The hydrodynamic (HD) model of semiconductor devices is solved numeric
ally in three-dimensions (3-D) for the MOSFET device. The numerical in
stabilities of the HD model are analyzed to develop a stable discretiz
ation. The formulation is stabilized by using a new, higher-order disc
retization for the relaxation-time approximation (RTA) term of the ene
rgy-balance (EB) equation. The developed formulation is used to model
the MOSFET.