The improvements of the AlGaAs crystal quality grown on Si substrate and the AlGaAs/Si tandem solar cell have been studied with varying the growth conditions. The crystal quality of the AlGaAs layer was evaluated by photoluminescence, deep level transient spectroscopy, time-resolved photoluminescence and double crystal X-ray diffraction while varying the thermal cycle annealing temperature. The optimum thermal cycle annealing temperature and the buffer layer thickness for the growth of high efficiency AlGaAs/Si tandem solar cells have been presented, The active-area conversion efficiency of 21.2% and 21.4% (AM0 and 1 sun at 27 degrees C) has been demonstrated with two-terminal and four-terminal configuration, respectively, by the perfect photocurrent matching between the top cell and the bottom cell.