Growth of nanowires - Sciencesconf.orgpulse-school.sciencesconf.org/conference/pulse-school/... · 2015-09-22 · Nanowires of semiconductors Catalyst-free growth Amiri et al, Phys

Growth of nanowires

Jean-Christophe Harmand

Laboratoire de Photonique et de NanostructuresRoute de Nozay, 91460 Marcoussis

GdR PULSE, Summer School, Porquerolles, Sept 17th 2015

This lecture will focus on:

Semiconductor nanowires (III-V mainly)

(other types of nanowires: metallic, dielectric)

elaborated by CVD or MBE

(other methods: laser ablation, HVPE, wafer annealing, low temperature solution,

electrochemical deposition…)

via the catalyst-assisted vapor liquid solid (VLS) mechanism

(other mechanisms: catalyst free growth, selective growth, dislocation- mediated growth,

ligand-aided solid-solution growth…)

Nanowires of semiconductors

Catalyst-free growth

Amiri et al, Phys. Stat. Sol. B 250, 2132 (2013)

GEMAC, VersaillesLPN, Marcoussis

GaN

ZnO

III-V

InPGaAs

3 µm

GaP

500 nm

InAs

500 nm

300 nm

IVII-VI

ZnTeGe

Institut Néel, Grenoble

IEF, Orsay

LPN, MarcoussisRueda et al, Nano Lett. 14, 1877 (2014)

Au-assisted growth

Typical diameter ranges between a few nm and several 100 nmTypical length from < 1 µm to several 100 µm

Self-catalyzed growth

LPN, Marcoussis

50

nm

GaAs

F. Jabeen et al, Nanotechnol. 19, 275711 (2008)C. Colombo et al. PRB 77, 155326 (2008)

Nanowires of semiconductors: various objects, flexible growth

Ramdani et al, Nano Lett. 10, 1836 (2010)

HVPE, very long GaAs NWs (Rg = 170 µm/h)Institut Pascal, Clermont Ferrand

MBE, GaAs NWs grown on glassLPN Marcoussis, T. Jegorel

MBE, GaAs NWs grown on patterned SiLPN Marcoussis, F. Oehler

Outline

Generalities on catalyst-assisted nanowire growth

Kinetics of nanowire growth

Nucleation in VLS growth

Formation of heterostructures in nanowires

Why is Au such a successful catalyst?

No oxidation in air

Schmidt et al, Chem. Rev. 110, 361, 2010

Metal catalysts for Si NW growthAu ≡ Deep level

Small droplets are easily obtainedColloïdsThin film deposition + dewetting

Au forms eutectic alloyswith Si, Ge, Ga, In, Al, Zn, Cd…

VLS growth is possible

Eutectic temperaturesAu-Si 363°C

Au-Ge 361°C

Au-Al 525°C

Au-Ga 349°C

Au-In 224°C

Au-Zn 403°C

Au-Cd 309°C

The catalyst is a reservoir of NW constituents

Au-Ge 1L

Au

L

Ge xx

growth

no growthL

Ge x must be higher than the equilibrium concentration to start growing

Group III atoms are much more soluble than group V atoms

Au0.5Ga0.5 phase

Catalyst composition afterGaAs NW growth

Case of III-V compounds

Both group III and group V atoms must dissolve in the catalyst

AuGaAs liquid catalyst

0 0.01 0.02 0.03 0.04 0.05 0.06-300

-200

-100

0

100

200

300

400

500 cGa

= 0.7

cGa

= 0.35

cGa

= 0.2

T = 760 K

T = 820 K

T = 880 K

(m

eV

/pair)

cAs

Glas, J. Appl. Phys. 108, 073506 (2010)

),,( Txx L

As

L

Ga

1 L

Au

L

As

L

Ga xxx

How much of each constituent in the reservoir?

During growth

Ga composition: several 10% ≡ tens to hundreds of monolayers of solid NW

As composition: not more than a few % ≡ a few monolayers of solid NW (can be less than 1ML)

0 10 20 30 40 500.1

1

10

100

Eq

uiv

ale

nt

nu

mb

er

of

Ga

As M

Ls

Nanowire radius (nm)

xGa=0.01

xGa=0.05

xGa=0.2

xGa=0.6

Drop contact angle 90°

To fabricate heterostructures, it is more favorable to commute group V atoms

(less soluble faster to purge)

Compounds with same group III atoms have comparable ranges of growth temperature

350 450400 500 550 600 650

InP

InAs

GaAs

GaP

Temperature range for NW growth by MBE of different III-V compounds

Preferential growth axis

Au-catalyzed semiconductornanowires

Cubic(Zinc Blende)

Hexagonal (Wurtzite)

(001) GaAs substrate

In most cases, the growth axis is [-1-1-1] for cubic phase or [0001] for hexagonal phase


Au


Outline





Constituents are brought as directionalbeams of atoms or simple molecules

(Si , Ge, Ga, In, P2, As4…)

no chemical reaction needed

The metal droplet promotesincorporation of atoms in the solid phase

« Physical catalyst »

MBECVD

Precursors are gas molecules(TMGa, AsH3, SiH4…)

The metal droplet can promotetheir decomposition

« Chemical catalyst »

Precursor flow from the vapor to the droplet

Why is growth faster under the metal drops ?

The liquid drop is a dense phase:

Aggregation of atoms to form solidnuclei is faster at liquid/solidinterface than at vapor/solidinterface

Incorporation sites

Faster consumption inducessurface diffusion of adatoms to

the droplet

Case of III-V NW growth by MBE

Group III : sticking coefficient =1 Surface adsorption + surface diffusion

Group III atoms reach the droplet by-direct impingempent-surface diffusion

Different pathways to the droplet for group III or group V atoms

Group V : sticking coefficient <<1 Surface adsorption + reemission in the vapor phase

Group V atoms reach the droplet by-direct impingement-reemission

Surface diffusion of adatoms

0

s

sss

s nJnD

t

n

02

2

f

fff

f nJ

z

nD

t

n

rns

znf

z

Diffusion equations may be solved.... if L is known

Diffusion flux into the drop

dz

ndD f

f

L

f

s

dz

ndD

dr

ndD f

fs

s

0r

s

dr

nd

ffss nn

RxTn LLff ,...,,

0

0 lnf

fBffff n

nTknn

J

0sin1

2

2

f

fff

f nJ

z

nD

t

n

0cos

s

sss

s nJnD

t

n

r

Elongation rate is not constant

time t

NW length L

Ruth and Hirth, J. Chem. Phys. 41, 3139 (1964)

ls large

substrateContributiondominates

lf large

sidewallcontribution dominates

sss D l

fff D l

L(t)

Lt lf

fl~

(case of no growth on substrate or sidewalls)

Assume L is known

Dayeh, Yu, Wang, Nano Lett. 9, 1967 (2009)

InAs, MOVPE

20 nm

InP

As

substrate

Modulation period

Instantaneous elongation rate

L

L

substrate sidewalls liquid

x

Harmand, Glas, Patriarche, Phys. Rev. B 81, 235436 (2010)

Case study: InAsP nanowires grown by MBE

0 200 400 6000

200

400

600

800

L (

nm

)

t (s)

As4/P2

1:5 3:3

fl = 160 meV

sl = -145 meV

fl = 270 meV

sl = 18.4 meV

lf = 2000 nm

ls = 2 nm

Coupling between diffusion and incorporation

• Material balance evapgrowthdiffdirect IIII

LL xIxI ingrowth • Feedback

self-consistent determination of xL and growth ratepossible in principle in simple sytems

,..., L

L xT

dz

ndDI f

fdiff SLI growth

directI

,..., LxTIevap

TS

Length / radius dependence

2R

RRd

2RI direct

2RI evap

2Rdt

dLI growth

RI substratediff

RLI sidewallsdiff L

R

BA

dt

dL

dt

dL

R

~ 1/RFröberg et al., Phys. Rev. B 76, 153401 (2007)

InAs, CBE

L treated as a fitting parameter

Gibbs Thomson effect

Gibbs Thomson effect in a spherical droplet

The Gibbs Thomson effect describes the increase of chemical potential in a particular phase due the Laplace pressure which results from curvature effects

For a sphere

Nanodroplets are under very high pressures

Laplace pressure

GT effect in the catalyst droplet of a nanowire

Generally, the shape of the catalyst is a truncated sphere on top of the nanowire of radius Rwire

Although the geometry has changed, we still have: with R = Rdrop

Change of free enthalpy after transferring one atom from the vapor to the liquid droplet

For a Si atom dissolved in an Au droplet on top of a NW of 10 nm radius

Kelvin effect: Equilibrium partial pressure is higher (desorption from the drop is higher)

for a NW of 10 nm radius

Outline





Monolayer by monolayer (1ML = 2 atomic planes)

If top facet is narrow enough, mononuclear regime

1 ML 1 nucleation event

At least one new 2D nucleus is needed for each ML

How does VLS growth proceed

Wen et al., Science 326, 1247 (2009)

Flat heterointerfaces

AlGaAs insertion in GaAs NW

Si NW growth in a TEM

Classical 2D nucleation theory

Supersaturated phase (gas, liquid, adatoms) Venables et al, Rep. Prog. Phys. 47, 399 (1984)

Gibbs free energy of nucleus formation

0

0

Nucleation rate:Probability of forming a 2D nucleus

/(unit time x unit area)

r<rc nuclei decompose easilyr>rc nuclei can extend by step flow

Nucleation barrier

Where ?

Nucleus entirely surrounded by liquid

Nucleus at the periphery

Liquid Vapor

NW

Liquid

NW

Wen, Science 326, 1247 (2009)VSS growth of Si NW in UHV TEM

AlAu catalyst

nVLV

nL

F. Glas et al., Phys. Rev. Lett. 99, 146101 (2007)

sinLVnLnV Nucleation at the triple phase line if

Easily satisfied for 90°

catalyst

nanowire

Some experimental indications of nucleation at TPL

Impact of nucleation at the TPL on the crystal phase

In this case, the ZB nucleus is the stabler (like in bulk III-Vs)

Difference of cohesion energy:

ZB

eff

WZ

eff nL eff

nL

Nucleussurrounded by liquid

pairGaAsmeVEEE WZZB

coh /24

sin3

1

3

2eff LVnVnL

nV

nL

Nucleus at the periphery

)(3

1 WZ

nV

ZB

nV

WZ

eff

ZB

eff

WZ

nV

ZB

nV

In this case the nucleation barrier can be lower for the WZ nucleus

And we haveSee DFT calculations byPankoke, Phys. Rev. B 84 , 075455 (2011)

0

0

WZ

ZBG

r

Different barriers to form a ZB or WZ nucleus

Zinc blende / wurtzite polytypism

2ZB

effZB

c ghG

EWZ

eff

ZB

eff

ZB

eff

22

2

ZB

c

WZ

c GG

EghG

WZ

effWZ

c

2

We have

when

, critical nucleus becomes smaller, edge energy weighs more, favorable to WZ

Glas, Harmand, Patriarche, Phys. Rev. Lett. 99, 146101 (2007)

Experimental evidence of phase transitions

10 nm

Beginning of growth

ZB

ZB

WZ

Phase transition when > c

End of growth under AsThe drop is purged

Reverse transition when < c

WZ

ZB

30 60 90 120 150

50

100

150

(m

eV

/ I

II-V

pa

ir)

Contact angle (°C)

Role of the contact angle

WZ

ZBZB

ZB

sin3

1

3

2LV

WZ

nV

WZ

nL

WZ

eff cohWZ

eff

ZB

eff

ZB

eff

c E

22

2

The critical supersaturation depends on

145°

ZB

Faulted ZB

Faulted WZ

WZ

Faulted WZ

ZB

30 60 90 120 150

50

100

150

(m

eV

/ III-V

pa

ir)

Contact angle (°C)

WZ

ZBZB

Formation of 1 ML

Comparing 2D and NW growth

2D

NW

Infinite surfaceinfinite parent phase

• Many nuclei• Step flow• Coalescence

Time to form 1ML = cst

Statistics of nucleation events is hidden

Limited surface area parent phase ≡ finite and open nanovolume

• 1 nucleation event is needed at each new ML• Extension by step flow until the ML is completed• Composition of the parent phase may fluctuate

Time to form 1ML cst

Depends on nucleation statistics

Fluctuations

40 60 800

20

40

60

80

Occu

rre

nce

Number of monolayers per time period

Experiment

Distribution of segment lengths

Nucleation statistics

Use of chemical markers (here AlGaAs in GaAs NW)introduced periodically (period ) during growth

L

For each period, elongation L is measured= number of MLs grown in the time period

= number of nucleation events during

if growth regime is mononuclear

2000 2500 300040

50

60

70

80

Elo

ng

atio

n b

etw

ee

n 2

ma

rke

rs (

ML

s)

Time (s)

Poisson

Sub-poissonian statistics Probability of nucleation varies with time

Glas, Harmand, Patriarche PRL 104, 135501 (2010)

Self-regulated growth

Nucleation Rapid depletion of the reservoir

New nucleationTime for refilling

This mechanism regulates the nucleation events which become anti-correlated.

Concentrations of the NW constituents vary with time:

Rapid decrease when a ML forms after a nucleation event Slow refilling rate between two nucleations

ModelNucleation probability

with and

with and

Expanding

After 1 ML completion in a NW with

Self catalyzed growth: Ga droplet with a small concentration of AsWe use parameters extracted from a study of self-catalyzed growth kinetics

Ramdani, Harmand, Glas, Patriarche, Travers, Cryst. Growth & Des. 13, 91 (2013)

Glas, Ramdani, Patriarche, Harmand, Phys. Rev. B 88, 195304 (2013)


Simulation of a sequence of nucleations

0.02

0.03

0.04

c

V

t (a.u.)

Refilling of the drop atconstant rate

Nucleation event:Sudden depletion of the dropFormation of 1ML

0.0

0.5

1.0

1.5

2.0

P/P

0

t (a.u.)

The regulation effect is due to the low concentration of group V atoms in the droplet The thinner the NW, the larger the effect

2RhNNN MLVIII tNtN V III

Modeling the nucleation statistics

Simulation

Set of parameters

60 800

20

40

60

80

Occu

rre

nce

Number of monolayers per oscillation

Self-regulatedgrowth

Poisson

Growth kinetics of these NWs wasfitted with very similar values…

Ramdani et al, Cryst. Growth & Des. 13, 91 (2013)

Glas et al, Phys. Rev. B 88, 195304 (2013)

Saturation of the standard deviation

Self-regulated

Poisson

The lengths of NWs grown from identical droplets can be very uniform


m

Outline





Heterostructures in NWs

GaP/GaAs superlatticesG. Priante (LPN)

Axial

QD

Axial + radial

In(P,As) QDin InP NW (LPN)

• Control of dimensions via NW seed or mask pattern and growth time

• Strain accommodation easier in NWs than in 2D layers

B

A

Radial (core-shell)

In(P,As)/InP core-shellL. Liu (LPN)

BAB

The reservoir effect in axial heterostructures

The reservoir effect is critical for the constituents which are highly soluble in the catalyst

Au catalyst: Si/Ge heterostructuresGaAs/InAs, GaAs/AlAs

Length of gradedcomposition R

Au catalyzed Si/SiGe NWs Periwal et al, Nano Lett. 14, 5140 (2014)

Getting around the reservoir effect

Solid reservoir: VSS growth

Solubility of NW element(s) ismuch lower in a solid catalyst

Wen et al., Science 326, 1247 (2009)

Sharp interfaces... but VSS growth is very slow

T= 507°C T= 503°C

L S

Si


No reservoir: Catalyst-free growth

GaN/AlN heterostructures

E. Galopin et al, Nanotechnology 22, 245606 (2011)LPN, Marcoussis


Modify the catalyst to lower the solubility of NW constituent

Perea et al., Nano Lett. 11, 3117 (2011)

Au catalyst

Au0.66Ga0.34 catalyst

Si/Ge heterostructures


Commute elements of low solubility

GaAs/GaP heterostructures

Ga(As,P)

GaP

Jabeen, Patriarche, Glas, Harmand, J. Cryst. Growth 323, 293 (2011)LPN Marcoussis

Au catalyst


Purge the droplet at the heterointerface

GaAs/GaP heterostructures / self-catalyzed growth

GaAs growth No flux

Equilibrium As concentration

As Ga As As

Ga and P fluxes GaP gowth

GaGaP P

Priante, Patriarche, Oehler, Glas, Harmand, Nano Lett. 15, 6036, 2015

0 5 10 15

3 ml

12 ml

HA

AD

F in

ten

sity (

a.

u.)

Distance (nm)

no interruption

20 s interruption

60 s interruption

6 ml

As-rich

P-rich

Conclusions

Catalyst-assisted nanowire growth is governed by specific mechanisms which differfrom those at play in standard 2D growth

• Catalyst particle ≡ dense reservoir of constituents

• Faster growth at the catalyst/nanowire interface

• Diffusion of adatoms to the drop

• Non-constant growth rate

• Stochastic formation of monolayers, but can be regulated by diluteconstituents in the droplet

• Nucleation at the triple phase line is favorable and metastable crystalphase can form

• Formation of abrupt interfaces is challenging

AcknowledgementsCo-workers at LPNFrank GlasGilles PatriarcheLudovic LargeauFabrice OehlerNoëlle GogneauLaurent Travers, Olivia Mauguin, Elisabeth Galopin

Post-docs at LPNMaria Tchernycheva, Corinne Sartel, Linsheng Liu, Damien Lucot, Fauzia Jabeen, RedaRamdani

PhDs at LPNYann Cohin, Giacomo Priante, Theo Jegorel, Vishnuvarthan Kumaresan

Vladimir Dubrovskii, George Cirlin St Petersburg Academic University of the RAS and Ioffe Institute

Documents

Growth of nanowires - Sciencesconf.orgpulse-school.sciencesconf.org/conference/pulse-school/... · 2015-09-22 · Nanowires of semiconductors Catalyst-free growth Amiri et al, Phys