Why does the reverse saturation current not vary with the reverse voltage?
This current is due solely to carrier generation within the depletion region due to phonon interactions creating an electron-hole pain every once in awhile. Once this hole and electron are generated in this region of high electric field, they are swept in opposite directions. Since there's so few carriers being generated due to thermal interactions generally, your reverse current is very little and isn't at all dependent upon the reverse voltage until you get to to the zener voltage which allows tunneling to occur or until you get to the avalanche voltage where the e-field is adding so much energy to the carriers that they can knock other electrons free thereby creating more electron-hole pairs. Up to either of these two points, you've got the trickle of current due solely to thermally generated carriers within the depletion region of the p-n junction. This is also why the reverse current is highly dependent upon the temperature of the junction. Without any temperature, you'd have no phonons to generate the e-h pairs.