Accounting for incomplete ionization in modeling silicon based semiconductor devices

The authors review the approaches used to describe incomplete ionization quantitatively. They describe a simple approach that can easily be incorporated into device modeling programs and that appears to yield good results. At low doping concentrations, the model is equivalent to the incomplete ionization formulae presented in device engineering textbooks. At high doping concentrations, the model predicts that all impurities are ionized, as is observed experimentally. The model is a phenomenological one, with two parameters that make connections with physical parameters at low and high doping concentrations. A least-squares method that yields these parameters is discussed. Finally, the authors give some device simulation results and describe how incomplete ionization must enter into the current continuity equations for electrons and holes