Burton-Cabrera-Frank theory for surfaces with alternating step types
Abstract
Burton-Cabrera-Frank (BCF) theory has proven to be a versatile framework to relate surface morphology and dynamics during crystal growth to the underlying mechanisms of adatom diffusion and attachment at steps. For an important class of crystal surfaces, including the basal planes of hexagonal close-packed and related systems, the steps in a sequence on a vicinal surface can exhibit properties that alternate from step to step. Here we develop BCF theory for such surfaces, relating observables such as alternating terrace widths as a function of growth conditions to the kinetic coefficients for adatom attachment at steps. Additionally, we include the effects of step transparency and step-step repulsion. A general solution is obtained for the dynamics of the terrace widths, assuming quasi steady-state adatom distributions on the terraces. An explicit simplified analytical solution is obtained under widely applicable approximations. From this we obtain expressions for the full-steady-state terrace fraction as a function of growth rate. Fits of the theoretical predictions to recent experimental determinations of the steady state and dynamics of terrace fractions on GaN (0001) surfaces during organometallic vapor phase epitaxy give values of the kinetic coefficients for this system. In Appendixes, we also connect a model for diffusion between kinksmore »
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1846081
- Alternate Identifier(s):
- OSTI ID: 1862671
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Published Article
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Name: Physical Review B Journal Volume: 105 Journal Issue: 5; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; crystal growth; growth; growth processes; hexagonal close-packed; solid-gas interfaces; surface growth; Wurtzite; methods in transport
Citation Formats
Ju, Guangxu, Xu, Dongwei, Thompson, Carol, Highland, Matthew J., Eastman, Jeffrey A., Walkosz, Weronika, Zapol, Peter, and Stephenson, G. Brian. Burton-Cabrera-Frank theory for surfaces with alternating step types. United States: N. p., 2022.
Web. doi:10.1103/PhysRevB.105.054312.
Ju, Guangxu, Xu, Dongwei, Thompson, Carol, Highland, Matthew J., Eastman, Jeffrey A., Walkosz, Weronika, Zapol, Peter, & Stephenson, G. Brian. Burton-Cabrera-Frank theory for surfaces with alternating step types. United States. https://doi.org/10.1103/PhysRevB.105.054312
Ju, Guangxu, Xu, Dongwei, Thompson, Carol, Highland, Matthew J., Eastman, Jeffrey A., Walkosz, Weronika, Zapol, Peter, and Stephenson, G. Brian. Tue .
"Burton-Cabrera-Frank theory for surfaces with alternating step types". United States. https://doi.org/10.1103/PhysRevB.105.054312.
@article{osti_1846081,
title = {Burton-Cabrera-Frank theory for surfaces with alternating step types},
author = {Ju, Guangxu and Xu, Dongwei and Thompson, Carol and Highland, Matthew J. and Eastman, Jeffrey A. and Walkosz, Weronika and Zapol, Peter and Stephenson, G. Brian},
abstractNote = {Burton-Cabrera-Frank (BCF) theory has proven to be a versatile framework to relate surface morphology and dynamics during crystal growth to the underlying mechanisms of adatom diffusion and attachment at steps. For an important class of crystal surfaces, including the basal planes of hexagonal close-packed and related systems, the steps in a sequence on a vicinal surface can exhibit properties that alternate from step to step. Here we develop BCF theory for such surfaces, relating observables such as alternating terrace widths as a function of growth conditions to the kinetic coefficients for adatom attachment at steps. Additionally, we include the effects of step transparency and step-step repulsion. A general solution is obtained for the dynamics of the terrace widths, assuming quasi steady-state adatom distributions on the terraces. An explicit simplified analytical solution is obtained under widely applicable approximations. From this we obtain expressions for the full-steady-state terrace fraction as a function of growth rate. Fits of the theoretical predictions to recent experimental determinations of the steady state and dynamics of terrace fractions on GaN (0001) surfaces during organometallic vapor phase epitaxy give values of the kinetic coefficients for this system. In Appendixes, we also connect a model for diffusion between kinks on steps to the model for diffusion between steps on terraces, which quantitatively relates step transparency to the kinetics of atom attachment at kinks, and consider limiting cases of diffusion-limited, attachment-limited, and mixed kinetics.},
doi = {10.1103/PhysRevB.105.054312},
journal = {Physical Review B},
number = 5,
volume = 105,
place = {United States},
year = {Tue Feb 22 00:00:00 EST 2022},
month = {Tue Feb 22 00:00:00 EST 2022}
}
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