Molecular Dynamics Simulation of Thermal Conduction over Silicon-Germanium Interface

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

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

11. 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)

12. Results Calculations • Interface conductance results

13. 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?)

14. 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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