Calculating Fermi Dirac Probability - Part B Guide

In summary, the conversation revolves around a question about the fraction of holes left behind in the valence band when electrons move to the conduction band. The suggestion is to post the question in the advanced physics section for a more thorough explanation. Additionally, the textbook provides a probability distribution for holes as 1 - W(p) and using this, along with Wv instead of Wc, can help in finding the answer.
  • #1
falcon555
12
0
Hi dear friends
Please reffer to my work , I did part ( a )
20160909_171333.jpg
20160909_171413.jpg
only
Could you please help me to do part ( b )
I don't know how to do it.
 
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  • #2
falcon555 said:
Hi dear friends
Please reffer to my work , I did part ( a ) View attachment 105669 View attachment 105670only
Could you please help me to do part ( b )
I don't know how to do it.
(a) is correct.
(b): If p is the fraction of electrons in the conduction band (at energy EG/2) & coming from the valence band, what would be the fraction of holes left behind in the valence band, seeing as those electrons came from the top of the valence band?
Hint: no electrons going to the conduction band ⇒no missing holes!
 
  • #3
Thanks rude man...
I'm not getting what you mean. ...
Can you explain it in a different way or show on a diagram. ...
 
  • #4
falcon555 said:
Thanks rude man...
I'm not getting what you mean. ...
Can you explain it in a different way or show on a diagram. ...

I may work on this some more but I think you should post this in the advanced physics section where I think it belongs. I covered this material many years ago in a graduate course (taught by a future Nobelist!).
 
  • #5
Then the equation may change to the below
20160910_112813.jpg


I guess. .
If this is correct then we have to write an equation for W h in term of Wg and Wf to eliminate Wf.
What will be that equation?
 
  • #6
How to shift this post to the advanced physics section?
 
  • #7
falcon555 said:
Then the equation may change to the below View attachment 105702

I guess. .
If this is correct then we have to write an equation for W h in term of Wg and Wf to eliminate Wf.
What will be that equation?
OK, after a bit more perusal on my part:

My textbook gives the probability distribution for holes as not W(p) as it is for electrons, but as 1 - W(p). Without a believable rationale, but I'm sure it's correct, because later on they use that expression for deriving the totality of free carriers for electrons and for holes and get roughly the same number for each, which has to be correct. That was supposed to be my hint in post 2 but as I say it wasn't based on good argument.

So, bottom line, if you use 1 - W(p) for the holes, and use Wv in lieu of Wc, and proceedig exactly as you did in part (a), you will get your answer. Do that and let us know what you come up with.

I am going to ask a moderator to move your post to the advanced physics section for you.
 
Last edited:

Related to Calculating Fermi Dirac Probability - Part B Guide

What is Fermi Dirac probability?

Fermi Dirac probability is a statistical concept in quantum mechanics that describes the likelihood of a particle occupying a specific energy state within a system, taking into account the exclusion principle for fermions. It is named after physicists Enrico Fermi and Paul Dirac who developed the concept in the 1920s.

How is Fermi Dirac probability different from classical probability?

Fermi Dirac probability is different from classical probability because it takes into account the quantum nature of particles and the exclusion principle, which states that no two identical fermions can occupy the same energy state simultaneously. This means that the probability of a particle occupying a specific energy state decreases as more particles are added to the system, unlike classical probability where the probability remains constant regardless of the number of particles.

What is the Fermi-Dirac distribution function?

The Fermi-Dirac distribution function is a mathematical formula that describes the probability of a fermion occupying a specific energy state within a system at a given temperature. It takes into account the exclusion principle and is used to calculate the average number of fermions in a system at a given energy level.

What is the significance of Fermi Dirac probability in the study of materials?

Fermi Dirac probability is significant in the study of materials because it helps to explain the behavior of fermions, such as electrons, in materials. It is used to understand properties such as electrical conductivity, thermal conductivity, and magnetic properties of materials.

What other areas of physics use the concept of Fermi Dirac probability?

The concept of Fermi Dirac probability is also used in other areas of physics such as nuclear physics, astrophysics, and cosmology. It is a fundamental concept in understanding the behavior of fermions in various systems and plays a crucial role in many theories and models in these fields.

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