How does applying potential affect the energy band diagram for a diode?

[jaus tail]

TL;DR Summary

Why does band diagram shift in diode?

Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/pnjun2.html
Hyperphysics Asstr

Why does the band diagram shift up or down when I apply potential? Why does it shift down when positive potential is applied? Professor said it's because electron has negative charge and so we consider downward direction as positive because we have -qE as some energy for electron to enter free space.

But I didn't understand it. If I apply n-region with positive potential, then am I increasing or decreasing electron concentration in Surface. From Energy band diagram I am increasing Electron concentration as the Ef is toward Ec now. But I don't understand how?

 

[eq1]

The y-axis in a band diagram is energy. When one applies a voltage to a charge one changes its electric potential, and therefore its total energy, which moves its position in the diagram.

https://en.wikipedia.org/wiki/Band_diagram#Band_bending

 

[jaus tail]

But why does it move down and why not up? The y-axis is energy to do what?

 

[eq1]

Do you know how to calculate the electric potential energy for a test charge in an electric field? In band diagrams the position of the charge is fixed so if you make the field more positive it should be obvious what happens to the electric potential energy.

The y-axis is total energy. Potential energy is energy to do... something. It’s equivalent to asking what a weight whose height was changed can (or cannot) do.