Doping and Band Diagrams

/ edmundsj
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In this video, I describe how semiconductor doping affects the band diagram of the semiconductor, and how we can use quantum mechanics to understand what is happening when we add dopant atoms to the semiconductor lattice.
This is part of my series on semiconductor physics (often called Electronics 1 at university). This is based on the book Semiconductor Physics and Devices by Donald Neamen, as well as the EECS 170A/174 courses taught at UC Irvine.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.

[@MrGeragon]

In the case of the intrinsic semiconductor, the chance of finding the electron at the Fermi level is 50% while when you n-dope the semiconductor is less likely to find it in the middle and more likely to occupy a higher level. It is like moving the distribution towards higher concentration. The same argument could be applied for the p-doped. That's how I explain it intuitively in my mind. Thank you very much for your videos they are very helpful.

[@ahmedhabib727]

Lol that's exactly how I think about it!

[@milanirodrigo]

There is a little mistake. There is no "degree Kelvin" since Kelvin is an absolute scale. Therefore it is just Kelvin.

[@JordanEdmundsEECS]

I think this might be the most common comment on this video xD You are correct, thanks :)p

[@kogumilaan]

excuse the pedantry but kelvin is not a degree scale

[@JordanEdmundsEECS]

#mostCommonComment 🤣

[@jacobvandijk6525]

@ 2:22 Room-temperature 300 K??? Now I know where this global warming is coming from :-)

[@JordanEdmundsEECS]

Horseshoes and hand grenades xD

[@rachelarnold5585]

you are a good teacher and you speech is clear and audible. thank you!

[@mishrasupriya]

It should be group 13( Boron family) and group 15( Nitrogen family) rather than group 3 and 5 which belong to the transition metals like Sc and V

[@ashlynnundlall]

Please can you do a full derivation of equation 4.11 of Neaman. 4th Edition. Their are some other derivations by people but I don't understand them.

[@redox7483]

Yo you are the fucking goat

[@jvdp9660]

Shouldn't the Fermi level be in in between the donor level and the conduction band? At 0 k there are namely states which are occupied above the Fermi level.

[@nimanemati2641]

How can I prove Mathematically n*p=n^2 ?

[@firesup77]

The concentration of electron charge carriers n and hole charge carriers p is approximately the same, call it n_i. Therefore, we can say n * p = n_i * n_i = (n_i)^2

[@yuanli9382]

Hi Jordan, the doping introduced the doping level in the band gap (close to Ec or Ev), and based on the ionized energy, the ionized percentage, can we say that doping can change or narrow the band gap of a semiconductor? Or we need a Case-by-case discussion, the shallow/deep doping (doping energy level), and the doping concentration (lightly doped / heavily doped) to decide whether the doping can change the band gap in the energy-band structures? In most instances, the ionization energy of (III, IV, V) impurities is about ~ several meV compared with the intrinsic bandgap ~several eV, which is too small to be ignored. But the metal dopant's ionization energy (~0.xxeV) is comparable to the original band gap energy, how can we discuss these conditions? Can we call that condition: semiconductor alloys to tune the bandgap in the bandgap engineering area? also, can you talk more about 2D materials doping and their bandgap engineering? Many thanks. Best,

[@conorsweet9078]

In the last video, you said that adding electrons by doping decreases the number of holes because the electrons and holes "collide." How is this possible if the electrons are part of the new Energy state near the conduction band, and the holes are only in Ev? Also, a quick google gives the definition for Fermi Energy (Ef) as "the highest occupied energy level of a material as 0K." How does this make sense in our band diagram, since electrons can still go up to higher energy states in the conduction band?

[@Mike_212]

Hi Jordan, your videos are excellent and all concepts are so clearly explained - thank you very much! What drawing software do you use for them?

[@user-ge8hj9br6w]

Ef doesn't change , its the Ec and Ev changing which give an impression that Fermi level changed. am i correct?

[@JordanEdmundsEECS]

No, the fermi level does actually depend on the doping.

[@tilki3114]

Sir i got a question. Is Nc "effective density of states" change with doping?

[@다람쥐-q4s]

Thank you for your explanation. It helped a lot

[@HridyanshPareek-dg1fw]

What a nice explanation! Cleared all my concepts.

[@shubham1999]

Sir, I think we need atleast 150 K (not 300K) for all the electrons to reach to E_c from E_d since the energy gap is roughly 2kT.

[@JordanEdmundsEECS]

Definitely, the temperature at which you get a reasonable amount of ionization is below 300K most of the time. I believe the energy gap between the conduction band and the donor level is ~0.045eV (for phosphorous). If you want to find out precisely how many carriers are still left in their donor states, you simply integrate the fermi function from Ec to infinity and then compare that to the value of the fermi function at the donor level. In general, the ionization percentage is going to depend both on the temperature *and* the fermi level.

[@alihasuna1]

The best in the world.

[@BorisGrishenco]

Best solid state videos :)

[@mokoepa]

This is beautiful

[@poulamibag2660]

So, can I say that all the excess electrons of the donor atoms get leveled at Ed at T=0 K ??

[@JordanEdmundsEECS]

Exactly! At T=0K, the electrons won't have any energy to jump up into the conduction band, and they will stay stuck at the energy level Ed.

[@poulamibag2660]

thanks :)

[@biswajeetpatro9990]

Jordan please tell me, what is reason behind the origin of band gap?

[@Upgradezz]

Samij aav.