These theoretical calculations from the McMaster team show the conversion efficiencies possible for a double-junction solar cell.

With the lower junction based on silicon, which has a bandgap of 1.1 eV, the plot shows that the optimum bandgap of the material used in the upper junction would be about 1.65 eV.

At 1.43 eV, the bandgap of GaAs is a little low, but AlSb (1.6 eV) could allow a better match.

Image credit: McMaster.