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

• HunterDX77M
In summary: 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?The band bending VB is the energy needed to bend the energy bands in the material so that they are continuous. This is usually done by adding or removing charge carriers from the junction.

## Homework Statement

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.

## Homework Equations

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

## 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?

My question is about band bending. What is it and how do I calculate it?
Is usually covered in your course textbook
I looked through the relevant chapter in my text-book, but I couldn't find any reference to it.
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.

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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?

## What is band bending?

Band bending refers to the change in the energy levels of the electrons in a material near the surface, interface, or junction between two different materials. This occurs due to the presence of an electric field, which causes the energy levels to shift and creates a bending of the energy bands.

## How does band bending occur?

Band bending occurs due to the difference in the work function (energy required to remove an electron from a material) of the two materials in contact. This creates an imbalance in the number of electrons at the interface, leading to an electric field that causes the energy levels to bend.

## What is the significance of band bending?

Band bending plays a crucial role in many electronic devices as it affects the movement of electrons and the flow of current. It also determines the behavior of interfaces and junctions between different materials, which are essential in creating functional devices.

## How does band bending relate to Fermi energy?

Fermi energy refers to the maximum energy level of electrons in a solid at absolute zero temperature. In the presence of an electric field, the Fermi energy level shifts to balance the number of electrons on either side of the interface, resulting in band bending.

## Can band bending be controlled?

Yes, band bending can be controlled by varying the work function of the materials in contact or by applying an external electric field. This is crucial in optimizing the performance of electronic devices and creating specific functionalities.