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 What is Fermi Dirac function?

Fermi Dirac function gives the probability that a energy level with energy ‘E’ will be occupied by an electron. It is given by

Where K is Boltzmann constant, E is the energy of a state in electron volts, Ef is Fermi level, and T is absolute temperature in Kelvin.

 What is Fermi level?

Fermi level is the maximum energy that any electron may possess at absolute zero (or) it represents the energy state with 50 percent probability of being filled if no forbidden band exists. The last statements can be explained as follows, at T = 0 K if E > Ef then (E- Ef)/ (KT) tends to positive infinity  tends to 0 or maximum energy that any electron may possess at absolute zero then (E- Ef) / (KT) tends to negative infinity  tends to 1. Hence the maximum energy that any electron may possess at absolute zero is Fermi level.

Now assume some arbitrary temperature T above 0 Kelvin E = Ef then  = (1/2), 50 percent probability of getting filled if no forbidden gap exists.

Equations of conductivity in metal and semiconductors?

Metals conducts current by means of electrons, whereas semiconductors conducts current by two charge carrying particles of opposite sign one is electron(negative charge) and other is hole (positive charge).Therefore the equations for conductivity in metals and semiconductors are

                                                                               In metals

                                                        In semiconductors

Where n is electron concentration, p is hole concentration, Q is electronic charge = 1.6*10^(-19),  µn is electron mobility, µp is hole mobility.

What is drift velocity?

In a metal when a voltage is applied between its ends the electrons are accelerated by the voltage applied, while accelerating the electrons experience inelastic collisions with the ions. At each collision electron loses energy and a steady state condition is reached where a finite speed is attained which is known as drift velocity. 

What is the Variation of mobility with temperature?

ANS: As temperature increases at first mobility increases as T^1.5. At these range of temperatures impurity scattering dominates over lattice scattering. It reaches a maximum then mobility starts to decrease as T^-1.5 when lattice scattering dominates impurity scattering.

Variation of mobility with temperature

Variation of mobility with temperature

           

Direct band gap and indirect band gap semi conductor?

ANS:  In direct band gap semiconductors the highest energy level in valence band and the lowest energy level in conduction band occur at the same momentum or wave number. After the Direct recombination of electron with hole in valence band, energy of the photon released will be exactly equal to difference in energy of lowest energy level in conduction band and highest energy level in valence band.

Note: Momentum and direction of electrons will remain same.

In direct band gap semiconductors the highest energy level in valence band and the lowest energy level in conduction band do not occur at the same momentum or wave number. Since momentum has to be conserved a phonon which is a quantum of vibration energy should exist to assist recombination, hence such recombination of electron with hole are termed as indirect recombination. After the indirect recombination of electron with hole in valence band, energy of the photon released will be less (or) high compared to difference in energy of lowest energy level in conduction band and highest energy level in valence band. This is because some of energy is gained from phonon (or) lost to phonon in recombination process.

Note: Momentum and direction of electron changes after recombination.

Direct and Indirect band gap semiconductor

Direct and Indirect band gap semiconductor

 

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