Indium Phosphide Solar Cell
Indium phosphide solar cells can be extremely rad hard. A 2 micron thick cell with a drift field is 12.3% efficient after 7E11/cm2 1MeV proton flux. InP density is 4.81, or 9.6 grams per meter squared for a 2 micron film. Indium costs around $600/kg, so the indium is 0.787 (= 114.8/145.8) by weight, so the indium cost of this film is 0.6*9.6*0.8 = $4.60/m2. Assuming 75% illumination time and 1366W/m2, the film can produce 0.123 * 1366 * 0.75 = 126 W/m2, so the average cost per kilowatt is $36.50 .
Total reserves of indium are currently 6000 tonnes, but indium is about 0.9 ppm of the Earth, which weighs 5.98e24 kg, implying 5.4e15 tonnes in the whole planet, three times as common as silver (which is mined at 18,000 tonnes per year). If the cells are placed lunar distances (no eclipse), with 99% usage, they will produce 0.123 * 1366 * 0.99 W/ ( 0.8*9.6 g) or 21.6 MW/tonne. Producing 100TW of power on earth (assuming 50% cell-to-wallplug efficiency) would require 1E14/(0.5*2.16E7) = 9.3 million tonnes of indium, about 500 years of production at silver mining rates. At $73/kW delivered, that would be $7.3 trillion dollars worth of indium. Not likely.
So, we might be able to supply a TW or so of indium solar cells in orbit, but we will need to find cheaper direct bandgap meta-materials for planetary scale power, made with common materials: O, Si, Al, Fe, Ca, Na, Mg, K, Ti, ... . There will be powerful economic incentives to search for them.
Note that moon rock has a similar elemental abundance as the Earth's crust, and with launch loop technologies we can supply moon rock to lunar halo orbits for about 2kWh / kg launch energy, as opposed to about 60 kWh / kg from Earth. A 1GW SBSP array, feeding a lunar launch loop at 70% efficency, could launch 350 kg per second, about 10 million tons per year. If our hypothetical metamaterial produced only 10 MW/ton, we could launch a global power supply in about 2 years.
References
- RADIATION HARD AND GRAVIMETRIC EFFICIENT THIN FILM INP SOLAR CELLS - Yanning Sun, Jerry M. Woodall, John L. Freeouf, and Robert J. Walters