Density of States Derivation Part 1

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In this video, I derive the equation for the density of states, and I show how finding the most convoluted way possible to count apples helps us do this.

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.

[christosvasiliou]

i am a MSc studend in adv. materials and nano, and i have a module of semiconductors. Your video series helped a lot with my midterm and realising to the full everything i have been told to the lectures. Godd job and thank you in advnace

[lowerlowerhk]

The apple counting part helps me a lot. For this concept of density of state, I do need somebody explaining it to me like I am a 5 year old.

[abebe]

I think number of state should be volume*volume density. I mean N=v*(n /a^3), not N=v/(n/z^3). I think the equation written at 4:37 is not right: even the unit does not give us the number of apples. Other than that your videos are life savers!!!

[lorenzo]

At minute 2:26 n is not the number of electrons but the concentration of electrons per unit of volume. Thanks for the wonderful lesson!

[jozokukavica]

Oh thank you so much for this. A year and a half ago i was googling and youtubeing to find a good explanation on this and couldn't find it. Embarking upon this is such a delight, thank you. Finally a good enough explanation. Thank you!

[sl]

The volume of a spherical shell: recall volume of a sphere V = 4/3.pi.r^3, so dV = 4.pi.r^2. dr//

[shrutijain]

Excellent explanations sir!!
Love n support from India!

[anot]

Did we choose the shell because different radial distances corresponds to different energy levels? so that we can find the quantity of different energy levels.

[rsbpg]

Congrats on your channel! Clear and easy to understand. One question... if we use finite quantum wells instead of infinite ones, would the final g(E) change much? I mean, do you think g(E) (as in the video) would be accurate for a metal like copper?

[gehjbrw]

discrete sum can be found from integration

[AndreKuhlmannDesign]

Thanks for the video Jordan. There is one thing though I cannot wrap my mind around "k-space". Can you give me a hint on what "k-space" is?

[seandafny]

Seems kind of backwards to me to use the volume per states to find the state per volume but I guess the difference come in because one of the volumes uses real space and one of them uses only k space

[kirthi]

Hi, I'm confused what you mean by a "state" of an electron. You said that each "state" can have 2 electrons, that means a state corresponds to a given (n, m, l) value. But here, you considered each state to correspond to a single "n" value only. For a given "n", wouldnt there be multiple states for different m and l values?

I think I'm missing something.. pls let me know if you can clarify! Thanks!

[RohitSharma-migt]

for 2d materials, would the vol be replaced by area?

[xandersafrunek]

I followed this video and the next and everything is understandable, EXCEPT shouldn't the distance from the center to the edge of the sphere in "k-space" just be k and not k^2? This makes sense to me because of the way you plug in k as if it were equal to r as explained previously. Also, if possible can you better explain this transition from euclidean space to "k-space"? Is this just a geometric interpretation or does it have physical meaning?

[한두혁]

Hello! I have a question..
in 2:28 (the number of charge carriers in unit voulme) what you did is you multiplied #of state with probability of that state occupied. However, shouldn't it be #of particles for that state instead of probability of occupancy?
I'm quite confused about it because if was probability, then it should give you 1 if properly integrated(without density of state multiplied)...
By the way, it was a really good lecture thank you!

[suruchiverma]

At 4.34 you say that we take the volume and divide by volume density. But if we do volume divided by (number per volume) it doesn't work. So either it should be volume divided by (volume per number) or else volume multiplied by (number per volume). Am i right?

[nellvincervantes]

The confusing part of this is there is stil a probability of occupancy of electrons on forbidden band based on Fermi Dirac statistics. But when you get the density of state (I think it is the average = integral g(E)P(E)dE) on forbidden gap, it will be zero.

[aneelahassan]

Asslam o alikum sir.. I have a question that this particular derivation of density of state (you have done) and derivations of density of states in 3D for nanomaterials is same or different?

[SampleroftheMultiverse]

For those That prefer a mechanical analog you can look at harmonics of a guitar string and such.

The video I present is another mechanical method of quantizing a system. It is one of two methods where structures can actually be produced.


Area under a curve is often equivalent to energy.

Buckling of an otherwise flat field shows a very rapid growth of this area. If my model applies, it may show how the universe’s energy naturally developed from the inherent behavior of fields.

Under the right conditions, the quantization of a field is easily produced.

The ground state energy is induced via Euler’s contain column analysis.
Containing the column must come in to play before over buckling, or the effect will not work.
The sheet of elastic material “system” response in a quantized manor when force is applied in the perpendicular direction.

Bonding at the points of highest probabilities and maximum duration( ie peeks and troughs) of the fields “sheet” produced a stable structure when the undulations are bonded to a flat sheet that is placed above and below the core material.