Lecture1 - Crystal Properaties and planes.pptx

‫الرحمي‬ ‫الرمحن‬ ‫هللا‬ ‫ِسم‬‫ب‬
International University of Africa (I.U.A)
Faculty of Engineering
Electronic & Electrical Department
Semiconductor Electronic & Devices
‫الجامدة‬‫الحالة‬‫ونبائط‬ ‫إلكترونيات‬
Semester -3
Lecture One ( Crystal Properties)
Mussaab I. Niass
2022
1

TEXTBOOKS:
 Ben. G. Streetman – Sanjay Kumar,” Solid State Electronic
Devices”, PHI Learning, New Delhi, 6th Edition, 2009.
 L. Boylestad, Louis Nashlesky,” Electronic Devices and Circuit
theory”, Person, 11th Edition, 2013.
 Thomas L. Floyd,” Electronic Devices Conventional current
version”, Prentice Hall, 9th Edition, 2012.
 Razavi, ”Introduction to Microelectronics”, wiley,2006
 ‫أاللكترونات‬
،‫المعاصرة‬
‫يس‬
‫أحمد‬
‫الشبول‬ – ‫الطبعة‬
‫االولي‬ - ‫الجزء‬
‫االول‬- 2005
2

COURSE CONTENTS GENERAL
 Basic semiconductor physics “ atoms,
crystal, lattice, …. Etc”.
 Properties and formation of P-N junction.
 Analyze the V-I characteristic of diode.
 Describe different diode applications and
types.
 Introduction to BJT and FET transistor and
its basic applications, configurations.
3

TODAY’S LECTURE AGENDA:
1. Basic semiconductor definitions
2. Types of semiconductor
3. Crystal lattices
4. Types of solids
5. Cubic lattices and their types.
6. Planes & directions “Miller Indices”
7. The diamond lattice
8. Bonding Forces in Solids (Ionic, Covalent)
9. Energy levels
10. Temperature dependence of Eg.
4

1. SEMICONDUCTOR MATERIALS:

‫الموصلة‬ ‫شبه‬ ‫المواد‬
:
 Semiconductors – ‫الموصالت‬ ‫أشباه‬:
Are a group of materials having electrical conductivities
intermediate between metals and insulators.
 What are the conductivities - ‫?الموصالت‬
The degree to which a specified material conducts electricity.
“Copper, aluminum, Gold and Silver”.
 What are the Insulators? Exp. “plastics, paper, glass and dry air”
 * Semiconductor materials are found in column 4 and neighboring
Columns of the periodic table. Exp “SI “Silicon”, Ge “Germanium”,
..”.
5

3. Crystal lattices
4. Types of solids
9. Energy levels
8

TYPES OF SEMICONDUCTORS ‫الموصالت‬ ‫أشباه‬ ‫أنواع‬:
 1. Elemental: They are composed of single species of
atoms.
 Exp “ Si, Ge, C “Carbon”
 2. Compound semiconductors:
Compounds of column 3 and column 5 atoms, as well
as certain combinations from 2 and 6, and from 4
The compounds are widely used in high-speed
devices and devices requiring the emission or
absorption of light. The two-element (binary) 3-5
compounds such as GaN “Gallium nitride”, GaP
“gallium phosphide”, and GaAs”gallium arsenide”
are common in light-emitting diodes (LEDs)”is a
semiconductor device that emits visible light when an
electric current passes through it.”.
9

TYPES OF SEMICONDUCTORS ‫الموصالت‬ ‫أشباه‬ ‫أنواع‬:
CONT.
 Fluorescent materials such as those used in
television screens usually are 2-6 compound
semiconductors such as ZnS ”zinc
sulphide”.
 The elemental semiconductor Ge was widely
used in the early days of semiconductor
development for transistors and diodes.
Silicon is now used for the majority of
rectifiers, transistors, and integrated
circuits. 10

3. Crystal lattices
4. Types of solids
9. Energy levels
12

CRYSTAL LATTICES ‫البلورية‬ ‫الشبيكات‬:
 In this section we discuss the arrangements of atoms
in various solids. We shall distinguish ‫تمييز‬ between
single crystals and other forms of materials and then
investigate ‫بحث‬the periodicity of crystal lattices.
Certain important crystallographic terms will be
defined and illustrated in reference to crystals having
a basic cubic structure.
 Atoms are the basic building blocks of ordinary
matter. Atoms can join together to form
molecules, which in turn form most of the objects
around you.
 Atoms are composed of particles called protons,
electrons and neutrons.
13

CRYSTALS ‫البلورات‬
 Are solids that form by a regular repeated
pattern of molecules "‫"جزيئات‬ connecting
together.
 The molecules: a group of atoms bonded
together, representing the smallest
fundamental unit of a chemical compound
that can take part in a chemical reaction.
14

Molecules formed of atoms ‫جزيئات‬
Crystals ‫بلورات‬
15

PERIODIC STRUCTURES ‫الدورية‬ ‫البنيات‬:
 Types of solids:
 A crystalline solid: Is distinguished ‫تميز‬by
the fact that the atoms making up the crystal
are arranged in a periodic fashion ‫بصورة‬
‫دورية‬.
 Amorphous solid: No periodic structure at
all.
 Poly crystalline solid: Are composed of
many small regions of single-crystal material.
16

WHAT IS THE LATTICE?
 The periodicity in a crystal is defined in terms
of a symmetric array of points in space.
18

3. Crystal lattices
4. Types of solids
9. Energy levels
19

 An example of lattice is Rhombic Lattice
‫الشبيكة‬
‫ذات‬
‫الشكل‬
‫المعيني‬ as shown in Figure
bellow:
 Where Rhombic Lattice is two-dimensional
arrangement of atoms, With a primitive cell
ODEF, which is the smallest such cell. Notice that
we can define vectors a and b such that if the
primitive cell is translated by integral multiples of
these vectors, a new primitive cell identical to the
original is found (e.g., O'D'E'F') - These vectors, a
and b (and c if the lattice is three dimensional),
are called the primitive vectors for the lattice.
Points within the lattice are indistinguishable ‫ال‬
‫يمكن‬
‫تميزه‬ if the vector between the points is
20

 r = pa + qb + sc
 where p, q, and s are integers.
Note that, in a primitive cell, the lattice points at the corners are
shared with adjacent cells; thus, the effective number of lattice points
belonging to the primitive cell is always unity.
21

 The importance of the unit cell lies in the fact that we
can analyze the crystal as a whole by investigating a
representative volume. For example, from the unit cell
we can find the distances between nearest atoms and
next nearest atoms for calculation of the forces holding
the lattice together; we can look at the fraction of the
unit cell volume filled by atoms and relate the density
of the solid to the atomic arrangement. But even more
important for our interest in electronic devices, the
properties of the periodic crystal lattice determine the
allowed energies of electrons that participate in the
conduction process. Thus the lattice determines not
only the mechanical properties of the crystal but also its
electrical properties.
22

3. Crystal lattices
4. Types of solids
9. Energy levels
23

CUBIC LATTICES:
 The simplest three-dimensional lattice is one in
which the unit cell is a cubic volume, such as the
three cells shown below:
 Simple cubic: structure (abbreviated SC)has an
atom located at each corner of the unit cell.
 The body centered cubic (BCC):lattice has an
additional atom at the center of the cube,
 Face-centered cubic (FCC): unit cell has atoms
at the eight corners and centered on the six faces.
24

 Figure bellow illustrates the packing of spheres
in a face-centered cubic cell of side a, such that
the nearest neighbors touch. The dimension a
for a cubic unit cell is called the lattice
constant. For the FCC lattice the ((nearest
neighbor distance)) is one-half the diagonal
‫قطر‬of a face:
27

 The radius of the sphere must be one-half the nearest
neighbor distance:
28

3. Crystal lattices
4. Types of solids
9. Energy levels
31

PLANES AND DIRECTIONS
‫واالتجاهات‬ ‫المستويات‬
 In discussing crystals it is very helpful to be able to refer to
planes and directions within the lattice.
 The notation system generally adopted uses a set of three
integers to describe the position of a plane or the direction
of a vector within the lattice.
 The three integers describing a particular plane are found in
the following way:
32

CONT.
1. Find the intercepts ‫تقاطع‬ of the plane with the crystal axes and
express these intercepts as integral multiples of the basis vectors.
2. Take the reciprocals ‫المقلوبات‬ of the three integers found in step 1
and reduce these to the smallest set of integers h, k, and L, which
have the same relationship to each other as the three reciprocals.
3. Label the plane (hkl).
33

 The three integers h, k, and I are called the Miller indices ‫مؤشرات‬
‫ميلر‬ ;
these three numbers define a set of parallel planes in the lattice.
 Notes:
 One intercept is infinity for a plane parallel to an axis; however, the
reciprocal of such an intercept is taken as zero.
 If an intercept occurs on the negative branch of an axis, the minus sign
is placed above the Miller index for convenience, such as (h k l)
 [hkl] represents a direction
 <hkl> represents a family of directions
 (hkl) represents a plane
 {hkl} represents a family of planes
35

EXAMPLE1:
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)
36

EXAMPLE2:
 This plane cuts all three crystallographic ‫مت‬
‫علق‬
‫بعلم‬
‫البلورات‬ axes.
 • Intercepts = (1,1,1) ----> (111)
37

EXAMPLE3:
 This plane cuts two of the reference axes, but not equi-
dimensionally.
 Intercepts: (½,1,∞) ----> (210)
38

DIRECTIONS:
 A direction in a lattice is expressed as a set of three integers with
the same relationship as the components of a vector in that
direction.
39

3. Crystal lattices
4. Types of solids
9. Energy levels

THE DIAMOND LATTICE:
 The basic crystal structure for many important semiconductors is the FCC
lattice with a basis of two atoms, giving rise to the diamond structure,
characteristic of Si, Ge, and C in the diamond form.
 In many compound semiconductor atoms are arranged in a basic diamond
structure, but are different on alternating sites. This is called a zinc blende
(ZNS) ZN = Zinc, S= Sulfur, structure.
 The diamond structure can be thought of as an FCC lattice with an
 Extra atom placed at a/4 + b/4 + c/4 from each of the FCC atoms.
41

CONT.
 Angstrom (Å) = 10^-8 Cm = 10^-10 meter
42

BONDING FORCES IN SOLIDS:
‫الجوامد‬ ‫في‬ ‫الترابط‬ ‫قوي‬
:
 The interaction of electrons in neighboring atoms of a solid serves
the very important function of holding the crystal together.
 For example, (alkali halides) ‫القلويات‬
‫الهااليدية‬ such as NaCl Sodium
Chloride are typified ‫ممثل‬by ionic bonding. In the NaCl lattice,
each Na atom is surrounded by six nearest neighbor CI atoms, and
vice versa. Four of the nearest neighbors are evident ‫موضحة‬in the
two-dimensional representation shown in Figure bellow:
46

 The electronic structure of Na (Z “Atomic number” = 11), 1S2,
2S2, 2P6, 3S1. And CI (Z = 17) , 1S2, 2S2, 2P6, 3S2, 3P5.
Subshell
label
ℓ
Max
electrons
Shells containing it Historical name
s 0 2 Every shell sharp
p 1 6 2nd shell and higher principal
d 2 10 3rd shell and higher diffuse
f 3 14 4th shell and higher fundamental
g 4 18
5th shell and higher
(theoretically)
(next in alphabet after
f)[5]
Shell
name
Subshell
name
Subshell
max
electrons
Shell
max
electrons
K 1s 2 2
L
2s 2
2 + 6 = 8
2p 6
M
3s 2
2 + 6 + 10
= 18
3p 6
3d 10
N
4s 2
2 + 6 +
10 + 14
= 32
4p 6
4d 10
4f 14
O
5s 2
2 + 6 +
10 + 14 +
18 = 50
5p 6
5d 10
5f 14
5g 18
In the lattice each Na atom gives up its outer 3s
electron to a CI atom, so that the crystal is made up
of ions with the electronic structures of the inert
‫خامل‬atoms.
An important observation in the NaCl structure is
that all electrons are tightly ‫باحكام‬ bound to atoms.
48

 Compound semiconductors such as (Gallium arsenide) GaAs have
mixed bonding, in which both ionic and covalent bonding forces
participate. Some ionic bonding is to be expected in a crystal such
as GaAs because of the difference in placement of the Ga and As
atoms in the periodic table.
49

COVALENT BONDING:
 To fully appreciate why Si, Ge,
and GaAs are the semiconductors
of choice for the electronics
industry requires some
understanding of the atomic
structure of each and how the
atoms are bound together to
form a crystalline structure.
 The Bohr model for the three
materials is provided by side:
50

CONT.
 As indicated, silicon has 14 orbiting electrons, germanium has 32 electrons,
orbiting electrons. For germanium and silicon there are four electrons in the
outermost shell, which are referred to as valence electrons . Gallium has
three valence electrons.
 Atoms that have four valence electrons ====> tetravalent
 three ====> trivalent , five =====> pentavalent
 # The term valence is used to indicate that the potential (ionization potential)
required to remove any one of these electrons from the atomic structure is
significantly lower than that required for any other electron in the structure.
51

CONT.
 This bonding of atoms, strengthened ‫مقوي‬by the sharing of electrons, is called
covalent bonding.
 Although the covalent bond will result in a stronger bond between the valence electrons
and their parent atom, it is still possible for the valence electrons to absorb sufficient
kinetic energy from external natural causes to break the covalent bond.
Covalent bonding of the silicon atom.
52

WHAT IS THE EXTERNAL NATURAL CAUSES?
 The external causes include effects such as light energy in the form of photons
and thermal energy (heat) from the surrounding medium. At room temperature
there are approximately 1.5*10^10 free carriers in 1cm^3 of intrinsic silicon
material, that is, 15,000,000,000 (15 billion) electrons in a space smaller than a
small sugar cube an enormous number.
 The term intrinsic‫نقي‬is applied to any semiconductor material that has been
carefully refined ‫مصفي‬to reduce the number of impurities to a very low level—
essentially as pure as can be made available through modern technology.
53

CONT.
 Before we leave this subject, it is important to underscore ‫تاكيد‬ the importance
of understanding the units used for a quantity.
 The unit of measure is appropriate ‫مناسبة‬ because W (energy) = QV (as derived
from the defining equation for voltage: V = W / Q ). Substituting the charge of
one electron and a potential difference of 1 V results in an energy level referred
to as one electron volt .
 That is,
54

ENERGY LEVELS:
Energy levels: discrete levels in isolated atomic structures
Energy levels: conduction and valence bands of an insulator, a semiconductor, and a conductor
56

CONT.
 An electron in the valence band of silicon must absorb more energy than one in the
valence band of germanium to become a free carrier. Similarly, an electron in the
valence band of gallium arsenide must gain more energy than one in silicon or
germanium to enter the conduction band.
 The design of photo-detectors sensitive to light and security systems sensitive to
heat would appear to be an excellent area of application for Ge device. Why?
 “ Because the Ge has a lowest Eg 0.67 e.V and due to a little external effect i.e. heat
it will conduct quickly rather than Si or GaAS.”
 The wider the energy gap, the greater is the possibility of energy being released in the
form of visible or invisible (infrared) light waves.
57

TEMPERATURE DEPENDENCE OF THE ENERGY BAND GAP
 The energy band gap of semiconductors tends to decrease as the temperature is
increased.
 The temperature dependence of the energy band gap, Eg , has been
experimentally determined yielding the following expression for E g as a
function of the temperature, T:
 where Eg(0), α and β are the fitting ‫مالئمة‬ parameters. These fitting parameters
are listed for germanium, silicon and gallium arsenide in Table bellow:
59

CONT.
Parameters used to calculate the energy band gap of germanium, silicon and gallium
arsenide (GaAs) as a function of temperature.
A plot of the resulting band gap versus temperature is shown in Figure bellow for
germanium, silicon and gallium arsenide.
Temperature dependence of the energy band gap of germanium (Ge), silicon (Si) and
gallium arsenide (GaAs)
60

EXAMPLE:
 Calculate the energy band gap of germanium, silicon and gallium
arsenide at 300, 400, 500 and 600 K?
 The band gap of silicon at 300 K equals:
Similarly one finds the energy band gap for germanium and gallium arsenide, as
well as at different temperatures, yielding:
62

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