Hierarchical Kinetics in 1/<i>f</i> Noise in Amorphous and Nanocrystalline Semiconductor Thin Films

We report studies of conductance fluctuations in hydrogenated amorphous germanium (a-Ge:H) that have an inverse frequency (1/f) spectral density with non-Gaussian statistics, as reflected in (1) histograms of the noise power per octave that are not described by Gaussian distributions, (2) strong correlations of the noise power in frequency-space and (3) power-law second spectra. In particular, histograms of the 1/f noise power per octave for a-Ge:H are well described by a log-normal distribution. The correlation coefficients across frequencies are non-zero and larger than expected for independently modulated fluctuators, and grow with averaging time with a logarithmic time-dependence. In contrast, the 1/f noise for polycrystalline Ge, and free-standing nanocrystalline thin films display Gaussian statistics. These results are discussed in terms of a model of filamentary conduction, where the conductance is modulated by hydrogen motion governed by hierarchical kinetics.