Charge Carrier Concentration of Doped Semiconductors

/ edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible.
In this video, I talk about how doping affects the electron and hole concentration of n-type and p-type semiconductors, and how this in turn affects the fermi energy level of the semiconductor, one of the most fundamental and useful quantities in semiconductor physics.
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.

[@weammoghazy3153]

I love this series of Semiconductor Physics videos! Seriously, everything is very well explained! It helped me get through my tough semiconductor physics class. Thank you so much!

[@JordanEdmundsEECS]

Aw thanks :D I’m very glad you found it helpful

[@Upgradezz]

Masha Allah

[@ruthwik8772]

I would like to watch all the videos ,but I couldn't because i have this topic for only one semester.So, I watch only some of your videos which I needed .Just loved the playlist.

[@kabandajamilu9036]

best teacher with best explanation

[@user-lv5zj4lr3f]

you are a perfect teacher

[@darkxz9731]

Wow , its an amazing Chanel with so much clarity , hope you get big

[@rasitcakir6699]

For 6:30 You can see the alternative formula here. kzbin.info/www/bejne/oqmtap9jatuofc0

[@devangshudutta561]

Hi Jordan, your videos are awesome, especially the way you make the math in Quan-Mech so easy! A silly question- at 7:02, will the power of the exponent be (Ef-Efi) or (Ec-Ef)?

[@Upgradezz]

Same question

[@HUEHUEUHEPony]

same question

[@nellvincervantes6233]

Maybe it is based from Boltzmann statistics: n = e^(a)*e^(-Ef/kT) (number of carriers @ energy level Ef) Nc = e^(a)*e^(-Ec/kT) (number of carriers @ energy level Ec) When you divide n by Nc (n/Nc): n/Nc = e^((-Ef+Ec)/kT)) n = Nc*e^((Ec-Ef)/kT)) Same for n/ni ni = e^(a)*e^(-Efi/kT) (number of carriers @ energy level Efi) n/ni = e^((-Ef+Efi)/kT)) n = ni*e^((Efi-Ef)/kT)) Maybe im wrong

[@sender1496]

If an electron is excited from a "doped energy level" (one of those energy levels that are added initially when you add for instance P-atoms), does that leave a hole in the initial energy level? Similarly, does a hole moving down to the valence-band (from the initial state) correspond to an electron filling in the old state?I'm finding it hard to wrap my head around how a hole can move to the valence band without an electron filling in. My guess is that an electron moving into the conduction-band should always leave a hole, but that this hole won't be able to move around if it's not in the valence-band (which it wouldn't be if created in the initial, doped state). Similarly, a hole moved into the valence-band is replaced by an electron, but the electron won't be able to move freely since it's not in the conduction-band (in the case for p-type-doping). Is this true or am I missing something?

[@JordanEdmundsEECS]

Yup, that’s pretty much how I think of it.

[@sender1496]

@@JordanEdmundsEECS Alright, thank you for the response! :)

[@TheDrGX]

Hi Jordan, nice videos, thanks a lot. however, i have two questions about getting ni at any temperature. 1. assume we start from quantum mechanics and numerically get E-k diagram, this should give us Eg and perhaps effective mass of e and h at any given k (or E), is this E-k diagram temperature depended? as there seems no T factor in the equation. 2. for effective density of state Nc and Nv, which value of effective mass of e and h should be applied in the equation? as they are different at various k/E positions. thanks

[@nellvincervantes6233]

I have a question sir. Can we use this equation (dont know if this is Maxwell Equation), E = -gradient V - partial dA/dt Where E = electric field V = voltage/scalar potential A = vector potential t = time In this case, No electric field hence E = 0 but has potential difference (gradient of charge to produce diffusion current). ?

[@Upgradezz]

At 7:09 we find that n decreases with increase in T!? Isn't that incorrect

[@halilkarsant8971]

sir ,i cant undertstand n=ni e(ef-efi)/kt can you explain it?btw your videos are amazing.

[@HUEHUEUHEPony]

same question

[@spaschannel9527]

hello Jordan, I'm grateful to have this series of video, it help me a lot. but. i have not get well in n=Nc* Exp(-ve)(Ec-Ef), ~n=ni*Exp (Ef-Efi), my question why -ve sign not involved in expression? of Ef-Efi=KT*ln(Nd/ni). i thought may be expression it could look like Ef-Efi=KT*ln (ni/Nd)

[@AndreFF001]

I'm sorry sorry, this is probably a stupid question, but what do you mean by Donor concentration (N sub D)?

[@JordanEdmundsEECS]

Not at all! Donors are atoms that you add (like Phosphorus) to the silicon that “donate” an electron to the silicon, which means you have one more electron to do stuff with.

[@mhdcharaf1165]

Great explanation as always , but we have learned in an earlier video that Fermi`s function at Fermi energy equals 1/2 which means an electron can occupy a state in Fermi energy and we also know that there is no states in the energy gap so how can the intrinsic Fermi energy be in the midgap when there is no states in it What am I missing?

[@JordanEdmundsEECS]

It’s better to think of the fermi factor as an “occupancy” - the fraction of states which are occupied by electrons. In this case, there are no states, so a 50% occupancy of zero is still zero.

[@mhdcharaf1165]

@@JordanEdmundsEECS Thank you for responding

[@ma_ludivine]

What happens if we dope a semiconductor with a dopant concentration that is larger than the effective density of states?

[@rasitcakir6699]

Number of dopants cannot be more than number of the main atoms. They are normally 1 in a million.

[@ly3282]

6:55 how did u derive that equation with intrinsic concentration from the equation with Nc?

[@JordanEdmundsEECS]

This can be derived using the Boltzmann approximation and then the knowledge that n*p=ni^2 (which we don’t derive, but is a result from chemistry)

[@ly3282]

@@JordanEdmundsEECS I meant how to derive n＝ni e(Ef-Efi)/KT ，btw your videos have been very helpful to me and your channel is so underrated，u definitely deserve more attention！

[@HUEHUEUHEPony]

@@ly3282 Did you figure out how he did it, I want to know this too. This mathematical trickery, where you were the exponent is first -(E_c-E_f) and changes to E_f-E_fi

[@WaniEria]

Hi