Cell-centered finite volume schemes for semiconductor device simulation

Although the traditional finite volume scheme based on boxes obtained from the dual Voronoi grid has been employed successfully for classical semiconductor device simulation for decades, certain drawbacks such as the required Delaunay property of the underlying mesh limit its applicability for two-and particularly three-dimensional device simulations on unstructured meshes. We propose a discretization based on mesh cells rather than dual boxes around vertices, which circumvents the Delaunay requirement, yet preserves all the important features of the traditional method such as exact current conservation. The applicability of our method is demonstrated for classical and semiclassical models to tackle current engineering problems: We consider three-dimensional drift-diffusion simulations of geometric variations of the fin in a FinFET and present results from spatially two-dimensional simulations of a high-voltage nLDMOS device based on spherical harmonics expansions for direct solutions of the Boltzmann transport equation.