Phonon Scatterings in the Lattice Thermal Conductivity of Si_(1-x) Ge_x Alloy Nanowires: Theoretical Study
American Journal of Nano Research and Applications
Volume 2, Issue 2, March 2014, Pages: 21-27
Received: Feb. 14, 2014; Published: Mar. 20, 2014
Views 3015      Downloads 187
Author
Soran Mohammed Mamand, Department of Physics, Faculty of Science and Science Education, University of Sulaimani, Sulaimanyah, Iraqi Kurdistan, Iraq
Article Tools
PDF
Follow on us
Abstract
Theoretical investigation of the alloy concentration and temperature dependences of the lattice thermal conductivity of silicon-germanium nanowires is performed using the Steigmeier and Abeles model. Phonon scattering processes are represented by frequency-dependent relaxation time approximation. In addition to the commonly considered acoustic three-phonon umklapp processes, phonon-boundary and point-defect scattering mechanisms are assumed. No distinction is made between longitudinal and transverse phonons. The importance of all the mechanisms involved in the model is clearly demonstrated. Analysis of the results shows that: (1) alloy scattering is the dominant scattering mechanism at intermediate and high temperatures; (2) thermal conductivity is mainly depends on the alloy concentration across the full range of temperatures; (3) weak diameter dependence of thermal conductivity is observed in Si_(1-x) Ge_x alloy nanowires; (4) the roughness of nanowires depends on the alloy concentration and has a major role in decreasing thermal conductivity at low temperatures; (5) the anharmonicity parameter is not size-dependent, as compared to Si and Ge nanowires. These findings provide new insights into the fundamental understanding of high-performance nanostructural semiconductors of relevance to optoelectronic and thermoelectric devices.
Keywords
SiGe Alloy, Lattice Thermal Conductivity, Phonon Scattering, Nanowires
To cite this article
Soran Mohammed Mamand, Phonon Scatterings in the Lattice Thermal Conductivity of Si_(1-x) Ge_x Alloy Nanowires: Theoretical Study, American Journal of Nano Research and Applications. Vol. 2, No. 2, 2014, pp. 21-27. doi: 10.11648/j.nano.20140202.12
References
[1]
M. Pitkethly, Materials Today 7 (Supplement 1) (2004)20.
[2]
C. Lieber and Z. L.Wang, Mat. Res. Bull. 32 (2007) 99.
[3]
E.Sutter and P. Sutter, Nano Lett. 8 (2008) 411.
[4]
CRC Handbook of Thermoelectrics, edited by D. Rowe (CRC, Boca Raton, FL, 1995).
[5]
G. S. Nolas, J. Sharp and H. Goldsmid, Thermoelectrics: Basic Principles and New Materials Developments (Springer, New York, 2001).
[6]
Thermoelectrics Handbook: Macro to Nano, edited by D. Rowe (CRC, Boca Raton, 2006).
[7]
A. Majumdar, Science 303 (2004) 777.
[8]
M. S. Dresselhaus, G. Chen, M. Y. Tang, R. G. Yang, H. Lee, D. Z. Wang, Z. F. Ren, J. P. Fleurial and P. Gogna, Adv. Mater. 19 (2007) 1043.
[9]
G. Joshi, H. Lee, Y. Lan, X. Wang, G. Zhu, D. Wang, R. W. Gould, D. C. Cuff, M. Y. Tang and M. S. Dresselhaus, Nano Lett. 8 (2008) 4670.
[10]
D. Li, Y. Wu, P. Kim, L. Shi, P.Yang and A. Majumdar, Appl. Phys. Lett. 83 (2003) 2934.
[11]
A. I. Boukai, Y. Bunimovich, J. Tahir-Kheli, J. K. Yu, W. A. Goddard and J. R. Heath, Nature 451 (2008) 168.
[12]
X. Liu, R. Wang, Y. Jiang, Q. Zhang, X. Shan and X. H. Qiu, Appl. Phys. 108 (2010) 54310.
[13]
I. Hochbaum, R. Chen, R. Delgado, W. Liang, E. Garnett, M. Najarian, A. Majumdar and P. Yang, Nature, 451 (2008) 163.
[14]
C. Wood, Rep. Prog. Phys. 51 (1988) 459.
[15]
C. Bhandari and D. Rowe, Contemp. Phys. 21 (1980) 219.
[16]
G. A. Slack and M. S. Hussain, J. Appl. Phys. 70 (1991) 2694.
[17]
C. Vining, J. Appl. Phys. 69 (1991) 331.
[18]
C. Vining, W. Laskow, J. Hanson, V. Beck and P. D. Gorsuch, Appl. Phys. 69 (1991) 4333.
[19]
D. Rowe, L. Fu and S. G. Williams, J. Appl. Phys. 73 (1993) 4683.
[20]
J. Martinez, P. Provencio, S. Picraux, J. Sullivan and B. Swartzentruber, Appl. Phys. 110 (2011) 074317.
[21]
H. Kim, I. Kim, H. Choi and Woochul Kim, Appl. Phys. Lett. 96 (2010) 233106.
[22]
E. Lee, L. Yin, Y. Lee, J. Lee, S. Lee, J. Lee, S. Cha, D. Whang, G. Hwang, K. Hippalgaonkar, A. Majumdar,Ch. Yu, B. Choi, J. Min Kim and K. Kim, Nano Lett. 12 (2012) 2918.
[23]
L. Yin, E. Lee, J. Lee, D. Whang, B. Choi and Ch. Yu, Appl. Phys. Lett. 101 (2012) 043114.
[24]
P. G. Klemens, Proc. Phys. Soc. LXVIII 12-A (1955), P-1113.
[25]
A. Balandin and K. Wang, Phys. Rev. B 58 (1998) 1544.
[26]
D. Cahill, W. Ford, K. Goodson, G. Mahan, A. Majumdar, H. Maris, R. Merlin and S. Phillpot, J. Appl. Phys. 93 (2003) 793.
[27]
E. Steigmeier and B. Abeles, Phys. Rev. 136 (1964) A1149.
[28]
J. Callaway, Phys. Rev. 113 (1957) 1046.
[29]
E. Steigmeier and L. Kudman, Phys. Rev. 1M(1963) 508.
[30]
R. E. Peierls, Ann. Phys. (Leipzig) 3 (1929) 1055.
[31]
P. Carruthers, Rev. of Mod. Phys. 33 (1961) 9.
[32]
G. Slack and S. Galginaitis, Phys. Rev. 133 (1964) A253.
[33]
J. Zou, D. Kotchetkov, A. Balandina, D. Florescub and F. Pollak, Appl. Phys. 92 (2002) 2534.
[34]
Zh. Wang and N. Mingo, Appl. Phys. Lett. 97 (2010) 101903.
[35]
B. Abeles, Phys. Rev. 131 (1963) 1906.
[36]
H. G. Casimir, Physica 5 (1938) 495.
[37]
R. Berman, F. E. Simon and J. M. Ziman, Proc. R. Soc. London, Ser. A 220 (1953) 171.
[38]
J. M. Ziman, Electrons and Phonons,Oxford University Press, New York,1967.
[39]
S. B. Soffer, J. Appl. Phys. 38 (1967) 1710.
[40]
J. Vandersande, Phys. Rev. B 15 (1977) 2355.
[41]
M. Kazan, G. Guisbiers, S. Pereira, M. Correia, A. Bruyant, S. Volz and P. Royer, Appl. Phys. 107 (2010) 083503.
[42]
S. Barman and G. Srivastava, Phys. Rev. B 73 (2006) 205308.
[43]
D. Morelli, J. Heremans, G. Slack, Phys. Rev. B 66 (2002) 195304.
[44]
S. M. Mamand, M.S. Omar , A.J. Muhammad, Mater. Res. Bull. 47 (2012) 1264.
[45]
A. Balandin, Phys. Low-Dim. Structure, 1/2 (2000) 1.
[46]
M. S. Omar and H. Taha, Sadhana (Indian Academy of Sciences), 35 (2010) 177.
[47]
S. M. Mamand and M. S. Omar, Adv. Mater. Res. 832 (2014) 33.
[48]
Y. Ezzahria and K. Joulain, J. Appl. Phys. 112 (2012) 083515.
[49]
A. Balerna and S. Mobilio, Phys. Rev. B 34 (1986) 2293.
[50]
J. Zou and A. Balandin, J. Appl. Phys. 89 (2001) 2932.
[51]
J. Zou, J. Appl. Phys. 108 (2010) 034324.
[52]
L. Liu and X. Chen, J. Appl. Phys.107 (2010) 033501.
[53]
G. A. Slack, Phys. Rev. 133 (1964) A253.
[54]
M. Asen-Palmer, K. Bartkowski, E. Gmelin, M. Cardona, A. Zhernov, A. Inyushkin, A. Taldenkov, V. Ozhogin, K. Itoh and E. Haller, Phys. Rev. B 56 (1997) 9431.
[55]
P. Martin, Z. Aksamija, E. Pop and U. Ravaioli, Phys. Rev. Lett. 102 (2009) 125503.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186