Molecular Dynamics Simulation of Thermal Conductivity of Si/SiGe Nanowire Superlattice

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Molecular Dynamics Simulation of Thermal
Conductivity of Si/SiGe Nanowire Superlattice

• Yongxing Shen1, Annica Heyman2, and Ningdong
  Huang2
• Departments of Materials Science and Engineering1
  and Applied Physics2
• Stanford University, CA 94305

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Introduction
Si / SiGe Nanowire Superlattices
(other names bamboo structures, axial
heterostructures)
1623 Å
38 Å
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Why Low Thermal Conductivity?
Definition

• Si / SiGe nanowire superlattices have phonon
  scattering centers like
• Imperfections (Ge)
• Surface
• Interfaces

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Earlier Experimental Results
(Li, et al, Appl. Phys. Lett. 2001)
kSi bulk 241 W/mK at 200 K
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Our Primary Goal
To study the interfacial effect on thermal
conductivity (k) of Si / SiGe nanowire
superlattice by comparing ks of
and
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Thermal Conductivity
J ?
T T1
T T2 lt T1
? T
Temperature gradient K/m
J - k ? T
Heat current W/m2 J/m2s
Thermal conductivity W/mK
But this is all in non-equilibrium .
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Fluctuation-Dissipation Theorem
Fully developed in the 1950s by R. Kubo.
Provides general relationship between
Internal fluctuations in the absence of
disturbance
Response of system to external disturbance

• Non-equilibrium
• Characterized by a response function

• Equilibrium
• Characterized by a correlation function (of
  relevant quantity)

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Calculating k using the FDT
Thermal conductivity
(a x, y, or z)
or
and Ei (Ekin)i (Epot)i
with
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Technical Details
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Simulations Steps

• Create initial structure
• Relax at T 0 K (conjugate gradient method)
• Equilibrate at T 300 K using Langevin dynamics
• Run at constant energy (NVE) to extract qa(t)
• Calculate k from q
• Repeat for different supercell sizes (for
  convergence) and different compositions,
  diameters, block lengths and structures (for real
  data)