A metamorphic GaInP/GaAs/GaInAs/Ge multi-junction solar cell with InAs quantum dots is investigated, and the analytical expression of the energy conversion efficiency on the multi-junction tandem solar cell is derived using the detailed balance principle and the Kronig-Penney model.The influences of interdot distance, quantum-dot size and the intermediate band location on the energy conversion efficiency are studied.This shows that the maximum efficiency,as a function of quantum-dot size and distance,is about 60.15%under the maximum concentration for only one InAs/GaAs subcell,and is even up to 39.69%for the overall cell.In addition,other efficiency factors such as current mismatch,the formation of a quasicontinuum conduction band and concentrated light are examined. A metamorphic GaInP / GaAs / GaInAs / Ge multi-junction solar cell with InAs quantum dots is investigated, and the analytical expression of the energy conversion efficiency on the multi-junction tandem solar cell is derived using the detailed balance principle and the Kronig-Penney model. These influences of interdot distance, quantum-dot size and the intermediate band location on the energy conversion efficiency are.This shows that the maximum efficiency, as a function of quantum-dot size and distance, is about 60.15% under the maximum concentration for only one InAs / GaAs subcell, and is even up to 39.69% for the overall cell. In addition, other efficiency factors such as current mismatch, the formation of a quasicontinuum conduction band and concentrated light are examined.