Interplay of instabilities in mounded surface growth

Area of Science:

• Surface science and statistical physics
• Nonlinear dynamics and pattern formation

Background:

• Conserved growth models are crucial for understanding thin-film growth and surface evolution.
• Competing linear (Ehrlich-Schwoebel) and nonlinear instabilities drive complex surface morphologies.
• Nonequilibrium phase transitions in driven systems lead to distinct macroscopic states.

Purpose of the Study:

• To numerically investigate a 1D conserved growth equation with competing linear and nonlinear instabilities.
• To identify and characterize a nonequilibrium phase transition between different mounded surface states.
• To analyze the coarsening dynamics and steady-state properties of these mounded phases.

Main Methods:

• Numerical simulations of a one-dimensional conserved growth equation.
• Systematic variation of a control parameter to induce phase transitions.
• Detailed analysis of mound coarsening behavior and steady-state configurations.

Main Results:

• A nonequilibrium phase transition was observed between two distinct mounded states.
• One mounded state exhibits slope selection, while the other does not.
• The coarsening behavior differs significantly between the two phases.
• Steady-state configurations critically depend on the dominant instability during early growth stages (in the absence of noise).

Conclusions:

• The interplay between linear and nonlinear instabilities dictates the surface morphology in conserved growth models.
• Slope selection is a key characteristic distinguishing different mounded phases.
• Early-time instability dominance is crucial for determining the final steady-state surface structure.