GaAsP/SiGe dual-junction solar cells have been epitaxially grown on silicon substrates which have the potential of achieving 1-sun tandem efficiencies of 40%. With the addition of light trapping this lattice-matched two-terminal structure can be current-matched and facilitates high performance from the III-V top cell while maintaining the cost advantages of silicon solar cells. The SiGe graded buffer allows for lattice matching of the top and bottom cell while providing a low dislocation interface between the silicon substrate and the device layers. This two-terminal dual-junction structure design is presented and demonstrates a 10.4% relative improvement in J(SC) and a 1.7% absolute improvement in efficiency over previous best devices. These initial structures have reached an efficiency of 18.9% under 1-sun. The devices suffer from high series resistance and exhibit reduced fill factors. A near term pathway to efficiencies approaching 25% is described. (c) 2015 Elsevier B.V. All rights reserved.