Abstract
The electronic structure of the tetradymites, Bi\(_2\)Te\(_3\), Bi\(_2\)Te\(_2\)Se, and Bi\(_2\)Se\(_3\), containing various dopants and vacancies, has been studied using first-principles calculations. We focus on the possibility of formation of resonant levels (RL), confirming the formation of RL by Sn in Bi\(_2\)Te\(_3\) and predicting similar behavior of Sn in Bi\(_2\)Te\(_2\)Se and Bi\(_2\)Se\(_3\). Vacancies, which are likely present on chalcogen atom sites in real samples of Bi\(_2\)Te\(_2\)Se and Bi\(_2\)Se\(_3\), are also studied and their charged donor and resonant behavior discussed. Doping of vacancy-containing materials with regular acceptors, such as Ca or Mg, is shown to compensate the donor effect of vacancies, and \(n-p\) crossover, while increasing the dopant concentration, is observed. We verify that the RL on Sn is not disturbed by chalcogen vacancies in Bi\(_2\)Te\(_2\)Se or Bi\(_2\)Se\(_3\), and for the Sn-doped materials with Se or Te vacancies, double doping, instead of heavy doping with Sn, is suggested as an effective way of obtaining the resonant level. This should help to avoid smearing of the RL, a possible reason for earlier unsuccessful experimental observation of the influence of the RL on the thermoelectric properties of Sn-doped Bi\(_2\)Te\(_2\)Se. Finally, we show that Al and Ga are possible new resonant impurities in tetradymites, hoping that this will stimulate further experimental studies.
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References
G.J. Snyder and E.S. Toberer, Nat. Mater. 7, 105 (2008)
R.J. Cava, H. Ji, M.K. Fuccillo, Q.D. Gibson, and Y.S. Hor, J. Mater. Chem. C 1, 3176 (2013)
M.Z. Hasan and C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)
Y.S. Hor, A. Richardella, P. Roushan, Y. Xia, J.G. Checkelsky, A. Yazdani, M.Z. Hasan, N.P. Ong, and R.J. Cava, Phys. Rev. B 79, 195208 (2009)
H.J. Goldsmid, Materials 7, 2577 (2014)
L.P. Caywood and G.R. Miller, Phys. Rev. B 2, 3209 (1970)
H. Köhler, Phys. Stat. Sol. (b) 62, 57 (1974)
P. Pecheur and G. Toussaint, Phys. Lett. A 135, 223 (1989)
S.K. Mishra, S. Satpathy, and O. Jepsen, J. Phys.: Condens. Matter 9, 461 (1997)
P. Larson, V.A. Greanya, W.C. Tonjes, R. Liu, S.D. Mahanti, and C.G. Olson, Phys. Rev. B 65, 085108 (2002)
V.A. Greanya, W.C. Tonjes, R. Liu, C.G. Olson, D.Y. Chung, and M.G. Kanatzidis, J. Appl. Phys. 92, 6658 (2002)
E. Kioupakis, M.L. Tiago, and S.G. Louie, Phys. Rev. B 82, 1 (2010)
W. Zhang, R. Yu, H.J. Zhang, X. Dai, and Z. Fang, New J. Phys. 12, 065013 (2010)
I.A. Nechaev, R.C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J.L. Mi, B.B. Iversen, S. Blügel, P. Hofmann, and E.V. Chulkov, Phys. Rev. B 87, 121111 (2013)
H. Scherrer, in Materials, Preparation, and Characterization in Thermoelectrics, ed. by D.M. Rowe (CRC Press, Boca Raton, 2012)
M.H. Francombe, Br. J. Appl. Phys. 9, 415 (1958)
S. Kaprzyk and A. Bansil, Phys. Rev. B 42, 7358 (1990)
A. Bansil, S. Kaprzyk, P.E. Mijnarends, and J. Tobola, Phys. Rev. B 60, 13396 (1999)
T. Stopa, S. Kaprzyk, and J. Tobola, J. Phys.: Condens. Matter 16, 4921 (2004)
H. Ebert, D. Ködderitzsch, and J. Minár, Rep. Prog. Phys. 74, 096501 (2011)
U. von Barth and L. Hedin, J. Phys.: Condens. Matter 5, 1629 (1972)
P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Techn. Universität Wien, Austria, 2001)
V.A. Kulbachinskii, N.B. Brandt, P.A. Cheremnykh, S.A. Azou, J. Horák, and P. Lošták, Phys. Stat. Sol. (b) 150, 237 (1988)
M. Zhitinskaya, S. Nemov, and T. Svechnikova, Phys. Solid State 40, 1297 (1998)
C.M. Jaworski, V. Kulbachinskii, and J.P. Heremans, Phys. Rev. B 80, 233201 (2009)
J. Friedel, Can. J. Phys. 34, 1190 (1956)
J.P. Heremans, B. Wiendlocha, and A.M. Chamoire, Energy Environ. Sci. 5, 5510 (2012)
B.L. Györffy and G.M. Stocks, in Electrons in Disordered Metals and Metallic Surfaces. NATO ASI Series, Physics, B42, ed. by P. Phariseau, B.L. Györffy, and L. Scheive (Plenum Press, New York, 1979)
B. Wiendlocha, Phys. Rev. B 88, 205205 (2013)
B. Wiendlocha, Appl. Phys. Lett. 105, 133901 (2014)
S. Kim, B. Wiendlocha, H. Jin, J. Tobola, and J.P. Heremans, J. Appl. Phys. 116, 153706 (2014)
B. Wiendlocha, K. Kutorasinski, S. Kaprzyk, and J. Tobola, Scr. Mater. 111, 33 (2016)
J.D. König, M.D. Nielsen, Y.B. Gao, M. Winkler, A. Jacquot, H. Böttner, and J.P. Heremans, Phys. Rev. B 84, 205126 (2011)
J.P. Heremans, V. Jovovic, E.S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, and G.J. Snyder, Science 321, 554 (2008)
C.M. Jaworski, B. Wiendlocha, V. Jovovic, and J.P. Heremans, Energy Environ. Sci. 4, 4155 (2011)
Q. Zhang, H. Wang, Q. Zhang, W. Liu, B. Yu, H. Wang, D. Wang, G. Ni, G. Chen, and Z. Ren, Nano Lett. 12, 2324 (2012)
Q. Zhang, B. Liao, Y. Lan, K. Lukas, W. Liu, K. Esfarjani, C. Opeil, D. Broido, G. Chen, and Z. Ren, Proc. Natl. Acad. Sci. 110, 13261 (2013)
H.P. Hjalmarson, P. Vogl, D.J. Wolford, and J.D. Dow, Phys. Rev. Lett. 44, 810 (1980)
S. Ahmad, K. Hoang, and S.D. Mahanti, Phys. Rev. Lett. 96, 056403 (2006)
K. Hoang and S.D. Mahanti, Phys. Rev. B 78, 085111 (2008)
H. Jin, B. Wiendlocha, and J.P. Heremans, Energy Environ. Sci. 8, 2027 (2015)
J.P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992)
M. Matyáš, M. Závětová, J. Horák, and P. Lošták, in Physics of Narrow Gap Semiconductors, vol. 152, ed. by E. Gornik, H. Heinrich, and L. Palmetshofer (Springer, Berlin, 1982), pp. 405–409
Z. Ren, A.A. Taskin, S. Sasaki, K. Segawa, and Y. Ando, Phys. Rev. B 85, 155301 (2012)
M. Fuccillo, S. Jia, M. Charles, and R. Cava, J. Electron. Mater. 42, 1246 (2013)
S.K. Kushwaha, Q.D. Gibson, J. Xiong, I. Pletikosic, A.P. Weber, A.V. Fedorov, N.P. Ong, T. Valla, and R.J. Cava, J. Appl. Phys. 115, 143708 (2014)
L.L. Wang, M. Huang, S. Thimmaiah, A. Alam, S.L. Bud’ko, A. Kaminski, T.A. Lograsso, P. Canfield, and D.D. Johnson, Phys. Rev. B 87, 125303 (2013)
D.O. Scanlon, P.D.C. King, R.P. Singh, A. de la Torre, S.M. Walker, G. Balakrishnan, F. Baumberger, and C.R.A. Catlow, Adv. Mater. 24, 2154 (2012)
D. West, Y.Y. Sun, H. Wang, J. Bang, and S.B. Zhang, Phys. Rev. B 86, 121201 (2012)
Z. Alpichshev, R.R. Biswas, A.V. Balatsky, J.G. Analytis, J.H. Chu, I.R. Fisher, and A. Kapitulnik, Phys. Rev. Lett. 108, 206402 (2012)
J. Androulakis and E. Beciragic, Solid State Commun. 173, 5 (2013)
Y.L. Chen, J.H. Chu, J.G. Analytis, Z.K. Liu, K. Igarashi, H.H. Kuo, X.L. Qi, S.K. Mo, R.G. Moore, D.H. Lu, M. Hashimoto, T. Sasagawa, S.C. Zhang, I.R. Fisher, Z. Hussain, and Z.X. Shen, Science 329, 659 (2010)
Y.B. Gao, B. He, D. Parker, I. Androulakis, and J.P. Heremans, Phys. Rev. B 90, 125204 (2014)
V.A. Kulbachinskii, V.G. Kytin, A.A. Kudryashov, and P.M. Tarasov, in AIP Conference Proceedings (2012), pp. 119
V. Kulbachinskii, V. Kytin, P. Tarasov, and N. Yuzeeva, Phys. Solid State 52, 1830 (2010)
Acknowledgements
This work was partially supported by the Polish National Science Center (NCN) (Project No. DEC-2011/02/A/ST3/00124) and the Polish Ministry of Science and Higher Education.
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Wiendlocha, B. Resonant Levels, Vacancies, and Doping in Bi2Te3, Bi2Te2Se, and Bi2Se3 Tetradymites. J. Electron. Mater. 45, 3515–3531 (2016). https://doi.org/10.1007/s11664-016-4502-9
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DOI: https://doi.org/10.1007/s11664-016-4502-9