Electron-phonon coupling in transition metals beyond Wang's approximation

The electron-phonon coupling is the primary mechanism responsible for material relaxation after ultrafast laser irradiation. However, it remains an elusive variable that is extremely challenging to extract experimentally, especially at high electron temperatures. Various previous theoretical approaches to determine electron-phonon coupling demonstrated large degree of inconsistency. In this paper, we present a first-principles framework for simulating the electron-phonon coupling parameter based on the electron-phonon spectral function, going beyond the approximation introduced by Wang et al. [Phys. Rev. B 50, 8016 (1994)0163-182910.1103/PhysRevB.50.8016]. Our simulations provide electron-temperature-dependent electron-phonon coupling values for transition metals Ru, Pd, and Au. Our findings reveal significant differences between the values obtained from the exact and approximated spectral functions, thus highlighting the limitations of Wang's approximation at elevated electron temperatures.</p

X-ray standing wave characterization of the strong metal–support interaction in Co/TiOx model catalysts

The strong metal–support interaction (SMSI) is a phenomenon observed in supported metal catalyst systems in which reducible metal oxide supports can form overlayers over the surface of active metal nanoparticles (NPs) under a hydrogen (H2) environment at elevated temperatures. SMSI has been shown to affect catalyst performance in many reactions by changing the type and number of active sites on the catalyst surface. Laboratory methods for the analysis of SMSI at the nanoparticle-ensemble level are lacking and mostly based on indirect evidence, such as gas chemisorption. Here, we demonstrate the possibility to detect and characterize SMSIs in Co/TiOx model catalysts using the laboratory X-ray standing wave (XSW) technique for a large ensemble of NPs at the bulk scale. We designed a thermally stable MoNx/SiNx periodic multilayer to retain XSW generation after reduction with H2 gas at 600°C. The model catalyst system was synthesized here by deposition of a thin TiOx layer on top of the periodic multilayer, followed by Co NP deposition via spare ablation. A partial encapsulation of Co NPs by TiOx was identified by analyzing the change in Ti atomic distribution. This novel methodological approach can be extended to observe surface restructuring of model catalysts in situ at high temperature (up to 1000°C) and pressure (≤3 mbar), and can also be relevant for fundamental studies in the thermal stability of membranes, as well as metallurgy

Role of heat accumulation in the multi-shot damage of silicon irradiated with femtosecond XUV pulses at a 1 MHz repetition rate

The role played by heat accumulation in multi-shot damage of silicon was studied. Bulk silicon samples were exposed to intense XUV monochromatic radiation of a 13.5 nm wavelength in a series of 400 femtosecond pulses, repeated with a 1 MHz rate (pulse trains) at the FLASH facility in Hamburg. The observed surface morphological and structural modifications are formed as a result of sample surface melting. Modifications are threshold dependent on the mean fluence of the incident pulse train, with all threshold values in the range of approximately 36-40 mJ/cm². Experimental data is supported by a theoretical model described by the heat diffusion equation. The threshold for reaching the melting temperature (45 mJ/cm²) and liquid state (54 mJ/cm²), estimated from this model, is in accordance with experimental values within measurement error. The model indicates a significant role of heat accumulation in surface modification processes

Effect of Atomic-Temperature Dependence of the Electron–Phonon Coupling in Two-Temperature Model

Ultrafast laser irradiation of metals can often be described theoretically with the two-temperature model. The energy exchange between the excited electronic system and the atomic one is governed by the electron–phonon coupling parameter. The electron–phonon coupling depends on both, the electronic and the atomic temperature. We analyze the effect of the dependence of the electron–phonon coupling parameter on the atomic temperature in ruthenium, gold, and palladium. It is shown that the dependence on the atomic temperature induces nonlinear behavior, in which a higher initial electronic temperature leads to faster electron–phonon equilibration. Analysis of the experimental measurements of the transient thermoreflectance of the laser-irradiated ruthenium thin film allows us to draw some, albeit indirect, conclusions about the limits of the applicability of the different coupling parametrizations

Modeling of XUV-induced damage in Ru films: the role of model parameters

We perform a computational study of damage formation in extreme ultraviolet (XUV)-irradiated ruthenium thin films by means of combining the Monte Carlo approach with the two-temperature model. The model predicts that the damage formation is most affected by ultrafast heating of the lattice by hot electrons, and is not very sensitive to the initial stage of the material excitation. Numerical parameters of the model were analyzed, as well as different approximations for the thermal parameters, showing the importance of the temperature dependence of the electron thermal conductivity and the electron–phonon coupling factor. Our analysis reveals that the details of photoabsorption and ultrafast non-equilibrium electron kinetics play only a minor role in the XUV irradiation regime

Refined extreme ultraviolet mask stack model

A refined model of an extreme ultraviolet (EUV) mask stack consisting of the Mo/Si multilayer coated by a Ru protective layer and a TaBN/TaBO absorber layer was developed to facilitate accurate simulations of EUV mask performance for high-NA EUV photo-lithography (EUVL) imaging. The model is derived by combined analysis of the measured EUV and x ray reflectivity of an industry-representative mask blank. These two sets of measurements were analyzed using a combined free-form analysis procedure that delivers high-resolution x ray and EUV optical constant depth profiles based on self-adapted sets of sublayers as thin as 0.25 nm providing a more accurate description of the reflectivity than obtained from only EUV reflectivity. “Free-form analysis” means that the shape of the layer interfaces in the model is determined experimentally and is not given a priori by the structure model. To reduce the numerical effort for EUV imaging simulations, a low-resolution model of the multilayer and absorber stack with sublayer thicknesses larger than 2 nm, that fits to only the EUV reflectance, was derived from the high-resolution model. Rigorous high-NA EUVL simulations were done to compare the performance of the new model to our previous work