BITS Pilani
BITS Pilani
Pilani Campus
Sindhu S
Dept of Physics, BITS Pilani, Pilani Campus
Dept of EEE, WILP Division, Bangalore
MELZG 611
IC Fabrication Technology
Lecture No.3
Date . 05/08/2023
What is a Semiconductor?
 Low resistivity => “conductor”
 High resistivity => “insulator”
 Intermediate resistivity => “semiconductor”
 conductivity lies between that of conductors and
insulators
 generally crystalline in structure for IC devices
 In recent years, however, non-crystalline
semiconductors have become commercially
very important
polycrystalline
amorphous
crystalline
Why Si?
 Ge:
 Narrower bandgap (~0.6eV), leakier, Oxide unstable,
 more expensive, less abundant.
 Higher electron mobilities than silicon (higher speed).
 Used only in select high performance applications with lower levels of
integration
 GaAs:
 Difficult to fabricate, higher defect densities, more expensive, difficult to
oxidize
 Used extensively in optoelectronic applications
 Si:
 Abundant, inexpensive, easier processing, excellent quality of SiO2, ideal
physical and chemical properties, lower defects, etc.
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Crystallography and crystal structure
 Crystals are described by their most basic structural element:
UNIT CELL.
 Crystal: array of unit cells repeated in a regular manner over
3D.
 Each edge of unit cell will have same length: cubic
symmetry.
 Common crystalline structures: simple cubic, BCC and FCC
Unit cell
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• An ideal crystal is a periodic array of structural
units, such as atoms or molecules.
• It can be constructed by the infinite repetition of these
identical structural units in space.
• Structure can be described in terms of a lattice, with
a group of atoms attached to each lattice point. The
group of atoms is the basis.
Bravais Lattice
 An infinite array of discrete points with an arrangement
and orientation that appears exactly the same, from any of
the points the array is viewed from.
 A three dimensional Bravais lattice consists of all points
with position vectors R that can be written as a linear
combination of primitive vectors. The expansion
coefficients must be integers.
Primitive Unit Cell
 A primitive cell or primitive unit cell is a volume of
space that when translated through all the vectors in a
Bravais lattice just fills all of space without either
overlapping itself or leaving voids.
 A primitive cell must contain precisely one lattice
point.
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 Crystals are described by their most basic structural
element: UNIT CELL.
 Crystal: array of unit cells repeated in a regular manner
over 3D.
 Each edge of unit cell will have same length: cubic
symmetry.
 Common crystalline structures: simple cubic, BCC and
FCC
Unit cell
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Unit cell types
 Correspond to 6 distinct shapes, named after the 6 crystal systems
 In each, representations include ones that are:
 Primitive (P) – distance between layers is equal to the distance
between points in a layer
 Body-centered (I) – extra point in the center
 End-centered (A,B,C) – extra points on opposite faces, named
depending on axial relation
 Face centered (F) – extra points at each face
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Bravais Lattices
 Assembly of the lattice points in 3-D results in 14
possible combinations
 Those 14 combinations may have any of the 6 crystal
system (class) symmetries
 These 14 possibilities are the Bravais lattices
c
c
c
b
a
b
b
P
P
a I
Monoclinic
a = g = 90o  
abc
a
Triclinic
a   g
abc
c
a
b
P
C
F
Orthorhombic
a =  = g = 90o a  b  c
I
=C
c
c
a2
a1
a2
P
a1
I
Tetragonal
a =  = g = 90o a1 = a2  c
P or C
R
Hexagonal
Rhombohedral
a =  = 90o g = 0o a =  = g  90o
a1 = a2 = a3
a1 = a2  c
a.k.a. Trigonal
a3
a2
a1
P
F
I
Isometric
a =  = g = 90o a1 = a2 = a3
Simple Crystal Structures
There are several types of simple crystal structures:
 Sodium Chloride (NaCl) -> FCC lattice, one
Na and one Cl atom separated by one half the
body diagonal of a unit cube.
 Cesium Chloride -> BCC lattice with one
atom of opposite type at the body center
 Hexagonal Closed packed structure (hcp)
 Diamond structure -> Fcc lattice with
primitive basis that has two identical atoms
 ZnS -> FCC in which the two atoms in the
basis are different.
Crystalline structure
Amorphous structure
Specifying
crystal
planes
:
Miller
Indices
Any of a set of three numbers or letters used to indicate
the position of a face or internal plane of a crystal and
determined on the basis of the reciprocal of the intercept of
the face or plane on the crystallographic axes.
Z
Z
Y
X
Y
X
(100)
Z
Y
X
(110)
(111)
MILLER INDICES
Directions
Planes
MILLER INDICES
Lattices
Crystals
Both are imaginary
 Miller indices are used to specify directions and
planes:
 These directions and planes could be in lattices
or in crystals:
 The number of indices will match with the
dimension of the lattice or the crystal; in 1D
there will be 1 index and 2D there will be two
indices etc:
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How to find the Miller Indices for an arbitrary direction?  Procedure
 Consider the example below
 Subtract the coordinates of the end point from the starting point of the vector denoting the
direction  If the starting point is A(1,3) and the final point is B(5,1)  the difference
would be (4, 4)
 Enclose in square brackets, remove comma and
write negative numbers with a bar  [4 4]
 Factor out the common factor  4[11]
 If we are worried about the direction and
magnitude then we write  4[11]
 If we consider only the direction then we
write  [11]
 Needless to say the first vector is 4 times
in length
 The magnitude of the vector [11] = [11]
is (1) 2  (1) 2 = 2
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Further points
General Miller indices for a direction in 3D is written as
[u v w]
The length of the vector represented by the Miller indices
is:
Notation Summary
•(h,k,l) represents a point
•Negative numbers/directions are denoted with a bar on
top of the number
•[hkl] represents a direction
•<hkl> represents a family of directions
•(hkl) represents a plane
•{hkl} represents a family of planes
Miller Indices for directions
•A vector r passing from the origin to a lattice point can
be written as:
r = r1a + r2b + r3 c
where, a, b, c → basic vectors and
miller indices → (r1r2r3)
 Fractions in (r1r2r3) are eliminated by multiplying all
components by their common denominator.
[e.g. (1, ¾ ,½ ) will be expressed as (432)]
Index represents a set of all parallel vectos
Miller indices for planes
Consider the plane in
pink, which is one of an
infinite number of
parallel plane each a
consistent distance (“a”)
away from the origin
•The plane intersects the x-axis at point a.
It runs parallel along y and z axes.
•Thus, this plane can be designated as
(1,∞,∞)
Here the yellow plane
can be designated as
(∞,1,∞)
•And the green plane can
be written as (∞,∞,1)
• Miller Indices are the reciprocals
of the parameters of each crystal
face. Thus:
• Pink Face
= (1/1, 1/∞, 1/∞) = (100)
• Green Face
= (1/∞, 1/∞, 1/1) = (001)
• Yellow Face
= (1/∞, 1/1, 1/∞) = (010)
Miller indices here?
The plane of interest cuts two of the crystallographic axes.
• Intercepts: (1,1, ∞) → (110)
• This plane cuts all three crystallographic axes.
• Intercepts = (1,1,1) → (111)
This plane cuts two of the reference axes,
but not equidimensionally.
•Intercepts: (½, 1, 0) → (210)
Family of Directions
It’s a set of directions related by symmetry operations of the lattice.
Importance of Material Science
In Materials Science it is important to have a notation system
for atomic planes since these planes influence
•Optical properties
•Reactivity
•Surface tension
•Dislocations