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Linear stability analysis for step meandering instabilities with elastic interactions and Ehrlich-Schwoebel barriers
Dong-Hee Yeon1, Pil-Ryung Cha, John S Lowengrub
1Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
Summary
Ehrlich-Schwoebel barriers and elastic stress influence step meandering instabilities in heteroepitaxial growth. Their interplay determines whether step patterns form, with terrace width and stress strength dictating the resulting morphology.
Area of Science:
- Surface science
- Materials science
- Condensed matter physics
Background:
- Vicinal surfaces exhibit morphological instabilities during step-flow growth.
- Heteroepitaxial systems are crucial for advanced material fabrication.
- Understanding step dynamics is key to controlling surface morphology.
Purpose of the Study:
- Investigate the impact of Ehrlich-Schwoebel (ES) barriers and elastic monopole-monopole interactions on step meandering instabilities.
- Analyze how these factors influence step patterns in heteroepitaxial growth.
- Establish phase diagrams for predicting step configurations.
Main Methods:
- Linear stability analysis of step meandering instabilities.
- Modeling of elastic monopole-monopole interactions from bulk stress.
- Incorporation of asymmetric adatom incorporation rates (ES barriers).
Main Results:
- ES barrier effects increase with terrace width; elastic interactions decrease.
- ES barriers favor in-phase steps; elastic stress favors out-of-phase steps.
- Instability growth rate becomes phase-shift independent for dominant ES or stress effects.
- Patterned step morphologies transition to random based on monopole strength, independent of terrace width.
Conclusions:
- The interplay between ES barriers and elastic stress dictates step morphology.
- Phase diagrams predict ES-barrier-dominant vs. elastic-interaction-dominant instability regions.
- Controlling terrace width and stress strength allows tuning of step configurations.
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