Equilibrium Distribution of Electrons and Holes

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Discussion Overview

The discussion revolves around understanding the equilibrium distribution of electrons and holes in semiconductors, specifically focusing on the Fermi distribution and its implications in the context of a provided diagram. Participants seek clarification on specific aspects of the diagram and the mathematical relationships described in the text.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests a general description of a diagram related to semiconductor behavior, indicating confusion about its content.
  • Another participant explains the Fermi distribution function f(E) and its relationship to the density of states, noting that it approaches 0 for high energy states and 1 for low energy states.
  • A participant seeks clarification on a specific sentence regarding the symmetry of the Fermi function around the Fermi energy, asking how f(E) for E=Ef+dE relates to 1-f(E) for E=Ef-dE.
  • In response, a participant mentions that the function is nearly point symmetric near the Fermi energy at low temperatures, suggesting that this symmetry is a key aspect of the discussion.
  • There are multiple requests for clarification and further explanation, indicating ongoing confusion among participants regarding the concepts presented.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confusion regarding the concepts discussed, with no clear consensus reached on the specific interpretations of the diagram or the mathematical relationships involved.

Contextual Notes

Participants reference specific lines from a text and images that are not visible to all, which may limit the clarity of the discussion. The reliance on these external materials introduces potential gaps in understanding.

shayaan_musta
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Hello. I was studying the Semiconductor and I am confused with this diagram.
I have attached the diagram. Please tell me briefly what does this diagram say. So that I could ask further. I have confusion with this diagram. I don't want to be specific so that you describe the whole diagram briefly and I will try to understand it.

Thank you.
 

Attachments

  • Equilibrium distribution of electrons and holes.PNG
    Equilibrium distribution of electrons and holes.PNG
    40.9 KB · Views: 1,325
Physics news on Phys.org
fF(E) is the probability that a state is occupied, as determined by the Fermi distribution (left=0, right=1). It is close to 0 for states of high energy (top part of the plot) and close to 1 for states of low energy (bottom).
gc is the density of states in the conducting band with that specific energy - it is zero at Ec and increasing for higher energy.

To find the number of electrons with a specific energy, you multiply both functions, and get the shaded area. Its area is (proportional to) the total number of electrons.

gv is the same in the valence band.
 
@mfb

Thank you for your kind reply. Here is another image.
I am confused with a sentence "We note previously that the function f(E) for E>EF is symmetrical to ...", last four line of the first paragraph.

Would you please help me in understanding how f(E) for E=Ef+dE is equal to the function 1-f(E) for E=Ef-dE.

Thank you.
 
I don't see another image.

Close to the Fermi energy and for small temperatures (always true in semiconductors), the function is nearly point symmetric with f(EF)=1/2 as symmetry point.
That relation is just another way to express this symmetry.
 
Here is another image. sorry friend.

Now you can see the last 4 lines of the first paragraph in the given image.
Thank you for your reply.
 

Attachments

  • equilibrium distribution of electrons and holes.PNG
    equilibrium distribution of electrons and holes.PNG
    70.1 KB · Views: 703
Anyone help me
 
I don't see any open questions.
 
Hello friend.
What do you mean by open question?
I am asking you to clear the last four line of the first paragraph from the attached image.
Thank you.
 
I posted an explanation in post 4.
 
  • #10
I read your post several times and I got what you have said. Thank you. It is cleared now. I hope you will help me next time if I post another thread for help.

Thank you.
 

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