Comments on: Recombination in low mobility semiconductors: Langevin theory http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/ Addressing confusion about physics of disordered materials, and adding to it... ;-) Sat, 28 Jan 2012 20:59:59 +0000 hourly 1 http://wordpress.com/ By: deibel http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-499 Fri, 27 Jan 2012 12:42:01 +0000 http://deibel.wordpress.com/?p=54#comment-499 Hi Miriam, thanks for your comment. In the blog post, the derivation of the Langevin equation is shown. In the paper, we expand the original theory somewhat by explaining the prefactor (which we call \zeta) sometimes necessary to fit experimental polaron dynamics with bimolecular recombination. This prefactor stems in part from spatial gradients of the charge carrier distribution. Thus, if at one end of your device there are many more electrons than holes, the assumption n(x)\approx p(x) \approx \bar{n} (where \bar{n} is the average carrier concentration which can be determined experimentally) does not work any more. In our paper [Deibel 2010] we just show how the additional prefactor \zeta can be calculated if the gradients are known. Does that answer your question? Best wishes, Carsten

]]> By: Miriam http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-497 Fri, 27 Jan 2012 11:18:17 +0000 http://deibel.wordpress.com/?p=54#comment-497 Hey,
I am just trying to understand your paper (phys. rev. b 82, 2010) and I was wondering how you get the connection between what you explain here in this (really nice) blog and the equation R = (q/e0er) (µn+µp)(np-ni^2) labeled with equ. 6 in your paper.

Cheers and greetings to my home area Lower Franconia ;)
Miriam

]]> By: deibel http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-418 Wed, 02 Nov 2011 08:16:27 +0000 http://deibel.wordpress.com/?p=54#comment-418 Unfortunately not, but I recommend you have a look at the book by Pope and Swenberg (1999) for background – or use google translate on Langevin’s original paper;-)

]]> By: Jiebing http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-417 Tue, 01 Nov 2011 22:03:29 +0000 http://deibel.wordpress.com/?p=54#comment-417 Thank you very much for your clear explanation.

BTW, do you happen to have an English version of the paper Langevin 1903 (Ann. Chim. Phys. 28, 433)? I want to read the original paper. Thanks.

]]> By: deibel http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-416 Tue, 01 Nov 2011 19:03:41 +0000 http://deibel.wordpress.com/?p=54#comment-416 n_i is the intrinsic carrier concentration. The contribution proportional to -n_i^2 is opposing recombination and is thus a generation term, not a second generation path. Essentially, you can interpret it as the charge carrier densities n and p never being lower than n_i. Once np=n_i^2, there is no more Langevin recombination. This corresponds to the mass action law you find in semiconductor text books. The Langevin recombination equations works for an ensemble of charge carriers, thus is “on average”, so there is no need (and no way) that a charge carrier can “choose” its recombination partner. Regards, C

]]> By: Jiebing http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-415 Tue, 01 Nov 2011 15:42:52 +0000 http://deibel.wordpress.com/?p=54#comment-415 Thanks for your useful post. Can you explain the second term n_i^2 in R_Langevin = \gamma *(np-n_i^2)?

I was thinking some holes may have multiple choices (path) to choose which electron to “marry” to, which causes overestimate of the current. Do this term account for this or for other reasons? Thanks.

]]> By: deibel http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-358 Sat, 03 Sep 2011 07:34:15 +0000 http://deibel.wordpress.com/?p=54#comment-358 I am sorry, there is nothing more to it than written in the post. The particle is free once it does not feel the Coulomb attraction to the other particle any more, which is the case when thermal energy = coulomb energy. That equation is then rearranged to give the Coulomb radius, as described.

]]> By: Carlos Augusto http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-357 Thu, 01 Sep 2011 14:51:08 +0000 http://deibel.wordpress.com/?p=54#comment-357 I jsut didn’t understand what is the Coulomb radius. Can you explain me?

.

]]> By: armismelas http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-231 Thu, 18 Nov 2010 23:58:47 +0000 http://deibel.wordpress.com/?p=54#comment-231 Wow :) didn’t expect it to be that small. That’s so interesting, I’ll keep reading!
Thanks for claryfing those points for me

]]> By: deibel http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-230 Thu, 18 Nov 2010 18:27:34 +0000 http://deibel.wordpress.com/?p=54#comment-230 \zeta is typically in the range between 10-3 and 0.1, as reported by Juska, Durrant or our group. Still fascinating that despite this lowered prefactor, the open circuit voltage is so heaviliy influenced by bimolecular recombination!

]]> By: armismelas http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-229 Thu, 18 Nov 2010 09:44:14 +0000 http://deibel.wordpress.com/?p=54#comment-229 I got it now :) sorry for the confusion. The additional prefactor \zeta you mentioned clarified it for me. Thanks

I am just curious how large those deviations could be? I mean the values of \zeta

]]> By: deibel http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-227 Thu, 11 Nov 2010 17:42:41 +0000 http://deibel.wordpress.com/?p=54#comment-227 I am really sorry, but I just don’t get your point. Why an exponent of only 0.8 (your previous comment), and where should the proportionality constant come from? Of course, you get a prefactor when solving the continuity equation, but that does not change the recombination rate R (which is actually, more precisely, R_\text{Langevin} = \gamma (np - n_i^2), but that’s another story;-) Experimentally, though, you can of course have deviations from Langevin’s theory; ,in our group, we call this additional prefactor \zeta.

]]> By: armismelas http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-226 Thu, 11 Nov 2010 16:13:37 +0000 http://deibel.wordpress.com/?p=54#comment-226 Apologies, I meant - A /gamma n p

]]> By: armismelas http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-225 Thu, 11 Nov 2010 16:12:39 +0000 http://deibel.wordpress.com/?p=54#comment-225 Calculating the recombination rate: I realise the recombination current is -\gamma q p and in addition the recombination rate should also be proportional to electron density. What I don’t understand is why isn’t there a proportionality factor A A -\gamma n p
I apologize if I am making this really unclear but I just want to understand :)

]]> By: deibel http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-220 Wed, 10 Nov 2010 17:58:28 +0000 http://deibel.wordpress.com/?p=54#comment-220 Not sure where the 0.8 exponent should come from: could you elaborate, please?

]]> By: armismelas http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-218 Wed, 10 Nov 2010 14:07:12 +0000 http://deibel.wordpress.com/?p=54#comment-218 Thanks, I got it now :)
Regarding the second question I meant why is it -\gamma n p ? Why not -\gamma n^{0.8} p ?

]]> By: deibel http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-217 Tue, 09 Nov 2010 22:48:28 +0000 http://deibel.wordpress.com/?p=54#comment-217 Hi! Langevin’s theory is very simple but pretty effective. Of course, both electron and hole move, and if they come to within the Coulomb radius, the Coulombic attraction exceeds the thermal energy sufficient for escape. The clever assumption was to make a clear cut: Langevin proposed that every electron-hole pair with a radius smaller than r_c recombines, all others do not. This is then generalised to account for the carrier concentrations, i.e., these assumptions are used to calculate a recombination current, and from that the recombination rate including the Langevin prefactor.

Your question concerning the last equation is a bit unclear to me. The last equation is dn/dt = \dots - \gamma n p, thus the recombination rate is proportional to Langevin recombination strength times electron density times hole density.

Best, C

]]> By: armismelas http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-216 Tue, 09 Nov 2010 12:27:25 +0000 http://deibel.wordpress.com/?p=54#comment-216 Yet again nicely presented!

I have a few questions. Calculating the Langevin recombination strength we assume that the hole is moving in an electric field equal to that generated by two point charges seperated by Coulumb radius? Why? I realise if they don’t get within Coulumb radius then thermal energy is sufficient to escape recombination and if they do get within Coulumb radius then they recombine. Is that so? Could you clarify this point to me, thank you
And in the last formula why is the recombination proportional to langevin recombination strength times electron density n? Why not n^2? I realise it should depend on both carrier densities but why a simple multiplication?

thank you

]]> By: Pedro http://blog.disorderedmatter.eu/2008/04/04/recombination-in-low-mobility-semiconductors-langevin-theory/#comment-50 Mon, 02 Mar 2009 15:49:39 +0000 http://deibel.wordpress.com/?p=54#comment-50 Clear!

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