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Comparison of Nb- and Ta-doping of anatase TiO2 for transparent conductor applications
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25.The error in the calculated heats of formation can vary just as well as that of the gap between various wide band gap oxides. HSE06 happens to reproduce both very accurately in TiO2.20 The heat of formation for anatase was calculated to be −9.68 eV, within ∼1% of the experimental value, −9.78 eV. Since the error is considerably bigger in the pentoxides, we use the experimental heat of formation for those.
26.We note that the heat of formation for Nb2O5 is lower than for Ta2O5 by 1.5 eV. Therefore, the lower formation energy of TaTi stems from the interaction with the TiO2 environment.
27. P. Deák, B. Aradi, and T. Frauenheim, “ The theory of the oxygen vacancy in TiO2,” in preparation.
28. S. Zhang, S. B. Ogale, W. Yu, X. Gao, T. Liu, S. Ghosh, G. P. Das, A. T. S. Wee, R. L. Greene, and T. Venkatesan, Adv. Mater. 21, 2282 (2009).
31. J. Sólyom, Fundamentals of the Physics of Solids (Springer, Berlin 2010), Vol. 2, p. 379.
32.Due to the finite number of calculated data points, the number of polynomials with increasing exponent must be kept low.
33.Note that in our previous work, using the volume integral, the second derivative of the |kz| term did not contribute to the effective mass. Therefore, the values presented here for the parallel mass in case of Nb are slightly different.
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