Renormalization of stochastic lattice models: epitaxial surfaces

Area of Science:

• Surface science and materials physics
• Computational modeling and simulation
• Statistical mechanics and renormalization group theory

Background:

• Epitaxial surface growth is crucial for fabricating advanced materials.
• Understanding morphological evolution from atomistic processes to continuum models is challenging.
• Previous methods focused on 1D systems, requiring adaptation for 2D surfaces.

Purpose of the Study:

• To apply a coarse-graining method for deriving stochastic partial differential equations from atomistic models of 2D epitaxial surfaces.
• To investigate the morphological evolution of surfaces under material deposition.
• To analyze the behavior of Edwards-Wilkinson, Wolf-Villain, and concurrent deposition-diffusion models.

Main Methods:

• Derivation of stochastic partial differential equations from atomistic processes.
• Coarse-graining via renormalization-group (RG) trajectories.
• Application to 1D and 2D models including Edwards-Wilkinson, Wolf-Villain, and a model with concurrent random deposition and surface diffusion.

Main Results:

• The Edwards-Wilkinson model showed no significant crossover in either 1D or 2D.
• The 2D Wolf-Villain model exhibited a transition from smooth to unstable growth under repeated coarse-graining.
• Concurrent surface diffusion led to extended transient roughening regimes but did not alter the instability; RG trajectories matched kinetic Monte Carlo simulations.

Conclusions:

• The methodology successfully addresses technical challenges in applying coarse-graining to 2D surfaces.
• The study explains experimental observations on Ge(001), linking early-stage relaxation mechanisms to later-stage epitaxial breakdown.
• The derived RG trajectories for concurrent deposition and diffusion align with established theoretical models.