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.