Energy of an electron with Schrodinger's equation

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Discussion Overview

The discussion revolves around modeling an electron tunneling through potential barriers in a conductor to a heterojunction involving semiconductor and oxide layers. Participants explore the relationship between the energy of the electron (E) and the potential (V) in this context, particularly focusing on how these quantities are defined and related to the circuit voltage.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes that E could be related to the Fermi level in the conductor and questions whether V is half of the band gap, suggesting a need for clarification on these definitions.
  • Another participant argues that the expression k = sqrt(E - V) may not apply in solids and emphasizes that the k(E) relation is material-dependent, indicating that E is simply the energy of the incoming electron.
  • A later reply questions the relationship between the voltage applied in the circuit and the energy of the electron, suggesting that 1 V does not directly translate to 1 eV of energy due to the electron not freely accelerating in a vacuum.
  • One participant asserts that absolute energy is meaningless and emphasizes the importance of considering energy relative to potential, suggesting that the effective energy could be less than 1 eV.
  • Another participant reflects on the concept of energy levels, indicating that with a 1 V drop, the electron's energy can be considered 1 V higher relative to a defined zero of energy at the exit, which leads to a downward slope in the potential seen by the electron.

Areas of Agreement / Disagreement

Participants express differing views on how to define and relate the energy of the electron and the potential barriers. There is no consensus on the definitions of E and V, nor on the implications of circuit voltage on electron energy.

Contextual Notes

Participants highlight the complexity of the problem and the potential for varying interpretations based on material properties and definitions of energy levels.

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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.
 
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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.
 
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mfb said:
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.

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

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.
 
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