Single Quantum Dots: Fundamentals, Applications, and New Concepts

355 Pages·2003·8.53 MB·English

by  Pierre M. Petroff (auth.)

Epitaxial Growth and Electronic Structure
of Self-Assembled Quantum Dots
Pierre M. Petroff
Materials Department,University of California,
SantaBarbara, CA 93103, USA
[e-mail]
Abstract. Semiconductor self assembled quantum dots have emerged as one of
thesimplest meansofexploringandexploitingthephysicsanddeviceapplications
of carriers and excitonsin thethreedimensional confinementregime. This chapter
covers the epitaxial growth processes involved in the formation of self-assembled
quantum dots. A numberof approaches for self-ordering and positioning quantum
dots using direct epitaxial growth are also developed. The electronic structures
of quantum dots using capacitance and luminescence spectroscopy techniques are
presented to demonstrate the analogy between the quantum dots and “artificial
atoms”. To emphasize the difference with the properties of the isolated artificial
atom, the role of the quantum dot coupling to the outside environment and the
importance of many-body effects on the electronic properties of the quantum dot
are also discussed. Finally we give examples of several quantum dot devices that
exploit some of the quantum dot electronic and optical properties. Some of these
quantum dot devices could lead to the implementation of quantum computing or
quantumcryptography applications.
1 Introduction
The use of strain induced islands as a process for forming self assembled
quantum dots (QDs) [1] in III–V semiconductors using epitaxy has been
part of a large effort to exploit the novel quantum properties which arise
from the three dimensional (3D) quantum confinement of carriers and ex-
citons. The other methods for producing self assembled QDs are based on:
a) the monolayer thickness fluctuations of a quantum well [2]; b) the elec-
trostatically defined quantum dots in a two dimensional electron gas [3]; or
c) the self-assembly of colloidal clusters using solution chemistry [4]. Each
method has its strength and weaknesses and it is safe to say that presently,
the epitaxial self-assembly method provides the best means of incorporating
quantumdots into a wide variety ofdevices andexploitsomeoftheir unique
properties [5,6,7,8]. It should also be mentioned that the carrier confine-
ment provided by the self-assembled quantum dots is much larger than that
provided by the electrostatically defined quantum dots or by the quantum
well-quantumdots[2].Theseself-assembledQDshavealsoprovidedaconve-
nient “laboratory bench” for studies of carrier confinement and many-body
effects in semiconductors.Because of the possibility of band gap engineering
P.Michler(Ed.):SingleQuantumDots,TopicsAppl.Phys.90,1–25(2003)
(cid:1)c Springer-VerlagBerlinHeidelberg2003
2 Pierre M. Petroff
theselfassembledQDstructures,ithasbeenpossibletomakeawidevariety
of solid state devices such as electrically pumped QD lasers [6,9] or infrared
detectors [10] some of which are now near the industrial production stage.
The role of self assembled islands as an efficient strain relieving process
was first identified in the investigation of SiGe/Si strained layers [11] and
the growth of self assembled islands as a useful method to fabricate QDs [1]
was also recognized later. The direct crystal growth of self-assembled QDs
hasbeenwidelyappliedtoavarietyofstrainedlayersemiconductorsystems:
severalIII–V compounds systems aswellas II–VI andgroupIVheterostruc-
tures systems [5,6,7] and wide band gapIII–V compounds [12] allow a range
of wavelengths between 0.3µm and 1.5µm to be spanned.
The formation of QDs using epitaxy is based on the deposition of an
epitaxial film on a lattice mismatched substrate. The elastic strain energy
during the film deposition builds up as the square of the lattice strain. The
totalenergyinthefilm,includingstrainenergy,interfacialenergyandsurface
energy,willbeminimizedduringgrowththroughtheformationofcoherently
strained islands at the surface. These islands are transformed into QDs by
embedding them into a larger band gap material.
This chapter covers the crystal growth processes involved in the QD for-
mation using epitaxy as well as some of the newer methods for producing
self-orderedQDlattices.We reviewsomeofthe QDelectronicpropertiesrel-
evant to the shell atom model which applies to the self-assembled QD elec-
tronicstructure.WethenuseexamplesofQDdeviceswhichmaybeinvolved
in the implementation of quantum computing and quantum cryptography.
Throughoutthis contribution, we will take the InGaAs/GaAs QD system as
a model system since it has been the most extensively studied.
2 Formation of Quantum Dots, Quantum Rings
and Strain Effects on Island Nucleation
Thermodynamics and kinetics are both involved in the formation of self-
assembledquantumdots.Todiscussthenucleationandgrowthoftheislands,
we will take the InAs/GaAs system since this is the one which has been the
most studied. For this system, the InAs is in compression to accommodate
thestrainassociatedwiththesmallerlatticeconstantoftheGaAs.Theinitial
stageintheQDformationistheformationofislandsduringdepositionofan
epitaxial layerwith a small lattice mismatch(a few percent) on a crystalline
substrate. As illustrated in Fig. 1 for the case of III–V compounds semi-
conductors deposited by molecular beam epitaxy, In and As atoms falling
on a clean GaAs substrate held at high temperature will self assemble into
smoothdefectfreeepitaxialatomiclayersifthelatticemismatchbetweenthe
materialdeposited andthe substrateis not toolarge.The diffusion lengthof
some of the groupIII elements deposited by molecularbeam epitaxy (MBE)
are sufficiently large to insure the layer by layer growth until a build up in
Epitaxial Growth and Electronic Structure 3
Fig.1.SchematicoftheislandgrowthprocessillustratedforthedepositionofInAs
on GaAs. Capping of the islands will transform the islands into quantum dots.
An increase in the film thickness beyond the island formation stage will produce
island coarsening and theintroduction of misfit dislocations. The graph shows the
criticalthicknessforislandformationmeasuredexperimentallyasafunctionofthe
In content x in the InxGaxAs layer. The three fields in this plot distinguish the
three growth regimes: layer-by-layer growth, island growth and layer growth with
dislocations. The lower field region characterizes thethicknessof the wetting layer
connecting thequantum dots
the strainand surfaceenergyof the epitaxialfilm switches the growthto the
island growth mode. This change in the surface morphology is induced by
the minimization of the total film energy. This interplay between the strain
andsurfaceenergyofthe filmcanbe used,aswewillseelater,to controlthe
island nucleation and promote self-ordering of islands.
Figure 1 also shows that increasing the film thickness, for a given com-
position of the InxGa1−xAs alloy, beyond the island formation stage will in-
troduce misfit dislocations. The formationof a thin wetting layer is inherent
to the island formation process. However as indicated in Fig. 1, the wetting
layer can become very thick (up to 30 monolayers)for low In content in the
film.Inthiscase,thewettinglayerthicknessapproachesthatoftheQDsand
will play an important role in the carrier confinement and relaxation pro-
cesses and device characteristics since the active layer of the device becomes
a corrugated quantum well or quantum well coupled to a QD layer.
The growth of self-assembled quantum dots is achieved by covering the
smaller band gap material of the islands with a wider band gap epitaxial
film. The islandcoveringstep will drasticallychange the islandcomposition,
shape and dimensions.
A listing of some of the general structural characteristics for this type of
QDisinformativeasabackgroundfordesigningQDdevicesandunderstand-
ing some of their physical properties:
a) TheislandsandQDsarealldeposited“insitu”inareactorandarecoher-
ently strained and their growth remains essentially defect and impurity
4 Pierre M. Petroff
free. This view is supported by the very high internal quantum efficiency
for optically pumped QDs.
b) The epitaxial QDs can easily be incorporated within an epitaxial struc-
ture thus making it possible to use band gap engineering techniques for
electrical or optical injection and developing novel devices.
c) The QD size distribution is poorly controlled. Their size dispersion is in
general ≈ 10% and is a function of the substrate deposition tempera-
ture and surface growth kinetics. Although the initial nucleation of is-
lands takes place preferentially at surface step edges, random nucleation
events on terraces will eventually dominate as the QD density is increas-
ing. Random island nucleation and coarseningkinetics during growthare
controlling the size distribution.
d) The exact shape, dimensions and composition of QDs are not known ac-
curately. Although the island shape and dimensions are well character-
ized using atomic force microscopy (AFM) [13,14], they will dramatically
change during the capping by the wider band gap film. Surface exchange
reactions and diffusion processes are playing an important role on the fi-
nal shape, dimensions and composition of the QDs. Detailed studies of
the QD composition in the InAs/GaAs system using X-ray diffuse scat-
tering and AFM haveshownthe presence ofanIn concentrationgradient
within the QDs [15]. The existence of this gradient and its magnitude
should strongly depend on the deposition conditions. In many instances
theshapeoftheislandisnotahemisphericalcapandismoreoftenatrun-
cated pyramid. The elongated base of this pyramid reflects the crystallo-
graphic orientation dependence of the diffusion coefficient of the species
during growth.
Several of these characteristics can affect the properties of quantum dot
devices and a great deal of effort has been directed to address some of these
problems.
3 Positioning and Ordering Quantum Dots
The absorption coefficient of QDs is small and for some device applications,
a very high local QD density would be desirable. This would be the case for
QDlaserorfarinfrared(FIR)photodetectordevices[9,10].Theoptimization
ofcoupledQD-microcavitydeviceswillalsorelyheavilyonthecontrolledpo-
sitioning and ordering of QDs. In fact, controlling the island nucleation sites
and density are difficult problems which involve both the thermodynamics
and kinetics of growth. We discuss in this section two techniques which are
yielding promising results.
The first method uses the directed migration of adatoms to a localized
surface site that will promote preferential nucleation. This can be achieved
byengineeringthesurfacechemicalpotential[16,17,18]usingapre-patterned
Epitaxial Growth and Electronic Structure 5
Fig.2.Schematicsoftwopossibleconfigu-
rations for controlled nucleation on a pat-
terned substrate. (a) The strain distribu-
tion in the structure is illustrated by ar-
InGa As
(A) x 1-x rows and the InGaAs layer growth will
GaAs
preferentially occur in the valleys between
themesas.In(b)acoherentlystrainedIn-
GaAs stressor layeris usedtoenhancethe
strain on the mesa edge tops. The growth
InGa As of islands will preferentially occur on the
x 1-x
(B) GaAs mesa topswhere thestrain buildup isthe
largest
Fig.3. AFM pictures of the GaAs {100} surface with surface depressions after
a GaAs buffer layer regrowth and an InAs thin layer deposition. In (a) the In flux
wasadjustedtogrowbetweenonaverage2InAsislandsperdepression.Thefeatures
observed between the depressions have been identified as surface defects and not
QDs.In (b),thestatistical distribution of Inallows theformation of asingle InAs
island in some of thesurface depressions [19]
substratesurface.Aloweringofthesurfacechemicalpotentialduetocapillar-
ityeffectsinducesadrivingforceforadatomdiffusiontowardsaconcavesur-
face site and causes island nucleation before the critical thickness for island-
ing is reached in other parts of the surface. Figure 2a illustrates a patterned
surface and the preferential growth of the InxGa1−xAs QDs taking place
preferentially in the concave surface sites. This preferential accumulation of
InxGa1−xAs requires a fast In diffusion on the surface and is energetically
favored[19].ThelocalstressbuildupinducedbyathickerInxGa1−xAslayer
will trigger the InAs island nucleation first in these areas. An illustration
of the technique is shown in the atomic force microscopy (AFM) pictures
(Fig. 3). In this example, the periodicity between the surface depressions
formed by e-beam lithography prior to the InAs deposition is 4µm.
The InAs islands are found to form only in the surface depressions. The
measured In surface diffusion using this technique is ≈15µm.
6 Pierre M. Petroff
One of the drawbacks of this approach is associated with the formation
of facets in the surface depression which takes place during the regrowth of
a thin GaAs buffer layer following the pre-patterning step. The formation of
anInrichwirelikeregionatthejunctionoffacetscantakeplacepriortothe
formationofthe QDsandthe resultingcouplingbetweenthewirelikeregion
and the QDs may be problematic for some devices.
3.1 Island Nucleation and Quantum Dot Lattices
Bycontrollingtheislandnucleationprocesstowelldefinedareas,itispossible
to minimize random nucleation and improve the island size uniformity. The
interaction of strain fields between nucleating islands can promote nearly
identicalgrowthratesforallislands.Thismethodwasinitiallyintroducedto
orderislandsonamesaridgewherethediffusionkineticsfavoredabuildupof
strainononeedgeofthemesa[16].Usingthismethod,stringsofInAsislands
wereproducedinapatternedGaAssurfaceandMonteCarlosimulations[17]
support the view that enhanced island interactions will induce a significant
narrowing of the island size distribution.
The thermodynamics and diffusion kinetics of the In atoms are changed
during growth by introducing a local sub-surface strain field. As shown in
Fig.2bthis canbe achievedby growinga coherentlystrainedfilmofInGaAs
below the surface. In this case, the InAs film will grow more rapidly on the
mesa tops and induce a preferential growth on InAs islands on top of the
subsurface stressors [20].
In this method, a substrate is first patterned using optical holography
and chemical etching on a GaAs surface to form a lattice of mesas. After
desorptionofthe nativeoxidefromthe GaAspatternedsurface,athinGaAs
buffer layer and an InGaAs stressor layer are deposited by molecular beam
epitaxy (MBE) (see Fig. 2b). The InGaAs islands are then deposited after
athinGaAslayerisdepositedontopofthe InGaAsstressorlayer.As shown
in the AFM pictures (Fig. 4), the lattice orientation can be adjusted by the
orientation of the mesa lattice on the pre-patterned substrate. The number
ofislandsinthelatticebasisisfoundtodependonthemesashapeandwidth
and on the In flux.
A finite element calculation of the strain distribution in these structures
indicates that the InAs islands nucleate at the surface sites where the stress
is highest, i.e. the mesa edges and end points of the mesa ridges [20]. This
effect is supported by experimental results shown in Fig. 5a. InAs islands
lattice with a basis of one, two or three islands is deposited using a reduced
InfluxcomparedtothatshowninFig.4.Thestraindistributiononthemesa
surface controls the island nucleation sites. The number of islands per mesa
will greatly depend on the shape of the mesas and on the In flux. In Fig. 5b,
a double rowof islands is observedoneachmesa since the mesa topis larger
than ≈60nm.
Epitaxial Growth and Electronic Structure 7
Fig.4.ExamplesoforderedInAsislandlattices[7].TheInAsislandsaredeposited
onaGaAspatternedsubstrateandtheschematicoftheunitcellofthesetwolattices
corresponds to each of the atomic force micrographs. The mesa lattice parameter
is ≈250nm [20]
Fig.5. (a) Atomic force micrograph of a lattice of mesas on which InAs islands
weredepositedusingthestrainengineerednucleationmethod.QDsappearasbright
spotsontopofthemesa.Notethatthenumberofislandspermesavariesbetween
one and three. The islands nucleate preferentially on the surface sites where the
strain is maximum. (b) A double row of QDs is deposited on each mesa when the
mesatopislarger.Themesalatticeparameteris410nm.Cross-sectiontransmission
electronmicroscopyofthesedevicesrevealstheexistenceofathinwettinglayeron
themesa top
Developinga processingthat allowsto reproducibly fabricate mesaswith
the desired dimensions and shapes is crucial to further progress in this field.
The sub-surface stressorapproachallows for the highest possible island den-
sity locally. Under optimal conditions and for a pyramidal shape mesa, one
should be able to form lattices with one island per mesa.
Onceatwo-dimensionalislandlatticeisformedonthesurface,thegrowth
ofathree-dimensionalislandlatticeusingthestraincoupling[21]betweenis-
landlayersiseasilyachieved.AsshowninFig.6,thetwo-dimensionallattices
of islands is replicated along the growth direction through the preferential
nucleation of islands on top of each other along the growth direction if the
interlayer spacing is smaller than ≈12nm.
The challenge for the future will be to reduce the size of the unit cell
by developing a patterning process which is cheap and suitable for a rapid
processing of large areas.Making this process compatible with the band gap
engineeringofthedesireddevicescouldalsoberequired.Thismaybedifficult
8 Pierre M. Petroff
Fig.6. Cross-section TEM through a three-
dimensional quantumdot lattice. The InAsstacked
quantum dots along the (cid:4)100(cid:5) growth direction are
separated by a 10nm thick GaAs layer. The quan-
tum dots are detected through their strain fields.
Thebottom schematicisanidealizedreconstruction
of the three-dimensional quantum dot lattice with
the dimensions of theunit cell indicated
in some instances since the InGaAs stressorlayerbehavesas a quantumwell
which may interfere with the intended functionality of the device.
The nucleation site engineering method may be a very useful approach
for increasingthe QD density andthis may leadto largeimprovementin the
gain characteristics of QD lasers [9]. The lateral coupling of QDs on mesa
tops may also provide new avenues to control the absorption characteristics
in QD infrared detectors [10].
4 Strain Effects and Growth Characteristics
of Quantum Dots
Strainintheepitaxiallayerscontrolsnotonlythespeciessurfacediffusionand
interdiffusiononthesurfacebutalsothekineticsofnucleationandgrowthof
theislands.Theseeffectsareillustratedbyexperimentsinwhichtwoelectron-
ically uncoupled QD layers have been deposited under identical or different
growth conditions. These layers are close enough to each other to retain the
strain alignment of the QDs from one layer to the other yet it is too large
to allow electronic coupling of the energy levels between QDs of each layer.
Their photoluminescence spectra (Fig. 7) provide a rapid method of analyz-
ingtheirsizeand/orcompositiondistribution.Thedistance(12nm)between
the two QD layers is sufficient to insure strain coupling and a stacking of
the QDs in the 2 layers along the growth direction. This interlayer distance
is too large to provide an electronic coupling between the stacked QDs. The
growth conditions of the second layer are adjusted by using a partial cov-
erage of the islands (PCI) with various amounts of GaAs prior to the final
capping of the islands [22]. In Fig. 7 the PL spectra of island layers grown
under identical conditions show two peaks indicative of differences in their
size and/or composition.
Accordingtothemacro-PLspectra,theobserveddifferencesintheground
state energies (≈ 50meV) can be reduced to zero by changing the growth
Epitaxial Growth and Electronic Structure 9
Fig.7. (a) Photoluminescence spectra (excitation power 0.1µW, λexc = 633nm,
T =10K)from sampleswithahighdensityofvertically stackedQDs(d=120˚A).
The seed layer QD1 in each sample has 30˚A of GaAs partial capping, while the
partial capping in the 2nd QD2 layer is varied as indicated on each spectrum.
Gaussian curve fittings are applied to each curve to identify the two QD layer’s
ground state peaks. As the second QD2 layer’s PCI thickness is increased, the
ground state energy of that QD decreases [23]. The numbers associated with each
spectrum indicate the thickness (in ˚A) of the PCI layer for the first and second
layerofQDsrespectively.(b)Micro-photoluminescencespectraofasingleQDpair
from the sample indicated by the arrow in (a). The different micro-PL spectra
correspond to different pump powers
conditions (PCI thickness of≈4.1nm, Fig. 7a) for the secondQD layer[23].
Not surprisingly, the micro-PL spectra of this sample show that even with
a single macro-PL peak, the energy difference between the ground state ex-
citon luminescence for individual QD pairs is not zero and varies between
9 and 15meV depending on the QD pair. The energy separation for these
linescannotbeassociatedwithanelectroniccouplingbetweentheQDssince
the tunneling distance of 12nm is too large. Rather, a small change in the
size or compositionof the 2 QDs in a pair is responsible for the observedPL
structure. From this type of experiment and studies of the QD luminescence
in close proximity to a coherently strained quantum well, it has been shown
that the nucleation and growth of QD layers in a stack of layers is strongly
dependent on the presence of In floating or diffusing to the surface during
growth [23].
We conclude this section by noting that much remains to be done to
understand and control the nucleation, growth, positioning and ordering
of self assembled quantum dots. QD systems other than the well-studied
InGaAs/GaAs system should be explored. Surprisingly, little work has been
done with QD materials systems with wider band gap and larger confine-
ment energies. In QD systems such as AlInGaAs/AlGaAs [24] and GaN/
AlGaN [12,25], the conduction and valence band offsets are larger than in
10 Pierre M. Petroff
InGaAs/GaAs and the interband and inter-subband energy levels can be in-
creasedwithoutfurtherreducingthesizeoftheQDs.Agoodcontrolofthese
systems should permit the exploitation of QD devices which exhibit the full
potential of the three dimensional confinement at room temperature.
5 Fundamental Electronic Properties
of Self-Assembled Quantum Dots
The three-dimensional quantum confinement (3D) of carriers and excitons
confers “atom like” properties to the quantum dots. However, this analogy
should be carefully reconsidered since the contribution of the matrix (e.g.,
phonons) and the many-body effects should be taken into account. In this
section we review some of the important physical QD properties.
5.1 The “Atom-Like” Shell Model for the Quantum Dots
OneofthestrikingpropertiesoftheepitaxiallydepositedsemiconductorQDs
is their “atom like” electronic properties which originate from the three-di-
mensionalcarrierconfinementinsidetheQDs.Theexpecteddiscreteelectron-
icenergylevelshellstructurewasfirstobservedusingcapacitance(C-V)and
infrared spectroscopy measurements on large ensemble of InAs QDs [26,27]
embedded into a GaAs/AlGaAs MIS device structure. Figure 7 shows the
schematics of the device and the associated conduction band diagram.
The capacitance versus voltage spectrum (Fig. 8) for a diode containing
≈106 InAs QDs shows two series of peaks associated, respectively, with the
s- and p-shell loading when electrons are tunneling from the back n+ gate
as a positive voltage is applied to the front one. The width of the peaks is
due to the QD size dispersion and the large number of QDs (≈ 106) in the
measured device. The Coulomb charging energy corresponding to loading
of the second s electron peak into the s-shell is measured to be approxi-
mately 25meV. The four peaks corresponding to the p-shell loading reflect
the growth axis cylindrical symmetry of the QDs confining potential. The
electron energy difference between the s- and p-shell levels is found to be
∆E ≈ 50meV. A similar picture emerges for the hole shell structure of
es−p
InAs QDs. However the energy level differences for s- and p-shell holes are
smaller (∆E ≈ 10meV) than for electrons [27]. Modeling of the capaci-
hs−p
tance spectra based on the quantum tunneling of electrons from a back gate
reservoir into the QDs ensemble has confirmed the C-V spectra interpreta-
tion [28]. Measurements and modeling of the intra-subband levels using FIR
and capacitance spectroscopy have established that the confining potential
is roughly parabolic [5,26]. For the InAs/GaAs QD system, the conduction
andvalencebandoffsetsare≈400–500meVand≈70–100meV,respectively,
and the number of electrons which can be confined to the QDs is controlled
by their dimensions. Thus many-body effects due to exchange and Coulomb
interactions are expected to dominate at low temperature.