Semiconductors

Energy bands are formed due to the degenerated energy leads in a crystal structure or bulk of the material. The energy bonds which are completely filled at OK are called valence bands. The bonds with higher energies are called conduction bonds.
For bidden energy gap, where E_V is topmost energy of valence band and EC is the bottom most energy of the conduction band.
In metals, E_y → 0 is valance band and conduction band overlap so that a large number of electrons lie in the conduction band. In semiconductors, E_g ~ 1 eV.. At OK semiconductor is perfect insulator. But at room temperature, KT ≈ 1eV and so it behaves as a conductors. Fermi level is an imaginary level which lies between valance band and conduction band such that the probability of finding an electron is 50% or 1/2.
and
In insulators,
The resistivity of semiconductors falls with rise in temperature. Semiconductors are of two types
(a) intrinsic or pure
(b) extrinsic or doped.
In intrinsic semiconductor no impurity is added, so the density of electron in conduction band is equal to density of holes in valence band.
i.e. [ here i stands for intrinsic)
Extrinsic semiconductor is of two types P and n types.
In p-type third group impurity (B, Al, Ga, In) is added to make is so majority carriers are holes i.e. .
In n-type, 5th group elements (P, As, Bi, Sb) is added and its majority carriers are electrons i.e.
In thermal equilibrium,

In thermal equilibrium, [here e stands for extrinsic)

[here e stands for extrinsic)

In an intrinsic semiconductor conductivity
Where μ_n and μ_h are mobility of electrons and holes respectively.
 

1. p-n Junction

When p-and n-type of semiconductor of same material either both Si or both Ge are joined to form a homojunction, called pn-junction.
Depletion layer : Close to the junction, a layer exists devoid of carriers due to the migration of carrier to the opposite sides, which create a potential barrier.

(a)Forward biasing
If positive terminal of external battery is connected to p-type and negative terminal to n-type. This reduces potential barrier and have depletion layer width decreases. The current is therefore due to majority carries.
(b)Reserve biasing
If positive terminal of battery is connected to n-type and negative terminal to p-type, the potential barrier increased and the current in due to minority carriers.
Equation of current in pn junction
Where, I_s – reverse saturation current
V = applied potential
V_T = thermal voltage
V at 300 K
[k = Boltzmann’s constant, T = temperature of an electron, e = charge of an electron]

 

2. Rectifier

It is a circuit which converts AC to unidirectional pulsating output. Rectifier are of two types
(a)Half –wave rectifier


Ripple factor = 1.2
Rectification efficiency =
(b)Full wave rectifier

Ripple factor = 0.48
Rectification efficiency

3. Transistor

Transfer + resistor
It is used as an amplifier through the transfer of resistor
Transistor is basically of two types
(a)BJT: (Bipolar junction transistor): pnp and nPn
(b)FET: (Field effect transistor): JFET (junction field effect transistor)
MOSFET (metal oxide semiconductor field effect transition and IGFET (insulated gate field effect transistor)



(c),
∴ and