World-record solar-to-electricity energy conversion efficiency has been previously achieved by photovoltaic devices that maximize the use of the solar spectrum, such as multi-junction tandem solar cells. These cells are made of III-V materials whose high cost is a strong limitation on their widespread commercial application. One solution to suppress the cost of these types of devices is to grow III-V solar cells on low-cost carrier materials such as silicon. We will discuss the material, structure and analysis of GaAsP/SiGe-on-silicon multi-junction tandem solar cells. A low threading dislocation density is realized by effective lattice-matching of the top and bottom cells which demonstrate a device that achieves high open-circuit voltage in the top solar cell. The GaAsP/SiGe solar cells have reached a measured efficiency of 20.6% under one sun concentration. Analysis of these results based on the product of the best parameters shows efficiency potential of 26% under one sun, 30.8% at 20× and 35.1% at 400×.