Fractal model of a porous semiconductor

In the present paper, it is shown that a porous silicon can be presented as a set of clusters of silicon atoms surrounded by SiOx, 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. (C) 2000 Elsevier Science B.V. All rights reserved.