Semiconductor Crytals:
Semiconductor crystals are composed of atoms from column IV, III & V, or column II & VI
Most commonly used is Si b/c it readily grows a insulating thermal oxide (Si02)
Properties and Growth
3 basic solid types:
Crystalline (ordered)
diamond
Amorphous (disordered)
window glass
Polycrystalline (single crystallines ordered together randomly)
polysilicon
Crystal: periodic array of atoms
Structure described by:
Bravais lattice – periodic array of points
Defined by a set of ‘translation vectors’
Unit Cell
– shape can be translated via translation vectors to fill volume
(Cannot be rotated)
Will contain a net of one lattice point and one atomic basis set
Atomic basis fixed array of one or more atoms assoc. with each b.lattice
If structure cannot be reproduced using smaller atomic basis
called
primitive
Cubic lattice types:
Simple cubic
Bodycentered cubic
Facecentered cubic
primitive lattice of most semiconductors
Diamond and Zincblende have a fcc primitive lattice with a two atom basis
Diamond: two atoms are same type
Si, or Ge (column IV)
Zincblende: two atoms are different types
GaAs or AlAs (column III,
V)
Atom is bonded to its four nearest neighbors is a tetrahedral arrangement
can also be described with a sc lattice with eight atom basis
For all cubic lattices there are 48 equivalent directions
(6 permutations based on order * 8 based on sign)
Except in case where coordinate coefficients are the same or zero
Miller Indices:
Direction:
e
Write the direction vector
r
in terms of the lattice
translation/basis vectors
r
=
p
a
1
+
q
a
2
+
s
a
3
r
Scale
p, q,
and
s
via a positive number to obtain the smallest
set of integers that have the same ratio to each other,
h, k
and
l. (Find and multiply by smallest common denominator,
or divide by largest common factor.)
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use [] for parallel directions, and <> for equivalent direction
Planes:
take the reciprocals of
P, Q
and
S
to obtain
p, q
and
s
,
respectively:
p
= 1/
P, q
= 1/
Q
and
s
= 1/
S
.
r
Scale
p, q,
and
s
to obtain the smallest set of integers that have
the same ratio to each other,
h, k
and
l
(usually).
Use () for parallel planes, and {} for equivalent plane
For sc [hkn] is normal to (hkn)
Planes:
Bulk Crystal Growth:
Need for high purity and large semiconductor crystals
Obtaining large metal ingot (high purity semiconductor crystal)
Czolchralski method: using single seed crystal, large ingot grown, and then pulled from it melt
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 Spring '08
 Banjeree
 Condensed matter physics, valence band, Fermi level, majority carrier concentration, primitive Cubic lattice

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