The classical diffusion theory of the silicon p-n junction solar cell is modified to include the junction generation-recombination current enhanced by field lowering of the thermal bandgap. The method of calculating the short-circuit current from the solar spectrum and the bandgap is refined so as to include optical and electrical losses in the cell. The modified theory explains a wide body of data on three generations of silicon solar cells and removes the previous dilemma of the fall-off in open-circuit voltage and efficiency with increasing doping. Finally, it teaches optimum choices for substrate thickness and doping, and sets goals for future high efficiency cells.