imroze99 said:
With our discussion I have come across the following points regarding Fermi level
*Fermi level is the just an energy level where the value of Fermi Dirac function comes to be .5
*Fermi level is in forbidden gap where density of states is zero therefore no electron will exist at FL.
This last statement is wrong. Or rather, it isn't always true. It is true in the case of an insulator, but false in the case of a metal.
The Fermi level is not always in a forbidden gap. The Fermi level is only in a forbidden gap in the case of an insulator. In the case of a metal, the Fermi level is never in a forbidden gap. One special case of insulator is high resistivity semiconductors.
In the case of an n-type metal (e.g., silver, copper) , the Fermi level is above the bottom of the conduction band. In that case, there are electrons in the conduction band. In the case of a p-type metal (e.g., aluminum), the Fermi level is below the bottom of the conduction band. In that case, there are holes in the valence band. In the case of an insulator (e.g., sulfur), the Fermi level is right between the two bands. There are no free electrons or holes in an insulator.
Semiconductors are not "semi" in having an in-between conductivity. Semiconductors are "semi" because their conductivity is easier to change then true metals or true insulators. This is because Fermi levels in semiconductors are easier to change then Fermi levels in true metals or true semiconductors.
imroze99 said:
*When analysed by sea level analogy the top of the sea level is valence band and the electron flow should take place due to concentration gradient of Valence electrons.
This analogy is wronger than other analogies. All analogies by definition are wrong, but many of the facilitate analysis of more precise theories. Your analogy does not facilitate the analysis.
I don't think this analogy as stated facilitates accurate analysis because the valence bands don't align. The Fermi levels align, not the valence bands. So your analogy, as stated, leads to incorrect predictions.
I modified your analogy in a previous post. I said that the valence band is more closely analogous to the sea bottom. Perhaps you can address this point.
In my sea level analogy, the surface of the sea is the Fermi level. The bottom of the sea is the valence band. The tropopause is the conduction band.
The conduction band and the valence band are defined in terms of electron density of states, not electron occupancy. The conduction band can be empty of electrons and still exist. The valence band can be filled of electrons and still exist. After one dopes the crystal, the conduction band can have electrons and the valence band can have holes. Obviously, the still exist.
The forbidden gap still exists whether or not the bands are full or empty. The energy gap varies only a little with doping. Adding electrons to the conduction band can lower the energy gap by a small fractional amount, but it doesn't change it. The energy gap is mostly determined by the lattice and types of atom that make up the lattice. Occupancy doesn't affect the energy gap very much.
Because the conduction band is defined in terms of density of states, the conduction band doesn't align with other conduction bands. Because the valence band is defined in terms of density of states, the valence band doesn't align with other valence bands. The Fermi level aligns with other Fermi levels.
My suggested analogy was that the Fermi level of a region of crystal is like the surface level of a sea, lake or river. The valence band is like the bottom of a sea, lake, or river.
Water flows from a high lake level to a low sea level when the seas are connected. If the system reaches equilibrium, then the lake and sea levels are aligned.
The bottom of the sea, lake, or river doesn't move no matter how much water is being moved. Well, there is a little erosion. However, the bottom of the sea, lake or river doesn't move.
If because of rain and evaporation there is no equilibrium, then water can pour through the river lake indefinitely. The lake and sea levels can remain constant. If the lake runs out of water, then the lake will be dry.
Equilibrium comes about when the sea has the same level as the lake. There may or may not be water in the lake when equilibrium is reached. However, the new level of both sea and lake are the same when there is equilibrium.
When the lake has dried up, the lake level will be the same as the sea level. However, the sea level is below the bottom of the lake. If enough water has flowed in the sea, there may not even be an aquifer below the bottom of the lake. Even though there is no water in the lake, the lake level is well defined. It is the same as the sea level.
The point is that the local sea level is not defined by the surface of water at that location. It is defined as the level to which the water would go if it were allowed to move.
imroze99 said:
Are these points correct?
Considering the above points I wanted to know that what is so special about the Fermi Level that in p-n junction the electron movement flow takes place till the alignment of their respective quasi Fermi level.
I said that these points were wrong in a previous post. I repeat my argument in this post. Perhaps you could tell me how I am incorrect.
What makes the Fermi level special is the Pauli exclusion principle and thermodynamics. Two electrons can not have the same quantum numbers by the Pauli exclusion principle. The crystal has a minimum energy according to thermodynamics. The electrons lose energy until they reach a minimum energy allowed by the Pauli exclusion principle and thermodynamics.