3 Basic Concepts and Methods
1.2. fs-laser excitation of metal surfaces: the two temperature model
figure3.10.
1. Basic concepts
1.2. fs-laser excitation of metal surfaces: the two temperature model
The excitation of the metal surface due to fs-laser irradiation is discussed. Therefore, the macroscopic quantities reflection and absorption have to be correlated to a microscopic des-cription in terms of the interaction between the light field (respectively the photons) and the metal electrons. The absorption is due to the creation of electron-hole (e-h) pairs which thermalize via electron-electron scattering and cool down to thermal equilibrium with the phonon temperature because of electron-phonon scattering and diffusion. The temporal evo-lution of the transient electron and phonon temperatures Tel and Tph can be described via the two-temperature model, which is based on the following assumptions:
3
Figure 1.7.: Two-temperature model scheme (left) [Ani74] and an example for the transient electron and phonon surface temperatures Tel and Tph after fs-laser excitation of ruthenium with a 100 fs, 800 nm laser pulse and a fluence ofhFi= 60 J/m2. Electronic peak temperatures of several thousand Kelvin are achievable.
The absorption of light induces an instantaneously thermalized hot-electron distribution, represented by an electron heat bath, whose energy content is expressed by a Fermi-Dirac distribution with Tel. This electron heat bath transfers energy either to the substrate by thermal diffusion or to a phonon heat bath via electron-phonon coupling. The phonon heat bath is characterized by Tph of a Bose-Einstein distribution which represents the energy content in this subsystem. The scheme of the two coupled heat baths is depicted in Fig. 1.7.
The temporal evolution of the energy contents in the electronic and phononic sub-systems are represented by a set of coupled differential equations [Ani74]:
thermal diffusion e-ph coupling excitation
The first equation describes the temporal change in the energy content of the electron gas which is due to absorption of the laser pulseS(z, t), energy transfer to the latticeH(Tel, Tph) via electron-phonon coupling and due to transport into the bulk via diffusion. z denotes the distance from the surface into the bulk. It is sufficient to apply the calculations only to this
Figure 3.10: Scheme of the two-temperature model [215] and the time evolution of Tel and Tph after fs-laser excitation of ruthenium with a 100 fs, 800 nm laser pulse with a fluence of 60 J/m2. From [210].
If no heat transport by electron diffusion and no further energy supply takes place, Tel can only change by the electron-phonon coupling and equation 3.5 simplifies to
Cel(Tel)∂Tel
∂t =−G(Tel−Tph). (3.7)
If the electronic system is not yet thermalized, e.g. if electron and electron-phonon scattering take place on the same timescale, characterization only by a temperature is not suitable. In that case the electron distribution can be described by the Boltzmann transport equation under the relaxation-time approximation. The Boltzmann equation is divided into thermal and non-thermal parts [109]:
f =fnonthermal(E, t) +fthermal[Tel(t)]
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3.5 Dynamics in Bulk Materials
The thermal part fthermal corresponds to the Fermi-Dirac distribution and only de-pends on the temperature, whereas the non-thermal partfnonthermal depends on the electron density. The relaxation offnonthermal is governed by the differential equation
∂fnonthermal
where f0 is the primary electron distribution, δE = E −EF and τth a constant.
Energy is transferred from the non-thermalized distribution to the thermalized one, while energy is dissipated from fthermal to the lattice at the same time. The change in energy of the electron gas is given by
Cel(Tel)∂Tel
For surfaces covered with an adsorbate, the energy from excitation can also trigger reactions such as desorption, which is one of the most simple surface reactions. In surface science, a photon induced excitation is called “direct”, if the photons are absorbed by adsorbate molecules directly and “indirect” or “substrate-mediated”, if absorbed by the substrate.
Figure 3.11illustrates the energy flow between the different subsystems of an adsor-bate covered metal surface.
In case of direct photodesorption, photons couple directly to the dipole moment of the substrate-adsorbate bond or transition dipole moment of the substrate-adsorbate complex.
Coupling to the dipole moment leads to ladder-climbing (figure 3.12), which can be observed using IR-photons even at metal substrates (acting as IR-mirror). How-ever, this process is strongly hindered by the anharmonicity of the potential, which causes the vibrational level spacing to decrease with increasing vibrational quantum number, pushing some of the required transitions off-resonance as a consequence.
Nevertheless, IR-lasers can be tuned in resonance with an intramolecular adsorbate vibration and energy will be transfered by anharmonic coupling from the initially excited mode to the substrate-adsorbate vibration and to substrate phonons. This might also lead to desorption, if enough energy is accumulated in the substrate-adsorbate vibration [218].
Figure 3.11: Scheme of the energy flow at adsorbate covered metal surfaces after fs-laser excitation. Direct adsorption in the adsorbate can be neglected for thin atomic or molecular layers [21]. The laser pulse excites the electronic system, which can thermalize with the lattice. Surface reactions can be driven either by the electron or phonon system, the latter mechanism is slower. Modified from [217].
Direct excitation of the transition dipole moment and induction of an electronic transition (anlagous to the DIET7-mechanism, see page50below) dominates in the UV/vis range at semiconductor surfaces.
In contrast to semiconductors, metal surfaces have a high absorptivity for UV/vis light, thus preferring indirect mechanisms (absorption in thin atomic or molecular adsorbate layers can be neglected). Indirect processes involve two steps: Initial absorption of the photons by the substrate and subsequent energy transfer to the adsorbate. Direct and indirect processes can be discriminated experimentally by the dependence of the desorption yield on the polarization of the light. The cross section for direct excitation is highest for light polarized along the dipole/transition dipole moment of the bond to be broken, whereas for indirect routes (substrate mediated) the polarization plays only a minor role [219].
Since the indirect, substrate mediated routes are dominant for optical excitations at metal surfaces and metal clusters are studied within the presented work, a brief overview over these mechanisms will be given. In a simplified picture, a metal sub-strate can be viewed as consisting of two heat baths, the lattice and the electron gas (section3.5.2). Each of these subsystems can couple independently to the adsorbate and transfer energy, which was originally gained by photoexcitation and distributed among the different subsystems as depicted in figures3.8 and 3.11. Desorption can then be driven by different processes:
7DIET: desorption induced by electronic transitions
3.5 Dynamics in Bulk Materials
• The conventional picture for the desorption process is given by an electronically adiabatic8 energy transfer in the electronic ground state of the system and is called ladder climbing process (figure 3.12): Substrate and adsorbate atoms are coupled by their vibrations, until enough kinetic energy is accumulated in the adsorbate to overcome the barrier towards desorption. Both systems are in thermal equilibrium. The reaction rate k for thermally activated processes depends nonlinear on the temperature and is usually given by an Arrhenius-like equation of the form k = ν0·eEdeskB T, where Edes is the activation energy necessary for desorption and ν0 the so-called “attempt” frequency. The CO-desorption from a Ru-surface was explained by this mechanism [220,221].