Theory of MBE Growth of Nanowires on Reflecting Substrates

Selective area growth (SAG) of III-V nanowires (NWs) by molecular beam epitaxy (MBE) and related epitaxy techniques offer several advantages over growth on unpatterned substrates. Here, an analytic model for the total flux of group III atoms impinging NWs is presented, which accounts for specular re-emission from the mask surface and the shadowing effect in the absence of surface diffusion from the substrate. An expression is given for the shadowing length of NWs corresponding to the full shadowing of the mask. Axial and radial NW growths are considered in different stages, including the stage of purely axial growth, intermediate stage with radial growth, and asymptotic stage, where the NWs receive the maximum flux determined by the array pitch. The model provides good fits with the data obtained for different vapor-liquid-solid and catalyst-free III-V NWs.