A Brief Review of Semiconductor Physics

Rutherford and Bohr developed postulates with regards to atoms.

Since Bohr's postulates is still in use I would like to state them below:

1.   Electrons can move only in certain permitted orbits.
2.   The energy of an electron in a particular orbit is definite.
3.   Each permitted orbit is associated with a level of energy.
4.   Atoms radiate out only when an electron jumps from one orbit to another.
5.   If E₂ and E₁ are the energies corresponding to two orbits before and after the jump the frequency of the emitted photon is given by: hf = E₂ - E₁.

According to Bohr's model, centrifugal force acting on the revolving electron must balance the electrostatic pull by the positively charged nucleus.

Equation:   mv² / r  = ze² / 4πε₀r²

Furthermore, their angular momentum can only have integral multiples of a certain value

Equation:   mvr = nh / 2π

Eliminating r from the two equations, the orbital radius is:

r_n = ε₀n²h² / πmZe²

where:
Z    =   Atomic Number
ε₀   =   Permittivity of free space
e    =   Charge on an Electron
m   =   Mass of an Electron
h    =   Planck's Constant
n    =   Principal Quantum Number

The radii of the permitted orbit vary as the square of the principal quantum number.
The velocity of electrons can be found and it is inversely proportional to orbital radius. This implies that the electron in the innermost orbit has the highest velocity

There are two types of electron energy:

1.   Kinetic Electron Energy
2.   Potential Electron Energy


Equation of Kinetic Electron Energy = Ze² / 8πε₀r

Equation of Potential Electron Energy = -Ze² / 4πε₀r

The orbital energy is the sum of the potential electron energy and the kinetic electron energy.

Equation of the Orbital Electron Energy = -mZ²e⁴ / 8ε₀²n²h²

Electron energy is inversely proportional to the square of the principal quantum number.

The drawing of horizontal lines to an energy scale is known as energy level diagram.
A group of sub orbits is known as shell.

Azimuthal quantum number helps to determine the shape of different sub shells (circular or elliptical).

Pauli's Exclusion Principle states that no two electrons in an atom should have the same sets of values for its four quantum numbers.
Pauli's exclusion principle does not allow the electron energy levels to be the same so that one obtains a set of closely spaced energy levels forming an energy band.

Principal quantum number determines the size of the orbital.

If an electron jumps to an inner energy level, a photon (that is a quantum of electromagnetic energy) will be emitted. The valence band is highest occupied band

Pauli's Exclusion Principle