• What is a single crystal?
• Single crystals cost a lot of money.
• When and why is the cost justified?
– Current semiconductor devices on an IC have characteristic dimensions of ¼ micron.
– What happens if grain size is on the scale of microns?
– What makes optical materials look translucent?
– What happens when a “weapons grade laser beam” hits an inhomogeneity in an optical component?

For what applications are single crystals necessary?
1. Semiconductor optoelectronics (substrate materials)
Transistors, diodes, integrated circuits: Si, Ge, GaAs, InP
LEDs and lasers: GaAs, GaInAs, GaInP, GaAsP, GaP:N, ruby
Solar cells: Si, GaAs, GaInP/GaAs tandems
Microwave sources: GaAs
2. Non-glass optics (see previous lecture for transmission ranges): alkali halides, alkaline earth halides, thallium halides, Ge, sapphire
3. Electromechanical transducers
Ultrasonic generators, sonar: ADP, KDP
Strain gauges: Si
Optical modulators: LiNbO
3
, BaTiO
3
, BaNaNiO
3
Piezoelectric microphone sources: quartz
4. Radiation detectors: HgI
2
, NaI:Tl, CsI:Tl, LiI:Eu, Si, Ge, III-V, II-VI, PbS

5. Micromechanical devices: Si Utah Neural Array (SEM image)
6. Research: everything. Why?
7. Artificial gems: sapphire, ruby, TiO
2
, ZrO
2
Why are they necessary for those applications? (Numbers correspond)
1. Electrical homogeneity on the length scale of the device; minimum carrier scattering
2. Optical homogeneity on the length scale of the light being transmitted; minimum light scattering
3. Mechanical strength and homogeneity; availability of processing technology: nickel-based super alloy turbine blades
4. Purity; well-defined material
In all cases: optical, electronic or mechanical properties superior to nonsingle crystal competition.

Aps.org

Technique
Melt:
”Directional
Solidification”
Examples
Elemental & Compound semiconductors: Si, Ge,
GaAs, InP
Advantages
FAST
Large sizes possible
Disadvantages
Often energy intensive some materials decompose before melting
Bridgman
(horizontal/vertical)
CuInSe
2
, MCT, CdTe, ZnSe,
GaSe Oxides-insulators: sapphire
Reasonable K eff
Seeded: predetermined orientation
Crucible can be a problem
Czochralski ("Cz")
Windows: sapphire
Scintillators: BGO, CdWO
4
NLO materials: LiNbO
3
,
CsLiB
6
O
10
Alkali scintillators-CsI:Tl
Halides: windows-wide transmitting filters
Always the technique of choice
Dopants can be volatile
Contamination

Vapor
Technique Examples Advantages Disadvantages
Physical vapor transport
(evaporation & condensation)
HgI
Hg
2
2
, CdS, ZnS, NH
Cl
2
, CdS
4
X
Molecular Organics!
Can be used with materials that decompose or have excessive vapor pressure at melting point or with destructive phase transitions or extremely high melting points or which react with containers.
Materials must have reasonable vapor pressure at temperature where surface kinetics is adequate
Typically slow
Difficult to control
Chemical vapor deposition
(open flow)
Chemical vapor transport
(closed system)
Solution/Flux
Refractories: SiC, PBN
Semiconductor epitaxy!
TiO
2
, EuS, "halogen lamps"
SnO
2
, In
2
S
3
Very slow; batch process
ADP, KDP, Refractories
Hydrothermal quartz
Diamond: 1450 C, 742 kpsi,
Ni flux
Proteins, Minerals, Mo
2
C
High T c superconductors;
BiSrCaCuO
Morton’s tablesalt
Large sizes possible
Potentially low cost, large scale
Reduced temperature
 less container contamination
Can be inexpensive
Very slow
Temperature control very important
K eff often very small
 doping difficult

• Electronic materials are only interesting when doped
• Carrier type: “n”
• Dopant: “P”
• “Res”:
“1-20 ohms”

• On previous label, ρ = 1-20 Ohm (presumably 1-
20 Ω-cm)
• As you know: σ = 1/ρ = ne μ
• For silicon at 10 Ω-cm with μ
= 3.7x10
14 /cm 3 n
= 1700 cm 2 /V-sec
•
• n n
P
Si
= 2.33 gm/cm 3 ) x(6.02x10
23 atoms/mole)
÷(28.068 gm/mole) = 4.997x10
22 atoms per mole
• n
P
/ n
Si
= 7x10 -9 = 7 ppb!
• Background impurity level must be small on this scale!

• Coefficient can be greater or less than unity
• Nutrient volume is finite
– Causes major problems with dopant uniformity
– Can be resolved by adding dopant to melts during growth
• Only works for K>1!

W. G. Pfann, Zone Melting

n.b.: exactly the same process is used to grow large single crystals “from the melt”!
W. G. Pfann, Zone Melting

W. G. Pfann, Zone Melting

W. G. Pfann, Zone Melting
Molten zone of length l is passed through ingot of length L
Also the process used to make “float zone silicon”

(Less efficient than normal freezing)
W. G. Pfann, Zone Melting

W. G. Pfann, Zone Melting

• Segregation of impurities/dopants is a fact that you must deal with as an aspect of materials preparation
• Segregation can be used as part of an elegant purification process
• Zone refining can be very effective for materials purification

(Wikipedia)
• Siemens process: high-purity silicon rods are exposed to trichlorosilane at 1150 °C. The trichlorosilane gas decomposes and deposits additional silicon onto the rods, enlarging them:
• 2 HSiCl
3
→ Si + 2 HCl + SiCl
4
• Silicon produced from this and similar processes is called polycrystalline silicon .
Polycrystalline silicon typically has impurity levels of less than 10 −9 .

www.people.seas.harvard.edu
Synthesis may or may not be part of growth
GaAs may be pre-synthesized or a premeasured quantity
As may be bubbled through Ga metal
Li H synthesized from Li and H
2
(or D
2
)
Typical sizes: Si 12" φ, 200 kg charge; GaAs 4" φ
We have grown from a 2 g melt of isotopically pure K 13 C 15 N
Typical growth rates: cm/hr

Melting point isotherm is directionally translated through an ingot from a spatially confined region.
Typically unseeded
 no seed necessary
Can be seeded: quality as high as
Czochralski
High yield: all starting material is recovered as single crystal
Diameters to 22 inches; 40 cm 2 square KDP
Used extensively for alkali halide scintillators, transducers and windows