Numerical Simulation of Hot-Electron Phenomena

Abstract

An accurate two-dimensional numerical model for MOS transistors incorporating avalanche processes is presented. The Laplace and Poisson equations for the electrostatic potential in the gate oxide and bulk and the current-continuity equations for the electron and hole densities are solved using finite-difference techniques. The current-continuity equations incorporate terms modeling avalanche generation, bulk and surface Shockley–Read–Hall thermal generation-recombination, and Auger recombination processes. The simulation is performed to a depth in the substrate sufficient to include the depletion region, and the remaining substrate is modeled as a parasitic resistance. The increase in the substrate potential caused by the substrate current flowing through the substrate resistance is also included. The hot-electron distribution function is modeled using Baraff’s maximum anisotropy distribution function. The model is used to study hot-electron phenomena including negative-resistance avalanche breakdown in short-channel MOSFET’s and electron injection into the gate oxide. The model accurately predicts the positive-resistance branch of the drain current–voltage characteristic and could, in principle, predict the negative-resistance branch and the sustain voltage. The gate injection current is computed by summing the flux of electrons scattered into the gate oxide by each mesh volume element. The number of electrons in each element whose component of momentum normal to the oxide is sufficient to surmount the oxide potential barrier is approximated using Baraff’s distribution function, and scattering along the electron trajectories is modeled using an appropriate mean free path. The flux scattered into the oxide can be expressed as an iterated six-fold integral which is evaluated using the potential and electron current density distributions produced by the model. Nakagome et al. [1] recently observed two new types of gate injection phenomena: avalanche injection and secondary ionization induced injection. The former is caused by carriers heated in the drain avalanche plasma, and the latter is caused by electrons generated by secondary impact ionization in the depletion region. The model yields gate current curves qualitatively similar to the experimental results.