  We report optical reflectivity study on Nd$_{2-x}$Ce$_x$CuO$_4$ over a broad
doping range 0$\leq x\leq$0.20. The study reveals a systematic shift of
chemical potential with doping. A pronounced peak structure specific to the
electron-doped cuprate is observed in optical scattering rate based on the
extended Drude model analysis. The energy scale of the peak could be very
different from that of the peak in conductivity spectrum. We clarify that the
"hot spots" gap probed in photoemission experiments correlates directly with
the sharp suppression feature in scattering rate rather than conductivity
spectra. The gap is associated with the short-range antiferromagnetic
correlation, and disappears in a manner of fading away with increasing doping
and temperature. In the heavily overdoped region, a dominant
$\omega^2$-dependence of the scattering rate is identified up to very high
energy.
