Fractal model of a porous semiconductor

Abstract

In the present paper, it is shown that a porous silicon can be presented as a set of clusters of silicon atoms surrounded by SiO x , whereas the single crystalline silicon substrate can be considered as an infinite cluster. The formulae for the estimation of variable porosity of the material (including the value of critical porosity — the percolation threshold, after which the characteristic phenomena are expected in porous silicon) and the forbidden bandgap value of clusters are suggested as functions of sizes of nanocrystallites. A new fractal model of the pore creation on the surface of a material is also proposed. The cases of semi-spherical, conical (V-groove dielectric isolation technology) and cylindrical (U-groove dielectric isolation technology) are considered. Formulae for the formed surface area S, porosity p of the material as a function of the depth and fractal dimension are obtained.