First-principle calculation of the pressure-induced variation in the formation energy of iron defect in Si1−xGex alloy
- 38 Downloads
Abstract
We report on the systematic first-principle calculations of the formation volumes of a single Fe (neutral iron) in Si1−xGex at various Ge compositions (x = 4.7–20.3%). The formation volume was defined as the derivative of the Fe formation energy with respect to the pressure within 0–0.8 GPa. Interestingly, the formation volume was found to be equivalent to the difference between the volumes of the relaxed bulk and defective structures. The formation volume versus ‘x’ exhibited a nonlinear pattern with regions of Fe-induced volume contraction (within x < 50%, i.e., Si-rich region) and expansion (x > 50%, i.e., Ge-rich region). These results explain the reported observation that Fe prefers Si-rich environment and that Ge does not favor to be a nearest neighbor to Fe.
Notes
Acknowledgements
The authors would like to thank the Africa City of Technology (Sudan) for access to their high performance computing facilities to compute some of our structures.
References
- 1.I. Yonenaga, in Reference Module in Materials Science and Materials Engineering. Six Ge1−x Bulk Crystals (Elsevier, Amsterdam, 2016). https://doi.org/10.1016/B978-0-12-803581-8.03687-0 Google Scholar
- 2.Y. Shiraki, N. Usami, Silicon-Germanium (SiGe) Nanostructures: Production, Properties and Applications in Electronics (Elsevier, Amsterdam, 2011)CrossRefGoogle Scholar
- 3.A. Mesli et al., Iron in relaxed Si1 − x Gex alloy: band gap related levels, diffusion, and alloying effects. Phys. Rev. B 66(4), 045206 (2002)ADSCrossRefGoogle Scholar
- 4.M.A.H. Khalafalla, A. Mesli, First principle calculations of iron and iron–boron transition levels in Si1−xGex alloy. Eur. Phys. J. B 90(6), 103 (2017)ADSCrossRefGoogle Scholar
- 5.K. Nauka, T.I. Kamins, Deep state defects in strained and relaxed epitaxial Si1−xGex on Si introduced by 3d transition metal and 5d noble metal impurities. Phys. B Condens. Matter 273–274, 603–607 (1999)ADSCrossRefGoogle Scholar
- 6.C. Claeys, E. Simoen, in Metal Impurities in Silicon-and Germanium-Based Technologies. Modeling of Metal Properties in Si, Si1−xGex and Ge (Springer, New York, 2018), pp. 389–433Google Scholar
- 7.A. Walsh, A.A. Sokol, C.R.A. Catlow, Free energy of defect formation: thermodynamics of anion Frenkel pairs in indium oxide. Phys. Rev. B 83(22), 224105 (2011)ADSCrossRefGoogle Scholar
- 8.A. Carvalho, J. Coutinho, R. Jones, M. Barroso, J. Goss, P. Briddon, Density-functional theory study of interstitial iron and its complexes with B and Al in dilute SiGe alloys. Mater. Sci. Semicond. Process. 11(5–6), 332–335 (2008)CrossRefGoogle Scholar
- 9.A. van de Walle et al., Efficient stochastic generation of special quasirandom structures. Calphad 42, 13–18 (2013)CrossRefGoogle Scholar
- 10.A. Van De Walle, M. Asta, G. Ceder, The alloy theoretic automated toolkit: a user guide. Calphad 26(4), 539–553 (2002)CrossRefGoogle Scholar
- 11.Alloy Theoretic Automated Toolkit (ATAT) Home Page. [Online]. https://www.brown.edu/Departments/Engineering/Labs/avdw/atat/. Accessed 09 Jul 2019
- 12.A.R. Denton, N.W. Ashcroft, Vegard’s law. Phys. Rev. A 43(6), 3161–3164 (1991)ADSCrossRefGoogle Scholar
- 13.P. Giannozzi et al., QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21(39), 395502 (2009)CrossRefGoogle Scholar
- 14.R.G. Parr, in Horizons of Quantum Chemistry, ed. by K. Fukui, B. Pullman. Density Functional Theory of Atoms and Molecules, vol. 3 (Internationale Des Sciences Moléculaires Quantiques Science, Springer, Dordrecht, 1980)Google Scholar
- 15.J.E. Northrup, S. Zhang, Dopant and defect energetics: Si in GaAs. Phys. Rev. B 47(11), 6791 (1993)ADSCrossRefGoogle Scholar
- 16.J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77(18), 3865 (1996)ADSCrossRefGoogle Scholar
- 17.D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41(11), 7892 (1990)ADSCrossRefGoogle Scholar
- 18.G. Bachelet, D. Hamann, M. Schlüter, Pseudopotentials that work: from H to Pu. Phys. Rev. B 26(8), 4199 (1982)ADSCrossRefGoogle Scholar
- 19.H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations. Phys. Rev. B 13(12), 5188 (1976)ADSMathSciNetCrossRefGoogle Scholar
- 20.P.E. Blöchl, O. Jepsen, O.K. Andersen, Improved tetrahedron method for Brillouin-zone integrations. Phys. Rev. B 49(23), 16223 (1994)ADSCrossRefGoogle Scholar
- 21.Y.G. Gogotsi, A. Kailer, K.G. Nickel, Pressure-induced phase transformations in diamond. J. Appl. Phys. 84(3), 1299–1304 (1998)ADSCrossRefGoogle Scholar
- 22.H. Warlimont, W. Martienssen, Springer Handbook of Materials Data (Springer, New York, 2018)CrossRefGoogle Scholar