Ellipsometric characterization of nanocrystals in porous silicon

Porous silicon layers (PSLs) were prepared by electrochemical etching of p-type single-crystalline silicon (c-Si) wafers having different dopant concentrations to obtain systematically changing sizes of nanocrystals (walls). The microstructure of the porous material was characterized using spectroscopic ellipsometry with multi-layer effective medium approximation (EMA) models. The dielectric function of PSL is conventionally calculated using EMA mixtures of c-Si and voids. The porosity is described by the concentration of voids. Some PSL structures can be described only by adding fine-grained polycrystalline silicon (nc-Si) reference material to the EMA model. Modified model dielectric functions (MDF) of c-Si have been shown to fit composite materials containing nanocrystalline regions, either by fitting only the broadening parameter or also other parameters of the parametric oscillator in MDF. The broadening parameter correlates with the long-range order in the crystalline material, and, as a consequence, with the size of nanocrystals. EMA and MDF models were used to describe systematically changing nanostructure of PSLs. Volume fraction of nc-Si in EMA and broadening parameter in MDF provide information on the nanocrystal size. The longer-term goal of this work is to provide a method for the quantitative characterization of nanocrystal size using quick, sensitive and non-destructive optical techniques.