Effective density & Intrinsic carrier concentration

In summary, in order to prove the relationship "n=ni*e(Ef-Efi)/KT", we can consider the intrinsic semiconductor case where n=p=ni and the intrinsic Fermi level is denoted as Efi. Given the equation "n=Nc*e-(Ec-Ef)/KT", we can see that "ni=Nc*e-(Ec-Efi)/kT". Therefore, by substitution, we can prove that "n=ni*e(Ef-Efi)/KT". Additionally, this result can be applied to any non-degenerate semiconductor. There may be some discrepancies in the values of Nc depending on the unit system used.
  • #1
Mimi
11
0

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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  • #2
Is there given any relation between Nc and ni ?
Can you say more about Nc? What is the expression of Nc??
 
  • #3
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...
 
  • #4
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:
 
  • #5
oh..I see.
Thank you so much tnho!
 

1. What is effective density?

Effective density refers to the density of charge carriers (such as electrons or holes) that are available for conduction in a material. It takes into account the actual number of carriers present as well as their effective mass, which can be influenced by factors such as temperature and impurities.

2. How is effective density related to intrinsic carrier concentration?

Effective density and intrinsic carrier concentration are closely related. Intrinsic carrier concentration is a material-specific value that represents the number of charge carriers that would be present in a pure, ideal crystal lattice at a given temperature. Effective density takes this value into account, along with other factors, to determine the actual number of carriers available for conduction in a real material.

3. What is the significance of intrinsic carrier concentration?

Intrinsic carrier concentration is an important parameter in semiconductor physics and device design. It helps to determine the electrical properties of a material, such as its conductivity and resistivity, and can be used to predict the behavior of devices made from that material.

4. How does temperature affect effective density and intrinsic carrier concentration?

Temperature has a significant impact on both effective density and intrinsic carrier concentration. As temperature increases, the number of thermally generated charge carriers also increases, leading to a higher effective density and intrinsic carrier concentration. This is why most materials exhibit higher conductivity at higher temperatures.

5. Can impurities affect effective density and intrinsic carrier concentration?

Yes, impurities can have a significant impact on both effective density and intrinsic carrier concentration. Impurities can introduce additional charge carriers into a material, increasing the effective density and changing its electrical properties. This is often used in semiconductor technology to control the conductivity of materials and create specific types of devices.

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