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We investigate the impact of threading dislocation densities on the photovoltaic performance of single-junction (1J) n+/p GaAs and dual-junction (2J) n+/p InGaP/GaAs solar cells on Si substrate. Using our calibrated model, simulation predicts an efficiency of greater than 23% for a 1J GaAs cell on Si at AM1.5G spectrum at a threading dislocation density of 106 cm-2. The design of a metamorphic 2J InGaP/GaAs solar cell on Si was optimized by tailoring the 2J cell structure on Si to achieve current matching between the subcells, taking into account a threading dislocation density of 106 cm-2. Finally, we present a novel and an optimized 2J InGaP/GaAs solar cell design on Si at a threading dislocation density of 106 cm-2, which exhibited a theoretical conversion efficiency of greater than 29% at AM1.5G spectrum, indicating a path for viable III-V multijunction cell technology on Si.