We present a theoretical study of the thermal conductivity of amorphous silicon (a-Si) based on molecular and lattice dynamics. We find that the majority of heat carriers are quasi-stationary modes; however the small proportion of propagating vibrations contributes to about half of the value of . We show that in bulk samples the mean free path of several long-wavelength modes is on the order of microns; this value may be substantially decreased either in thin films or in systems with etched holes, resulting in a smaller thermal conductivity. Our results provide a unified explanation of several experiments and show that kinetic theory cannot be applied to describe thermal transport in a-Si at room temperature.
REFERENCES
1.
H.
Wada
and T.
Kamijoh
, Jpn. J. Appl. Phys., Part 2
35
, L648
(1996
).2.
B. L.
Zink
, R.
Pietri
, and F.
Hellman
, Phys. Rev. Lett.
96
, 055902
(2006
).3.
H. -S.
Yang
, D. G.
Cahill
, X.
Liu
, J. L.
Feldman
, R. S.
Crandall
, B. A.
Sperling
, and J. R.
Abelson
, Phys. Rev. B
81
, 104203
(2010
).4.
D. G.
Cahill
, M.
Katiyar
, and J. R.
Abelson
, Phys. Rev. B
50
, 6077
(1994
).5.
B. S. W.
Kuo
, J. C. M.
Li
, and A. W.
Schmid
, Appl. Phys. A
55
, 289
(1992
).6.
S.
Moon
, M.
Hatano
, M.
Lee
, and C. P.
Grigoropoulos
, Int. J. Heat Mass Transfer
45
, 2439
(2002
).7.
X.
Liu
, J. L.
Feldman
, D. G.
Cahill
, R. S.
Crandall
, N.
Bernstein
, D. M.
Photiadis
, M. J.
Mehl
, and D. A.
Papaconstantopoulos
, Phys. Rev. Lett.
102
, 035901
(2009
).8.
L.
Wieczorek
, H. J.
Goldsmid
, and G. L.
Paul
, in Thermal Conductivity
, edited by D. P. H.
Hasselman
and J. R.
Thomas
(Plenum
, New York
, 1989
), Vol. 20
, p. 235
.9.
J. L.
Feldman
, P. B.
Allen
, and S. R.
Bickham
, Phys. Rev. B
59
, 3551
(1999
).10.
P. B.
Allen
and J. L.
Feldman
, Phys. Rev. B
48
, 12581
(1993
).11.
Y. H.
Lee
, R.
Biswas
, C. M.
Soukoulis
, C. Z.
Wang
, C. T.
Chan
, and K. M.
Ho
, Phys. Rev. B
43
, 6573
(1991
).12.
M. S.
Love
and A. C.
Anderson
, Phys. Rev. B
42
, 1845
(1990
).13.
J. J.
Freeman
and A. C.
Anderson
, Phys. Rev. B
34
, 5684
(1986
).14.
J. L.
Feldman
, M. D.
Kluge
, P. B.
Allen
, and F.
Wooten
, Phys. Rev. B
48
, 12589
(1993
).15.
J.
Fabian
and P. B.
Allen
, Phys. Rev. Lett.
77
, 3839
(1996
).16.
D. 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
).17.
R. O.
Pohl
, X.
Liu
, and E.
Thompson
, Rev. Mod. Phys.
74
, 991
(2002
).18.
G. A.
Slack
, in CRC Handbook of Thermoelectrics
, edited by D. M.
Rowe
(CRC Press
, Boca Raton, FL
, 1995
), p. 407
.19.
D. A.
McQuarrie
, Statistical Mechanics
(University Science Books
, Sausalito, CA
, 2000
), p. 641
.20.
F.
Müller-Plathe
, J. Chem. Phys.
106
, 6082
(1997
).21.
J.
Tersoff
, Phys. Rev. B
39
, 5566
(1989
).22.
Crystalline Si was heated up to 3500 K, then rapidly cooled down to 1400 K, and annealed for about 20 ns before the final quench to 300 K.
23.
D. P.
Sellan
, E. S.
Landry
, J. E.
Turney
, A. J. H.
McGaughey
, and C. H.
Amon
, Phys. Rev. B
81
, 214305
(2010
).24.
L.
Wei
, M.
Vaudin
, C. S.
Hwang
, G.
White
, J.
Xu
, and A. J.
Steckl
, J. Mater. Res.
10
, 1889
(1995
).25.
In a disordered system, at , except for the three acoustic modes; however, inspection of dispersion curves shows that low frequency modes are indeed propagating and one can define an interval in proximity of over which is well-defined and finite. We defined effective group velocities as , without taking the limit .
26.
where is computed as a function of the mode amplitude, by projecting the atomic displacements of MD trajectories on eigenmode .
27.
J. E.
Turney
, E. S.
Landry
, A. J. H.
McGaughey
, and C. H.
Amon
, Phys. Rev. B
79
, 064301
(2009
).28.
Y.
He
, D.
Donadio
, J. -H.
Lee
, J.
Grossman
, and G.
Galli
, ACS Nano
5
, 1839
(2011
).© 2011 American Institute of Physics.
2011
American Institute of Physics
You do not currently have access to this content.