Heat and Mass Transfer

, Volume 46, Issue 11–12, pp 1287–1293 | Cite as

Thermal analysis of thin multi-layer metal films during femtosecond laser heating

  • A. Karakas
  • M. Tunc
  • Ü. CamdaliEmail author


Multi-layer metals films are widely used in modern engineering applications such as gold-coated metal mirrors used in high power laser systems. A transient heat flux model is derived to analyze multi-layer metal films under laser heating. The two separate system composed of electrons and the lattice is considered to take into account the electron–lattice interaction. The present model predicted the effects of underlying chromium’s thermal properties on temperature rise of the top gold layer. The effects of two adjacent and different metals with different electron–lattice coupling factors are analyzed for the heating mechanism of different lattices. The derived transient model combined with the two different conservation equations for the lattice and electrons are applied for the ultra short-pulse laser heating of a multi-layer film composed of gold and chromium.


Laser Heating Lattice Temperature Chromium Layer Thin Metal Film Boltzmann Transport Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Heat capacity (J m−3 K−1)


Electron lattice coupling factor (W m−3 K−1)


Laser pulse intensity (J m−3)


Boltzmann constant (J K−1)


Film thickness (m)


Heat flux (W m−2)


Surface reflectivity


Source term (W m−3)


Time (s)


Laser pulse duration (s)


Temperature (K)


Spatial coordinate (m)

Greek symbols


Radiation penetration depth (m)


Thermal conductivity (W m−1 K−1)


Electron relaxation time (s)








The authors would like to acknowledge Deniz Seker, M.S. for his contribution on computer applications.


  1. 1.
    Qiu TQ, Tien CL (1992) Short-pulse laser heating of metals. Int J Heat Mass Transfer 35:719–726CrossRefGoogle Scholar
  2. 2.
    Qiu TQ, Tien CL (1994) Femtosecond laser heating of multi layer metals. I. Analysis. Int J Heat Mass Transfer 37(17):2789–2797CrossRefGoogle Scholar
  3. 3.
    Majumdar A (1998) Microscale energy transport in solids. In: Tien CL, Majundar A, Gerner FM (eds) Microscale energy transport. Taylor & Francis, Washington, DC, pp 3–93Google Scholar
  4. 4.
    Yilbas BS (2002) Short-pulse laser heating of gold–chromium layers: thermo-elasto-plastic analysis. J Phys D Appl Phys 35:1210–1217CrossRefGoogle Scholar
  5. 5.
    Musikant S (1985) Optical materials: an introduction to selection and application. Marcel-Dekker, New YorkGoogle Scholar
  6. 6.
    Joseph EE, Presiozi L (1989) Heat waves. Rev Mod Phys 61:41–73zbMATHCrossRefGoogle Scholar
  7. 7.
    Maurer MJ (1969) Relaxation model for heat conduction in metals. J Appl Phys 40(13):5123–5130CrossRefGoogle Scholar
  8. 8.
    Kaganov MI, Lifshitz IM, Tanatarov LV (1957) Relaxation between electrons and the crystalline lattice. Sov Phys JETP 4:173–178zbMATHGoogle Scholar
  9. 9.
    Anisimov SI, Kapeliovich BL, Perel’man TL (1974) Electron emission from metal surfaces exposed to ultra short laser pulses. Sov Phys JETP 39:375–377Google Scholar
  10. 10.
    Qiu TQ, Tien CL (1993) Heat transfer mechanisms during short-pulse laser heating of metals. ASME J Heat Transfer 115:835–842CrossRefGoogle Scholar
  11. 11.
    Ziman JM (1965) Principles of the theory of solids. Cambridge University Press, CambridgeGoogle Scholar
  12. 12.
    Yilbas BS (2001) Material response to thermal loading due to short pulse laser heating. Int J Heat Mass Transfer 44:3787–3798zbMATHCrossRefGoogle Scholar
  13. 13.
    Yilbas BS (2002) Laser short-pulse heating of gold–copper two-layer assembly: thermo-elasto-plastic analysis. Jpn J Appl Phys 41:5226–5234CrossRefGoogle Scholar
  14. 14.
    Wilson AH (1954) The theory of metals, 2nd edn. Cambridge University Press, New YorkGoogle Scholar
  15. 15.
    Ziman JM (1960) Electrons and phonons: the theory of transport phenomena in solids. Clarendon Press, OxfordzbMATHGoogle Scholar
  16. 16.
    Majumdar A (1993) Microscale heat conduction in dielectric thin films. ASME J Heat Transfer 115:7–16CrossRefGoogle Scholar
  17. 17.
    Goodson KE (1996) Thermal conduction in nonhomogeneous CVD diamond layers in electronic microstructures. ASME J Heat Transfer 118:279–286CrossRefGoogle Scholar
  18. 18.
    Fujimoto JG, Liu JM, Ippen EP (1984) Femtosecond laser interaction with metallic tungsten and nonequilibrium electron and lattice temperatures. Phys Rev Lett 53:1840–1847CrossRefGoogle Scholar
  19. 19.
    Elsayed-Ali HE, Norris TB, Pessot MA, Mourou GA (1987) Time resolved observation of electron–phonon relaxation in copper. Phys Rev Lett 58:1212–1215CrossRefGoogle Scholar
  20. 20.
    Brorson SD, Fujimoto JG, Ippen EP (1987) Femtosecond electronic heat transfer dynamics in thin gold film. Phys Rev Lett 59:1062–1065CrossRefGoogle Scholar
  21. 21.
    Allen PB (1987) Theory of thermal relaxation of electrons in metals. Phys Rev Lett 59:1460–1463CrossRefGoogle Scholar
  22. 22.
    Elsayed-Ali HE, Jushasz T (1993) Femtosecond time-resolved thermomodulation of thin gold films with different crystal structures. Phys Rev B 47:13599–13610CrossRefGoogle Scholar
  23. 23.
    Eesley GL (1986) Observation of nonequilibrium electron and lattice temperatures in copper by picosecond laser pulses. Phys Rev B 33:2144–2151CrossRefGoogle Scholar
  24. 24.
    Scouler WJ (1967) Temperature modulated reflectance of gold from 2 to 10 eV. Phys Rev Lett 18:445–448CrossRefGoogle Scholar
  25. 25.
    Chapman S, Cowling TG (1953) The mathematical theory of non-uniform gases. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.University of California at DavisDavisUSA
  2. 2.Department of System EngineeringYeditepe UniversityIstanbulTurkey
  3. 3.Mechanical Engineering Department, Faculty of Engineering and ArchitectureAbant Izzet Baysal UniversityBoluTurkey

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