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A simplified hot-electron subpopulation hydrodynamic model for impact ionization in silicon
A simplified hydrodynamic (HD) model has been developed for the study of impact ionization (II) phenomena in silicon semiconductor devices. The model is based on the average energy of the hot electron subpopulation (HES) which is believed to be more relevant to the II than the average energy of the total electron population (TEP).^ In order for any HD model to be readily usable in industry, it must be physically accurate and numerically robust. To this end, two efforts have been made. One is to calibrate transport parameters of the HD model using the sophisticated Monte Carlo (MC) simulation method. The other is to develop a simplified HES HD model easily implementable in realistic device simulations.^ For the purpose of model parameter extraction, an isotropic two-band model has been incorporated in the MC simulator. This model gives almost the same physical accuracy as the full-band model, yet is computationally much more efficient. The transport parameters of the HD model have been calibrated based on a series of MC simulation results under the homogeneous (bulk) and inhomogeneous (device) conditions. We have also developed a so-called rare event enhancing scheme to enhance the statistical significance of rarely observable events to readily investigate the physical quantities of interest.^ For the development of the HD transport model, a further simplification in the existing HD models of the UMass and the SNU/Stanford groups has been made resulting in a single HD transport equation consisting of the average energy of the HES as the variable. By solving this simplified HD model, the II coefficient is calculated only as a function of the average energy of the HES. This simplified HES HD model is numerically much easier to handle than the commonly used DD or HD models.^ To test the newly developed HES HD model, calculations of substrate currents of realistic submicron MOSFET's are carried out. The HD model based on the average energy of the TEP is also implemented. The results of both the HES HD and TEP HD models are presented and compared with the MC results whenever available. ^
Engineering, Electronics and Electrical
"A simplified hot-electron subpopulation hydrodynamic model for impact ionization in silicon"
(January 1, 1997).
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