We study the effects of Cu composition on the CdTe/ZnTe:Cu back contact and the bulk CdTe. For the back contact, its potential barrier decreases with Cu concentration while its saturation current densit y increases. For the bulk CdTe, the hole densit y increases with Cu concentration. We identif y a Cu-related deep level at -0.55 eV whose concentration is significant when the Cu concentration is high. The device performance, which initially improves with Cu concentration then decreases, reflects the interpla y between the positive influences (reducing the back contact potential barrier while increasing the saturation current densit y of the back contact and hole densit y in CdTe bulk) and negative influences (increasing deep levels in CdTe) of Cu.