  We present studies on crystal structure and ionic diffusion behaviors of
superionic Cu$_{2-\delta}$Se ($\delta$=0, 0.04, and 0.2) by utilizing neutron
powder diffraction and quasi-elastic neutron scattering. In the superionic
phase, the structural model with Cu ions occupying the Wyckoff sites of 8$c$
and 32$f$ provides the best description of the structure. As the content of Cu
increasing in Cu$_{2-\delta}$Se, the Cu occupancy increases on the 32$f$ site,
but decreases on the 8$c$ site . Fitting to the quasi-elastic neutron
scattering spectra reveals two diffusion modes, the localized diffusion between
the 8$c$ and 32$f$ sites and the long-range diffusion between the adjacent 8$c$
sites using the 32$f$ site as a bypass, respectively. Between 430 and 650 K, we
measured that the compound with more Cu content exhibits a larger long-range
diffusion coefficient. Temperature in this range does not affect the long-range
diffusion process obviously. Our results suggest the two diffusion modes
cooperative and thus provide a microscopic understanding of the ionic diffusion
of the Cu ions in superionic Cu$_{2-\delta}$Se.
