Weighted estimates for tangential boundary behaviour

Abstract

Thin nanocrystalline silicon layers with nanovoids exhibit enhanced optical absorption in the visible spectrum but their resistivity is usually too high for many device applications. To understand the electrical transport properties of nanocrystalline silicon with nanovoids, a simple model of carrier density based on the existence of void-silicon interface states is developed in this paper. Average carrier density as a function of doping concentration of the starting material, void radius, porosity and void-silicon interface state density of the film is computed using this model. The effect of band gap enhancement due to quantum confinement of the carriers in the nanocrystallites as well as the effect of dopant spacing has been incorporated in this model. It has been shown that reasonably high average carrier density (close to the bulk) is achievable by carefully controlling the bulk doping concentration, void radius, void-Si interface state density and porosity of the nanovoid film to some specific values. This modelling appears to be applicable for predicting the electrical behaviour of any thin semiconductor film having a distribution of nanovoids.

On Estimates for Maximal Operators Associated with Tangential Regions

“…Di Biase [8], Di Biase-Stokolos-Svensson-Weiss [9]. Sjögren [39,40,41], Rönning [32,33,34], Katkovskaya-Krotov [22,26], Krotov [24,25], Brundin [6], Mizuta-Shimomura [29], Aikawa [3] studied fractional Poisson integrals with respect to the fractional power of the Poisson kernel and obtained some tangential convergence properties for such integrals. More precisely they considered the integrals Theorem C (see [39,32,33]).…”