Simulation of an $$n^{+}\hbox {-}n\hbox {-}n^{+}$$ n + - n - n + Diode by Using Globally-Hyperbolically-Closed High-Order Moment Models

By the moment closure of the Boltzmann transport equation, the extended hydrodynamic models for electron transport have been derived in Cai et al. (J Math Phys 53:103503, 2012). With the numerical scheme developed in Li et al. (2012) recently, it has been demonstrated that the derived extended hydrodynamic models can capture the major features of the solution of kinetic equations. As the application of the models and the numerical scheme proposed therein, we in this paper carry out the numerical simulation to investigate the carrier transport in $$n^{+}$$ n + - $$n$$ n - $$n^{+}$$ n + structures by solving the moment system derived from the Boltzmann---Poisson equations. Without any additional empirical parameters than that used in directly solving the kinetic equations, we obtain numerical results by the extended hydrodynamic models with very satisfied agreement with the solution of the kinetic equations, even in case that the length of the channel is as short as 50 nm.