Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon

Kim, D. S.; Hellman, O.; Herriman, J.; Smith, H. L.; Lin, J. Y. Y.; Shulumba, N.; Niedziela, J. L.; Li, C. W.; Abernathy, D. L.; Fultz, B.

doi:10.1073/pnas.1707745115

Title: Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon

Journal Article · Tue Feb 13 00:00:00 EST 2018 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.1707745115· OSTI ID:1420356

^[1]; Hellman, O. ^[1]; Herriman, J. ^[1]; Smith, H. L. ^[1];

^[2]; Shulumba, N. ^[3]; Niedziela, J. L. ^[4]; Li, C. W. ^[5]; Abernathy, D. L. ^[6]; Fultz, B. ^[1]

Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, CA 91125,
Neutron Data Analysis and Visualization Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831,
Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125,
Instrument and Source Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831,
Department of Mechanical Engineering, University of California, Riverside, CA 92521,
Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831

Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. Here, to test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.

View Journal Article

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-03ER46055; AC02-05CH11231

OSTI ID:: 1420356

Alternate ID(s):: OSTI ID: 1543904

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Vol. 115 Journal Issue: 9; ISSN 0027-8424

Publisher:: Proceedings of the National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 64 works

Citation information provided by
Web of Science

References (56)

Intrinsic localized mode and low thermal conductivity of PbSe Shulumba, Nina; Hellman, Olle; Minnich, Austin J. Physical Review B, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevB.95.014302	journal	January 2017
Temperature-dependent effective third-order interatomic force constants from first principles Hellman, Olle; Abrikosov, I. A. Physical Review B, Vol. 88, Issue 14 https://doi.org/10.1103/PhysRevB.88.144301	journal	October 2013
Mantid—Data analysis and visualization package for neutron scattering and $μ$ SR experiments Arnold, O.; Bilheux, J. C.; Borreguero, J. M. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 764 https://doi.org/10.1016/j.nima.2014.07.029	journal	November 2014
Projector augmented-wave method Blöchl, P. E. Physical Review B, Vol. 50, Issue 24, p. 17953-17979 https://doi.org/10.1103/PhysRevB.50.17953	journal	December 1994
Introduction to Lattice Dynamics Dove, Martin T. Cambridge Topics in Mineral Physics and Chemistry https://doi.org/10.1017/CBO9780511619885	book	February 2010
Anharmonic free energies and phonon dispersions from the stochastic self-consistent harmonic approximation: Application to platinum and palladium hydrides Errea, Ion; Calandra, Matteo; Mauri, Francesco Physical Review B, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevB.89.064302	journal	February 2014
Interference Effects in Neutron and X Ray Scattering Glyde, H. R. Canadian Journal of Physics, Vol. 52, Issue 22 https://doi.org/10.1139/p74-298	journal	November 1974
Path-integral simulation of solids Herrero, C. P.; Ramírez, R. Journal of Physics: Condensed Matter, Vol. 26, Issue 23 https://doi.org/10.1088/0953-8984/26/23/233201	journal	May 2014
Phonon anharmonicity in silicon from 100 to 1500 K Kim, D. S.; Smith, H. L.; Niedziela, J. L. Physical Review B, Vol. 91, Issue 1 https://doi.org/10.1103/PhysRevB.91.014307	journal	January 2015
Anharmonic line shift and linewidth of the Raman mode in covalent semiconductors Lang, G.; Karch, K.; Schmitt, M. Physical Review B, Vol. 59, Issue 9 https://doi.org/10.1103/PhysRevB.59.6182	journal	March 1999
Introduction to the Theory of Thermal Neutron Scattering Squires, G. L. https://doi.org/10.1017/CBO9781139107808	book	May 2012
Ab initio study of the volume dependence of dynamical and thermodynamical properties of silicon Rignanese, G. -M.; Michenaud, J. -P.; Gonze, X. Physical Review B, Vol. 53, Issue 8 https://doi.org/10.1103/PhysRevB.53.4488	journal	February 1996
Temperature dependence of silicon Raman lines Tsu, Raphael; Hernandez, Jesus Gonzalez Applied Physics Letters, Vol. 41, Issue 11 https://doi.org/10.1063/1.93394	journal	December 1982
Vibrational thermodynamics of materials Fultz, Brent Progress in Materials Science, Vol. 55, Issue 4 https://doi.org/10.1016/j.pmatsci.2009.05.002	journal	May 2010
A radial collimator for a time-of-flight neutron spectrometer Stone, M. B.; Niedziela, J. L.; Loguillo, M. J. Review of Scientific Instruments, Vol. 85, Issue 8 https://doi.org/10.1063/1.4891302	journal	August 2014
Scattering of Neutrons by an Anharmonic Crystal Maradudin, A. A.; Fein, A. E. Physical Review, Vol. 128, Issue 6 https://doi.org/10.1103/PhysRev.128.2589	journal	December 1962
Ab initiomolecular dynamics for liquid metals Kresse, G.; Hafner, J. Physical Review B, Vol. 47, Issue 1, p. 558-561 https://doi.org/10.1103/PhysRevB.47.558	journal	January 1993
Negative thermal expansion of diamond and zinc-blende semiconductors Biernacki, Slawomir; Scheffler, Matthias Physical Review Letters, Vol. 63, Issue 3 https://doi.org/10.1103/PhysRevLett.63.290	journal	July 1989
Functional designed to include surface effects in self-consistent density functional theory Armiento, R.; Mattsson, A. E. Physical Review B, Vol. 72, Issue 8 https://doi.org/10.1103/PhysRevB.72.085108	journal	August 2005
Implementing and testing the AM05 spin density functional Mattsson, Ann E.; Armiento, Rickard Physical Review B, Vol. 79, Issue 15 https://doi.org/10.1103/PhysRevB.79.155101	journal	April 2009
Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional Sun, Jianwei; Remsing, Richard C.; Zhang, Yubo Nature Chemistry, Vol. 8, Issue 9 https://doi.org/10.1038/nchem.2535	journal	June 2016
Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K Okada, Yasumasa; Tokumaru, Yozo Journal of Applied Physics, Vol. 56, Issue 2, p. 314-320 https://doi.org/10.1063/1.333965	journal	July 1984
Anharmonic self-energies of phonons in silicon Narasimhan, Shobhana; Vanderbilt, David Physical Review B, Vol. 43, Issue 5 https://doi.org/10.1103/PhysRevB.43.4541	journal	February 1991
Horace : Software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments Ewings, R. A.; Buts, A.; Le, M. D. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 834 https://doi.org/10.1016/j.nima.2016.07.036	journal	October 2016
Thermal expansion behavior of silicon at low temperatures Shah, Jayant S.; Straumanis, M. E. Solid State Communications, Vol. 10, Issue 1 https://doi.org/10.1016/0038-1098(72)90371-7	journal	January 1972
Anharmonic effects in light scattering due to optical phonons in silicon Balkanski, M.; Wallis, R. F.; Haro, E. Physical Review B, Vol. 28, Issue 4 https://doi.org/10.1103/PhysRevB.28.1928	journal	August 1983
Thermal expansion coefficient of single-crystal silicon from 7 K to 293 K Middelmann, Thomas; Walkov, Alexander; Bartl, Guido Physical Review B, Vol. 92, Issue 17 https://doi.org/10.1103/PhysRevB.92.174113	journal	November 2015
Anharmonic effects in the phonons of III–V semiconductors: first principles calculations Debernardi, A. Solid State Communications, Vol. 113, Issue 1 https://doi.org/10.1016/S0038-1098(99)00374-9	journal	November 1999
Thermodynamics of Crystals Wallace, Duane C.; Callen, Herbert American Journal of Physics, Vol. 40, Issue 11 https://doi.org/10.1119/1.1987046	journal	November 1972
Isotope effects on the lattice parameter of cubic SiC Herrero, Carlos P.; Ramírez, Rafael; Cardona, Manuel Physical Review B, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevB.79.012301	journal	January 2009
First-principles thermodynamical properties of semiconductors Fleszar, A.; Gonze, X. Physical Review Letters, Vol. 64, Issue 24 https://doi.org/10.1103/PhysRevLett.64.2961	journal	June 1990
Dependence of the silicon lattice constant on isotopic mass Herrero, C. P. Solid State Communications, Vol. 110, Issue 5 https://doi.org/10.1016/S0038-1098(99)00082-4	journal	April 1999
Raman scattering and phonon dispersion in Si and GaP at very high pressure Weinstein, Bernard A.; Piermarini, G. J. Physical Review B, Vol. 12, Issue 4 https://doi.org/10.1103/PhysRevB.12.1172	journal	August 1975
Ab initio calculation of thermodynamic properties of silicon Wei, Siqing; Li, Changlin; Chou, M. Y. Physical Review B, Vol. 50, Issue 19 https://doi.org/10.1103/PhysRevB.50.14587	journal	November 1994
Phonons and related crystal properties from density-functional perturbation theory Baroni, Stefano; de Gironcoli, Stefano; Dal Corso, Andrea Reviews of Modern Physics, Vol. 73, Issue 2 https://doi.org/10.1103/RevModPhys.73.515	journal	July 2001
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Kresse, G.; Furthmüller, J. Computational Materials Science, Vol. 6, Issue 1, p. 15-50 https://doi.org/10.1016/0927-0256(96)00008-0	journal	July 1996
Lattice Vibrations in Silicon and Germanium Brockhouse, B. N. Physical Review Letters, Vol. 2, Issue 6 https://doi.org/10.1103/PhysRevLett.2.256	journal	March 1959
Isotope dependence of the lattice parameter of germanium from path-integral Monte Carlo simulations Noya, José C.; Herrero, Carlos P.; Ramírez, Rafael Physical Review B, Vol. 56, Issue 1 https://doi.org/10.1103/PhysRevB.56.237	journal	July 1997
The AM05 density functional applied to solids Mattsson, Ann E.; Armiento, Rickard; Paier, Joachim The Journal of Chemical Physics, Vol. 128, Issue 8 https://doi.org/10.1063/1.2835596	journal	February 2008
Temperature dependent effective potential method for accurate free energy calculations of solids Hellman, Olle; Steneteg, Peter; Abrikosov, I. A. Physical Review B, Vol. 87, Issue 10 https://doi.org/10.1103/PhysRevB.87.104111	journal	March 2013
Study of the Homology between Silicon and Germanium by Thermal-Neutron Spectrometry Nilsson, G.; Nelin, G. Physical Review B, Vol. 6, Issue 10 https://doi.org/10.1103/PhysRevB.6.3777	journal	November 1972
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
Anharmonic phonon quasiparticle theory of zero-point and thermal shifts in insulators: Heat capacity, bulk modulus, and thermal expansion Allen, Philip B. Physical Review B, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevB.92.064106	journal	August 2015
Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium Kresse, G.; Hafner, J. Physical Review B, Vol. 49, Issue 20, p. 14251-14269 https://doi.org/10.1103/PhysRevB.49.14251	journal	May 1994
Lattice Constants and Thermal Expansivities of Silicon and of Calcium Fluoride between 6° and 322°K Batchelder, D. N.; Simmons, R. O. The Journal of Chemical Physics, Vol. 41, Issue 8 https://doi.org/10.1063/1.1726266	journal	October 1964
Orbitally driven giant phonon anharmonicity in SnSe Li, C. W.; Hong, J.; May, A. F. Nature Physics, Vol. 11, Issue 12 https://doi.org/10.1038/nphys3492	journal	October 2015
Thermal expansion of some diamondlike crystals Slack, Glen A.; Bartram, S. F. Journal of Applied Physics, Vol. 46, Issue 1 https://doi.org/10.1063/1.321373	journal	January 1975
Theory of the thermal expansion of Si and diamond Xu, C. H.; Wang, C. Z.; Chan, C. T. Physical Review B, Vol. 43, Issue 6 https://doi.org/10.1103/PhysRevB.43.5024	journal	February 1991
Empirical tight-binding force model for molecular-dynamics simulation of Si Wang, C. Z.; Chan, C. T.; Ho, K. M. Physical Review B, Vol. 39, Issue 12 https://doi.org/10.1103/PhysRevB.39.8586	journal	April 1989
The rise of self-consistent phonon theory Klein, M. L.; Horton, G. K. Journal of Low Temperature Physics, Vol. 9, Issue 3-4 https://doi.org/10.1007/BF00654839	journal	November 1972
Design and operation of the wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source Abernathy, D. L.; Stone, M. B.; Loguillo, M. J. Review of Scientific Instruments, Vol. 83, Issue 1 https://doi.org/10.1063/1.3680104	journal	January 2012
Plane-wave pseudopotential implementation and performance of SCAN meta-GGA exchange-correlation functional for extended systems Yao, Yi; Kanai, Yosuke The Journal of Chemical Physics, Vol. 146, Issue 22 https://doi.org/10.1063/1.4984939	journal	June 2017
Anharmonic Phonon Lifetimes in Semiconductors from Density-Functional Perturbation Theory Debernardi, Alberto; Baroni, Stefano; Molinari, Elisa Physical Review Letters, Vol. 75, Issue 9 https://doi.org/10.1103/PhysRevLett.75.1819	journal	August 1995
Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory Gonze, Xavier; Lee, Changyol Physical Review B, Vol. 55, Issue 16 https://doi.org/10.1103/PhysRevB.55.10355	journal	April 1997
Thermal Expansion Anomaly Regulated by Entropy Liu, Zi-Kui; Wang, Yi; Shang, ShunLi Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep07043	journal	November 2014
Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and $α - S n$ : Anharmonic effects Menéndez, José; Cardona, Manuel Physical Review B, Vol. 29, Issue 4 https://doi.org/10.1103/PhysRevB.29.2051	journal	February 1984

Similar Records

Anharmonic Origin of the Giant Thermal Expansion of NaBr

Journal Article · Fri Aug 21 00:00:00 EDT 2020 · Physical Review Letters · OSTI ID:1420356

Shen, Yang; Saunders, Claire N.; Bernal, Camille M.; +3 more

Thermal expansion and phonon anharmonicity of cuprite studied by inelastic neutron scattering and ab initio calculations

Journal Article · Tue May 31 00:00:00 EDT 2022 · Physical Review. B · OSTI ID:1420356

Saunders, Claire N.; Kim, D. S.; Hellman, O.; +8 more

Phonon anharmonicity in silicon from 100 to 1500 K

Journal Article · Wed Jan 21 00:00:00 EST 2015 · Physical Review. B, Condensed Matter and Materials Physics · OSTI ID:1420356

Kim, D. S.; Smith, Hillary L.; Niedziela, Jennifer L.; +3 more

Related Subjects

42 ENGINEERING
Science & Technology
Other Topics
thermal expansion
phonon anharmonicity
inelastic neutron scattering
nuclear quantum effects
silicon

Title: Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon

Citation Formats

References (56)

Similar Records

Related Subjects