Skip to main content Accessibility help
×
Home

Excitation spectrum of point defects in semiconductors studied by time-dependent density functional theory

  • Adam Gali (a1)

Abstract

A common fingerprint of the electrically active point defects in semiconductors is the transition among their localized defect states upon excitation, which may result in characteristic absorption- or photoluminescence spectrum. Identification of such point defects by means of density functional theory (DFT) calculations with traditional (semi) local functionals suffers from two problems: the “band gap error” and the many-body nature of the electron-hole interaction of the excited state. We show that non local hybrid density functionals may effectively mimic the quasiparticle correction of the band edges and the defect levels within the band gap in group-IV semiconductors, thus they can effectively heal the “band gap error.” The electron-hole interaction can be calculated by time-dependent DFT (TD-DFT) method. Here, we apply TD-DFT on three topical examples: nitrogen-vacancy defect in diamond, silicon-vacancy and divacancy defects in silicon carbide that are candidates in effective development of solid-state quantum bits.

Copyright

Corresponding author

a)Address all correspondence to this author. e-mail: agali@eik.bme.hu

References

Hide All
1.de Walle, C.G.V. and Neugebauer, J.: First-principles calculations for defects and impurities: Applications to III-nitrides. J. Appl. Phys. 95, 38513879 (2004).
2.Estreicher, S.K., Backlund, D., Gibbons, T.M., and Doçaj, A.: Vibrational properties of impurities in semiconductors. Modell. Simul. Mater. Sci. Eng. 17, 084006 (2009).
3.Blöchl, P.E.: First-principles calculations of defects in oxygen-deficient silica exposed to hydrogen. Phys. Rev. B Condens. Matter 62, 6158 (2000).
4.Son, N.T., Carlsson, P., ul Hassan, J., Janzén, E., Umeda, T., Isoya, J., Gali, A., Bockstedte, M., Morishita, N., Ohshima, T., and Itoh, H.: Divacancy in 4H-SiC. Phys. Rev. Lett. 96, 055501 (2006).
5.Umeda, T., Son, N.T., Isoya, J., Janzén, E., Ohshima, T., Morishita, N., Itoh, H., Gali, A., and Bockstedte, M.: Identification of the carbon antisite-vacancy pair in 4H-SiC. Phys. Rev. Lett. 96, 145501 (2006).
6.Ceperley, D.M. and Alder, B.J.: Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566 (1980).
7.Perdew, J.P. and Zunger, A.: Self-interaction correction to density-functional approximations for many–electron systems. Phys. Rev. B Condens. Matter 23, 5048 (1981).
8.Perdew, J.P. and Wang, Y.: Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B Condens. Matter 45, 1324413249 (1992).
9.Perdew, J.P., Burke, K., and Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 38653868 (1996).
10.Deák, P.: Modeling of defects in solids. Phys. Status Solidi B 217, 9 (2000).
11.Baraff, G.A. and Schlüter, M.: Calculation of the total energy of charged point defects using the Green’s-function technique. Phys. Rev. B Condens. Matter 30, 1853 (1984).
12.Aradi, B., Gali, A., Deák, P., Lowther, J.E., Son, N.T., Janzén, E., and Choyke, W.J.: Ab initio density-functional supercell calculations of hydrogen defects in cubic SiC. Phys. Rev. B Condens. Matter 63, 245202 (2001).
13.Deák, P., Frauenheim, T., and Gali, A.: Limits of the scaled shift correction to levels of interstitial defects in semiconductors. Phys. Rev. B Condens. Matter 75, 153204 (2007).
14.Hedin, L. and Lundqvist, S.: Solid State Physics. (Academic, 23, New York, NY, 1969).
15.Furthmüller, J., Cappellini, G., Weissker, H.C., and Bechstedt, F.: GW self-energy calculations for systems with huge supercells. Phys. Rev. B Condens. Matter 66, 045110 (2002).
16.Ma, Y., Rohlfing, M., and Gali, A.: Excited states of the negatively charged nitrogen-vacancy color center in diamond. Phys. Rev. B Condens. Matter 81, 041204 (2010).
17.Bockstedte, M., Marini, A., Pankratov, O., and Rubio, A.: Many–Body effects in the excitation spectrum of a defect in SiC. Phys. Rev. Lett. 105, 026401 (2010).
18.Gali, A., Deák, P., Ordejón, P., Son, N.T., Janzén, E., and Choyke, W.J.: Aggregation of carbon interstitials in silicon carbide: A theoretical study. Phys. Rev. B Condens. Matter 68, 125201 (2003).
19.Gali, A., Deák, P., Rauls, E., Son, N.T., Ivanov, I.G., Carlsson, F.H.C., Janzén, E., and Choyke, W.J.: Correlation between the antisite pair and the DI center in SiC. Phys. Rev. B Condens. Matter 67, 155203 (2003).
20.Deák, P., Gali, A., Sólyom, A., Buruzs, A., and Frauenheim, T.: Electronic structure of boron-interstitial clusters in silicon. J. Phys. Condens. Matter 17, S2141 (2005).
21.Knaup, J.M., Deák, P., Frauenheim, T., Gali, A., Hajnal, Z., and Choyke, W.J.: Defects in SiO2 as the possible origin of near interface traps in the SiC/SiO2 system: A systematic theoretical study. Phys. Rev. B Condens. Matter 72, 115323 (2005).
22.Knaup, J.M., Deák, P., Frauenheim, T., Gali, A., Hajnal, Z., and Choyke, W.J.: Theoretical study of the mechanism of dry oxidation of 4H -SiC. Phys. Rev. B Condens. Matter 71, 235321 (2005).
23.Gali, A., Son, N.T., and Janzén, E.: Electrical characterization of metastable carbon clusters in SiC: A theoretical study. Phys. Rev. B Condens. Matter 73, 033204 (2006).
24.Gali, A.: Ab initio study of nitrogen and boron substitutional impurities in single-wall SiC nanotubes. Phys. Rev. B Condens. Matter 73, 245415 (2006).
25.Deák, P., Buruzs, A., Gali, A., and Frauenheim, T.: Strain-free polarization superlattice in silicon carbide: A theoretical investigation: Phys. Rev. Lett. 96, 236803 (2006).
26.Gali, A., Hornos, T., Son, N.T., Janzén, E., and Choyke, W.J.: Ab initio supercell calculations on aluminum-related defects in SiC. Phys. Rev. B Condens. Matter 75, 045211 (2007).
27.Rurali, R., Aradi, B., Frauenheim, T., and Gali, A.: Accurate single-particle determination of the band gap in silicon nanowires. Phys. Rev. B Condens. Matter 76, 113303 (2007).
28.Saunders, V.R., Dovesi, R., Roetti, C., Causá, M., Harrison, N.M., Orlando, R., and Zicovich-Wilson, C.M.: CRYSTAL98 User’s Manual (University of Torino, Torino, 1998).
29.Becke, A.D.: Density-functional thermochemistry. IV. A new dynamical correlation functional and implications for exact-exchange mixing. J. Chem. Phys. 104, 10401046 (1996).
30.Ernzerhof, M. and Scuseria, G.E.: Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional. J. Chem. Phys. 110, 50295036 (1999).
31.Heyd, J., Scuseria, G.E., and Ernzerhof, M.: Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 82078215 (2003).
32.Heyd, J. and Scuseria, G.E.: Assessment and validation of a screened Coulomb hybrid density functional. J. Chem. Phys. 120, 72747280 (2004).
33.Kresse, G. and Hafner, J.: Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B Condens. Matter 49, 14251 (1994).
34.Kresse, G. and Furthmüller, J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B Condens. Matter 54, 11169 (1996).
35.Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I., Dal Corso, A., de Gironcoli, S., Fabris, S., Fratesi, G., Gebauer, R., Gerstmann, U., Gougoussis, C., Kokalj, A., Lazzeri, M., Martin-Samos, L., Marzari, N., Mauri, F., Mazzarello, R., Paolini, S., Pasquarello, A., Paulatto, L., Sbraccia, C., Scandolo, S., Sclauzero, G., Seitsonen, A.P., Smogunov, A., Umari, P., and Wentzcovitch, R.M.: QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).
36.Marsman, M., Paier, J., Stroppa, A., and Kresse, G.: Hybrid functionals applied to extended systems. J. Phys. Condens. Matter 20, 064201 (2008).
37.Wadehra, A., Nicklas, J.W., and Wilkins, J.W.: Band offsets of semiconductor heterostructures: A hybrid density functional study. Appl. Phys. Lett. 97, 092119 (2010).
38.Deák, P., Aradi, B., Frauenheim, T., Janzén, E., and Gali, A.: Accurate defect levels obtained from the HSE06 range-separated hybrid functional. Phys. Rev. B Condens. Matter 81, 153203 (2010).
39.Komsa, H.P., Broqvist, P., and Pasquarello, A.: Alignment of defect levels and band edges through hybrid functionals: Effect of screening in the exchange term. Phys. Rev. B Condens. Matter 81, 205118 (2010).
40.Casida, M.E.: All-Electron Local and Gradient-Corrected Density-Functional Calculations of Nan Dipole Polarizabilities for n=1-6. In Recent Advances in Density Functional Theory; Chong, D.P., ed, World Scientific: Singapore, 1995; p. 155.
41.Reining, L., Olevano, V., Rubio, A., and Onida, G.: Excitonic effects in solids described by time-dependent density-functional theory. Phys. Rev. Lett. 88, 066404 (2002).
42.Onida, G., Reining, L., and Rubio, A.: Electronic excitations: Density-functional versus many-body Green’s-function approaches. Rev. Mod. Phys. 74, 601659 (2002).
43.Uchino, T., Takahashi, M., and Yoko, T.: Structure and formation mechanism of Ge E′ center from divalent defects in Ge-doped SiO2 glass. Phys. Rev. Lett. 84, 14751478 (2000).
44.Raghavachari, K., Ricci, D., and Pacchioni, G.: Optical properties of point defects in SiO2 from time-dependent density functional theory. J. Chem. Phys. 116, 825831 (2002).
45.Zyubin, A.S., Mebel, A.M., and Lin, S.H.: Photoluminescence of oxygen-containing surface defects in germanium oxides: A theoretical study. J. Chem. Phys. 123, 044701 (2005).
46.Zyubin, A.S., Mebel, A.M., Hayashi, M., Chang, H.C., and Lin, S.H.: Quantum chemical modeling of photoadsorption properties of the nitrogen-vacancy point defect in diamond. J. Comput. Chem. 30, 131 (2009).
47.Zyubin, A.S., Mebel, A.M., Hayashi, M., Chang, H.C., and Lin, S.H.: Quantum chemical modeling of photoabsorption properties of two- and three-nitrogen vacancy point defects in diamond. J. Phys. Chem. C 113, 1043210440 (2009).
48.Paier, J., Marsman, M., and Kresse, G.: Dielectric properties and excitons for extended systems from hybrid functionals. Phys. Rev. B Condens. Matter 78, 121201 (2008).
49.Blöchl, P.E.: Projector augmented-wave method. Phys. Rev. B Condens. Matter 50, 17953 (1994).
50.Kresse, G. and Joubert, D.: From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B Condens. Matter 59, 1758 (1999).
51.Gali, A., Fyta, M., and Kaxiras, E.: Ab initio supercell calculations on nitrogen-vacancy center in diamond: Electronic structure and hyperfine tensors. Phys. Rev. B Condens. Matter 77, 155206 (2008).
52.Sanchéz-Portal, D., Ordejón, P., Artacho, E., and Soler, J.M.: Density-functional method for very large systems with LCAO basis sets. Int. J. Quantum Chem. 65, 453 (1997).
53.Troullier, N. and Martins, J.L.: Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B Condens. Matter 43, 1993 (1991).
54.Gali, A., Janzén, E., Deák, P., Kresse, G., and Kaxiras, E.: Theory of spin-conserving excitation of the N–V– center in diamond. Phys. Rev. Lett. 103, 186404 (2009).
55.Ahlrichs, R., Bär, M., Häser, M., Horn, H., and Kölmel, C.: Electronic structure calculations on workstation computers: The program system turbomole. Chem. Phys. Lett. 162, 169 (1989).
56.Schuchardt, K.L., Didier, B.T., Elsethagen, T., Sun, L., Gurumoorthi, V., Chase, J., Li, J., and Windus, T.L.. Basis set exchange: A community database for computational sciences. J. Chem. Inf. Model. 47, 1045 (2007).
57.Gruber, A., Drabenstedt, A., Tietz, C., Fleury, L., Wrachtrup, J., and Borczyskowski, C.: Scanning confocal optical microscopy and magnetic resonance on single defect centers. Science 276, 2012 (1997).
58.Drabenstedt, A., Fleury, L., Tietz, C., Jelezko, F., Kilin, S., Nizovtzev, A., and Wrachtrup, J.: Low-temperature microscopy and spectroscopy on single defect centers in diamond. Phys. Rev. B Condens. Matter 60, 11503 (1999).
59.Jelezko, F., Popa, I., Gruber, A., Tietz, C., Wrachtrup, J., Nizovtsev, A., and Kilin, S.: Single spin states in a defect center resolved by optical spectroscopy. Appl. Phys. Lett. 81, 2160 (2002).
60.Jelezko, F., Gaebel, T., Popa, I., Gruber, A., and Wrachtrup, J.: Observation of coherent oscillations in a single electron spin. Phys. Rev. Lett. 92, 076401 (2004).
61.Jelezko, F., Gaebel, T., Popa, I., Dunham, M., Gruber, A., and Wrachtrup, J.: Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Phys. Rev. Lett. 93, 130501 (2004).
62.Epstein, R.J., Mendoza, F., Kato, Y.K., and Awschalom, D.D.: Anisotropic interactions of a single spin and dark-spin spectroscopy in diamond. Nat. Phys. 1, 94 (2005).
63.Hanson, R., Mendosa, F.M., Epstein, R.J., and Awschalom, D.D.: Polarization and readout of coupled single spins in diamond. Phys. Rev. Lett. 97, 087601 (2006).
64.Brouri, R., Beveratos, A., Poizat, J.P., and Gragier, P.: Photon antibunching in the fluorescence of individual color centers in diamond. Opt. Lett. 25, 1294 (2000).
65.Beveratos, A., Brouri, R., Gacoin, T., Poizat, J.P., and Grangier, P.: Nonclassical radiation from diamond nanocrystals. Phys. Rev. A: At. Mol. Opt. Phys. 64, 061802(R) (2002).
66.Childress, L., Taylor, J.M., Sørensen, A.S., and Lukin, M.D.: Fault-tolerant quantum communication based on solid-state photon emitters. Phys. Rev. Lett. 96, 070504 (2006).
67.Jiang, L., Hodges, J.S., Maze, J.R., Maurer, P., Taylor, J.M., Cory, D.G., Hemmer, P.R., Walsworth, R.L., Yacoby, A., Zibrov, A.S., and Lukin, M.D.: Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae. Science 326, 272 (2009).
68.Childress, L., Gurudev Dutt, M.V., Taylor, J.M., Zibrov, A.S., Jelezko, F., Wrachtrup, J., Hemmer, P.R., and Lukin, M.D.: Coherent dynamics of coupled electron and nuclear spinqubits in diamond. Science 314, 281 (2006).
69.Gurudev Dutt, M.V., Childress, L., Jiang, L., Togan, E., Maze, J., Jelezko, F., Zibrov, A.S., Hemmer, P.R., and Lukin, M.D.: Quantum register based on individual electronic and nuclear spin qubits in diamond. Science 316, 312 (2007).
70.du Preez, L.: Ph.D. Dissertation, University of Witwatersrand, (1965).
71.Davies, G. and Hamer, M.F.: Optical studies of the 1.945 eV Vibronic band in diamond. Proc. R. Soc. London Ser. A 348, 285 (1976).
72.Loubser, J.H.N. and van Wyk, J.P.: Electron Spin Resonance in Annealed Type 1b Diamond. (Diamond Research (London), London, 1977; p. 47).
73.Loubser, J.H.N. and van Wyk, J.A.: Electron spin resonance in the study of diamond. Rep. Prog. Phys. 41, 1201 (1978).
74.Collins, A.T.: Luminescence decay time of the 1.945 eV centre in type Ib diamond. J. Phys. C: Solid State Phys. 16, 2177 (1983).
75.Goss, J.P., Jones, R., Breuer, S.J., Briddon, P.R., and Öberg, S.: The twelve- line 1.682 eV luminescence center in diamond and the vacancy—silicon complex. Phys. Rev. Lett. 77, 3041 (1996).
76.Larsson, J.A. and Delaney, P.: Electronic structure of the nitrogen-vacancy center in diamond from first-principles theory. Phys. Rev. B Condens. Matter 77, 165201 (2008).
77.Watts, R.K.: Point Defects in Crystals (Wiley-Interscience Publication, New York, 1977).
78.Weber, J.R., Koehl, W.F., Varley, J.B., Janotti, A., Buckley, B.B., de Walle, C.G.V., and Awschalom, D.D.: Quantum computing with defects. Proc. Natl. Acad. Sci. U S A 107, 85138518 (2010).
79.Vörös, M. and Gali, A.: Optical absorption of diamond nanocrystals from ab initio density-functional calculations. Phys. Rev. B Condens. Matter 80, 161411 (2009).
80.Sörman, E., Son, N.T., Chen, W.M., Kordina, O., Hallin, C., and Janzén, E.: Silicon vacancy related defect in 4H and 6H SiC. Phys. Rev. B Condens. Matter 61, 26132620 (2000).
81.Baranov, P.G., Bundakova, A.P., Soltamova, A.A., Orlinskii, S.B., Borovykh, I.V., Zondervan, R., Verberk, R., and Schmidt, J.: Silicon vacancy in SiC as a promising quantum system for single-defect and single-photon spectroscopy. Phys. Rev. B Condens. Matter 83, 125203 (2011).
82.Mizuochi, N., Yamasaki, S., Takizawa, H., Morishita, N., Ohshima, T., Itoh, H., and Isoya, J.: Continuous-wave and pulsed EPR study of the negatively charged silicon vacancy with S = 3/2 and C symmetry in n -type 4H–SiC. Phys. Rev. B Condens. Matter 66, 235202 (2002).
83.Mizuochi, N., Yamasaki, S., Takizawa, H., Morishita, N., Ohshima, T., Itoh, H., Umeda, T., and Isoya, J.: Spin multiplicity and charge state of a silicon vacancy (T V2a) in 4H -SiC determined by pulsed ENDOR. Phys. Rev. B Condens. Matter 72, 235208 (2005).
84.Isono, H., Tajima, M., Hoshino, N., and Sugimoto, H.: Rapid Characterization of SiC Crystals by Full-Wafer Photoluminescence Imaging under Below-Gap Excitation. Mater. Sci. Forum 600603, 545 (2009).
85.Janzén, E., Gali, A., Carlsson, P., Gällström, A., Magnusson, B., and Son, N.T.: The silicon vacancy in SiC. Physica B 404, 4354 (2009).
86.Janzén, E., Gali, A., Henry, A., Ivanov, I.G., Magnusson, B., and Son, N.T.: Defects in SiC. in Defects in Microelectronic Materials and Devices Fleetwood, D.M., Pantelides, S.T., and Schrimpf, R.D., eds, Taylor & Francis Group: Boca Raton, FL, 2009; p. 615. Chapter 21.
87.Magnusson, B. and Janzén, E.: Optical characterization of deep level defects in SiC. Mater. Sci. Forum 483485, 341 (2005).
88.Lowther, J.E.: Excited states of the vacancy in diamond. Phys. Rev. B Condens. Matter 48, 1159211601 (1993).
89.Vörös, M., Deák, P., Frauenheim, T., and Gali, A.: The absorption spectrum of hydrogenated silicon carbide nanocrystals from ab initio calculations. Appl. Phys. Lett. 96, 051909 (2010).
90.Madelung, O., ed: Semiconductors. Group IV Elements and II-V Compounds, (Data in Science and Technology) (Springer, Berlin, 1991).
91.Levinshtein, M.E., Rumyantsev, S.L., and Shur, M.S., eds: Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, and SiGe (John Wiley and Sons, New York, NY, 2001).

Keywords

Related content

Powered by UNSILO

Excitation spectrum of point defects in semiconductors studied by time-dependent density functional theory

  • Adam Gali (a1)

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.