Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model

TL;DR

This paper investigates the morphological instability and evolution of strained epitaxial films using an amplitude equation approach within the phase field crystal model, revealing universal scaling laws and crystalline effects.

Contribution

It introduces a mesoscopic model that captures both crystalline structure and continuum properties, analyzing instability and scaling in strained epitaxial films.

Findings

Universal scaling law between island size and misfit strain.

Crossover from continuum elasticity to lattice relaxation behavior.

Asymmetry observed between tensile and compressive strains.

Abstract

Morphological properties of strained epitaxial films are examined through a mesoscopic approach developed to incorporate both the film crystalline structure and standard continuum theory. Film surface profiles and properties, such as surface energy, liquid-solid miscibility gap and interface thickness, are determined as a function of misfit strains and film elastic modulus. We analyze the stress-driven instability of film surface morphology that leads to the formation of strained islands. We find a universal scaling relationship between the island size and misfit strain which shows a crossover from the well-known continuum elasticity result at the weak strain to a behavior governed by a "perfect" lattice relaxation condition. The strain at which the crossover occurs is shown to be a function of liquid-solid interfacial thickness, and an asymmetry between tensile and compressive strains is observed. The film instability is found to be accompanied by mode coupling of the complex amplitudes of the surface morphological profile, a factor associated with the crystalline nature of the strained film but absent in conventional continuum theory.