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I am interested in this subject: Applied Mathematics in Electrical Engineering. I am interested in finding an expression for the tunnel current of a tunnel diode in the negative differential resistance region.

I know the basics of quantum mechanics and how to find the wave function of a single electron inside a potential well.

The potential function V(x) of an electron inside the P-N junction can be split into 3 regions.1 region(A) is the region of increasing potential due to the fact electrons have to jump from the valence band to the conduction band of the N-type semiconductor.1 region(B) is the region of increasing potential due to the electric field of the P-N junction and 1 region(C) is the region of decreasing potential due to the fact the electron loses its energy and goes in the valence band of the P-type semiconductor.

Questions: for region A can I consider the graph of the potential to be a straight vertical line with height equal to the band gap?

for region C can I consider the graph of the potential to be a straight vertical line with height equal to the band gap?

for region B does someone know the function of the potential V(x) inside the P-N junction?I need to solve the time-independent Schrodinger equation for an electron.Can I approximate the function V(x) with a line?

Can I approximate V(x) to be something like this?

Help appreciated.

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  • $\begingroup$ I am afraid, it is not a question for chemists. $\endgroup$
    – Maurice
    Sep 10, 2022 at 20:49
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    $\begingroup$ The RCA Tunnel Diode Manual, linked in the answer here might provide a bit of help. But this question really should be migrated to the electrical engineering stack exchange. Or the physics one. $\endgroup$
    – Ed V
    Sep 10, 2022 at 21:11

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The potential across the p-n junction depends on the type of bias applied, but your approximation is valid for extremely narrow p-n junctions. The Esaki diode needs a difference in Fermi levels across the junction in order for an appreciable current to flow. Here is a diagram from a professor at Vassar showing the potential across the diode:

The difference in band energies across a p-n junction for an Esaki diode

You can see that they also approximate it as linear and that the valence band of the p-doped side is higher in energy than the conduction band of the n-doped side.

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