# I Energy of an electron with Schrodinger's equation

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1. Dec 4, 2017

### cc94

Hello, I was trying to make a simple model of an electron tunneling through several potential barriers. The electron will flow through a conductor to a heterojunction of possibly semiconductor/oxide layers. I assume the electron is coming as a plane wave from the left with some energy E. We know that k = sqrt(E - V) for each layer, but my question is, how do you determine E and V? Is E the fermi level in the conductor? Is V half of the band gap, which is the distance something at the fermi level would have to tunnel to reach the conduction band of the semiconductor/insulator? This problem is likely more complicated than this, but I just need somewhere to start.

2. Dec 5, 2017

### Staff: Mentor

That expression doesn't have to work in solids. There will be a k(E) relation (dispersion relation), but it doesn't have to be a square root function. It depends on details of your material.

E is simply the energy of your incoming electron.

3. Dec 5, 2017

### cc94

Thanks for the reply. For the energy of the incoming electron, is there a simple way to relate it to say the voltage on the circuit? I don't think applying 1 V on a circuit actually gives the electron 1 eV of energy, because the electron isn't freely accelerating in vacuum.

4. Dec 5, 2017

### Staff: Mentor

The absolute energy is meaningless, you need the energy relative to the potential only, and that will probably be less than 1 eV.

5. Dec 6, 2017

### cc94

Ah I think I finally understand. So if I had a voltage drop of 1 V across the entire structure, the electron's energy is 1 V, because I can call the exit the zero of energy, so the electron is 1 V higher (i.e. the Fermi level of the entrance side is 1 eV higher than at the exit). The potential that the election sees will also slope downward towards the zero.