14. vapour-liquid-solid growth

14. Vapour-Liquid-Solid growth

Dr. Roberto Bergamaschini

Selected Chapters from Semiconductor Physics:

Theory and modelling of epitaxial growth

✉ [email protected]

L-NESS and Department of Materials Science, University of Milano-Bicocca (Italy)

✉ [email protected]

mailto:[email protected]

mailto:[email protected]

Vapour-Solid vs. Vapour-Liquid-Solid growth

Vapour-solid (VS)

Vapour-liquid-solid (VLS)

04/06/202114. Vapour-Liquid-Solid growth

• Droplet epitaxy (III-V compounds)

• VLS Nanowire growth

Self-assembly is the viable strategy for growing nanostructures. By using the vapour-liquid-solid

technique we introduce an alternative way to control the growth dynamics: the whole growth dynamics

becomes mediated through the liquid catalyst droplet, at conditions where normal Vapour-solid does

not work. By controlling the droplet properties, geometry, composition one directly controls the material

that is deposited and hence the (nano)-structure growth.

Stranski Krastanow QDs

Hard to grow NWs

Droplet epitaxy of III-V compounds


Droplet Epitaxy (DE): separate in time the supply of the group-III metal from that of the group-V species.

STAGE 1. Deposition of the metal droplets

Compact

QDs

Nanorings

Droplet epitaxy is very commonly implemented

for most III-V systems

GaAs/AlGaAs; InSb/CdTe; In(Ga)As/GaAs;

GaAs/Si; GaSb/GaAs; GaN/AlGaN; GaP/GaAs

STAGE 2. Droplet crystallization by annealing

in group-V atmosphere

Gurioli et al., Nature

Mater. 18, 799 (2019)

STAGE 1. Deposition of the metal droplets


Typically the process starts on a metal-stabilized surface

(common on (001) and (111)A)

It consists of the nucleation and self-assembly of droplets via

the Volmer-Weber growth mode

Tunable by:

Temperature (150-500°C)

Coverage (few MLs)

Size: 10-30nm

Size dispersion within 10% (comparable to SK)

Density: 103-0.1µm-2

At variance with SK growth, metal droplets (and hence subsequent crystal structures)

• Can form without any wetting layer (no electronic states interconnecting the dots). Eventually a layer

of desired thickness and composition can be grown on purpose.

• Are substantially independent of the substrate (can be formed on any surface, lattice matched or with

any mismatch)

STAGE 2. Annealing in group-V atmosphere


Crystallization at the droplet-substrate

interface: group-V atoms are dissolved in the

metallic droplet. Supersaturation results in the

precipitation of the III-V compound at the liquid-

solid interface

Diffusion of group-III atoms out of the droplet

Adsorption of the group-V atoms on the surface

around the droplets makes the surface V-

terminated and hence suitable for the diffusion

of metal atoms driven by capillarity (tendency to

flatten the droplet)Low Temperature High

High group-V partial pressure Low

Short diffusion length of

group III-atoms (~1nm)

Long diffusion length of

group III-atoms (~1nm)

Compact

QDs

Hollow structures,

Nanorings

vs.

+ group-V:

As, P, N Low-T process: 150-350°C

General concepts of VLS NW growth


Most semiconductors, either group-IV (Si, Ge, SiC), III-V-compounds and II-VI compounds, can be grown into

NWs by VLS. Lateral dimension: few nm to µm. Length up to tens of µm.

Both VPE/MOVPE and MBE are suitable.

Catalytic role of the droplet:

lower nucleation barrier at the solid-liquid

interface than at the solid-vapour interface

(lower growth T)

efficient condensation: atoms can

join the liquid at any site, while desorption

is limited → higher solute concentration

with respect to equilibrium solubility

Crystal growth proceeds only across the droplet-substrate interface:

wire diameter = droplet diameter

Vapor-solid incorporation at sidewalls is suppressed due to the low-T growth

The supply of atoms to be incorporated in the growing wire proceeds

through the dissolution of the semicondutor elements within an alloy

droplet of a metal catalyst. This can be:

• a noble metal: Au, Ag, Cu, Ni, Pd… (low-T eutectic)

• In III-V NWs, the group-III metal itself (higher-T eutectic but no

contamination): : self-catalyzed growth

GAS

LIQUID

1

2

3

4

NW

substrate

Metal catalyzed NW growth


Deposition of a film

of the metal catalyst

The reaction of gas precursors at

the droplet surface introduces

further Si in the alloy which becomes

supersaturated. Then Si is deposited

at the solid-liquid interface starting

the growth of the NW.

The droplet rests on top of the

growing layers thus setting the radius

of the NW. The incorporation

continues through the interface

resulting in the elongation of the NW

(no growth at sidewalls by T<1000°C)

Most favorable alignment for the growth:

axis along close-packed directions

Diamond phase → (111)-axis

Wagner and Ellis. Appl. Phys. Lett. 4, 89 (1964)

Au layer breaks into

droplets which dissolve

part of the underlying Si

(up to 𝐶𝑒𝑞).

High T annealing

(900°C)

Self-catalyzed NW growth: III-V compounds


Same starting point of droplet epitaxy: deposition of group-III metal drops but the subsequent exposure to group-

V species is done without stopping the III-flux.

The III-rich droplet is not thermodynamically stable but it is preserved by the steady-state transport kinetics

between the wire and the droplet. Only a small amount (~1%) of group-V species is soluble within the droplet

and its availability is the growth-rate limiting factor: the growth rate is linearly proportional to the group-V flux

and almost independent on the group-III flux.

Cubic III-V

Axis: (111)B (anion terminated) facet.

Sidewalls: 6 {110} facets (eventually

6 small {112} segments).

Wurtzite III-V

Axis: (0001) basal plane

Sidewalls: 6 {10ത10} and/or

6 {11ത20} facets

GaN

Axis: 0001 Ga or 000ത1 N.

Sidewalls: 6 {10ത10} planes.

Top (0001)Ga: pyramid with 6 {1ത102} facets

Thermodynamic considerations


Hyp: vapour-droplet equilibrium = identical rate of re-evaporation and dissolution → concentration 𝐶𝑉𝑆𝐶𝑉𝑆 > 𝐶𝑒𝑞 → the droplet is still supersaturated with respect to the solid by

𝛾𝐿𝑉𝐶𝑉𝑆

LIQUID

SOLID

GAS

Δ𝜇 r = Δ𝜇∞ −2𝛾𝐿𝑉𝑉𝑚,𝐿

r

Δ𝜇∞ = 𝑘𝑇 ln 𝐶𝑉𝑆/𝐶𝑒𝑞 = supersaturation for the infinite bulk phases

By decreasing the radius and hence the NW diameter the evaporation from the droplet

accelerate while the solubility of Si increases → reduction of the supersaturation Δ𝜇.

There exists a minimum critical radius 𝑟min below which the supersaturation becomes

null (Δ𝜇 = 0), i.e. such that the NW cannot grow:

r

Droplets are curved, finite → Thomson−Gibbs equation for liquid−vapour equilibrium

𝑟min =2𝛾𝐿𝑉𝑉𝑚,𝐿

Δ𝜇∞

NW growth rate


GAS

LIQUID

1

2

3

4

NW

substrate

𝜇𝑣𝑎𝑝 > 𝜇𝑙𝑖𝑞 > 𝜇𝑁𝑊

1. Mass transport in gas phase

2. Surface reaction/dissolution of precursors into the liquid droplet

3. Fluid-dynamic transport within the liquid phase

4. Incorporaton at the liquid-solid interface (typical rate-limiting step)

The growth rate is expected to change according to

Δ𝜇 r as:

v r ≈ 𝛽Δ𝜇 𝑟

𝑘𝑇

𝑛

= 𝛽Δ𝜇∞ − 2𝛾𝐿𝑉𝑉𝑚,𝐿/r

𝑘𝑇

𝑛

with fittable parameters 𝛽 and 𝑛 ≈2.

Kinetic limitations typically result in a decrease of v rfor large diameters (~µm).

If incorporation at sidewalls is negligible and the diffusion length is very long, also the

material deposited there (or on the substrate) will diffuse into the droplet, increasing

the rate for longer wires.

ZB vs WZ phase competition


Size effect: due to the high surface-to-volume ratio, the stability of

one or the other phase is affected by the energy of the exposed

facets. Ab-initio: wurtzite phase have less dangling bonds.

Supersaturation → at high Δ𝜇 the wurtzite phase is more favorable

critical radius: 𝑟WZ−ZB =𝛾sidewall ZBΔ𝜇WZ−ZB

Sidewalls

ZB: 110 , 11ത2WZ: {1ത100}, {11ത20}

Dubrovskii and Sibirev. Phys. Rev. B 77, 035414 (2008)

Crystals in bulk:

most-stable phase

Si, Ge =diamond

III-As,P,Sb = zincblende

III-N = wurtzite

NW(111B) axis

ZBWZZB

ZB vs WZ phase competition


Panciera et al. Nano Lett. 20,1669 (2020)

Crystals in bulk:

most-stable phase

Si, Ge =diamond

III-As,P,Sb = zincblende

III-N = wurtzite

NW(111B) axis

Droplet contact angle φ controls the stability and volume of the droplet

→ position where a new layer starts, the crystal phase, growth direction

and possible tilting, force balance at triple-phase-line (TPL)

III/V NWs → continuous variation of contact angle by the change in

droplet volume via the V/III ratio (> flux group-V < size)

φ=

12

5°

φ=

10

0°

Edge truncation at the TPL.

Quasi-Instantaneous

completion of ML (As from

truncated facet)

No edge truncation at the TPL.

Slow completion of each ML (As from

the vapour phase)

Step-flow

Ordering NWs: substrate patterning and self-induced growth


Catalyst-free selective area growth (SAG)

III-V NWs tend to grow spontaneously, not by

VLS, at high (>1) V/III ratio in selective area

growth on SiO2-Si(111) via MOVPE and MBE

Tomioka et al. J. Mater. Res. 26, 2127 (2011)

GaAs/GaAs(111)B InAs/InP(111)B

Selective area vapor-liquid-solid growth

Metal-catalyst droplets are introduced into the mask

windows to localize the VLS process at specific sites

Gold-catalyzed

WZ-GaP/AlGaP

core-shell NWs

in a nanoimprint

pattern

Assali et al.

Nano Lett. 13,

1559 (2013)

Self-catalyzed

GaAsSb NWs in a

nanoimprint pattern

on 40nm SiO2

Ren et al. Nano

Lett. 16, 1201

(2016)

Heterostructures on nanowires: axial


Dis

locati

on

cri

tical

thic

kn

ess

(here

60°

dis

location

sin

FC

C)

NW radius (cylindrical)

No

pla

sti

cit

y

Glas. Phys. Rev. B 74, 121302R (2006)

Changing the material during growth is straightforward in VPE/MOVPE or MBE. Very sharp junctions can be

achieved if solubilities in the droplet are low (e.g. for group-V elements). Viceversa, a gradual variation in

composition is obtained for a change in the group-III metal in order to restore the droplet supersaturation.

1. Growth sequence: as in general 𝛾 are different for A and B, only one growth sequence A/B or B/A is

energetically favorable. In the other, we obtain kinked or downward growth → kinetic control or choice of

compounds with similar 𝛾 (GaAs/GaP, InAs/InP)

2. Strain relaxation: thanks to the

small lateral dimension of a NW,

elastic relaxation via lateral free-

surfaces is very efficient thus

allowing for the growth of much

thicker layers than on planar

substrate, even for large misfit

systems, before plastic relaxation.

Importantly, for a certain misfit,

there exists a critical radius below

which a coherent structure can be

achieved for any thickness.

Yuan. Appl. Phys. Rev. 8, 021302 (2021)

Heterostructures on nanowires: radial (core-shell)


Shell

growth

(radial)

Hauge et al. Nanoletters

15, 5855 (2015)

hex. Si

WZ

GaP

Heiss et al. Nature Mater. 12, 439 (2013)

• stop VLS axial growth by

evaporating the catalyst droplet

• enable the Vapor-Solid growth mode

by activating precursors reaction and

incorporation at the NW sidewalls

VLS NW

core

growth

(axial)

raise temperature

raise V/III ratio (for GaAs NWs the formation

of As-trimers on the top {111}B facet at high As

partial pressure, suppresses the axial growth)

Multiple concentric quantum wells Embedded QD

Template effect:

continuation of the

core phase even if

metastable one

Customizable design of radial heterostructures

Kinetic

segregation

𝑫𝑨𝒍 ≪ 𝑫𝑮𝒂

Lattice-mismatched core-shell NWs: strain release


The axial symmetry of the NW naturally returns an enhancement of the strain relaxation in the shell by strain

partitioning to the core region. The effect is negligible for thin shells and becomes dominant for thicker ones.

What matters is the areal ratio 𝜂 = 𝑟𝑐2/𝑟𝑠

2

Thin shell/early growth stages:

𝑐 ≫ 𝑎 → 𝜀𝑧𝑐𝑜𝑟𝑒 → 0

Thick shell/late growth stages:

𝑐 ≪ 𝑎 → 𝜀𝑧𝑐𝑜𝑟𝑒 → f, 𝜀𝑧

𝑠ℎ𝑒𝑙𝑙 → 0

𝜀𝑧𝑧𝑐𝑜𝑟𝑒 = (1 − 𝜂)𝑓 𝜀𝑧𝑧

𝑠ℎ𝑒𝑙𝑙 = −𝜂𝑓

𝑟𝑐

𝑟𝑠𝜀𝑧𝑧𝑐

Cylidrical core-shell NW

𝜀𝑧𝑧𝑠

radial

tangential

The efficacy of strain release in NW structures enables to

overtake limitations imposed by the strain energy cost in bulk

or simply 2D structures. An example is the solubility of Sn in

GeSn which is a mere 1% in bulk but grows significantly

(above 10%) when a GeSn shell is grown on a Ge core NW.

FEM calculations

10.5% Assali et al.

Nanoscale 10,

7250 (2018)

14. vapour-liquid-solid growth

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