Finding the Hole Concentration in a Semiconductor

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In this video I calculate the concentration of holes in a semiconductor. It's basically the same as calculating the concentration of electrons, with a couple of subtleties involved which I explain.
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.

[@astrologyfit]

Came to this channel for a rather boring MOSFET yesterday. But today for what I love. You are cutting through semiconductor physics like its a piece of butter. Everything looks so effortless at 2x speed. Cannot imagine how you have created this entire playlist. This is not just for my course. But, my passion as a physicist-engineer has been reignited. I am seeing this channel reaching 1M in near future. I very much liked the Gibbs factor derivation of FD function. This is the EE channel as opposed to some high school stuff in Khan Academy! I would love to study some vector field electrodynamics and Maxwell equation solving here. Observing your style and approach, you are the perfect teacher for classical and quantum statistical mechanics too!. Belled Subscriber here.

[@omnikmaurya1358]

these are best videos to binge (actually listening and taking notes ) during lockdown..... absolutely fabulous style of teaching.. Love from India..

[@flyingbirds6794]

thank you very much,it was very beneficial for me

[@97Kok]

Hey! Thank you for making this videos! They may make the difference of me finishing my bachelor or not. However, there is one fact that highly frustrated me, near the end, when you introduced n_i and said it is 1.5*10^10, you kept referring to it as "[...] semiconductor", when it is actually the intrinsic concentration of silicon, not all semiconductors. Just a nitpick, but I needed to mention it. Thanks again for your great work!

[@JordanEdmundsEECS]

Hahahaha thank you very much xD yes you are completely correct I definitely mis-spoke, the intrinsic carrier concentration is indeed semiconductor-dependent.

[@bharadwaj767]

n_i = 3*10^10 ? Wouldn't these electrons concentration and holes concentration add up = whole charge carrier concentration of the semiconductor (silicon). Please clarify me

[@xmuel]

Hi - @ 1:31 you mention notation convention p and n; I think I read somewhere that the letters are chosen for for charge desnity: p for +ve (holes can be read as +ve charge moving) and n for -ve (electrons are -ve charge)

[@JordanEdmundsEECS]

OMG. I cannot believe I never realized that. Thank you!!

[@danielchibuzor3852]

Pls can you help me with this question A specimen of si is uniformly doped with acceptor atoms to produce an impurity concentration of 2 × 10¹⁴ per cm³ at near room temperature of (290k), the intrinsic carrier concentration is approximately 10¹⁰ per cm³. calculate the approximate row and electron concentrations in the material Ingor donor impurities.

[@jimitsoni18]

I have a question. What exactly is Fermi level of semiconductor because if it's the highest energy state of an electron, then it's presence in the centre of forbidden energy gap makes no sense. Because it means that no electron has passed the band gap and went to the conduction band. Hence, conduction is not possible. Also it means that there is possibility of finding electron in band gap which I've never heard before. Please correct me if I'm wrong

[@JordanEdmundsEECS]

In metals at T=0K, the Fermi energy is the energy of the highest-energy electron. In semiconductors, the most general definition is that it is the energy when the occupancy factor f(E) (also called the Fermi Function) is equal to 1/2. This may or may not be in the middle of the bandgap, where there are no available states. The Fermi function only tells you *if there were states* what fraction of them would be filled. With 0 states available, 0 will be filled regardless of the value of the fermi function.

[@jfht318]

just a bit of confusion, is the density of states g(E) the number of states per unit energy or .... the number of states per unit energy per cm^3 ?

[@JordanEdmundsEECS]

Number of states per unit energy per unit volume, yup.

[@abhinandankumar225]

At 5:00 while calculating the number of hole you are taking the limits from (Ev to infinity) . I think it should be from (-infinity to Ev). Rectify if I misunderstood it. Thanks.

[@JordanEdmundsEECS]

Abhinandan Kumar Absolutely correct, if doing the integral over E you should flip the bounds, my mistake.

[@ioanniskariofyllis3726]

can we prove n=p with maths?

[@nellvincervantes6233]

So the probability of zero occupancy orrates vacancy = probability of finding a hole? And the probability of occupancy (only 1 electron because of pauli exclusion principle) = probability of finding an electron?

[@JordanEdmundsEECS]

Yup! Precisely.

[@ruicao7054]

We use 'n' to represent electron concentration because the electrons carry 'negative' charges;we use 'p' to represent hole concentration because the holes carry 'positive' charges.😁

[@abdou290]

Isn't it that the number of holes is equal to the number of electrons?

[@JordanEdmundsEECS]

Not quite, the number of holes is equal to the number of *negative charges*. These can be electrons, but in this case they are actually mostly ions.

[@gerritlaube9449]

I think you mix up axes when you draw the density of states function in the band diagram, don't you? Energy should be vertical, so the square root of E bends the other way around, doesn't it?

[@user-ge8hj9br6w]

is Ec>0 and Ev

[@bharadwaj767]

Suppose Electrons in valence band have some "X" eV and electrons in conduction band have "Y" eV, X-Y=1.12eV (Si). Anybody please add your opinions tooo !!