More electrons than photons

edx, Solar Energy, MOOC, photon flux, coulombs, EQE, efficiency, charge carriers, ampere, joule, watt

Suppose <a href="http://pveducation.org/pvcdrom/properties-of-sunlight/photon-flux">3e21 photons are hitting a square meter in one second</a>. You can produce more charge-carrying electrons than photons. So you get more than 483 coulombs (defined as the charge carried by 6.2e18 electrons), since 6.2e18 * 483 = 3e21. If you can collect all those electrons in a circuit, you get more current than the photon flux would produce without using clever engineering techniques to down-convert, up convert, and otherwise raise the <a href="http://www.kuro5hin.org/story/2014/10/31/21555/291">External Quantum Efficiency over 100%</a>.

We should hold engineering challenges to raise External Quantum Efficiency.

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Consider <a href="http://subbot.org/edx/solarenergy/efficiency.png">the math used</a> to calculate the efficiency of a solar cell.

In the calculator app at the bottom of the screenshot, you see an equation used to calculate the efficiency of an example solar cell, <a href="http://subbot.org/edx/solarenergy/efficiency_setup.png">specified</a> before. (<a href="http://subbot.org/edx/solarenergy/efficiency_setup2.png">More setup</a>.)

The correct answers were redacted to comply with the <a href="http://www.kuro5hin.org/tag/honor%20code">Honor Code</a> (since this is an exam question, rather than a practice question).

Anyway, I raised the EQE (which is used in the <a href="http://subbot.org/edx/solarenergy/EQE_question.png">efficiency calculation of a solar cell</a>) from 0.65 to 4.65, to get an efficiency of 104%. This would produce a short-circuit current of 130.2 mA/cm^2, for the example problem.

So, output flux = 
130.2 mA/cm^2 * (6.241e18 electrons * 0.001 A/mA) = 8.126e17 electrons/(s*cm^2)

Incoming flux = 
(10e16 + 11e16 + 6e16) photons/(cm^2*s) = 2.7e17 photons/(s*cm^2)

Thus, to get 104% efficiency out of the example solar cell, you would need to produce, on average, 8.127e17/2.7e17 = 3 electrons per photon. You could do this with down converters, or quantum dots, or hot carriers, etc. This is an engineering problem, not a theoretical impossibility.

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<a href="http://science.slashdot.org/story/02/01/08/2036212/light-stopped-held-and-re-emitted-by-a-crystal">Light trapping</a> might be one way to increase the EQE. If you can <a href="http://science.slashdot.org/story/14/11/06/1934204/first-experimental-demonstration-of-a-trapped-rainbow-using-silicon">trap</a> all the high-energy photons, you can turn each of them into two or more lower-energy photons, which still have enough electron-Volts each to produce charge carriers.