Diffusion Capacitance Derivation

/ 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 go over my derivation for calculating the diffusion capacitance of a PN junction diode under forward bias (I have not seen this derivation elsewhere, but it gives me much less of a headache than those in Neamen and Pieret, and gets the same result).
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.

[@JordanEdmundsEECS]

I made a subtle mistake: the 1/2 at the very end actually comes from the fact that we counted the charge twice (the electron charge and the hole charge), while normally we only count the charge on one of the capacitor plates. However, we need to double-count the charge, because, in general the added hole charge will not be the same as the added electron charge. We can then average this positive and negative charge over a single cycle of a sinusoid, and so the final result is still valid. However, you should be aware of this interesting asymmetry in the capacitance.

[@zixuwang2350]

Thanks Sir. I want to ask that why the added hole charge will not equal to the added electron charge. And where do we counted the charge twice? I mean that the current caused by the electrons and the holes should have been calculated separately and added up, and I don't see anything wrong.

[@supravatdebnath9464]

You sire are a gem. And this series of yours is going to teach people the beauty of semiconductor physics for generations to come.

[@maxattack3000]

Kind of wish you were my prof for all of my EE & physics coursework. This is great stuff

[@MandeepSingh-tz8hs]

Thanks for the tutorial sir , your teaching is great

[@JordanEdmundsEECS]

Mandy Thank you :)

[@MandeepSingh-tz8hs]

@@JordanEdmundsEECS Sir are you planning to give lectures on BJT

[@bolshevik7943]

Wonderful video！But I still have a little question: after getting the expression of Q(V), why not differentiate V directly？The definition of C is：C ==dQ/dV , right?

[@shubham1999]

Thanks Sir. I liked the video. I am also an EE student. I wanted to ask that why do we neglect the effect of depletion capacitance during forward bias volatge. I mean if we consider a practical lightly doped diode, then the depletion layer will be of significant width and have its effect.

[@JordanEdmundsEECS]

You are absolutely right we should always consider the depletion capacitance, even under forward bias (we just call the capacitors by two different names because they arise from two different physical sources). We can just model this as a capacitor in parallel with the diffusion capacitance. For “normal” diodes, the diffusion capacitance will generally be much larger than the depletion capacitance.

[@DW-iq8lt]

Thank you for the video! You calculated the hole concentration on n side. But, shouldn't we also calculate the major carrier - electrons - on n side? I guess they form a capacitor with holes on p side too.

[@sender1496]

I'm guessing that the charge Q is the total charge in the region without respect to the intrinsic charge? But maybe it doesn't matter, since we're later only concerned with the change of charge.

[@JordanEdmundsEECS]

Yup.

[@shubham1999]

Just I had one more question. What is thermal runaway in BJT and how it causes a feedback in BJT? And what is the significance of hybrid parameters in BJT? Sorry, to take your precious time Sir.

[@JordanEdmundsEECS]

No problem at all :). "Hybrid paramaters" are just a fancy way of talking about a specific kind of small-signal parameters and I don't find it to be particularly useful. Thermal runaway is when you have some current flowing through your BJT -> which causes the BJT to heat up -> which causes the current to increase -> which causes the BJT to heat up -> which causes the current to increase, ad infinitum until your BJT burns up.

[@wilson26836]

Does depletion region has charge?

[@ashlynnundlall]

What is the order of magnitude of the Diffusion capacitance compared to the junction Capacitance ?

[@JordanEdmundsEECS]

It depends on the currents involved, but under typical operating conditions for off the shelf diodes you might have a depletion capacitance of ~pF and a diffusion capacitance of ~nF

[@ashlynnundlall]

@@JordanEdmundsEECS Could you explain why the order of magnitudes differ ?

[@shambukarijayanth7120]

What is Ln and why write it in the case of calculating capacitance due to minority electrons of p-side instead of Lp.

[@JordanEdmundsEECS]

The “n” refers to the minority carrier type (the one that is responsible for all this interesting behavior). In general “Ln” refers to the diffusion length *for electrons*, whether that is in an n- p- or I-type semiconductor.

[@shashanktripathi3034]

It really helped.. thanks ✌🏻✌🏻

[@JordanEdmundsEECS]

You’re welcome:D

[@martinsimbona6145]

Lovely