Carrier scattering with sources and absorbers in Nanoscale Systems

We present a novel method based on sources and absorbers to examine scattering in finite, nanoscale systems. The Cauchy (mixed) boundary conditions (BCs) needed in an action integral formulation of scattering are reduced to simpler Dirichlet BCs by introducing totally absorbing elements, or “stealth elements,” whose material properties are optimized to give decaying solutions that vanish at the boundaries. The method retains all the physical aspects of the usual theory while providing new insights into scattering effects and predicts highly accurate numerical “near-field” solutions. The action integral is discretized and evaluated to derive the wavefunction everywhere. In 1D, we provide concrete examples and demonstrate the accuracy of this method. In 2D confined waveguides, we obtain scattered wavefunctions for geometrically complex scattering centers, and multiple scattering that go beyond the traditional perturbative and far field approximations. The modal analysis of reflected and transmitted waves allows us to obtain transmission coefficients for both propagating and evanescent modes. The Landauer conductance and thermopower for the ballistic transport as well as in the presence of scatterers are calculated.