Effective density & Intrinsic carrier concentration

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Homework Help Overview

The discussion revolves around proving a relationship between electron concentration (n) and intrinsic carrier concentration (ni) in the context of semiconductor physics. The problem involves understanding the equations related to quasi-Fermi energies and the expressions for Nc and ni.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between Nc and ni, questioning the definitions and expressions for these variables. There is an attempt to connect the equations involving Fermi levels and intrinsic carrier concentrations.

Discussion Status

Some participants have provided equations for Nc and ni, and there is a discussion about the implications of these relationships in the context of intrinsic and extrinsic semiconductors. A clarification regarding the units used in the equations has also been raised, indicating a productive exploration of the topic.

Contextual Notes

Participants are considering the implications of using different unit systems and how that might affect the expressions for Nc. There is also a focus on the assumptions related to non-degenerate semiconductors.

Mimi
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Homework Statement


Given "n=Nc*e-(Ec-Ef)/KT", prove "n=ni*e(Ef-Efi)/KT"


Homework Equations


Quasi-Fermi Energies..? Ef is Fermi level (extrinsic) and Efi is Fermi level (intrinsic). Ec is Fermi level (conduction).


The Attempt at a Solution


Very honestly, I cannot figure out how to start...
I know the value of "Nc", but I don't know how to deal with "ni" to prove the relationship.
 
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Is there given any relation between Nc and ni ?
Can you say more about Nc? What is the expression of Nc??
 
Nc=2[(2pi*m*KT)/h^2]^(3/2). (m=m*, effective mass for n)
ni^2=NcNv*e^-(Ec-Ev)/KT.
These are the only values I know...
 
Mimi said:
Nc=2[(2pi*m*KT)/h^2]^(3/2). (m=m*, effective mass for n)
ni^2=NcNv*e^-(Ec-Ev)/KT.
These are the only values I know...

You have Nc and Nv, i guess Nv is something related to the holes, right?
having Nv=2[(2pi*m*KT)/h^2]^(3/2). (m=m*, effective mass for p)
and p=Nv*e-(Ef-Ev)/KT. :blushing:

Consider intrinsic semiconductor case (ie n=p=ni)
we denote the intrinsic Fermi level as Efi and
n=Nc*e-(Ec-Ef)/KT
gives
ni=Nc*e-(Ec-Efi)/kT

Then, it can be seen that
n=ni*e(Ef-Efi)/KT

Notes: This result can be applied to any non-degenerate semiconductor (ie not just intrinsic/undoped semiconductor)

Once little thing i want to confirm is that,
what i learn for Nc is as a form of 2[(m*KT)/2pi*h^2]^(3/2) but not 2[(2pi*m*KT)/h^2]^(3/2).
Are you using cgs unit system?? I don't know this makes the difference or not...:redface:
 
oh..I see.
Thank you so much tnho!
 

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