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Analytical solution for temperature field in thin film initially heated by a short-pulse laser source

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Abstract

Analytical solution for electron and lattice temperature distribution in the solid initially heated by a laser short-pulse is presented. Strained parameters method is introduced when formulating electron and lattice temperature distributions. Laser short pulse heating of gold film is simulated numerically and temperature data at the end of the heating pulse are adopted as initial condition to the governing equations of energy transport for analytical solutions. This enables to solve the governing equations of energy analytically in the cooling period. It is found that electron temperature decays sharply while lattice site temperature increases gradually in the surface regions during the cooling cycle. As the depth from the surface increases change in both temperatures become gradual.

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Abbreviations

C e :

Electron specific heat capacity, J/m3 K

C l :

Lattice site specific heat capacity, J/m3 K

d:

= \(\frac{1} {\lambda }\), 1/m

G:

Electron–phonon coupling factor, W/m3 K

I 0 :

Peak power intensity, W/m2

k :

Thermal conductivity, W/mK

L :

Film thickness, m

m e :

Electron mass, kg

N :

Electron number density, 1/m3

r f :

Surface reflectivity

t :

= \( \frac{{\bar t}}{{C_{\text{e}} /G}} \)

\({\bar t}\) :

time, s

T e :

Electron temperature, K

T l :

Lattice site temperature, K

T o :

Reference temperature, K

\({\bar V}\) :

Electron mean velocity, m/s

x:

\( =\bar x\;d\)

\({\bar x}\) :

Distance along the x-axis, m

δ:

Absorption depth, (1/m)

α:

=\( \frac{{kd^2 }}{G}\)

ε :

= \( \frac{{C_{\text{e}} }} {{C_l }}\)

λ:

Electron mean free path, m

θ e :

= \( \frac{{T_{\text{e}} }}{{T_o }}\)

θ l :

= \( \frac{{T_l }}{{T_o }}\)

τ s:

Electron mean free time between electron and phonon coupling, s

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Acknowledgements

The authors acknowledge the support of King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for this work.

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Authors and Affiliations

  1. ME Department, KFUPM, Dhahran, Saudi Arabia

    B. S. Yilbas, M. Pakdemirli & S. Bin Mansoor

  2. ME Department, Celal Bayar University, Manisa, Turkey

    M. Pakdemirli

Authors
  1. B. S. Yilbas
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  2. M. Pakdemirli
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  3. S. Bin Mansoor
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Correspondence to B. S. Yilbas.

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Yilbas, B.S., Pakdemirli, M. & Mansoor, S.B. Analytical solution for temperature field in thin film initially heated by a short-pulse laser source. Heat Mass Transfer 41, 1077–1084 (2005). https://doi.org/10.1007/s00231-004-0607-4

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  • DOI: https://doi.org/10.1007/s00231-004-0607-4

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