Mapped discretization strategies for curvilinear adaptively redistributed grids in semiconductor device modeling Original Research Article

We develop numerical solution schemes for semiconductor device models based on mapped discretization strategies and curvilinear, nonuniform grids. Such grids typically arise in adaptive redistribution schemes, and they offer several advantages when gridding irregular domain shapes or resolving complex solution profiles. We consider the hydrodynamic class of equations as a representative model for carrier transport. A mathematical transformation of variables is used to map the device equations from the physical coordinate system to a reference system in which the numerical discretization is performed. We develop a Scharfetter–Gummel type of discretization, formulated in the mapped reference domain, for the current density and energy flux terms in the transport model. The solution of the mapped discrete system is carried out in a fully-coupled, implicit form, and nonsymmetric gradient-type iterative strategies are used for solving the algebraic systems. Numerical results demonstrating the performance of the scheme with and without mesh adaptation are presented for test problems.