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Thermal conductivity and its anisotropy research of germanium thin film

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Abstract

Germanium is an important element in semiconductor and microelectronics industries. Its thermal conductivity is an invariable and isotropic parameter in germanium crystal in the same temperature and its thermal conductivity is difficult to be measured in thin film. In the present paper, using the non-equilibrium molecular dynamics simulation method and Stillinger–Weber potential model, the normal and tangential thermal conductivity of germanium thin film are studied. There are remarkable anisotropy and size effect of thermal conductivity in normal and tangential direction of germanium thin film. In the theoretical analysis, Boltzmann transport theory is used to analyze the phonon transport in germanium thin film. Theoretical results further demonstrate the anisotropy and size effect of thermal conductivity in thin film, which indicate the significant decrease of phonon mean free path and predominant boundary phonon scattering in germanium thin film.

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Abbreviations

A :

Heat transfer area potential experiment parameter

B :

Potential experiment parameter

c :

Heat specific per unit volume

d :

Thickness of thin film

ΔE k,in :

High temperature wall heat quantity

ΔE k,out :

Low temperature wall heat quantity

F ij :

Acting force of atom j on atom i

F :

Decrement gene

k :

Thermal conductivity

k B :

Boltzmann constant number

L b :

Casimir length of the crystal

l :

Phonon mean free path

m :

Atom mass

N L :

The atom number in L layer

r ij :

Distance of atom i and j

r cut :

Cutoff distance of the potential

R :

Dubey model experiment parameter

T L,MD :

Average temperature in L layer

T w :

Reservoir temperature

t :

Time step

U :

Total potential

u :

Potential

v :

Atom velocity

∇T :

Temperature gradient

σ :

Potential experiment parameter

τ :

Relaxation time

α :

Wall scattering energy transmission coefficient

δ :

Reduced thickness, δ = d/l ∞

η :

Potential experimental parameter

γ :

Potential experimental parameter

θ jik :

Angle between r ij and r ik

θ1, θ2, θ3, θ4 :

Integration parameters

ω1, ω2:

Transverse phonons frequencies

ω1, ω4:

Longitudinal phonons frequencies

i, j, k:

Different atom

T:

Transverse phonons

L:

Longitudinal phonons

eff :

Film valid parameter

∞:

Bulk crystal parameter

w:

Reservoir or wall

C, T:

Combined relaxation rates for transverse phonons

C, L:

Combined relaxation rates for longitudinal phonons

T1, T2:

Transverse phonons

L1, L2:

Longitudinal phonons

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Acknowledgments

The authors appreciate the support of Major State Basic Research Development Program of China (2009GB104001) and Dean Fund of Graduate University of Chinese Academy of Sciences (085101DM03).

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Authors and Affiliations

  1. College of Physical Sciences, Graduate University of Chinese Academy of Sciences, 100049, Beijing, China

    Z. H. Wang & M. J. Ni

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  1. Z. H. Wang
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  2. M. J. Ni
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Correspondence to Z. H. Wang.

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Wang, Z.H., Ni, M.J. Thermal conductivity and its anisotropy research of germanium thin film. Heat Mass Transfer 47, 449–455 (2011). https://doi.org/10.1007/s00231-010-0731-2

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  • DOI: https://doi.org/10.1007/s00231-010-0731-2

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