2. Calculate the length scale associated with the recombination region. Do this by solving the differential equation in the 3rd video and thereby finding p(x) for x greater than \(x_d\).
3. Sketch a graph of p(x).
4. Sketch a graph of the hole diffusion current.
Solution notes.
The length scale refers to the characteristic length associated with the exponential form of p(x) and J(x). Since it is exponential, the enhancement technically extends infinitely far, but it drops by 1/e at a distance of about 2100 nm away from x_d, so we call that the characteristic length. Does that make sense?
So, to speed things up and so you will be confident you are on the right track, you can ask me questions in the comments to HW 4, like:
ReplyDeleteIs this differential eqn correct?
Does the differential equation just involve p(x)?
Is this the right form for p(x)?
Is this the right length scale?
That way, if you get off track you can get right back on a good track quickly. I will post this also as a comment to the HW 4 post, and I am thinking that is the preferred place for this particular discussion. (About HW 4.)
Also, if you like, I can have office hours after class. Let me know if you would like to talk after class on Tuesday.
I am thinking that for 3 and 4 you will infer that the range of interest is x greater than xd? Is that true?
ReplyDeleteExcellent points! Thanks.
ReplyDeleteDoes that have units of length? basically yes, but make sure the units are length and not something else or inverse length.
ReplyDeletemc^2 = 0.5 x 10^6 eV
ReplyDeleteExcellent point! Allisin.
ReplyDeleteI think the negative sign shouldn't be there.
ReplyDeleteWe define J=(kTe(Tau)/m)(+dp/dx), but I think it should be -dp/dx.
I'm taking a negative away from the differential equation. I hope this is right!
ReplyDeleteI have faith in you. I believe it is right!
Delete(Also, the homework 4 solutions you sent me last night look really good.)