The following article is based on the Outstanding Young Investigator Award presentation given by Peidong Yang of the University of California, Berkeley, on April 14, 2004, at the Materials Research Society Spring Meeting in San Francisco.Yang was cited for “innovative synthesis of a broad range of nanowires and nanowireheterostructure materials, and the discovery of optically induced lasing in individual nanowire devices.” One-dimensional nanostructures are of both fundamental and technological interest.They not only exhibit interesting electronic and optical properties associated with their low dimensionality and the quantum confinement effect, but they also represent critical components in potential nanoscale devices. In this article, the vapor–liquid–solid crystal growth mechanism will be briefly introduced for the general synthesis of nanowires of different compositions, sizes, and orientation. Unique properties, including light-emission and thermoelectricity, will be discussed. In addition to the recent extensive studies on “single-component” nanowires, of increasing importance is incorporating different interfaces and controlling doping profiles within individual single-crystalline nanowires. Epitaxial growth plays a significant role in fabricating such nanowire heterostructures. Recent research on superlattice nanowires and other nanostructures with horizontal junctions will be presented. The implication of these heterojunction nanowires in light-emission and energy conversion will be discussed. Ways to assemble these one-dimensional nanostructures will also be presented.

A semidiscretization in time of a fourth order nonlinear parabolic system in several space dimensions arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential. Exploiting the stability of the discretization, convergence is shown in the multi-dimensional case. Under some assumptions on the regularity of the solution, the rate of convergence proves to be optimal.

In this paper we present a novel exponentially fitted finite elementmethod with triangular elements for the decoupled continuity equations in the drift-diffusion model of semiconductor devices.The continuous problem is first formulated as a variational problem using a weighted inner product. A Bubnov-Galerkinfinite element method with a set of piecewise exponential basis functions is then proposed. The method is shown to be stable and can be regarded asan extension to two dimensions of the well-known Scharfetter-Gummel method.Error estimates for the approximate solution and its associated flux are given. These h-order error bounds depend on some first-order seminorms of the exact solution, the exact fluxand the coefficient function of the convection terms.A method is also proposed for the evaluation of terminal currentsand it is shown that the computed terminal currents are convergent andconservative.