Question

describe energy band structure and Fermi distribution function of intrinsic semiconductor, n-type semiconductor and p-type semiconductor.

Answer 1

In solid state, determination of electrical conductivity of solid is based on the conduction band and valence band that closest to the Fermi level. The electrons in the valence bands are bound to the atoms of the materials. There have a energy difference in between valence band and conduction band. This energy gap is called as band gap. Many electrons in the collection of individual atoms occupy in almost similar level of energies. We can consider it is a band, valance band. This valance energy level will be lower than the fermi level. And the level above fermi level is called as conduction band. In some of the materials, the electron can jump from valence band to the conduction band with the help of discrete amount of external energy(eg: heat) and can make it in to a conductor from a non conductor. this type of materials called intrinsic semiconductors.

When an electron in an intrinsic semiconductor gets enough energy, it can go to the conduction band and leave behind a hole. This process is called ”electronhole pair (EHP) creation”.

Probability function called the Fermi-Dirac distribution function. f(E) is the probability that a level with energy E will be filled by an electron, and the expression is:

f(E) = 1 /[1 + exp^{( (E − EF )/(kBT) )}]

where k_B is Boltzmann’s constant, 8.62×10⁻⁵ [eV/K], and T is the temperature in degrees Kelvin. EF is called the Fermi energy or Fermi level.

Extrinsic semiconductors are made by introducing different atoms, called dopant atoms, into the crystal.

n-type. The dopant atoms added to the semiconductor crystal in this case are donor atoms

Phosphorus (P), arsenic (As) or antimony (Sb) as donors can be use as dopants for silicon.

p-type. The dopant atoms in this case are acceptor atoms

Boron (B), Aluminum (Al) and Gallium (Ga) are the well known acceptors for extrinsic semi conductors.