I UNIT SEMICONDUCTOR MATERIALS
Energy band theory of crystals – insulators, semiconductor, conductors-intrinsic semiductor-extrinsic semiconductorMobility and conductivity-Hall effect and its application –Drift and diffusion currents-Potential with a graded
semiconductor.
1. Energy band theory of crystals
1) Most metals and semiconductor are crystal in structure.
2) Crystal consists of an array of atoms which regularly repeats in 3D to form some structural fundamental units.
3) Each single free atom as its own energy level.
4) When these atoms form a crystal their energy is a function of contribution of energy atom in the crystal.
5) These energy levels are determined by Quantum mechanics.
6) Consider a crystal consisting of an N atom.
7) Imagine that the spacing between atoms can be varied without disturbing the crystal structure.
8) With the atoms are far apart then their energy P coincide with Isolated atoms
9) The two outer sub shells have 2S2P electrons.
10) Inner shell energy levels are ignored so they are 2N electrons filling 2N possible S levels and remaining 2N
electrons fill 6N states so in P atomic sub shell only one third is filled.
11) With the interatomic spacing D is reduced atoms will exert force at its neighbor.
12) Now the crystals must obey Pauli’s exclusion principle (No two electrons have same energy levels.)
13) So 2N electrons in S states must spread out their energy similarly in P states also spread out their energy,
14) These large numbers of discreet but closely spaced energy levels is called Energy Band.
15) When D is decreased further these bands will overlap so the upper 6N and lower 2N states merge together to
give 8N levels.
16) Out of 8N levels half of which 4N level is only filled.
17) Now this electron does not belong to S P sub shell but they belong to entire crystal.
18) The 4N electrons occupy a band which is completely filled known as Valance Band.
19) Band in which 4N states are completely empty is known as conduction band.
20) The Energy gap between Valence band and Conduction band is called Forbidden Energy gap.
21) This Energy band structure which is Energy Gap EG determines the properties of the material.
22) The Orientation of the atoms in the crystal also determines the property.
2. Insulator, Semiconductor and Metals
INSULATORS.

In an insulator the region containing no energy stage is several electron volts (eV) (typically e.g. (ele -6ev).

The large forbidden gap separates the filled valence band from the vacant conduction band,

Even the external applied, filled will be insufficient to carry the charged carries from the filled valence band
to the vacant conduction band is impossible in an insulator Eg. Diamond, which is a form of carbon.
Semiconductor.

The width of the forbidden energy region is relatively small (above 1ev) the practical semiconductor material
are Germanium and silicon of EG of Ge is 0.785 ev and Si is 1.21 ev at ‘0 Kelvin.2

Even energies of this magnitude cannot be acquire from applied field ,hence they are insulators at low
temperature.

When the temperature is increased the conductivity increases .it is due to some of the electrons in the
valence band acquire thermal energy and moved into conduction band.

At 300K energy for Ge is 0.72ev and Si is 1.1ev.

The absence of electron on the valence band is called hole.

It certain impurities are added into the crystal, then new energy level will occur in the forbidden Energy gap.
This type of semiconductor is called Extrinsic Semiconductor.
METAL.

In a metal there is no forbidden energy gap and valence band overlaps with the conduction band, so even a
small applied field can helping in conduction.
ELECTRON & HOLE IN AND INTRINSIC SEMICONDUCTOR.

Germanium and silicon are two most important semiconductors used in electronic devices.

The crystal structure of Ge and Si is the form of Tetra hedron with an atom at each vertex.

Each Ge and Si atom contributes four valence electron so they are called tetravalent atoms.

The inert ionic core of the atom is +4.

Each atom is shared by four nearest neighbors (each valence electron of an atom 4of its nearest valence
electron)

A very low temperature (0⁰) the crystal behaves as a insulator.

At room temperature some of the covalent bond is broken because of thermal energy and conduction
becomes possible.

Now the electrons get free from the covalent bond and become free electrons.
Ntype and P type semiconductor (extrinsic):-
Donor and Acceptor impurities.
N type
Pentavalent Elements: - Phosphorous, Antimony, arsenic (Donor impurities)
P type
Trivalent Elements: - Boron, Gallium, Indium (Acceptor impurities)

In a pure silicon crystal a small amount pentavalent impurities having 5 valence electrons is added.
This impurity atom from the covalent bond with four affix nearest neighbor, remaining one electron
remain free, these electron is called free electron.

The energy required to detach the 5th electron is 0.05ev for silicon and 0.01 ev for Germanium.

These impurities donate excess electron carries so they are called Donor Impurities.

The semiconductor doped with donor impurities is called ‘N” type semiconductor in which electrons
are the majority charged carries and the holes are minority charged carriers.

When a trivalent element such as Boron, Gallium, Indium) is added to a semiconductor is formed.

These trivalent atoms form a covalent bond with three of its neighbor leaving a hole in the four
covalent bond.

So in a P type semiconductor holes are the majority charged carriers and Electrons are the minority
charged carriers
Charge Densities in semiconductor
Let
n
-
Electron concentration
p
-
Hole concentration
ni
-
Intrinsic carrier concentration
ND
-
Donor atom concentration
NA
-
Acceptor atom concentration

In a Intrinsic semiconductor n = p= ni so np = ni 2

Let the concentration of donor atoms ND which is positively charged.

So the total positive charge in the semiconductor ND + p

With the Acceptor atoms NA which is negatively charged so that the total negative is
semiconductor is NA + N

Since the semiconductor is electrically neutral with the carrier concentration with positive
and negative charge should be equal.

In a N type material
NA = 0; ND = n
Np = ni 2 / n
P = ni 2 / ND

In a p type material
NA = p; ND = 0
Np = ni 2
Np = ni 2 / p
n = ni 2 / NA
Dirft and diffusion currents
Drift current :N-type material
Vdn = -µnE
E
Where Vdn → Drift Velocity of electrons
µn → electron Mobility
E
→Electric Field
Jn
→ Current density of N type material in ampere unit area
Jn
= -enµn Vdn
Vdn
Jn
= -en(-µnE)
= enµnE

When a electric field E is applied to a semiconductor , it produces a force that acts on Free electrons and
holes.which experience the drift velocity there is a net movement of charge carriers.

When electric field E is applied to a N type semiconductor in one direction it produce a force on electrons
are negetively charged.

The electrons acquire the drift velocity Vdn = -µnE

µn of low dopped silicon is typically 1350 cm2/V second

The Mobility indicates how easily an electron moves in a semiconductor

This Electron drift produces drift current curent density Jn in the opposite direction.
Jn
= -enµn Vdn
= -en(-µnE)
= enµnE
P-type material
Vdp = -µnE
Where Vdp → Drift Velocity of holes
E
µn → Mobility of holes
E
→Electric Field
Jp
→ Current density of p type material in ampere unit area
Jp
= -epµp Vdp
= -ep(-µpE)
= epµpE
Vdp
Jp

The typical value of µp = 480 cm2/V second
Total Drift Current density
J
J
=
Jdn + Jdp
=
enµnE + epµpE
=
(enµn + epµp)E
=
GE
Where G is the conductivity (enµn + epµp)
=
1/R x E
Where R is the resistivity
Diffusion Current density
n
Electron
diffusion
Electron Diffusing
density
X
p
Hole Diffusion
Hole Diffusion Density
X




In diffusion particulars moves from region of higher concentration .
Consider that electron concentration varies as function of distance ‘X’.
The Diffusion of electrons in negetive X direction.
Since the elctrons are negetively charged the flow of diffusion current density id positive current ‘X’
direction