Fermi level can be defined for semiconductors as an ideal level at which the probability of occupation with electrons is 50% which lies in the band gap at (T=0K) . In metals, it’s defined as the top occupied energy level in the conduction band at (T=0K). Thus we have two definitions, one for semiconductors and the other for metals.
Why we don’t try to unify the definitions?
I mean let us go deep in the Fermi Dirac distribution function, the 50% occupation rule is obvious. What about the second definition of metal?
Metal's conduction band is practically a continuous energy band, i. e. energy levels are very closely spaced such that they can practically be considered continuous (I found it in 'Principle of Solid State Physics' by Levy). Now what happens if we say that the first definition is also working in metals?
The top occupied level in metals is very close to the above unoccupied level (they are almost overlapping). Now, the ideal energy level which lies between the top occupied level and the lower unoccupied level is practically the top occupied level. Why we don't say that the first definition leads to the second and vice versa?
The thing you're proposing is already pretty much the standard thing.
Anyway, the usual definition of Fermi energy is the limit of the chemical potential as the temperature goes to zero. In practice some people use "chemical potential" and "Fermi energy" as synonyms and even talk about "quasi Fermi energies" for non equilibrium situations in which the electron and hole densities aren't consistent with the temperature and the doping level.
The thing you're proposing is already pretty much the standard thing.
Anyway, the usual definition of Fermi energy is the limit of the chemical potential as the temperature goes to zero. In practice some people use "chemical potential" and "Fermi energy" as synonyms and even talk about "quasi Fermi energies" for non equilibrium situations in which the electron and hole densities aren't consistent with the temperature and the doping level.
In compensated semiconductors, definition of the chemical potential is more complex: :Its position is defined from the condition of equal equilibrium concentration of electrons and holes. It depends on the effective masses of both and on the temperature; In nondegenerate case, it is shfted towards the band with smaller effective mass (usually the conduction band). Only in the case when the effective masses are equal, it is placed in the middle of the forbidden gap.
The physical situation in metals is basically different, so that the standard definition is appropriate for them.
Dear Abdulghefar,
Dear colleagues,
The definition of the Fermi energy level is derived directly from the Fermi-Dirac energy distribution function which gives the probability of occupation of an energy level with Femions such as electrons in solid materials. Recalling this function:
f(E)=1/[ 1 + exp(E-Ef)/kT], with the terms have their usual meaning.
There are two distinct points in this function:
- The first one is that f(Ef)= 1/2 at all values of T>0k
-The other definition is that f(E
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