Qualitative Band Diagram of Intrinsic and Extrinsic Materials

Probablity Distribution Function

Electrons are fermions, which satisfy the exclusion principle. So, it maintains the Fermi-Dirac distribution.

Where, K is Boltzmann’s constant.

K=1.38×10^-23J/K

Or K=8.62×10^-5eV/K

T is absolute temperature.

E_F is Fermi level.

Let, E=E_F

So that, f(E)= ½

So E_F is the Fermi energy level at which the PDF is ½ .

If T=0K the distribution takes the simple rectangular, shown in figure.

Intrinsic & Extrinsic Materials

Intrinsic Material:

The material in which the electron and the hole concentration are same, is known as intrinsic material.

Electron concentration, n_o = Hole concentration, p_o

Electron concentration, n_i = Hole concentration, p_i

Extrinsic Material:

The carrier concentration (no & po) are not same i.e. they differes from intrinsic concentration (ni & pi), is known as extrinsic material.

Electron concentration, n_o ≠ Hole concentration, p_o

Electron concentration, n_i ≠ Hole concentration, p_i

Also n_i ≠ n_o and p_o ≠ n_i

Effective Mass

The mass of electron in free space differes from the massin solid, due to different energy levels or bands. The mass in solid is represented by effective mass. It is denoted by M_e* or M_n*.

Electrons and Holes

Hole:

An empty state in the valence band is reffered to as hole.

Electron Hole Pair(EHP):

If the conduction band electron and the hole are created by the excitation of a valence band electron to the conduction band, they are called an electron-hole pair.

N-Si Energy Band Diagram

Energy Bands

Naturally an individual atom has orbitals of different energy levels which can be represented by wave functions. When the atoms are brought together, their antibonding atoms diminisles and bonding orbitals form a band of energy.