Stochastic model for spontaneous formation of molecular wires

A stochastic model which may be used to analyze the formation of bonds connecting the interface formed by a substrate surface and a scanning tunneling microscope (STM) tip is presented. The model is tested by means of kinetic Monte Carlo simulations, and analytical predictions are given for some limiting cases. In the case of long time observations, the model may be applied to obtain information on the rate constants associated with the process and on the number of molecules trapped at the gap. In the case of short time observations, the results of the model for the probability of observing a given number of molecules bridging the gap are compared with the experimental results from the literature, showing a good predicting power.