Microcrystalline silicon ( c-Si:H) thin films were prepared at 300°C on glass. Their structure and transport properties were studied in a wide range of film thickness ranging from 10 nm to 1 m. The crystal fraction increases monotonously from ϳ64% to ϳ100% as film thickness increases. Electron mobility first increases with increasing film thickness at thicknesses smaller than 50 nm but saturates at larger thickness. This mobility behavior is explained by percolation transport through crystalline grains. These results are different from those obtained with preferentially oriented polycrystalline silicon films. It is related to the difference in the microstructure evolution in which subsequent film growth is influenced by the growth surface structure. A single-electron transistor fabricated in 30-nm-thick c-Si:H exhibits Coulomb blockade effects at 4.2 K. This result indicates that amorphous phases which exist between crystalline grains behave as tunnel barrier for electrons.
The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external potential due to existing system conditions. The fluctuation of accuracy due to varying system conditions leads to a diffusion of the matrix elements. We show that, for single-well potentials, the diffusion can be described by a common mathematical formulation where system information enters through a single parameter. This further leads to a characterization of physical properties by an infinite range of single-parametric universality classes.
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