Maximum-entropy principle for nonlinear hydrodynamic transport in semiconductors

We present, in a strong nonlinear context, a full-band hydrodynamic approach by using the first 13 moments of the distribution function in the framework of extended thermodynamics. Following this approach we show that: (1) the full-band effects of the band structure are described accurately up to high electric fields both in homogeneous and nonhomogeneous conditions; (2) the effectiveness of the dissipation processes can be properly investigated, in homogeneous conditions, only in a strong nonlinear context; and (3) the hyperbolicity region of the system is very large, also in the nonlinear conditions. In this way, by using a strong nonlinear closure, it is possible to describe accurately the transport phenomena in submicron devices, when very high electric fields and field gradients occur (E ≈ 220 kV/cm, E/(dE/dx) ≈ 100 Å).