This document provides an overview of band theory of solids. It discusses effective mass of electrons in solids, the concept of holes, and the energy band structure of conductors, semiconductors, and insulators. Intrinsic and extrinsic semiconductors are described, along with p-type and n-type materials. Simple diode and Zener diode operation is summarized, including forward and reverse bias conditions.

1. BAND THEORY OF
SOLID
Course: B.Tech
Subject: Engineering Physics
Unit: I
Chapter: 2

2.  OBJECTIVES
• Effective Mass of electron
• Concept of Holes
• Energy Band Structure of Solids:
 Conductors, Insulators and Semiconductors
• Semiconductors
 Intrinsic and Extrinsic Semiconductors
• Type of diodes
 Simple Diode
 Zener Diode

3.  EFFECTIVE MASS OF ELECTRON
 An electron moving in the solid under the
influence of the crystal potential is subjected to
an electric field.
 We expect an external field to accelerate the
electron, increasing E and k and change the
electron’s state.
1

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Effective Mass Revisited
 This relates the curvature of the band to the “effective
mass.”
 One can show that a free electron “band” gives an effective
mass equal to the rest mass of an electron.
 Electrons in a crystal are accelerated in response to an
external force just as though they were free electrons with
effective mass me.
 Usually , me < m0.(m0=9.1 x 10-31kg)

7.  CONCEPT OF HOLES
 Consider a semiconductor with a small
number of electrons excited from the valence
band into the conduction band.
 If an electric field is applied,
• the conduction band electrons will
participate in the electrical current
• the valence band electrons can “move
into” the empty states, and thus can also
contribute to the current.
2

8.  CONCEPT OF HOLES
 If we describe such changes via “movement” of
the “empty” states – the picture will be
significantly simplified. This “empty space” is
called a Hole.
 “Deficiency” of negative charge can be treated
as a positive charge.
 Holes act as charge carriers in the sense that
electrons from nearby sites can “move” into the
hole.
 Holes are usually heavier than electrons since
they depict collective behavior of many
electrons.

9. Electrical current for holes and electrons in the same direction
3

10. To understand hole motion, one requires
another view of the holes, which represent
them as electrons with negative effective mass
m*.
For example the movement of the hole think
of a row of chairs occupied by people with one
chair empty, and to move all people rise all
together and move in one direction, so the
empty spot moves in the same direction

11.  Energy Band Structure of Solids
Conductor, Semiconductor and
Insulator
 In isolated atoms the electrons are arranged in
energy levels.
4

12.  ENERGY BAND IN SOLID
The following are the important energy
band in solids:
 Valence band
 Conduction band
 Forbidden energy gap or Forbidden band
5

13. Valance band
The band of energy occupied by the valance
electrons is called valence band. The electrons in
the outermost orbit of an atom are known as
valance electrons. This band may be completely or
partial filled.
Electron can be move from one valance band
to the conduction band by the application of
external energy.

14.  Conduction band
The band of energy occupied by the
conduction electrons is called conduction band.
This is the uppermost band and all electrons in the
conduction band are free electrons.
The conduction band is empty for insulator
and partially filled for conductors.

15.  Forbidden Energy Gap or Forbidden band
The gap between the valance band and
conduction band on energy level diagram known as
forbidden band or energy gap.
Electron are never found in the gap. Electrons
may jump from back and forth from the bottom of
valance band to the top of the conduction band. But
they never come to rest in the forbidden band.

16.  According to the classical free electron
theory, materials are classified in to three
types:
 Conductors
 Semiconductors
 Insulators

17. Conductors
There is no forbidden gap and the conduction
band and valence band are overlapping each other
between and hence electrons are free to move about.
Examples are Ag, Cu, Fe, Al, Pb ….
 Conductor are highly electrical conductivity.
 So, in general electrical resistivity of conductor is
very low and it is of the order of 10-6 Ω cm.
 Due to the absence of the forbidden gap, there is no
structure for holes.
 The total current in conductor is simply a flow of
electrons.
 For conductors, the energy gap is of the order of
0.01 eV.

18. Semiconductors
Semiconductors are materials whose electrical
resistivity lies between insulator and conductor.
Examples are silicon (Si), germanium (Ge) ….
 The resistivity of semiconductors lie between 10-4 Ω
cm to 103 Ω cm at room temperature.
 At low temperature, the valence band is all most full
and conduction band is almost empty. The forbidden
gap is very small equal to 1 eV.
 Semiconductor behaves like an insulator at low
temperature. The most commonly used
semiconductor is silicon and its band gap is 1.21 eV
and germanium band gap is 0.785 eV.

19. When a conductor is heated its
resistance increases; The atoms vibrate more
and the electrons find it more difficult to move
through the conductor but, in a
semiconductor the resistance decreases with
an increase in temperature. Electrons can be
excited up to the conduction band and
Conductivity increases.
6

20. Insulators
In insulator, the valence band is full but the
conduction band is totally empty. So, free electrons
from conduction band is not available.
 In insulator the energy gap between the valence and
conduction band is very large and its approximately
equal to 5 eV or more.
 Hence electrons cannot jump from valence band to
the conduction band. So, a very high energy is
required to push the electrons to the conduction
band.
 The electrical conductivity is extremely small.
 The resistivity of insulator lie between 103 to 1017
Ωm, at the room temperature
 Examples are plastics, paper …..

21.  TYPES OF SEMICONDUCTORS
Semiconductors
Intrinsic Semiconductor Extrinsic Semiconductor
p - type n - type

22.  INTRINSIC SEMICONDUCTOR
 The intrinsic semiconductor are pure semiconductor
materials.
 These semiconductors posses poor conductivity.
 The elemental and compound semiconductor can be
intrinsic type.
 The energy gap in semiconductor is very small.
 So even at the room temperature, some of electrons from
valance band can jump to the conduction band by
thermal energy.
 The jump of electron in conduction band adds one
conduction electron in conduction band and creates a
hole in the valence band. The process is called as
“generation of an electron–hole pair”.
 In pure semiconductor the no. of electrons in conduction
band and holes in holes in valence bands are equal.

23.  EXTRINSIC SEMICONDUCTOR
 Extrinsic semiconductor is an impure semiconductor
formed from an intrinsic semiconductor by adding a
small quantity of impurity atoms called dopants.
 The process of adding impurities to the
semiconductor crystal is known as doping.
 This added impurity is very small of the order of one
atom per million atoms of pure semiconductor.
 Depending upon the type of impurity added the
extrinsic semiconductors are classified as:
(1) p – type semiconductor
(2) n – type semiconductor

24. The application of band theory to n-type and
p-type semiconductors shows that extra levels have been
added by the impurities.
In n-type material there are electron energy levels
near the top of the band gap so that they can be easily
excited into the conduction band.
In p-type material, extra holes in the band gap allow
excitation of valence band electrons, leaving mobile holes in
the valence band.
7

25. P – TYPE SEMICONDUCTOR
The addition of trivalent impurities such as
boron, aluminum or gallium to an intrinsic
semiconductor creates deficiencies of valence
electrons,called "holes". It is typical to use
B2H6 diborane gas to diffuse boron into the silicon
material.
8

26. N – TYPE SEMICONDUCTOR
The addition of pentavalent impurities such as
antimony, arsenic or phosphorous contributes free
electrons, greatly increasing the conductivity of the
intrinsic semiconductor. Phosphorous may be added
by diffusion of phosphine gas (PH3).
9

27.  SIMPLE DIODE (P N- JUNCTION
DIODE)
 The two terminals are called Anode and Cathode.
 At the instant the two materials are “joined”, electrons
and holes near the junction cross over and combine with
each other.
 Holes cross from P-side to N-side and Free electrons
cross from N-side to P-side.
 At P-side of junction, negative ions are formed.
 At N-side of junction, positive ions are formed.
10

28.  Depletion region is the region having no free carriers.
 Further movement of electrons and holes across the junction
stops due to formation of depletion region.
11

29.  Depletion region acts as barrier opposing further
diffusion of charge carriers. So diffusion stops within
no time.
 Current through the diode under no-bias condition is
zero.

30. REVERSE BIAS
 Positive of battery connected to n-type material (cathode).
 Negative of battery connected to p-type material (anode).
12

31. REVERSE BIAS…..
 Free electrons in n-region are drawn towards
positive of battery, Holes in p-region are drawn
towards negative of battery.
 Depletion region widens, barrier increases for the
flow of majority carriers.
 Majority charge carrier flow reduces to zero.
 Minority charge carriers generated thermally can
cross the junction – results in a current called
“reverse saturation current” Is , Is is in micro or
nano amperes or less. Is does not increase
“significantly” with increase in the reverse bias
voltage

32. FORWARD BIAS
 Positive of battery connected to p-type (anode)
 Negative of battery connected to n-type (cathode)
13

33. FORWARD BIAS…
 Electrons in n-type are forced to recombine with
positive ions near the boundary, similarly holes in
p-type are forced to recombine with negative ions.
 Depletion region width reduces.
 An electron in n-region “sees” a reduced barrier at
the junction and strong attraction for positive
potential.
 As forward bias is increased, depletion region
narrows down and finally disappears – leads to
exponential rise in current.
 Forward current is measured in milli amperes

34. 14

35.  ZENER DIODE
A diode which is heavily doped and which
operates in the reverse breakdown region with a
sharp breakdown voltage is called a Zener diode.
This is similar to the normal diode except
that the line (bar) representing the cathode is
bent at both side ends like the letter Z for Zener
diode.
15

36. In simple diode the doping is light; as a
result, the breakdown voltage is high and not
sharp. But if doping is made heavy, then the
depletion layers becomes very narrow and even
the breakdown voltage gets reduced to a sharp
value.
 Working Principle
The reverse breakdown of a Zener diode
may occur either due to Zener effect or
avalanche effect. But the Zener diode is
primarily depends on Zener effect for its
working.

37.  When the electrical field across the
junction is high due to the applied voltage, the
Zener breakdown occurs because of breaking
of covalent bonds and produces a large number
of electrons and holes which constitute a steep
rise in the reverse saturation current (Zener
current IZ). This effect is called as Zener effect.
 Zener current IZ is independent of the
applied voltage and depends only on the
external resistance.

38. I-V CHARACTERISTIC OF A ZENER
DIODE
The forward characteristic is simply that
of an ordinary forward biased junction diode.
Under the reverse bias condition, the
breakdown of a junction occurs.
Its depends upon amount of doping. It can
be seen from above figure as the reverse voltage
is increased the reverse current remains
negligibly small up to the knee point (K) of the
curve.

39.  At point K, the effect of breakdown
process beings. The voltage corresponding to
the point K in figure is called the Zener
breakdown voltage or simply Zener voltage
(VZ), which is very sharp compared to a
simple p-n junction diode. Beyond this voltage
the reverse current (IZ) increases sharply to a
high value.
 The Zener diode is not immediately burnt
just because it has entered the breakdown
region.
 The Zener voltage VZ remains constant
even when Zener current I increases greatly.

40. The maximum value of current is denoted by
IZ max and the minimum current to sustain
breakdown is denoted by IZ min. By two points A
and B on the reverse VI characteristic, the Zener
resistance is given by the relation,
rz = ( Δ VZ / Δ IZ) -----(1)
16

41.  ZENER DIODE APPLICATIONS:
I. Zener diodes are used as a voltage
regulator.
II. They are used in shaping circuits as peak
limiters or clippers.
III. They are used as a fixed reference voltage
in transistor biasing and for comparison
purpose.
IV. They are used for meter protection against
damage from accidental application of
excessive voltage.

42. IMAGE REFERENCE LINKS
1. http://postimg.org/image/sl3tj8a71
2. http://web.utk.edu/~cnattras/Phys250Fall2012/modules/module%204/conduction_in_solids.htm
3. http://mystudyexpress.com/12%20th%20science%20cbse/physices/Electronic%20devices/unit%2
0image/1--band.gif
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5. https://lh5.googleusercontent.com/-
16m5gmPuujM/VKZDTCWuH5I/AAAAAAAAAYE/c7hh5fUbsug/w475-h377-
no/New%2BPicture%2B%2825%29.png
6. http://s15.postimg.org/arf492z13/New_Picture_26.jpg?noCache=1420186429
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9. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/imgsol/nsem.gif
10. http://www.engineersgarage.com/sites/default/files/imagecache/Original/wysiwyg_imageupload/1
/Internal-structure-of-p-n-Diode.jpg
11. http://rsandas.com/images/Zener_Symbol.jpg
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3e3d63e9c7.gif
13. https://encrypted-
tbn1.gstatic.com/images?q=tbn:ANd9GcSruAypsy5B4GX6xIrC2mzrjNqsA7bm8dNgnHeZ43Hz
C-8PSVBg
14. http://s3.postimg.org/wzdlbz75r/New_Picture_31.jpg?noCache=1420188304
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