TEMPERATURE DEPENDENCE OF ANHARMONIC EXAFS OSCILLATION OF CRYSTALLINE SILICON
DOI:
https://doi.org/10.51453/2354-1431/2020/435Keywords:
EXAFS analysis; Debye-Waller factor; Anharmonic correlated Einstein model; Crystalline silicon.Abstract
In this work, the anharmonic extended X-ray absorption fine structure (EXAFS) oscillation of crystalline silicon (c-Si) is presented in terms of the Debye-Waller factor using the cumulant expansion approach up to the fourth-order. The first four EXAFS cumulant has been calculated based on the classical anharmonic correlated Einstein (ACE) model and suitable analysis procedure, in which thermodynamic parameters are derived from the anharmonic effective potential obtained using the first shell near-neighbor contribution approach. The analysis of the temperature dependence of the EXAFS oscillation is performed via evaluating the influence of the cumulants on the amplitude reduction and the phase shift of the anharmonic EXAFS oscillation. The numerical results are found to be in good agreement with those obtained using the quantum ACE model and experiments at various temperatures. The obtained results are useful in analyzing the experimental EXAFS data of c-Si.
Downloads
References
[1] F.W. Lytle, D.E. Sayers, E.A. Stern, Extended x-ray-absorption fine-structure technique. II. Experimental practice and selected results, Phys. Rev. B 11 (1975) 4825-4835.
[2] G. Beni and P.M. Platzman, Temperature and polarization dependence of extended x-ray absorption fine-structure spectra, Phys. Rev. B 14 (4) (1976) 1514-1518.
[3] J.J. Rehr and R.C. Albers, Theoretical approaches to x-ray absorption fine structure, Rev. Mod. Phys. 72 (3) (2000) 621-654.
[4] G. Bunker, Applications of the ratio method of EXAFS analysis to disordered systems, Nucl. Instrum. Methods 207 (1983) 437-444.
[5] N.V. Hung, T.S. Tien, N.B. Duc, D.Q. Vuong, High-order expanded XAFS Debye-Waller factors of HCP crystals based on classical anharmonic correlated Einstein model, Mod. Phys. Lett. B 28 (21) (2014) 1450174.
[6] N.V. Hung and J.J. Rehr, Anharmonic correlated Einstein-model Debye-Waller factors, Phys. Rev. B 56 (1) (1997) 43-46.
[7] E.A. Stern, P. Livins, Z. Zhang, Thermal vibration and melting from a local perspective, Phys. Rev. B 43 (11) (1991) 8850-8860.
[8] T.S. Tien, N.V. Hung, N.T. Tuan, N.V. Nam, N.Q. An, N.T.M. Thuy, V.T.K. Lien, N.V. Nghia, High-order EXAFS cumulants of diamond crystals based on a classical anharmonic correlated Einstein model, J. Phys. Chem. Solids 134 (2019) 307-312.
[9] T.S Tien, Advances in studies of the temperature dependence of the EXAFS amplitude and phase of FCC crystals, J. Phys. D: Appl. Phys. 53 (2020) 315303.
[10] T. Yokoyama, K. Kobayashi, T. Ohta, A. Ugawa, Anharmonic interatomic potentials of diatomic and linear triatomic molecules studied by extended x-ray-absorption fine structure, Phys. Rev. B 53 (10) (1996) 6111-6122.
[11] L.A. Girifalco and V.G. Weizer, Application of the Morse potential function to cubic metals, Phys. Rev. 114 (3) (1959) 687-690.
[12] V.V. Hung and H.K. Hieu, Study the Temperature Dependence of EXAFS Cumulants of Si and Ge by the Anharmonic Correlated Einstein Model, Commun. Phys. 21 (1) (2011) 25-34.
[13] M. Benfatto, C.R. Natoli, A. Filipponi, Thermal and structural damping of the multiple-scattering contributions to the x-ray-absorption coefficient, Phys. Rev. B 40 (14) (1989), 9626-9635.
[14] R.A.Swalin, Theoretical calculations of the enthalpies and entropies of diffusion and vacancy formation in semiconductors, J. Phys. Chem. Solids 18 (4) (1961) 290-296.
[15] N.V. Hung, C.S. Thang, N.B. Duc, D.Q. Vuong, T.S. Tien, Temperature dependence of theoretical and experimental Debye-Waller factors, thermal expansion and XAFS of metallic Zinc, Physica B 521 (2017)198-203.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
All articles published in SJTTU are licensed under a Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA) license. This means anyone is free to copy, transform, or redistribute articles for any lawful purpose in any medium, provided they give appropriate attribution to the original author(s) and SJTTU, link to the license, indicate if changes were made, and redistribute any derivative work under the same license.
Copyright on articles is retained by the respective author(s), without restrictions. A non-exclusive license is granted to SJTTU to publish the article and identify itself as its original publisher, along with the commercial right to include the article in a hardcopy issue for sale to libraries and individuals.
Although the conditions of the CC BY-SA license don't apply to authors (as the copyright holder of your article, you have no restrictions on your rights), by submitting to SJTTU, authors recognize the rights of readers, and must grant any third party the right to use their article to the extent provided by the license.
