Open-circuit voltage (V-OC) is an important parameter in determining the performance of polymer solar cells (PSCs). Given the desire for superior V-OC values in PSCs, we have designed and synthesized a series of 'medium bandgap' donor-acceptor (D-A) copolymers containing carbazole (Cz) and quinoxaline (Qx) (PCzDT-Qx, PCzDT-fQx, and PCzDT-ffQx). As a result of their deep-lying HOMO levels (-5.45 to -5.61 eV), high V-OC values are achieved in PSCs with the resulting copolymers, despite the expense of shortcircuit current density (J(SC)) and fill factor (FF) parameters. In this study, in addition to the best powerconversion efficiency (PCE) of up to 4.03% from PCzDT-fQx-based on PSCs, we have demonstrated a V-OC value exceeding 1.0 V with PSCs of PCzDT-ffQx, which is among the highest V-OC values achieved to date. Moreover, a comprehensive investigation on the mechanism of charge recombination and transport characteristics can determine a clear structure-property correlation in this class of molecules, which is helpful for designing better materials with maximum V-OC without scarifying other key photovoltaic parameters