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A parametrization of the density of states (DOS) near the band edge of phosphorus-doped crystalline silicon is derived from photoluminescence and conductance measurements, using a recently developed theory of band gap narrowing. It is shown that the dopant band only `touches` the conduction band at the Mott (metal-insulator) transition and that it merges with the conduction band at considerably higher dopant densities. This resolves well-known contradictions between conclusions drawn from various measurement techniques. With the proposed DOS, incomplete ionization of phosphorus dopants is calculated and compared with measurements in the temperature range from 300 to 30 K. We conclude that (a) up to 25% of dopants are nonionized at room temperature near the Mott transition and (b) there exists no significant amount of incomplete ionization at dopant densities far above the Mott transition. In a forthcoming part II of this paper, equations of incomplete ionization will be derived that are suitable for implementation in device simulators. (c) 2006 American Institute of Physics.