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Research Papers: Micro/Nanoscale Heat Transfer

Influence of Inter- and Intraband Transitions to Electron Temperature Decay in Noble Metals After Short-Pulsed Laser Heating

[+] Author and Article Information
Patrick E. Hopkins

Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0346pehopki@sandia.gov

J. Heat Transfer 132(12), 122402 (Sep 17, 2010) (6 pages) doi:10.1115/1.4002295 History: Received July 02, 2009; Revised April 27, 2010; Published September 17, 2010; Online September 17, 2010

This work examines the effects of photonically induced interband excitations from the d-band to states at the Fermi energy on the electron temperature decay in noble metals. The change in the electron population in the d-band and the conduction band causes a change in electron heat capacity and electron-phonon coupling factor. In noble metals, due to the large d-band to Fermi energy separation, the contributions to electron heat capacity and electron-phonon coupling factor of intra- and interband transitions can be separated. The two temperature model describing electron-phonon heat transfer after short-pulsed laser heating is solved using the expressions for heat capacity and electron-phonon coupling factor after intra- and interband excitations, and the predicted electron temperature change of the intra- and interband excited electrons are examined. A critical fluence value is defined that represents the absorbed fluence needed to fill all available states at a given photon energy above the Fermi level. At high absorbed laser fluences and pulse energies greater than the interband transition threshold, the interband and intraband contributions to thermophysical properties differ and are shown to affect temporal electron temperature profiles.

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Copyright © 2010 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Schematic depicting intraband transition and various interband transitions in a noble metal in terms of electron density of states as a function of energy. The occupied energies are depicted by the shaded regions and the various transitions are represented as a filled circle to an unfilled circle. Whereas an intraband transition creates an electron/hole pair in the same band, an interband transition creates an electron/hole pair in different bands. The ITT is the minimum separation of the d-band edge from the Fermi energy at T=0. As the temperature is increased, photons with energies less than the ITT can excite an interband transition due to Fermi smearing which creates empty states in the s/p-bands below the Fermi energy.

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Figure 2

Number of available states in the conduction band, navailable (solid lines), as a function of temperature in Au and critical absorbed fluence required to excite enough electrons from the d-band to fill all the empty states in the conduction band, Ac (dashed lines)

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Figure 3

Predictions of (a) Ce(Te) and (b) G(Te) when only 50% and 25% of the available states 4.65 eV above the conduction band are filled; that is, when the absorbed fluence is only 50% or 25% of Ac. As the absorbed fluence decreases, the change in Ce(Te) and G(Te) from the case of no photonic excitation becomes less significant. In the limit of zero electrons excited from the d-band to empty states in the conduction band (i.e., nexcited=0), the predictions of Ce(Te) and G(Te) reduce to the case of no photonic excitation (i.e., “s+d band”).

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Figure 4

Change in temperature of electrons excited via inter- (dashed lines) and intraband (dotted lines) transitions in a 75 nm Au film irradiated with a 4.65 eV, 500 fs laser pulse assuming (a) 475 J m−2 absorbed fluence (approximately the critical fluence) and (b) 237 J m−2 absorbed fluence (approximately 50% of the critical fluence). This temperature change was calculated with the intra- (Eq. 13) and interband (Eq. 14) TTMs, and assumes that the pulse has been completely absorbed and the electron system is fully thermalized. The insets show calculations of the energy densities in the inter- and intraband excited electron systems.

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