a lock-in
amplifier. This detection technique allows to measure the differential reflectivity with a noise
floor at /R R∆ ~10-6
.
TRDR time-traces are subsequently recorded by monitoring the demodulated probe
signal as a function of the pump-probe delay time, which is mechanically varied by an optical
delay line. The TRDR time traces show a rising edge which is sensitive for the carrier capture
and relaxation time in the quantum rods, and a trailing edge which is the sum of the radiative
and non-radiative decay times of the QRs. This chapter entirely focuses on the trailing edge,
Chapter 4
64
which will be denoted as the TRDR lifetime which turns out to be “polariton-like” for reasons
which will become clear further on.
4.4 Results and discussion
The TRDR lifetimes of these QRs are presented in Fig. 4.4 and Fig. 4.5. At low pump
excitation density, the probe reflectivity at delay τ monitors the occupation of the QR ground
state at a delay τ . As a consequence, the TRDR lifetime is expected to be identical to the
exciton radiative lifetime. The exciton radiative lifetime is observed to be slowly decreasing
with the probe photon energy as shown in Fig. 4.4. The observed dependence of the
reflectivity lifetime on the QR transition energy is well understood and is governed by the
variation of the QR-size and by the subsequent variations of the wavefunction overlap
[98,99]. At low photon energy, the probe is sensitive to the largest QRs within the size
distribution in which the wavefunction overlap is also small leading to a large exciton
lifetime. At high probe photon energy, the small QDs within the size distribution are studied
in which the wavelength overlap is more tight, leading to a smaller exciton lifetime. The
wavelength dependence of the TRDR lifetime is similar to the wavelength dependence of the
PL-lifetime previously obtained in a time-resolved photoluminescence experiment by Bellesa
et al. [98]. Thus the TRDR decay times at low excitation density can be interpreted as the
uncoupled exciton lifetime. It should be emphasized that the observation of the well known
wavelength dependence of the exciton lifetime by the TRDR technique, in the case that the
excited QR density is very low, also proves that the TRDR technique provides reliable results.
Subsequently, the pump excitation density is increased, which leads to an increase of
the excited QR density and thus to an increased probability for mutual radiative coupling
between the excited QRs. The TRDR lifetime as a function of probe photon energy at higher
pump excitation density is presented in Fig. 4.5 and shows a resonant type of behavior in the
middle of the QR size distribution.
Anomalous radiative lifetime
65
1.10 1.151000
1500
2000
2500
Probe photon energy (eV)
QR
-TR
DR
lifetim
e (
ps)
Excitation density: 104 W/cm2
5 K
Fig. 4.4: The QR lifetime at 5 K for an excitation density of 104 W cm-2
as a function of the
probe photon energy. The lifetime shows a typical exciton lifetime behavior.
This very remarkable behaviour was first observed by Bogaart [91] in a QD sample. A
similar behaviour is observed in the QR sample at a pump excitation of 0.66 and 1.3 kW/cm2.
At these pump power densities, the TRDR lifetime develops an unexpected “resonance” with
a maximum lifetime of 3 ns. The resonance of TRDR lifetime roughly coincides with the
maximum of the QR size distribution, indicated by the maximum of the PL-peak. At the edges
of the QR size distribution, the TRDR lifetime shows the opposite behaviour and even
becomes smaller than the exciton lifetime measured at low excitation density. When
comparing the TRDR lifetime in the centre of the QR size distribution with the TRDR
lifetime at the edge of the QR size distribution a six-times enhancement at the centre of the
size distribution is observed. It should be noted that the TRDR lifetime spectra are slightly
shifted with respect to the PL spectrum which might provide an indication for a depolarisation
shift [105].
Chapter 4
66
1.10 1.15 1.200
1000
2000
3000
PL in
tensity
(arb
. units
)
Probe photon energy (eV)
QR
-TR
DR
lifetim
e (
ps)
0.1 kW/cm2
0.66 kW/cm2
1.3 kW/cm2
5 K
PL
Fig. 4.5: Pump excitation dependence of the TRDR lifetime in InAs/GaAs quantum rods,
showing the transition between the uncoupled exciton lifetime () at low excitation and the
anomalous polariton-like lifetime (,) at high pump excitation.
It should be noted that the observed probe photon energy dependence of the radiative
lifetime is clearly in contradiction with a carrier re-distribution between different quantum
rods, since it would result in a large radiative lifetimes at the low energy tail of the spectrum
and a decreasing lifetime towards the high-energy tail of the spectrum. A second possible
explanation for an increasing lifetime at increasing pump-excitation is due to state-filling of
the confined levels inside the QD. It has also been shown [113] that state-filling increases the
observed ground-state exciton lifetime due to refilling of the ground-state level by carriers
initially occupying the excited-state QD levels. This explanation is however not capable to
explain the probe photon energy dependence of the observed QR lifetime. A third possible
explanation is due to the bright and dark excitons within the QR. At higher excitation density,
the probability for double occupation of a single QD increases. When the QD is occupied with
a bi-exciton, the two excitons occupying the ground-state will both recombine as bright
excitons. On the other hand, when the QD is only occupied with a single electron-hole pair,
the resulting exciton can be either a bright (J=1) exciton or a dark (J=2) exciton. This
mechanism will however shorten the total lifetime at higher excitation density, which is
opposite to the observations in this thesis. Finally, the observed lifetime spectrum at increased
excitation density develops a kind of “subradiant” behaviour near the centre of the PL-peak,
Anomalous radiative lifetime
67
which is clearly in contradiction with the idea that a population inversion of the quantum rods
would result in stimulated emission and thus a shorter radiative lifetime.
The observed resonance of the exciton radiative lifetime at high excitation density,
which roughly coincides with the QR size distribution, seems to indicate that the exciton
radiative lifetime is determined by the density of excited QRs which are “resonant” with the
probe laser spectrum. The 2 ps probe laser pulses have an estimated 1 meV spectral width and
are resonant with approximately 2% of the QRs within the full size distribution. Thus in the
centre of the QR size distribution, the probe is resonant with a sub-ensemble of QRs with a
relatively high density ( )jN ω (small QR separation QDd , see Fig. 4.1), while in the wing of
the QR size distribution, the probe laser is resonant with a very low density sub-ensemble of
QRs (large QR separation QDd ). It is clear from Eq. (4.13) that for inverted QRs (w>0), a
small QR separation, QDd , corresponds to a larger reflectivity lifetime at the centre of the QD
size distribution, which is indeed observed experimentally as a larger TRDR lifetime. In the
tail of the QR size distribution (large QDd ), the reflectivity lifetime is predicted to be
determined by the decay time of an isolated QR. The decrease of the TRDR lifetime below
the exciton radiative lifetime as measured at the lowest excitation density is presently not yet
understood.
In order to understand the linewidth of the resonant polariton-like lifetime curve, the
inverse QD separation ( ) 1QDd
− in a sub-ensemble of resonant QDs is replaced by a sub-
ensemble density ( )jN ω . The average distance between the QDs within each sub-ensemble
depends on the location of these QDs within the overall size distribution, and is governed by
( ) ( )1j QD j
QD
N N Gd
ω ω= = , in which QDN is the area QD density and ( )jG ω is a
(Gaussian) line shape function for the QD ensemble. By inserting this in Eq. (4.13), the decay
rate for a coupled array of QDs with size distribution ( )N ω is obtained [91]:
20 02
0
3( ) ( ) ( )QDcoupled
inhh
wNw G
k
πω ω
εΓ = Γ − Γ − Γ (4.14)
Eq. (4.14) predicts that the width of the polariton lifetime spectrum is a factor 2
narrower than the QD size distribution ( )jN ω due to the quadratic dependence as shown by
Bogaart [91] for stacked QDs. It can be observed in Fig. 4.5 that the TRDR lifetime spectrum
Chapter 4
68
at 0.66 kW/cm2
is indeed narrower than the PL spectrum. But the data do not allow to
accuarately confirm the square root of two narrowing.
To further investigate the electromagnetic coupling phenomena, the TRDR lifetime is
also measured at higher temperature. At elevated temperature, the dephasing time quickly
increases [114], implying that homΓ becomes much larger than the correction due to the
electromagnetic coupling, ( )QDB d , in Eq. (4.13). From Appendix B, it can be expected that
at elevated temperature, the exciton lifetime picture is recovered again. In Fig. 4.6, it can be
observed that the usual exciton lifetime behavior is indeed recovered at elevated temperature.
This observation is directly in accordance with the straightforward notion that a TRDR
experiment is expected to yield the exciton radiative lifetime. The transition from the
polariton regime to the exciton regime is however not properly accounted for in the present
theory.
1.10 1.150
500
1000
QR
-TR
DR
life
tim
e (
ps)
Probe photon energy (eV)
158 K
Excitation density: 662 W/cm2
Fig. 4.6: Quantum rod TRDR lifetime at 158 K, showing again an exciton lifetime behavior.
The pump excitation was 662 W/cm2.
Finally, the polariton lifetime at very high excitation density in the saturation regime is
studied. In the usual carrier dynamics picture, one would expect that in the saturation regime,
following each carrier recombination event, the QD ground state is immediately refilled by
carriers which relax down from an excited level towards the ground state, or by carriers which
relax down from the wetting layer towards the QD ground-state. The usual carrier dynamics
Anomalous radiative lifetime
69
picture thus predicts an increasing “effective” lifetime as a function of excitation density. An
exactly opposite effect, a reduction of the TRDR lifetime at an increasing saturation level is
observed, as shown in Fig. 4.7.
1.05 1.10 1.15
500
1000
1500
2000
2500
3000 1.3 kW/cm2
2.8 kW/cm2
3.7 kW/cm2
Probe photon energy (eV)
QR
-TR
DR
life
tim
e (
ps)
Fig. 4.7: Resonant enhancement of the QR TRDR lifetime at high excitation density (1.3 (),
2.8 (♦) and 3.7 (*) kW/cm2
pump excitation density) in the saturation regime at 5 K.
In Fig. 4.7, the resonance of the TRDR lifetime near the centre of the QR size
distribution at 1.3 kW/cm2, which was already shown in Fig. 4.5,
is shown again. At
increasing saturation level, the resonant enhancement of the TRDR lifetime is however slowly
washed out. A possible explanation is the expected decrease of the dephasing time due to
carrier-carrier scattering and Auger scattering. Strong dephasing is again expected to decrease
the relative importance of the electromagnetic coupling term ( ) 0QDB d Γ as compared to
homΓ . It will be shown in Appendix B that this might be a reason for the observed saturation
behavior, although it should be stressed that the present theory is not including the saturation
effects yet. It should also be pointed out that the arrows in Fig. 4.7 seem to indicate a fine-
structure which might be connected to the polariton splitting observed by Bogaart [91].
4.5 Conclusions
In conclusion, a clear resonance enhancement of the QR lifetime in reflectivity is
observed near the centre of the quantum rod size distribution. The observed anomalous TRDR
Chapter 4
70
lifetime point towards an electromagnetic coupling between “resonant” QRs, leading to a
collective lifetime of the QR sub-ensemble, which is larger than the bare exciton lifetime. In
addition, the TRDR technique correctly recovers the well-known exciton lifetime behavior at
low excitation density and at elevated sample temperature. The reason for the decrease of the
TRDR lifetime below the exciton lifetime at low and high probe energies is not clearly
accounted for in the theory.
Appendix A: An expression for the phenomenological parameter QDω
As seen in Eq. (4.4), the modified polarizability of a QD under the influence of an EM
field can be written as:
( )
( )
0
3
30 hom
3
233 9
3
QD QD
QDh QD QD
QD QD
R w
wi i k R w
R w
i
ωα ω
ωω ω ε ω
ω
ω ω
=− + + Γ −
=− + Γ
(A.1)
such that 0 01
3 QDwω ω ω= − and hom 0wΓ = Γ − Γ as stated in Eq. (4.5) and Eq. (4.6) in
the Chapter. Consider for a moment that hom 0Γ = , then Eq. (A.1) can be re-written as:
( )
( )0
3
3239
QD QD
h QD QD
R w
i k R w
ωα ω
ω ω ε ω
=− −
(A.2)
For a two-level system, the polarizabilty can generally be written as:
( )
0 0
1
iα ω
ω ω− − Γ∼ (A.3)
The imaginary part of the pole of Eq. (A.2) provides the radiative lifetime of a QD.
Comparing Eq. (A.2) and Eq. (A.3) and taking 1w = , an expression for the
phenomenological parameter QDω can be directly obtained as:
( )
03
9
2QD
h QDk Rω
ε
Γ= (A.4)
Anomalous radiative lifetime
71
Finally, by substituting 0Γ from Eq. (4.7) into Eq. (A.4) the required expression for the
phenomenological parameter QDω in terms of the dipole matrix element 0µ is obtained and is
given as:
20
3
20
3
4
QDQD h
QD h
R
V
µω
ε
πµ
ε
=
=
(A.5)
where the QD volume is 34
3QD QDV Rπ
=
Appendix B: The detected TRDR signal
In the experiment, the pump laser excites electron-hole pairs within the GaAs barrier
which are subsequently captured into the QDs where they further relax down towards the QD
ground-state. During this relaxation process, the coherence with the pump laser will be fully
lost. Subsequently, ground-state excitons within the different QDs will recombine with a
exciton radiative lifetime 1τ ( 1τ is the population decay time). Here it is assumed that at a
delay time τ after the pump pulse, the QD ensemble can be treated as if one fraction is still
occupied while the other fraction has already recombined radiatively. The number of excited
QDs within the sub-ensemble of all QDs which are resonant with the probe laser thus reads:
1/2
1( )
( )exc
exc QD sub ensembleexc QD
N N ed
τ τττ
−− −
−≡ = (B.1)
in which excQD sub ensembleN − − is the number of excited QDs within the resonant sub-ensemble
only for a given pump excitation density and ( )exc QDd τ− is the average distance between
excited QDs within the sub-ensemble at a given pump density and at delay τ with respect to
the pump pulse.
Recalling Eq. (4.13),which is effectively a formula for the dephasing:
02
3
( )coupled
h exc QD
w
kd
π
ε −
ΓΓ = Γ − (B.2)
The amplitude of the reflected probe signal at a delay τ after the pump pulse can thus be
expressed as:
Chapter 4
72
( )02
3( ) ( )exp
( )QD QD
h exc QD
wr t r t
kd
πτ τ τ
ε −
Γ − = − Γ − − (B.3)
which determines the decay of the reflected signal in real time “t”. From Eqs. (2.24-2.28) it
can be seen that the reflected probe intensity is equal to the interference term between the QR
reflectivity and the surface reflectivity such that:
( ) ( ) ( )*refl surf QDI t r t r tτ τ τ− = − − (B.4)
The reflected probe intensity, at a pump-probe delay τ , is measured with a slow
detector which integrates the reflected probe intensity over real time, thus giving:
( )0*
2
3( ) ( )exp
( )surf QD
h exc QD
wS dt r r t
k dτ
πτ τ τ
ε
∞
−
Γ = − Γ − − ∫ (B.5)
In this formula, ( )exc QDd τ− is determined by the delay τ , the resonant sub-ensemble and the
pump excitation density. Now insert that 1/( ) (0)QD QDr r e τ ττ −= and the integral is
performed using Eq. (B.1), to obtain:
( ) 1
1
* /
0 /2
(0)/( )
31
surf QD
excQD sub ensemble
h
r r eS
wNe
k
τ τ
τ τ
τπ
ε
−
− − −
Γ= Γ − Γ
(B.6)
The functional expression for the detector signal now reads:
1
1
/
/( )
1
AeS
Ce
τ τ
τ ττ
−
−=−
(B.7)
in which the constants A and C are given by:
*
02
(0)/
3
surf QD
excQD sub ensemble
h
A r r
wNC
k
π
ε
− −
= Γ
Γ=
Γ
(B.8)
These expressions clearly show that in the case 0Γ >> Γ , the constant C , which contains
the radiative coupling between the QDs becomes small and the TRDR signal decays with the
exciton radiative lifetime 1τ only.
5
Photoluminescence from low
temperature grown
InAs/GaAs quantum dots
Abstract
A set of self-assembled InAs/GaAs quantum dots (QDs) formed by molecular beam
epitaxy at low temperature (LT, 250 °C) and post-growth annealing is investigated. A QD
photoluminescence (PL) peak around 1.01 eV was observed. The PL efficiency quickly
quenches between 6 and 40 K due to the tunneling of carriers out of the QD into traps within
the GaAs barrier. The PL-efficiency increases by a factor of 50-300 when exciting below the
GaAs bandgap, directly into the InAs QD layer at 5 K. This points towards good optical
quality QDs, which are embedded in a LT-GaAs barrier with a high trapping efficiency.
Chapter 5
74
5.1 Introduction
Ultrafast all-optical switching requires materials with a high bandwidth and thus a fast
temporal response of the nonlinear absorption, a high absorption modulation and a low
absorption loss when the material is saturated [33,115]. Stransky-Krastanow (SK) quantum
dots (QDs) have enhanced optical non-linearity due to their delta-function like density of
states which results in a sharp absorption line with high peak absorption. In addition, the
presence of a single electron-hole pair within a QD is able to bleach the absorption line under
resonant excitation, while two electron hole pairs generate optical gain, indicating a large
optical nonlinearity, which occurs already at very low pump power. A switching energy as
low as 6 fJ in InAs/InP QDs embedded into a Mach-Zehnder switch [41] has been recently
observed. Nakamura et al. has demonstrated QD absorption saturation at a pulse energy
density as low as 13 fJ/µm2, under resonant excitation [8].
The time response of the optical nonlinearity is determined by the combination of the
radiative and non-radiative decay and by carrier escape out of the QD. It has already been
demonstrated that low temperature (LT) grown bulk GaAs as well as InGaAs/InAlAs
quantum wells show ultrafast carrier recombination [33,34,115]. LT growth leads to the
presence of excess Arsenic, which acts as a trapping center. The ultrafast response is thus
attributed due to trapping of carriers into Arsenic anti-site defects [33,115]. In this Chapter, a
study of LT InAs/GaAs QDs grown using Molecular Beam Epitaxy (MBE) is presented as an
attempt to combine the large QD-nonlinearity with an ultrafast response time.
5.2 Sample and experimental details
A set of InAs/GaAs QDs formed by LT growth and post-growth annealing [116,117]
is investigated in this Chapter. All the samples studied here were grown on a (100) GaAs
substrate. The sample structure has a 500 nm thick GaAs buffer layer grown at 580 °C. The
samples were subsequently cooled down to 250 °C for the growth of a 500 nm LT-GaAs
bottom layer, followed by the deposition of 2 monolayers of InAs which forms the QDs. The
samples R207, R200, R198, R191, R181 and R152 were all grown at 250 °C. The samples
further received different annealing treatments which are detailed in Table 5·1. It has been
shown by Zhan et al. [116,117] that well-developed InAs dots are formed in these samples
after post-growth annealing above 450 °C as observed by atomic force microscopy. Finally all
samples were capped with a 200 nm LT-GaAs capping layer. In R200 and R207, the
structural quality of the LT-GaAs matrix grown on top of the quantum dots was improved by
Photoluminescence from LT QD
75
Table 5.1: Growth details [116,117] of different LT-QD samples. All samples have a 500 nm
thick GaAs buffer layer grown at 580 °C, a lower LT-GaAs barrier layer of 500 nm and a
capping layer of 200 nm LT-GaAs, both grown at 250 °C.
Temperature (°C), Time (minutes*)
Sample QDs + Interlayer
First anneal Second anneal
R152 2 ML InAs (250 °C)
No No
R181 2 ML InAs (250 °C)
480 °C, 15 min No
R191 2 ML InAs (250 °C)
480 °C, 10 min 480 °C, 10 min
R198 2 ML InAs (250 °C)
480 °C, 10 min 600 °C, 10 min
R200 2 ML InAs (250 °C)+
3 nm GaAs (480 °C)
No No
R207 2 ML InAs (250 °C)+
3 nm GaAs (480 °C)
580 °C, 10 min No
R228 2 ML InAs (480 °C)
No No
*Ramping time is not included.
Buffer
SI-substrate
LT-GaAs
matrix
QDs
GaAs
matrix
Buffer
SI-substrate
LT-GaAs
matrix
QDs
GaAs
matrix
Fig. 5.1: Schematic representation of the QD sample structure.
Chapter 5
76
inserting a 3 nm GaAs interlayer deposited at 480 °C directly on top of the LT-QDs
[116,117]. In addition, sample R228 which consists of high temperature QDs grown at 480 °C
in an identical LT GaAs matrix as in the other samples is also investigated. The schematic
representation of the sample structure is given in Fig. 5.1.
Photoluminescence (PL) spectra were taken using 250 mW excitation power of a
Ti:Sapphire laser operating at 770 nm, providing a high excitation density of 10 kW/cm2. The
PL was collected and further detected by a monochromator and a cooled InGaAs detector
array. The PL spectra of all seven samples at 5 K are shown in Fig. 5.2.
5.3 Results and discussion
It is observed that all the samples have a peak around 1.01 eV, which is slightly
shifted for each sample, indicating that the peak is from the QDs and not from a deep center in
the LT-GaAs. The spectra are also broadened and show a reproducible fine structure
commonly observed in micro-PL, where emission from individual QDs can be observed. The
fine structure probably reflects the QD size distribution showing statistical fluctuations,
indicating that the density of radiative dots is low. Another possible reason for the fine
structure is the Coulomb effect between electron-hole pairs within the QD and a nearby defect
state [118-120]. The PL-peaks are superimposed on a slowly rising background extending
down to 0.78 eV, which is the edge of the detector responsivity. In contradiction with the QD
photoluminescence, the rising background in the spectra is not quenched at elevated
temperature, as shown in Fig. 5.3. The peak emission energy of the background could not be
measured using the experimental setup used, making it difficult to assign the defect state
accurately to any particular arsenic anti-site defect.
Next, the PL efficiency was investigated as a function of the measurement
temperature. It is found that all the samples exhibit a very strong temperature dependence of
the PL efficiency from the QDs around 1 eV. The PL from the QDs is completely quenched
above a temperature of 40 K, which is also observed for the high temperature grown QDs
(sample R228). The background PL is not quenched and even slightly increases with
temperature. Fig. 5.3 shows the temperature dependence of sample R198. The other samples
show similar temperature dependence.
Photoluminescence from LT QD
77
0.8 1.0 1.20
R228
R207R198
X0.2
R200
R191
R181 R152
PL
in
ten
sity (
arb
.un
its)
Photon energy (eV)
Fig. 5.2: Photoluminescence from LT grown InAs/GaAs QDs at a temperature of 5 K and a
high 10 kW/cm2 excitation density.
0.8 1.0 1.2
0
39K
32K
24K
20K
15K
10K6K
PL
in
ten
sity
(arb
.un
its)
Photon energy (eV)
Fig. 5.3: Temperature dependence of the PL spectrum for sample R198 showing rapid
quenching of the PL from the LT-QDs with increasing temperature.
Chapter 5
78
Finally, the behavior of PL efficiency with respect to the pump excitation energy was
studied. The samples were excited with an excitation energy range extending from 1.4 eV to
1.6 eV, ie, both below the GaAs bandgap directly into the InAs QD layer (< 1.518 eV) and
also above the GaAs bandgap in the GaAs barrier (> 1.518 eV). The resulting PL efficiency
was recorded for all the samples. The measurements were carried out at liquid helium
temperature. Fig. 5.4 shows the PL peak intensity as a function of excitation energy for all the
seven samples. A huge increase in PL efficiency is observed when excited below the GaAs
bandgap directly into the InAs QD layer which is exactly opposite as observed for
conventional QDs. The increase in efficiency varies between a factor of 45 for R198 and 280
for R152. The highest step is observed for R152, which is not annealed and thus has the
highest concentration of trapping centers leading to the highest trapping probability for
excitation in the GaAs barrier.
1.4 1.5 1.6
P
L p
eak in
tensity
(arb
.un
its)
Excitation energy (eV)
R 152
R 181 R 191
R 198 R 200
R 207 R 228
Excitation in QD only Excitation in GaAs barrier
Fig. 5.4: Excitation energy dependence on PL efficiency showing an unexpected increase of
the QD PL-efficiency when exciting below the GaAs bandgap directly into the QD layer.
It has already been shown that during LT growth, excess As is incorporated as As
antisite point defects (AsGa) [33,34,121], which are fast trapping centers for the carriers. These
are mid bandgap point defects which can act as double donors [33,34]. The concentration of
the point defects can be increased by further decreasing the growth temperature [79]. It was
estimated by Haiml et al. [33] that around 10% of all AsGa centers are ionized AsGa+
states due
to Ga-vacancies which act as acceptor states. The remaining AsGa are neutral. The electrons
Photoluminescence from LT QD
79
are trapped by the ionized AsGa+
in the GaAs barrier, which leads to the well known fast
response in LT-GaAs. Surprisingly, it is not observed that these trapping centers are also
present inside the QDs since the PL efficiency at 4 K is quite reasonable for excitation below
the GaAs bandgap. The capture of an electron into the defects in the LT-GaAs can occur
along two routes [85]. First is the direct capture of electrons which are optically excited in the
LT-GaAs barrier and which are directly trapped into the trapping centers before they are
captured into a QD. A second channel is electron relaxation from the barrier into the QD
level, followed by a multiphonon assisted tunneling out of the QD into the trapping center
located in its vicinity. Sercel [85] has theoretically shown that the interaction between the
electronic wave functions of the QD and the deep trap is likely to provide a tunneling
transition.
The rapid fall and the subsequent complete quenching of the PL efficiency with rising
temperature can be explained by the tunneling induced trapping of carriers out of the QD into
the defects in the LT-GaAs. As temperature increases, the carriers acquire enough energy to
tunnel across and get trapped, thus quenching the PL efficiency with rising temperature. The
excitation wavelength dependence confirms the observation made in the Thesis that the PL
quenching centers are located only in the GaAs barrier and not inside the QDs. This is in
agreement with Deep Level Transient Spectroscopy (DLTS) studies reporting point defects in
the near neighbourhood [118-120] of the QDs within the GaAs barrier, but not within the
InAs QDs themselves. In conventional high temperature grown QDs, carriers created in the
barrier region above the GaAs bandgap diffuse towards the QDs in which they relax down
towards the QD ground state. For high temperature grown QDs, it is well known that the
carrier density excited in the GaAs barrier is much higher than the carrier density for
excitation below the GaAs bandgap in the QD layer. Thus, excitation into the QD layer is
expected to yield a low PL efficiency since the absorption probability for the excitation beam
is very small. Contrary to this observation in normal high temperature grown dots, the PL
efficiency is found to be much higher when excited below the GaAs bandgap into the QD
layer. This is true even for the high temperature QDs embedded in a low temperature grown
GaAs barrier. It can be thus concluded that in a LT-GaAs barrier layer, optically excited
carriers are efficiently trapped into defects in the barrier before being captured into the QDs.
When the carriers are generated in the QD layer, diffusion through the high trapping
efficiency LT-GaAs barrier is circumvented, leading to a much higher PL efficiency. Since
the PL quenching centers are not present in the wetting layer and QDs, trapping is now only
possible when carriers tunnel out of the QD into a trap, which is clearly a less probable
trapping mechanism at 4 K. As a result, a higher PL efficiency is observed when the carriers
Chapter 5
80
are excited into the QD layer. If the optical absorption in the QD layer itself is considered and
the much larger absorption in the LT-GaAs layer is neglected for the moment, the PL
efficiency is still considerably higher for excitation in the QD layer below the GaAs bandgap
than for excitation inside the QD layer above GaAs bandgap. When the excitation energy is
tuned above the GaAs bandgap, optically generated carriers in above-the-barrier unconfined
QD levels diffuse towards the LT-GaAs and are subsequently trapped in the LT-GaAs. It can
thus be concluded that, even when the carriers are initially within the unconfined levels of QD
layer, diffusion followed by trapping is more efficient than relaxation within the InAs QD
layer towards the confined QD levels. Sercel [85] had proposed that electrons can not only
tunnel out of the QD towards a trap but can also tunnel back to the dot from a trap. So an
equilibrium density of electrons will be present inside the dots leading to the observed PL at 5
K. When the temperature increases, the probability for tunneling out of the QD into a trap
rapidly increases, leading to the decrease in the PL efficiency. This also explains the high
pump excitation density needed to observe the PL spectra.
5.4 Conclusions
In conclusion, it is observed that LT growth gives rise to efficient trapping centers due
to excess Arsenic in the LT-GaAs barrier but not inside the LT-grown QDs. This leads to a
reduction in the number of carriers relaxing into the QDs, resulting in a reduction of the QD-
PL efficiency when excited in the barrier. The strong increase of the PL efficiency when
excited directly into the QDs shows that the dots are of good optical quality without the
presence of PL quenching traps inside the dots. LT grown InAs/GaAs QDs thus constitute of
good optical quality radiative QDs, embedded in an optically “dead” GaAs barrier material
which traps away the carriers before they diffuse into the QDs.
6
Time Resolved Differential
Reflectivity from low
temperature grown
quantum dots
Abstract
Low temperature (LT) grown quantum dots (QDs) are investigated for combining the
enhanced optical nonlinearities in a QD with the ultrafast response expected in LT grown
GaAs. The second objective of this Chapter is to gain insight into the trapping dynamics of
confined carriers within a QD by AsGa anti-site defects in the GaAs barrier around the QDs.
The trapping dynamics are studied using the Time Resolved Differential Reflectivity (TRDR)
technique. The photoluminescence from the LT-QDs indicates a QD peak around 1.035 eV.
The TRDR measurements show an initial fast decay (80 ps) followed by a slow decay of
about 800 ps, which is much slower than the expected ultrafast response in LT-grown
material. The PL efficiency shows a strong temperature dependence in the temperature region
below 39 K, which is not observed in the TRDR signal. The slow TRDR response is
attributed to the fact that although electrons are quickly trapped in AsGa anti-site defect within
the GaAs barrier for T > 40 K, the TRDR signal mainly monitors the hole dynamics which is
taking place at a much slower rate.
Chapter 6
82
6.1 Introduction
Stransky-Krastanow Quantum Dots (QDs) have enhanced optical non-linearity
[8,9,41] due to their delta-function like density of states which results in a sharp absorption
line with a high peak absorption. Under resonant excitation, the presence of a single electron-
hole pair within a QD is able to bleach the absorption line, while two electron-hole pairs
generate optical gain, indicating a large optical nonlinearity, which occurs already at a very
low pump power. The time response of the optical nonlinearity is determined by the
combination of the radiative and nonradiative decay times and the carrier escape out of the
QD. In low-temperature (LT) grown QDs, an ultrafast response is expected due to trapping of
carriers into Arsenic anti-site defects. It has been shown by several groups that LT grown
GaAs features an ultrafast carrier recombination time [33,34]. Low-temperature growth has
demonstrated that the response time in III-V quantum wells can be reduced to < 1 ps [38,39].
This chapter presents a study of LT InAs/GaAs QDs grown by Molecular Beam Epitaxy
(MBE) using the Time Resolved Differential Reflectivity (TRDR) technique. As was seen
from the results presented in Chapter 5, the LT InAs/GaAs QDs do not contain Arsenic
antisite defects within the QDs themselves, but the strong decrease of the PL intensity when
increasing the temperature above 39 K suggests efficient carrier tunneling towards antisite
defects in the GaAs barrier in the vicinity of the QDs. In this chapter, the carrier
recombination from these LT-QDs is investigated by TRDR.
6.2 Sample and experimental details
The sample investigated in this Chapter (sample R207 presented in Chapter 5) consists
of LT-grown (250 °C) InAs QDs on top of a 500 nm LT-grown (250 °C) GaAs lower barrier
[116]. The QDs have been annealed at 480 °C directly after QD growth. The QDs are
subsequently capped with a high temperature grown (480 °C) 4 nm GaAs layer before
growing the 200 nm LT-GaAs upper cladding. Finally, the sample is given a post growth
anneal at 580 °C. The sample was first characterized by photoluminescence measurements
which were already presented in Chapter 5. The details of the PL measurements are also given
by Sreenivasan et al. [84]. The PL spectrum is broad with a QD photoluminescence peak
around 1.035 eV. To explain the carrier dynamics, two-color pump-probe TRDR
measurements are performed. The sample is excited using a mechanically chopped (~ 3 kHz)
pump beam from a mode-locked Ti:Sapphire laser operating at 1.58 eV. The excitation energy
is tuned to be well above the GaAs barrier band gap. The capture and subsequent decay of the
carriers in the dots are probed using the output of the optical parametric oscillator (OPO)
TRDR from LT QD
83
pumped by a second femtosecond Ti:Sapphire laser. The pump and probe pulses are
synchronized in time using a synchrolock system with a timing jitter below 2 ps. The set up is
similar to the one used for the measurements explained in Chapter 4, where two separate laser
sources are used and synchronized externally. The probe laser is tuned in resonance with the
QD energy levels. A time delay is introduced between the two beams by introducing a
movable optical delay in the path of the pump beam. Both the beams are focused on the
sample with pump beam diameter of 50 mµ and probe diameter of 30 mµ . The reflected
signal is detected using a balanced detector. The measurements are carried out as a function of
temperature and also by varying the probe energy. In both the cases, the pump photon energy
is kept constant.
6.3 Results and discussion
Fig. 6.1 shows a typical TRDR signal from the LT-QD sample at 5 K (sample R207)
with the probe laser tuned at 1.06 eV. The time response of the differential reflectivity is fitted
with a single exponential rise-time and a bi-exponential decay since the decay dynamics
clearly showed a multi-exponential nature. The fitting is done using the equation given below:
( )( ) ( )1 2
1 20
decay decay riset t tR
t Ae Ae AeR
τ τ τ− − −∆+ − (6.1)
with the requirement that the amplitudes of the different contributions satisfy the condition,
1 2A A A+ = − , in which riset and decayt are the rise time and the decay time of the signal
respectively.
The fit yields a rise-time of ~12 ps and a decay with an initial fast decay of ~80 ps
followed by a longer decay of 800 ps. The other LT-QD samples show similar long tails of
the TRDR life times. Since most of the photo-generated electrons are expected to be trapped
within the LT-GaAs barrier, only a small fraction of the electrons are expected to be captured
into the QDs. Referring back to the results presented in Chapter 3, this means that only those
electrons which are initially excited within the capture volume surrounding a quantum dot,
have a probability of being captured into the QDs before being trapped away. The inset of
Fig. 6.1 shows that the peak reflectivity approaches a saturation limit around an excitation
power of 2.7 kW/cm2. The observed high saturation excitation power is also a consequence of
the fact that most electrons excited within the GaAs barrier will be trapped away before they
reach the nearest QD. The saturation excitation power is thus expected to be limited by the
Chapter 6
84
hole occupation of the QDs only. All subsequent measurements are done in the linear pump
power regime to ensure that only the QD ground state is occupied.
0 500 1000 1500 2000 25001.5
2.0
2.5
3.0
0 1000 2000 3000 4000 5000 6000
1
Excitation energy density (W/cm2)
Pe
ak ∆
R/R
0 (
arb
. un
its)
∆∆ ∆∆
R/R
0 (
arb
. u
nit
s)
Pump-probe delay (ps)
Excitation density: 1 kW/cm2
Fig. 6.1: The TRDR signal of low-temperature grown quantum dots (LT-QDs) at 5 K. The
pump and probe energies are tuned to 1.57 eV and 1.06 eV respectively. The inset shows the
excitation density dependence of the peak reflectivity. The arrow denotes the intensity used for
further measurements.
Since the PL-efficiency from this sample shows a very strong dependence on
temperature between 5 K and 39 K (inset of Fig. 6.2), which suggests tunneling of electrons
out of the LT-QDs followed by trapping in anti-site defects [6], the TRDR lifetime was also
studied as a function of temperature. Based on the observations from the PL measurements,
the TRDR time traces were also expected to be strongly dependent on temperature and are
therefore expected to show a faster decay at increasing temperature. In the TRDR
measurements, the probe energy is tuned to 1.068 eV with a constant intensity of 21 W/cm2.
Fig. 6.2 shows the TRDR at four different temperatures from 5 K to room temperature. The
temperature dependence of the TRDR time traces seems, at first sight, to be in contradiction
with the observed strong dependence of the PL signal with temperature, since both the initial
fast (~80 ps) decay of the TRDR signal as well as the slower second decay of ~800 ps is
found to be completely independent of the sample temperature.
TRDR from LT QD
85
0 500 1000 1500 2000 2500
3
8 K
0.8 1.0 1.20
30000
Excitation energy = 1.609 eV
25K
Sample: R207
30K
20K
15K
10K
5K
PL
In
ten
sit
y (
arb
.un
its
)
Photon energy (eV)
∆∆ ∆∆R
/R0 s
ign
al
(arb
. u
nit
s)
Pump probe delay (ps)
4
6
15 K
2
48 K
0
2
4
290 K
Fig. 6.2: Decay of the TRDR signal at different temperature. The inset shows the PL
temperature dependence of the same sample.
The TRDR signal is expected to be sensitive to the dynamics of both the electrons and
the holes by the factor e hN N+ , in which eN and hN are the carrier occupation factors for
the electron and hole levels in the QD. The PL spectrum is the result of the radiative
recombination of electrons and holes (excitons), and is thus proportional to the product
e hN N× . It is well known that the probability [81] for electron trapping into the AsGa+ center
is much higher than the probability for hole trapping. It can thus be interpreted that the strong
temperature dependence of the PL intensity between 4 K and 39 K is due to tunneling of
electrons out of the QD [85] followed by subsequent trapping of electrons into the AsGa+
center. Since the initial fast decay of the TRDR signal is also temperature independent, the
initial fast decay can not be interpreted as a remnant of the fast electron trapping.
In LT-grown QDs, it is expected that the majority of the electrons which are photo-
excited in the LT-GaAs barrier are already trapped into the AsGa+ anti-site defects before they
reach the QDs. The photo-excited holes in the LT-GaAs barrier have a much smaller trapping
probability into the neutral AsGa0 anti-site defects and will thus be able to diffuse towards the
LT-QDs and subsequently be captured within the QDs. Consequently, the average hole
occupation of the LT-QDs is expected to be much larger than the average electron occupation
in the QDs. In other words, the hole occupation is expected to be of the order of unity
Chapter 6
86
( )1hN ≈ or above, while the average electron occupation is expected to be far below unity
( )1eN . For this reason, the TRDR measurements are only sensitive to the “majority” hole
dynamics within the LT-QDs and TRDR does not observe the dynamics of the very low
electron concentration within the LT-QDs. The observed TRDR risetime is thus expected to
be mainly due to the diffusion and capture of holes into the QDs. The decay of the TRDR
signal is thus sensitive to the hole dynamics which is expected to be determined by the
tunneling of holes out of the LT-QD, followed by trapping of the hole into a neutral AsGa0
anti-site defect. Alternatively, this process can be described by the tunneling [85] of initially
trapped electrons in AsGa+ back into the LT-QDs, followed by carrier recombination within
the LT-QDs. The latter process is not necessarily a two-step process, but can also be described
as a one-step process in which a hole confined within the LT-QD recombines with an electron
trapped at an anti-site defect in close vicinity to the LT-QD. Although these three descriptions
are phrased quite differently, the net effect is the same in each of the three descriptions.
0.8 1.0 1.20
0.8 1.0 1.2
-2
0
2 PL
Probe energy (eV)
PL
in
ten
sit
y (
arb
.un
its)
PL energy (eV)
79 meV
TRDR
Pea
k ∆∆ ∆∆
R/R
0 (
arb
.un
its
)
1.068 eV
1.11 eV
Fig. 6.3: Peak reflectivity spectrum (5 K) compared to PL spectrum (5 K).
The magnitude of the TRDR spectrum at 5 K for sample R 207, with the pump energy
fixed at 1.58 eV is shown in Fig. 6.3. By varying the probe energy, a TRDR time-trace is
obtained for each probe photon energy. The peak reflectivity of each TRDR time trace is
plotted versus probe wavelength in Fig. 6.3. The excitation power density is kept constant at a
TRDR from LT QD
87
value of 1 kW/cm2 and the probe power density is also kept steady at a very low value of 21
W/cm2. The TRDR signal is obtained only in the probe energy range between 1.03 and 1.13
eV, since further tuning to lower energy was restricted by the limit of the KTP crystal of the
OPO. The main peak of the TRDR spectrum is red shifted in energy with respect to the PL
spectrum by an amount of 79 meV, while the zero of the observed TRDR spectrum is shifted
by 121 meV from the PL peak. It should be noted that the PL spectrum also exhibits a weak
satellite peak around 1.05 eV which becomes more clear when the background PL remaining
at high temperature is subtracted. After subtracting the background PL an asymmetry of the
PL peak towards high energy can be clearly observed, which coincides with the observed
peak in the magnitude of the TRDR traces.
As discussed earlier in the Chapter, QDs are most probably occupied by photo-excited
holes ( )1hN > , while the electron occupation is very small ( )1eN , after the photo-
excitation of LT-QD sample. In this case, the TRDR measurements are mainly sensitive to the
hole occupation of the QDs, while PL is mainly sensitive to the electron occupation. The
TRDR measurements thus probes the hole occupation within the excited QD state, while PL
mainly probes the ground-state electron-hole recombination. Due to the high occupation
probability of holes in the case of LT-QDs, the excited states of the QDs will also be occupied
by the holes. In this picture, the peak reflectivity spectrum shown in Fig. 6.3 reflects the hole
occupation in the excited QD level. The magnitude of the TRDR signal which is shown in
Fig. 6.3 is proportional to the modulation of the hole occupation within the QD due to the
pump laser. The large magnitude of the peak reflectivity due to the excited QD level suggests
that the hole occupation within the excited QD level is more strongly modulated by the pump
laser than the hole occupation within the ground-state level. This is to be expected since it is
very well possible that the ground-state QD level will remain populated with holes for time
delays > 13 ns, i.e. the pulse repetition rate, while the holes within the excited QD state
recombine/trap with the AsGa0 anti-site defects in the GaAs barrier at a 800 ps time scale. This
makes it difficult to see the ground-state hole dynamics in TRDR which may very well
explain the red shift observed for the reflectivity spectrum with respect to the PL spectrum.
There can be a second, less probable explanation, which treats the red shift between
the reflectivity spectrum and the PL spectrum by assuming that the TRDR peak reflectivity
monitors the ground-state density of states of the QDs. In that case, the red shift of the PL-
peak would indicate that the main PL peak is not the ground-state exciton transition, but a QD
transition modified by acceptor levels, most probably due to VGa. A similar but smaller shift
between the PL spectrum and the TRDR spectrum has also been observed by Bogaart et al.
Chapter 6
88
[122] on a QD sample which was probably of lower quality. This comparison between PL and
TRDR would imply that the PL spectrum probes defect related transitions below the QD
ground state. This explanation is however not very probable since it is already shown in
Chapter 5 that the LT-QDs do not contain any anti-site defects within the QDs itself.
Consequently, it is not very probable that the QDs would contain many VGa acceptor levels.
As seen in Eq. (2.32), the reflectivity response function is a sum of two terms:
( )
( ) ( ) ( )tot
LR L
ωω ω ω
∂ ∆ = ∆Γ Γ + ∂Γ
(6.2)
If the QDs are taken to be uncoupled and abbreviate 0ω ω ω− = ∆ , then from Eq. 2.28 the
Lorentzian line shape function ( )L ω can be re-written as:
( )2 2
cos sin( ) ( )
k k
sL Arφ ω φ
ω ωω
Γ −∆ = − ∆ + Γ
(6.3)
Substituting Eq. (6.3) into Eq.(6.2), the differential reflectivity can be written as:
( ) ( )( )( )( )
2 2 2
22 2
2 cos sin( ) 2 ( )
k ktot sR Ar
ω φ ω ω φω ω
ω
Γ ∆ −∆ ∆ − Γ ∆ = − ∆Γ ∆ + Γ
(6.4)
Eq. (6.4) shows that the TRDR amplitude is even in ω∆ when twice the capping layer
thickness is equal to an integer number of wavelength, ie. The QD-reflectivity and the surface
reflectivity interfere constructively. The TRDR amplitude is expected to become “dispersion-
like” (odd in ω∆ ) shape when the interference is destructive. The experimentally observed
“dispersion-like” shape of the TRDR amplitude spectrum which crosses zero near 1.11 eV
indicates that the sin kφ term is the dominant one. The sample presented in the Thesis has a
capping layer thickness of 204 nm implying that 2.44kφ π= and thus
cos 0.19, sin 0.98k kφ φ= = , which explains the observed dispersive “odd in ω∆ ”
signature.
6.4 Conclusions
In conclusion, the PL technique probes the dynamics of the very small electron
occupation within the LT-QDs, whereas the TRDR technique probe the much larger hole
occupation in the LT-QDs. In the PL studies reported in Chapter 5, a strong decrease of the
PL-efficiency of LT-QDs between 4 K and 39 K is observed, which is due to tunneling of
TRDR from LT QD
89
electrons out of the QD into AsGa+
antisite defects in the GaAs barrier. Using the TRDR
technique, a long TRDR lifetime which is independent of the sample temperature is observed.
The long TRDR lifetime is attributed to the hole dynamics which is determined by the
trapping/recombination of holes in the LT-QDs with the neutral AsGa0 antisite defect in close
vicinity to the LT-QD, within the LT-barrier. This trapping/recombination process occurs at
an 800 ps timescale and is measured to be temperature independent. We finally remark that
the TRDR lifetime, which is sensitive to both the electron and hole dynamics within the QDs,
is expected to be most relevant to device applications based on ultrafast switching in LT-QDs.
References 91
References
[1] V.M. Goldschmidt, "Crystal structure and chemical constitution", Trans. Faraday
Society, 25, 253-283, 1929.
[2] Zh. I. Alferov, V.M. Andreev, V.I. Korol'kov, E.L. Portnoi, and D.N. Tret'yakov,
"Injection properties of n-AlxGa1-xAs-p-GaAs heterojunctions", Fizika i Tekhnika
Poluprovodnikov, 2 (7), 1016-1017, 1968.
[3] Zh.I. Alferov, V.M. Andreev, V.I. Korol'kov, E.L. Portnoi, and D.N. Tret'yakov,
"Coherent radiation of epitaxial heterojunction structures in the AlAs-GaAs system",
Fizika i Tekhnika Poluprovodnikov, 2 (10), 1545-1547, 1968.
[4] M. Grundmann, The physics of Semiconductors - An introduction including devices
and nanophysics, Springer-Verlag, 2006.
[5] L. Esaki and R. Tsu, "Superlattice and negative differential conductivity in
semiconductors", IBM J. Res. Dev., 14 (1), 61-65, 1970.
[6] L. Esaki, L.L. Chang, R. Tsu, A one-dimensional `superlattice' in semiconductors,
12th international conference on low temperatures physics., Sci. Council, Japan,
Kyoto, Japan, 1970.
[7] R. Dingle, W. Wiegmann, and C.H. Henry, "Quantum states of confined carriers in
very thin AlxGa1-xAs-GaAs-AlxGa1-xAs heterostructures", Phys. Rev. Lett., 33 (14),
827-830, 1974.
[8] H. Nakamura, S. Nishikawa, S. Kohmoto, K. Kanamoto, and K. Asakawa, "Optical
nonlinear properties of InAs quantum dots by means of transient absorption
measurements", J. Appl. Phys., 94 (2), 1184-1189, 2003.
[9] H. Nakamura, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Ishikawa, and K.
Asakawa, "Nonlinear optical phase shift in InAs quantum dots measured by a unique
two-color pump/probe ellipsometric polarization analysis", J. Appl. Phys., 96 (3),
1425-1434, 2004.
[10] P.M. Petroff, A.C. Gossard, R.A. Logan, and W. Wiegmann, "Toward quantum well
wires: fabrication and optical properties", Appl. Phys. Lett, 41 (7), 635-638, 1982.
[11] M.A. Reed, R.T. Bate, K. Bradshaw, W.M. Duncan, W.R. Frensley, J.W. Lee, and
H.D. Shih, "Spatial quantization in GaAs-AlGaAs multiple dots", J. Vac. Sci. Technol.
B, 4 (1), 358-360, 1986.
[12] M. Sugawara, Self-Assembled InGaAs/GaAs Quantum Dots, Academic Press, 1999.
[13] I.N. Stranski and L. Krastanow, "Zur Theorie der orientierten Ausscheidung von
Ionenkristallen aufeinander", Ber. Akad. Wiss. Wien, Abt. IIb, 146, 797, 1938.
References
92
[14] M. Tabuchi, S. Noda, A. Sasaki, Mesoscopic structure in lattice-mismatched
heteroepitaxial interface layers, In: Namba, S., Hamaguchi, C., and Ando, T. (Eds.),
Science and Technology of Mesoscopic Structures, Springer-Verlag, Tokyo, Japan,
1992.
[15] Y. Masumoto and T. Takagahara, Semiconductor Quantum Dots - Physics,
Spectroscopy and Applications, Springer-Verlag, 2002.
[16] R. Leon, S. Fafard, D. Leonard, J.L. Merz, and P.M. Petroff, "Visible luminescence
from semiconductor quantum dots in large ensembles", Appl. Phys. Lett, 67 (4), 521-
523, 1995.
[17] V.M. Ustinov, A.E. Zhukov, A.Y. Egorov, A.R. Kovsh, S.V. Zaitsev, N.Y. Gordeev,
V.I. Kopchatov, N.N. Ledentsov, A.F. Tsatsulnikov, B.V. Volovik, P.S. Kopev, Z.I.
Alferov, S.S. Ruvimov, W.Z. Liliental, and D. Bimberg, "Low threshold quantum dot
injection laser emitting at 1.9 µm", Electron. Lett, 34 (7), 670-672, 1998.
[18] D. Guimard, S. Tsukamoto, M. Nishioka, and Y. Arakawa, "1.55 µm emission from
InAs/GaAs quantum dots grown by metal organic chemical vapor deposition via
antimony incorporation", Appl. Phys. Lett, 89 (8), 083116/1-083116/3, 2006.
[19] K. Nishi, H. Saito, S. Sugou, and S.L. Jeong, "A narrow photoluminescence linewidth
of 21 meV at 1.35 µm from strain-reduced InAs quantum dots covered by In0.2Ga0.8As
grown on GaAs substrates", Appl. Phys. Lett, 74 (8), 1111-1113, 1999.
[20] Q. Gong, R. Notzel, G.J. Hamhuis, T.J. Eijkemans, and J.H. Wolter, "Leveling and
rebuilding: An approach to improve the uniformity of (In,Ga)As quantum dots", Appl.
Phys. Lett, 81 (10), 1887-1889, 2002.
[21] T. van Lippen, R. Notzel, G.J. Hamhuis, and J.H. Wolter, "Ordered quantum dot
molecules and single quantum dots formed by self-organized anisotropic strain
engineering", J. Appl. Phys., 97 (4), 44301-44301, 2005.
[22] D. Zhou, R. Notzel, F.W.M. van-Otten, P.J. van-Veldhoven, and T.J. Eijkemans,
"InAs/InGaAsP sidewall quantum dots on shallow-patterned InP (311)A", J. Appl.
Phys., 100 (6), 63505/1-63505/4, 2006.
[23] T. Mano, R. Notzel, D. Zhou, G.J. Hamhuis, T.J. Eijkemans, and J.H. Wolter,
"Complex quantum dot arrays formed by combination of self-organized anisotropic
strain engineering and step engineering on shallow patterned substrates", J. Appl.
Phys., 97 (1), 14304/1-14304/5, 2005.
[24] E. Selcuk, T. van Lippen, G.J. Hamhuis, and R. Notzel, "Guided quantum dot ordering
by self-organized anisotropic strain engineering and step engineering on shallow-
patterned substrates", J. Cryst. Growth, 301-302, 701-704, 2007.
[25] D. Bimberg, "Quantum dots for lasers, amplifiers and computing", J. Phys. D, 38 (13),
2055-2058, 2005.
References
93
[26] Y. Ueno, S. Nakamura, and K. Tajima, "Ultrafast 168 GHz 1.5 ps 1 fJ symmetric-
Mach-Zehnder-type all-optical semiconductor switch", Jpn. J. Appl. Phys. Part 2 Lett.,
39 (8A), L806-L808, 2000.
[27] R. Schreieck, M. Kwakernaak, H. Jackel, E. Gamper, E. Gini, W. Vogt, and H.
Melchior, "Ultrafast switching dynamics of Mach-Zehnder interferometer switches",
IEEE Phot. Technol. Lett., 13 (6), 603-605, 2001.
[28] E. Dirk, D. Fattal, E. Waks, G. Solomon, Z. Bingyang, T. Nakaoka, Y. Arakawa, Y.
Yamamoto, and J. Vuckovic, "Controlling the spontaneous emission rate of single
quantum dots in a two-dimensional photonic crystal", Phys. Rev. Lett., 95 (1),
013904/1-013904/4, 2005.
[29] M. Bayer, T.L. Reinecke, F. Weidner, A. Larionov, A. McDonald, and A. Forchel,
"Inhibition and enhancement of the spontaneous emission of quantum dots in
structured microresonators", Phys. Rev. Lett., 86 (14), 3168-3171, 2001.
[30] P. Lodahl, L.F. van-Driel, I.S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh,
and W.L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots
by photonic crystals", Nature, 430 (7000), 654-657, 2004.
[31] K.J. Vahala, "Optical microcavities", Nature, 424 (6950), 839-846, 2003.
[32] S. Gupta, M.Y. Frankel, J.A. Valdmanis, J.F. Whitaker, G.A. Mourou, F.W. Smith,
and A.R. Calawa, "Subpicosecond carrier lifetime in GaAs grown by molecular beam
epitaxy at low temperatures", Appl. Phys. Lett, 59 (25), 3276-3278, 1991.
[33] M. Haiml, U. Siegner, G.F. Morier, U. Keller, M. Luysberg, P. Specht, and E.R.
Weber, "Femtosecond response times and high optical nonlinearity in beryllium-doped
low-temperature grown GaAs", Appl. Phys. Lett, 74 (9), 1269-1271, 1999.
[34] A. Krotkus, K. Bertulis, L. Dapkus, U. Olin, and S. Marcinkevicius, "Ultrafast carrier
trapping in Be-doped low-temperature-grown GaAs", Appl. Phys. Lett, 75 (21), 3336-
3338, 1999.
[35] M.C. Beard, G.M. Turner, and C.A. Schmuttenmaer, "Subpicosecond carrier dynamics
in low-temperature grown GaAs as measured by time-resolved terahertz
spectroscopy", J. Appl. Phys., 90 (12), 5915-5923, 2001.
[36] M. Mikulics, S. Wu, M. Marso, R. Adam, A. Forster, H.A. van-der, P. Kordos, H.
Luth, and R. Sobolewski, "Ultrafast and highly sensitive photodetectors with recessed
electrodes fabricated on low-temperature-grown GaAs", IEEE Phot. Technol. Lett., 18
(7), 820-822, 2006.
[37] Q. Han, Z.C. Niu, L.H. Peng, H.Q. Ni, X.H. Yang, Y. Du, H. Zhao, R.H. Wu, and
Q.M. Wang, "High-performance 1.55 µm low-temperature-grown GaAs resonant-
cavity-enhanced photodetector", Appl. Phys. Lett, 89 (13), 131104/1-131104/3, 2006.
References
94
[38] T. Okuno, Y. Masumoto, M. Ito, and H. Okamoto, "Large optical nonlinearity and fast
response time in low-temperature grown GaAs/AlAs multiple quantum wells", Appl.
Phys. Lett, 77 (1), 58-60, 2000.
[39] T. Okuno, Y. Masumoto, Y. Sakuma, Y. Hayasaki, and H. Okamoto, "Femtosecond
response time in beryllium-doped low-temperature-grown GaAs/AlAs multiple
quantum wells", Appl. Phys. Lett, 79 (6), 764-766, 2001.
[40] R. Takahashi, H. Itoh, and H. Iwamura, "Ultrafast high-contrast all-optical switching
using spin polarization in low-temperature-grown multiple quantum wells", Appl.
Phys. Lett, 77 (19), 2958-2960, 2000.
[41] R. Prasanth, J.E.M. Haverkort, A. Deepthy, E.W. Bogaart, J.J.G.M. van-der-Tol,
Patent-EA, G. Zhao, Q. Gong, P.J. van-Veldhoven, R. Notzel, and J.H. Wolter, "All-
optical switching due to state filling in quantum dots", Appl. Phys. Lett, 84 (20), 4059-
4061, 2004.
[42] H. Benisty, C.M. Sotomayor-Torres, and C. Weisbuch, "Intrinsic mechanism for the
poor luminescence properties of quantum-box systems", Phys. Rev. B, 44 (19), 10945-
10948, 1991.
[43] Q.L. Xin, H. Nakayama, and Y. Arakawa, "Phonon bottleneck in quantum dots: Role
of lifetime of the confined optical phonons", Phys. Rev. B, 59 (7), 5069-5073, 1999.
[44] E.A. Zibik, L.R. Wilson, R.P. Green, G. Bastard, R. Ferreira, P.J. Phillips, D.A.
Carder, J.P. Wells, J.W. Cockburn, M.S. Skolnick, M.J. Steer, and M. Hopkinson,
"Intraband relaxation via polaron decay in InAs self-assembled quantum dots", Phys.
Rev. B, 70 (16), 161305(R)/1-161305(R)/4, 2004.
[45] A.V. Uskov, J. McInerney, F. Adler, H. Schweizer, and M.H. Pilkuhn, "Auger carrier
capture kinetics in self-assembled quantum dot structures", Appl. Phys. Lett, 72 (1),
58-60, 1998.
[46] I. Magnusdottir, S. Bischoff, A.V. Uskov, and J. Mork, "Geometry dependence of
Auger carrier capture rates into cone-shaped self-assembled quantum dots", Phys. Rev.
B, 67 (20), 205326/1-205326/5, 2003.
[47] G.A. Narvaez, G. Bester, and A. Zunger, "Carrier relaxation mechanisms in self-
assembled (In,Ga)As/GaAs quantum dots: efficient PtoS Auger relaxation of
electrons", Phys. Rev. B, 74 (7), 075403/1-075403/7, 2006.
[48] Jagdeep Shah, Ultrafast spectroscopy os semiconductors and semiconductor
nanostructures, Springer, 1996.
[49] P.W.M. Blom, C. Smit, J.E.M. Haverkort, and J.H. Wolter, "Carrier capture into a
semiconductor quantum well", Phys. Rev. B, 47 (4), 2072-2081, 1993.
References
95
[50] J. Siegert, S. Marcinkevicius, and Q.X. Zhao, "Carrier dynamics in modulation-doped
InAs/GaAs quantum dots", Phys. Rev. B, 72 (8), 085316/1-085316/7, 2005.
[51] F.K. Reinhart, "Excitation dependence of photoluminescence due to nonlinear
recombination and diffusion", J. Appl. Phys., 99 (7), 073102/1-073102/9, 2006.
[52] A.R. Vasconcellos, A.C. Algarte, and R. Luzzi, "Diffusion of photoinjected carriers in
plasma in nonequilibrium semiconductors", Phys. Rev. B, 48 (15), 10873-10884, 1993.
[53] H. Hillmer, A. Forchel, S. Hansmann, M. Morohashi, E. Lopez, H.P. Meier, and K.
Ploog, "Optical investigations on the mobility of two-dimensional excitons in
GaAs/Ga1-xAlxAs quantum wells", Phys. Rev. B, 39 (15), 10901-10912, 1989.
[54] S. Raymond, K. Hinter, S. Fafard, and J.L. Merz, "Experimental determination of
Auger capture coefficients in self-assembled quantum dots", Phys. Rev. B, 61 (24),
R16331-R16334, 2000.
[55] T.S. Sosnowski, T.B. Norris, H. Jiang, J. Singh, K. Kamath, and P. Bhattacharya,
"Rapid carrier relaxation in In0.4Ga0.6As/GaAs quantum dots characterized by
differential transmission spectroscopy", Phys. Rev. B, 57 (16), R9423-R9426, 1998.
[56] I. Magnusdottir, A.V. Uskov, S. Bischoff, B. Tromborg, and J. Mork, "One- and two-
phonon capture processes in quantum dots", J. Appl. Phys., 92 (10), 5982-5990, 2002.
[57] R. Ferreira and G. Bastard, "Phonon-assisted capture and intradot Auger relaxation in
quantum dots", Appl. Phys. Lett, 74 (19), 2818-2820, 1999.
[58] J. Feldmann, S.T. Cundiff, M. Arzberger, G. Bohm, and G. Abstreiter, "Carrier
capture into InAs/GaAs quantum dots via multiple optical phonon emission", J. Appl.
Phys., 89 (2), 1180-1183, 2001.
[59] M. De Giorgi, C. Lingk, G. Von Plessen, J. Feldmann, S. De Rinaldis, A. Passaseo, M.
De Vittorio, R. Cingolani, and M. Lomascolo, "Capture and thermal re-emission of
carriers in long-wavelength InGaAs/GaAs quantum dots", Appl. Phys. Lett, 79 (24),
3968-3970, 2001.
[60] J.L. Pan, "Intraband Auger processes and simple models of the ionization balance in
semiconductor quantum-dot lasers", Phys. Rev. B, 49 (16), 11272-11287, 1994.
[61] B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa, "Rapid carrier
relaxation in self-assembled InxGa1-xAs/GaAs quantum dots", Phys. Rev. B, 54 (16),
11532-11538, 1996.
[62] V.N. Gladilin, S.N. Klimin, V.M. Fomin, and J.T. Devreese, "Optical properties of
polaronic excitons in stacked quantum dots", Phys. Rev. B, 69 (15), 155325/1-
155325/5, 2004.
References
96
[63] M. Bissiri, H.G. Baldassarri-Hoger-von, M. Capizzi, V.M. Fomin, V.N. Gladilin, and
J.T. Devreese, "Polaron interaction in InAs/GaAs quantum dots and resonant
photoluminescence", Phys. Status Solidi B, 224 (3), 639-642, 2001.
[64] J.T. Devreese, S.N. Klimin, V.M. Fomin, and F. Brosens, "Optical absorption of a
many-polaron system confined in a quantum dot", Solid State Commun., 114 (6), 305-
310, 2000.
[65] Y. Toda, O. Moriwaki, M. Nishioka, and Y. Arakawa, "Efficient carrier relaxation
mechanism in InGaAs/GaAs self-assembled quantum dots based on the existence of
continuum states", Phys. Rev. Lett., 82 (20), 4114-4117, 1999.
[66] B. Urbaszek, E.J. McGhee, M. Kruger, R.J. Warburton, K. Karrai, T. Amand, B.D.
Gerardot, P.M. Petroff, and J.M. Garcia, "Temperature-dependent linewidth of
charged excitons in semiconductor quantum dots: strongly broadened ground state
transitions due to acoustic phonon scattering", Phys. Rev. B, 69 (3), 035304/1-
035304/6, 2004.
[67] A. Vasanelli, R. Ferreira, and G. Bastard, "Continuous absorption background and
decoherence in quantum dots", Phys. Rev. Lett., 89 (21), 216804/1-216804/4, 2002.
[68] E.W. Bogaart, J.E.M. Haverkort, T. Mano, T. van Lippen, R. Notzel, and J.H. Wolter,
"Role of the continuum background for carrier relaxation in InAs quantum dots",
Phys. Rev. B, 72 (19), 195301/1-195301/7, 2005.
[69] J. Urayama, T.B. Norris, J. Singh, and P. Bhattacharya, "Observation of phonon
bottleneck in quantum dot electronic relaxation", Phys. Rev. Lett., 86 (21), 4930-4933,
2001.
[70] F.W. Smith, A.R. Calawa, C.L. Chen, M.J. Manfra, and L.J. Mahoney, "New MBE
buffer used to eliminate backgating in GaAs MESFETs", IEEE Electron Device
Letters, 9 (2), 77-80, 1988.
[71] M. Klingenstein, J. Kuhl, R. Notzel, K. Ploog, J. Rosenzweig, C. Moglestue, A.
Hulsmann, J. Schneider, and K. Kohler, "Ultrafast metal-semiconductor-metal
photodiodes fabricated on low-temperature GaAs", Appl. Phys. Lett, 60 (5), 627-629,
1992.
[72] M.C. Beard, G.M. Turner, and C.A. Schmuttenmaer, "Transient photoconductivity in
GaAs as measured by time-resolved terahertz spectroscopy", Phys. Rev. B, 62 (23),
15764-15777, 2000.
[73] I. Lahiri, D.D. Nolte, E.S. Harmon, M.R. Melloch, and J.M. Woodall, "Ultrafast-
lifetime quantum wells with sharp exciton spectra", Appl. Phys. Lett, 66 (19), 2519-
2521, 1995.
References
97
[74] P.W. Juodawlkis, D.T. McInturff, and S.E. Ralph, "Ultrafast carrier dynamics and
optical nonlinearities of low-temperature-grown InGaAs/InAlAs multiple quantum
wells", Appl. Phys. Lett, 69 (26), 4062-4064, 1996.
[75] U. Keller, "Ultrafast all-solid-state laser technology", Appl. Phys. B, B58 (5), 347-363,
1994.
[76] A. Othonos, "Probing ultrafast carrier and phonon dynamics in semiconductors", J.
Appl. Phys., 83 (4), 1789-1830, 1998.
[77] M. Haiml, U. Siegner, G.F. Morier, U. Keller, M. Luysberg, R.C. Lutz, P. Specht, and
E.R. Weber, "Optical nonlinearity in low-temperature-grown GaAs: Microscopic
limitations and optimization strategies", Appl. Phys. Lett, 74 (21), 3134-3136, 1999.
[78] M.R. Melloch, J.M. Woodall, E.S. Harmon, N. Otsuka, F.H. Pollak, D.D. Nolte, R.M.
Feenstra, and M.A. Lutz, "Low-Temperature Grown III-V Materials", Annu. Rev.
Mater. Sci., 25, 547-600, 1995.
[79] X. Liu, A. Prasad, W.M. Chen, A. Kurpiewski, A. Stoschek, W.Z. Liliental, and E.R.
Weber, "Mechanism responsible for the semi-insulating properties of low-
temperature-grown GaAs", Appl. Phys. Lett, 65 (23), 3002-3004, 1994.
[80] U. Siegner, R. Fluck, G. Zhang, and U. Keller, "Ultrafast high-intensity nonlinear
absorption dynamics in low-temperature grown gallium arsenide", Appl. Phys. Lett, 69
(17), 2566-2568, 1996.
[81] M. Sudzius, A. Bastys, and K. Jarasiunas, "Optical nonlinearities at transient
quenching of EL2 defect at room temperature", Opt. Commun., 170 (1-3), 149-160,
1999.
[82] A. Krotkus and J.L. Coutaz, "Non-stoichiometric semiconductor materials for
terahertz optoelectronics applications", Semicond. Sci. Technol., 20 (7), S142-S150,
2005.
[83] A. Krotkus, K. Bertulis, M. Kaminska, K. Korona, A. Wolos, J. Siegert, S.
Marcinkevicius, and J.L. Coutaz, "Be-doped low-temperature-grown GaAs material
for optoelectronic switches", IEE Proceedings Optoelectronics, 149 (3), 111-115,
2002.
[84] D. Sreenivasan, J.E.M. Haverkort, T.J. Eijkemans, and R. Notzel, "Photoluminescence
from low temperature grown InAs/GaAs quantum dots", Appl. Phys. Lett, 90 (11),
112109/1-112109/3, 2007.
[85] P.C. Sercel, "Multiphonon-assisted tunneling through deep levels: A rapid energy-
relaxation mechanism in nonideal quantum-dot heterostructures", Phys. Rev. B, 51
(20), 14532-14541, 1995.
References
98
[86] E.S. Harmon, M.R. Melloch, J.M. Woodall, D.D. Nolte, N. Otsuka, and C.L. Chang,
"Carrier lifetime versus anneal in low temperature growth GaAs", Appl. Phys. Lett, 63
(16), 2248-2250, 1993.
[87] H.M. van-Driel, X.Q. Zhou, W.W. Ruhle, J. Kuhl, and K. Ploog, "Photoluminescence
from hot carriers in low-temperature-grown gallium arsenide", Appl. Phys. Lett, 60
(18), 2246-2248, 1992.
[88] M. Kaminska, E.R. Weber, W.Z. Liliental, R. Leon, and Z.U. Rek, "Stoichiometry-
related defects in GaAs grown by molecular-beam epitaxy at low temperature", J. Vac.
Sci. Technol. B, 7 (4), 710-713, 1989.
[89] D.J. Eaglesham, L.N. Pfeiffer, K.W. West, and D.R. Dykaar, "Limited thickness
epitaxy in GaAs molecular beam epitaxy near 200 °C", Appl. Phys. Lett, 58 (1), 65-67,
1991.
[90] F. Tassone, F. Bassani, and L.C. Andreani, "Quantum-well reflectivity and exciton-
polariton dispersion", Phys. Rev. B, 45 (11), 6023-6030, 1992.
[91] E.W. Bogaart, "Transient differential reflection spectroscopy on quantum dot
nanostructures", Ph.D Thesis, 2006.
[92] D. Morris, N. Perret, and S. Fafard, "Carrier energy relaxation by means of Auger
processes in InAs/GaAs self-assembled quantum dots", Appl. Phys. Lett, 75 (23),
3593-3595, 1999.
[93] R. Oulton, J.J. Finley, A.I. Tartakovskii, D.J. Mowbray, M.S. Skolnick, M.
Hopkinson, A. Vasanelli, R. Ferreira, and G. Bastard, "Continuum transitions and
phonon coupling in single self-assembled Stranski-Krastanow quantum dots", Phys.
Rev. B, 68 (23), 235301-235301, 2003.
[94] R. Heitz, M. Veit, N.N. Ledentsov, A. Hoffmann, D. Bimberg, V.M. Ustinov, P.S.
Kop'ev, and Zh.I. Alferov, "Energy relaxation by multiphonon processes in
InAs/GaAs quantum dots", Phys. Rev. B, 56 (16), 10435-10445, 1997.
[95] K.W. Sun, J.W. Chen, B.C. Lee, C.P. Lee, and A.M. Kechiantz, "Carrier capture and
relaxation in InAs quantum dots", Nanotechnology, 16 (9), 1530-1535, 2005.
[96] U. Jahn, S. Dhar, R. Hey, O. Brandt, S.J. Miguel, and A. Guzman, "Influence of
localization on the carrier diffusion in GaAs/(Al,Ga)As and (In,Ga)(As,N)/GaAs
quantum wells: a comparative study", Phys. Rev. B, 73 (12), 125303/1-125303/8,
2006.
[97] T. Mano, R. Notzel, G.J. Hamhuis, T.J. Eijkemans, and J.H. Wolter, "Direct imaging
of self-organized anisotropic strain engineering for improved one-dimensional
ordering of (In,Ga)As quantum dot arrays", J. Appl. Phys., 95 (1), 109-114, 2004.
References
99
[98] J. Bellessa, V. Voliotis, R. Grousson, X.L. Wang, M. Ogura, and H. Matsuhata,
"Quantum-size effects on radiative lifetimes and relaxation of excitons in
semiconductor nanostructures", Phys. Rev. B, 58 (15), 9933-9940, 1998.
[99] M. Sugawara, "Theory of spontaneous-emission lifetime of Wannier excitons in
mesoscopic semiconductor quantum disks", Phys. Rev. B, 51 (16), 10743-10754,
1995.
[100] R.S. Schmitt, D.A.B. Miller, and D.S. Chemla, "Theory of the linear and nonlinear
optical properties of semiconductor microcrystallites", Phys. Rev. B, 35 (15), 8113-
8125, 1987.
[101] G.Y. Slepyan, S.A. Maksimenko, V.P. Kalosha, A. Hoffmann, and D. Bimberg,
"Effective boundary conditions for planar quantum dot structures", Phys. Rev. B, 64
(12), 125326/1-125326/8, 2001.
[102] S.A. Maksimenko, G.Y. Slepyan, N.N. Ledentsov, V.P. Kalosha, A. Hoffmann, and
D. Bimberg, "Light confinement in a quantum dot", Semicond. Sci. Technol., 15 (6),
491-496, 2000.
[103] S.A. Maksimenko, G.Y. Slepyan, V.P. Kalosha, N.N. Ledentsov, A. Hoffmann, and
D. Bimberg, "Size and shape effects in electromagnetic response of quantum dots and
quantum dot arrays", Mat. Sci. Eng. B, 82 (1-3), 215-217, 2001.
[104] G.Y. Slepyan and S.A. Maksimenko, Private communications.
[105] G.Y. Slepyan, S.A. Maksimenko, A. Hoffmann, and D. Bimberg, "Quantum optics of
a quantum dot: local-field effects", Phys. Rev. A, 66 (6), 063804/1-063804/17, 2002.
[106] D.E. Aspnes, "Local-field effects and effective-medium theory: a microscopic
perspective", Am. J. Phys., 50 (8), 704-709, 1982.
[107] J.D. Jackson, Classical electrodynamics, John Wiley & Sons Inc., 1999.
[108] G.Y. Slepyan, S.A. Maksimenko, V.P. Kalosha, J. Herrmann, N.N. Ledentsov, I.L.
Krestnikov, Zh.I. Alferov, and D. Bimberg, "Polarization splitting of the gain band in
quantum wire and quantum dot arrays", Phys. Rev. B, 59 (19), 12275-12278, 1999.
[109] R. Atanasov, F. Bassani, and V.M. Agranovich, "Mean-field polariton theory for
asymmetric quantum wells", Phys. Rev. B, 49 (4), 2658-2666, 1994.
[110] J. He, R. Notzel, P. Offermans, P.M. Koenraad, Q. Gong, G.J. Hamhuis, T.J.
Eijkemans, and J.H. Wolter, "Formation of columnar (In,Ga)As quantum dots on
GaAs(100)", Appl. Phys. Lett, 85 (14), 2771-2773, 2004.
[111] E. Martinet, F. Reinhardt, A. Gustafsson, G. Biasiol, and E. Kapon, "Self-ordering and
confinement in strained InGaAs/AlGaAs V-groove quantum wires grown by low-
pressure organometallic chemical vapor deposition", Appl. Phys. Lett, 72 (6), 701-703,
1998.
References
100
[112] J. Bellessa, V. Voliotis, T. Guillet, D. Roditchev, R. Grousson, X.L. Wang, and M.
Ogura, "Carrier scattering by Auger mechanism in a single quantum wire", Eur. Phys.
J. B, 21 (4), 499-505, 2001.
[113] M. Dworzak, P. Zimmer, H. Born, and A. Hoffmann, "Dephasing and energy
relaxation processes in self-assembled In(Ga)As/GaAs quantum dots", AIP
Conference Proceedings (772), 633-634, 2005.
[114] P. Borri, W. Langbein, S. Schneider, U. Woggon, R.L. Sellin, D. Ouyang, and D.
Bimberg, "Exciton relaxation and dephasing in quantum-dot amplifiers from room to
cryogenic temperature", IEEE J. Quantum Electron., 8 (5), 984-991, 2002.
[115] K. Biermann, D. Nickel, K. Reimann, M. Woerner, T. Elsaesser, and H. Kunzel,
"Ultrafast optical nonlinearity of low-temperature-grown GaInAs/AlInAs quantum
wells at wavelengths around 1.55 µm", Appl. Phys. Lett, 80 (11), 1936-1938, 2002.
[116] H.H. Zhan, R. Notzel, G.J. Hamhuis, T.J. Eijkemans, and J.H. Wolter, "Self-
assembled InAs quantum dots formed by molecular beam epitaxy at low temperature
and postgrowth annealing", J. Appl. Phys., 93 (10), 5953-5958, 2003.
[117] H.H. Zhan, R. Notzel, G.J. Hamhuis, T.J. Eijkemans, and J.H. Wolter, "Low-
temperature growth of self-assembled InAs dots on GaAs by molecular beam epitaxy",
J. Cryst. Growth, 251 (1-4), 135-139, 2003.
[118] M.M. Sobolev, A.R. Kovsh, V.M. Ustinov, A.Y. Egorov, A.E. Zhukov, M.V.
Maksimov, and N.N. Ledentsov, "Deep-level transient spectroscopy in InAs/GaAs
laser structures with vertically coupled quantum dots", Semiconductors, 31 (10), 1074-
1079, 1997.
[119] M.M. Sobolev, I.V. Kochnev, V.M. Lantratov, N.A. Bert, N.A. Cherkashin, N.N.
Ledentsov, and D.A. Bedarev, "Thermal annealing of defects in InGaAs/GaAs
heterostructures with three-dimensional islands", Semiconductors, 34 (2), 195-204,
2000.
[120] M. Kaniewska, O. Engstrom, A. Barcz, and C.M. Pacholak, "Deep levels induced by
InAs/GaAs quantum dots", Mat. Sci. Eng. C, 26 (5-7), 871-875, 2006.
[121] P.W. Yu, G.D. Robinson, J.R. Sizelove, and C.E. Stutz, "0.8-eV photoluminescence of
GaAs grown by molecular-beam epitaxy at low temperatures", Phys. Rev. B, 49 (7),
4689-4694, 1994.
[122] E.W. Bogaart, J.E.M. Haverkort, T. Mano, R. Notzel, J.H. Wolter, P. Lever, H.H. Tan,
and C. Jagadish, "Picosecond time-resolved bleaching dynamics of self-assembled
quantum dots", IEEE Trans. Nanotech, 3 (3), 348-352, 2004.
Summary
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Capture, relaxation and recombination in quantum dots
Summary
Quantum dots (QDs) have attracted a lot of interest both from application and
fundamental physics point of view. A semiconductor quantum dot features discrete atomic-
like energy levels, despite the fact that it contains many atoms within its surroundings. The
discrete energy levels give rise to very narrow optical emission lines at low temperature.
When exciting an ensemble of quantum dots, the discrete emission lines are however
broadened by the size distribution of the quantum dots. In particular, the advancement of
different growth techniques like Molecular Beam Epitaxy and Metal Organic Vapour Phase
Epitaxy has lead to the development of different types of ultrapure QD nanostructures with
well-defined size, shape and composition. Nowadays QDs can even be grown in laterally
ordered patterns. In the last decade, great progress has been obtained in the detailed physical
understanding of these semiconductor nano-structures. A complete understanding of the
carrier dynamics in QDs, which is essential for exploiting the utilization potential predicted
for these QDs, is nevertheless lacking. In this thesis, the carrier dynamics of different types of
InAs/GaAs QDs is investigated.
When the carriers are photo-generated in the barrier layer much above the QD
bandgap, they diffuse towards the QDs, in which they are captured and subsequently undergo
relaxation towards the QD ground state. After the relaxation, each electron-hole pair within
the QD ground-state with total spin J=±1, recombines radiatively and emits a single photon
with an energy corresponding to the separation of the confined energy level within the QD. In
this Thesis, QD-materials in which many defects are intentionally included by low-
temperature growth, is also investigated. In this case, the photo-generated carriers in the bulk
GaAs-barrier and in the QDs can also be nonradiatively trapped into nearby defect states. An
overview of the carrier capture, relaxation and trapping routes in both high quality QD
structures and in low temperature grown QD structures is presented in Chapter 2.
In this Thesis, the carrier dynamics within III-V semiconductor QDs are studied using
the Time Resolved Differential Reflectivity (TRDR) and Photoluminescence (PL)
measurement techniques. The TRDR experiment employs a two-color pump-probe system, in
which the pump laser has a photon energy tuned above the GaAs barrier bandgap. The
optically generated carriers are captured into the QDs inducing a refractive index change of
the QDs. The resulting change of the reflectivity of the probe beam, which is tuned in
Summary
102
resonance with the QD ground state, is subsequently detected as a function of the pump-probe
delay to obtain the carrier dynamics. The reflectivity is interpreted under the assumption that
the QD layer can be considered as a thin continuous layer with an effective dielectric
constant. In this case, the observed reflectivity signal is basically the interference between the
surface reflection and the small reflection from the QD-layer. The advantage of TRDR
technique lies in the fact that it is non-destructive since it does not require etching of the
substrate. Secondly, the TRDR technique allows the study of the QD-samples not only at low
temperature but also up to room temperature. Finally, the TRDR technique allows the study of
samples in which the non-radiative recombination is (intentionally) very high and in which
the PL efficiency is thus too small to be measured.
In Chapter 3, an array of InAs/GaAs QDs grown on a quantum wire (QWR)
superlattice (SL) template is investigated to understand the capture and relaxation mechanism
in these QDs. This particular QD structure is chosen since it is expected to reduce the carrier
diffusion from the bottom barrier layer into the QDs, allowing a more controlled study of the
actual carrier capture mechanism. The quantum wire superlattice is spectrally well separated
from the QDs, thereby also allowing the study of re-distribution of carriers from the QWR
template into the QDs. First, the PL spectrum from this sample is studied and observed a clear
carrier re-distribution from the QWR template to the QDs at temperatures between 40 K and
100 K. Subsequently, TRDR experiments were performed, showing a distinct increase of the
TRDR rise time between 40 K and 100 K. TRDR experiments as a function of the pump
excitation density at 5 K showed a TRDR risetime which decreases from 28 ps at a low
excitation density to 5 ps for high excitation density, also showing a plateau for excitation
densities above 1 kW cm-2
. At room temperature, the TRDR risetime is apparently
independent of the excitation density. These observations make it clear that a simple Auger or
phonon relaxation picture is not capable of explaining the carrier capture and relaxation in this
sample. The data presented in this Thesis can be explained by taking into account the carrier
diffusion through the barrier layers towards the capture volumes of the QDs. The diffusion
through the barrier is modified by the capture and re-emission of carriers from the superlattice
template. At low excitation density, the number of carriers excited directly within the QD
capture volume is less than unity, implying that the carrier have to first diffuse through the
barrier towards the QDs, thereby resulting in a longer risetime. As the excitation density is
increased, more carriers are excited directly within the capture volume, thereby decreasing the
risetime. At low temperature, the carriers generated in the bottom barrier layer are all captured
by SL template, thus reducing the effective diffusion length. When the temperature increases,
Summary
103
carrier re-emission from the SL template increases the effective carrier diffusion length, thus
explaining the observed increase of the TRDR risetime.
In Chapter 4, a study of an InAs/GaAs Stransky-Krastanow grown quantum rod (QR)
ensemble is presented, which have been grown by the leveling and rebuilding technique. In
these structures the TRDR decay dynamics was investigated, which was found to be modified
by the number of resonant QDs probed within the total QR size distribution. It is found that
the TRDR decay time develops a clear resonance at high excitation densities, while at low
excitation density the well-known excitonic behavior is regained. At very high excitation
density, and also at high temperature, the resonant enhancement of the TRDR decay time
gradually decreases. These results are interpreted in terms of an electromagnetic coupling of
the excited QRs. Due to this coupling, the QRs collectively decay, giving rise to a polariton-
like picture. The experimental results can be interpreted in a picture in which the TRDR
lifetime of the QRs is determined by the separation between identical and excited QRs, which
are in resonance with the probe. At low excitation density, the density of excited QRs is too
small for such a collective decay behavior, leading to the excitonic life time. At high
temperature and also at very high excitation density, the exciton dephasing rate becomes
much larger than the radiative decay rate, which washes out the electromagnetic coupling.
Chapter 5 presents the investigation of low temperature (250 °C) grown InAs/GaAs
QDs which have been subjected to different annealing conditions. The purpose is to
investigate the low temperature (LT) grown QDs as a potential device material to be used in
ultra-fast optical switching. It was found that the PL-efficiency of the QDs is reasonable at
low temperature, but rapidly quenches with increasing temperature and disappears at 40 K. It
is also observed that the PL efficiency substantially increases when the LT-QDs are excited
below the GaAs bandgap, directly into the QDs. These results indicate that LT growth indeed
provides many anti-site defects within the GaAs barrier which act as fast trapping centers for
the photo-excited carriers, but the QDs itself are free from these PL quenching centers.
Finally, in Chapter 6, the decay dynamics of the LT-QDs is studied using the TRDR
technique, since the TRDR technique is expected to be still sensitive at room temperature and
for samples in which the PL is quenched by excess nonradiative recombination. From the
rapid quenching of the PL-efficiency between 5 and 40 K observed in Chapter 5, a strong
decrease of the TRDR decay time was expected for these LT-QDs. The TRDR decay time is
however observed to be slow. Quite surprisingly, the TRDR decay time is measured to be
independent of the temperature. These data are interpreted by noting that the photo-excited
Summary
104
electrons in the GaAs barrier are very efficiently trapped by the charged anti-site defects,
while the holes are less efficiently trapped by neutral anti-site defects. As a result, the holes
will be captured within the LT-QDs, while the electrons will mainly remain within the traps in
the GaAs barrier. The TRDR signal is proportional to the sum of the electron and hole
occupation within the LT-QDs and will thus mainly probe the hole dynamics which is not
expected to be ultra-fast. The PL technique probes the product of the electron and hole
densities, and thus effectively probes the very small electron occupation within the QDs. The
TRDR decay time is interpreted as the trapping recombination time between holes confined
within the LT-QDs and the neutral anti-site defect within the GaAs barrier, in close proximity
to the LT-QD.
105
List of publications
Journal papers
D. Sreenivasan, J.E.M. Haverkort, T.J, Eijkemans and R. Nötzel, “Photoluminescence from
low temperature grown InAs/GaAs Quantum Dots”, Applied Physics Letters, 90, 112109,
(2007)
D. Sreenivasan, J.E.M. Haverkort, O. Ipek, B. Martinez-Vazquez, T.J. Eijkemans, T. Mano
and R. Nötzel, “Anomalous temperature dependence of the carrier capture time into
InAs/GaAs quantum dots grown on a quantum wire array”, Physica E (In press)
D. Sreenivasan, J.E.M. Haverkort, S.A. Maksimenko, G.Ya. Slepyan and R. Nötzel, “Exciton
radiative lifetime of quantum rods in reflectivity”, Physica E (In press)
Conference proceedings
D. Sreenivasan, J.E.M. Haverkort, O. Ipek, B. Martinez-Vazquez, T.J. Eijkemans, T. Mano
and R. Nötzel, “Anomalous temperature dependence of the carrier capture time into
InAs/GaAs quantum dots grown on a quantum wire array”, 13th
International Conference on
Modulated Semicnductor Structures, Genova, Italy, Abstracts page: 330, (2007)
D. Sreenivasan, J.E.M. Haverkort, R. Nötzel, S.A. Maksimenko, and G.Ya. Slepyan
“Resonant radiative lifetime in quantum rods”, 13th
International Conference on Modulated
Semicnductor Structures, Genova, Italy, Abstracts, page: 344, (2007)
D. Sreenivasan, J.E.M. Haverkort, R. Nötzel, S.A. Maksimenko, and G.Ya. Slepyan,
“Anomalous radiative lifetime in quantum rods”, Nanomodelling II Conference, San Diego,
USA, Proceedings of SPIE, 6328, 63280T, (2006)
D. Sreenivasan, J.E.M. Haverkort. H.H. Zhan, T.J. Eijkemans, and R. Nötzel, “Time resolved
reflectivity of low temperature grown InAs/GaAs quantum dots”, Nanophotonics Conference,
Strassbourg, France, Proceedings of SPIE, 6195, 619520, (2006)
D. Sreenivasan, J.E.M. Haverkort. H.H. Zhan, T.J. Eijkemans, and R. Nötzel, “Carrier
dynamics of LT InAs/GaAs QDs using time resolved differential reflectivity”, IEEE/LEOS
Symposium Benelux Chapter, Mons, Belgium, Proceedings page: 265, (2005)
D. Sreenivasan, J.E.M. Haverkort. H.H. Zhan, T.J. Eijkemans, R. Nötzel, and J.H. Wolter,
“Photoluminescence on InAs/GaAs quantum dots”, IEEE/LEOS Symposium Benelux
Chapter, Ghent, Belgium, Proceedings page: 291, (2004)
D. Sreenivasan, J.E.M. Haverkort. H.H. Zhan, T.J. Eijkemans, R. Nötzel, and J.H. Wolter,
“Photoluminescence study of low-temperature grown InAs/GaAs quantum dots”, Photonics
2004, Cochin, India, Conference proceedings page OMD 2.5, (2004)
List of publications
106
D. Sreenivasan, E.W. Bogaart, J.E.M. Haverkort, R. Nötzel, S.A. Maksimenko, and G.Ya.
Slepyan, “Carrier lifetime resonance in InAs/GaAs quantum dots”, SANDiE Optics Meeting,
Berlin, 11 January (2007)
107
Acknowledgements
The four years I spent in Netherlands has been a wonderful experience for me-
exploring new frontiers, both scientific and cultural. This time was all the more enjoyable
through the association of my friends and colleagues. In this section, I would like to take the
opportunity of acknowledging the caring, support and help offered by them.
First of all, I would like to thank my supervisor, Dr. Jos Haverkort for his active
support and guidance. Jos, thank you so much for patiently listening to my doubts and helping
me out in difficult situations, especially in the lab. You always motivated me to work
efficiently and gave me a new perspective in technical writing. The unscheduled lengthy
discussions we had during my countless walk-in visits to your office are very much
appreciated. Your timely and experienced advice helped me to be focused and always on track
to realize this work..
I would also like to thank my first promoter Prof. Paul Koenraad for his valuable
comments and support. Paul, it was always nice talking to you and you always managed to
impart a lot of enthusiasm towards scientific research. Thank you very much for critically
reading the Thesis and giving valuable suggestions.
I would like to thank my second promoter Prof. Huub Salemink for his support and
encouragement. I thank Prof. Joachim Wolter for the faith he showed in me and giving me the
opportunity to do Ph.D in the group. I thank Prof. Herman Beijerinck for his valuable advices
about managing my Ph.D. I would also like to acknowledge the contribution of Gregory
Slepyan and Sergey Maksimenko for helping me give an additional dimension to my
experimental results, through the theoretical concept discussed in Chapter 4 of this Thesis.
Of course, the research work presented in this Thesis was made possible due to the
samples provided by the growth team. I would like to express my gratitude towards Richard
Notzel for his valuable suggestions and samples. Thanks to Mano, Jun He and Zhan whose
samples I used in this Thesis.
It is not easy to build an experimental set up and get it working. Jos thanks for all the
times you got my vacuum systems running. Frans, thanks for helping with the electronics, and
Tom, thanks for your guidance with labview, optics and for letting me use the PL set up. Rian,
Acknowledgements
108
Rene, Peter, Cees and Frank – thank you for helping me with samples and useful suggestions.
Thank you all for being so nice to me and sparing the time to sort out the problems.
I have always enjoyed the atmosphere in our group. Whether it is the serious group
meetings and discussions or our fun filled group outings and wine tasting parties, it always
felt great to be a part of the group. I also had a chance to strengthen my knowledge through
the discussions with the group members. Thank you all for the same. I would like to thank my
room mates Twan, Willem, Ozlem and Bea for the cheerful atmosphere in the room. Ozlem
and Bea, I hope that you enjoyed working in the lab with me as much as I did. Of course how
can I forget my dear friends- Cem, Guido, Nut, Peter, Sanguan and Jun He. I always enjoyed
the dinner and movie outings with you all. It felt good to unwind after long hours in the lab. I
will always cherish the fond memories of our trips. I acknowledge the help rendered by
Dayong whenever I needed it. I would like to extend my thanks to Andrea Fiore, Rob van der
Heijden, Andrei Silov, Jens, Christina, Carl – Frederick, Jose, Xia, Alexei, David, Nicolas,
Pavel, Erik, Robbie, Andrei Yakunin, Tom Campbell Ricketts, Harm, Niek, Ekber, Laurent,
Murat and Fransesco. All the best to the new Ph.Ds: Salman, Ineke and Joris. Margriet, I
don’t know how to thank you. Your enthusiasm is infectious. You were always very caring to
me. Thank you very much for the umpteen number of things you have taken care for me and
being there for me. You are the best.
I am grateful to my Professor in India, Prof. V.P.N. Nampoori, for introducing me to
the world of research and supporting me in the decision to come to Eindhoven. Sir, thankyou
very much for being an inspiration and motivation for me. I also thank Sajan for his
inspiration.
I would like to acknowledge all the good times spend with my dear friends outside
university hours. Pam and Ewelina, it was always great fun to hang out with you. You are
wonderful friends. Greg, Ash and Suhina, I have shared a lot of sweet moments with you.
Thanks to Lopa, Harish, Nischal, Anitha, Vishal, Shalaka, Dhanya, Nidhi, Chaitya, Kalyani,
Saba, Snehal, Neelesh and Yogesh for keeping the spirit of Indian festivals alive. How can I
forget, my malayali gang. Jinesh, Merina, Prasanth, Aneesh, Jojo, Aziz, Bhahju, Denny,
Rajesh, Sony, and Sivaji. Our get togethers and tours are quite memorable. They will always
remain close to my heart. Special thanks to Prasanth and Anish, for the advices. It helped me
a lot both at work and also outside. Merina, you are no less than a sister to me. It always felt
good to know that I can count on you no matter what. We had a great time together both in
Eindhoven and also traveling around Europe. The memories of the crazy trips we did together
Acknowledgements
109
always make me laugh. Jinesh, the weekend cooking sessions and outings with you were
great. It was always fun to talk about the good old days of Master class. Also thanks to my
friends, Priya, Archu, Lechu, Anisha, Nambo, Vinod, Rajmo, Arun, Dinish and the rest for
being there for me and keeping the warmth of friendship alive even though we are spread out
all over the world. Also thanks for discussions regarding the research topic. Reba, you are
such a great friend.
Staying away from family, especially in a foreign country is not a very easy task. But,
thanks to Els and Ling, I found in Overpeltlaan 20, a place I could call home. We all had a
great time there. Els, you were more of a mother than a landlady. Your motherly affection was
always a welcome relief. You made the tiredness of the day fade away with your hug. Ling,
you are like my sister. Your smile and cheerful nature makes me keep my spirits always high.
We did cook up some Indo-Chinese food, isn’t it? At the end of the day, I was happy to come
home to you both.
I would like to thank my other family in Eindhoven. The Smul gang-Merina, Joe,
Gaby, Vinayak, Vishwa and Vinit provided the space to unwind, have fun and also sometimes
seriously argue on worthless debates. I enjoyed our trips throughout Europe and also the
weekend nightouts or just hanging around in the house with you all. I also appreciate the
concern and care shown towards me. I know that I can count on you guys any time.
Above all, I would like to express my gratitude to my parents (achan and amma) and
my little sister. Thanks is a very short word to express my feelings for them. Whatever I am, I
owe everything to them. Thank you for the selfless support and love you have given me. You
always stood by me in every decision I have taken. I know it was not very easy for you. But
your faith in me gave me the strength to keep going. I can only say that I am lucky to have
you as my family and I am proud of you. I also would like to thank mummy and Shaishu for
their support and understanding.
Finally, I would like to thank Vinit for being a caring and understanding husband. You
have patiently listened to all my complaints and frustrations about research and helped me
maintain the positive spirit. Thank you for being there for me. I love you.
111
About the author
Dilna Sreenivasan was born in Alavil, Kerala, India on 22nd
September 1977. She received her
Master of Science degree in Physics from the Cochin University of Science and Technology
(CUSAT) in November 2000. From June 2001 onwards she worked as a junior research
fellow in the International School of Photonics of CUSAT in the field of Laser Induced
Plasma. In October 2003, she joined for Ph.D under the supervision of dr. J.E.M. Haverkort in
the Department of Applied Physics of Eindhoven University of Technology, The Netherlands.