We conduct linear and nonlinear stability analyses on a paradigmatic model of nanostructure self-assembly. We focus on the spatio-temporal dynamics of the concentration field of deposition on a substrate. The physical parameter of interest is the mean concentration C0 of the monolayer. Linear stability analysis of the system shows that a homogeneous monolayer is unstable when C0 lies within a band symmetric about C0 = frac(1, 2). On increasing C0 from zero, the homogeneous solution destabilizes to a hexagonal array, which then transitions to stripes. Transitions to and from the hexagonal state are subcritical. Square patterns are unstable for all values of C0 transitioning either to hexagons or stripes. Further, we present stability maps for striped arrays by considering possible instabilities. The analytical results are confirmed by numerical integrations of the Suo-Lu model. Our formalism provides a theoretical framework to understand guided self-assembly of nanostructures.
- Stability analysis