Computing in SCienCe & engineering This arTicle has been peer-reviewed. 17 H i g h-P e r f o r m a n c e C o m p u t i n g E d u c a t i o n

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In this paper, we present a numerical method for evaluating the full Wigner function throughout a device by solving a steady-state quantum kinetic equation in two dimensions, in the linearresponse regime. This method has two advantages over conventional treatments of mesoscopic devices. First, dissipative processes can be included within the device, thus allowing a smooth transition from the quantum to the semiclassical regime. Second, the contacts are treated in the same manner as in semiclassical device analysis. A short phase-breaking time can be used in the contact regions so that oscillations in the electron density due to interference e6'ects die out quickly; this is particularly useful when obtaining self-consistent solutions with the Poisson equation. Any quantity of interest, such as electron density or current density per unit energy, can be computed throughout the entire device. We will first show that under low-bias, low-temperature conditions, the diagonal elements of the Wigner function can be used to define a local electrochemical potential (p) that lends insight into the internal transport physics. We show that separate electrochemical potentials pL and p& for leftand right-moving electrons show unphysical behavior when defined in a local sense. But sensible results are obtained when these potentials are defined in an average sense over regions the size of a de Broglie wavelength. We then examine the diKculties associated with measuring p, with numerical examples. Next, we use the local electrochemical potential profile to clarify the nature of the spreading resistance associated with the narrowing of a current lead. Finally, we show that the electrostatic potential (P) can be viewed as a convolution of p with a screening function and present example computations of P.

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The consideration of space charge in the analysis of resonant tunneling devices leads to a substantial modification of the current-voltage relationship. The region of negative differential resistance (NDR) is shifted to a higher voltage, and broadened along the voltage axis. Moreover, the peak value of current prior to NDR is reduced, leading to a reduction in the predicted peak-to-valley ratio. An approach is presented to include space-charge effects, and a recently fabricated GaAs-AlxGa1−xAs structure is analyzed, to underscore the importance of a self-consistent electrostatic potential in theoretical calculations.

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Device analysis has traditionally been based on the semiclassical Boltzmann transport equation. Despite its impressive successes, this approach suffers from an important limitation; it cannot describe transport phenomena in which the wave nature of electrons plays a crucial role. A variety of such quantum effects have been discovered over the years, such as tunnelling, resonant tunnelling, weak and strong localisation, and the quantum Hall effect. Since 1985, experiments on ultrasmall structures (dimensions 5100 rim) have revealed a number of new effects such as the Aharanov-Bohm effect, conductance fluctuations, non-local effects and the quantised resistance of point contacts. For ultrasmall structures at low temperature, these phenomena have clearly shown that electron transport is influenced by wave interference effects not unlike those well known in microwave networks. New device concepts are being proposed and demonstrated that are based on these wave properties.In this article we review quantum interference effects that have been observed in ultrasmall structures, and their implications for future electronic devices. We also review the current theoretical understanding of such phenomena and discuss some of the unresolved questions that have to be answered in order to develop accurate models for quantum device simulation.