Band theory of solid

1. Band Theory of Solid

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.

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6.  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.

7.  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.

8. Electrical current for holes and electrons in the same
direction

9. • 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

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

11.  Energy Band in Solid
The following are the important energy
band in solids:
 Valence band
 Conduction band
 Forbidden energy gap or Forbidden band

12. 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.

13.  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.

14.  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.

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

16. 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.

17. 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.

18. 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.

19. 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 …..

20.  Types of semiconductors
Semiconductors
Intrinsic Semiconductor Extrinsic Semiconductor
p - type n - type

21.  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.

22.  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

23. 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.

24. 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.

25. 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).

26.  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.

27. 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.
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.

28. Positive of battery connected to n-type material
(cathode).
Negative of battery connected to p-type material
(anode).

29. 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

30. Forward bias
 Positive of battery connected to p-type (anode)
 Negative of battery connected to n-type (cathode)

31. 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

33.  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.

34. 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.

35.  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.

36. 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.

37.  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 IZ increases greatly.

38. 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)

39.  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.