A dynamic Monte Carlo program, including an improved bombardment-induced Gibbsian segregation (BIGS) model was employed to study the matrix effect of BIGS and its influence on Cu depletion at the subsurface under 1 keV Ar ion bombardment of a Cu-Ni alloy. The calculated results show that not only at high fluence (the steady-state) but also at low fluence the Cu subsurface depletion depends on its bulk composition. This is because the atomic jump rate W-21 of Cu from the second layer to the first layer is correlated to Cu bulk composition at any fluence. We also found that the product of the nonsegregating species concentration in the first layer with the segregating species concentration in the second layer plays a more important role than other parameters in determining W-21 under low current conditions.