Crystal GrowthCrystal Growth

1.) INTRODUCTION: 1.) INTRODUCTION: – Melt growth, solution growth and vapor growth.Melt growth, solution growth and vapor growth.

2.) 2.) Process for crystal growth from meltProcess for crystal growth from melt::– 2.1 Directional solidification/Bridgman process.2.1 Directional solidification/Bridgman process.

– 2.2 Zone melting and floating zone.2.2 Zone melting and floating zone.

– 2.3 Czochralski method.2.3 Czochralski method.

– 2.4 Liquid encapsulated Czochralski.2.4 Liquid encapsulated Czochralski.

3) Convection and segregation3) Convection and segregation

1) Introduction1) Introduction

Motivation for growth of single crystalsMotivation for growth of single crystals– Research (physics/materials):Research (physics/materials):

» Properties of solids are obscured by grain Properties of solids are obscured by grain boundaries (to understand solids we must boundaries (to understand solids we must understand crystals).understand crystals).

MetalsMetals SemiconductorsSemiconductors SuperconductorsSuperconductors Protein crystalsProtein crystals

ApplicationsApplications

» Uniform properties on microscopic levelUniform properties on microscopic level Micro-devices: electronic, optical, and mechanicalMicro-devices: electronic, optical, and mechanical

» No creep, fatigue…No creep, fatigue…

» Beautiful objectsBeautiful objects

Methods for Crystal GrowthMethods for Crystal Growth

Boules 25 wafers/inch(substrate for IC)

VLSI~ 106

devices

•Directional solidification from the melt ~ cm/hr

•Solution growth (supersaturation) ~ mm/day

•Vapor growth (sublimation-condensation) ~ µm/hr

Thin layersBoules

a.) Growth from the melt:a.) Growth from the melt: Conditions:Conditions:

– Material must Material must melt congruentlymelt congruently (no change in (no change in composition during melting) e.g. Yttrium iron composition during melting) e.g. Yttrium iron garnet (YIG) is grown from solutions because it garnet (YIG) is grown from solutions because it does not melt congruently.does not melt congruently.

– Material Material must not decomposemust not decompose before melting. e.g. before melting. e.g. SiC is grown from vapor phase (sublimation-SiC is grown from vapor phase (sublimation-condensation) because it decomposes before condensation) because it decomposes before melting.melting.

– Material Material must not undergo a solid state phase must not undergo a solid state phase transformationtransformation between melting point and room between melting point and room temperature. e.g. SiOtemperature. e.g. SiO22 is grown from solution is grown from solution (hydrothermal growth) because of a α-β quartz (hydrothermal growth) because of a α-β quartz transition at 583°C.transition at 583°C.

Advantages of solidification:Advantages of solidification:

Fast (~Fast (~cm/hrcm/hr); growth rate depends on heat ); growth rate depends on heat transfer (not on mass transfer).transfer (not on mass transfer).

Variety of techniques developed (e.g. Variety of techniques developed (e.g. crystal pulling and directional and zone crystal pulling and directional and zone solidification).solidification).

b.) Growth from solution:b.) Growth from solution:

For materials that: For materials that: – (i) melt non congruently or (i) melt non congruently or – (ii) decompose before melting or (ii) decompose before melting or – (iii) undergo a solid state phase transformation (iii) undergo a solid state phase transformation

before melting or before melting or – (iv) have very high melting point. (iv) have very high melting point.

Classification is based on the solvent type.Classification is based on the solvent type. Key requirement: High purity solvent which Key requirement: High purity solvent which

is insoluble in the crystal.is insoluble in the crystal.

b.1) Molten salt (flux) growth:b.1) Molten salt (flux) growth:

Common solvents: PbO, PbFCommon solvents: PbO, PbF22, B, B22OO33, KF., KF.

Used for oxides with very high melting points (or Used for oxides with very high melting points (or melt congruently, decompose or undergo a solid melt congruently, decompose or undergo a solid phase transformation).phase transformation).

e.g. Yttrium iron garnet (YIG) is grown from e.g. Yttrium iron garnet (YIG) is grown from solutions because it does not melt congruently.solutions because it does not melt congruently.– Advantages: carried on at much lower temperatures Advantages: carried on at much lower temperatures

than melt growth.than melt growth.

– Limitations: very slow; borderline purity, platinum Limitations: very slow; borderline purity, platinum crucibles, stoichiometry is hard to control.crucibles, stoichiometry is hard to control.

b.2) Metallic solution growth:b.2) Metallic solution growth:

Liquid phase Epitaxy – for high quality epitaxial Liquid phase Epitaxy – for high quality epitaxial layers of III-V compounds and boules;layers of III-V compounds and boules;– GaAs from Ga solution (melt with > 50% Ga).GaAs from Ga solution (melt with > 50% Ga).

– GaSb from Ga solution (melt with > 50% Ga).GaSb from Ga solution (melt with > 50% Ga).

– Terary III-V compounds (solid solutions of III-V Terary III-V compounds (solid solutions of III-V compounds): Gacompounds): Ga1-x1-xlnlnxxAs, GaAsAs, GaAsxxPP1-x1-x..

» Advantages: Advantages: growth at lower temperatures than melt growth growth at lower temperatures than melt growth yields high quality.yields high quality.

» Limitations: Limitations: very slowvery slow = small crystals or thin layers. = small crystals or thin layers.

b.3) Hydrothermal growth:b.3) Hydrothermal growth:

Aqueous solution at high temperature and Aqueous solution at high temperature and pressure (e.g. SiOpressure (e.g. SiO22 is grown by is grown by

hydrothermal growth at 2000 bars and hydrothermal growth at 2000 bars and 400400°C because of α-β quartz transition at °C because of α-β quartz transition at 583°C).583°C).

c.) Growth from the vapor phase:c.) Growth from the vapor phase:

Boule growth: only when Boule growth: only when other methods are not useful other methods are not useful (SiC, AlN sublimation-(SiC, AlN sublimation-condensation).condensation).

Thin layers, i.e., vapor Thin layers, i.e., vapor phase epitaxy: extensively phase epitaxy: extensively used (chemical vapor used (chemical vapor deposition, sputtering). E.g. deposition, sputtering). E.g. SiC is grown from vapor SiC is grown from vapor phase (sublimation-phase (sublimation-condensation) because it condensation) because it decomposes before melting.decomposes before melting.

2) Processes for crystal growth 2) Processes for crystal growth from the from the meltmelt::

2.1 Directional solidification, i.e. 2.1 Directional solidification, i.e. Bridgman Bridgman processprocess

2.2 Czochralski Method (CZ) and LEC2.2 Czochralski Method (CZ) and LEC 2.3 Zone melting and floating zone (FZ)2.3 Zone melting and floating zone (FZ)

It’s a Boy!!Born May 8, 2001 at 10:35 p.m.

Weight: 14 lbs, 9 ozLength: 15 inches

Crystal growth furnace for SUBSA investigation, destined for Space Station Alpha in May 2002.

Directional Solidification, i.e.Directional Solidification, i.e.Vertical Bridgman GrowthVertical Bridgman Growth

1.1. Charge and the seed Charge and the seed are placed into the are placed into the cruciblecrucible

1.1. Conservative process: Conservative process: no material is added or no material is added or removed from either removed from either solid or liquid phase, solid or liquid phase, except by crystallization except by crystallization (R.A. Laudise).(R.A. Laudise).

1.1. Axial temperature Axial temperature gradient is imposed gradient is imposed along the crucible.along the crucible.

1.1. Growth:Growth: Interface is Interface is advanced by moving the advanced by moving the container or the gradient container or the gradient (furnace/ heat source).(furnace/ heat source).

1.1. Seeding:Seeding: part of the part of the seed is seed is moltenmolten

Advantages of the Bridgman Process:Advantages of the Bridgman Process:

1.1. Simple: in confined growth, the shape of the crystal is Simple: in confined growth, the shape of the crystal is defined by the container.defined by the container.

2.2. Radial temperature gradients are not needed to Radial temperature gradients are not needed to control the crystal shape.control the crystal shape.

3.3. Low thermal stresses result in low level of stress-Low thermal stresses result in low level of stress-induced dislocations.induced dislocations.

4.4. Crystals may be grown in sealed ampules Crystals may be grown in sealed ampules (stoichiometry of melts with volatile constitutes is (stoichiometry of melts with volatile constitutes is easy to control).easy to control).

5.5. Relatively low level of natural convection; Melt Relatively low level of natural convection; Melt exposed to stabilizing temperature gradients (VB exposed to stabilizing temperature gradients (VB only).only).

6.6. Process requires little attention (maintenance).Process requires little attention (maintenance).

DrawbacksDrawbacks– Confined growth: container pressure on the crystal Confined growth: container pressure on the crystal

during cooling.during cooling.– Hard to observe the seeding process and growing Hard to observe the seeding process and growing

crystal.crystal.– Level of natural convection changes as the melt is Level of natural convection changes as the melt is

depleted, forced convection is hard to impose.depleted, forced convection is hard to impose.– Ampule and seed preparation, sealing, etc., does not Ampule and seed preparation, sealing, etc., does not

lend itself to high throughput production.lend itself to high throughput production.

Applications:Applications:– Melts with volatile constituents: III-V (GaAs, lnP, Melts with volatile constituents: III-V (GaAs, lnP,

GaSb) and II-VI compounds (CdTe).GaSb) and II-VI compounds (CdTe).– Ternary compounds (Ga1-lnxAs, Ga1-xlnxSb, Hg1-Ternary compounds (Ga1-lnxAs, Ga1-xlnxSb, Hg1-

xCdxTe).xCdxTe).

Liquid Encapsulation

Advantages:

Properties of a good encapsulant

- Prevents contact between the crystal and the melt

- Reduced nucleation

- Thermal stresses are reduced

- Reduced evaporation

- Melting temperature lower than the crystal

- Low vapor pressure

- Density lower than the density of the melt

- No reaction with the melt or the crucible

Best encapsulans:

- B2O3

- LiCl, KCl, CaCl2, NaCl

Crucible

Encapsulant

Melt

Crystal

Bridgman growth with the Submerged Baffle

H ~ 10 cm

H ~ 1 cmzonemelt

Fbuoyancy ~ g T H 3Fbuoyancy ~ g T H 3Fbuoyancy ~ g T H 3

•H(t) ~10 cmH(t) ~10 cm•large dT/drlarge dT/dr•free surfacefree surface

•H ~ 1 cm H ~ 1 cm •low dT/drlow dT/dr•no free surfaceno free surface•forced convectionforced convection

Gr gTH 3

2

Reducing ²T and H3 has the same effect as reducing g

2.2 Czochralski Method (CZ):2.2 Czochralski Method (CZ):

Conservative process: no material Conservative process: no material is added or removed from either is added or removed from either solid or liquid phase, except by solid or liquid phase, except by crystallization.crystallization.

Charge is held at temperature Charge is held at temperature slightly above melting point.slightly above melting point.

Seed is dipped into the melt and Seed is dipped into the melt and slowly withdrawn.slowly withdrawn.

Crystal grows as the atoms from Crystal grows as the atoms from the melt adhere themselves to the melt adhere themselves to the seed.the seed.

Advantages:Advantages:

• Growth from free surface (accommodates Growth from free surface (accommodates volume change).volume change).

• Crystal can be observed.Crystal can be observed.• Forced convection easy to impose.Forced convection easy to impose.• High throughput; large crystals can be obtained.High throughput; large crystals can be obtained.• High crystalline perfection can be achieved.High crystalline perfection can be achieved.• Good radial homogeneity.Good radial homogeneity.

Drawbacks:Drawbacks:Materials with high vapor Materials with high vapor

pressure can not be grown.pressure can not be grown.

Batch process; hard to adapt for Batch process; hard to adapt for continuous growth; result: axial continuous growth; result: axial segregation.segregation.

The crystal has to be rotated; The crystal has to be rotated; rotation of the crucible is rotation of the crucible is desirable.desirable.

Process requires continuous Process requires continuous attention (seeding, necking) attention (seeding, necking) and sophisticated control.and sophisticated control.

Drawbacks (continued):Drawbacks (continued):

Melt is thermally upside down.Melt is thermally upside down.

Temperature gradients are high to control the Temperature gradients are high to control the crystal diameter.crystal diameter.

High thermal stresses.High thermal stresses.

Shape and size of the crystal is hard to control if Shape and size of the crystal is hard to control if temperature gradients are low.temperature gradients are low.

Liquid encapsulated Czochralski method Liquid encapsulated Czochralski method (LEC)(LEC)

Advantages:Advantages:• Materials with high Materials with high

vapor pressure can be vapor pressure can be grown.grown.

• Retains most of CZ Retains most of CZ advantages: growth advantages: growth from a free surface, from a free surface, etc.etc.

• B2O3 prevents B2O3 prevents reaction between melt reaction between melt and crucible: prevents and crucible: prevents reaction between melt reaction between melt and ambient; dissloves and ambient; dissloves oxides (eg. Ga2O3).oxides (eg. Ga2O3).

Drawbacks:Drawbacks:

• Some loss of volatile constituent.Some loss of volatile constituent.• ““Contamination” by BContamination” by B22OO33..• BB22OO33 is too viscous below 1000 is too viscous below 1000°C.°C.• Encapsulant becomes opaque towards the end Encapsulant becomes opaque towards the end

of growth.of growth.

2.3 Zone melting and floating zone:2.3 Zone melting and floating zone:

• Nonconservative Nonconservative process: material is process: material is added to molten added to molten region.region.

• Only a small part of th Only a small part of th charge is molten charge is molten (except the seed).(except the seed).

• Axial temperature Axial temperature gradient is imposed gradient is imposed along the cruciblealong the crucible

• Molten zone (the Molten zone (the interface) is advanced interface) is advanced by moving the charge by moving the charge or the gradient.or the gradient.

AdvantagesAdvantages::

Charge is purified by repeated passage of the zone Charge is purified by repeated passage of the zone (zone refining).(zone refining).

Crystals may be grown in sealed ampules or without Crystals may be grown in sealed ampules or without containers (floating zone).containers (floating zone).

Steady-state growth possible.Steady-state growth possible.Zone leveling is possible; can lead to superior axial Zone leveling is possible; can lead to superior axial

homogeneity.homogeneity.Process requires little attention (maintenance).Process requires little attention (maintenance).Simple: no need to control the shape of the crystal.Simple: no need to control the shape of the crystal.Radial temperature gradients are high.Radial temperature gradients are high.

DrawbacksDrawbacks::

• Confined growth (except in floating zone).Confined growth (except in floating zone).• Hard to observe the seeding process and the Hard to observe the seeding process and the

growing crystal.growing crystal.• Forced convection is hard to impose (except in Forced convection is hard to impose (except in

floating zone).floating zone).• In floating zone, materials with high vapor In floating zone, materials with high vapor

pressure can not be grown.pressure can not be grown.

3) Convection and segregation3) Convection and segregation

y

xcrystal

melt

LC

D

V(y)

VD

C(x,y)

d i f f u s i o n

solute boundary layer

V

convection

Cs/k

y

xcrystal

melt

LC

D

V(y)

VD

C(x,y)

d i f f u s i o n

solute boundary layer

V

convection

Cs/k

liquidsolid

liquid

b)

c)

a)

liquid

solid

solid

Enclosure Heated from Below

Bernard Configuration

Cold

Hot

Cooled

Heated

R. Krishnamurti, J. Fluid Mech. 60 (1973) pp. 285-303

NaturalNatural

buoyancy forces moving boundary

less difficult predict (at S/L interface)

hard to predict,model and control

Magnitude: Gr g T L3

2

Features:

V ~ w L

unsteady: Gr > 5,000 turbulent:

Re R

disk2

Re 3x105

Driving mech.

Forced ConvectionForced Convection

L and T = f (time) ° f (time)

Growth process:

all CZ, FZ

Comparison of Natural and Forced ConvectionComparison of Natural and Forced Convection

c) Impose forced convectionforced convection- Accelerated Crucible Rotation Technique

- Coupled Vibrational Stirring

- Rotating Baffle

Control of Crystal Homogeneity

a) ReduceReduce natural convection:- Reduced gravity (µg)

- Magnetic fields

- Submerged baffle

b) Enhance Enhance natural convection - centrifuges

No motion of phase boundary

Beginning of motion

CSCL

k =

CLCS

T

Liquidus

Solidus

Conc.

CS

CL

Solid Liquid

CL= C0

Solid Liquid

time

CL(0)

V = Const

CS

Mass Transfer: Solid-Liquid Interface

LS kCC

• Te-doped InSb (R=1.5 cm/hr) • Ga-doped Ge (R=1.5 cm/hr) • mixed crystals (R=0.1 cm/hr)

~ 0.05 cm

~ 0.5 cm

~ 5 cm

C0

k · C0y

Diffusion-controlled segregation Tiller et al.Diffusion-controlled segregation Tiller et al.

CS

CL(y)

y

R [cm/r]

CL

02

2

x

CR

x

CD LL

x

D

RCCCC aL exp00

x

D

Rkkk

C

xCS exp110

0,

,0

CCxat

CCxat

L

aL

Perfect Mixing Scheil (1942), Pfann(1952)Perfect Mixing Scheil (1942), Pfann(1952)

LS kCC

∆ fS = change in solid fraction

Solidified Fraction, fS

CS

Cs

CL = CL

C0

k · C0

Solid Liquid

0 1

• no steady state• axial inhomogeneity (k<<1)

1-kS0S )f-(1CC k

interfaceat

rejected

solute

fractionliquidin

ionconcentrat

soluteofchange

sSLLs fCCCf 1

CS = k • CL

• assumption: 1-D flow (?)• Stagnant solute layer, at y = 0, v=0

Burton, Prim and Slichter’s Burton, Prim and Slichter’s BPS ModelBPS Model

x

D

Rkk

k

C

xCk S

eff exp1 00

0

0

Cs

C0

k · C0

0 1Solidified Fraction, g

x

axial and radialinhomogeniety

2

2

x

CD

y

Cv

x

CRu LLL

x

CDR

SL CC

CL = C0 at x = BPS

at x = 0

momentum B. L 4

Levich:

Kodera (1953): measurement of D [cm2/s]Kodera (1953): measurement of D [cm2/s]

BPS D(Levich)

measure k, R, , CS, CL

use BPS & D (Levich) to compute D

Levich soulution -Czochralski only-crucible = finite melt-natural convection, -couterrotation-turbulence

2/16/13/16.1 D

x

D

Rkk

k

C

xCk

BPS

SBPS

exp10

Burton, Prim and Slichter’s Burton, Prim and Slichter’s BPS Model, cont.BPS Model, cont.

D

RBPS

JCD = C(y) 0

D

u(y) dy

QAC = QBD + QCD = RL + u(y) dy 0

D

Solute Conservation in CV: JAC JBD JCD

JAC = CL QAC

y

Solute layer

JAC

DB

CA

L

D

JBD

J AC

JCD

x

Melt

CL

Cs

JBD CS R L

velocity concentration

y

Cs/kV(y)

VDV

LC

VD

C(y)

D

Ostrogorsky & Müller: Integral CV approachOstrogorsky & Müller: Integral CV approach

DL

SL

yC

k

CCyC

1)(

DD

yVyV

)(

D and VD are real physical parameter; analytical solutions exist.

·laminar and turbulent flow

a = 1/6

Ostrogorsky and Müller: Integral control-volume approach (cont.)

Table 1 D and V∞ for several important melt growth techniques

(CZ=Czochralski, FZ = Floating Zone, Gr = Grashof number)

n

D

Dx

4

n

D

D

V

xx

4

R

D 4.6 D

Driving Mechanism

GrowthMethod D V∞

Crystal rotation Cz, FZ V∞ L

Natural Convection

Bridgman V∞ ~Gr (/L)

Weak natural convectionin microgravity

Bridgman V∞~Gr(/L)1/2

kLR

Va

LR

Va

C

Ck

DD

DD

L

Seff 1

1

1

Growth rate R [µm/s]

keff

806040200

100

10

1.0

0.1

0.01

0.001

Ga (144 RPM)

Sb (144 RPM)

B (60 RPM)

data, Bridgers model

• Cochran's ∞ rotating disc:

V ~ R

J.Appl.Phy. 27(1956)686

VD ~ R • Sc1/2

• Levich (Sparrow and Gregg)

D ~ 4

• Sc1/2

Model of Ostrogorsky and Müller and Data of Bridges

kRDRD

C

Ck

L

Seff

132

1

32

1

keff versus growth rate R and for Czochralski grown crystals.

cold hot

V

cold hot

V

V [ m/s]

pulling rate

growth rateV [ m/s]

pulling rate

growth rate

LC

CL(0)

CS = k • C

L(0)

Microscopic Inhomogeneity (1m to 1 mm)

Caused by unsteady conditions:

•Unsteady (turbulent) flow, temperature, composition

•Crystal rotation

•Vibrations

Bridgman growth with the Submerged Baffle

H ~ 10 cm

H ~ 1 cmzonemelt

Fbuoyancy ~ g T H 3Fbuoyancy ~ g T H 3Fbuoyancy ~ g T H 3

•H(t) ~10 cmH(t) ~10 cm•large dT/drlarge dT/dr•free surfacefree surface

•H ~ 1 cm H ~ 1 cm •low dT/drlow dT/dr•no free surfaceno free surface•forced convectionforced convection

Gr gTH 3

2

Reducing ²T and H3 has the same effect as reducing g

Micro-segregation (a) Bridgman and (b) BaffleMicro-segregation (a) Bridgman and (b) Baffle

Car

rier

Con

cent

rati

on [

cm-3

] x

1e18

Without baffle

0 250 500 750 1000

Distance Grown [micron]

1.0

1.5

2.0

Car

rier

Con

cent

rati

on [

cm-3

] x

1e18

Without baffle

0 250 500 750 1000

Distance Grown [micron]

1.0

1.5

2.0

Car

rier

Con

cent

rati

on [

cm-3

] x

1e18

With baffle

0 200 400 600 8002.0

2.5

3.0

Distance Grown [micron]

Car

rier

Con

cent

rati

on [

cm-3

] x

1e18

With baffle

0 200 400 600 8002.0

2.5

3.0

Distance Grown [micron]

Spreading Resistance in 6 cm diameter Ga-doped Ge-2%Si alloySpreading Resistance in 6 cm diameter Ga-doped Ge-2%Si alloyMeasurements conducted by M. Lichtensteiger at NASA-MSFC [9]Measurements conducted by M. Lichtensteiger at NASA-MSFC [9]