- Scalar and Vector Fields
- Gradient, Del and Curl Operators
- Gauss-Divergence Theorem and its Physical Interpretation
- Stokes’ Theorem
- Differential Form of Gauss’s Law
- Differential form of Faraday’s Law
- Differential Form of Ampere’s Law
- Continuity Equation
- Maxwell’s Equations
- Electromagnetic Wave Equations
Electronic Properties of Solids
What is Fermi Energy?
For example in your classroom, the last three rows are vacant and all the students are occupied in the rest of the rows from first onward. So, some rows are filled and some are empty. The last row of the students is a measure of a level to decide that beyond that no student has occupied the sit and below that all sits are full.
Similarly, inside the atoms, molecules, and solids some states are filled and some states are empty. Here, in solid metal, Fermi Level actually divide the filled and unfilled states. All the energy states below it are filled and above are empty. On the scale of energy in metal, the corresponding energy of Fermi Level is called the “Fermi Energy”.
Before, you understand the derivation of this topic that how the density of states are defined by using the momentum space (or k-space). You have to understand what assumptions are used here!!
In k-space, a sphere of radius kF is considered. Why radius kF ? Because in metal, the free electrons which are responsible for the conductivity of the metal have a range of velocity. All the free electrons are not moving with the same speed inside the metals. So their kinetic energy will vary accordingly. The maximum energy will be at the Fermi level. From lowest to the maximum that is equal to the Fermi energy. In momentum space, the sphere radius is represented by the kF, maximum distance from the center.
The range of the radius varies (or you can say the value) and hence the energy of the free electrons. The free electrons have maximum energy EF at the Fermi Level.
For example, you have a big sphere and you know the volume of it, now you want to know, the number of balls this sphere can accommodate. You also know the volume of small balls. What you will do? You will divide the volume of the big sphere by the volume of a small ball. By this way, one can determine the number of total balls. Actually, these number of balls in the big sphere are energy states in which electrons are accommodated.
According to Pauli’s exclusion principle in each energy state, only two electrons can exist. At least one quantum number should be different out of the four, for the second one. This is the reason to multiply by the two factors the number of states you find in the derivation.
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