Variation of Electrostatic Coupling and Investigation of Current Percolation Paths in Nanocrystalline Silicon Cross Transistors

Nanocrystalline silicon thin films are promising materials for the development of advanced Large Scale Integration compatible quantum-dot and single-electron charging devices. The films consist of nanometer-scale grains of crystalline silicon, separated by amorphous silicon or silicon dioxide grain boundaries up to a few nanometer thick. These films have been used to fabricate single-electron transistor and memory devices, where the grains form single-electron charging islands isolated by tunnel barriers formed by the grain boundaries. The grain boundary tunnel barrier isolating the grains is also of great importance, as this determines the extent of the electrostatic and tunnel coupling between different grains. These effects can lead to the nanocrystalline silicon thin film behaving as a system of coupled quantum dots.& more..

Gauss-Legendre Sampling on the Rotation Group

We propose a Gauss-Legendre quadrature based sampling on the rotation group for the representation of a band-limited signal such that the Fourier transform (FT) of a signal can be exactly computed from its samples. Our figure of merit is the sampling efficiency, which is defined as a ratio of the degrees of freedom required to represent a band-limited signal in harmonic domain to the number of samples required to accurately compute the FT. The proposed sampling scheme is asymptotically as efficient as the most efficient scheme developed very recently. For the computation of FT and inverse FT, we also develop fast algorithms of complexity similar to the complexity attained by the fast algorithms for the existing sampling schemes. The developed algorithms are stable, accurate and do not have any pre-computation requirements. We also analyse the computation time and numerical accuracy of the proposed algorithms and show, through numerical experiments, that the proposed Fourier transforms are accurate with errors on the order of numerical precision