Molecular Dynamics Simulation of Thermal Conduction over SiliconGermanium Interface

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Molecular Dynamics Simulation of Thermal
Conduction over Silicon-Germanium Interface

• Ruxandra Costescu
• Erica Saltzman
• Zhi Tang

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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

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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).

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

• Periodic in lateral dimensions
• Hard-wall in longitudinal dimension

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Temperature Regulations

• Initial conditions hot, cold, and intermediate
  temperatures
• Velocity rescaling in hot and cold reservoirs

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Tersoff Potential
Parameters
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Calculations
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Results
Simulation results
Typical data

• At 120 K

Temperature profile
Thermal flux
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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)

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Results
Calculations

• Interface conductance results

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Results
Discussion

• ?SiGe(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?)

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Results
Improvements further study

• Fe (fictitious force)
• quantum correction
• direction of temperature gradient
• interface geometry
• compare t.c. results to exactly equivalent
  experimental data

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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/diffusi
  on/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.