Einstein relation and transport equations in heavily doped silicon

This paper proposes two forms of generalized Einstein relation that embed all heavy doping effects in such a way that corresponding transport equations retain their form as in lightly doped silicon. In the first corresponding form of the transport equations all heavy doping effects are added to their diffusion components through so-called effective diffusion coefficients. The second form of the transport equations is based on the effective carrier concentrations and is suitable for application in device simulation programs. Concrete dependencies of relevant physical parameters are given for silicon, heavily doped by phosphorous, while the whole theory is generally applicable for all semiconductors whose bandgap behaviour in terms of its dependence on doping is known.