The length distribution of nanowires with forward and backward surface diffusion

The length distributions of III — V nanowires growing by direct impingement and surface diffusion of adatoms are of fundamental and instrumentation interest. Here, we study kinetic rate equations for the length distribution of nanowires with forward and backward surface diffusion along their growing axes, where the average nanowire length either increases infinitely with time or saturates to a constant. We have obtained the exact solution to the discrete rate equations in the form of a modified Polya distribution, investigated its continuum approximation and analyzed the available experimental data on the length distributions of different III — V nanowires. The obtained results can be used to model various growth systems with size-linear forward and backward rate constants.