A simple model to describe AC electronic charge transport in hydrogenated microcrystalline silicon

By using a simple structural model of hydrogenated microcrystalline silicon (μc-Si:H) comprising crystalline columns in an amorphous matrix we have been able to derive analytical expressions for the conductivity and effective permittivity measured in thin films with sandwich geometry in the low and high frequencies limits. Both conductivity and permittivity can be dependent on crystallinity and length of samples. It is shown that the effective permittivity can be much higher than that of silicon. The orders of magnitude of the conductivities of crystalline and amorphous phases can be derived from the expressions of the conductivity. The frequency spectra of AC conductivity are also determined. The simple AC response is compared with numerical simulation performed using a sophisticated model of μc-Si:H recently proposed in the literature.