How many photons does the sun generate to

[heynow999]

Homework Statement

how many photons does the sun generate to knock one electron across the bandgap in a PV panel? I am doing a college level night school course on Photovoltaics and I have to do a short presentation on photons and how they produce useable energy. I thought it would be interesting to work out this question. Assume a panel is %15 efficient and %40 of the photons are blocked by the atmosphere.

Homework Equations

The Attempt at a Solution

I assume it takes one photon to knock one electron across the bandgap. So working backwards, the panel is %15 efficient so 1/.15=6.66. Next, we lost %40 to the atmosphere so 6.66/.4=16.66 so 16.66 photons would have to strike the atmosphere to knock one electron across the bandgap. I am stumped by the next step but I know it will be a huge number. Let's assume no photons are lost in the trip from the sun. Does this even make sense?

Thanks

 

[JaWiB]

More electrons will be excited across the band gap than actually contribute to the current from the cell (due to recombination) so if you were considering power conversion efficiency then you might be overestimating the number of photons that need to come from the sun.

This is also complicated by the fact that it's not so much the energy of the incoming radiation that matters as it is the number of photons capable of producing charge carriers. For instance, if only two flavors of photons were incident in equal quantities--one with energy below the bandgap and one with energy above the bandgap--then half of the photons would carry more than half of the energy. I suspect you would actually need to know the bandgap in order to calculate the percentage of incident photons which excite an electron across the bandgap.

 

[Antiphon]

Start with the airmass 1.5G spectrum and truncate it at 1107nm, assuming you have silicon cells. Convert the watts/square meter into a photon count by using Planck's constant together with the wavelengt at each wavelength. This will convert the blackbody-like solar spectrum into more of a bell-shaped curve. This is the number of photons striking one sqaure meter of solar panel. Apply the external quantum efficiency of the panel (which you can work out from am1.5g integrated to give total solarr watts together with your 15% panel efficiency.)