A two-dimensional model for predicting substrate current in submicrometer MOSFETs

The authors present a more rigorous hydrodynamic postprocessing approach than that implemented by J.W. Slotboom et al. (1991). The proposed model is 2-D and is based on the 1-D form of energy equation described by R.K. Cook et al. (1982), implemented into the 2-D drift-diffusion simulator PISCES as a postprocessor to calculate substrate current. This new approach involves the determination of the average energy along many current contours using the 1-D energy conservation equation and the local electric fields calculated by PISCES along each current path. The impact ionization rates are calculated using an energy parameterized form of the Chynoweth law. These coefficients along with the current densities calculated by PISCES are then used to determine the 2-D distribution of generation rates, and the generation rates are integrated over the entire 2-D device structure to calculate the substrate current. The authors have demonstrated very good agreement with substrate current characteristics measured on a broad range of LDD (lightly doped drain) NMOSFET devices with varying channel lengths, gate biases, and drain biases.