Detailed Notes on Semiconductor

Those material whose conductivity is lies in between conductor and insulator is known as semiconductor. The semiconductor material have electrical resistivity lying between those of good conductor and insulator.

The resistivity of semiconductor varies from 10 to the power minus 5 to 10 to the power 4 ohm metre as compared to conductor whose resistivity values from 10 to the power minus 8 to 10 to the power minus 6 ohm m. The resistivity range of insulator is 10 to the power 7 to 10 to the power 8 ohm metre.

The example of semiconductors are silicon and germanium which belong to group 4 of periodic table. some compounds such as calcium sulphide Indium phosphate etc which are formed from the combination of elements of group 3 and 5 or group 2 and 6.

There are some properties like negative temperature coefficient of resistance emission or absorption of wavelength makes semiconductor important in providing industrial use.

Semiconductor materials can be modified by introduction of impurities which strongly affected electronic and electrical and optical properties. depending upon the nature of impurity and its semiconductors are classified as:

1. Pure semiconductor (intrinsic)

2. Impure semiconductor (extrinsic)

Intrinsic semiconductor:

It is a pure semiconductor have no free electrons are available since all the covalent bonds are completed at absolute zero the electronic conduction is not possible and hence it behave as an insulator.

When the temperature is raised or even at room temperature semiconductor is a gtes a particular behaviour. The resistance of semiconductor decreases with increase in temperature.

At higher temperature Bond breaks and the electron move away. A vacancy is done created in the block and covalent bond, the vacancy is called hole.

The free electron and holes are always generated in pair. The concentration of free electrons and holes will always be equal in intrinsic semiconductor. Thus for instances semiconductor

Ni = Pi

Ni = NiPi

=Ni2

Career concentration in intrinsic semiconductor

Electron concentration in conduction band

The number of free electrons in conduction band is in the energy range E + dE can be obtained by formula :

d(n) = F(E).D(E).dE -(i)

Where d(E) is density of state defined as the total number of allowed electronic state per unit volume in semiconductor.

Where F(E) is Fermi distribution function which represent the probability of occupation of state with energy E.

to find the concentration of electron we use Fermi Dirac distribution function.

Here:

Where

EF = Fermi energy level

Kb = Boltzmann’s Constant

F(E) = Fermi distribution function.

The density of state

Using equation (ii) and equation (iii) in equation (i):

In equation (iv) E is replaced by (E-Ec)

Where mn* is effective mass of electron in the conduction band.

The number of electron concentration can be obtained by integrating equation (v) taking limit of integration Ec to infinity.

The value of KbT at room temperature is about 26 meV.

Hence the energy > Ec, we have:

On solving equation (6) we get:

The last term

is probability of occupancy level denoted by

is probability of occupancy level denoted by

=NC

Here NC is effective density of state of electron at the conduction band is

n = NCf(Ec)

Holes concentration in Valance band in Intrensic Semiconductor

The number of holes per unit volume in the range E and (E+dE) is given by:

dnp= D(E).[1-F(E)].dE — (i)

Now

In such case in the valence band (E<Ef). Therefore the denominator can be neglected hence:

Equation (iii) shows that the probability of finding the holes decreases exponentially with increase in depth into the valence band and kinetic energy of a hole in energy state (E) in valence band:

K.E. = (Ev — E)

therefore the density energy state per unit volume Independence band is given by:

Now using equation (iii), equation (iv) and equation (i):

On solving this equation we get:

Hence,

np=Nv.f(Ev)

From the concentration of electrons in conduction band and hole in valence band we can define the Fermi level (Ef) we know that in intrinsic semiconductor the electron and holes are generated simultaneously in pairs and

n = p = ni

again

Taking log both side:

Putting the value of NV and NC in above equation:

At absolute temperature at T= 0K

Thus we can conclude that at 0k the Fermi level lies in middle of the conduction band and valence band.

If the effective mass of holes is equal to the effective mass of electron either mp* is equal to mn* then the Fermi level exist in the middle of the conduction band and valence band at all temperature.

If mp* > mn* then Fermi level is raised slightly at T > 0K.