Dynamics of Droplet Consumption in Vapor-Liquid-Solid III-V Nanowire Growth

We study experimentally and theoretically the consumption of the apical gallium droplet that mediates the self-catalyzed vapor-liquid-solid growth of GaP nanowires. Consumption is achieved after growth by providing only phosphorous, and its progress is monitored ex situ in nanowire arrays fabricated by molecular beam epitaxy. We develop detailed calculations of the process, taking into account four channels of liquid gallium consumption. These include the formation of GaP using phosphorous delivered to the droplet by direct impingement or after re-emission from the substrate. We show that two other channels contribute significantly, namely, the diffusion of phosphorous along the sidewalls and gallium back diffusion from the droplet. All currents are calculated analytically as a function of droplet geometry. Complementary experiments are performed to extract the two model parameters governing the diffusion currents. We then numerically compute the dynamics of the system exposed to a constant external phosphorous flux. Our quantitative model allows one to predict how the droplet contact angle and radius change while operating blindly in a standard epitaxy chamber. Controlling these parameters is crucial for tailoring the crystal phase of III-V nanowires and fabricating quantum size structures.