How do single crystals differ from polycrystalline samples ...

Crystal

• How do single crystals dif
samples?
Single crystal specimens ma
over macroscopic distances
typically 0.1 mm – 10 cm).

• Why would one go to the e
crystal?
-Structure determination and
measurements are preferab
carried out on single crystals
-For certain applications, mo
optical and/or electronic pro
semiconductors, etc.), single

Growth

ffer from polycrystalline

aintain translational symmetry
s (crystal dimensions are

effort of growing a single

d intrinsic property
bly, sometimes exclusively,
s.
ost notably those which rely on
operties (laser crystals,
e crystals are necessary.

1

Estimated shares of world
(Reprinted from H. J. Sche
211(2000) 1–12.

crystal production in 1999.
eel, J. Cryst. Growth

2

• What factors control the s
crystals?

- Nucleation and Growth. If n
growth is rapid, large crystal
if nucleation is rapid, relative
even polycrystalline samples

• What can be done to incre

- In order to attain the rapid g
macroscopic crystals, diffusi
Hence, crystal growth typica
solid from another state of m
(a) Liquid (Melt) ÆSolid (Fre
(b) Gas (Vapor) Æ Solid (C
(c) Solution Æ Solid (Pr

• It should be noted that def
increase as the growth rat

Consequently the highest qu
slowly.

size and purity of single

nucleation rates are slow and
ls will result. On the other hand,
e to growth, small crystals or
s will result.
ease the growth rates?
growth rates needed to grow
ion coefficients must be large.
ally occurs via formation of a
matter :
eezing)
Condensation)
recipitation)
fect concentrations tend to
te increases.
uality crystals need to be grown

3

• What can be done t
of nucleation sites?

Several techniques ar
in combination to ind
solid phase at a slow
(a) Slow Cooling of M
(b) Temperature Gra
(c) Introduction of Se

to limit the number
?

re used separately or
duce nucleation of the
w and controlled rate :
Melts
adients
eed Crystals

4

Slow cooling o

• With congruently melting mate
same composition on melting), o
desired composition then cools
through the melting point.

• More difficult with incongruentl
of the phase diagram is needed

• Very often, the phase diagram i
is no guarantee that crystals wil

• Molten salt fluxes are often used
systems where melting points a
melting occurs.

• Crystals grown in this way are o
method is frequently used in res
appropriate for applications whe

of the melt

erials (those which maintain the
one simply melts a mixture of the
slowly (typically 2-10 °C/h)

ly melting materials, knowledge
d.

is not known. Consequently, there
ll have the intended stoichiometry.

d to facilitate crystal growth in
are very high and/or incongruent

often rather small. Thus, this
search, but usually not
ere large crystals are needed.

5

Congruent and Incon
in Binary and Tern

• The thermal behavior of in
of three basic types: congr
melting, or dissociation.

• An intermediate compound
two end members of a bina
diagram that forms a differ
the two solids.

• Congruency of melting is im
determination of phase an
drawing crystallization path

ngruent Melting
nary Systems

ntermediate compounds is
ruent melting, incongruent

d is a combination of the
ary or ternary phase
rent component between

mportant in the
nalysis diagrams and in
hs.

6

Congruen

• Binary Systems
– In binary systems, compounds ar
composed of various ratios of the
two end members (A & B), or the
basic components of the system.
– These end members are assume
to melt congruently.
– The intermediate compound AB2
melts congruently, because at so
temperature (the top of the AB2
phase boundary line) it coexists
with a liquid of the same
composition.

nt Melting

re
e
e
.
ed

2

ome

7

Incongrue

• Binary Systems
– The end components in this bin
phase diagram also melt
congruently.

– The intermediate compound in t
diagram (XY2) however is
incongruently melting.

– Incongruent melting is the
temperature at which one solid
phase transforms to another so
phase and a liquid phase both o
different chemical compositions
than the original composition.

– This can be seen in this diagram
XY2 melts to Y and liquid.

ent Melting

nary

this

olid
of
s
m as

8

Multiple Incong
Regi

• Binary Systems
– This diagram shows many
different intermediate
compounds (Q,R,&S) that
melt incongruently.
– Each of these
intermediate compounds
melts to a liquid and a
solid of a different
composition.

gruent Melting
ions

y
t

9

The Development of Crys

HANS J. SCHEEL
SCHEEL CONSULTING, CH-8808

Figure 1.1 Stages of flame-fusion (
formation of sinter cone and central m
growth of the neck by adjustment of
oxygen flame, (c) Increase of the dia
cap for the growth of the single-cryst
Cryst. Growth 211(2000) 1–12)

ystal Growth Technology

8 Pfaeffikon SZ, Switzerland

(Verneuil) growth of ruby, schematic: (a)
melt droplet onto alumina rod, (b)
powder supply and the hydrogen-
ameter without overflow of the molten
tal boule. (Reprinted from H. J. Scheel, J.

10



11



Modification of
Verneuil’s
principles of
nucleation control
and increasing
crystal diameters in
other crystal-
growth techniques.

(Reprinted from H. J.
Scheel, J. Cryst.
Growth 211(2000) 1–
12.

12



13

Figure 1. The Stockbarger-type furnace.

14



15



16



17

Zone Melting

• A polycrystalline specimen i
shape of a cylinder and plac
seed crystal near the top of

• The sample cylinder is place
narrow hot zone (sometimes
lamps as heat sources).

• The portion of the cylinder c
heated to the melting point,
slowly pulled through the ho

• Zone melting setups are mo
Bridgman or Stockbarger me

• Bridgman -- Hot zone moves
Stockbarger -- Crucible mov

is prepared, typically in the
ced into a crucible, with a
the crucible.
ed in a furnace with a very
s this is done using halogen

containing the seed crystal is
and the rest of the cylinder is
ot zone.
odifications of either the
ethods of crystal growth.
s, crucible stationary
ves, hot zone stationary

18

Czochralsk

• A seed crystal is attache
rotated slowly.

• The seed crystal is dipp
temperature slightly abo

• A temperature gradient
rod and slowly withdraw
surrounding atmosphere

• Decreasing the speed w
pulled from the melt, inc
crystals (fewer defects)
growth rate.

ki Method

ed to a rod, which is

ped into a melt held at a
ove the melting point.
is set up by cooling the
wing it from the melt (the
e is cooler than the melt)
with which the crystal is
creases the quality of the
but decreases the

19

• The advantage of the
is that large single cr
thus it used extensive
semiconductor indus

• In general this metho
incongruently melting
course the need for a
same composition lim
exploratory synthetic

e Czochralski method
rystals can be grown,
ely in the
stry.
od is not suitable for
g compounds, and of
a seed crystal of the
mits its use as tool for
c research.

20



21

Wafer Tec

• It may appear rather trivial now to
after some polishing, result in the
material for chip production. How

• While a wafer does not look like m
Again, making wafers is a closely
even more difficult to see a wafer
crystal production.

• First, wafers must all be made to
specifications. Not only must the
precisely what they ought to be, b
about 1 µm. This means that the
most about 1 µm from an ideally f
areas of more than 1000 cm2 for
just true for one wafer, but for all
one factory.

• The number of Si wafers sold in 2
roughly 300.000 a day! Only tight
plenty of know-how and expensiv
specifications. The following pictu
step of a many-step polishing pro

chnology

o cut the crystal into slices which,
e wafers used as the starting
wever, it is not trivial.

much, its not easy to manufacture.
y guarded secret and it is possibly
r production than a single Si

exceedingly tight geometric
diameter and the thickness be
but the flatness is constrained to
e polished surface deviates at
flat reference plane - for surface
a 300 mm wafer! And this is not
10.000 or so produced daily in

2001 is about 100.000.000 or

tly controlled processes with

ve equipment will assure these

ure gives an impression of the first

ocedure. 22



23



24

Chemical Vapor Transport
- A polycrystalline sample, A,
are sealed together inside a tu
- Upon heating the transportin
sample to produce a gaseous
- When AB reaches the other
different temperature, it decom

If formation of AB is endother
cold end of the tube.
A (powder) + B (g) Æ AB (g) (
AB (g) ÆA (crystal) + B (g) (c

If formation of AB is exotherm
hot end of the tube.
A (powder) + B (g) Æ AB (g) (

AB (g) ÆA (crystal) + B (g) (h

and a transporting species, B,
ube.
ng species reacts with the
s species AB.
end, which is held at a
mposes and re-deposits A.

rmic crystals are grown in the

(hot end)
cold end)

mic, crystals are grown in the

(cold end) 25
hot end)