Density-Functional-Theory Calculations of Formation Energy of the Nitrogen-Doped Diamond

Sholihun Sholihun(1*), Hana Pratiwi Kadarisman(2), Pekik Nurwantoro(3)

(1) Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia
(2) Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia
(3) Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia
(*) Corresponding Author


The geometry optimization of the nitrogen-doped diamond has been carried out by the density functional theory (DFT) calculations. We model the defective diamond of substitutional and interstitial nitrogen atoms by using a simple-cubic supercell. Atoms in the supercell are relaxed by allowing them to move so that the atomic forces are less than 5.0 × 10-3 eV/Å. We calculate the formation energy for substitutional and interstitial sites. We find that the formation energy for the substitutional defect is10.89 eV. We check the convergence of the calculation with respect to the k×k×k - Monkhorst-Pack grids. We show that the energy difference between k = 4 and 6 is very small (7.0 meV). We also check the calculations by using a 216-sites supercell and find that the energy difference is 0.10 eV. Thus, the calculations of the formation energy converge well. As for the interstitial defect, we model some possible configurations and find that the smallest formation energy is 21.88 eV. Therefore, the most stable configuration of the nitrogen-doped diamond belongs to the substitutional site.


formation energy; diamond; nitrogen doping

Full Text:

Full Text PDF


[1] Walker, J., 1979, Optical absorption and luminescence in diamond, Rep. Prog. Phys., 42, 1605–1658.

[2] Abbaschian, R., Zhu, H., and Clarke, C., 2005, High pressure–high temperature growth of diamond crystals using split sphere apparatus, Diamond Relat. Mater., 14 (11-12), 1916–1919.

[3] Poferl, D.J., Gardner, N.C., and Angus, J.C., 1973, Growth of boron‐doped diamond seed crystals by vapor deposition, J. Appl. Phys., 44, 1428.

[4] Fu, K.C., Santori, C., Barclay, P.E., Rogers, L.J., Manson, N.B., and Beausoleil, R.G., 2009, Observation of the dynamic Jahn-Teller effect in the excited states of nitrogen-vacancy centers in diamond, Phys. Rev. Lett., 103 (25), 256404.

[5] Kaiser, W., and Bond, W.L., 1959, Nitrogen, a major impurity in common type I diamond, Phys. Rev., 115 (4), 857–863.

[6] Golter, D.A., Oo, T., Amezcua, M., Stewart, K.A., and Wang, H., Optomechanical quantum control of a nitrogen-vacancy center in diamond, Phys. Rev. Lett., 116 (14), 143602.

[7] Iwasaki, T., Ishibashi, F., Miyamoto, Y., Doi, Y., Kobayashi, S., Miyazaki, T., Tahara, K., Jahnkae, K.D., Rogers, L.J., Naydenov, B., Jelezko, V., Yamasaki, S., Nagamachi, S., Inubushi, T., Mizuochi, N., and Hatano, M., 2015, Germanium-vacancy single color centers in diamond, Sci. Rep., 5, 12882.

[8] Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., and Zeilinger, A., 1997, Experimental quantum teleportation, Nature, 390, 575–579.

[9] Gisin, N., Ribordy, G., Tittel, W., and Zbinden, H., 2002, Quantum cryptography, Rev. Mod. Phys., 74, 145–195.

[10] Makhov, D.V., and Lewis, L.J., 2004, Stable fourfold configurations for small vacancy clusters in silicon from ab initio calculations, Phys. Rev. Lett., 92, 255504.

[11] Sholihun, Ishii, F., and Saito, M., 2016, First-principles calculations of multivacancies in germanium, Jpn. J. Appl. Phys., 55 (1), 011301.

[12] Fitriana, A.S., Pranowo, H.D., and Purwono, B., 2016, Chalcone based colorimetric sensor for anions: experimental and TD-DFT study, Indones. J. Chem., 16 (1), 80–86.

[13] Śpiewak, J.P., Vanhellemont, J., and Kurzydłowski, K.J., 2011, Improved calculation of vacancy properties in Ge using the Heyd-Scuseria-Ernzerhof range-separated hybrid functional, J. Appl. Phys., 110, 063534.

[14] Childress, L., Dutt, M.V.G., Taylor, J.M., Zibrov, A.S., Jelezko, F., Wrachtrup, J., Hemmer, P.R., and Lukin, M.D., 2006, Coherent dynamics of coupled electron and nuclear spin qubits in diamond, Science, 314, 281–285.

[15] Lee, S.Y., Widmann, M., Rendler, T., Doherty, M.W., Babinec, T.M., Yang, S., Eyer, M., Siyushev, P., Hausmann, B.J.M., Loncar, M., Bodrog, Z., Gali, A., Manson, N.B., Feder, H., and Wrachtup, J., 2013, Readout and control of a single nuclear spin with a metastable electron spin ancilla, Nat. Nanotechnol., 8, 487–492.

[16] Lombardi, E.B., Mainwood, A., Osuch, K., and Reynhardt, E.C., 2003, Computational models of the single substitutional nitrogen atom in diamond, J. Phys. Condens. Matter, 15 (19), 3135–3149.

[17] Deak, P., Aradi, B., Kaviabi, M., Frauenheim, T., and Gali, A., 2014, Formation of NV centers in diamond: A theoretical study based on calculated transitions and migrations of nitrogen and vacancy related defects, Phys. Rev. B, 89, 075203.

[18] PHASE,

[19] Birch, F., 1947, Finite elastic strain of cubic crystal, Phys. Rev., 71 (11), 809–824.

[20] Zhuravlev, K., 2007, PbSe vs. CdSe: Thermodynamic properties and pressure dependence of the band gap, Physica B, 394 (1), 1–7.

[21] Staroverov, V.N., Scuseria, G.E., Tao, J., and Perdew, J.P., 2008, Erratum: Tests of a ladder of density functionals for bulk solids and surfaces, Phys. Rev. B, 78 (23), 239907.

[22] Haas, P., Tran, F., and Blaha, P., 2009, Calculation of the lattice constant of solids with semilocal functionals, Phys. Rev. B, 79, 085104.

[23] Corsetti, F., and Mostofi, A.A., 2011, System-size convergence of point defect properties: The case of silicon vacancy, Phys. Rev. B, 84, 035209.

[24] Probert, M.I.J., and Payne, M.C., 2003, Improving the convergence of defect calculations in supercells: An ab initio study of the neutral silicon vacancy, Phys. Rev. B, 67, 075204.


Article Metrics

Abstract views : 1273 | views : 1388

Copyright (c) 2018 Indonesian Journal of Chemistry

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.


Indonesian Journal of Chemistry (ISSN 1411-9420 / 2460-1578) - Chemistry Department, Universitas Gadjah Mada, Indonesia.

Analytics View The Statistics of Indones. J. Chem.