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 . 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.
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