Table Of ContentSERIES EDITORS
EICKE R. WEBER
Director
Fraunhofer-Institut
für SolareEnergiesysteme ISE
Vorsitzender, Fraunhofer-Allianz Energie
Heidenhofstr. 2,79110
Freiburg, Germany
CHENNUPATI JAGADISH
Australian Laureate Fellow
andDistinguished Professor
Department ofElectronic
MaterialsEngineering
Research Schoolof Physics
andEngineering
Australian National University
Canberra,ACT0200
Australia
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CONTRIBUTORS
ErikBakkers
EindhovenUniversityofTechnology,Eindhoven,andKavliInstituteofNanoscience,
DelftUniversityofTechnology,Delft,TheNetherlands.(ch5)
SoniaConesa-Boj
EindhovenUniversityofTechnology,Eindhoven,TheNetherlands.(ch5)
VladimirG.Dubrovskii
St.PetersburgAcademicUniversity,St.Petersburg,andIoffePhysicalTechnicalInstitute
RAS,St.Petersburg,Russia.(ch1)
FrankGlas
CNRS—LaboratoiredePhotoniqueetdeNanostructures,Marcoussis,France.(ch2)
Mo¨ıraHocevar
InstitutNe´elCNRS/UJF,Grenoble,France.(ch5)
YoungJoonHong
FacultyofNanotechnology&AdvancedMaterialsEngineering,GrapheneResearch
Institute,SejongUniversity,Seoul,SouthKorea.(ch3)
NariJeon
DepartmentofMaterialsScienceandEngineering,NorthwesternUniversity,Evanston,
Illinois,USA.(ch6)
LincolnJ.Lauhon
DepartmentofMaterialsScienceandEngineering,NorthwesternUniversity,Evanston,
Illinois,USA.(ch6)
Chul-HoLee
KU-KISTGraduateSchoolofConvergingScienceandTechnology,KoreaUniversity,
Seoul,SouthKorea.(ch3)
Gyu-ChulYi
DepartmentofPhysicsandAstronomy,SeoulNationalUniversity,Seoul,SouthKorea.
(ch4)
HosangYoon
DepartmentofPhysicsandAstronomy,SeoulNationalUniversity,Seoul,SouthKorea.
(ch4)
vii
PREFACE
Prior to 1990 known as whiskers and nowadays as nanowires, filamentary
crystalswithadiameterinthenanoscalerrangehaverecentlyinspiredmany
scientistsandengineers.Thankstothesmalldimensionsandparticularlydue
to their special shape, nanowires have enabled novel applications and
improvedexistingonesinabroadrangeoffields.Theseincludethediscov-
ery of new phenomena in one-dimensional physics, next-generation solar
cells, lasers, solid-state lighting, biosensing, and integrated circuits. Addi-
tionally, they have provided an excellent platform to study crystal growth
in 1D and to synthesize materials in new phases, combinations, and archi-
tectures that are not possibly attained otherwise.
Obtaining nanowires with the tailored size, shape, crystal phase, orien-
tation, and composition profile is the key requisite for enabling any appli-
cation. Today, exquisite control on many of these properties has already
beendemonstrated,thankstothefocusedandextensiveeffortsofthescien-
tificcommunityinthelastdecadeswhichdevelopedimpressiveunderstand-
ingoftheirgrowthandoftailoringtheirproperties.Itisthereforetimelyto
disseminatetheseresultsandtoprovideacomprehensivetreatmentofnano-
wire growth and theory, particularly for the III–V and II–VI compound
semiconductor materials.
In this first volume, we review important aspects of nanowire growth.
The first chapter concerns with the theory of VLS growth in compound
semiconductors which is influenced by complex contributions of many
growth parameters that are not typically present in elemental whisker or
nanowiregrowth.Thesecondchaptertreatstheroleofstraininnanowires
andrelatedheterostructures,akeycharacteristicfortuningboththegrowth
and properties of semiconductor nanowires. The third chapter discusses a
recently emerging growth mechanism of 1D nanowires on 2D materials:
van der Waals heteroepitaxy. The fourth chapter comprises a summary
on the studies of position-controlled growth of ZnO nanostructures. The
fifth chapter provides one archetypical example of what nanowires enable
in contrast to thin-film technology: the quasi defect-free integration of
groupIVandIII–Vsemiconductorsinasinglestructure.Thesixthandlast
chapterreviewsatomprobetomographystudiesonnanowires,animportant
techniqueforthethree-dimensionalmappingofthechemicalcomposition
innanowires.Ourexamplesconcernsemiconductormaterials.Nevertheless,
ix
x Preface
the implications are in fact much more general and concern many more
materials systems.
AnnaFontcubertaiMorral,EcolePolytechniqueFe´de´raledeLausanne
Shadi A. Dayeh, University of California, San Diego
Chennupati Jagadish, Australian National University
Editors
CHAPTER ONE
Theory of VLS Growth of
Compound Semiconductors
Vladimir G. Dubrovskii1
St.PetersburgAcademicUniversity,St.Petersburg,Russia
IoffePhysicalTechnicalInstituteRAS,St.Petersburg,Russia
1Correspondingauthor:e-mailaddress:[email protected]
Contents
1. Introduction 1
2. FundamentalsofVLSGrowth 2
3. ChemicalPotentialsforAu-CatalyzedVLSGrowthofIII–VNanowires 11
4. GrowthKineticsofIII–VNanowires 15
5. Transport-LimitedGrowthofNanowires 18
6. NucleationRateinVLSNanowires 33
7. Position-DependentNucleationinNanowires 40
8. Self-consistentGrowthEquation 42
9. Ga-CatalyzedGrowthofGaAsNanowires 47
10. FormationofTernaryAu-CatalyzedIII–VNanowires 56
11. ImpactofGrowthConditionsontheCrystalStructureofIII–VNanowires 62
References 73
1. INTRODUCTION
This chapter deals with growth and structural modeling of vapor–
liquid–solid (VLS) III–V nanowires catalyzed by either Au or group III
metals. We have tried to balance a semi-quantitative description of the
VLSgrowthprocessandpresentationofthewell-knownresultswithsome
newlydevelopedmodels.Consequently,theexpositionofthechapteristhe
following.Section2containsanintroductiontotheVLSgrowthmethodin
the case of III–V nanowires, which should be helpful to the beginners.
Section 3describesthe drivingforce—the liquid chemical potential in ter-
naryAu-III–Valloys.InSection4,webrieflydescribetheVLSgrowthkinet-
icsinthesteadystatewheresignificantsimplificationsinmodelingbecome
possible. Section 5 presents a detailedanalysis of the transport-limited axial
SemiconductorsandSemimetals,Volume93 #2015ElsevierInc. 1
ISSN0080-8784 Allrightsreserved.
http://dx.doi.org/10.1016/bs.semsem.2015.09.002
2 VladimirG.Dubrovskii
and radial growth rates, with some refinements of the existing models.
In Section 6, we consider our recently published results on the Zeldovich
nucleation rate in Au-catalyzed III–V nanowires along with a self-
consistency renormalization which appears very important in applications.
Section 7 describes the position-dependent nucleation in nanowires. In
Section8,wepresentasimpleself-consistentgrowthequationwhichallows
onetodescribethevastvarietyofexperimentaldata.
Thenextsectionscontainmainlynewresults.InSection9,weconsider
somenewdataonGa-catalyzedgrowthofGaAsnanowiresandinparticular
theeffectoftheradiusself-equilibration.Section10dealswithAu-catalyzed
ternary InGaAs nanowires where we develop a new atomistic growth
picture.Despiteitssimplicity,ithelpstoimproveourunderstandingofcom-
plex growth phenomena in ternary nanowires. Finally, Section11 presents
a refined model of crystallographic polytypism in Au-catalyzed III–V
nanowires. This model is capable of describing the thresholds between
mononucleation, polynucleation, and atomistic growth, and explains very
welltherecentlyobservednonmonotonicbehaviorsofthepreferredcrystal
structure versus different parameters such as the group V flux.
2. FUNDAMENTALS OF VLS GROWTH
Insimpleterms,theVLSmethod(WagnerandEllis,1964)makesuse
of catalytic effect of a liquid metal droplet (e.g., Au) to fabricate semicon-
ductor nanowires that grow away from the substrate with the position
and width determined by the initial location and size of this droplet, as
showninFig.1.Usually,nanowiresgrowinh111idirectionperpendicular
to(111)substrate.Parasiticgrowthon nonactivatedparts ofthesubstrateis
eithercompletelysuppressedorproceedsatalowerratethanthatofnano-
wires.Fastelongationofnanowiresoccursbecausemuchmoresemiconduc-
tormaterialarrivestothedropletthantothesubstrate.Inchemicalepitaxies
such as metal organic chemical vapor deposition (MOCVD) or hydride
vapor phase epitaxy (HVPE), a liquid metal largely enhances the cracking
efficiency of semiconductor precursors, while in molecular beam epitaxy
(MBE)thedropletactsasamaterialcollectorthatdirectsthediffusionfluxes
tothenanowiretop(Dubrovskii,2014a).Whateveristheepitaxytechnique
usedtoproducenanowires,theVLSprocessnecessarilyinvolvestwophase
transitionsofasemiconductormaterial:fromvapor(e.g.,GaandAs beams
2
inMBE)toliquid(Au–Ga–Asliquidalloyinthedroplet)andfromliquidto
solid (GaAs nanowire), which explains the term “vapor–liquid–solid.”
TheoryofVLSGrowthofCompoundSemiconductors 3
Au film
(1) Deposition of GaAs buffer layer
solid Au film
GaAs (111B) substrate
Au–Ga–As droplets
(2) Anneal above the GaAs buffer layer
melting temperature
GaAs (111B) substrate
2D layer
(3) Epitaxial growth
of GaAs nanowires
GaAs buffer layer
GaAs (111B) substrate
Figure1 Au-assistedVLSgrowthofGaAsnanowiresonGaAs(111)BsubstratebyMBE
with predeposition of (cid:2)1-nm-thick solid Au layer. Atomic force microscopy images
show the surface after Au deposition (first stage) and 3D droplets after annealing
(secondstage).Scanningelectronmicroscopy(SEM)imageshowstheverticallyaligned
GaAsnanowires(thirdstage).Thesenanowireshaveratherbroadlengthanddiameter
distributionsduetoirregularityoftheinitialensembleofdropletsachievedbythermal
dewetting.
The VLS growth usually consists of the following steps schematized
in Fig. 1:
(1) Preparationoftheinitialcatalystlayerorcatalystparticleswhichcanbe
organized into regular arrays by lithographical surface patterning.
(2) Annealofthesurfaceabovethemeltingtemperatureofagivenmetal–
semiconductor alloy to produce liquid droplets.
(3) Materialdepositionwherethestructuralpropertiesofnanowireensem-
bles(length,width,shape,andeventhecrystalphase)canbetunedby
depositionconditionssuchasthegrowthtime,temperature,groupIII
and V fluxes.
Figure2presentstheexamplesofregulararraysofInPnanowiresgrownby
chemical beam epitaxy (CBE) from organized Au seeds in the openings of
inertSiN masklayeronInP(111)B(Kelrichetal.,2013,2015).Sincever-
x
ticalandradialgrowthratesaredeterminedbythedropletdiameter,lateral
spacing, and deposition conditions while fluctuations within the nanowire
ensemble(e.g.,randomnessofstartingtimesforgrowthorinhomogeneityof
material influxes into different nanowires) are usually negligible, all nano-
wires can be made almost exactly identical. This feature of catalytic
4 VladimirG.Dubrovskii
A B
500 nm
Figure2 (A)PlanviewSEMimageofaregular2DarrayofAunanoparticlesinsidethe
SiN openingspriortoCBEgrowth.(B)45°tiltedSEMimageofaregulararraysofInP
x
nanowires grown from 127-nm diameter openings at T¼420°С, TMI flow
correspondingto110nm/h2DgrowthrateonInP(100)at500°С,andPH flowrate
3
of3sccm(Kelrichetal.,2013).Taperingandcrystalstructureofthesenanowirescan
becontrolledbythegrowthtemperatureandphosphorusflux(Kelrichetal.,2015).
nanostructures is very advantageous for applications. Such a level of size
uniformity cannot be achieved in self-induced approaches due to random
characterofnucleation.Itshouldbenoted,however,thatperfectlyregular
nanowirescanalsobeobtainedbyselectivearea(SA)methods(Noborisaka
etal.,2005)sothattheVLStechniqueisnotexclusiveinthisrespect.Onthe
other hand, SA growth can acquire the VLS character under the excessive
group III influx to the nanowire top.
TheVLSmechanismappliesonlywhenthealloyofmetalandsemicon-
ductorremainsliquidduringgrowth.Thestateofcatalystparticlesdepends
onmanyfactorssuchasthegrowthtemperature,dropletcomposition,and
particlesize.Alternatively,theso-calledvapor–solid–solid(VSS)mechanism
ofIII–VcompoundsintroducedbyPerssonetal.(2004)andfurtherdevel-
opedbyDicketal.(2005)suggeststhatthecatalystparticleatthenanowire
tipissolidduringgrowth.InPerssonetal.(2004),throughinsitutransmis-
sionelectronmicroscopy(TEM)analysisandenergy-dispersiveX-rayspec-
troscopy (EDXS) measurements of GaAs nanowires grown by CBE, the
authors observedthecrystallinity oftheAu–Gaparticleand alowGacon-
centrationbelowtheeutecticmelt.TheanalysisofDicketal.(2005)refers
tothecaseofAu-catalyzedInAsnanowiresgrownbyMOCVDbelowthe
eutectic temperature of bulk Au–In alloy at 454.3°С. Indeed, the VLS
growth mechanism is always guaranteed for self-catalyzed III–V nanowires
with group III metal catalysts, while in Au-catalyzed III–V nanowires
the interplay between VLS and VSS modes requires close examination.
In particular, the Au–Ga–As droplets should be liquid at typical MBE
TheoryofVLSGrowthofCompoundSemiconductors 5
temperatures above 500°C (Harmand et al., 2005), while Au-catalyzed
MBE growth of InAs nanowires within the temperature window from
380 to 430°C most probably yields partly solidified catalyst particles
(Tchernycheva et al., 2007).
As any epitaxial growth, the VLS process should occur at a positive
difference of the effective chemical potentials of a semiconductor material
in the vapor (V) and solid (S) phases, Δμ ¼μ (cid:3)μ . However, the VLS
VS V S
growthnecessarilyinvolvesanintermediateliquid(L)stateofthissemicon-
ductor at the chemical potential μ . The latter should be larger than μ to
L S
ensure solidification but smaller than μ to drive the vapor-to-liquid tran-
V
sition.Therefore,theclassicaladsorption-inducedVLSgrowthoccurswhen
μ >μ >μ or Δμ >μ >0: (1)
V L S VS LS
For III–V semiconductors, the definitions of these chemical potentials
requiresomecare.First,weneedtoconsideratomicchemicalpotentialsof
IIIandVelementsinvaporsuchthatμ ¼μV+μV(hereandbelow,thesub-
V 3 5
script“3”standsforgroupIII,“5”forgroupV,and“35”forasolidIII–Vpair).
Thesearegivenbytheatomic fluxesofgroupIIIandV elementsontothe
droplet surface—I and I , respectively, MBE growth geometry or the
3 5
correspondingcrackingefficienciesinchemicalepitaxies(seeFig.3forillus-
tration of the main parameters in VLS III–V nanowires). For Au-catalyzed
VLSgrowth,theliquidchemicalpotentialatthesurfacetemperatureTisgen-
erally defined as (Glas, 2010a): μ ðc ,c ,TÞ¼ μLðc ,c ,TÞ+μLðc ,c ,TÞ.
L 3 5 3 3 5 5 3 5
Here, c and c are the relative atomic concentrations of group III and
3 5
V atoms dissolved in gold such that the atomic concentration of Au equals
c ¼1(cid:3)c (cid:3)c . The solid chemical potential refers to a bound III–V pair
Au 3 5
instoichiometriczincblende(ZB)crystal:μ ¼μS ðTÞandgenerallycannot
S 35
bedecoupledtothesumofthegroupIIIandVcontributions.Ifthenanowire
phaseiswurtzite(WZ),thesolidchemicalpotentialchangestoμ +ψ,withψ
S
asthebulkenergydifferencebetweentheWZandZBphases(Dubrovskii,
2014a)(forconventionalIII–Vmaterials,ψ ispositive).Duetotheknown
low solubility of most group V elements such as As in liquid metals, the
VLSprocessusuallyproceedsatc ≪c .Inthiscase,wecanneglectthedepen-
5 3
denceofμLonc andwriteapproximately(Dubrovskii,2014b)
3 5
Δμ ðc ,c ,TÞ¼μLðc ,TÞ+μLðc ,c ,TÞ(cid:3)μS ðTÞ: (2)
LS 3 5 3 3 5 3 5 35
Therefore,thegroupVchemicalpotentialinliquidisthemostdifficult
one since it depends on concentrations of both growth species.
