Understanding Quasi Fermi Levels & Calculating QFL Equation

[loneRanger86]

Hello all!

My professor talked about the quasi fermi levels in my Photonics class. While he did make a good effort, I still am not able to understand the concept. I do plan on going to him on Tuesday to get a clearer idea.

But I was wondering if any of you folks could give a general definition of what quasi fermi level is. He worked out a problem on calculating the quasi fermi levels, but I didnt quite get it.

Could you let me know what equation is typically used to calculate the quasi fermi levels?

Thanks a lot!

 

[BackEMF]

OK, no problem. So the normal Fermi Levels used only apply when there are no excess carriers. Have you studied PN junction theory? If you have I can give you examples of Quasi-Fermi Levels from that, but if not it would probably only confuse you at this stage.

As you probably know, you can use your knowledge of the location of the Fermi Level to find out the concentration of carriers:

$$\begin{gather} n_{0}=n_{i}e^{\frac{E_{F}-E_{i}}{kT}}\\ p_{0}=n_{i}e^{\frac{E_{i}-E_{F}}{kT}} \end{gather}$$.

Where (1) gives you the equilibrium electron concentration and (2) gives you the equilibrium hole concentration. So if you know the Fermi Level you can work out both concentrations. However this is not the case when there are excess carriers, in that case these formulae will not give you the correct concentration. But engineers like working with Fermi Levels, so, the concept of Quasi-Fermi Levels was introduced. However instead of one Fermi Level, you now need two, usually called:

$$F_n$$
&
$$F_p$$.

The electron & hole quasi Fermi-Level respectively. So, now using these we can find out the concentrations by the following equations (note how similar they are to the previous equations above):

$$\begin{gather*} n=n_{i}e^{\frac{F_{n}-E_{i}}{kT}}\\ p=n_{i}e^{\frac{E_{i}-F_{p}}{kT}} \end{gather}$$.

So, what does Fp & Fn mean qualitatively? Well the difference between Fn & Ef and between Fp and Ef describe how much the electron & hole concentrations differ from their equilibrium values n0 & p0.

Hope this helps a bit & I haven't confused you more. Let me know if anything isn't clear.

 

[loneRanger86]

OK, no problem. So the normal Fermi Levels used only apply when there are no excess carriers. Have you studied PN junction theory? If you have I can give you examples of Quasi-Fermi Levels from that, but if not it would probably only confuse you at this stage.



...

Hope this helps a bit & I haven't confused you more. Let me know if anything isn't clear.

BackEMF: thanks a lot for the great explanation. I did get a good understanding of the concept- now I am going to put it to use in my homework... hopefully it works out and I won't have to bug you all more.

Thanks again.

 

[akpec]

Hello, can you please tell me how to calculate electron & hole quasi Fermi-Levels (say in n-type semiconductor)? I mean, how to determine Fp and Fn that you mentioned.

Thanks!