  A charge density wave (CDW) ground state is observed in polycrystalline
Cu$_2$Se below 125 K, which corresponds to an energy gap of 40.9 meV and an
electron-phonon coupling constant of 0.6. Due to the polycrystalline structure,
the Peierls transition process has been expanded to a wide temperature range
from 90 to 160 K. The Hall carrier concentration shows a continuous decrease
from 2.1$\times$10$^{20}$ to 1.6$\times$10$^{20}$ cm$^{-3}$ in the temperature
range from 160 K to 80 K, while almost unchanged above 160 K and below 90 K.
After entering the CDW ground state, a wave-like fluctuation was observed in
the I-V curve near 50 K, which exhibits as a periodic negative differential
resistivity in an applied electric field due to the current. We also
investigated the doping effect of Zn, Ni, and Te on the CDW ground state. Both
Zn and Ni doped Cu$_2$Se show a CDW character with increased energy gap and
electron-phonon coupling constant, but no notable Peierls transition was
observed in Te doped Cu$_2$Se. Similar wave-like I-V curve was also seen in
Cu$_{1.98}$Zn$_{0.02}$Se near 40 K. The regular fluctuation in $\it{dc}$ I-V
curve was not magnetic field sensitive, but temperature and sample size
sensitive.
