Most efficient way to generate 3-4 volts from less than 0.5 to 1.5 volts
The Base-Emitter saturation voltage for silicon is about .7 volts.  I think this prevents typical charge-pump circuits (using only silicon) from functioning at such low voltage levels.

Germanium junctions, however, have a typical saturation voltage of .25 volts.  Check the specs for the NTE103A.

I think that by replacing the switching device in the first one or two stages of a typical charge-pump circuit, such as a Dickson multiplier, you could boost the voltage.  This would not be more efficient , but it is conceivable that with the right photo-voltaic device and the right LED, the LED would illuminate.