Lateral Grain Sizes of μc-Si Photovoltaic Layers Derived from Self-Similarity of Growth-Induced Surface Roughness

A statistical method for estimating the lateral grain size and nucleus density of microcrystalline Si (μc-Si) film has been proposed from the fractal concepts, and the estimating results on μc-Si films with the (220) preferred orientation, which are usually preferred for the photovoltaic layers in thin-film solar cells, are compared to those on μc-Si films with the (111) preferred orientation, which are not preferable. The μc-Si films were prepared mainly by VHF(100 MHz)-PECVD with thicknesses, d, of 0.5-4 μm. Surface heights were measured by an atomic force microscope (AFM) with differing the scan scales of 0.1×0.1-10×10 μm². From the height-height correlation functions, the lateral correlation lengths, ξ, were estimated, and we found that the lateral grains sizes, σ_L, defined as 2ξ correspond to the lateral grain sizes of μc-Si observed in AFM surface images. Besides, alternative power-law relations are found between ξ and d with the scaling exponents 1/z´ reflecting the cross-sectional lineshape of μc-Si. The relation also reveals the nucleus density, N_d, estimated at d=0.1 μm and highly dense nucleation is found in the (220)-oriented μc-Si. These experimental results are discussed in conjunction with the preparation conditions: a high frequency, a high pressure and a large power, which are suitable in preparing the photovoltaic absorbers. The growth mechanism including the non-local effects is also discussed