It is pretty clear that non-radiative recombination (surface recombination) greatly reduce the Voc in solar cells. How about radiative recombination. I would think of high radiative recombination resulting in low Voc, since high Rrad gives rise to lower minority carrier lifetime and thus lower Voc. However, when I read a paper "
Photonic design principles for ultrahigh-efficiency photovoltaics", there is one equation got my attention.
qVoc=Eg(1-T/Tsun)-kT[ln(omega_emit/omega)+ln(4n^2/I)-ln(QE)]
where QE=Rrad/(Rad+Rnrad)
Then as this equation tells, to obtain a higher Voc, one has to increase Rrad. Why? I cannot understand this mechanism from physics side.
Dear Chinjin,
I agree with your prognosis for the effect of radiative and nonradiative recombination on the open circuit voltage of the solar cell.
According to the well known formula for solar cells following the single diode model of the open circuit voltage:
Voc= Vt ln ( Iph/ I0), where Vt is the temperature equivalent voltage, Iph is the photogenerated current which is equal to the shortcircuit current of the solar cell and I0 is the reverse saturation current of the solar cell diode.
It is so that Iph is reduced by the increase of the recombination rate whether it is radiative and nonradiative. While I0 increases with the recombination rate. Then clearly Voc will be reduced with increasing the recombination rate irrespective of the recombination mechanism.
I do not know the equation which you introduced in your question for the Voc.
However, previously we debated the solaced recycling of the radiative radiation.
Where the radiated radiation is captured again in the active region of the soar cell and forced to produce electron hole pairs. In this case it will not be lost as it is will be recycled. In this case it enhance the the generated current and consequently increase the open circuit voltage and the conversion efficiency of the solar cells.
wish you success
Several sources have been proposed which could enhance the open-circuit voltage; none of these sources is significant enough in the sense that experimentally it can be verified. So, these remain in the realm of speculation.
Hi Abdelhalim,
Thanks for your comment. I agreed with what you said. From my point of view, high radiative recombination, in another way, does imply there is the high potential for generation of EHP. But on average, it may not work for the increase in Voc, since it takes time to regeneration EHP. Indeed, it is quite a complex problem and there might be no conclusion of this question yet.
Chenjin,
I understand the QE-related theory was initially proposed by Prof. Yablonovitch. I do not understand the theory well. I would say spontaneous emission is a loss. Taking into account the re-absorption and photo-recycling only reduces the loss, because part of it still comes out from the front surface (a smaller net spontaneous emission). However, a higher QE does help the performance, because it simply means the material is better. If the nonradiative recombination can take away 50% photo-generated carriers from radiative recombination (in open circuit condition), it will also take away a major part of the carriers that would otherwise available for generating current. Thus, a high QE does mean a better cell performance.
Did anyone ever see the derivation of the Eq.1 in the reference mentioned?
Yong
Hi Yong,
Yes, agreed. If nonradiative recombination plays an important role and thus results in a low QE, the cell performance will definitely drop a lot. Thus low Rnrad gives a high QE leading to a larger current. However, what I do not understand is the effect of the radiative recombination from the Eq.1 as mentioned above. It is quite wired that high Rrad can also help the cell performance if I think of it from pure physics concept as I said above. From the math, a high Rrad gives to a high QE. Since a large QE means better material property, we could probably say eq.1 works fine, but hard to understand it starting from radiative recombination point of view.
Chenjin
You should try to find the derivation of eq. 1. It is a pity that paper did not give any reference nor derivation. Perhaps in the original paper(s) of Prof. Yablonovitch's group?
However, I do believe the standard equation needs to be revised, because the I0 does not catch all the effect.
Prof. Abdelhalim Zekry is correct. For LED radiative recombination is important but for solar cell radiative recombination enhance recombination current. In this process if system temperature is further raises then additional Io increment as compared to Vt must reduce Voc. Actually temperature is the crucial factor to reduce Voc due to much increment of Io.
Chenjing Lu:
Would you please look into the following paper for some clarifications to your question and solution methods thus employed:
The paper titled: "Effects of Internal Luminescence and Internal Optics On Voc and Jsc of III-V solar cells."
URL: http://oa.upm.es/26283/1/INVE_MEM_2013_163250.pdf
Chenjing Lu:
I find the paper that you were originally referring to this question has been cited for more than 400 times and contains very illustrative analysis. Why don't you probe the contents of this paper more intensely and also try whether the earlier paper URL link I attached can give you some more thought into reaching answers to your question even though might not be direct.
I would lie to thank Nabil for the paper in his given link. The matter is now clear. It is so that the equation for the open circuit voltage takes into consideration only the radiative recombination and assumes that the nonradiative recombination is zero. So, the other terms takes into consideration explicitly the radiative recombination only to obtain the theoretical limit of the the open circuit voltage. practically, there is nonradiative recombination in addition to the radiative recombination and this must be taken into consideration as the last term in the equation brought in the question.
So, if the nonradiative recombination rate is zero the loss term will be zero which means that the radiative recombination is taken into consideration in the other terms.
By increasing the nonradiative recombination in the last term, the radiative efficiency decreases and the open circuit voltages decreases.
This is the right interpretation of your equation.
wish you success
Hi Abdelhalim,
You made an important point "if the nonradiative recombination rate is zero the loss term will be zero", i.e., if nonradiative rate is zero, it does not what the radiative rate is, even it is very small. Therefore, essentially this term is introduced empirically to measure the material quality. One could replace it with something else, for instance, the ratio of the intrinsic diffusivity and the diffusivity with the presence of defects.
Hope this makes sense :).
The paper I attached to give Chenjing more thoughtful perspective has the similar discussion pattern as the paper Chenjing originally referred. Both the paper states that radiative recombination results in loss of Voc but the papers actually quote optically maneuvered enhancement processes that actually result in higher Voc. I hope this message is clearly noticed by the respondent of my previous answers.
Besides the previously-mentioned paper "Effects of Internal Luminescence and Internal Optics On Voc and Jsc of III-V solar cells" (https://www.researchgate.net/publication/279021052) there is also the theory paper "Strong Internal and External Luminescence as Solar Cells Approach the Shockley–Queisser Limit" (https://www.researchgate.net/publication/260688271) dealing with this question.
Article Effects of Internal Luminescence and Internal Optics on V-oc...
Article Strong Internal and External Luminescence as Solar Cells App...
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