Kronig-Penny Model: Effective Mass

Here I go cover energy/momentum diagrams in more depth, and I explain how we can use them to determine how electrons and holes move in the semiconductor through the concept of effective mass.

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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.

[Jacob-gepy]

I actually almost cried with relief when I found this. Your explanation is so much clearer than any lecture I have ever been to.

[KeenestObserver]

Holy shit. I learned and understood SO MUCH in 13 minutes !! My lecturer's slides are completely horrible and he's bad at explaining intuitively. Thank you loads <3

[JyotiDeka]

I completed my under-graduation 9 years ago and today, I understood the meaning of effective mass of an electron... :)... Thank you so much Jordan for these lectures...

[bryantcombs]

My lecturer for Quantum Mechanics is too smart for his own good. He is horrible at explaining stuff, you are going to save my GPA and my degree, thanks Homie.

[shubhamtanwar]

Thanks for the excellent video!
Physics should never be taught without explaining what "should sound awkward" and what "should sound intuitive". Great approach.

[roonilwazlib]

Wow excellent explanation !! I have been trying to wrap my head around this for so long but you explained it so simply!

[jahnavilothugedda]

Oh Thank you so much helped lot cuz I have an exam was literally so easy when you explained it....

[martinsimbona]

Ooh man, that was so helpful. I neede to prove that formula for effective mass and found it nowhere else.
Can't thank you enough, thanks for Sharing!!

[erikchavarin]

This was awesome. I so wish my prof. made electronics this exciting.

[srchang]

Dear sir, I am the person who asked you a question regarding calculation of effective mass from the E-k relation. I got your answer already. Thank you very much. But I would like to discuss a little bit more. The E-k relation is actually an equation containing a complicate function of E and cos k(a+b), where a is the width of the potential barrier and b is the width of the potential well. Therefore, k can be varied by its period without changing the value of E. Consequently, the value of k in the E-k curve is not uniquely defined; it can be shifted by the amount of the period. Therefore, choosing a pair of E-k values from the curve to calculate effective mass, as you mentioned at 3:20, will lead to a wrong answer. Using the curvature (calculating the 2nd derivative) can avoid the problem of k-value shift, because the curvature is not changed by the shift of k. Moreover, only the bottom of the curve (near k = 0) can be represented by a parabola function, so we use this part of the curve to conveniently ontain the 2nd derivative. Please let me know if I am right or wrong. Thanks.

[밤고구마-zi]

I really appreciated it. It's very helpful for me to understand the concept of an effective mass. 😌

[lightningllama]

Is there an intuitive explanation for energy-band diagrams with multiple sub-bands?
Some materials such as GaAs have different effective masses which lead to multiple overlapping E-K curves. Spin-Orbit interaction also causes band splitting.

I'd love an explanation on this!

[RexGalilae]

I think that, atleast physically, the effective mass is just a way of accounting for the change in potential energy as an electron moves between potential wells.
Since we stated that E = p^2/2m, we're compensating for the lack of the V term by treating mass as a non-constant.
Other than that, I don't really see any reason why the mass should change in a non-relativistic scenario

[benwinstanleymusic]

Brilliantly explained, thank you so much!

[Saptarshi.Sarkar]

I always thought that the effective mass formula must have something to do with Taylor series. Today I understood why it is. It's just like how we find the frequency for small oscillations due to any arbitrary potential.

Thanks!

[prashantupadhyay]

It's 1 min 46 second only, learned lot

[KnowWithMalvika]

Just Amazing!!! Really a profound lecture.

[ashlynnundlall]

I thought 'p' was momentum and 'k' was the wave number so why is it called the Energy vs momentum curve when "k" wave number is the independent variable?

[srijanisallyouneed]

From #Kolkata, India🇮🇳
Really appreciate your golden Lecture Sir
But 1 question : *In solid state physics from where the Kronig penny graph(which u have drawn) come from? Is it derived by experiment or hypothetical*

[subhashyadav]

For K=0 E must be zero but in EK diagram for k=0 there is some energy E why ?