Fractal modeling of porous semiconductors

Abstract

In the present paper it is shown that one can present the porous semiconductor as a set of clusters of silicon atoms surrounded by SiOx, as well as the single crystalline silicon substrate can be considered as an infinite cluster also. 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 the sizes of nanocrystallites. A new fractal model of pore creation on the surface of a material is proposed also. 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, material porosity p as a function of the depth and fractal dimension are obtained.