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Molecular Dynamics Simulation of Thermal Conduction over Silicon-Germanium Interface

Molecular Dynamics Simulation of Thermal Conduction over Silicon-Germanium Interface. Ruxandra Costescu Erica Saltzman Zhi Tang. Purpose. Thermal conductivity ( )  a measure of thermal transport

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Molecular Dynamics Simulation of Thermal Conduction over Silicon-Germanium Interface

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  1. Molecular Dynamics Simulation of Thermal Conduction over Silicon-Germanium Interface Ruxandra Costescu Erica Saltzman Zhi Tang

  2. 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

  3. 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).

  4. Geometry Visualization of silicon-germanium beam. Yellow spheres represent germanium atoms; green spheres represent silicon atoms. Hot and cold baths in silicon-germanium beam.

  5. Boundary Conditions • Periodic in lateral dimensions • Hard-wall in longitudinal dimension

  6. Temperature Regulations • Initial conditions: hot, cold, and intermediate temperatures • Velocity rescaling in hot and cold reservoirs

  7. Tersoff Potential Parameters

  8. Calculations

  9. Results Simulation results: Typical data • At 120 K Temperature profile Thermal flux

  10. Results Results Calculations • Thermal conductivity • 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)

  11. Results Calculations • Interface conductance results

  12. Results Discussion • 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?)

  13. Results Improvements & further study • Fe (“fictitious force”) • quantum correction • direction of temperature gradient • interface geometry • compare t.c. results to exactly equivalent experimental data

  14. References • 1. S.M. Lee, D.G. Cahill, and R. Venkatasubramanian, Appl. Phys. Lett. 70 22 (1997) 2957. • 2. S. Berber, Y.K. Kwon, and D. Tomanek, Phys. Rev. Lett. 84 20 (2000) 4613. • 3. D.G. Cahill, A. Bullen, and S.-M. Lee, High temp. - High press. 32 (2000) 134. • 4. S. Volz, J.B. Saulnier, G.Chen, and P. Beauchamp, Microelect. J. 75 14 (1999) 2056. • 5. J. Zi, K. Zhang and X. Xie, Appl. Phys. Lett. 57 2 (1990) 165. • 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. M. Dornheim and H. Teichler, Phys. Stat. Sol. (A) 171 (1999) 267. • 8. M.A. Osman and D. Srivastava, Nanotechn. 12 (2001) 21. • 9. J. Che, T. Cagin, and W. A. Goddard, Nanotec. 11 (2000) 65. • 10. S.G. Volz and G. Chen, Appl. Phys. Lett. 75 14 (1999) 2056. • 11. A. Maeda and T. Munakata, Phys. Rev. E, 52 1 (1995) 234. • 12. A. Maiti, G.D. Mahan, and S.T. Pantelides, Solid-State Communications 102 7 (1997) 517. • 13. S. Petterson and G.D. Mahan, Phys. Rev. B, 42 12 (1990) 7386. • 14. R. Stoner and H.J. Maris, Phys. Rev. B, 48 22 (1993) 16373. • 15. E.T. Swartz and R.O. Pohl, Rev. Mod. Phys., 61 (1989) 605. • 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. J. Tersoff, Phys. Rev. B, 37 (1988) 6991. • 18. J. Tersoff, Phys. Rev. B, 39 (1989) 5566. • 19. D.W. Brenner, Phys. Rev. B, 42 (1990) 9458. • 20. Theoretical Biophysics Group, University of Illinois, "VMD - Visual Molecular Dynamics". Available URL: http://www.ks.uiuc.edu/Research/vmd.

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