Scaling effects upon fractal etch pattern formation on silicon photoelectrodes

Fractal etch structures on n-type silicon photoelectrodes were obtained under anodic bias in concentrated ammonium fluoride solution. The propagating branches of the structures generally reflect the surface lattice geometry of the substrates on a micrometer-scale while inner topographies are characterized by ensembles of slow-etching planes. In a medium and high photon flux range, scaling effects on Si(1 0 0) were observed for gradually increased light intensities: while the number of structures increases, the structure size reduces to the sub-micrometer range. Simultaneously, the thickness of integrally measured anodic oxides, analyzed by X-ray photoelectron spectroscopy, was found to decrease. These observations are addressed in model considerations where multi-axial stress at the SiO₂/Si interface is assumed to provide the feedback mechanism of the dynamic system and to result in locally increased substrate dissolution. A simplified flow-diagram for computer simulations, in agreement with numerical in-plane stress analysis, was finally developed which allows for prediction of the propagation process on arbitrary lattice geometries and for varied experimental conditions.