108N. MOS Capacitor: Energy band diagram, accumulation, depletion, and inversion, threshold voltage

Analog Circuit Design (New 2019) Professor Ali Hajimiri, Caltech
Course material at: chic.caltech.edu/links/
© Copyright, Ali Hajimiri

[@IAN-fn6bo]

Dear prof, thanks really much for your lecture! Just a simple question, @1:07:52, should the q in the expression be 1/q as for unit consistency?

[@AliHajimiriChannel]

You are absolutely correct. It should be 1/q as lower case \phi_ms has units of volts and capital PHIs have units of energy.

[@IAN-fn6bo]

Thanks so much for the reply!

[@coolwinder]

00:00 MOSCAP is important to understand MOSFET transistor 03:00 Conductor energy-band diagram 04:55 Insulator energy-band diagram 08:00 Semiconductor energy-band diagram 10:40 Putting CIS together 15:20 MOSCAP cross-section 18:50 Accumulation - application of positive voltage on the gate 24:40 Depletion - application of negative voltage on the gate 36:40 Inversion - higher negative voltage that triggers hole formation 42:00 Holes come from thermal generation in the semiconductor - slow process 49:20 Little bit more quantitative 1:01:00 When does inversion happen 1:07:10 Return to our assumptions of flat-band

[@AliHajimiriChannel]

Thank you for your help.

[@coolwinder]

​@@AliHajimiriChannel It's the least I can do, thank you for sharing your grate work!

[@ashikjayamon3963]

@Skodra Dude you are everywhere. I've seen you do the same stuff with Dr. Razavi's videos. Anyways good job.

[@coolwinder]

@@ashikjayamon3963 My question is, why are more people not doing the same and better stuff with this content haha? Thanks :)

[@mhmd_rjb]

god bless you for what you did here and in razavi's videos

[@fjord2141]

This lecture is a work of art.

[@summeryang987]

You don't come across lectures this good every femto second. Bravo.

[@achalakankanamge9109]

Ahahaha 😂, was confused when I saw this, but just reached that point of the lecture!

[@caleb7799]

It was great to see that my right ear could join the party mid-lecture!

[@chetanjadhav9730]

Thanks a lot sir, for the improved audio quality. greetings from India.

[@sunkarasaigoutham]

This was the lecture I have been searching for to understand the transition between depletion and inversion. This is so important to understand and explain the working of mosfet.

[@makum_otaku]

Thanks to such prof. ..explaining with such enthusiasm !!! Otherwise this can easily be bored with mathematical derivations.

[@azmnowzeshhasan7948]

Very fascinating & in-depth lecture, easy to understand. Thank you, professor.

[@omarmohamed3473]

Amazing educational content!

[@sunkarasaigoutham]

This is such an eye opening lecture to me. Like Professor my intuition was that as the negative potential is made more negative, the depletion region should keep increasing. This explains why that that is not the case.

[@chashandeepsingh3201]

Thanks a lot, professor this is the first time I have enjoyed electronics.

[@reemalshanbari]

Greetings from Saudi. Thank you professor!

[@kartikeyapandey1302]

thank u very much for the improved audio quality

[@aswenam1170]

Amazing session sir! The concepts are understandable and yea it took time for me to clearly learn the concepts but you made it look more simpler.Hoping to be in one of your classes.thank you!

[@LakshmipriyaNarayanan]

great lecture loved it

[@aaronbraun841]

Great lecture. Thank you.

[@iiigme5990]

It was much more easier to learn ...watching ur videos

[@AMRITSINGH-ro4lq]

Thank you sir u really explained very well

[@siddharthapaul7963]

Great Lecture Professor! I love the way you teach, and the best thing about it is how intuitive you make these things sound, so much so I get mind-boggled. Actually one thing that has bugged me for a while, is, does the depletion region keep increasing after the onset of "WEAK INVERSION"? I mean, weak inversion is the point where free carriers start to pour in right? So it makes sense that the number of fixed charges we have stop growing(i.e., after we have ionized all donor atoms near the surface). Or, in the case of the step input gate voltage, the depletion region first extends far enough for charge neutrality, but then shrinks back to the point when the weak inversion would have set in. Are my deductions correct? Related to this fact, I have a tiny query at 47:09. The C-V characteristic that you drew is the one i keep seeing everywhere. However, the problem I have is, the point where the Capacitance starts rising back up (for the Low Frequency case). That point, evidently, has the lowest capacitance. Now, when in the depletion mode, the capacitance keeps falling, as long as the depletion charge or region keeps growing. So in fact, IF the depletion mode DOES stop growing after the onset of weak inversion, does it mean we can mark the point of the minimum capacitance as VT- (phi F) on the voltage axis?

[@subhra9127]

In the example where the instant step input is given and the capacitance is plotted, how the capacitance value is varying? Because the depletion region is shrinking but the charge remains constant as holes are created so I am not able to understand there.

[@wissameboutaghou1144]

Thank you so much for this explanation sir

[@whatever3041]

Does the mass action law apply in the depletion region?

[@sunkarasaigoutham]

This lecture gives you clear understanding of mos operation that 10 books like Razavi. Thank you Professor.

[@tharun541]

For beginners in analog electronics, should we follow this series or Razavi lectures ?

[@sunkarasaigoutham]

@@tharun541 for beginners Razavi lectures are better

[@seinfan9]

@@tharun541 This is graduate level. Razavi's online lectures are meant for undergrads.

[@SharifMdSadaf]

What is the textbook used for this course, Sir?

[@jnaneswar1]

Sir, Why you considered the direction of electric field while making the equation for E(x), Is it supposed to be in right hand side direction? If so why?

[@joorashis6277]

If you please professor @ali hajimiri why is the fi s = double the fi f I understand the strong inversion assumption n=p and that fi m = Ef - Ei but Fi s is the Ev - E f so can you help me ?

[@niralipatel3601]

after almost 4-5 hrs of different lecture , i understand the concept perfectly!! thank you so much but i have que,@1:09 min you subtract Qss/Cox from workfunction difference of M AND SC to get Vfb . why do we subtract it? why not addition?

[@coolwinder]

Professor, from my observation, isn't Fermi level, actually potential energy of any electron on that x? So that calculating work function from fermi (potential) energy actually makes sense? Not just that, that fermi energy changes when we introduce electrical potential, with electric field, or when there exists chemical potential, like with concentration gradient / diffusion tendency?

[@harshitagrawal74]

on applying Vg ( positive or negative ) does fermi level of semiconducter also moves or it remains aligned with the fermi level of metal that we defined initially along with metal fermi level for Vgs= 0?

[@AliHajimiriChannel]

As mentioned in the lecture, the applied voltage appears as a different between the two energy levels. For potential energy only the difference really matters and the absolute value is essentially arbitrary.

[@joorashis6277]

@ 41:00 the holes that appeared are 100 percent from intrinsic semi conductor atoms not from the donors as phosphorus or they can be the second electron taken from phosphorus and also create a hole ?

[@kunliu5004]

Hi professore Hajimiri, thanks for sharing your lecture! The lectures is very important and helpful for me. Just a simple question, why fermi level energy band of N type semiconductor wasn't bending when there is a bias apply to the gate? I noticed that Conduction band, intrinsic fermi energy band, and valence band was bending when there is a bias voltage apply to the gate.

[@mr.rachetphilanthrophist601]

Can you please tell me one thing, when you draw fermi dirac distribution of electrons and holes on band diagram itself(near uphill for both electrons, holes and you say hot electrons will cross the band) then what axis is what, the vertical axis is f(E) and horizontal axis E or otherwise. It's a very powerful way of understanding electron and hole movement by using band diagram, and you exploit it very much in your lectures, that's why i want to know, thanks for your response

[@kunwarpratapsingh7733]

sir plz explain why depletion width is not reaching beyond maximum width which occurs at strong inversion , why we not take 2.5 times of fermi potential and so onn , why depletion width form only upto 2 times of fermi potential

[@nagarjunsahu5265]

Sir , Are mos diode and mis diode same? What is the difference between them and why ? Sir please reply..I'm confused in that topic.

[@ariureplete9377]

10000000 better than my lecturer xd

[@AMRITSINGH-ro4lq]

🙏🙏🙏🙏

[@harshitagrawal74]

Sir the depletion region is called depletion region because at oxide semiconducter interface the intrinsic fermi level of the semiconducter tends to the fermi level of the semiconducter which according to the equation n= ni*exp(Ef-Efi/KT) giives negligible charges, is this true?

[@AliHajimiriChannel]

Essentially yes. As mentioned in the lecture, the lower density of the free carriers corresponds to a region "depleted" from free charge carriers.

[@hamzakourta4509]

where can i find some exercise relevant to the subject?

[@amalkrishna10sreekutten10]

Can you suggest any good book on solid state devices

[@user-rajesh7441]

I cleared with n substrate band Bending but little confused p substrate Can you please post on p substrate band Bending

[@user-yr1ve8ut5v]

Dear professor, is the example @35:40 a npn mos? Since you said the positive change are ions, which means p type material has been doped into semiconductor? Thanks

[@user-yr1ve8ut5v]

However as your energy level graph showed, the fermi level nears the condition band, it seems that it is a n type doped 😢

[@ly3282]

sir, i think u forgot to put negative sign at 53:47, shouldn't it be -qND/(2ε)*(X-Xd)^2

[@priyo3050]

sir, can I have some notes on MOS capacitor as pdf files?

[@AliHajimiriChannel]

See the free book draft at the CHIC website.

[@yashgupta3127]

You said there is difference between moscap and mos transistor capcitence can you pls explain that.

[@yashgupta3127]

@@nikshepbangera5416 yes brother actually iisc mein interview mein I was asked and I was so dumb I thought we use mos transistor as cap but now I know .

[@siuharry5881]

Dear Sir, may I know why psi s = 2 psi f?

[@AliHajimiriChannel]

Start watching from @1:01 on for a few minutes. It is a rather arbitrary definition but we define the onset of strong inversion as when the surface has the same charge density (of the opposite charge) as the bulk.

[@ronaksh8040]

Where does holes come from its not clear

[@AliHajimiriChannel]

Where as explained in the video, the holes in a MOS capacitor have to come from the thermal generation process and hence are slow in formation. In the case of a PMOS, the holes would come from the drain and source.

[@ananthchellappa7202]

Anyone else notice that the audio only comes out of one headphone? Is it easy to fix? I verified that it's an issue with this channel only. Other channels don't have the issue. If you can, please upload content with the fix. Thanks! Edit : it's only till 43 min in this video - seems to be fixed after that. Other videos in this channel do seem to have the problem though.. Edit : It's only fixed for a few seconds after 43 min :) Would be nice to get it cleaned up.

[@Priyajit_Ghosh]

change from stereo to mono in headphone