As a result of developing wide bandgap InGaP double hetero structure tunnel junction for sub-cell interconnection, InGaAs middle cell lattice-matched to Ge substrate, and InGaP-Ge heteroface structure bottom cell, we have demonstrated 38.9% efficiency at 489-suns AM1.5 with InGaP/InGaP/Ge 3-junction solar cells by in-house measurements. In addition, as a result of developing a non-imaging Fresnel lens as primary optics, a glass-rod kaleidoscope homogenizer as secondary optics and heat conductive concentrator solar cell modules, we have demonstrated 28.9% efficiency with 550-suns concentrator cell modules with an area of 5445 cm(2). In order to realize 40% and 50% efficiency, new approaches for novel materials and structures are being studied. We have obtained the following results: (1) improvements of lattice-mismatched InGaP/InGaAs/Ge 3-junction solar cell property as a result of dislocation density reduction by using thermal cycle annealing, (2) high quality (In)GaAsN material for 4- and 5-junction applications by chemical beam epitaxy, (3) 11.271%, efficiency InGaAsN single-junction cells, (4) 18.27% efficiency InGaAs/GaAs potentially modulated quantum well cells, and (5) 7.65% efficiency InAs quantum dot cells. (c) 2007 Elsevier Ltd. All rights reserved.