Kinetics of nucleus growth from a nanophase

We present a theoretical analysis of the growth kinetics of a nucleus from a nano-sized mother phase with a restricted amount of material in the presence of the stopping effect due to the depletion of supersaturation. Such a regime is typical for GaAs nanowires grown by the vapor-liquid-solid mechanism from a Ga droplet and is observed by in situ growth monitoring inside a transmission electron microscope. An analytical solution is obtained for the time-dependent size of the nucleus and atomic concentration in a nano-phase. A principally new time-scale hierarchy is found, whereby the entire growth process id divided into 3 stages – (1) fast nucleus growth to the stopping size, (2) slow nucleus growth at the rate of refill of a mother phase, and (3) further refill of a mother phase to resume the initial supersaturation. A general criterion is formulated for observing the stopping effect depending on the size of a nano-phase.