How does diffusion of high energy electrons shift band structure?

[eyeweyew]

TL;DR Summary

How does the highest energy electrons diffuse to the p-side from the CB of n-side shift the entire band structure of n-side downward?

When an n-type material comes in contact with a p-type material to form pn-junction, electrons with the highest energy in the conduction band will diffuse to the p-side to reach equilibrium so the entire band structure on n-side will shift down relative to p-side as described in the following page and books:

https://instrumentationtools.com/energy-diagrams-pn-junction-depletion-region/

NOTE: Scrolling to the next couple of pages and scrolling back if it says a page is unavailable
Section 3.4.1
https://www.google.ca/books/edition/Principles_of_Electronics/ciJW8A9mpIUC?hl=en&gbpv=1&dq=3.4.1 energy band diagram of pn-junction at equilibrium&pg=PA57&printsec=frontcover

Page 1024
https://books.google.ca/books?id=sDscEAAAQBAJ&pg=PA1024&lpg=PA1024&dq=why+conduction+band+shift+down+on+n+side&source=bl&ots=t0WO_TTp30&sig=ACfU3U20025MsjKjmORBXkw8p12aDyQzEw&hl=en&sa=X&ved=2ahUKEwjlyajts5j6AhX1IDQIHf8hCewQ6AF6BAgtEAM#v=onepage&q=why conduction band shift down on n side&f=false

The 2nd book is stating that losing high energy electrons in the conduction band on the n-side will decrease the fermi level of that side because fermi level represents the average energy of electrons. The author defined fermi level as the average energy possessed by electrons participating in conduction in metals at T>0K on page 963 of its book:

https://books.google.ca/books?id=sDscEAAAQBAJ&pg=PA963&lpg=PA963&dq=fermi+energy+is+the+average+energy+possessed+by+electrons+participating+in+conduction+in+metals+at+temperatures+above+0k&source=bl&ots=t0WO-_-x5Y&sig=ACfU3U3JL57aLDbwKoguStMc-iIk-vdPcw&hl=en&sa=X&ved=2ahUKEwiTm7z_zZ36AhW0Jn0KHQXnDc8Q6AF6BAgwEAM#v=onepage&q=fermi energy is the average energy possessed by electrons participating in conduction in metals at temperatures above 0k&f=false

I am not sure if this is correct and if not, how losing high energy electrons on the n-side decreases its fermi level and thereby decreases the entire band structure on the n-side?

 

[eljose79]

Thank you for bringing up this interesting topic. I can confirm that the information provided in the sources you have mentioned is correct.

Firstly, let's understand what a fermi level is. The fermi level is the energy level at which there is a 50% probability of finding an electron. In other words, it represents the average energy of electrons in a material. This is true for metals at temperatures above 0K, as mentioned in the book.

Now, when an n-type material comes in contact with a p-type material to form a pn-junction, there is a difference in the energy levels of the two materials. The n-type material has excess electrons in its conduction band, while the p-type material has holes (deficiency of electrons) in its valence band. When these two materials come in contact, the excess electrons in the n-type material will diffuse to the p-type material to fill the holes and reach equilibrium.

As the high energy electrons from the n-type material diffuse to the p-type material, the average energy of the electrons in the n-type material decreases. This, in turn, decreases the fermi level of the n-type material. This decrease in fermi level is reflected in the entire band structure of the n-type material, causing it to shift down relative to the p-type material.

To summarize, the loss of high energy electrons on the n-type material decreases its fermi level, which in turn decreases the entire band structure on the n-type material. This phenomenon is essential in creating a depletion region at the pn-junction, which is crucial for the proper functioning of electronic devices such as diodes.

I hope this explanation helps clarify your doubts. Please let me know if you have any further questions.