LAUSR

We present a growth model that describes the nanowire length and radius versus time in the absence of evaporation or scattering of semiconductor atoms (group III atoms in the case of III-V NWs) from the substrate, nanowire sidewalls or catalyst nanoparticle. The model applies equally well to low-temperature metal-catalyzed or selective area growth of elemental or III-V nanowires on patterned substrates. Surface diffusion transport and radial growth on the nanowire sidewalls are carefully considered under the constraint of the total material balance, yielding some new effects. The nanowire growth process is shown to proceed in two steps. In the first step, the nanowire length increases linearly with time and is inversely proportional to the nanowire radius squared and the nanowire surface density, without radial growth. In the second step, the nanowire length obeys the Chini equation, resulting in a non-linear increase in length with time and radial growth. The nanowire radii converge to a stationary value in the large time limit, showing a kind of size-narrowing effect. The model fits the data on the growth kinetics of a single self-catalyzed GaAs nanowire on a Si substrate well.