A lucky drift model, including a soft threshold energy, for the relation between gate and substrate currents in MOSFETs

Abstract

Substrate and gate currents in MOSFETs are formulated by interpreting the lucky drift model with a soft threshold energy from the distribution function point of view. A modified Keldysh formula is introduced to the ionization relaxation time. Unknown parameters in the formulation are determined by fitting the calculation to the measured relations between gate and substrate currents in MOSFETs. Impact ionization coefficient reported by Lee et al. [16], is also subsidiarily used for determining the parameters. The model can eliminate the nonphysical fitting parameter on the Schottky barrier lowering effect, which was necessary in past models. Fitting parameters concerning the ionization relaxation time, thus obtained, are compared with various theoretical calculations. It is recognized that the relation between gate and substrate currents in MOSFETs reflects the energy dependent ionization rate which originates from electron-electron interaction in the complicated energy band structure of silicon.