  The electron-doped cuprates Pr_{2-x}Ce_xCuO_4 and Nd_{2-x}Ce_xCuO_4 have been
studied by electronic Raman spectroscopy across the entire region of the
superconducting (SC) phase diagram. The SC pairing strength is found to be
consistent with a weak-coupling regime except in the under-doped region where
we observe an in-gap collective mode at 4.5 k_{B}T_c while the maximum
amplitude of the SC gap is ~8 k_{B}T_{c}. In the normal state, doped carriers
divide into coherent quasi-particles (QPs) and carriers that remain incoherent.
The coherent QPs mainly reside in the vicinity of (\pi/2, \pi/2) regions of the
Brillouin zone (BZ). We find that only coherent QPs contribute to the
superfluid density in the B_{2g} channel. The persistence of SC coherence peaks
in the B_{2g} channel for all dopings implies that superconductivity is mainly
governed by interactions between the hole-like coherent QPs in the vicinity of
(\pi/2, \pi/2) regions of the BZ. We establish that superconductivity in the
electron-doped cuprates occurs primarily due to pairing and condensation of
hole-like carriers. We have also studied the excitations across the SC gap by
Raman spectroscopy as a function of temperature (T) and magnetic field (H) for
several different cerium dopings (x). Effective upper critical field lines
H*_{c2}(T, x) at which the superfluid stiffness vanishes and
H^{2\Delta}_{c2}(T, x) at which the SC gap amplitude is suppressed by field
have been determined; H^{2\Delta}_{c2}(T, x) is larger than H*_{c2}(T, x) for
all doping concentrations. The difference between the two quantities suggests
the presence of phase fluctuations that increase for x< 0.15. It is found that
the magnetic field suppresses the magnitude of the SC gap linearly at
surprisingly small fields.
