Fermi Function Explained

[@anuragyadav_8572]

i fell in love with you, my god i have been trying to get this type of explanation for 3 days , YOU ARE GREAT , WORLD NEEDS MORE TEACHERS LIKE YOU!!.

[@JordanEdmundsEECS]

Thank you :)

[@ocayaro]

It is interesting to explain to students what happens at T = 0K. The way that I do it is to divide the interval into two, piecewise continuous energy intervals. Then, we note that the exponents will either be negative or positive. Then taking limits with T -> 0K, we note that f(E) tends to 1 on the left interval and to 0 on the rightmost interval. I teach solid-state and semiconductor physics at a university in South Africa and I still enjoy watching your videos for their intuitive approach.

[@gawayne1374]

4:40 does quantum physics, but feels unsure about counting. The life of a scientist

[@faizanhasan9715]

Awesome professor. I have no words to thank you! Extremely well explained. The whole semiconductor series got me A+ grade in exams and will definitely help me in my career too. I would like to thank you from the bottom of my heart.

[@JordanEdmundsEECS]

Thank you Faizan :) this makes me happy to hear.

[@kaixuanyang1250]

Hello, Mr. Jordan Edmunds, I am a student in China, currently studying semiconductor device physics.Your video has given me a lot of benefits, I hope I can move your video bilibili, let more people see this video.We hope to get your approval and look forward to your reply

[@sofiallacer5951]

Thanks a lot for your explanation! It was very useful when learning about semiconductors in solid-state physics. I just wanted to mention that generally one writes 1000K, not 1000 'degrees' K. Keep it up with the great content!

[@maximh1163]

Writing °K instead of K is kind of cringe

[@theonewhoaskedtheonewhocar9780]

😭😭

[@junpengwang2473]

3 mathematicians disliked this

[@sanyamkaul9239]

6:49 - Temp. should be 300K. Kelvin scale is not a 'degree' scale like C and F. By the way amazing explanation! Thanks for the video.

[@JordanEdmundsEECS]

Haha yup I actually learned that from an identical comment a few months ago. Many thanks :)

[@sanyamkaul9239]

@@JordanEdmundsEECS That was me saying to myself, "Atleast I know something" haha.. Keep up the amazing work!

[@aatt3209]

Bravo, fantastic lecturer, I am hooked on your series. Moving onto the next lesson.

[@NickKek-pz8kc]

Im from germany, ive watched multiple german videos, red about it but never understood anything, but this video, which is english and normally hard to understand for me, explained it all perfectly. Thank you very much.

[@eddill2638]

Same here, damn that's a great video

[@salanove]

Hi. Thanks for the videos first of all. Just one question... you say that Ef is known, we can calculate it... I'm struggling quite a lot to see how can one actually know the value of Ef??

[@JordanEdmundsEECS]

In this video, I assumed that EF was known. In general, we calculate EF using the doping of the semiconductor (EF = kT*ln(ND/ni) for n-type semiconductors). It's basically cheating. We're using the idea of EF to derive a bunch of cool stuff, and *then* we're calculating what EF actually is for any given semiconductor.

[@N0ob.At.Life.936]

Not sure how well this applies to semi-conductor physics, but in thermal physics we use chemical potential µ instead of E_F for the same equation. We can find µ by deriving Energy with respect to number of particles while keeping the entropy and volumes of the system constant

[@SciHeartJourney]

Wow, only 3 minutes in and this video has made this so much easier to understand than after 3 weeks of reading our textbook! Thank you so very much. 👍👍👍🎩

[@JordanEdmundsEECS]

xD Dear god trying to read solid state textbooks. Often rough. Anything in particular you think that made it easy to understand?

[@SciHeartJourney]

@@JordanEdmundsEECS I think the graphics along with the explanation that bring it to life and therefore easier to understand.

[@zinhaboussi]

thank you so much awesome explanation

[@Galileosays]

kT is the thermal energy. the ratio (E-Ef)/kT defines the ratio between electronic kinetic energy and thermal energy (random atom vibration). So if (E-E`F)/kT >> 1 than the free electrons have more knietic energy than the random motion of the atoms in the lattice. If (E-E`F)/kT 0 than there will be free electrons, that could be in the conduction band. For E-Ef

[@danielcollins4847]

I'm an undergrad chemical engineering student at Texas. Currently brushing up on all of semiconductor physics before an internship interview with a big semiconductor company. I really appreciate these videos! You present quantum mechanics in a very intuitive way, while still conveying a lot of information. You are gonna save me in this interview. Thank you so much!

[@iansweet8978]

Hey, love the video! I couldn’t help but notice the shape of the fermi function looks a lot like windowing functions used in discrete and continuous signal processing. In those cases, attenuation of the amplitude as you get further from the 0 point on the x axis is expressed in dB. I was wondering if there’s anything similar for the fermi function

[@54Immortal]

Thanks this is a great video, really helped me understand. But just wondering, why do you use °K instead of just K for Kelvin.

[@Chunat]

OMG, I don't need other materials to understand semiconductors, if not throughly, but more than I needed than your video. Thank you so much!

[@mattkan3275]

You teach much better than the professor

[@anonymousperson7390]

I hope someone would explain Bose - Einstein distribution like this.

[@wertzuio2127]

Great explanation. Was a very good refresher for me!

[@MUZICAVECHESIBUNA]

Thank you very much for the explanation! Really helped me in understanding the graph. Congratulations, you have very nice lessons.

[@rhs5683]

I am becaming a mathematican, but I gave you I like, because you are able to explain that physics-stuff.

[@rhs5683]

P.S. We will say: "x lim-> + \infinity (1/x) = 0"

[@annankldun4040]

You should really mention that it's not the number of electrons you find but the electron DENSITY.

[@SumriseHD]

Why don't you participate in Khan Academy?

[@KiyanAmirian]

thank you very much for your explanations, they are very very useful.

[@luwang404]

I found this channel just recently. Have watched some videos. Wow! I feel like I found a diamond mine. Thank you for such high quality contents.

[@tejobhiru1092]

awesomesssst of explanations...!!! indebted to you , jordan..!!!

[@nadirbouziani4620]

wish they teach us like this in college thank you very much

[@sinpi6332]

Bro you deserve Noble

[@hongfeiy476]

you are absolut top for teaching .thank you so much

[@fritzahern1380]

absolute blessing finding this channel, thank you

[@IremBatbey]

Great video!! ^^

[@armeshasharma2334]

nicely explained.... :) really good

[@rationalthinker9612]

Where are you getting Ef = 0.5 ? I have googled fermi energy and I can't find any tables with values???

[@nikhilmani1]

In one of your early video in the comment section you have written "A single state can have only one electron. But at a single energy we can actually have two states, or two spins (these states are called degenerate)". But at time ~4.22 in this video you said f(E0)=0.2 means an electron in one of the bucket out of 5, why not 2 electrons in a single bucket since you are dealing with f(E0) and not directly with states?

[@JordanEdmundsEECS]

That’s a really great and subtle question! It actually took me a bit of thinking. In my analogy, the “buckets” correspond to individual states, not individual energies. If they corresponded to energies, then we would indeed expect 2 electrons in each ‘bucket’, as you pointed out.

[@nikhilmani1]

@@JordanEdmundsEECS This means corresponding to the concern energy value we have 5 degeneracy. And in that case, I am bit confused, if we consider spin up and spin down electrons then how they will be orientated in each degeneracy according to the Pauli's rule?

[@sachingurjar5196]

this is miraculous for me i cant express what is the level of teaching . i cant understand it without you you gave me what i searching for thank you for making this type of video

[@JordanEdmundsEECS]

Thank you :) Anything in particular you liked about it?

[@eriknunezalbermann9993]

Clear explanation, appreciate it

[@0403AUSTIN]

thanks

[@JordanEdmundsEECS]

You're welcome!

[@ServitorSkull]

Oooo new microphone 🥸👍

[@nauman543]

Its very nice explanation. If possible i just want to ask what is chemical potential and what its role in fermi dirac distribution function because in some books we have seen chemical potential instead of fermi energy. thanks

[@JordanEdmundsEECS]

Yeah I believe the electrochemical potential is equivalent to the Fermi energy. It’s basically a way of discribing equilibrium by encapsulating the energy to due diffusion (the chemical part) and the energy due to electric fields (the electro-part) into a single energy.

[@nauman543]

@@JordanEdmundsEECS thank u very much

[@milesknudtson8022]

We can fudge it

[@hashbanah4074]

Such a great series, really clear explanations !!

[@joaquincapo8486]

So you are saying that a state is the energy/momentum electrons and holes are able to give to the mean or system where they are?

[@JordanEdmundsEECS]

A *state* just represents an energy/momentum the electrons are *allowed* to have within the semiconductor. The energy and momentum that electron has will indeed determine how it interacts with the rest of the system (for example if it crashes into an atom it will deliver some of its momentum and energy to that atom).

[@BrikaEXE]

Impressive

[@shubham1999]

You say that a state can contain n no. of electrons. But according to what I have read, a state can contain only one electron or no electron. But in your derivation of Gibbs factor you have used P(N) as the probability fn representing a state containing N electrons.

[@JordanEdmundsEECS]

Yup! Everything you said is correct. The Gibbs factor, however, is more general and can be used for things other than electrons (both bosons and fermions). So for electrons, N can only take the value 0 or 1. For photons, it can take any value.

[@shubham1999]

@@JordanEdmundsEECS Oh. Ok. Means by N, you means 0 or 1.

[@JordanEdmundsEECS]

Yes sir

[@shubham1999]

@@JordanEdmundsEECS Sir, were you taught Quantum Mechanics in your Bachelor's Degree of EE. We were only given a general introduction in freshmen year. Currently, I am a sophomore. Did you also have a Machines course?

[@JordanEdmundsEECS]

I have taken a class on thermal physics, which covers statistical mechanics (the fermi-Dirac function, etc.), but have not taken an upper-division physics course on quantum mechanics yet. It’s more of a hobby

[@bic1349]

Thank you!

[@JordanEdmundsEECS]

You're welcome!

[@MrMishra814]

What exactly is a state?

[@JordanEdmundsEECS]

I love that question. Precisely speaking, a “state” is a unique solution to the time-independent Schrodinger equation. Solving the Schrodinger equation basically tells you how much energy/momentum electrons and holes are allowed to have given the system they are in (here, a crystal).

[@MrMishra814]

@@JordanEdmundsEECS Thanks for the prompt response. Your explanation makes sense.

[@SmoothChino]

the state of trance. dance.