On Properties of Boundaries and Electron Conductivity in Mesoscopic   Polycrystalline Silicon Films for Memory Devices
  We present the results of molecular dynamics modeling on the structural properties of grain boundaries (GB) in thin polycrystalline films. The transition from crystalline boundaries with low mismatch angle to amorphous boundaries is investigated. It is shown that the structures of the GBs satisfy a thermodynamical criterion. The potential energy of silicon atoms is closely related with a geometrical quantity -- tetragonality of their coordination with their nearest neighbors. A crossover of the length of localization is observed. To analyze the crossover of the length of localization of the single-electron states and properties of conductance of the thin polycrystalline film at low temperature, we use a two-dimensional Anderson localization model, with the random one-site electron charging energy for a single grain (dot), random non-diagonal matrix elements, and random number of connections between the neighboring grains. The results on the crossover behavior of localization length of the single-electron states and characteristic properties of conductance are presented in the region of parameters where the transition from an insulator to a conductor regimes takes place. 
G.P. Berman, G.D. Doolen, R. Mainieri, J. Rehacek, D.K. Campbell, V.A.   Luchnikov and K.E. Nagaev