Morphological instability of misfit-strained core-shell nanowires

Abstract

We investigate the morphological instability of a misfit-strained cylindrical core-shell nanowire by performing a linear stability analysis. For this aim, the stress and strain distributions of a core-shell nanowire with a sinusoidally perturbed surface are calculated to first order, properly accounting for the core-shell interface. In addition, the effect of surface stress on the stress and/or strain distributions is considered. Due to the large surface-to-volume ratio of nanosized objects, this is indispensable. The outcome of the stability analysis is threefold: First, our calculation shows that surface stress strongly influences the nature of the fastest growing mode of perturbation. It turns out that the axially symmetric mode does not necessarily grow fastest. Second, we find that the system is most unstable in the initial phase of shell growth, i.e., for thin shell thicknesses. Interestingly, considering thin shells and large misfits $(\ensuremath{\gtrsim}3%)$, we find that there exists a core radius for which stability becomes maximal. Under the conditions considered this radius is in the range of about 5--10 nm. Third, there exists a parameter range for which the experimental observation that Ge-rich islands grown on thick silicon nanowires tend to be aligned in two rows on the opposite sides of the nanowire agrees with the outcome of our calculation.