Debye-Waller Factor in an Isotopically Disordered Semiconductor Crystal

• Authors: S. Gairola
• Languages of publication: EN

Abstracts

EN

The diagonal and non-diagonal parts for the Debye-Waller factor have been established using equation of motion technique of quantum dynamics and the Dyson equation approach. The double time temperature dependent phonon Green function has been taken to find the phonon linewidth and phonon shift. Renormalized mode frequency has been investigated in terms of electron-phonon coupling constant and temperature. The effect of electron-phonon interaction on the Debye-Waller factor has been studied in low temperature limit in low impurity concentration in semiconductor crystals.

Keywords

EN

63.70.+h; 87.64.Bx; 63.20.-e; 63.20.Pw; 64.70.kg

Discipline

• 63.70.+h: Statistical mechanics of lattice vibrations and displacive phase transitions
• 87.64.Bx: Electron, neutron and x-ray diffraction and scattering
• 64.70.kg: Semiconductors
• 63.20.-e: Phonons in crystal lattices(for phonons in superconductors, see 74.25.Kc; see also 43.35.Gk Phonons in crystal lattice, quantum acoustics—in Acoustics Appendix)
• 63.20.Pw: Localized modes

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2016
• Volume: 129
• Issue: 6
• Pages: 1141-1146

Dates

published

2016-06

received

2015-03-16

(unknown)

2016-04-27

(unknown)

2016-05-24

Contributors

author

S. Gairola

• Department of Physics (School of Sciences), H.N.B. Garhwal University (A Central University) Campus Pauri, Pauri-246001, Uttarakhand, India

References

• [1] R. Ishikawa, R. Mishra, A.R. Lupini, S.D. Findlay, T. Taniguchi, S.T. Pantelides, S.J. Pennycook, Phys. Rev. Lett. 113, 155501 (2014), doi: 10.1103/PhysRevLett.113.155501
• [2] B. Saikia, A. Kumar, Pramana J. Phys. 71, 143 (2008)
• [3] J.E. Anthony, A. Facchetti, M. Heeney, S.R. Marder, X. Zhan, Adv. Mater. 22, 3876 (2010), doi: 10.1002/adma200903628
• [4] B. Lal, P. Aghamkar, S. Kumar, M.K. Kashyap, Eur. Phys. J. D 61, 717 (2011), doi: 10.1140/epjd/e2010-10455-9
• [5] D.W. Snoke, Ann. Phys. 523, 87 (2011), doi: 10.1002/andp.201000 102
• [6] S. Kumar, M. Khorasaninejad, M.M. Adachi, K.S. Karim, S.S. Saini, A.K. Sood, Pramana J. Phys. 79, 471 (2012), doi: 10.1007/s12043-012-0337-y
• [7] Y. Ezzahri, K. Joulain, J. Appl. Phys. 112, 083515 (2012), doi: 10.1063/1.4759366
• [8] H. Shimizu, S. Umetsu, T. Kaihara, Jpn. J. Appl. Phys. 52, 028006 (2013), doi: 10.7567/JJAP.52.028006
• [9] T.T. Zhang, P. Barate, C.T. Nguyen, A. Balocchi, T. Amand, P. Renucci, H. Carrere, B. Urbaszek, X. Marie, Phys. Rev. B 87, 041201(R) (2013), doi: 10.1103 /PhysRevB.87.041201
• [10] Xin Chen, D. Parker, D.J. Singh, Phys. Rev. B 87, 045317 (2013), doi: 10.1103/PhysRevB.87.045317
• [11] N. Rani, M. Yadav, Y.K. Mathur, Int. J. Appl. Eng. Res. 9, 59 (2014)
• [12] A.A. Maradudin, A.E. Fein, Phys. Rev. 128, 2589 (1962)
• [13] B.P. Bahuguna, C.P. Painuli, B.D. Indu, Int. J. Theor. Phys. 30, 807 (1991)
• [14] H.K. Hieu, V.V. Hung, N.V. Hung, Proc. Natl. Conf. Theor. Phys. 35, 109 (2010)
• [15] J. Callaway, Quantum Theory of the Solid State (Part A), Academic Press, New York 1974, Ch. 1, p. 46
• [16] M.S. Kushwaha, Phys. Rev. B 24, 2115 (1981), doi: 10.1103/PhysRevB.24.2115
• [17] S.G. Sahaya Sheba, K. Sadaiyandi, Int. J. Pure Appl. Phys. 7, 139 (2011)
• [18] H.G. Bohn, W. Zinn, F. Tasset, J. Phys. Coll. 43 C7, 141 (1982)
• [19] Sang-Wook Han, Jpn. J. Appl. Phys. 42 10, 6303 (2003), doi: 10.1143/JJAP.42.6303
• [20] D.Y. Song, M. Basavaraj, S.A. Nikishin, M. Holtz, V. Soukhoveev, A. Usikov, V. Dmitriev, J. Appl. Phys. 100, 113504 (2006), doi: 10.1063/1.2361159
• [21] N.V. Hung, N.C. Toan, N.B. Duc, D.Q. Vuong, Open Phys. 13, 242 (2015), doi: 10.1515/phys-2015-0031
• [22] Z.M. Hund, K.J. Nihill, D. Campi, K.T. Wong, N.S. Lewis, M. Bernasconi, G. Benedek, S.J. Sibener, J. Chem. Phys. 143, 124705 (2015), doi: 10.1063/1.4931178
• [23] J.P. Rino, P.S. Pizani, S.C. Costa, Braz. J. Phys. 34, 347 (2004), doi: 10.1590/S0103-97332004000300003
• [24] M. Schowalter, A. Rosenauer, J.T. Titantah, D. Lamoen, Microsc. Microanal. 13 S03, 128 (2007), doi: 10.1017/S1431927607080646
• [25] N.V. Hung, C.S. Thang, N.C. Toan, H.K. Hieu, Vacuum 101, 63 (2014)
• [26] N.V. Hung, J.J. Rehr, Phys. Rev. B 56, 43 (1997), doi: 10.1103/PhysRev B.56.43
• [27] N.V. Hung, N.B. Duc, R.R. Frahm, J. Phys. Soc. Jpn. 72, 1254 (2003), doi: 10.1143/JPSJ.72.1254
• [28] N.V. Hung, N.B. Trung, B. Kirchner, Physica B 405, 2519 (2010), doi: 10.1016/j.physb.2010.03.013
• [29] N.V. Hung, T.S. Tien, N.B. Duc, D.Q. Vuong, Mod. Phys. Lett. B 28, 1450174 (2014), doi: 10.1142/S0217984914501747
• [30] N.V. Hung, N.B. Trung, N.B. Duc, D.D. Son, T.S. Tien, J. Phys. Sci. Appl. 4, 43 (2014)
• [31] A.A. Maradudin, in: Solid State Physics, Eds. F. Seitz, D. Turnbull, Academic Press, New York 1966, Vol. 18, p. 273
• [32] A.A. Maradudin, Astrophysics and The Many-Body Problem, Benjamin, New York 1963, p. 109
• [33] A.A. Maradudin, P. Mazur, E.W. Montroll, G.H. Weiss, Rev. Mod. Phys. 30, 175 (1958), doi: 10.1103/RevModPhys.30.175
• [34] B.D. Indu, Int. J. Mod. Phys. B 4, 1379 (1990), doi: 10.1142/S021797929000067X
• [35] O. Madelung, in: Introduction to Solid-State Theory, Springer Series in Solid-State Sciences, Eds. M. Cardona, P. Fulde, H.-J. Queisser, Springer, Berlin 1978, Vol. 2, Ch. 4, p. 183
• [36] S.C. Gairola, Ind. J. Phys. 86, 967 (2012), doi: 10.1007/s12648-012-0164-5
• [37] C. Kittel, Quantum Theory of Solids, Wiley, New York 1963, Ch. 7
• [38] R.C. Shukla, E.R. Muller, Phys. Rev. B 21, 544 (1980), doi: 10.1103/PhysRevB.21.544
• [39] R.C. Shukla, Phys. Rev. B 22, 5810 (1980), doi: 10.1103/PhysRevB.22.5810
• [40] A.A. Maradudin, E.W. Montroll, G.H. Weiss, I.P. Ipatova, Solid State Physics, Theory of Lattice Dynamics in the Harmonic Approximation, Suppl. 3, 2nd ed., Academic Press, New York 1971, Ch. 2, p. 56
• [41] H. Frohlich, in: New Perspectives in Modern Physics, Ed. R.E. Marshak, Wiley, New York 1966, p. 539
• [42] H.Y. Fan, Elements of Solid State Physics, Wiley, New York 1987, p. 183 and 184
• [43] D. Feinberg, S. Ciuchi, F. de Pasquale, Int. J. Mod. Phys. B 4, 1317 (1990), doi: 10.1142/S0217979290000656
• [44] G.C. Mahanty, S.N. Behera, Can. J. Phys. 61, 1160 (1983), doi: 10.1139/p83-146
• [45] S.N. Behera, S.G. Mishra, Phys. Rev. B 31, 2773 (1985), doi: 10.1103/PhysRevB.31.2773
• [46] J.M. Ziman, Elements of Advanced Quantum Theory, Cambridge University Press, Cambridge 1969, Ch. 2, p. 38 and 43
• [47] P.K. Sharma, R. Bahadur, Phys. Rev. B 12, 1522 (1975), doi: 10.1103/PhysRevB.12.1522
• [48] D.N. Sahu, P.K. Sharma, Phys. Rev. B 28, 3200 (1983), doi: 10.1103/PhysRevB.28.3200
• [49] S. Srivastava, Y.P. Raiwani, S.C. Gairola, B.D. Indu, Physica B 223-224, 538 (1996), doi: 10.1016/0921-4526(96)00167-6
• [50] D.N. Zubarev, Usp. Fiz. Nauk 71, 71 (1960) [Eng. Transl. Sov. Phys. Usp. 3, 320 (1960)]
• [51] K.N. Pathak, Phys. Rev. 139, A1569 (1965), doi: 10.1103/PhysRev.139.A1569
• [52] M. Schowalter, A. Rosenauer, J.T. Titantah, D. Lamoen, Acta Cryst. A 65, 227 (2009), doi: 10.1107/S0108767309004966

Identifiers

DOI

10.12693/APhysPolA.129.1141