Thermal conductivity of ZnTe nanowires Keivan Davami, Annie Weathers, Nazli Kheirabi, Bohayra Mortazavi, Michael T. Pettes et al. Citation: J. Appl. Phys. 114, 134314 (2013); doi: 10.1063/1.4824687 View online: http://dx.doi.org/10.1063/1.4824687 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v114/i13 Published by the AIP Publishing LLC. Additional information on J. Appl. Phys. Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors
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Thermal conductivity of ZnTe nanowiresKeivan Davami, Annie Weathers, Nazli Kheirabi, Bohayra Mortazavi, Michael T. Pettes et al. Citation: J. Appl. Phys. 114, 134314 (2013); doi: 10.1063/1.4824687 View online: http://dx.doi.org/10.1063/1.4824687 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v114/i13 Published by the AIP Publishing LLC. Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors
Michael T. Pettes,2,a) Li Shi,2,5 Jeong-Soo Lee,1 and M. Meyyappan1,6,b)
1Department of IT Convergence Engineering, Pohang University of Science and Technology (POSTECH),Pohang, South Korea2Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas, USA3Centre de Recherche Public Henri Tudor, Department of Advanced Materials and Structures, 66,rue de Luxembourg BP 144, L-4002 Esch/Alzette, Luxembourg4Institut de M�ecanique des Fluideset des Solides, University of Strasbourg/CNRS, 2 Rue Boussingault,67000 Strasbourg, France5Center for Nano and Molecular Science and Technology, Texas Materials Institute,The University of Texas at Austin, Austin, Texas, USA6NASA Ames Research Center, Moffett Field, California 94035, USA
(Received 21 May 2013; accepted 24 September 2013; published online 4 October 2013)
The thermal conductivity of individual ZnTe nanowires (NWs) was measured using a suspended
micro-bridge device with built-in resistance thermometers. A collection of NWs with different
diameters were measured, and strong size-dependent thermal conductivity was observed in these
NWs. Compared to bulk ZnTe, NWs with diameters of 280 and 107 nm showed approximately
three and ten times reduction in thermal conductivity, respectively. Such a reduction can be
attributed to phonon-surface scattering. The contact thermal resistance and the intrinsic thermal
conductivities of the nanowires were obtained through a combination of experiments and
molecular dynamic simulations. The obtained thermal conductivities agree well with theoretical
As a summary of our method, a reference nanowire with
Pt-C deposited on the contacts was considered. For this
nanowire, the parameter R0c in Eq. (7) with the units of W
m/K (the thermal resistance between the nanowire and the
contact per unit length) is estimated from the interface ther-
mal resistance per unit area, R00c (in W m2/K), obtained by the
MD simulation. The relation was assumed to be
R0c ¼R00c=ðNW DiameterÞ, since the nanowire was totally sur-
rounded by Pt-C in this case. Then Eqs. (7) and (8) were
used to calculate the R00c value for the nanowires without Pt-C
deposited on their contacts. The contact width b was needed
to obtain R0c for each individual nanowire without Pt-C depo-
sition, by scaling the calculated R00c value as R0c¼R00c=b.
Calculation results for most of the NWs revealed that
the contact thermal resistance was �20% of the total meas-
ured thermal resistance. However, this contribution
decreased to only 5% after deposition of Pt-C on the con-
tacts. The intrinsic thermal conductivities of NWs with dif-
ferent diameters at room temperature are compared with the
theoretical predictions of Mingo7 in Fig. 5. In this figure, the
effect of the contacts was calculated and extracted from
the results, and just the intrinsic thermal conductivity of the
ZnTe nanowires is shown.
The error in Fig. 5 was calculated using the following
method. The interfacial thermal resistance, R00c , using MD for
ZnTe/Pt interface was calculated. Even though the exact num-
ber for R00c for this interface was not available in the literature,
we note that the reported R00c for ZnTe/Pt interface as well as
other II-IV/Pt was in the order of 10�9 K m2/W in Ref. 31. R00cfor other metal/dielectric interfaces at room temperature was
reported to be in the range of 10�9-10�8 K m2/W.32 Also,
it is in the range of (1.5–1.8)� 10�8 K m2/W for the
Ge2SbTe5/ZnS:SiO2 interface.32 Assuming that R00c is in the
range of (1.55–3.55)� 10�8 K m2/W, and there is a 5% uncer-
tainty in thermal contact resistance, R, 3% in cross section
area, A, 3% in length, L, 5% in contact length, CL, and 5% in
contact width, CW, the following equation can be used to cal-
culate upper and lower error bars via a root sum square:
U�j ¼ �kint
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiUR00 c
R00 c
!2
þ U �R
�R
� �2
þ U �A
�A
� �2
þ U�L
�L
� �2
þUCL
CL
� �2
þUCW
CW
� �2
vuut ; (12)
where UR00c,U �R , U �A ;U�L ;UCL ;UCW are the uncertainties in the
interfacial thermal resistance, contact total thermal resistance
of the contacts (at both ends),cross section area, length, con-
tact length, and contact width, respectively.
The intrinsic thermal conductivity values of our samples
decrease for smaller NW diameters and the experimental
results agree with the theoretical model quite well. The
minor differences are due to the assumptions in the model
FIG. 5. Calculated intrinsic thermal conductivity (filled symbols), and theo-
retical values predicted by Mingo in Ref. 7 (unfilled symbols) versus diame-
ter at T¼ 300 K. Except for the NW with d¼ 280 nm, the reported intrinsic
thermal conductivity results for the rest of the NWs are calculated from the
measurements prior to Pt-C deposition.
134314-6 Davami et al. J. Appl. Phys. 114, 134314 (2013)
such as the ideal case of NW being pure ZnTe with a one to
one ratio between Zn and Te, while the VLS-grown NWs are
not exactly stoichiometric. Different compositions of the
NWs cause some discrepancy in their thermal conductivities.
As seen in this plot, the calculated intrinsic thermal conduc-
tivity for the nanowire with 145.6 nm diameter is more than
that for the diameter of 280 nm, which is attributed to the
aforementioned points.
IV. CONCLUSION
In summary, ZnTe nanowires were synthesized using a
VLS method and NWs with diameters in the range of
107 nm to 280 nm were assembled on micro-bridge devices
with integrated resistance thermometers, for measuring ther-
mal conductance at different temperatures before and after
the deposition of platinum on the contacts. The thermal
boundary resistance between ZnTe and Pt was estimated
using MD simulations, which was then used to calculate the
thermal contact resistance between the NWs and the micro-
bridge device to be around 20% and 5% of the total meas-
ured thermal resistance before and after Pt-C deposition,
respectively. The resulting intrinsic thermal conductivities at
room temperature showed strong size dependence, with an
order of magnitude decrease compared to bulk ZnTe for the
smallest NW with a diameter of 107 nm. The experimental
results are also in good agreement with theoretical predic-
tions in the literature for ZnTe NWs. The suppressed thermal
conductivity for small diameter NWs can be attributed to
phonon-surface scattering phenomena.
ACKNOWLEDGMENTS
This work was supported by the World Class University
program through the National Research Foundation of Korea
funded by the Ministry of Education, Science and Technology
under Project No. R31-2008-000-10100-0. Moreover, the
research was also partly supported by a grant (Code No. 2011-
0031638) from the Center for Advanced Soft Electronics
under the Global Frontier Research Program of the Ministry
of Education, Science and Technology, Korea. Most of this
work was done at UT Austin during Keivan Davami’s visit
and Professor Shi’s group is acknowledged for hosting the
visit. Bohayra Mortazavi greatly appreciates Dr. Toniazzo at
CRP Henri-Tudor for providing computational facilities.
1C. B. Vining, Nature 8, 83 (2009).2C. J. Vineis, A. Shakouri, A. Majumdar, and M. G. Kanatzidis, Adv.
Mater. 22, 3970 (2010).3T. M. Tritt, Annu. Rev. Mater. Res. 41, 433 (2011).4L. D. Hicks and M. S. Dresselhaus, Phys. Rev. B 47, 16631 (1993).5D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H.
J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).6L. Shi, NMTE 16, 79 (2012).7N. Mingo, Appl. Phys. Lett. 85, 5986 (2004).8N. Mingo, Appl. Phys. Lett. 84, 2652 (2004).9F. Zhou, J. H. Seol, A. L. Moore, L. Shi, Q. L. Ye, and R. Scheffler,
J. Phys.: Condens. Matter 18, 9651 (2006).10F. Zhou, A. L. Moore, J. Bolinsson, A. Persson, L. Froberg, M. T. Pettes,
H. Kong, L. Rabenberg, P. Caroff, D. A. Stewart, N. Mingo, K. A. Dick,
L. Sauelson, H. Linke, and L. Shi, Phys. Rev. B 83, 205416 (2011).11K. Davami, D. Kang, J. S. Lee, and M. Meyyappan, Chem. Phys. Lett.
504, 62 (2011).12K. Davami, H. M. Ghassemi, R. S. Yassar, J. S. Lee, and M. Meyyappan,
ChemPhysChem 13, 347 (2012).13K. Davami, B. Mortazavi, H. M. Ghassemi, R. S. Yassar, J. S. Lee, Y.
Remond, and M. Meyyappan, Nanoscale 4, 897 (2012).14D. Li, Y. Wu, P. Kim, L. Shi, P. Yang, and A. Majumdar, Appl. Phys.
Lett. 83, 2934 (2003).15C. Yu, S. Saha, J. Zhou, L. Shi, A. M. Cassell, B. A. Cruden, Q. Ngo, and
J. Li, J. Heat Transfer 128, 234 (2006).16J. H. Seol, A. L. Moore, S. K. Saha, F. Zhou, L. Shi, Q. L. Ye, R.
Scheffler, N. Mingo, and T. Yamada, J. Appl. Phys. 101, 023706 (2007).17M. T. Pettes and L. Shi, Adv. Funct. Mater. 19, 3918 (2009).18A. I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M.
Najarian, A. Majumdar, and P. Yang, Nature 451, 163 (2008).19L. Shi, D. Li, C. Yu, W. Jang, D. Kim, Z. Yao, P. Kim, and A. Majumdar,
J. Heat Transfer 125, 881 (2003).20G. A. Slack, Phys. Rev. B 6, 3791 (1972).21U. Philipose, A. Saxena, H. E. Ruda, P. J. Simpson, Y. Q. Wang, and K. L.
Kavanagh, Nanotechnology 19, 215715 (2008).22M. I. D. Hertog, C. Cayron, P. Gentile, F. Dhalluin, F. Oehler, T. Baron,
and J. L. Rouviere, Nanotechnology 23, 025701 (2012).23S. Plimpton, J. Comput. Phys. 117, 1 (1995).24M. B. Kanouna, A. E. Merada, H. Aouragb, J. Cibertc, and G. Merad,
Solid Sci. 5, 1211(2003).25H. Wang and W. Chu, J. Alloys Compd. 485, 488 (2009).26S. M. Foiles, M. I. Baskes, and M. S. Daw, Phys. Rev. B 33, 7983 (1986).27A. K. Rappe, C. J. Casewit, K. S. Colwell, W. A. Goddard, and W. M.
Skid, J. Am. Chem. Soc. 114, 10024 (1992).28M. T. Pettes, I. Jo, Z. Yao, and L. Shi, Nano Lett. 11, 1195 (2011).29R. Prasher, Phys. Rev. B 77, 075424 (2008).30F. Zhou, A. Persson, L. Samuelson, H. Linke, and L. Shi, Appl. Phys. Lett.
99, 063110 (2011).31H. Wang, Y. Xu, M. Shimono, Y. Tanaka, and M. Yamazaki, Mater.
Trans. 48, 2349 (2007).32E. K. Kim, S. I. Kwun, S. M. Lee, H. Seo, and J. G. Yoon, Appl. Phys.
Lett. 76, 3864 (2000).
134314-7 Davami et al. J. Appl. Phys. 114, 134314 (2013)