molecular dynamics simulation of thermal conduction over silicon-germanium interface

Molecular Dynamics Simulation of Thermal Conduction over Silicon-Germanium Interface

Ruxandra CostescuErica Saltzman

Zhi Tang

Purpose Thermal conductivity () a measure of

thermal transport behavior across interfaces is little-

understood and drastically different from bulk behavior; interface thermal conductance (C) is significant for ultra-thin films (~100 nm).

Si and Ge are important to semiconductor and microelectronics industries

Previous Research

Multilayer and superlattice structures have been investigated experimentally and through simulation, but the behavior across a single-interface remains poorly described and explained (4).

Several MD methods have been attempted: Direct MD, which exhibits inefficient convergence (2) Equilibrium MD, which is strongly dependent on the initial

conditions and has a slowly-converging autocorrelation function (2).

MD with non-equilibrium thermodynamics (thermostat and zero-limited thermal force) yields best results (11).

Geometry

Visualization of silicon-germanium beam. Yellow spheres represent germanium atoms; green spheres represent silicon atoms.

Hot and cold baths in silicon-germanium beam.

Boundary Conditions Periodic in lateral dimensions Hard-wall in longitudinal dimension

Temperature Regulations Initial conditions: hot, cold, and

intermediate temperatures Velocity rescaling in hot and cold

reservoirs

Tersoff Potential

Parameters

Calculations

ResultsSimulation results:

Temperature profile Thermal flux

Typical data

At 120 K

Thermal conductivity

T (K) 62.9 80.8 142 146 164

(W m-1 K-1) 0.358 0.430 0.264 0.278 0.305

eq (W m-1 K-1) 0.420 0.482 0.616 0.621 0.633

NOTES:•In addition: one run at 77.1 K (with opposite direction of thermal gradient) and another run at 19.1K •Used: Fe= 0.2 Å-1 (2)

Results CalculationsResults

Results Interface conductance results

Calculations

1.00E+06

1.00E+07

1.00E+08

1.00E+09

50 70 90 110 130 150 170

Temperature (K)

Th

erm

al c

on

du

ctan

ce (

W m

-2 K

-1)

~DMM

Results

Si+Ge(MD) smaller than eq as expected and the right order of magnitude; but dependence on temperature unclear

DMM prediction of ~108 W/(m2 K) at 80 K reasonably close to calculated range of CSi/Ge

Our values range from ~ 2 - 5 107 W/(m2 K) the right order of magnitude of C

Preliminary calculation for opposite direction of temp. gradient shows drastically different behavior (approximations fail?)

Discussion

Results

Fe (“fictitious force”) quantum correction direction of temperature gradient interface geometry compare t.c. results to exactly

equivalent experimental data

Improvements & further study

References1. 1. S.M. Lee, D.G. Cahill, and R. Venkatasubramanian, Appl. Phys. Lett. 70 22 (1997) 2957. 2. 2. S. Berber, Y.K. Kwon, and D. Tomanek, Phys. Rev. Lett. 84 20 (2000) 4613. 3. 3. D.G. Cahill, A. Bullen, and S.-M. Lee, High temp. - High press. 32 (2000) 134. 4. 4. S. Volz, J.B. Saulnier, G.Chen, and P. Beauchamp, Microelect. J. 75 14 (1999) 2056. 5. 5. J. Zi, K. Zhang and X. Xie, Appl. Phys. Lett. 57 2 (1990) 165. 6. 6. S.Q. Zhou, G. Chen, J.L. Liu, X.Y. Zheng, and K.L. Wang, HTD Proc. of ASME Heat Transfer Division 361-4

(1998) 249. 7. 7. M. Dornheim and H. Teichler, Phys. Stat. Sol. (A) 171 (1999) 267. 8. 8. M.A. Osman and D. Srivastava, Nanotechn. 12 (2001) 21. 9. 9. J. Che, T. Cagin, and W. A. Goddard, Nanotec. 11 (2000) 65. 10. 10. S.G. Volz and G. Chen, Appl. Phys. Lett. 75 14 (1999) 2056. 11. 11. A. Maeda and T. Munakata, Phys. Rev. E, 52 1 (1995) 234. 12. 12. A. Maiti, G.D. Mahan, and S.T. Pantelides, Solid-State Communications 102 7 (1997) 517. 13. 13. S. Petterson and G.D. Mahan, Phys. Rev. B, 42 12 (1990) 7386. 14. 14. R. Stoner and H.J. Maris, Phys. Rev. B, 48 22 (1993) 16373.

15. 15. E.T. Swartz and R.O. Pohl, Rev. Mod. Phys., 61 (1989) 605.

16. 16. S. Matsumoto, S. Munejiri, and T. Itami, National Space Development Agency of Japan, Space Utilization Program Document. Available URL: http://jem.tksc.nasda.go.jp/utiliz/surp/ar/diffusion/3_6_.pdf.

17. 17. J. Tersoff, Phys. Rev. B, 37 (1988) 6991. 18. 18. J. Tersoff, Phys. Rev. B, 39 (1989) 5566. 19. 19. D.W. Brenner, Phys. Rev. B, 42 (1990) 9458. 20. 20. Theoretical Biophysics Group, University of Illinois, "VMD - Visual Molecular Dynamics". Available URL:

http://www.ks.uiuc.edu/Research/vmd.