# Would a semiconductor shined with monochromatic laser light matching its band-gap have a 100% efficiency if all of the light was absorbed & converted?

The idea of transporting power through laser light is an interesting area of research. Conversions of up to 54% have been reported for long distance transmission. I would assume reflectance/transmission (non absorption) plays a role in the loss of efficiency, but aside from hole recombination, is there any other loss-factors?

My question is what if, all of this band-gap-energy matching light was absorbed by the semiconductor, and no electron-holes recombine before the electrons are extracted. Then would the electrical output be close to 100%? Or is there a loss when traveling through the PN junction that results in heat emission? If so, then what is this called?

• How about Ohmic dissipation which is always present? Besides, what is your basis for assuming all the light will be absorbed and resulted in purely pair generation? – Pooya Nov 20 '14 at 13:11
• Part of the problem is that solid-state mechanics suggest it's essentially impossible for 100% band-gap absorption of photons to occur in the first place. But if you had some $P-N$ junction made out of doped unobtanium, then you could get one electron for every photon. – Carl Witthoft Nov 20 '14 at 13:38
• Not to mention SRH recombination at defects, surface recombination, changes in the depletion layer with increasing carrier concentrations, ... – Jon Custer Nov 20 '14 at 14:22
• Is Ohmic dissipitation really able to account for ~50% of the loss? My question is more relating to the energy conversion on a quantum scale.... ie.... if a single photon is converted and extracted, shouldn't the force that its produce be roughly equivalent to the band gap of the semiconductor that was excited? Or does the difference in potential in the PN Junction place a limit on the amount of voltage extracted per exciton? – Scott Nov 20 '14 at 22:26

## 2 Answers

I believe that what you are asking is what is the maximal power conversion efficiency of a semiconductor p-n junction. The answer comes from Shockley and Queisser who, in a 1961 paper show that, using a solar spectrum the best you can do is 33.7% for a 1.1 eV gap. Using a concentrated source (like off-resonant laser excitation) with energies above the band gap of the material, the Shockley-Queisser limit is ~86%. http://en.wikipedia.org/wiki/Shockley-Queisser_limit http://scitation.aip.org/content/aip/journal/jap/32/3/10.1063/1.1736034

Hope this helps.

• As far as non radiative relaxation mechanisms, Auger recombination, defect trapping, and trapping due to dopant atoms should all play a role. – Nick Nov 25 '14 at 0:18

The electrical output will not be close to 100% in practice and even in theory. There are fundamental losses that go beyond just collecting all electrons and holes that are extremely hard or impossible to avoid. You're looking at absolute maximum 85% at the end of the day if you pull off some amazing feats of physics/engineering.

I'll summarize:

1) Carnot cycle losses (thermodynamics)

2) Entropy losses through absorption/emission

3) Entropy losses through random angle in spontaneous recombination

4) Imperfect light trapping

Solutions:

1) Impossible. Even cool to near absolute zero, and you freeze out dopants and you get no p-n junction.

2) Unavoidable.

3) Need a photonic crystal that can suppress this. Very tough.

4) Addressable in theory through optical design.

So you're up against entropic/thermodynamic limitations at the theoretical limit of efficiency.