Why Are Energy and Voltage Inversely Related in Band Diagrams?

[roeb]

My professor has said several times that if you increase the potential (electrostatic) you will get a lower energy in terms of a band diagram.

In particular, I have been working with MOS-Capacitors and this seems to be the case.
For example for an n-type semiconductor. If you apply a positive charge to the metal, the fermi energy level will increase on the metal side, because the voltage potential is decreasing.

My problem is that I have been unable to find an equation that expresses this inverse relationship. Does anyone know of anything that would show me why energy and voltage are inversely related in terms of this? Perhaps I am screwing my thinking up because E = Vq is what I remember from E&M.

Thanks
roeb

 

[BigJDubs]

elThe equation you are looking for is the Shockley equation, which deals with the relationship between energy and voltage in terms of a band diagram. It states that the energy level (E) is inversely proportional to the applied potential (V). The equation is as follows: E = E_0 - kTln(1+exp(-eV/kT))Where E_0 is the intrinsic Fermi level, k is Boltzmann's constant, T is temperature, e is the charge on an electron, and V is the applied voltage. This equation shows that as the applied voltage increases, the energy level decreases. This is because the exponential term decreases with increasing voltage, resulting in a lower energy level.