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PHYSICAL REVIEW B 85, 125311 (2012)

Influence of electronic coupling on the radiative lifetime in the (In,Ga)As/GaAs quantumdotquantum well system

M. Syperek,1,* J. Andrzejewski,1 W. Rudno-Rudzinski,1 G. Sek,1 J. Misiewicz,1 E. M. Pavelescu,2, C. Gilfert,2 and

J. P. Reithmaier2

1Institute of Physics, Wrocaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wrocaw, Poland2

Institute of Nanostructure Technologies and Analytics, Technische Physik, Universitaet Kassel, Heinrich-Plett-Strasse 40,34132 Kassel, Germany

(Received 16 November 2011; revised manuscript received 12 March 2012; published 22 March 2012)

In this paper, we present time-resolved photoluminescence of self-assembled (In,Ga)As quantum dots (QDs)

coupled to anInxGa1xAs quantum well (QW) through a thin GaAs barrier.The coupling strength is controlled by

the well width and material composition and has a direct influence on the QDQW system ground-state radiative

lifetime, which increases from 1.1 up to 1.82 ns as the coupling strength increases. A thorough explanation is

given for the reduction of the fundamental transition oscillator strength in the interacting system induced by

the transformation of related eigenstates from a noncoupled to a coupled regime. The experimental observations

have been fully confirmed by the results of three-dimensional band structure calculations of a coupled QDQW

system within the framework of eight-band kp theory.

DOI: 10.1103/PhysRevB.85.125311 PACS number(s): 78.66.Fd, 78.67.De, 68.65.Hb, 78.47.D

I. INTRODUCTION

Recent rapid advancement in the fabrication techniques of

semiconductor quantum dot (QD) structures has been followed

by a remarkable amount of research devoted to the exploration

of their unique optical properties. A number of spectroscopic

results on a single semiconductor QD have been obtained,

which confirmed its quasiatomic character being a conse-

quence of the three-dimensional (3D) carrier confinement.1,2

However, the QD is very rarely a standalone object. Its

coupling to the environment is of primary importance for

current application and future technological implementations,

including quantum data processing based on spin or charge

state.3,4 A QD can interact with other dots, defect states,surface states, etc., which in turn leads to the modification of

its intrinsic physical properties. In the following, we consider

the coupling of a quasi-0D QD ground state to quantum well

(QW) 2D extended states.

The concept of a coupled QDQW system has been

proposed for the realization of the tunnel injection of carriers

from their large reservoir (QW) to QDs. It has been suc-

cessfully implemented for single-electron transistors,5,6 tunnel

injection lasers,79 and QD-based memories.10 Surprisingly,

some basic physical phenomena in such coupled systems

remain unexplored or at least their nature is unclear. A few

interesting questions are still open related to the full band

structure picture, the intraband and interband carrier scatteringprocesses, charge- and spin-transfer mechanisms between

the QW and QD in either coherent or incoherent regimes,

and the carrier dynamics on the ground state of an entire

QDQW system in the presence of an electronic coupling.

The issue of a coherent charge transfer between resonantly

coupled high-energy states of the QW and QD has been very

recently addressed.11 In this work, we elucidate the role of a

coupling regime between the QD and QW and its strength on

the coupled-system ground-state carrier dynamics beyond the

coherent regime of interaction.

In this respect, we have performed continuous-wave

(CW) photoluminescence (PL) and photoreflectance (PR)

experiments, which let us identify the dipole-allowed ground-

state and excited-state interband transitions in a set of

(In,Ga)As/GaAs coupled QDQW structures. The variable

indium content in the well and the well-width changes allowed

us to control the coupling strength between the QD and QW,

defined as the influence of the well potential on the states

confined in QDs. For the sake of comparison, a reference

(In,Ga)As/GaAs QD structure has also been considered.

Information concerning a possible coupling regime is acquired

based on the data analysis of a time-resolved photolumines-

cence (TRPL) experiment, additionally supported by a 3D

band structure calculation of the entire system within the

eight-band kp approach.

II. EXPERIMENTAL DETAILS

The investigated structures, called CS1, CS2, CS3, and

QDref, were grown by molecular-beam epitaxy on a semi-

insulating (001) GaAs substrate.12 The CS1 consists of a

15-nm-wide In0.2Ga0.8As QW separated by a 2-nm-thick

GaAs barrier from In0.6Ga0.4As QDs obtained by depositing

nominally 1.8 monolayers of the (In,Ga)As material. The well

and dots are surrounded by two 15-nm-thick layers of GaAs,

and, finally, the entire QDQW system is sandwiched between

AlGaAs/GaAs superlattices. The CS2 and CS3 have a similar

layer structure and differ from the CS1 in the well width,

which is 7 nm for both, and in the In composition in thewell, which is nominally 23% and 27%. These parameters

are summarized in Table I. Additionally, the (In,Ga)As QDs

reference structure (QDref) has been produced under the same

growth conditions without the QW. The surface density of

dots in each structure is estimated to be on the order of

1010 cm2. The layer sequence of samples is schematically

depicted in Fig. 1. For the CW PL and TRPL experiments,

samples were held in a variable-temperature cryostat. In the

case of the CW experiment, the photoexcitation was provided

by the 532 nm line from the yttrium aluminum garnet laser.

For the TRPL experiment, the sample was excited by a

mode-locked Ti:sapphire laser, which generates pulses with

125311-11098-0121/2012/85(12)/125311(7) 2012 American Physical Society
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M. SYPEREK et al. PHYSICAL REVIEW B 85, 125311 (2012)

TABLE I. The parameters of the coupled QDQW structures.

Structure QW width (nm) QW [In] content (%)

CS1 15 17

CS2 7 23

CS3 7 27

a duration of 140 fs at a repetition rate of 76 MHz. In the

case of the TRPL experiment, the PL signal was dispersed

by a 0.3-m-focal-length monochromator and detected by a

streak camera system equipped with the S1 photocathode. The

overall time resolution was on the level of20ps.The CWPL

emission was measured using the same setup with the InGaAs

CCD linear array detector. The PR experiment has been

performed at room temperature on a separate setup described

in Ref. 13 (low-temperature PR has not been used due to strong

PL background). In order to compare the low-temperature CW

PL spectra with those obtained in the PR experiment, the latter

were shifted according to the temperature-induced band-gap

shift.

III. EXPERIMENTAL RESULTS

The high-excitation CW PL and PR spectra for investigated

structures are shown in Fig. 2. The QDref PL spectrum reveals

two emission bands centered at 1.25 and 1.31 eV. They are

FIG. 1. (Color online) The layer sequence of the coupled-system

(CS) structure (top), together with a simple sketch of the valence

band (VB) and conduction band (CB) energy profiles of the region

of interest (bottom). The QW ground state (GS) and QD GS denote

optical transitions between states primarily localized in the QW and

QD, respectively.

FIG. 2. (Color online) High-excitation, low-temperature CW

photoluminescence (red line) and room-temperature photoreflectance

spectra (blackline, shifted to higher energy accordingto the band-gap

temperature change) of a reference QD structure (QDref, top panel)

and coupled quantum dotquantum well systems (CS1CS3, bottom

panels).

attributed, respectively, to the ground-state and excited-state

transitions in the ensemble of dots. In the case of coupled

systems (CS1CS3), the interpretation of PL spectra is not so

evident. However, the lowest PL emission band centered at

1.22 eV can be assigned to the dipole-allowed ground-statetransition of the entire QDcoupledQW system. To identify

the origin of the higher-energy optical transitions, we per-

formed the PR experiment. The PR spectra presented in Fig. 2

for the coupled structures reveal a weak feature at 1.22 eV,

which corresponds well to the ground-state QD transition

observed in the emission spectrum. At the higher-energy side,

there appears a considerably more intensive PR resonance,

which changes itsposition from 1.348eV for theCS1 structure,

to 1.315 eV for CS2, down to 1.278 eV for CS3. This optical

transition involves confined states in thecoupled system, which

have acquired a significant amplitude of the eigenfunction on

the QW side (see sketch in Fig. 1, bottom). The transition

matrix elements between states primarily localized in the

QW (QW-like states) will exceed those of the QD-like or

mixed-type character, which are indirect in the real space.

Consequently, this should lead to the experimentally observed

increase in the PR resonance intensity contributed by a large

oscillator strength of such an optical transition. The spectral

redshift of the QW-like transition in the coupled system is

strongly related to the In content in the well and its width.

These two parameters define the QW potential depth and

thus can control the coupling regime of the coupled-system

fundamental state. One would expect that if the QW-like

transition is energetically closer to the ground-state transition

of the entire system, then the coupling strength increases. Such

a tentative hypothesis holds for the structures under study,

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INFLUENCE OF ELECTRONIC COUPLING ON THE . . . PHYSICAL REVIEW B 85, 125311 (2012)

FIG. 3. (Color online) Schematic picture of the square of wave

function moduli in the x-y plane (top panels) and in the cross section

along the z (growth) axis (bottom panels) for three coupling regimes.

as we will prove later. The energy distance E between the

QW-like andthe ground-state transition is equal to 128, 95, and

48 meV, respectively, for the CS1, CS2, and CS3 structures,

as illustrated in Fig. 2. The three possible coupling regimes

are schematically depicted in Fig. 3. The noncoupled regimeis characterized by the carrier probability density |(r)|2

restricted essentially to the QD area, while in the weakly

coupled QDQW system, the probability density slightly leaks

out from the QD confining potential toward the QW. Finally,

in the strongly coupled system, the carrier |(r)|2 is smearedover both the QD and QW confining potentials.

Let us turn to the QDref and CS structures ground-state

emission dynamics. The electron-hole recombination process

can be described within the scattering theory, which is usually

summarized in Fermis golden rule, which connects the

electron-hole pair radiative decay time () and the transition

oscillator strength (fosc) in the following expression: 1

fosc, while fosc |e,h(r)|2

. It leads to the conclusion thatmeasuringthe radiative decay timemaps out the spatial overlap

between the electron and hole wave functions and thus gives

insight into the coupling regime of the investigated system.

Figure 4(a) presents TRPL traces taken at the maximum

of the ground-state emission band for (In,Ga)As/GaAs QDs

(QDref) and (In,Ga)As/GaAs coupled QDQW structures

(CS1CS3) with different In content in the QW, and thus

different E. The structures were excited nonresonantly with

photons of 1.6 eV energy and the average pump power density

ofP = 0.42 W cm2. These excitation conditions correspond

to less than a single electron-hole pair generated per dot.

Note that the CW PL measurements presented above were

performed at a much higher excitation density than in the

TRPL experiment in order to obtain the emission from the

excited states of the system. Each of the experimental TRPL

traces can be described by a single exponential decay process:I (t) = A e(t/PL), where A is the preexponential factor andPL is the emission decay time constant. The fitting function

is given as a straight line in Fig. 4(a) in a semilogarithmic

scale. Since the experiment was performed at low temperature

(T = 4.5 K) and in weak excitation conditions below the level

corresponding to a single electron-hole pair created per dot,

we believe that the obtained PL is not considerably modified

by nonradiative recombination processes and/or multicharging

effects. Thus, PL is very close to the intrinsic electron-hole

radiative recombination time; see, e.g., Refs. 1416. However,

arb.units

FIG. 4. (Color online) (a) Low-temperature TRPL traces (open

circles) taken at maximum of PL intensity for (In,Ga)As/GaAs

QDs (QDref) and (In,Ga)As/GaAs QDQW coupled systems (CS1

CS3). The solid line indicates the fit to the experimental data.

(b) Experimental (full circles) and theoretical (open circles) PL

decay time constants vs detuning energy (E). Error bars are for

the theoretical values based on the uncertainty of the value of the

refractive index (5%). Dashed line indicates the PL decay timeconstant for the reference QD structure. Dotted line is a guide to

the eye. Laser photon energy is 1.6 eV, Ppump = 0.42 W cm2.

recent papers by the group of P. Lodahl17,18 claim that the

nonradiative component to the measured decay time of QD

emission cannot be neglected, thus the radiative decay time

is, in fact, probably longer than the measured one (the

difference being on theorder of 1020%, accordingto Ref. 18).

Even if this is true also for the structures investigated here

(which is not evident, since the PL decays we registered are

monoexponential, contrary to the ones in Refs. 17 and 18),

the potential changes in the nonradiative processes, which

decrease the total decay time, explain neither the directionof the changes in the lifetimes measured for coupled systems

nor their magnitudes.

The PL vsE in the coupled system is plotted in Fig. 4(b).

The QDref ground-state recombination time is shown by a

dashed line at the level of PL = 1.1 ns resulting from the

intrinsic properties of a set of similar QD emitters of a given

size, shape, and chemical content. If we assume that an in-

plane coupling between QDs is negligible, these QDs can

be treated as a good example of a quantum system being in

the noncoupled regime. The PL is defined in this case by

the spatial coherence of an electron-hole pair confined in the

QD.19,20 A very similar PL decay time of 1.1 ns has been

obtained for the CS1, where the QD structure was modified

by introducing the 15-nm-wide (In,Ga)As QW with 17% of

indium, and separated from the QD layer by a thin 2-nm-wide

GaAs barrier. An almost identical decay time constant for

the CS1 and QD structures suggests that the emitter has the

same or very similar parameters in both cases.It brings us to the

conclusion that the ground-state emission in the CS1 system

originates from the radiative recombination of electron-hole

pairs localized primarily in the quasi-0D potential of the dot.

Moreover, the dot itself remains in the noncoupled regime,

where the CS1 ground state is not significantly perturbed by

the presence of the QW [see Fig. 3(a)].

A considerable increase in the PL lifetime is observed for

the CS2 and CS3 structures compared to the QDref one. In

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FIG. 5. Excitation-power dependence of low-temperature PL

decay times.

order to explain the increase in PL for CS2 and CS3, we

exclude a number of effects which could have an impact on

the elongation of the decay time constant, and conclude that

it can only be affected by the increasing electronic couplingstrength in these structures, leading to the reduction of the

electron-hole wave-function overlap. We discard the following

alternative explanations:

(1) the ground-state filling effect similar to the one observed

in QDs;

(2) modification of the QD surface density, leading to the in-

plane coupling between them, thus increasing the probability

of charge-transfer processes or smearing the carrier probability

density function between adjacent dots;

(3) change of the dot size and/or shape, thus affecting the

coherence volume.

The ground-state filling effect is commonly observed at

high optical pumping regimes. In order to investigate thispossibility, we have measured the excitation-power depen-

dence of PL decay times for all samples. Figure 5 shows the

determined PL lifetimes for theQDref and CS1CS3structures

as a function of excitation-power density. The PL, for the

QDref and CS1, does not exhibit significant changes over the

three decades of the average excitation-power densities. On

the other hand, for CS2 and CS3, an increase in the excitation

density from 0.42 to 30 Wcm2 causes a noticeable increase

in PL from 1.33 up to 1.7 ns, and from 1.82 up to

3.5 ns, respectively. This can be explained by the state filling

due to the constant refilling of the ground state from the upper

lying states of the system. However, for both structures, there

is a range of excitation-power densities where the lifetimes

are almost constant andstill therelation between therespectivePL is conserved, meaning that the state filling effect alone

does not explain the observed behavior.

The QD ground-state radiative decay time can be modified

by the electronic coupling within the QD layer, which is

essentially controlled by the QD surface density or by changes

in the QD size. However, the growth process parameters for

the QDref and CS structures were the same. Although some

change in the QD size parameters could occur due to the

fact that the dots in the CS structures are grown on top of

the QW, we do not expect a considerable increase in the QD

surface density because the modification of strain is negligible,

as shown by our calculations and structural data. For the

same reason, the QD size will be affected only very slightly

and hence the coherence volume can also be assumed to be

constant. Considering the interdot coupling, for the dot surface

density of 1010 cm2, the average distance between two

adjacent dots in the layer exceeds 70 nm, which makes the

direct electronic coupling between them negligible.

IV. NUMERICAL CALCULATIONS

The TRPL experiment cannot identify whether the elec-

tronic coupling is related to the conduction- or valence-band

states simply due to the fact that we probe the temporal

evolution of the product of photogenerated electron and hole

distribution functions. To shine some light on this issue, we

have performed three-dimensional band structure calculations

of reference QD and coupled QDQW systems. We have

developed a 3D eight-band kp model, whose implementationincludes strain fields,21 piezoelectric effects, and spin-orbit

interaction.22,23 For simplicity, we neglected the Coulomb

correlation between electron-hole pairs (excitons). We believe

that even without taking into account excitons in our model,we can still well explain the observed experimental results

in a qualitative way. However, we discuss later the possible

influence of the Coulomb correlation between the electron and

hole on the radiative lifetimes. Potential approaches to the

modeling of the exciton are given in Ref. 24. All physical

equations were numerically solved using the finite-difference

method.22,23 The calculation of the ground-state energy level

in the QD and CS structures is performed in a similar approach

to Ref. 25, with some modifications. One is the introduction

of the effect of nonlinear piezoelectricity (which, however,

does not have a considerable influence on the current system

due to the small sizes of investigated QDs).22,26 Another,

more important modification is the proper inclusion of theboundary conditions that would correctly take into account the

existence of a QW-like substructure separated from the QD.

Typically, in order to calculate QW energy states, the 1D

picture is usedwith the confinement potential along the z

direction and a geometric translational symmetry used for

other directions, with free particlelike picture solutions. On

the other hand, in the standard QD-like structures, imposing

the Dirichlet boundary condition is sufficient. However, in our

case, we have to be able to calculate the energy levels in a

QW in the same 3D picture as for the QDs. Therefore, we

impose in our model the periodic boundary conditions so that

we can calculate the QW states in the 3D model, which agree

very well with the states calculated in the 1D model, even with

the strain-related effect switched on. The material parameters

connected with the piezoelectric effect are taken from Ref. 26.

Other necessary material parameters are from Ref. 27 without

any changes.

As a test of the model, we have determined the energy-

level structure of the standalone QD. Based on the structural

data, we assumed a pyramidal QD with a base length of 16

nm, truncated at 1.7 nm and sitting on a wetting layer, which

is 3 ML thick for this In content.28 The In0.5Ga0.5As QD is

immersed in the GaAs matrix. Lattice constants and energy-

band gaps are taken at T = 4.2 K. The calculated QD ground-

state energy is 1.25 eV, whereas the excited-state energy is

1.31 eV. It remains in a very good quantitative agreement with

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FIG. 6. (Color online) Projection of the 3D probability density

function for electron and hole ground state onto the x-y-z plane

calculated for the QD (top panels) and coupled QDQW system

(bottom panels) with 7-nm-wide QW and In content of 27% in the

well.

the PL spectrum in Fig. 2. In this respect, such a QD can be

treated as a good representative of the real QD family probed

in the experiment.

Once the QD band structure was established, we performed

further numerical calculations of the coupled QDQW system.

For the sake of the discussion given above, we were mostly

interested in fundamental energy levels and respective eigen-

functions for conduction and valence bands. We consistently

kept the same QD parameters, but changed the indium content

of the InxGa1xAs QW. In order to obtain a good agreement

between the numerical and experimental values of the energiesof the ground-state transitions, we tuned the [In] of the CS1

sample to 17%. In the next step, we performed calculations

for QW compositions around the nominal values for the two

QW widths ofd= 7 and 15 nm to determine the dependence

of PL lifetimes on QW parameters.

Figure 6 shows an example of the ground-state electron and

hole probability density ||e,h(r)|2 in the modeled standalone

QD and for coupled systems. It is clearly visible that in the

former case both the electron and hole are tightly localized

within the QD confining potential. However, if we only

introduce a QW with sufficiently high In content beside

the QD, then the electron wave-function density previously

localized in the dot pours out and feels the 2D confining

potential of the well. Note that the hole still remains strongly

confined within the QD, showing no difference with respect

to the standalone QD case. To provide more details, we have

calculated the fraction of a probability density function for the

electron and hole within the QD spatial area. We have plotted

it in Fig. 7 as a function of the In content in the InxGa1xAs

QW and the QW width.

First of all, the hole wave function is always strongly

limited to the QD area independently of the considered In

content in the well and the well width [see open and closed

circles in Fig. 7(a)]. Moreover, it is exactly the same as for

the standalone QD. It brings us to the conclusion that there

is no electronic coupling between the lowest-lying hole states

FIG. 7. (Color online) (a) The probability of finding a hole

(circles) or an electron (squares) on the QD side of the barrier

as a function of indium content in the QW, for two QW widths.

(b) Analogical dependence for calculated radiative lifetimes. Dotted

lines are a guide to the eye.

confined in the system with the QW. It becomes considerably

different in the case of electrons. The square of the electron

wave-function modulus even for the standalone QD is only

partially localized within the QD area, while the rest leaks

out to the environment. It does not change for the QDQW

system as far as the In content is low and is weakly dependent

on the well width. However, when the In content increases,

the lowest-lying electron state in the structure with QW is

transformed from noncoupled first to weakly and next-to-

strongly coupled regimes. The electron probability density is

then distributed over the QW and QD confining potential. For

a relatively high percentage of indium in the (In,Ga)As QW,

the lowest-lying electron wave function is almost fully out of

the QD. We can now translate the observed effects into the

radiative decay time of an electron-hole pair in the coupled

system being in its ground state.

The oscillator strength fosc is given by the equation

fosc =2

m0

|e |e p|h|2

Ee Eh, (1)

FIG. 8. (Color online) The calculated coupled QDQW system

band structure.

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where e, h are the 3D electron and hole single-particle

envelope functions with the energy Ee and Eh for electron

and hole, respectively, e is the polarization unit vector ofthe electromagnetic field, and p is the electron momentum.The momentum matrix element calculation also takes into

account the strain,29 and because of time-reversal symmetry

degeneration, incoherent averaging30 is used. The QD radiative

lifetime is inversely proportional to the oscillator strengthfosc as described by the following equation:

31

=60m0c

3

ne21

20fosc, (2)

where 0 = (Ee Eh)/h is the optical transition frequency, n

is the refractive index, m0 is the free electron mass, e is the

electron charge, and 0 is the vacuum permittivity.

Figure 7(b) illustrates calculated electron-hole radiative

lifetimes of the CS ground state vs the In content in the

QW. The point at In = 0% corresponds to the calculated

lifetime for the standalone QD, which is 1.0 ns. It fits quite

well the measured PL lifetime of 1.1 ns. As expected, forthe low [In], the ground state remains in the noncoupled regime

where the radiative lifetime is governed by the coherence

volumeoccupiedby the electron-hole pair. However, when[In]

exceeds a certain value, the radiative lifetime increases rapidly.

It is driven by the reduction of the electron-hole wave-function

overlap, which decreases the transition oscillator strength. In

this case, the system is already transformed to the coupled

regime. Qualitatively, the same tendency as in Fig. 7(b) is

observedfor measured PL lifetimes presentedin Fig.4(b), with

experimental lifetimes shorter than the calculated ones. This

discrepancy can be related to the lack of Coulomb interactions

in the model. The effect of Coulomb correlation on oscillator

strength depends on the confinement degree of carriers in eachof the QDQW coupled systems. Whereas holes are strongly

confined to QDs for all of the samples, the electron wave

function is localized in the QD for the reference and CS1

samples only, and spills out progressively more to the QW

layer for samples CS2 and CS3. Since the dots under study

can be considered small (the excitons Bohr radius exceeds the

dot dimensions), both typesof carriers in the referenceand CS1

samples are in the strong confinement regime, where quantum

confinement effects overwhelm the Coulomb interactions and

excitonic effects can be neglected.3234 The situation becomes

different for samples CS2 and CS3, where a considerable part

of the electron wave function is in the QW layer, i.e., separated

in the real space from the hole wave functions, meaning that

the confinement has been weakened. In this case, the Coulomb

attraction might be moreimportant; electronsare pulled toward

the positions closer to QDs, increasing the oscillator strength

and thus decreasing the lifetimes. The theoretically predicted

radiative lifetimes presented in Fig. 4(b) are expected to be

in better agreement with the measured ones if the Coulomb

correlation is included. Another reason for the divergence

between experimental and calculated lifetimes for the samples

with electron wave functions delocalized from QDs may

be the increasing nonradiative component to the measured

values, resulting from the electron scattering on the GaAs

barrier/interface states, providing nonradiative recombination

channels.

V. APPLICATION OUTLOOK

The experimental results presented above, supported by

theoretical consideration, can be of immediate relevance to the

device performance, where the coupled QDQW system plays

a crucial role. Here we will particularlyreferto tunnelinjection

(TI) lasers.79,12 Despite the fact that the results presented

above on the carrier dynamics and electronic structure inInGaAs/GaAs TI structures concern low-temperature data, the

conclusions can be at least extrapolated to room temperature,

i.e., normal conditions of the laser device operation. The

energy-level structure and hence the spatial distribution of

the probability densities for both types of carriers will not

change significantly at room temperature. For the structure

CS3, the measured energy difference (48 meV) between the

lowest electron and hole energy levels of the confined carrier

states in both parts of the system, i.e., in the QD-like and

the injector QW-like lowest levels, seems to not be very well

matched with the characteristic energies of the LO phonon

(35 meV) in GaAs. However, the related energy separation

between the respective QW-like and QD-like transitions is not

shared equally between the conduction and valence bands.

Our calculations show that the ratio is about 1:3 in favor of the

valence band (mainly due to the larger effective mass of the

holes and hence a much deeper confinement of the lowest hole

state within the QD potential; see Fig. 8), which gives around

36 meV for the holes. Moreover, with increasing temperature,

the carriers become distributed over the states of the QW sub-

band in the injector, and hence the energy difference between

the hot carriers in the injector and the lowest state in the dot can

approach the LO phonon energy also for electrons. This means

that an efficient carrier transfer mediated by an LO phonon can

take place in structures like the CS3. This is actually confirmed

in the experimental data of TI devices (Ref. 12), where a very

similar active region has been used, and where improvementsin the laser performance have been observed.

VI. CONCLUSIONS

In conclusion, we have investigated the role of cou-

pling strength on the ground-state carrier dynamics in self-

assembled (In,Ga)As quantum dots coupled to an InxGa1xAs

quantum wellthrough a 2-nm-wide GaAs barrier. Thecoupling

strength is controlled through the variations of the In content

in the well and the well width, and is directly monitored by

measuring the fundamental state PL lifetime of the systems

with the QW and the reference QD structure. The PL decay

time constant of 1.1 ns obtained for reference QDs and CS1

confirms that the latter system with In content of 17%

remains in the noncoupled regime in which the electron and

hole wave functions are not affected by the QW confining

potential. Increasing the In content leads to the elongation

of the PL lifetime of several hundreds of ps. This effect

is directly connected with the transformation of the related

fundamental eigenstates from a noncoupled to a coupled

regime, which was fully confirmed by the 3D band structure

calculations of the coupled systems. Moreover, the numerical

calculations suggest that in the structures with high indium

content, an increase in the coupling strength is related to the

delocalization of the electron wave function from 0D to 2D

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confining potential of the well, whereas holes remain strongly

localized in the QD.

ACKNOWLEDGMENTS

This work has been supported by the Polish Min-

istry of Science and Higher Education within Grant No.

N N515 518338 and by the DeLight Project No. 224366, 7th

Framework Programme of the European Commission. The

fellowship support for M.S. is co-financed by the European

Union within the European Social Fund. Part of this work

has been realized within the NLTK infrastructure, Project No.

POIG.02.02.00-00-003/08-00.

*[email protected] address: National Institute of Research and Development

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