# What is band bending and how does it relate to Fermi Energy?

1. Sep 30, 2013

### HunterDX77M

1. The problem statement, all variables and given/known data
Consider a pn junction in Si at 300K (other parameters given), with doping NA = 1021/m3 and ND = 1023/m3. Assume all impurities are ionized. On this basis find the Fermi level on each side. From this find the band bending VB and make a sketch of the pn junction.

2. Relevant equations
$N_e = N_C e^{\frac{-(E_G - E_F)}{k_B T}}$

3. The attempt at a solution
The Fermi energy calculation was fairly straightforward to solve for, since I just used the formula above for both sides and solved for EF. My question is about band bending. What is it and how do I calculate it? I looked through the relevant chapter in my text-book, but I couldn't find any reference to it. Can someone show me how it relates to the Fermi energy that I have already calculated?

2. Sep 30, 2013

### Simon Bridge

Is usually covered in your course text book
Then the chapter you looked in was not relevant to "band bending" ... look back to where it talks about how energy bands form in the first place - conduction and valence bands etc. Then read forward until you see diagrams of these bands being bent - usually where it starts talking about P-N junctions.

Basically - different materials will have energy bands at different energies.
The bands want to be continuous. The only way this happens for two different materials close enough together for electrical contact is if the bands bend in some way. This usually means that charge carriers get trapped close to the junction or something like that.

Last edited: Oct 1, 2013
3. Oct 1, 2013

### HunterDX77M

I found the following two equations in my lecture slides. Due to notational differences between my textbook and the lecture slides, I'm not sure if the variable EC represents the band gap energy (which is known in this problem). I am assuming that EFN is the Fermi level energy.

$E_{FN} = E_C - k_B T \times ln(N_C/N_e) \\ E_C - k_B T [ln(N_C/N_e) + ln(N_V/N_h)] = eV_B = E_{FN} - k_B T \times ln(N_V/N_h)$

If EC, is the band gap energy does this look like the correct relationship between Fermi Energy and the band bending VB?