Fractal analysis of collision cascades in pulsed-ion-beam-irradiated solids [Collision cascade densities in ion pulsed ion irradiated solids { a fractal approach]
Abstract
The buildup of radiation damage in ion-irradiated crystals often depends on the spatial distribution of atomic displacements within collision cascades. Although collision cascades have previously been described as fractals, the correlation of their fractal parameters with experimental observations of radiation damage buildup remains elusive. Here, we use a pulsed-ion-beam method to study defect interaction dynamics in 3C-SiC irradiated at 100 °C with ions of different masses. These data, together with results of previous studies of SiC and Si, are analyzed with a model of radiation damage formation which accounts for the fractal nature of collision cascades. Our emphasis is on the extraction of the effective defect diffusion length from pulsed beam measurements. Results show that, for both Si and SiC, collision cascades are mass fractals with fractal dimensions in the range of ~1–2, depending on ion mass, energy, and the depth from the sample surface. Within our fractal model, the effective defect diffusion length is ~10 nm for SiC and ~20 nm for Si, and it decreases with increasing cascade density. These results demonstrate a general method by which the fractal nature of collision cascades can be used to explain experimental observations and predict material’s response to radiation.
- Authors:
-
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Texas A & M Univ., College Station, TX (United States). Department of Nuclear Engineering
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1529188
- Report Number(s):
- LLNL-JRNL-730937
Journal ID: ISSN 2045-2322; 881115
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE
Citation Formats
Wallace, J. B., Aji, L. B. Bayu, Shao, L., and Kucheyev, S. O. Fractal analysis of collision cascades in pulsed-ion-beam-irradiated solids [Collision cascade densities in ion pulsed ion irradiated solids { a fractal approach]. United States: N. p., 2017.
Web. doi:10.1038/s41598-017-17781-5.
Wallace, J. B., Aji, L. B. Bayu, Shao, L., & Kucheyev, S. O. Fractal analysis of collision cascades in pulsed-ion-beam-irradiated solids [Collision cascade densities in ion pulsed ion irradiated solids { a fractal approach]. United States. https://doi.org/10.1038/s41598-017-17781-5
Wallace, J. B., Aji, L. B. Bayu, Shao, L., and Kucheyev, S. O. Thu .
"Fractal analysis of collision cascades in pulsed-ion-beam-irradiated solids [Collision cascade densities in ion pulsed ion irradiated solids { a fractal approach]". United States. https://doi.org/10.1038/s41598-017-17781-5. https://www.osti.gov/servlets/purl/1529188.
@article{osti_1529188,
title = {Fractal analysis of collision cascades in pulsed-ion-beam-irradiated solids [Collision cascade densities in ion pulsed ion irradiated solids { a fractal approach]},
author = {Wallace, J. B. and Aji, L. B. Bayu and Shao, L. and Kucheyev, S. O.},
abstractNote = {The buildup of radiation damage in ion-irradiated crystals often depends on the spatial distribution of atomic displacements within collision cascades. Although collision cascades have previously been described as fractals, the correlation of their fractal parameters with experimental observations of radiation damage buildup remains elusive. Here, we use a pulsed-ion-beam method to study defect interaction dynamics in 3C-SiC irradiated at 100 °C with ions of different masses. These data, together with results of previous studies of SiC and Si, are analyzed with a model of radiation damage formation which accounts for the fractal nature of collision cascades. Our emphasis is on the extraction of the effective defect diffusion length from pulsed beam measurements. Results show that, for both Si and SiC, collision cascades are mass fractals with fractal dimensions in the range of ~1–2, depending on ion mass, energy, and the depth from the sample surface. Within our fractal model, the effective defect diffusion length is ~10 nm for SiC and ~20 nm for Si, and it decreases with increasing cascade density. These results demonstrate a general method by which the fractal nature of collision cascades can be used to explain experimental observations and predict material’s response to radiation.},
doi = {10.1038/s41598-017-17781-5},
journal = {Scientific Reports},
number = 1,
volume = 7,
place = {United States},
year = {Thu Dec 14 00:00:00 EST 2017},
month = {Thu Dec 14 00:00:00 EST 2017}
}
Web of Science
Works referenced in this record:
Intermediate energy proton irradiation: Rapid, high-fidelity materials testing for fusion and fission energy systems
journal, February 2021
- Jepeal, S. J.; Snead, L.; Hartwig, Z. S.
- Materials & Design, Vol. 200
Measurement of defect profiles in reactive ion etched silicon
journal, January 1992
- Benton, J. L.
- Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, Vol. 10, Issue 1
Time constant of defect relaxation in ion-irradiated 3C-SiC
journal, May 2015
- Wallace, J. B.; Bayu Aji, L. B.; Shao, L.
- Applied Physics Letters, Vol. 106, Issue 20
Effect of collision cascade density on radiation damage in SiC
journal, May 2009
- Azarov, A. Yu.; Titov, A. I.; Karaseov, P. A.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 267, Issue 8-9
Radiation defect dynamics in Si at room temperature studied by pulsed ion beams
journal, October 2015
- Wallace, J. B.; Charnvanichborikarn, S.; Bayu Aji, L. B.
- Journal of Applied Physics, Vol. 118, Issue 13
Analysis of semiconductors by ion channelling: Applications and pitfalls
journal, March 1998
- Williams, J. S.; Conway, M.; Davies, J. A.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 136-138
Fractal geometry of collision cascades
journal, February 1989
- Rossi, François; Parkin, Don M.; Nastasi, Michael
- Journal of Materials Research, Vol. 4, Issue 1
Damage buildup in Si under bombardment with MeV heavy atomic and molecular ions
journal, October 2001
- Titov, A. I.; Kucheyev, S. O.; Belyakov, V. S.
- Journal of Applied Physics, Vol. 90, Issue 8
Energy spike effects in ion-bombarded GaN
journal, April 2009
- Kucheyev, S. O.; Azarov, A. Yu; Titov, A. I.
- Journal of Physics D: Applied Physics, Vol. 42, Issue 8
Damage buildup in Si under bombardment with MeV heavy atomic and molecular ions
journal, October 2001
- Titov, A. I.; Kucheyev, S. O.; Belyakov, V. S.
- Journal of Applied Physics, Vol. 90, Issue 8
Damage buildup in Ar-ion-irradiated 3 C -SiC at elevated temperatures
journal, September 2015
- Wallace, J. B.; Bayu Aji, L. B.; Li, T. T.
- Journal of Applied Physics, Vol. 118, Issue 10
The spatial structure of collision cascades
journal, January 1982
- Winterbon, K. B.
- Radiation Effects, Vol. 60, Issue 1-4
Fragmentation of displacement cascades into subcascades: A molecular dynamics study
journal, March 2015
- Antoshchenkova, E.; Luneville, L.; Simeone, D.
- Journal of Nuclear Materials, Vol. 458
Energy spike effects in ion-bombarded GaN
journal, April 2009
- Kucheyev, S. O.; Azarov, A. Yu; Titov, A. I.
- Journal of Physics D: Applied Physics, Vol. 42, Issue 8
Room‐temperature migration and interaction of ion beam generated defects in crystalline silicon
journal, June 1996
- Privitera, Vittorio; Coffa, Salvatore; Priolo, Francesco
- Applied Physics Letters, Vol. 68, Issue 24
Radiation effects in carbides: TiC and ZrC versus SiC
journal, May 2014
- Pellegrino, S.; Thomé, L.; Debelle, A.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 327
Lateral migration of point defects in Si induced by localized ion implantation
journal, May 1999
- Matsukawa, T.; Yokoyama, K.; Sawara, S.
- Applied Physics Letters, Vol. 74, Issue 18
Collision cascades as fractals
journal, October 1987
- Winterbon, K. B.; Urbassek, H. M.; Sigmund, P.
- Physica Scripta, Vol. 36, Issue 4
Room‐temperature migration and interaction of ion beam generated defects in crystalline silicon
journal, June 1996
- Privitera, Vittorio; Coffa, Salvatore; Priolo, Francesco
- Applied Physics Letters, Vol. 68, Issue 24
High density cascade effects
journal, January 1981
- Thompson, D. A.
- Radiation Effects, Vol. 56, Issue 3-4
Fractal structure of collision cascades
journal, March 1990
- Moreno-Marin, Juan Carlos; Conrad, Ulrich; Urbassek, Herbert M.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 48, Issue 1-4
Description of high energy collision cascades within the multifractal theory framework
journal, June 2008
- Luneville, L.; Simeone, D.; Baldinozzi, G.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 266, Issue 12-13
Damage accumulation in MgO irradiated with MeV Au ions at elevated temperatures
journal, September 2016
- Bachiller-Perea, Diana; Debelle, Aurélien; Thomé, Lionel
- Journal of Nuclear Materials, Vol. 478
Effects of the density of collision cascades: Separating contributions from dynamic annealing and energy spikes
journal, August 2009
- Titov, A. I.; Karaseov, P. A.; Azarov, A. Yu.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 267, Issue 16
Multifractality and multiscaling in collision cascades
journal, October 1994
- Kun, F.; Bardos, G.
- Physical Review E, Vol. 50, Issue 4
Damage buildup and the molecular effect in Si bombarded with PFn cluster ions
journal, March 2007
- Titov, A. I.; Azarov, A. Yu.; Nikulina, L. M.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 256, Issue 1
Solid-phase epitaxy of amorphous silicon induced by electron irradiation at room temperature
journal, November 1987
- Lulli, G.; Merli, P. G.; Antisari, M. Vittori
- Physical Review B, Vol. 36, Issue 15
Effects of the density of collision cascades: Separating contributions from dynamic annealing and energy spikes
journal, August 2009
- Titov, A. I.; Karaseov, P. A.; Azarov, A. Yu.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 267, Issue 16
SRIM – The stopping and range of ions in matter (2010)
journal, June 2010
- Ziegler, James F.; Ziegler, M. D.; Biersack, J. P.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 268, Issue 11-12
Description of high energy collision cascades within the multifractal theory framework
journal, June 2008
- Luneville, L.; Simeone, D.; Baldinozzi, G.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 266, Issue 12-13
Damage buildup and the molecular effect in Si bombarded with PFn cluster ions
journal, March 2007
- Titov, A. I.; Azarov, A. Yu.; Nikulina, L. M.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 256, Issue 1
High density cascade effects
journal, January 1981
- Thompson, D. A.
- Radiation Effects, Vol. 56, Issue 3-4
Radiation effects in carbides: TiC and ZrC versus SiC
journal, May 2014
- Pellegrino, S.; Thomé, L.; Debelle, A.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 327
Lateral migration of point defects in Si induced by localized ion implantation
journal, May 1999
- Matsukawa, T.; Yokoyama, K.; Sawara, S.
- Applied Physics Letters, Vol. 74, Issue 18
Pulsed Ion Beam Measurement of the Time Constant of Dynamic Annealing in Si
journal, August 2012
- Myers, M. T.; Charnvanichborikarn, S.; Shao, L.
- Physical Review Letters, Vol. 109, Issue 9
Formation of surface amorphous layers in semiconductors under low-energy light-ion irradiation: Experiment and theory
journal, December 2003
- Titov, A. I.; Belyakov, V. S.; Azarov, A. Yu.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 212
Transmission electron microscopy study of ion implantation induced Si amorphization
journal, May 1983
- Ruault, M. O.; Chaumont, J.; Bernas, H.
- Nuclear Instruments and Methods in Physics Research, Vol. 209-210
Trap-limited migration of vacancy-type defects in 7.5 keV H−-implanted Si
journal, March 2002
- Deenapanray, Prakash N. K.
- Applied Physics Letters, Vol. 80, Issue 9
Artificially layered heteropolytypic structures based on SiC polytypes: molecular beam epitaxy, characterization and properties
journal, May 2003
- Fissel, A.
- Physics Reports, Vol. 379, Issue 3-4, p. 149-255
Time constant of defect relaxation in ion-irradiated 3C-SiC
journal, May 2015
- Wallace, J. B.; Bayu Aji, L. B.; Shao, L.
- Applied Physics Letters, Vol. 106, Issue 20
Measurement of defect profiles in reactive ion etched silicon
journal, January 1992
- Benton, J. L.
- Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, Vol. 10, Issue 1
Damage buildup in Ar-ion-irradiated 3 C -SiC at elevated temperatures
journal, September 2015
- Wallace, J. B.; Bayu Aji, L. B.; Li, T. T.
- Journal of Applied Physics, Vol. 118, Issue 10
Mechanism for the molecular effect in Si bombarded with clusters of light atoms
journal, February 2006
- Titov, A.; Azarov, A.; Nikulina, L.
- Physical Review B, Vol. 73, Issue 6
Molecular effect in semiconductors under heavy-ion bombardment: Quantitative approach based on the concept of nonlinear displacement spikes
journal, September 2002
- Titov, A. I.; Belyakov, V. S.; Kucheyev, S. O.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 194, Issue 3
Atomic scale simulation of defect production in irradiated 3C-SiC
journal, September 2001
- Devanathan, R.; Weber, W. J.; Gao, F.
- Journal of Applied Physics, Vol. 90, Issue 5
The Displacement of Atoms in Solids by Radiation
journal, January 1955
- Kinchin, G. H.; Pease, R. S.
- Reports on Progress in Physics, Vol. 18, Issue 1
Some new aspects for the evaluation of disorder profiles in silicon by backscattering
journal, January 1973
- Schmid, K.
- Radiation Effects, Vol. 17, Issue 3-4
Some new aspects for the evaluation of disorder profiles in silicon by backscattering
journal, January 1973
- Schmid, K.
- Radiation Effects, Vol. 17, Issue 3-4
Atomic scale simulation of defect production in irradiated 3C-SiC
journal, September 2001
- Devanathan, R.; Weber, W. J.; Gao, F.
- Journal of Applied Physics, Vol. 90, Issue 5
Cascade overlap and amorphization in Defect accumulation, topological features, and disordering
journal, July 2002
- Gao, F.; Weber, W. J.
- Physical Review B, Vol. 66, Issue 2
Transmission electron microscopy study of ion implantation induced Si amorphization
journal, May 1983
- Ruault, M. O.; Chaumont, J.; Bernas, H.
- Nuclear Instruments and Methods in Physics Research, Vol. 209-210
Fractal dimension of collision cascades
journal, February 1997
- Kun, F.; Bardos, G.
- Physical Review E, Vol. 55, Issue 2
Cascade fragmentation under ion beam irradiation: A fractal approach
journal, July 2010
- Simeone, D.; Luneville, L.; Serruys, Y.
- Physical Review E, Vol. 82, Issue 1
The influence of the interaction potential on the fractal dimension of the collision cascade
journal, August 2001
- Martan, Janusz
- Vacuum, Vol. 63, Issue 4
Radiation stability of fluorite-type nuclear oxides
journal, June 2008
- Garrido, Frédérico; Vincent, Laetitia; Nowicki, Lech
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 266, Issue 12-13
Subcascade formation and defect cluster size scaling in high-energy collision events in metals
journal, July 2016
- De Backer, A.; Sand, A. E.; Nordlund, K.
- EPL (Europhysics Letters), Vol. 115, Issue 2
From Cascade to Spike—a Fractal-Geometry Approach
journal, May 1987
- Cheng, Y. -T.; Nicolet, M. -A.; Johnson, W. L.
- Physical Review Letters, Vol. 58, Issue 20
Effective defect diffusion lengths in Ar-ion bombarded 3 C -SiC
journal, April 2016
- Bayu Aji, L. B.; Wallace, J. B.; Shao, L.
- Journal of Physics D: Applied Physics, Vol. 49, Issue 19
Trap-Limited Migration of Si Self-Interstitials at Room Temperature
journal, February 1996
- Kyllesbech Larsen, K.; Privitera, V.; Coffa, S.
- Physical Review Letters, Vol. 76, Issue 9
Enhanced radiation tolerance of non-polar-terminated ZnO
journal, December 2013
- Charnvanichborikarn, S.; Myers, M. T.; Shao, L.
- Journal of Applied Physics, Vol. 114, Issue 21
Pulsed ion beam measurement of defect diffusion lengths in irradiated solids
journal, March 2013
- Charnvanichborikarn, S.; Myers, M. T.; Shao, L.
- Journal of Physics: Condensed Matter, Vol. 25, Issue 16
Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool
journal, December 2009
- Stukowski, Alexander
- Modelling and Simulation in Materials Science and Engineering, Vol. 18, Issue 1
Radiation defect dynamics studied by pulsed ion beams
journal, October 2017
- Wallace, J. B.; Bayu Aji, L. B.; Shao, L.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 409
Interface-mediated suppression of radiation damage in GaN
journal, July 2012
- Charnvanichborikarn, S.; Myers, M. T.; Shao, L.
- Scripta Materialia, Vol. 67, Issue 2
Enhanced radiation tolerance of non-polar-terminated ZnO
journal, December 2013
- Charnvanichborikarn, S.; Myers, M. T.; Shao, L.
- Journal of Applied Physics, Vol. 114, Issue 21
Effects of collision cascade density on radiation defect dynamics in 3C-SiC
journal, March 2017
- Bayu Aji, L. B.; Wallace, J. B.; Kucheyev, S. O.
- Scientific Reports, Vol. 7, Issue 1
Temperature dependence of damage formation in Ag ion irradiated 4H-SiC
journal, October 2010
- Wendler, E.; Bierschenk, Th.; Wesch, W.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 268, Issue 19
Radiation defect dynamics studied by pulsed ion beams
journal, October 2017
- Wallace, J. B.; Bayu Aji, L. B.; Shao, L.
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 409
Interface-mediated suppression of radiation damage in GaN
journal, July 2012
- Charnvanichborikarn, S.; Myers, M. T.; Shao, L.
- Scripta Materialia, Vol. 67, Issue 2
Radiation stability of fluorite-type nuclear oxides
journal, June 2008
- Garrido, Frédérico; Vincent, Laetitia; Nowicki, Lech
- Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 266, Issue 12-13
Effects of collision cascade density on radiation defect dynamics in 3C-SiC
journal, March 2017
- Bayu Aji, L. B.; Wallace, J. B.; Kucheyev, S. O.
- Scientific Reports, Vol. 7, Issue 1
Effect of the density of collision cascades on implantation damage in GaN
journal, April 2001
- Kucheyev, S. O.; Williams, J. S.; Titov, A. I.
- Applied Physics Letters, Vol. 78, Issue 18
Collision cascades as fractals
journal, October 1987
- Winterbon, K. B.; Urbassek, H. M.; Sigmund, P.
- Physica Scripta, Vol. 36, Issue 4
On the structure of irradiation-induced collision cascades in metals as a function of recoil energy and crystal structure
journal, February 1993
- Heinisch, H. L.; Singh, B. N.
- Philosophical Magazine A, Vol. 67, Issue 2
The Displacement of Atoms in Solids by Radiation
journal, January 1955
- Kinchin, G. H.; Pease, R. S.
- Reports on Progress in Physics, Vol. 18, Issue 1
Fragmentation of displacement cascades into subcascades: A molecular dynamics study
journal, March 2015
- Antoshchenkova, E.; Luneville, L.; Simeone, D.
- Journal of Nuclear Materials, Vol. 458
The spatial structure of collision cascades
journal, January 1982
- Winterbon, K. B.
- Radiation Effects, Vol. 60, Issue 1-4
Damage accumulation in MgO irradiated with MeV Au ions at elevated temperatures
journal, September 2016
- Bachiller-Perea, Diana; Debelle, Aurélien; Thomé, Lionel
- Journal of Nuclear Materials, Vol. 478
Radiation defect dynamics in Si at room temperature studied by pulsed ion beams
journal, October 2015
- Wallace, J. B.; Charnvanichborikarn, S.; Bayu Aji, L. B.
- Journal of Applied Physics, Vol. 118, Issue 13
The Fractal Geometry of Nature
journal, March 1983
- Mandelbrot, Benoit B.; Wheeler, John A.
- American Journal of Physics, Vol. 51, Issue 3
Works referencing / citing this record:
Radiation defect dynamics in GaAs studied by pulsed ion beams
journal, July 2018
- Bayu Aji, L. B.; Wallace, J. B.; Kucheyev, S. O.
- Journal of Applied Physics, Vol. 124, Issue 2
Control of superconductivity in MgB 2 by ion bombardment
journal, May 2019
- Baker, A. A.; Bayu Aji, L. B.; Bae, J. H.
- Journal of Physics D: Applied Physics, Vol. 52, Issue 29
Comparative study of radiation defect dynamics in 3C-SiC by X-ray diffraction, Raman scattering, and ion channeling
journal, December 2018
- Bayu Aji, L. B.; Stavrou, E.; Wallace, J. B.
- Applied Physics A, Vol. 125, Issue 1
Radiation defect dynamics in SiC with pre-existing defects
journal, June 2019
- Bayu Aji, L. B.; Wallace, J. B.; Kucheyev, S. O.
- Journal of Applied Physics, Vol. 125, Issue 23