Limits of applicability of the depletion approximation and its recent augmentation

A general analysis of nonuniformly doped, one-dimensional space-charge layers in the Boltzmann approximation is presented from which a direct connection is established to the depletion approximation. An error equation is derived with no additional approximations other than for the neglect of minority-carrier effects for relating the difference between the electric field and potential in depletion approximation and the Boltzmann approximation. From this error equation, the validity of the depletion approximation and its extension to include space-charge effects in the undepleted bulk are evaluated.