AN EVALUATION OF ENERGY-TRANSPORT MODELS FOR SILICON DEVICE SIMULATION

The reduction in feature size of silicon devices has resulted in operating conditions characterized by extremely large internal electric fields and field gradients. The rapid spatial variation of the electric field precludes a point-wise (or local) dependence of average carrier energy on the electric field. Because traditional drift-diffusion transport models and field-dependent hot-carrier models force a one-to-one correspondence between the local electric field and carrier energy, they fail to provide sufficient accuracy for contemporary device design. Impact ionization in submicron MOSFETs, for example, is poorly described by field-dependent ionization coefficients since impact ionization is an energy-dependent process. Energy transport models, which can account for the nonlocal energy-field relationship in submicron devices, have become especially attractive for design oriented silicon device simulation. The severe constraints that hot (high energy) carriers impose on current submicron MOSFET technology have motivated the development and application of energy transport models, such as the hydrodynamic model. In this work, the hydrodynamic model and a simple, efficient energy transport model are compared with a Monte Carlo model in order to evaluate their performance under submicron device conditions, and to better assess how they may be improved. The results indicate that energy transport models can predict peak average energy quite well, even under severely nonuniform electric field conditions. The hydrodynamic and simple energy transported models examined here, however, cannot accurately model carrier cooling associated with an abrupt decrease in the electric field. Discrepancies in cooling are shown to strongly influence drift velocity, and the implications of this for submicron device analysis are discussed.