Molecular Dynamics Simulation of Thermal Conduction over Silicon

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

Purpose n n n Thermal conductivity ( ) a measure of thermal transport behavior across interfaces is littleunderstood 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 n n 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: n n n 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 zerolimited 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 n n Periodic in lateral dimensions Hard-wall in longitudinal dimension

Temperature Regulations n n Initial conditions: hot, cold, and intermediate temperatures Velocity rescaling in hot and cold reservoirs

Tersoff Potential Parameters

Calculations

Results n Simulation results: Typical data At 120 K Temperature profile Thermal flux

Results n Calculations Thermal conductivity NOTES: • In addition: one run at 77. 1 K (with opposite direction of thermal gradient) and another run at 19. 1 K • Used: Fe= 0. 2 Å-1 (2)

Results n Calculations Interface conductance results

Results n n 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/(m 2 K) at 80 K reasonably close to calculated range of CSi/Ge Our values range from ~ 2 - 5 107 W/(m 2 K) the right order of magnitude of C Preliminary calculation for opposite direction of temp. gradient shows drastically different behavior (approximations fail? )

Results n n n 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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