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Question : How Conduction Band gets raised in energy when under a positive potential

I was trying to understand band bending with a simple model. Here, I am first considering a p-n junction that has attained equilibrium. (fig 1). The Fermi Levels coincide ensuring no more diffusion but the bends haven't been marked.

enter image description here

The diffusion of majority carriers has created a positively charged n-side and a negatively charged p-side. The charge separation creates a potential, which changes the energy of Conduction Band CB.

Initially, it was assumed that the electrons in the CB are under the influence of NO POTENTIAL. But now, because of the excess + charge, electrons on the n-side (under a positive potential) should be lowered in energy. Since Bands are just the energy levels of electrons, My intuition says the Conduction band should bend downward, lowering its energy on the n-side.

This gives me a bend like this :

enter image description here

This is not true for sure... But I cannot find my mistake. Maybe I took the energies wrong. Please clarify How Conduction Band gets raised in energy when under a positive potential

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  • $\begingroup$ Contemplate how the conduction band edge (valance band edge) should come closer to the Fermi level in n-type (p-type) material. $\endgroup$
    – Jon Custer
    Dec 10, 2021 at 21:13
  • $\begingroup$ Are you looking for an answer like "electric field is integral of charge and voltage is integral of field", or something else? Do you know about the vacuum level and how it should be continuous? $\endgroup$
    – Matt
    Dec 11, 2021 at 0:35
  • $\begingroup$ @Matt I'm looking for an explanation to : why conduction band rises up at the n-side even though the electrons have lower energy here. - - - - - How can continuity of vacuum level explain this? I can understand that bands should be continuous but I can't find what's wrong in the analysis. Continuity alone cannot specify the shape of the curve I believe. $\endgroup$ Dec 11, 2021 at 13:19
  • $\begingroup$ Why do you think electrons have lower energy in the depletion region than in the bulk n-type semiconductor? They do not. Consider energy required to move an electron from the bulk n-type through the depletion region. There is an electric field in the depletion region and it is in the opposite direction from what you have drawn in your band diagram. $\endgroup$
    – Matt
    Dec 11, 2021 at 14:49
  • $\begingroup$ @Matt Noo... It takes energy to cross the depletion region in my model also. But as u said energy of electron being higher in bulk n-type (than near the junction) is counter intuitive. But electrons having higher energy in a region of higher potential is also counter intuitive. - - - - I haven't marked the electric Field in the diagram but $\vec{E}$ is from n to p. $\endgroup$ Dec 15, 2021 at 11:25

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