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A detailed attempt to systematize the design of silicon solar cells is given. Design principles follow from three theorems. Two of these emphasize recombination in the nonilluminated solar cell. The third is a generalized reciprocity theory for semiconductor devices, which relates this recombination to the short-circuit current of an illuminated solar cell. The theorems exploit linearity. Thus the results hold only under low injection conditions in base and emitter regions. They hold, however, for arbitrary doping profiles and include the effects of drift fields, high/low junctions and heavy doping concentrations of donor or acceptor atoms. For the most part, the authors concentrate on one-dimensional models, but extensions are made to accommodate gridded structures on the back and front surface. Several optimal designs are derived from the theorems, one of which involves a three-dimensional morphology in the emitter region. The theorems are derived from a nonlinear differential equation of the Riccati form, the dependent variable of which is a normalized recombination particle current.