Sheet Pile Wall Design and Construction: A Practical Guide for Civil Engineer...
Basic Concepts of Material Science for Electrical and Electronic Materials Module 1.ppt
1. Complied by:
Prof. Vijaya Agarwala BE, MTech, PhD
Professor and Head, Center of Excellence Nanotechnology
&
Professor, Metallurgical and Materials Engineering and
IIT Roorkee
Electrical and Electronic Materials
L-3, T-1, P-0
4 credits: CWS-25%, MTE-25%, ETE-50%
2. Electrical and Electronic Materials 2
Electrical and Electronic Materials
Electrical Materials- High Current/ voltage
Electronic Materials- Low Current/ voltage
Why??
Any thing to do with the mechanism in atomic or electronic levels??
If yes how?
Accordingly how you classify the materials, study their behaviour in the
given environment…
Course comprises of 6 modules (36 Lectures):
Module-1 Basic concept of Material Science (10 L)
Module-2 Conduction in conductors (4 L)
Module-3 Wave theory (7L)
Module-4 Semiconductors (6 L)
Module-5 Magnetic Materials (4 L )
Module-6 Superconductors & Dielectric Materials (5 L)
4. Contents
4
S No
(units)
Topics
1 Atomic bonding energy
2 Crystal systems
3 Allotropes of carbon
4 Stacking sequence
5 Miller Index
6 X’ tal defects
7 Phase and phase diagrams
8 Nano X’ tal
9 Single X’ tal bulk growth
10 Epitaxial growth - coatings
11 Tutorial 1
Basic Materials Science concepts- Module 1
Electrical and Electronic Materials
6. The shell model of the atom in which electrons are confined to live within
certain shells and in subshells within shells
7. Fig 1.3
Electrical and Electronic Materials
Force is considered the change in potential energy, E, over a change in position.
F = dE/dr
8. Fig 1.8
The formation of ionic bond between Na and Cl atoms in NaCl. The attraction
Is due to coulombic forces.
Electrical and Electronic Materials
9. Fig 1.10
Sketch of the potential energy per ion-pair in solid NaCl. Zero energy
corresponds to neutral Na and Cl atoms infinitely separated.
Electrical and Electronic Materials
10. Electrical and Electronic Materials Fig 1.12
The origin of van der Walls bonding between water molecules.
(a) The H2O molecule is polar and has a net permanent dipole moment
(b) Attractions between the various dipole moments in water gives rise to
van der Walls bonding
11. Electrical and Electronic Materials 11
Covalent bonding
-sharing of electron
-strong bond, so high MP
-directional, low electrical conductivity
Metallic Bonding
-random movements of electron, electron cloud
-high electrical conductivity
12. Crystal Systems
• Most solids are crystalline with their atoms arranged in a
regular manner.
• Long-range order : the regularity can extend throughout the
crystal.
• Short-range order : the regularity does not persist over
appreciable distances. eg. amorphous materials such as glass
and wax.
• Liquids have short-range order, but lack long-range order.
• Gases lack both long-range and short-range order
Ref: http://me.kaist.ac.kr/upload/course/MAE800C/chapter2-1.pdf
12
Electrical and Electronic Materials
13. Crystal Structures (Contd…)
• Five regular arrangements of lattice points that can
occur in two dimensions.
(a) square; (b) primitive rectangular;
(c) centered rectangular; (d) hexagonal;
(e) oblique.
13
Electrical and Electronic Materials
17. Number of lattice points per cell
Where,
Ni = number of interior points,
Nf = number of points on faces,
Nc = number of points on corners.
17
Electrical and Electronic Materials
19. Any of the fourteen Bravais lattices may be referred to a
combinatin of primitive unit cells.
Face centered cubic lattice
shown may be referred to
the primitive cubic cell and
rhombohedral cell
(indicated by dashed lines,
its axial angle between a is
600, and each of its side is
√2 a, where a is the lattice
parameter of cubic cell.
19
Electrical and Electronic Materials
35. Coordination number
Number of nearest neighbors of an atom in the crystal lattice
35
Electrical and Electronic Materials
36. 5
• Rare due to poor packing (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)
(Courtesy P.M. Anderson)
SIMPLE CUBIC STRUCTURE (SC)
36
Electrical and Electronic Materials
Polonium is a chemical element with the symbol Po
and atomic number 84, discovered in 1898 by Marie
and Pierre Curie. A rare and highly radioactive
element ...
37. 6
• APF for a simple cubic structure = 0.52
Adapted from Fig. 3.19,
Callister 6e.
ATOMIC PACKING FACTOR
37
Electrical and Electronic Materials
38. • Coordination # = 8
7
Adapted from Fig. 3.2,
Callister 6e.
(Courtesy P.M. Anderson)
• Close packed directions are cube diagonals.
--Note: All atoms are identical; the center atom is shaded
differently only for ease of viewing.
BODY CENTERED CUBIC STRUCTURE (BCC)
38
Electrical and Electronic Materials
39. a
R
8
• APF for a body-centered cubic structure = 0.68
Unit cell c ontains:
1 + 8 x 1/8
= 2 atoms/unit cell
Adapted from
Fig. 3.2,
Callister 6e.
ATOMIC PACKING FACTOR: BCC
39
Electrical and Electronic Materials
40. 9
• Coordination # = 12
Adapted from Fig. 3.1(a),
Callister 6e.
(Courtesy P.M. Anderson)
• Close packed directions are face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded
differently only for ease of viewing.
FACE CENTERED CUBIC STRUCTURE (FCC)
40
Electrical and Electronic Materials
41. Unit cell c ontains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cell
a
10
• APF for a body-centered cubic structure = 0.74
Adapted from
Fig. 3.1(a),
Callister 6e.
ATOMIC PACKING FACTOR: FCC
41
Electrical and Electronic Materials
42. 14
Example: Copper
Data from Table inside front cover of Callister (see next slide):
• crystal structure = FCC: 4 atoms/unit cell
• atomic weight = 63.55 g/mol (1 amu = 1 g/mol)
• atomic radius R = 0.128 nm (1 nm = 10 cm)
-7
Compare to actual: Cu = 8.94 g/cm 3
Result: theoretical Cu = 8.89 g/cm 3
THEORETICAL DENSITY,
42
Electrical and Electronic Materials
44. metals •ceramic s •polymer s
16
Metals have...
• close-packing
(metallic bonding)
• large atomic mass
Ceramics have...
• less dense packing
(covalent bonding)
• often lighter elements
Polymers have...
• poor packing
(often amorphous)
• lighter elements (C,H,O)
Composites have...
• intermediate values
Data from Table B1, Callister 6e.
DENSITIES OF MATERIAL CLASSES
44
Electrical and Electronic Materials
46. 18
• Most engineering materials are polycrystals.
• Nb-Hf-W plate with an electron beam weld.
• Each "grain" is a single crystal.
• If crystals are randomly oriented,
overall component properties are not directional.
• Crystal sizes typ. range from 1 nm to 2 cm
(i.e., from a few to millions of atomic layers).
Adapted from Fig. K,
color inset pages of
Callister 6e.
(Fig. K is courtesy of
Paul E. Danielson,
Teledyne Wah Chang
Albany)
1 mm
POLYCRYSTALS
46
Electrical and Electronic Materials
47. 19
• Single Crystals
-Properties vary with
direction: anisotropic.
-Example: the modulus
of elasticity (E) in BCC iron:
• Polycrystals
-Properties may/may not
vary with direction.
-If grains are randomly
oriented: isotropic.
(Epoly iron = 210 GPa)
-If grains are textured,
anisotropic.
200 mm
Data from Table 3.3,
Callister 6e.
(Source of data is R.W.
Hertzberg, Deformation
and Fracture Mechanics
of Engineering
Materials, 3rd ed., John
Wiley and Sons, 1989.)
Adapted from Fig.
4.12(b), Callister 6e.
(Fig. 4.12(b) is courtesy
of L.C. Smith and C.
Brady, the National
Bureau of Standards,
Washington, DC [now
the National Institute of
Standards and
Technology,
Gaithersburg, MD].)
SINGLE VS POLYCRYSTALS
47
Electrical and Electronic Materials
48. Face-Centered Cubic
Nanoparticles
• Figure (a) shows the 12 neighbors that surround an atom
(darkened circle) located in the center of a cube for a FCC lattice.
• Figure (b) presents another perspective of the 12 nearest neighbors.
These 13 atoms constitute the smallest theoretical nanoparticle for an
FCC lattice.
• Figure (c) shows the 14-sided polyhedron, called a
dekatessarahedron, that is generated by connecting the atoms with
planer faces
48
Electrical and Electronic Materials
49. If another layer of 42 atoms is layed around the 13-atom
nanoparticle, one obtains a 55-atom nanoparticle with the
same dekatessarahedron shape.
Lager nanoparticles with the same polyhedral shape are
obtained by adding more layers, and the
sequence of numbers in the resulting particles, N
N=1, 13, 55, 147,.., which are called structural magic numbers.
49
Electrical and Electronic Materials
50. Atoms in nano clusters
• For n layers, the number of
atoms N and the number of
atoms on the surface Nsurf
in this FCC nanoparticle is
given by the formula,
N = 1/3(10 n3 −15 n2 +11 n −3)
Nsurf =10n2 − 20n +12
50
Electrical and Electronic Materials
51. Atomic packing
• In two dimensions the most efficient way to pack identical circles is
equilateral triangle arrangement shown in figure (a).
• A second hexagonal layer of spheres can be placed on top of the first
to form the most efficient packing of two layers, as shown in figure (b).
• For efficient packing, the third layer can be placed either above the
first layer with an atom at the location indicated by T or in the third
possible arrangement with an atom above the position marked by X on
the figure.
• In the first case a hexagonal lattice with a hexagonal close packed
(HCP) structure is generated, and in the second case a face-centered
cubic lattice results.
51
Electrical and Electronic Materials
52. Voids
X on figure is called an
octahedral site
The radius(aoct) of octahedral
site is = 0.41421ao
where ao is the radius of
the spheres.
There are also smaller
sites, called tetrahedral
sites, labeled T
This is a smaller site since its
radius aT= 0.2247ao
52
Electrical and Electronic Materials
60. Lattice
directions- MI
The direction of any line
in a lattice
may be described by first
drawing a line through
the origin parallel
to the given line and
then giving the
coordinates of any point
on the line
through the origin.
-smallest integer value
- Negative directions are
shown by bars eg.
0,0,0
-
60
Electrical and Electronic Materials
61. Plane designation by Miller indices
-Miller indices are always cleared of
fractions
- If a plane is parallel to a given
axis, its fractional intercept on that
axis is taken as infinity, Miller index
is zero
- If a plane cuts a negative axis, the
corresponding index is negative
and is written with a bar over it.
-Planes whose indices are the
negatives of one another are
parallel and lie on opposite sides of
the origin, e.g., (210) and (-2ī0).
-- Planes belonging to the same
family is denoted by curly bracket ,
{hkl}
61
Electrical and Electronic Materials
62. Fig 1.41
Labeling of crystal planes and typical examples in the cubic lattice
Electrical and Electronic Materials
63. Miller indices of lattice planes
63
Electrical and Electronic Materials
65. The hexagonal unit cell :
Miller –Bravais indices of planes and directions
66
Electrical and Electronic Materials
66. Zone= zonal planes + zonal axis
-Zone axis and (hkl) the zonal plane
All shaded planes belong to the same zone
i.e parallel to an axis called zone axsis 67
Electrical and Electronic Materials
u v w
h1 k1 l1
h2 k2 l2
79. Elastic stress field responsible for electron scattering and
increase in electrical resistivity
lattice strain around dislocation
83
Electrical and Electronic Materials
81. The closest packed plane and the closest packed direction of FCC
The plane and directions for the dislocation movement
85
Electrical and Electronic Materials
92. Definition of Phase:
• A phase is a region of material that is chemically
uniform, physically distinct, and (often)
mechanically separable.
• A phase is a physically separable part of the
system with distinct physical and chemical
properties. System - A system is that part of the
universe which is under consideration.
• In a system consisting of ice and water in a
glass jar, the ice cubes are one phase, the water
is a second phase, and the humid air over the
water is a third phase. The glass of the jar is
another separate phase.
98
Electrical and Electronic Materials
93. Gibbs' phase rule proposed by Josiah Willard Gibbs
The phase rule is an expression of the number of variables
in equation(s) that can be used to describe a system in equilibrium.
Degrees of freedom, F
F = C − P + 2
Where,
P is the number of phases in thermodynamic equilibrium with each other
C is the number of components
99
Electrical and Electronic Materials
94. Phase rule at constant pressure
• Condensed systems have no gas phase. When their
properties are insensitive to the (small) changes in
pressure, which results in the phase rule at constant
pressure as,
F = C − P + 1
100
Electrical and Electronic Materials
99. The Lever Rule
Finding the amounts of phases in a two phase region:
1. Locate composition and temperature in diagram
2. In two phase region draw the tie line or isotherm
3. Fraction of a phase is determined by taking the
length of the tie line to the phase boundary for the
other phase, and dividing by the total length of tie
line
The lever rule is a mechanical
analogy to the mass balance
calculation. The tie line in the
two-phase region is analogous to
a lever balanced on a fulcrum.
105
Electrical and Electronic Materials
101. Binary phase diagram
–2. limited solubility
• A phase diagram for a
binary system
displaying an eutectic
point.
107
Electrical and Electronic Materials
107. Fig 1.69
Electrical and Electronic Materials
The equilibrium phase diagram of the Pb-Sn alloy.
The microstructure on the left show the observations at various points during the cooling
of a 90% Pb-10% Sn from the melt along the dashed line (the overall alloy composition
remains constant at 10% Sn).
Pb-Sn system
110. Formation of nano crystallites/ grains
Nuclei of the solid phase form and they grow to
consume all the liquid at the solidus line.
13 atoms constitute to a theoretical nano-
particle for a FCC lattice having two layers. 55
and 147 atoms for 3 and 4 layer clusters.
If the size of the crystallites are in the nanometer
range, they are called nanocrystals/grains.
High temperature structure
can be retained at lower
temperature by quenching.
116
Electrical and Electronic Materials
111. Single crystal
A single crystal solid is a material in
which the crystal lattice of the entire
sample is continuous
no grain boundaries- grain boundaries can
have significant effects on the physical
and electrical properties of a material
single crystals are of interest to electric
device applications
118
Electrical and Electronic Materials
112. Doping
119
Minute addition of elements in a controlled way to
the matrix is called doping.
During Bulk crystal growth dopents can be added
An epitaxial layer can be doped during deposition
by adding impurities to the source gas, such as
arsine, phosphine or diborane. The concentration
of impurity in the gas phase determines its
concentration in the deposited film.
Doping can be done by diffusion, allowing the
dopents to diffuse at elevated temperature.
Ion implantation- bombarding the dopants at high
speed
Electrical and Electronic Materials
113. 120
Crystal Growth Techniques
1. Czochralski (CZ)
2. Bridgman (and variations)
3. Various floating zone methods
Thin films: Epitaxial growth
techniques
Electrical and Electronic Materials
114. Czochralski process
The process is named after Polish
scientist Jan Czochralski
Crystal growth method is used to obtain
single crystals
e.g. semiconductors : silicon, germanium
and gallium arsenide
metals : palladium, platinum, silver, gold
inorganinic/ceramics: salts, and synthetic
gemstones 121
Electrical and Electronic Materials
115. 122
quartz Seed
introduction
-Kept in Ar atmosphere
-Process variables:
•Pulling speed
•Rotation speed
Electrical and Electronic Materials
Melting of
polycrystalline Si
with doping
Crystal growth
begins
Crystal
pulling
Single xtal
residue of
melted Si
117. 125
300 mm diameter wafers
2 metres in length, weighing
few hundred kilograms
Crucibles
used in
Czochralski
method
Crucible after
being used
Electrical and Electronic Materials
118. 126
The next step up, 450 mm, was introduction in 2012.
Silicon wafers are typically about 0.2 - 0.75 mm thick
Polished to a very high flatness for making
integrated circuits, or textured for making solar cells
Electrical and Electronic Materials
119. 127
• During growth, the walls of the crucible dissolve into the
melt and Czochralski silicon therefore contains oxygen
at a typical concentration of 1018 cm−3.
• Oxygen impurities can have beneficial effects some times:
- Carefully chosen annealing conditions can allow the
formation of oxygen precipitates.
- These have the effect of trapping unwanted transition metal
impurities in a process known as gettering
Electrical and Electronic Materials
120. Bridgman Technique
128
• Uses a crucible
• Requires seed crystal
• Directional solidification
• Precise temperature gradient required
Electrical and Electronic Materials
121. Floating Zone Techniques
EB Floating Zone (electron beam) Floating Zone RF (radio frequency)
130
• Refractory, alloys including Nb, Ta, Mo and W
• Vacuum melting chamber, annular EB gun
• Crystal rotator and translator
• No crucible
•0.5–50 mm/min growth rates, 110 mm dia Nb
reported
Requires multiple passes to achieve pure
crystal,• Molten zone stability critical: Surface
tension, Cohesion, Levitation
Distribution coefficient=con. of imp. In solid
con. of imp. in liquid
Electrical and Electronic Materials
122. Thin films: Epitaxial growth
131
Epitaxy,
The term epitaxy comes from the Greek roots,
epi, meaning "above“
taxis, meaning "in ordered manner“
Epitaxial growth refers to the method of depositing a
monocrystalline film on a monocrystalline substrate.
The deposited film is denoted as epitaxial film or
epitaxial layer.
Electrical and Electronic Materials
123. Applications
132
Epitaxy is used in nanotechnology and in semiconductor
fabrication.
Semiconductor materials (technologically important ) are,
silicon-germanium, gallium nitride, gallium arsenide,
indium phosphide and graphene.
Epitaxy is also used to grow layers of pre-doped silicon
on the polished sides of silicon wafers, before they are
processed into semiconductor devices. This is typical of
power devices, such as those used in pacemakers, vending
machine controllers, automobile computers, etc.
Electrical and Electronic Materials
124. Methods
133
1. vapor-phase epitaxy (VPE), a modification
of chemical vapour deposition.
2. Liquid-phase epitaxy (LPE)
3. Solid-phase epitaxy is used primarily for crystal-damage healing
4. Molecular-beam epitaxy (MBE)
Electrical and Electronic Materials
125. 134
1. vapor-phase epitaxy (VPE), a modification
of chemical vapour deposition
Silicon is most commonly deposited from
silicon tetrachloride in hydrogen at 1200 °C:
SiCl4(g) + 2H2(g) ↔ Si(s) + 4HCl(g)
Growth rates above 2µ per minute produce
polycrystalline silicon.
Electrical and Electronic Materials
126. Hydrogenated amorphous silicon
135
High-quality hydrogenated amorphous silicon
films (a-Si:H) have been produced by decomposition
of low-pressure silane gas on a very hot surface with
deposition on a nearby, typically 210 °C substrate.
A high-temperature tungsten filament provides the
surface for heterogeneous thermal decomposition of
the low-pressure silane and subsequent evaporation
of atomic silicon and hydrogen.
The silane reaction occurs at 650 °C :
SiH4 → Si + 2H2
The substrates: flat, oxide-free, single-crystal silicon
Electrical and Electronic Materials
127. 2. Liquid-phase
136
From the melt containing dissolved semiconductor
on solid substrates.
The thermal expansion coefficient of substrate and grown
layer should be similar
Deposition rates for films range from 0.1 to 1 μm/minute.
Doping can be achieved by the addition of dopants.
Example :
ternary and quarternary III-V compounds
on gallium arsenide (GaAs) and
indium phosphide (InP) substrates
.
Electrical and Electronic Materials
128. 3. Solid-phase
137
Solid Phase Epitaxy (SPE) is a transition between the
amorphous and crystalline phases of a material.
It is usually done by first depositing a film of
amorphous material on a crystalline substrate.
The substrate is then heated to crystallize the film.
The single crystal substrate serves as a template for
crystal growth.
The annealing step used to recrystallize or heal silicon
layers amorphized during ion implantation is also
considered one type of Solid Phase Epitaxy.
Electrical and Electronic Materials
129. 4. Molecular-beam
138
In MBE, a source material is heated to produce an
evaporated beam of particles.
These particles travel through a very high vacuum
(10-8 Pa; practically free space) to the substrate,
where they condense.
MBE has lower throughput than other forms of
epitaxy.
This technique is widely used for growing III-V
semiconductor crystals.
Electrical and Electronic Materials
130. 139
Lattice matching- essential condition for the epitaxial growth
Matching of lattice structures between two different
semiconductor materials, allows a region of band gap change to
be formed in a material without introducing a change in crystal
structure.
It allows construction of advanced light-emitting diodes and
diode lasers.
For example, gallium arsenide, aluminium gallium arsenide, and
aluminium arsenide have almost equal lattice constants, making it
possible to grow almost arbitrarily thick layers of one on the other
one.
Electrical and Electronic Materials
131. 140
The beginning of the grading layer will have a
ratio to match the underlying lattice and the alloy
at the end of the layer growth will match the
desired final lattice.
For example, Indium gallium phosphide layers
with a band-gap above 1.9 eV can be grown on
Gallium Arsenide wafers with index grading
Lattice grading
Electrical and Electronic Materials
132. Design of semiconducting compound materials
141
Ternary and quaternary compounds
Basic criteria
Eg requirements
Application oriented
1. Design GaxAl(1-x)As for different
device applications.
2. How can GaxIn(1-x)AsyP(1-y) compound
is designed for device applications?
3. What is gradedsemiconducting
compound?
Electrical and Electronic Materials
133. Electrical and Electronic Materials 142
1. i. Consider a multicomponent alloy containing N elements. If w1, w2, w3,…..,wN are
the weight fractions of the components 1, 2, 3, …..,N in the alloy and M1, M2,
M3,……..,MN are the respective atomic masses of the elements, show that the
atomic fraction of the ith component is given by,
ni = wi ∕ Mi
------------------------------
w1 ∕M1+w2 ∕M2+------------+wN ∕MN
ii. Consider the semiconducting II-VI compound cadmium selenide, CdSe. Given the
atomic masses of Cd and Se, find the weight fraction of Cd and Se in the
compound and grams of Cd and Se needed to make 100 grams of CdSe.
2. Explain the general bonding principle of atoms to form a crystalline solid with the
help of energy verses inter-atomic distance plot.
3. i. State various physical and mechanical properties of materials.
ii. Explain how the bonding type affect the above properties. Give examples.
Indian Institute of Technology Roorkee
Department of Metallurgical and Materials Engineering
MT-202 Electrical and Electronic Materials
Tutorial 1
134. Electrical and Electronic Materials 143
4.
i.
ii.
iii.
iv.
v.
vi.
Define and explain the following with the help of suitable diagrams
Space lattice
Unit cell and lattice parameters
Crystal systems
Bravais lattice and their classification
Origin for the creation of FCC Bravais lattice from a primitive cubic lattice
Crystal voids and their coordinates
5. Calculate the following:
i.
ii.
iii.
iv.
v.
vi.
vii.
viii
.
Effective number of atoms in SC, BCC, FCC, HCP unit cells
Relationship between the size of the unit cell and atomic diameter in SC, BCC,
FCC, HCP unit cells
Packing factors of BCC, FCC, HCP unit cells
Packing factor of a diamond cubic crystal structure
Coordination numbers of BCC, FCC, HCP crystal lattice
c/a ratio for an ideal HCP unit cell
Size of largest sphere that can fit into the tetrahedral & octahedral interstitial sites
of a close packed structures without distorting the unit cell.
Volume of unit cell of germanium in cubic meters, the atomic radius of Ge having
Diamond Cubic structure being 1.223 Ao
135. Electrical and Electronic Materials 144
6.
i.
ii.
iii
.
iv.
v.
vi.
Show with the help of neat sketches in the unit cell the
following:
Planes whose Miller indices are (111), (210), (010), (0
Ī Ī), (002), (130), (212) and(3 Ī 2).
Directions whose Miller indices are [111], [110], [1Ī0],
[122], [301], [201] and [2 Ī 3].
[1210], [01 Ī0], [Ī011] directions and (1210), (Ī Ī 22),
(1230) planes (Miller Bravais Index) in HCP unit cell
In a cubic unit cell the (hkl) & [hkl] are perpendicular
to each other
Miller index of the direction that is common to both
planes (110) and (111) inside the unit cell of a cubic
crystal.
3 parallel planes of belonging to {111} inside a cubic
unit cell (may be touching the UC).
6 direction <110> on any one {111}
136. Electrical and Electronic Materials 145
7. i. Given the Si lattice parameter a=0.543 nm. Calculate the number of Si atoms per unit volume, in
nm-3.
ii. Calculate the number of atoms per m2 and per nm2 on the (100), (110), and (111) planes in the Si
crystal as shown in above figure. Which plane has the maximum number of atoms per unit area?
iii. The density of SiO2 is 2.27 g cm-3 . Given that its structure is amorphous, calculate the number of
molecules per unit volume, in nm-3 . Compare your result with (i) and comment on what happens
when the surface of a Si crystal oxidizes. The atomic masses of Si and O are 28.09 and 16,
respectively.
8. In device fabrication, Si is frequently doped by the diffusion of impurities (dopants) at high
temperatures , typically 950-12000C. The energy of vacancy formation in the Si crystal is about
3.6eV. What is the equilibrium concentration of vacancies in a Si crystal at 10000C ? Neglect the
change in the density with temperature which is less than 1 percent in this case.
137. Electrical and Electronic Materials 146
9 i. Describe with neat sketches, the 3 types of line defects and relate b, Burgers vector with
dislocation line.
ii. Describe planar defects ; grain boundaries and surface defects
iii. How do the defects affect the electrical conductivity of the materials?
10. i. What are the allotropically different forms of carbon?
ii. Give neat sketches of their crystal structures.
iii. How do you classify these materials in terms of electrical conductivity?
11. i. Why single crystals are used for electronic applications? Explain methods of bulk single crystal
growth.
ii. What is epitaxial growth? Explain with one example each of growth for; binary, ternary and
quaternary semiconductor compounds, with the help of Eg vs lattice parameter of the crystal
plot.
iii. What is the significance of ‘ distribution coefficient’ in zone refining?
12. i. How amorphous semiconductors are prepared? Give an example.
ii. Explain how the nonstoichiometeric, ZnO crystal with excess Zn at the interstitial sites contribute
free electron for conduction.
138. Electrical and Electronic Materials 147
13
. i.
Consider 50% Pb- 50% Sn solder alloy:
Sketch the microstructure of the alloy at various stages as it is cooled from the melt. What is the
importance of this alloy in electrical applications?
ii. At what temperature does the solid melt? What is the significance of this temperature?
iii. What is the temperature range over which the alloy is a mixture of melt and solid? what is the
micro structure of the solid ?
iv. Consider the solder at room temperature following cooling from 1830C. Assume that the rate of
cooling from 1830C to room temperature is faster than the atomic diffusion rates needed to
change the compositions of the α and β phases in the solid. Assuming the alloy is 1 kg. Calculate
the masses of the following components in the solid.
a) The primary α ( proeutectic), b) α in the whole alloy, c) α in the eutectic solid and
d) β in the alloy ( where is the β phase?)
e) For Pb-40Sn, find the degree of freedom at,
i) liquid region, ii) liquidus, iii) two phase mushy region, iv) solidus and v )at room temperature.
f13_07_pg196
