Drift-diffusion: A model for teaching spatial dispersion concepts and the importance of screening in nanoscale structures

Spatial dispersion has emerged as an extremely important concept in modeling metamaterials, including macro-, micro-, and nano-structured composites. However, the incorporation of spatial dispersion requires a considerable complication of the usual Ohm's law relationship with which students are familiar. In this note, the drift-diffusion equation is shown to be equivalent to the usual form of spatial dispersion in simple isotropic plasmas and metamaterials. It is suggested that the drift diffusion equation is physically clear and intuitive, and, therefore, can be effectively used to help teach concepts of spatial dispersion to beginning graduate students. Furthermore, the drift-diffusion equation leads to a simple treatment of charge screening, which is important for fundamental understanding, and for the electromagnetics of nanostructures