The wider-gap members of a semiconductor series such as diamond→Si→Ge or AlN→GaN→InN often cannot be doped n-type at equilibrium. We study theoretically if this is the case in the chalcopyrite family CuGaSe2→CuInSe2, finding that: (i) Bulk CuInSe2 (CIS, Eg=1.04 eV) can be doped at equilibrium n-type either by Cd or Cl, but bulk CuGaSe2 (CGS, Eg=1.68 eV) cannot; (ii) result (i) is primarily because the Cu-vacancy pins the Fermi level in CGS farther below the conduction band minimum than it does in CIS, as explained by the “doping limit rule; (iii) Cd doping is better than Cl doping, in that CdCu yields in CIS a higher net donor concentration than ClSe; and (iv) in general, the system shows massive compensation of acceptors (CdⅢ,VCu) and donors (ClSe,CdCu, InCud).