Six-dimensional potential energy surface for H2at Ru(0001)

A ReaxFF Molecular Dynamics Study of Hydrogen Diffusion in Ruthenium-The Role of Grain Boundaries

Ruthenium (Ru) thin films are used as protective caps for the multilayer mirrors in extreme ultraviolet lithography machines. When these mirrors are exposed to atomic hydrogen (H), it can permeate through Ru, leading to the formation of hydrogen-filled blisters on the mirrors. H has been shown to exhibit low solubility in bulk Ru, but the nature of H diffusion through Ru and its contribution to the mechanisms of blistering remain unknown. This work makes use of reactive molecular dynamics simulations to study the influence of imperfections in a Ru film on the behavior of H. For the Ru/H system, a ReaxFF force field which reproduces structures and energies obtained from quantum-mechanical calculations was parametrized. Molecular dynamics simulations have been performed with the newly developed force field to study the effect of tilt and twist grain boundaries on the overall diffusion behavior of H in Ru. Our simulations show that the tilt and twist grain boundaries provide energetically favorable sites for hydrogen atoms and act as sinks and highways for H. They therefore block H transport across their planes and favor diffusion along their planes. This results in the accumulation of hydrogen at the grain boundaries. The strong effect of the grain boundaries on hydrogen diffusion suggests tailoring the morphology of ruthenium thin films as a means to curb the rate of hydrogen permeation.

Tin, The Enabler-Hydrogen Diffusion into Ruthenium

Hydrogen interaction with ruthenium is of particular importance for the ruthenium-capped multilayer reflectors used in extreme ultraviolet (EUV) lithography. Hydrogen causes blistering, which leads to a loss of reflectivity. This problem is aggravated by tin. This study aims to uncover the mechanism via which tin affects the hydrogen uptake, with a view to mitigation. We report here the results of a study of hydrogen interaction with the ruthenium surface in the presence of tin using Density Functional Theory and charge density analyses. Our calculations show a significant drop in the energy barrier to hydrogen penetration when a tin atom or a tin hydride molecule (SnHx) is adsorbed on the ruthenium surface; the barrier has been found to drop in all tested cases with tin, from 1.06 eV to as low as 0.28 eV in the case of stannane (SnH₄). Analyses show that, due to charge transfer from the less electronegative tin to hydrogen and ruthenium, charge accumulates around the diffusing hydrogen atom and near the ruthenium surface atoms. The reduced atomic volume of hydrogen, together with the effect of electron⁻electron repulsion from the ruthenium surface charge, facilitates subsurface penetration. Understanding the nature of tin's influence on hydrogen penetration will guide efforts to mitigate blistering damage of EUV optics. It also holds great interest for applications where hydrogen penetration is desirable, such as hydrogen storage.

Quantum and classical dynamics of reactive scattering of H2 from metal surfaces

State-of-the-art theoretical models allow nowadays an accurate description of H₂/metal surface systems and phenomena relative to heterogeneous catalysis. Here we review the most relevant ones investigated during the last 10 years.

Concept of a single temperature for highly nonequilibrium laser-induced hydrogen desorption from a ruthenium surface

Laser-induced condensed phase reactions are often interpreted as nonequilibrium phenomena that go beyond conventional thermodynamics. Here, we show by Langevin dynamics and for the example of femtosecond-laser desorption of hydrogen from a ruthenium surface that light adsorbates thermalize rapidly due to ultrafast energy redistribution after laser excitation. Despite the complex reaction mechanism involving hot electrons in the surface region, all desorption product properties are characterized by equilibrium distributions associated with a single, unique temperature. This represents an example of ultrahot chemistry on the subpicosecond time scale.

Stochastic approach to laser-induced ultrafast dynamics: the desorption of H(2)/D(2) from Ru(0001)

The desorption of molecular hydrogen and deuterium induced by femtosecond-laser pulses is studied theoretically for the so-called DIMET (Desorption Induced by Multiple Electronic Transitions) process. These investigations are based on nonadiabatic classical Monte Carlo trajectory (CMCT) simulations on a ground and an excited state potential energy surface, including up to all six adsorbate degrees of freedom. The focus is on the hot-electron mediated energy transfer from the surface to the molecule and back, and the energy partitioning between the different degrees of freedom of the desorbing molecules. We first validate for a two-mode model comprising the desorption mode and the internal vibrational coordinate, the classical Monte Carlo trajectory method by comparing with Monte Carlo wavepacket (MCWP) calculations arising from a fully quantum mechanical open-system density matrix treatment. We then proceed by extending the CMCT calculations to include all six nuclear degrees of freedom of the desorbing molecule. This allows for a detailed comparison between theory and experiment concerning isotope effects, energy partitioning (translational, vibrational, and rotational energies and their distributions), and the dependence of these properties on the laser fluence. The most important findings are as follows. (i) CMCT agrees qualitative with the MCWP scheme. (ii) The basic experimental features such as the large isotope effect, the non-linear increase of yield with laser fluence, translationally hot products (in the order of several 1000 K) and non-equipartitioning of translational and internal energies (E(trans) > E(vib) > E(rot)) are well reproduced. (iii) Predictions concerning a strong angular dependence of translational energies at large observation angles are also made.

Ab initio molecular dynamics of hydrogen dissociation on metal surfaces using neural networks and novelty sampling

We outline a hybrid multiscale approach for the construction of ab initio potential energy surfaces (PESs) useful for performing six-dimensional (6D) classical or quantum mechanical molecular dynamics (MD) simulations of diatomic molecules reacting at single crystal surfaces. The algorithm implements concepts from the corrugation reduction procedure, which reduces energetic variation in the PES, and uses neural networks for interpolation of smoothed ab initio data. A novelty sampling scheme is implemented and used to identify configurations that are most likely to be predicted inaccurately by the neural network. This hybrid multiscale approach, which couples PES construction at the electronic structure level to MD simulations at the atomistic scale, reduces the number of density functional theory (DFT) calculations needed to specify an accurate PES. Due to the iterative nature of the novelty sampling algorithm, it is possible to obtain a quantitative measure of the convergence of the PES with respect to the number of ab initio calculations used to train the neural network. We demonstrate the algorithm by first applying it to two analytic potentials, which model the H2/Pt(111) and H2/Cu(111) systems. These potentials are of the corrugated London-Eyring-Polanyi-Sato form, which are based on DFT calculations, but are not globally accurate. After demonstrating the convergence of the PES using these simple potentials, we use DFT calculations directly and obtain converged semiclassical trajectories for the H2/Pt(111) system at the PW91/generalized gradient approximation level. We obtain a converged PES for a 6D hydrogen-surface dissociation reaction using novelty sampling coupled directly to DFT. These results, in excellent agreement with experiments and previous theoretical work, are compared to previous simulations in order to explore the sensitivity of the PES (and therefore MD) to the choice of exchange and correlation functional. Despite having a lower energetic corrugation in our PES, we obtain a broader reaction probability curve than previous simulations, which is attributed to increased geometric corrugation in the PES and the effect of nonparallel dissociation pathways.