  BiTeI exhibits large Rashba spin splitting due to its noncentrosymmetric
crystal structure. The study of chemical doping effect is important in order to
either tune the Fermi level or refine the crystal quality. Here, we report the
magneto-transport measurement in high quality BiTeI single crystals with
different copper dopings. We found that a small amount of copper doping
improves the crystal quality significantly, which is supported by the transport
data showing higher Hall mobility and larger amplitude in Shubnikov-de Haas
oscillation at low temperature. Two distinct frequencies in Shubnikov-de Haas
oscillation were observed giving extremal Fermi surface areas of $A_{S} = 9.1
\times 10^{12}$ cm$^{-2}$ and $A_{L} = 3.47\times 10^{14}$ cm$^{-2}$ with
corresponding cyclotron masses $m_S^*$ = 0.0353 $m_e$ and $m_L^*$ = 0.178
$m_e$, respectively. Those results are further compared with relativistic band
structure calculations using three reported Te and I refined or calculated
positions. Our analysis infers the crucial role of Bi-Te bond length in the
observed large bulk Rashba-type spin splitting effect in BiTeI.
