A new discretization scheme for current contiuity and energy balance equations, which comprise the hydrodynamic equation set, was developed to simulate semiconductor devices and compared with other scheme.
It was found that the results of the 1-dimensional simulation for the $N^+$-N-$N^+$ ballistic diode using our discretization method are well matched to the recently published data in the literature and our discretization method shows much better convergence speed and numerical stability compared to other method.
We also performed 2-dimensional simulation for the short channel n-type MOSFET with effective channel length of 0.88μm. Our hydrodynamic simulation requires about 4-times computing time as compare with the conventional device simulation using drift-diffusion model. While our simulation results show negligible difference in current-voltage characteristics, severe carrier heating near the drain edge is observed, which is responsible for the so called hot carrier effect. However, we also found all discretization schemes reported to data including us are not accurate enough to calculate the rapidly changing temperature profile.
