Phonon anharmonicity in silicon from 100 to 1500 K
Abstract
Inelastic neutron scattering was performed on silicon powder to measure the phonon density of states (DOS) from 100 to 1500 K. The mean fractional energy shifts with temperature of the modes were $$\langle$$Δεi/εiΔT$$\rangle$$=₋0.07, giving a mean isobaric Grüneisen parameter of +6.95±0.67, which is significantly different from the isothermal parameter of +0.98. These large effects are beyond the predictions from quasiharmonic models using density functional theory or experimental data, demonstrating large effects from phonon anharmonicity. At 1500 K the anharmonicity contributes 0.15kB/atom to the vibrational entropy, compared to 0.03kB/atom from quasiharmonicity. Lastly, excellent agreement was found between the entropy from phonon DOS measurements and the reference NIST-JANAF thermodynamic entropy from calorimetric measurements.
- Authors:
-
- California Inst. of Technology (CalTech), Pasadena, CA (United States). Dept. of Applied Physics and Materials Science
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Instrument and Source Division
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science & Technology Division
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Quantum Condensed Matter Division
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Spallation Neutron Source (SNS)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1185765
- Alternate Identifier(s):
- OSTI ID: 1180194
- Grant/Contract Number:
- AC05-00OR22725; FG02-03ER46055
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics
- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 1; Journal ID: ISSN 1098-0121
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE
Citation Formats
Kim, D. S., Smith, Hillary L., Niedziela, Jennifer L., Li, Chen W., Abernathy, Douglas L., and Fultz, B. Phonon anharmonicity in silicon from 100 to 1500 K. United States: N. p., 2015.
Web. doi:10.1103/PhysRevB.91.014307.
Kim, D. S., Smith, Hillary L., Niedziela, Jennifer L., Li, Chen W., Abernathy, Douglas L., & Fultz, B. Phonon anharmonicity in silicon from 100 to 1500 K. United States. https://doi.org/10.1103/PhysRevB.91.014307
Kim, D. S., Smith, Hillary L., Niedziela, Jennifer L., Li, Chen W., Abernathy, Douglas L., and Fultz, B. Wed .
"Phonon anharmonicity in silicon from 100 to 1500 K". United States. https://doi.org/10.1103/PhysRevB.91.014307. https://www.osti.gov/servlets/purl/1185765.
@article{osti_1185765,
title = {Phonon anharmonicity in silicon from 100 to 1500 K},
author = {Kim, D. S. and Smith, Hillary L. and Niedziela, Jennifer L. and Li, Chen W. and Abernathy, Douglas L. and Fultz, B.},
abstractNote = {Inelastic neutron scattering was performed on silicon powder to measure the phonon density of states (DOS) from 100 to 1500 K. The mean fractional energy shifts with temperature of the modes were $\langle$Δεi/εiΔT$\rangle$=₋0.07, giving a mean isobaric Grüneisen parameter of +6.95±0.67, which is significantly different from the isothermal parameter of +0.98. These large effects are beyond the predictions from quasiharmonic models using density functional theory or experimental data, demonstrating large effects from phonon anharmonicity. At 1500 K the anharmonicity contributes 0.15kB/atom to the vibrational entropy, compared to 0.03kB/atom from quasiharmonicity. Lastly, excellent agreement was found between the entropy from phonon DOS measurements and the reference NIST-JANAF thermodynamic entropy from calorimetric measurements.},
doi = {10.1103/PhysRevB.91.014307},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 1,
volume = 91,
place = {United States},
year = {Wed Jan 21 00:00:00 EST 2015},
month = {Wed Jan 21 00:00:00 EST 2015}
}
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Works referenced in this record:
Low-Temperature Grüneisen Parameters for Silicon and Aluminum
journal, August 1971
- Gauster, W. B.
- Physical Review B, Vol. 4, Issue 4
Generalized Gradient Approximation Made Simple
journal, October 1996
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
Temperature-dependent effective third-order interatomic force constants from first principles
journal, October 2013
- Hellman, Olle; Abrikosov, I. A.
- Physical Review B, Vol. 88, Issue 14
Silicon nanowires as efficient thermoelectric materials
journal, January 2008
- Boukai, Akram I.; Bunimovich, Yuri; Tahir-Kheli, Jamil
- Nature, Vol. 451, Issue 7175, p. 168-171
Phonon softening and metallization of a narrow-gap semiconductor by thermal disorder
journal, March 2011
- Delaire, O.; Marty, K.; Stone, M. B.
- Proceedings of the National Academy of Sciences, Vol. 108, Issue 12
Efficient silicon light-emitting diodes
journal, August 2001
- Green, Martin A.; Zhao, Jianhua; Wang, Aihua
- Nature, Vol. 412, Issue 6849
Neutron scattering measurements of phonons in nickel at elevated temperatures
journal, March 2007
- Kresch, M.; Delaire, O.; Stevens, R.
- Physical Review B, Vol. 75, Issue 10
Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]
journal, February 1997
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 78, Issue 7
Plasmonics for improved photovoltaic devices
journal, February 2010
- Atwater, Harry A.; Polman, Albert
- Nature Materials, Vol. 9, Issue 3, p. 205-213
Raman scattering and phonon dispersion in Si and GaP at very high pressure
journal, August 1975
- Weinstein, Bernard A.; Piermarini, G. J.
- Physical Review B, Vol. 12, Issue 4
Projector augmented-wave method
journal, December 1994
- Blöchl, P. E.
- Physical Review B, Vol. 50, Issue 24, p. 17953-17979
Experimental Determination of the Low-Temperature Grüneisen Parameter of Silicon from Pressure Derivatives of Elastic Constants
journal, February 1970
- Beattie, A. G.; Schirber, J. E.
- Physical Review B, Vol. 1, Issue 4
Ab initio calculation of thermodynamic properties of silicon
journal, November 1994
- Wei, Siqing; Li, Changlin; Chou, M. Y.
- Physical Review B, Vol. 50, Issue 19
Temperature-dependent Raman scattering studies in nanocrystalline silicon and finite-size effects
journal, December 2000
- Mishra, Puspashree; Jain, K. P.
- Physical Review B, Vol. 62, Issue 22
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996
- Kresse, G.; Furthmüller, J.
- Computational Materials Science, Vol. 6, Issue 1, p. 15-50
Phonons in aluminum at high temperatures studied by inelastic neutron scattering
journal, January 2008
- Kresch, M.; Lucas, M.; Delaire, O.
- Physical Review B, Vol. 77, Issue 2
Theory of static structural properties, crystal stability, and phase transformations: Application to Si and Ge
journal, November 1982
- Yin, M. T.; Cohen, Marvin L.
- Physical Review B, Vol. 26, Issue 10
Silicon-based visible light-emitting devices integrated into microelectronic circuits
journal, November 1996
- Hirschman, K. D.; Tsybeskov, L.; Duttagupta, S. P.
- Nature, Vol. 384, Issue 6607
Anharmonic line shift and linewidth of the Raman mode in covalent semiconductors
journal, March 1999
- Lang, G.; Karch, K.; Schmitt, M.
- Physical Review B, Vol. 59, Issue 9
Thermal Expansion of Some Crystals with the Diamond Structure
journal, October 1958
- Gibbons, D. F.
- Physical Review, Vol. 112, Issue 1
Enhanced thermoelectric performance of rough silicon nanowires
journal, January 2008
- Hochbaum, Allon I.; Chen, Renkun; Delgado, Raul Diaz
- Nature, Vol. 451, Issue 7175, p. 163-167
High Performance Silicon Nanowire Field Effect Transistors
journal, February 2003
- Cui, Yi; Zhong, Zhaohui; Wang, Deli
- Nano Letters, Vol. 3, Issue 2
Coaxial silicon nanowires as solar cells and nanoelectronic power sources
journal, October 2007
- Tian, Bozhi; Zheng, Xiaolin; Kempa, Thomas J.
- Nature, Vol. 449, Issue 7164, p. 885-889
Study of the Homology between Silicon and Germanium by Thermal-Neutron Spectrometry
journal, November 1972
- Nilsson, G.; Nelin, G.
- Physical Review B, Vol. 6, Issue 10
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996
- Kresse, G.; Furthmüller, J.
- Physical Review B, Vol. 54, Issue 16, p. 11169-11186
From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999
- Kresse, G.; Joubert, D.
- Physical Review B, Vol. 59, Issue 3, p. 1758-1775
Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium
journal, May 1994
- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 49, Issue 20, p. 14251-14269
Lattice Constants and Thermal Expansivities of Silicon and of Calcium Fluoride between 6° and 322°K
journal, October 1964
- Batchelder, D. N.; Simmons, R. O.
- The Journal of Chemical Physics, Vol. 41, Issue 8
Silicon as a mechanical material
journal, May 1982
- Petersen, K. E.
- Proceedings of the IEEE, Vol. 70, Issue 5
The thermodynamic and optical properties of germanium, silicon, diamond and gallium arsenide
journal, June 1966
- Dolling, G.; Cowley, R. A.
- Proceedings of the Physical Society, Vol. 88, Issue 2
Highly Reversible Lithium Storage in Nanostructured Silicon
journal, January 2003
- Graetz, J.; Ahn, C. C.; Yazami, R.
- Electrochemical and Solid-State Letters, Vol. 6, Issue 9
Thermodynamic modelling of crystalline unary phases: Thermodynamic modelling of crystalline phases
journal, December 2013
- Palumbo, M.; Burton, B.; Costa e. Silva, A.
- physica status solidi (b), Vol. 251, Issue 1
Inelastic-neutron-scattering study of phonon eigenvectors and frequencies in Si
journal, November 1994
- Kulda, Jiří; Strauch, Dieter; Pavone, Pasquale
- Physical Review B, Vol. 50, Issue 18
Design and operation of the wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source
journal, January 2012
- Abernathy, D. L.; Stone, M. B.; Loguillo, M. J.
- Review of Scientific Instruments, Vol. 83, Issue 1
Vibrational thermodynamics of materials
journal, May 2010
- Fultz, Brent
- Progress in Materials Science, Vol. 55, Issue 4
A radial collimator for a time-of-flight neutron spectrometer
journal, August 2014
- Stone, M. B.; Niedziela, J. L.; Loguillo, M. J.
- Review of Scientific Instruments, Vol. 85, Issue 8
Phonon dispersions of silicon and germanium from first-principles calculations
journal, July 1994
- Wei, Siqing; Chou, M. Y.
- Physical Review B, Vol. 50, Issue 4
Ab initiomolecular dynamics for liquid metals
journal, January 1993
- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 47, Issue 1, p. 558-561
Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory
journal, April 1997
- Gonze, Xavier; Lee, Changyol
- Physical Review B, Vol. 55, Issue 16
Negative thermal expansion of diamond and zinc-blende semiconductors
journal, July 1989
- Biernacki, Slawomir; Scheffler, Matthias
- Physical Review Letters, Vol. 63, Issue 3
First-principles calculations of the ferroelastic transition between rutile-type and -type at high pressures
journal, October 2008
- Togo, Atsushi; Oba, Fumiyasu; Tanaka, Isao
- Physical Review B, Vol. 78, Issue 13
Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K
journal, July 1984
- Okada, Yasumasa; Tokumaru, Yozo
- Journal of Applied Physics, Vol. 56, Issue 2, p. 314-320
Thermal Expansion Anomaly Regulated by Entropy
journal, November 2014
- Liu, Zi-Kui; Wang, Yi; Shang, ShunLi
- Scientific Reports, Vol. 4, Issue 1
Lattice dynamical Debye-Waller factor for silicon
journal, July 1999
- Flensburg, Claus; Stewart, Robert F.
- Physical Review B, Vol. 60, Issue 1
Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and : Anharmonic effects
journal, February 1984
- Menéndez, José; Cardona, Manuel
- Physical Review B, Vol. 29, Issue 4
Thermal expansion behavior of silicon at low temperatures
journal, January 1972
- Shah, Jayant S.; Straumanis, M. E.
- Solid State Communications, Vol. 10, Issue 1
Works referencing / citing this record:
Thermal conductivity of strained silicon: Molecular dynamics insight and kinetic theory approach
journal, August 2019
- Kuryliuk, Vasyl; Nepochatyi, Oleksii; Chantrenne, Patrice
- Journal of Applied Physics, Vol. 126, Issue 5
Super-resolution energy spectra from neutron direct-geometry spectrometers
journal, October 2019
- Islam, Fahima; Lin, Jiao Y. Y.; Archibald, Richard
- Review of Scientific Instruments, Vol. 90, Issue 10
Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon
journal, February 2018
- Kim, D. S.; Hellman, O.; Herriman, J.
- Proceedings of the National Academy of Sciences, Vol. 115, Issue 9
A nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon
text, January 2016
- Kim, D. S.; Hellman, O.; Herriman, J.
- arXiv
Thermal conductivity of strained silicon: molecular dynamics insight and kinetic theory approach
text, January 2019
- Kuryliuk, Vasyl; Nepochatyi, Oleksii; Chantrenne, Patrice
- arXiv