Fermi energy in semiconductors

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Discussion Overview

The discussion revolves around the concept of Fermi energy in semiconductors, particularly in the context of intrinsic semiconductors at absolute zero temperature (T=0). Participants explore the implications of adding electrons to the conduction band and the resulting energy changes, as well as the thermodynamic principles involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes the relationship between chemical potential and energy change when adding an electron to the conduction band of an intrinsic semiconductor at T=0, questioning why the Fermi energy is positioned in the middle of the band gap rather than at the conduction band minimum (E_c).
  • Another participant suggests that the Fermi energy could also be considered at the valence band maximum (E_v) when removing an electron, and notes that discussing T=0 is largely academic since absolute zero cannot be achieved.
  • A participant complicates the discussion by introducing the concept of configurational entropy when adding an electron, arguing that this could conflict with the third law of thermodynamics, which states that entropy should be zero at T=0.
  • One participant expresses skepticism about the assumption that the minimum of the conduction band is always non-degenerate, indicating a need for clarification on this point.

Areas of Agreement / Disagreement

Participants express differing views on the implications of adding electrons at T=0, particularly regarding the nature of the conduction band and the validity of certain thermodynamic principles. There is no consensus on the positioning of the Fermi energy or the implications of configurational entropy at absolute zero.

Contextual Notes

Limitations include the assumption of T=0 being a practical scenario, the potential for configurational entropy to affect thermodynamic laws, and the varying interpretations of degeneracy in the conduction band minimum.

hokhani
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From thermodynamics we have dU=Tds-Pdv+\mu dN. So the chemical potential is the energy change due to adding an extra particle when S and V are constant. Now consider an intrinsic semiconductor at T=0 in which the valence band is all-occupied and conduction band is empty. If we add an extra electron to the lowest point of conduction band (an specified point in the conduction band) the energy change would be E_c and so the Fermi energy (chemical potential).

Then, why the Fermi energy is in the middle of band gap and is not E_c?
 
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Why not E_v, as you can as well remove an electron?
Besides that, this is quite an academic discussion as T=0 cannot be reached. For finite temperatures mu is well defined. Hence you can take the limit T to 0.
 
Let's complicate things a little bit since you chose to discuss the T=0 case. If you add an electron to the semiconductor, then this will lead to a finite configurational entropy due to the degenerate states in which you can add the electron. But this would violate the third law of thermodynamics that is S=0 at T=0.

Discussing imperfections at 0K would always lead to complications. But it still fun to think about them!
 
Useful nucleus said:
Let's complicate things a little bit since you chose to discuss the T=0 case. If you add an electron to the semiconductor, then this will lead to a finite configurational entropy due to the degenerate states in which you can add the electron. But this would violate the third law of thermodynamics that is S=0 at T=0.

Discussing imperfections at 0K would always lead to complications. But it still fun to think about them!

I don't see why. The minimum of the conduction band is usually not degenerate.
 
DrDu, I agree with you if the minimum of the conduction band is non-degenerate, but that this is always the case, is something new to me.
 

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