Quantum Size Effect in Conductivity of Multilayer Metal Films

Conductivity of quantized multilayer metal films is analyzed with an emphasis on scattering by rough interlayer interfaces. Three different types of quantum size effect (QSE) in conductivity are predicted. Two of these QSE are similar to those in films with scattering by rough walls. The third type of QSE is unique and is observed only for certain positions of the interface. The corresponding peaks in conductivity are very narrow and high with a finite cutoff which is due only to some other scattering mechanism or the smearing of the interface. There are two classes of these geometric resonances. Some of the resonance positions of the interface are universal and do not depend on the strength of the interface potential while the others are sensitive to this potential. This geometric QSE gradually disappears with an increase in the width of the interlayer potential barrier.Comment: 12 pages, 10 figures, RevTeX4, to be published in Phys. Rev B (April 2003

Surface Roughness and Size Effects in Quantized Films

The effect of random surface roughness on quantum size effects in thin films is discussed. The conductivity of quantized metal films is analyzed for different types of experimentally identified correlation functions of surface inhomogeneities including the Gaussian, exponential, power-law correlators, and correlators with a power-law decay of the power density spectral function. The dependence of the conductivity σ on the film thickness L, correlation radius of inhomogeneities R, and the fermion density is investigated. The goal is to help in extracting surface parameters from transport measurements and to determine the importance of the choice of the proper surface correlator for transport theory. A peculiar size effect is predicted for quantized films with large correlation radius of random surface corrugation. The effect exists for inhomogeneities with Gaussian and exponential power spectrum; if the decay of power spectrum is slow, the films exhibit usual quantum size effect. The conductivity σ exhibits well-pronounced oscillations as a function of channel width L or density of fermions, and large steps as a function of the correlation radius R. These oscillations and steps are explained and their positions identified. This phenomenon, which is reminiscent of magnetic breakthrough, can allow direct observation of the quantum size effect in conductivity of nanoscale metal films. The only region with a nearly universal behavior of transport is the region in which particle wavelength is close to the correlation radius of surface inhomogeneities

Self-organized pore formation and open-loop-control in semiconductor etching

Electrochemical etching of semiconductors, apart from many technical applications, provides an interesting experimental setup for self-organized structure formation capable e.g. of regular, diameter-modulated, and branching pores. The underlying dynamical processes governing current transfer and structure formation are described by the Current-Burst-Model: all dissolution processes are assumed to occur inhomogeneously in time and space as a Current Burst (CB); the properties and interactions between CB's are described by a number of material- and chemistry- dependent ingredients, like passivation and aging of surfaces in different crystallographic orientations, giving a qualitative understanding of resulting pore morphologies. These morphologies cannot be influenced only by the current, by chemical, material and other etching conditions, but also by an open-loop control, triggering the time scale given by the oxide dissolution time. With this method, under conditions where only branching pores occur, the additional signal hinders side pore formation resulting in regular pores with modulated diameter

Quantum ratchet transport with minimal dispersion rate

We analyze the performance of quantum ratchets by considering the dynamics of an initially localized wave packet loaded into a flashing periodic potential. The directed center-of-mass motion can be initiated by the uniform modulation of the potential height, provided that the modulation protocol breaks all relevant time- and spatial reflection symmetries. A poor performance of quantum ratchet transport is characterized by a slow net motion and a fast diffusive spreading of the wave packet, while the desirable optimal performance is the contrary. By invoking a quantum analog of the classical P\'eclet number, namely the quotient of the group velocity and the dispersion of the propagating wave packet, we calibrate the transport properties of flashing quantum ratchets and discuss the mechanisms that yield low-dispersive directed transport.Comment: 6 pages; 3 figures; 1 tabl