The effects of electron–electron scattering on the electron energy distribution, as well as substrate and gate currents in short channel MOSFETs (metal-oxide-semiconductor field-effect transistors) are explored using the convective scheme, or CS, a method of characteristics. Effects of electron–electron scattering are explored for a MOSFET with uniform doping in the channel as well as for an asymmetric device structure, a focused-ion-beam (FIBMOS) transistor, for both 70 nm and 250 nm channel length devices. Effects of electron–electron scattering on a standard 35 nm channel length MOSFET are also included. The high substrate doping that is required for such short channel length devices leads to large electric fields. The purpose of the FIB implant is to improve hot-carrier reliability by reducing the electric field in the channel. Electron–electron scattering increases the amount of electrons in the tail, despite the fact that the applied potential is significantly below the threshold for injection of electrons into the gate oxide. The ratio of gate-to-substrate current, Ig/Isub, is investigated as an indicator of the level of degradation. At such short channel lengths, there are degrading and non-degrading components of gate and substrate current. The non-degrading components of gate and substrate current correlate strongly, so that the ratio of Ig/Isub is an efficient indicator of device degradation. The energy thresholds for impact ionization and for emission of electrons into the gate oxide are crucial in determining the ratio of these currents. The substrate and gate currents obtained indicate that hot-carrier effects continue to be an issue for device performance, even for nanometer-scale devices. The density of electrons is higher at very short channel lengths due to the need to have shallow junctions and leads to a greater amount of Coulomb collisions. Increased Coulomb collisions may lead to strongly reduced lifetimes in nanometer-scale devices.
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