Layer growth and connectivity calculations based on a stick-ball model: Application to silicon nanocrystals

Monte Carlo computer simulations based on a stick-ball model were performed in order to simulate the growth of layers built from nanoparticles impinging on a substrate. From the simulations, a bulk layer porosity P-infinity=0.85 +/- 0.01 was extracted. Furthermore, characteristics about the percolative charge transport during layer growth were deduced. The establishment of the first contact between coplanar contacts via paths through nanoparticles was investigated for a variety of geometrical parameters. The onset of conductance in the simulations after the establishment of the first contact can be well described by a shifted power law. The simulations were compared with experimental results on layers built from Si nanocrystals and good qualitative and to some extent quantitative agreement was found. A tolerance parameter was introduced into the simulations referring to the maximum distance at which tunneling between adjacent nanoparticles may occur. By choosing different tolerance values and extrapolating the data to comply with the experimental results, a tolerance parameter of 0.73 nm was estimated.