Hot-carrier energy distribution model and its application to the MOSFET substrate current

The lack of information for carrier energy distributions in the continuum drift-diffusion (DD) or hydro-dynamic (HD) device simulation has been a major obstacle in simulating the physical phenomena related to hot carriers. In this study, a practical construction method of the hot-carrier energy distribution is proposed. Results from Monte-Carlo (MC) simulation in the uniform field distribution are utilized to construct the electron energy distributions (EED) for arbitrary device structures and field distributions in the continuum simulation. For the NIN structure, the electron-hole pair generation rate by impact ionization using the HD simulation employing the proposed method agrees well with that from the MC simulation. We have calculated the substrate currents of nMOSFETs without using any fitting parameters which agree very well with measurements.