Band Theory
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Applied Physics GS-122
By Atif M.Khokhar
1
Intro Band theory Types of Energy Bands Formation of Energy Bands Explanation of Bands in Solids Semi conductors Semi conductors and Periodic Table
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
2
You will be able to
Understand band theory of solids The formation of bands Band description of solids
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
3
A theory that explains the bands formation in solids is know as band theory of solid. A useful way to visualize the difference between conductors, insulators and semiconductors and to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
4
According to B.T, In crystalline solid electron can have different energy levels found by Schrödinger.
Some of these energy levels are permissible and other are forbidden.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
5
Energy Level The possible definite discrete amounts of energy which a electron can have in an atom is known as Energy Level. These are only possible in Insulators.
6
The
subdivided energy levels having slightly different values of energy due to the influence of different neighboring atoms upon one another are Sub-Energy Levels.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
7
A
group of energy sub-levels (permissible) where they are so close that they appear to be continuous, is called Energy bands.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
8
9
10
A
band which is either vacant or partially filled is called conduction band.
It
is the upper most band of an atom(Solid)
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
11
The
complete filled band is called Valance band.
It
is the sandwich band of an atom(Solis).
The
electrons are tightly bounded to their nuclei in this band.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
12
A
band which can not accommodate more electrons is called Filled band.
It
is the band lying below the valance band of an atom
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
13
14
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
15
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
16
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
17
Bands in Solids
18
19
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
20
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
21
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
22
We usually don’t care about lower bands. LASER will be formed by electrons going from conduction to valence band... Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
23
RIPHAH INTERNATIONAL UNIVERSITY,ISLAMABAD, PAKISTAN
2/6/2008
24
25
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
26
RIPHAH INTERNATIONAL UNIVERSITY,ISLAMABAD, PAKISTAN
2/6/2008
27
RIPHAH INTERNATIONAL UNIVERSITY,ISLAMABAD, PAKISTAN
2/6/2008
28
The energy bands for the outermost electrons are qualitatively similar for carbon, silicon, germanium and tin. Though they will differ in detail, the generic band diagram below can show why these materials have different electrical properties.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
29
Semiconductors
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
30
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
31
Silicon Energy Bands At finite temperatures, the number of electrons which reach the conduction band and contribute to current can be modeled by the Fermi function. That current is small compared to that indoped semiconductors under the same conditions.
32
Germanium Energy Bands At finite temperatures, the number of electrons which reach the conduction band and contribute to current can be modeled by the Fermi function. That current is small compared to that in doped semiconductors under the same conditions.
33
By Atif M.Khokhar
1
Intro Band theory Types of Energy Bands Formation of Energy Bands Explanation of Bands in Solids Semi conductors Semi conductors and Periodic Table
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
2
You will be able to
Understand band theory of solids The formation of bands Band description of solids
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
3
A theory that explains the bands formation in solids is know as band theory of solid. A useful way to visualize the difference between conductors, insulators and semiconductors and to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
4
According to B.T, In crystalline solid electron can have different energy levels found by Schrödinger.
Some of these energy levels are permissible and other are forbidden.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
5
Energy Level The possible definite discrete amounts of energy which a electron can have in an atom is known as Energy Level. These are only possible in Insulators.
6
The
subdivided energy levels having slightly different values of energy due to the influence of different neighboring atoms upon one another are Sub-Energy Levels.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
7
A
group of energy sub-levels (permissible) where they are so close that they appear to be continuous, is called Energy bands.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
8
9
10
A
band which is either vacant or partially filled is called conduction band.
It
is the upper most band of an atom(Solid)
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
11
The
complete filled band is called Valance band.
It
is the sandwich band of an atom(Solis).
The
electrons are tightly bounded to their nuclei in this band.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
12
A
band which can not accommodate more electrons is called Filled band.
It
is the band lying below the valance band of an atom
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
13
14
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
15
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
16
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
17
Bands in Solids
18
19
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
20
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
21
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
22
We usually don’t care about lower bands. LASER will be formed by electrons going from conduction to valence band... Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
23
RIPHAH INTERNATIONAL UNIVERSITY,ISLAMABAD, PAKISTAN
2/6/2008
24
25
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
26
RIPHAH INTERNATIONAL UNIVERSITY,ISLAMABAD, PAKISTAN
2/6/2008
27
RIPHAH INTERNATIONAL UNIVERSITY,ISLAMABAD, PAKISTAN
2/6/2008
28
The energy bands for the outermost electrons are qualitatively similar for carbon, silicon, germanium and tin. Though they will differ in detail, the generic band diagram below can show why these materials have different electrical properties.
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
29
Semiconductors
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
30
Lecture delivered @ HITEC UNIVERSITY, Taxila, by Atif M. Khokhar
31
Silicon Energy Bands At finite temperatures, the number of electrons which reach the conduction band and contribute to current can be modeled by the Fermi function. That current is small compared to that indoped semiconductors under the same conditions.
32
Germanium Energy Bands At finite temperatures, the number of electrons which reach the conduction band and contribute to current can be modeled by the Fermi function. That current is small compared to that in doped semiconductors under the same conditions.
33
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