Material must melt congruently (no change in composition during melting) e.g. Yttrium iron garnet (YIG) is grown from solutions because it does not melt congruently.
Material must not decompose before melting. e.g. SiC is grown from vapor phase (sublimation-condensation) because it decomposes before melting.
Material must not undergo a solid state phase transformation between melting point and room temperature. e.g. SiO 2 is grown from solution (hydrothermal growth) because of a α-β quartz transition at 583°C.
Advantages of solidification:
Fast (~ cm/hr ); growth rate depends on heat transfer (not on mass transfer).
Variety of techniques developed (e.g. crystal pulling and directional and zone solidification).
b.) Growth from solution:
For materials that:
(i) melt non congruently or
(ii) decompose before melting or
(iii) undergo a solid state phase transformation before melting or
(iv) have very high melting point.
Classification is based on the solvent type.
Key requirement: High purity solvent which is insoluble in the crystal.
b.1) Molten salt (flux) growth:
Common solvents: PbO, PbF 2 , B 2 O 3 , KF.
Used for oxides with very high melting points (or melt congruently, decompose or undergo a solid phase transformation).
e.g. Yttrium iron garnet (YIG) is grown from solutions because it does not melt congruently.
Advantages: carried on at much lower temperatures than melt growth.
Limitations: very slow; borderline purity, platinum crucibles, stoichiometry is hard to control.
b.2) Metallic solution growth:
Liquid phase Epitaxy – for high quality epitaxial layers of III-V compounds and boules;
GaAs from Ga solution (melt with > 50% Ga).
GaSb from Ga solution (melt with > 50% Ga).
Terary III-V compounds (solid solutions of III-V compounds): Ga 1-x ln x As, GaAs x P 1-x .
Advantages: growth at lower temperatures than melt growth yields high quality.
Limitations: very slow = small crystals or thin layers.
b.3) Hydrothermal growth:
Aqueous solution at high temperature and pressure (e.g. SiO 2 is grown by hydrothermal growth at 2000 bars and 400 °C because of α-β quartz transition at 583°C).
c.) Growth from the vapor phase:
Boule growth: only when other methods are not useful (SiC, AlN sublimation-condensation).
Thin layers, i.e., vapor phase epitaxy: extensively used (chemical vapor deposition, sputtering). E.g. SiC is grown from vapor phase (sublimation-condensation) because it decomposes before melting.
2) Processes for crystal growth from the melt :
2.1 Directional solidification, i.e. Bridgman process
2.2 Czochralski Method (CZ) and LEC
2.3 Zone melting and floating zone (FZ)
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Directional Solidification, i.e. Vertical Bridgman Growth
Charge and the seed are placed into the crucible
Conservative process: no material is added or removed from either solid or liquid phase, except by crystallization (R.A. Laudise).
Axial temperature gradient is imposed along the crucible.
Growth: Interface is advanced by moving the container or the gradient (furnace/ heat source).
Seeding: part of the seed is molten
Advantages of the Bridgman Process:
Simple: in confined growth, the shape of the crystal is defined by the container.
Radial temperature gradients are not needed to control the crystal shape.
Low thermal stresses result in low level of stress-induced dislocations.
Crystals may be grown in sealed ampules (stoichiometry of melts with volatile constitutes is easy to control).
Relatively low level of natural convection; Melt exposed to stabilizing temperature gradients (VB only).
Process requires little attention (maintenance).
Confined growth: container pressure on the crystal during cooling.
Hard to observe the seeding process and growing crystal.
Level of natural convection changes as the melt is depleted, forced convection is hard to impose.
Ampule and seed preparation, sealing, etc., does not lend itself to high throughput production.
Melts with volatile constituents: III-V (GaAs, lnP, GaSb) and II-VI compounds (CdTe).
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: - B 2 O 3 - LiCl, KCl, CaCl2, NaCl Crucible Encapsulant Melt Crystal
Bridgman growth with the Submerged Baffle
H ~ 1 cm
no free surface
H(t) ~10 cm
Gr g T H 3 2
2.2 Czochralski Method (CZ):
Conservative process: no material is added or removed from either solid or liquid phase, except by crystallization.
Charge is held at temperature slightly above melting point.
Seed is dipped into the melt and slowly withdrawn.
Crystal grows as the atoms from the melt adhere themselves to the seed.
Growth from free surface (accommodates volume change).
Crystal can be observed.
Forced convection easy to impose.
High throughput; large crystals can be obtained.
High crystalline perfection can be achieved.
Good radial homogeneity.
Materials with high vapor pressure can not be grown.
Batch process; hard to adapt for continuous growth; result: axial segregation.
The crystal has to be rotated; rotation of the crucible is desirable.
Process requires continuous attention (seeding, necking) and sophisticated control.
Melt is thermally upside down.
Temperature gradients are high to control the crystal diameter.
High thermal stresses.
Shape and size of the crystal is hard to control if temperature gradients are low.
Liquid encapsulated Czochralski method (LEC)
Materials with high vapor pressure can be grown.
Retains most of CZ advantages: growth from a free surface, etc.
B2O3 prevents reaction between melt and crucible: prevents reaction between melt and ambient; dissloves oxides (eg. Ga2O3).
Some loss of volatile constituent.
“ Contamination” by B 2 O 3 .
B 2 O 3 is too viscous below 1000 °C.
Encapsulant becomes opaque towards the end of growth.
2.3 Zone melting and floating zone:
Nonconservative process: material is added to molten region.
Only a small part of th charge is molten (except the seed).
Axial temperature gradient is imposed along the crucible
Molten zone (the interface) is advanced by moving the charge or the gradient.
Charge is purified by repeated passage of the zone (zone refining).
Crystals may be grown in sealed ampules or without containers (floating zone).
Steady-state growth possible.
Zone leveling is possible; can lead to superior axial homogeneity.
Process requires little attention (maintenance).
Simple: no need to control the shape of the crystal.
Radial temperature gradients are high.
Confined growth (except in floating zone).
Hard to observe the seeding process and the growing crystal.
Forced convection is hard to impose (except in floating zone).
In floating zone, materials with high vapor pressure can not be grown.
3) Convection and segregation
Enclosure Heated from Below
Natural buoyancy forces moving boundary less difficult predict (at S/L interface) hard to predict, model and control Magnitude: Features: V ~ w L unsteady: Gr > 5,000 turbulent: Driving mech. Forced Convection L and T = f (time) ° f (time) Growth process: all CZ, FZ Comparison of Natural and Forced Convection
c) Impose forced convection - Accelerated Crucible Rotation Technique - Coupled Vibrational Stirring - Rotating Baffle Control of Crystal Homogeneity a) Reduce natural convection: - Reduced gravity (µg) - Magnetic fields - Submerged baffle b) Enhance natural convection - centrifuges
No motion of phase boundary Beginning of motion Mass Transfer: Solid-Liquid Interface
Diffusion-controlled segregation Tiller et al.
Perfect Mixing Scheil (1942), Pfann(1952) ∆ f S = change in solid fraction Solidified Fraction, f S • no steady state • axial inhomogeneity (k<<1)
Burton, Prim and Slichter’s BPS Model • assumption: 1-D flow (?) • Stagnant solute layer, at y = 0, v=0 C L = C 0 at x = BPS at x = 0
Burton, Prim and Slichter’s BPS Model, cont. Levich: Kodera (1953): measurement of D [cm2/s] Levich soulution -Czochralski only -crucible = finite melt -natural convection, -couterrotation -turbulence
Solute Conservation in CV: Ostrogorsky & Müller: Integral CV approach
Ostrogorsky and Müller: Integral control-volume approach (cont.)
D and V D are real physical parameter; analytical solutions exist.
laminar and turbulent flow
a = 1/6 Table 1 D and V ∞ for several important melt growth techniques (CZ=Czochralski, FZ = Floating Zone, Gr = Grashof number) Driving Mechanism Growth Method D V ∞ Crystal rotation Cz, FZ V∞ L Natural Convection Bridgman V ∞ ~Gr ( /L) Weak natural convection in microgravity Bridgman V ∞ ~Gr( /L) 1/2
• Cochran's ∞ rotating disc: J.Appl.Phy. 27(1956)686 • Levich (Sparrow and Gregg) Model of Ostrogorsky and Müller and Data of Bridges k eff versus growth rate R and for Czochralski grown crystals.