Semiconductors ch. 1

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Semiconductors - Ch. 1 ........By : M. Al-Alousi2

Semiconductors - Ch. 1 ........By : M. Al-Alousi
…………….. : General introduction
Chapter 1 : The Crystal Structure of Solids
Chapter 2 : Introduction to Quantum Mechanics
Chapter 3 : Introduction to the Quantum Theory of Solids
Chapter 4 : The Semiconductor in Equilibrium Carrier Transport Phenomena
Chapter 5 : Nonequilibrium Excess Carriers in Semiconductors
Chapter 6 : The pn Junction
Chapter 7 : The pn Junction Diode
Chapter 8 : Metal-Semiconductor and Semiconductor
Chapter9 : Heterojunctions
Chapter 10 : The Bipolar Transistor
Chapter 11 : Fundamentals of the Metal-Oxide-Semiconductor and Field-Effect Transistor
Chapter 13 : Metal-Oxide-Semiconductor Field-Effect Transistor , Additional Concepts
Chapter 12 : The Junction Field-Effect Transistor
Chapter 14 : Optical Devices
Chapter 15 : Semiconductor Power Devices
The Syllabus Of Semiconductor Subject
4

General Introduction
• The electrical resistance (R) of an electric conductor is a measure of the difficulty to
pass an electric current through that conductor. ( It is measured by ohm unit Ω).
• The electrical resistivity (ρ)(also known as resistivity, specific electrical resistance,
or volume resistivity) is a quantity of strongly a given material opposes the flow of
electric current. The SI unit of electrical resistivity is the ohm⋅metre (Ω⋅m)
• Important concepts
• The electrical conductance (G) is the ease with which an electric current passes.
The electrical conductance is measured in Siemens (S).
• The Electrical conductivity (σ) or specific conductance is the reciprocal of electrical
resistivity, and measures a material's ability to conduct an electric current. Its SI unit
is Siemens per meter (S/m) and CGSE unit is reciprocal second (s−1).
𝑅 =
𝑉
𝐼
→ Ω =
𝑣𝑜𝑙𝑡
𝑎𝑚𝑝𝑒𝑟
, 𝐺 =
𝐼
𝑉
→ 𝑆 =
𝑎𝑚𝑝𝑒
𝑣𝑜𝑙𝑡𝑟
, 𝜌 = 𝑅
𝐴
𝑙
→ 𝛺.m
𝜎 = 𝐺
𝐴
𝑙
→
1
𝛺.m
= (𝛺.m)−1
=
𝑆
𝑚
= (𝑆−1
)
5

What Are The Semiconductor Materials ?
Metals
Semiconductors
Semimetals
Cu
Na
K
As
Sb
Graphite
Bi
Ge (pure)
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
 Metals: s > 105 (W.m)-1 or S
 Semiconductors: 10-6 < s < 105 (W.m )-1
 Insulators: s < 10-6 (W.m )-1
Then ……..
The Semiconductors are materials which have
an Electrical Conductivity between the
conductors, and the insulators
Electrical Conductivity of materials
The conduction electrons concentrations

1.1 : Semiconductor Materials
1.2 : Types of Solids
1.3 : Space Lattices
1.3.1 : Primitive and Unit Cell
1.3.2 : Basic Crystal Structures
1.3.3 : Crystal Planes and Miller Indices
1.3.4 : The Diamond Structure
1.4 : Atomic Bonding
1.5 : Imperfections and Impurities in Solids
1.5.1 : Impegections in Solids
1.5.2 : Impuritler m Solids
1.6 : Growth of Semiconductor Materials
1.6.1 : Growth from a Melt
1.6.2 : Eptaxtul Growth
C H A P T E R 1
The Crystal Structure of Solids

A semiconductor may be as an elements
or compounds
• IV-VI (PbSe, SnTe)
• III-V (GaAs, InP, InSb)
• II-VI (CdS, HgTe, ZnTe, ZnO).
1.1 : Semiconductor Materials

10
Why Silicon:
The semiconductors have been used before 1949 a s a diodes in the rectifier and
photodiode applications.
In the firsts of 50s of last century, the germanium has been widely used as a
semiconductor materials, but it wasn’t efficient with many applications , because of its
leakage current at not significantly high temperatures.
Then, it was been replaced by Silicon.
Advantages of Silicon:
1. Infinitesimal of leakage current is the Si devices.
2. The easily configure of the high quality silicon by the thermal growth method.
3. Si is the cheapest in the present time

1.2 : Types of Solids
Completely ordered In segments
Entire solid is up of atoms in an orderly array
No recognizable Long – range order

1.3 : Space Lattices
The lattice is the periodic arrangement of atoms in the crystal
1.3.1 : Primitive and Unit Cell
a1
b1
Two-dimensional representation
of a single-crystal lattice
a1
b1
A
a2
b2
B
a3
b3
C
a4
b4
D
Two-dimensional representation of a single-crystal
lattice showing various possible unit cells.
A primitive cell is the smallest unit cell that can be repeated to form the lattice
A generalized primitive unit cell
𝒓 = 𝒑𝒂 + 𝒒𝒃 + 𝑺𝒄 … … … . (𝟏)
Where p, q, and s are integers
 Every equivalent lattice point in the three- dimensional
crystal can be found using the vector ( r ):

1.3.2 : Crystal Structures
1- The simple Cubic Lattice :
This lattice consist on one atom
𝒕𝒉𝒆 𝒏𝒖𝒃𝒆𝒓 𝒐𝒇 𝒂𝒕𝒐𝒎𝒔 𝒊𝒏 𝒕𝒉𝒆 𝒍𝒂𝒕𝒕𝒊𝒄𝒆 𝒊𝒔
𝟏 = 𝟖 × 𝟏
𝟖
a b
c
a = b = c
𝛼 = 𝛽 = 𝛾 = 90 𝑜
𝟏
𝟖
 𝒕𝒉𝒆 𝒗𝒍𝒖𝒎𝒆 𝒐𝒇 𝒍𝒂𝒕𝒕𝒊𝒄𝒆 𝒊𝒔 𝑽 = 𝒂 𝟑
 𝒕𝒉𝒆 𝒔𝒑𝒂𝒄𝒆′
𝒔 𝒗𝒍𝒖𝒎𝒆 𝒐𝒇 𝒂𝒕𝒐𝒎𝒔 𝒊𝒔
𝑽 =
𝟒
𝟑
𝝅 𝒓 𝟑
: 𝒓 is the radius of atom
 𝒕𝒉𝒆 𝑨𝒕𝒐𝒎𝒊𝒄 𝑷𝒂𝒄𝒌𝒊𝒏𝒈 𝑭𝒂𝒄𝒕𝒐𝒓 𝑨𝑨𝑭 𝒊𝒔
𝑨𝑨𝑭 =
𝟒 𝝅 𝒓 𝟑
𝟑𝒂 𝟑
 𝒕𝒉𝒆 𝒓𝒆𝒍𝒂𝒕𝒊𝒐𝒏 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒂 𝒂𝒏𝒅 𝒓 𝒊𝒔
a = 2r
2r
2r
A
B
C
𝑨𝑨𝑭 =
𝟒 𝝅 𝒓 𝟑
𝟑(𝟐𝒓) 𝟑
𝑨𝑨𝑭 =
𝝅
𝟔
13
Polonium is the only element has this
system

2- The body-centered cubic Lattice :
This lattice consist on two atoms
𝟐 = 𝟖 × 𝟏
𝟖 + 𝟏
a = b = c
𝛼 = 𝛽 = 𝛾 = 90 𝑜
𝑽 =
𝟒
𝟑
𝒏 𝝅 𝒓 𝟑
𝑨𝑨𝑭 =
𝟖 𝝅 𝒓 𝟑
𝟑𝒂 𝟑
 𝒕𝒉𝒆 𝒓𝒆𝒍𝒂𝒕𝒊𝒐𝒏 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 (𝒂) 𝒂𝒏𝒅 𝒓 𝒊𝒔
A
B
C
4r
a
(𝐴𝐵)2
= (𝐵𝐶)2
+ (𝐶𝐴)2
(4𝑟)2= ( 2𝑎)2+ 𝑎2
(4𝑟)2
= 3𝑎2
(4𝑟)2= 3𝑎2
16 𝑟2
= 3𝑎2
4 𝑟 = 𝑎 3
𝑟 = 𝑎
3
4
or 𝑎 =
4 𝑟
3
𝑯. 𝑾 𝒇𝒊𝒏𝒅 𝑨𝑨𝑭 𝒐𝒇 𝑩𝑪𝑪 𝒍𝒂𝒕𝒕𝒊𝒄𝒆
𝟐 𝒂
Semiconductors - Ch. 1 …………………………………………………………………………………………………………………………………......By : M.azin Al-Alousi
14
As the sodium (Na) and the tungsten (W)

3- The face-centered cubic Lattice :
This lattice consist on four atoms
𝟒 = 𝟖 × 𝟏
𝟖 +
𝟏
𝟐
×6
a = b = c
𝛼 = 𝛽 = 𝛾 = 90 𝑜
𝑽 =
𝟒
𝟑
𝒏 𝝅 𝒓 𝟑
𝑨𝑨𝑭 =
𝟏𝟔 𝝅 𝒓 𝟑
𝟑𝒂 𝟑 ( prove that ) :

The fourteen space lattices (Bravais lattices):
Find the volume density of atoms in
a body-centered cubic crystal, if
a = 5 x 10-8cm
Example:
Solution :
𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑁𝑜. 𝑜𝑓 𝐴𝑡𝑜𝑚𝑠
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑙𝑎𝑡𝑡𝑖𝑐𝑒
𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =
2
5 x 10−8 3
= 1.6 × 1022
𝑎𝑡𝑜𝑚/𝑐𝑚3
(𝑯. 𝑾 ): (1.2, 1.3, 1.12 and 1.14)
in Semiconductor Physics and
Devices(Donald A. Neamen) p.p.(21-22)
16

1.3.3 : The lattice’s planes :
The lattice’s planes are explained by Miller’s indices (hkl) . We can determine
Miller’s indices by a few steps as the following:
1. Choose the original point.
0
𝒙
𝒚
𝒛
2. Assume a plane crosses these axis at 𝒑𝒂
on 𝒙, 𝒒𝒃 on 𝒚 and 𝒓𝒄 on 𝒛.
𝒑𝒂
𝒒𝒃
𝒓𝒄
3. Take the reciprocal of the numbers( 𝒑𝒂, 𝒒𝒃 and 𝒓𝒄 )
3. Reduce to the integers having the same ratio, usually
the smallest three integers. The result, enclosed in
parentheses (ℎ𝑘𝑙), is called the index of the plane.

𝒙
𝒚
𝒛
Example:
1
1
1
𝑥 𝑦 𝑧
𝑖𝑛𝑡. ∞ 1 ∞
𝑟𝑒𝑝. 1
0
1
1
1
0
ℎ𝑘𝑙 0 1 0
010
In same method, we can find the other face planes
0
001
100
(𝑯. 𝑾 ): explain how you can find the hkl of the specified planes (a=1) in below figures.
𝑥
𝑦
𝑧
𝑥
𝑦
𝑧
𝑥
𝑦
𝑧
𝑥
𝑦
𝑧
𝑥
𝑦
𝑧
1
2

One important characteristic in semiconductor crystals is the surface concentration of
atoms on the surface , number per square centimeter (atom/cm2), that are cut by a
particular plane. This characteristic is called “ The surface density of atoms “ .
Again, a single-crystal semiconductor is not infinitely large and must terminate at some
surface.
 To calculate the surface density of atoms on a particular
plane in a crystal.
Consider the body-centered cubic structure and the (110)
plane . Assume the atoms can be represented as hard
spheres with the closest atoms touching each other. Assume
the lattice constant is a = 5 Å 𝒂
𝒃
𝒄
110
a
a
5 Å
5 Å
A
B
C
𝐴𝐵 = 𝐵𝐶2 + 𝐶𝐴2
= 𝑎2 + 𝑎2
= 2𝑎2
= 𝑎 2
= 5 2 Å
𝑻𝒉𝒆 𝒔𝒖𝒓𝒇𝒂𝒄𝒆 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 =
𝑵𝒐. 𝒐𝒇 𝑨𝒕𝒐𝒎
𝑨𝒓𝒆𝒂 𝒐𝒇 𝒑𝒍𝒂𝒏𝒆
=
𝟐 (𝒂𝒕𝒐𝒎)
𝟓 × 𝟓 𝟐 (Å)
=
𝟐 (𝒂𝒕𝒐𝒎)
(𝟓 × 𝟏𝟎−𝟖) 𝟐 . 𝟐 (𝑐𝑚)2
= 5.66 × 𝟏𝟎 𝟏𝟒
Atoms / (𝑐𝑚)2
(𝑯. 𝑾 ): E1.4 in Semiconductor Physics
and Devices(Donald A. Neamen) p.9
19

13.4: The Diamond Structure
Silicon is the most common semiconductor material. Silicon is referred to as a group IV
element and has a diamond crystal structure. Germanium is also a group IV element
and has the same diamond structure.
A unit cell of the diamond
structure.
The diamond structure refers to the particular lattice in
which all atoms are of the same species, such as silicon
or germanium. The zincblende (sphalerite) structure
differs from the diamond structure only in that there are
two different types of atoms in the lattice
A unit cell of the zincblende structure. (𝑯. 𝑾 ): E1.5 in Semiconductor Physics
and Devices(Donald A. Neamen) p.11
20

1.4 : ATOMIC BONDING
Atomic Bonding Types :
1. Ionic bonding .
2. Covalent bonding .
3. Co-ordinate ( dative covalent ) bonding.
4. Electronegativity.
5. Shaes of simple molecules and ions .
6. Metallic bonding .
7. Van der waals forces.
8. Hydrogen bonding
9. Bonding in organic compounds .
Covalent bonding
If we’ve two atoms , that are IV valency
Si SiSi
Si SiSi
Si SiSi
Si SiSi
Si SiSi
Si SiSi
21

1.5 : GROWTH OF SEMICONDUCTOR MATERIALS
• Czochralski’s method . ‫جوكرلسكي‬ ‫طريقة‬
In this technique, a small piece of
single-crystal material, known as a seed ,
is brought into contact with the surface
of the same material in liquid phase, and
then slowly pulled from the melt. As the
seed is slowly pulled, solidification
occurs along the plane between the
solid-liquid interface.

Epitaxial Growth
The word epitaxy is derived from the Greek “epi”— upon, and “taxis”— to arrange.
Thus, epitaxial silicon deposition requires the
ability to add and arrange silicon atoms upon a
single crystal surface. Epitaxy is the regularly
oriented growth of one crystalline substance
upon another.
Two different kinds of epitaxy are recognized:
• Homoepitaxy growth in which the epitaxial
layer is of the same material as the substrate.
• Heteroepitaxy growth in which the epitaxial
layer is a different material from the
substrate.

CVD (Chemical Vaporation deposition is a heterogeneous reaction involving at least the
following steps:
1. Bulk transport of reactants into the process volume
2. Gaseous diffusion of reactants to the surface
3. Absorption of reactants onto the surface
Removal of reactant by-products
1. Reaction by-product desorption (‫االم‬‫تزاز‬,‫المج‬)
2. Gaseous transport of by - products
3. Bulk transport of by-products out of process volume
Surface reaction
1. Surface reaction (reaction can also take place in the gas volume immediately above the surface)
2. Surface diffusion
3. Crystal lattice incorporation
24

Semiconductors ch. 1

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