A series of new two-dimensional copolymers, PBDTT-TABT, PBDTT-TANT and PBDTT-TSNT, with conjugated benzodiathiazole (BT) or naphthobisthiadiazole (NT) side chains were successfully synthesized and characterized for high performance polymer solar cells (PSCs). The NT unit showed a stronger electron-withdrawing ability and a larger conjugation than the BT unit, which induced a stronger ICT process between the benzodithiophene (BDT)-thiophene (T) backbone and the conjugated side chain for NT containing copolymers. As a result, PBDTT-TANT and PBDTT-TSNT showed lower-lying bandgaps and more red-shifted absorption than PBDTT-TABT. The alkylthio modification effect of conjugated side chains was also investigated in this work. This effect showed a positive role in lowering the HOMO energy level, and a negative role in elevating carrier mobility and molecular stacking properties in our two-dimensional polymeric systems. Bulk heterojunction (BHJ) PSCs were fabricated using these copolymers as the donor materials to evaluate their photovoltaic properties. The PBDTT-TABT, PBDTT-TANT and PBDTT-TSNT devices exhibited PCEs of 4.60%, 5.65% and 4.01%, respectively. In spite of the V_oc values, the highest J_sc, FF and PCE were achieved for the PBDTT-TANT device, which was attributed to its red-shifted absorption, improved carrier mobility and well-defined phase separation. It is interesting that the J_scs, FFs and PCEs of all these devices were elevated significantly when made using the solvent vapor annealing (SVA) method. The THF–SVA process would provide a driving force to facilitate the formation of a much more well-defined surface morphology, resulting in the enhanced J_sc and FF values. The PBDTT-TANT device showed the highest PCE of 8.04%, which is the top efficiency for this type of two-dimensional copolymer with donor (D)–donor (D) polymer backbones and donor (D)–acceptor (A) conjugated side chains. Our design strategy would give an instructive guide to developing high performance two-dimensional polymer donors to be used in organic photovoltaic applications.