| Metadata | Details |
|---|
| Publication Date | 2020-08-03 |
| Journal | Physical review. B./Physical review. B |
| Authors | Nikita Medvedev, Igor Milov |
| Institutions | Czech Academy of Sciences, Institute of Physics, Czech Academy of Sciences, Institute of Plasma Physics |
| Citations | 135 |
| Analysis | Full AI Review Included |
- Core Achievement: Developed and implemented a nonperturbative dynamical coupling approach within the XTANT-3 tight-binding molecular dynamics (TBMD) code to calculate the electron-phonon (e-ph) coupling parameter G at high electronic temperatures (Te).
- Model Validation: The calculated G(Te) for Aluminum (Al) and Gold (Au) shows strong agreement with available experimental data in the high-Te regime (up to 20 kK), validating the model where traditional Eliashberg formalism extensions often overestimate coupling.
- Universal Applicability: The method is universal, applicable to Te up to a few electron-Volts, and is not restricted to harmonic ion motion (phonons) or crystalline structures, making it suitable for melted or amorphous states.
- Extensive Data Set: Provides the first theoretical estimations of G(Te) for over 30 elemental solids, including fcc, hcp, and bcc metals (e.g., Pt, Ir, Ti, W, Nb), semiconductors (Si, Ge), and semimetals (Graphite).
- Identified Trends: G exhibits an inverse relationship with atomic mass (due to increased inertia) and shows periodic peaks corresponding to the half-filling of outermost d-shells (3d, 4d, 5d groups).
- Parametric Dependencies: Demonstrated that G scales linearly with both the atomic temperature (Ta) and the material density (V/V0), highlighting the necessity of controlling these variables in experimental measurements and TTM simulations.
| Parameter | Value | Unit | Context |
|---|
| Maximum Electronic Temperature (Te) | 20,000 - 30,000 | K | Upper limit of Te studied across various elemental solids (up to a few eV). |
| Atomic Temperature Range (Ta) | 300 - 2000 | K | Range used to study the dependence of G on Ta (e.g., for Gold and Chromium). |
| Excitation Photon Energy | 10 | eV | Used to ensure instantaneous electron thermalization and avoid non-equilibrium cascade effects. |
| Deposited Energy Dose | 3 - 4 | eV/atom | Energy input required to achieve the high electronic temperatures studied. |
| Molecular Dynamics Timestep (dt) | 1 | fs | Timestep used for simulations; convergence achieved for dt < 2 fs. |
| Minimum Supercell Size | ~200 | atoms | Required for convergence using single gamma-point TBMD simulations (e.g., 4x4x4 or 5x5x5 conventional unit cells). |
| Electron-Phonon Coupling (G) Range (Metals) | 1016 to 1018 | W/m3K | Typical range for G at Te = 10,000 K, depending on the material. |
| Coupling Parameter (G) Scaling with Ta (Gold) | y = 0.6557 + 0.00155*Ta | Arbitrary units | Linear fit demonstrating the scaling factorâs dependence on atomic temperature (Ta in K). |
| Relative Volume Range Studied (Gold) | 0.8 to 1.2 | V/V0 | Range used to analyze the linear dependence of G on material density. |
| Band Gap (Si) | ~0.15 | eV | Artificial band gap produced by single gamma-point sampling in Strontium (Sr) calculations. |
- Dynamical Coupling Approach: The electron-ion energy exchange is calculated using a nonperturbative extension of the dynamical coupling formalism. This method calculates the transition rate (Wij) between electronic eigenstates (i and j) based on the wave function overlap between consecutive molecular dynamics (MD) timesteps (dt).
- Tight-Binding Molecular Dynamics (TBMD): The dynamical coupling scheme is implemented into the XTANT-3 hybrid code. This code uses a transferable tight-binding (TB) formalism (NRL parameterization, sp3d LCAO basis set) to describe the transient electronic band structure and atomic potential energy surface.
- Non-Orthogonal Basis Set Extension: The formalism was generalized to handle non-orthogonal basis sets, requiring the inclusion of the overlap matrix (Sα,ÎČ) in the calculation of transition rates.
- Electronic State Modeling: The electronic ensemble is assumed to be instantly thermalized and follows a Fermi-Dirac distribution, defined by the electronic temperature (Te) and chemical potential (”).
- Collision Integral Calculation: The electron-ion collision integral (Ie-aij) is calculated using the transition rates (Wij) combined with the Boltzmann collision integral, ensuring detailed balance is fulfilled.
- Coupling Parameter Definition: The volumetric electron-phonon coupling parameter G(Te) is defined directly from the collision integral: G(Te) = (Te - Ta)-1 ÎŁ Ie-aij.
- Simulation Protocol: Ten independent simulations were run for each material using the NVE (microcanonical) ensemble, periodic boundary conditions, and a 1 fs timestep. Initial conditions (pulse duration 10-60 fs, dose 3-4 eV/atom) were varied to ensure robust averaging of G(Te).
- Ultrafast Laser Materials Processing: Provides critical G(Te) data necessary for accurate Two-Temperature Model (TTM) simulations used in femtosecond laser micromachining, enabling precise control over energy deposition, melting, and ablation thresholds in metals (Au, Pt, Cu) and semiconductors (Si, Ge).
- High-Energy-Density (HED) Physics Research: Essential for modeling the non-equilibrium relaxation of matter under extreme conditions, relevant to inertial confinement fusion (ICF) and the study of warm dense matter (WDM) created by intense X-ray or particle beams.
- Advanced Coating and Thin Film Manufacturing: The ability to model G dependence on density (V/V0) allows for better prediction of thermalization processes in materials under transient pressure or strain, relevant for pulsed laser deposition (PLD) and thin-film growth.
- Nonthermal Phase Transition Engineering: The model captures nonthermal effects (like displacive excitation of coherent phonons) that influence G, which is crucial for understanding and controlling ultrafast nonthermal melting in materials like Silicon and Germanium for novel device fabrication.
- Development of High-Power Optics: Accurate G values for refractory metals (W, Mo, Ta) are necessary for designing materials resistant to damage from high-intensity laser or EUV/X-ray irradiation, where rapid energy dissipation is key.
View Original Abstract
Electron-phonon coupling, being one of the most important parameters governing the material evolution after ultrafast energy deposition, yet remains the most unexplored one. In this work, we applied the dynamical coupling approach to calculate the nonadiabatic electron-ion energy exchange in nonequilibrium solids with the electronic temperature high above the atomic one. It was implemented into the tight-binding molecular dynamics code, and used to study electron-phonon coupling in various elemental metals. The developed approach is a universal scheme applicable to electronic temperatures up to a few electron-Volts, and to arbitrary atomic configuration and dynamics. We demonstrate that the calculated electron-ion (electron-phonon) coupling parameter agrees well with the available experimental data in high-electronic-temperature regime, validating the model. The following materials are studied here - fcc metals: Al, Ca, Ni, Cu, Sr, Y, Zr, Rh, Pd, Ag, Ir, Pt, Au, Pb; hcp metals: Mg, Sc, Ti, Co, Zn, Tc, Ru, Cd, Hf, Re, Os; bcc metals: V, Cr, Fe, Nb, Mo, Ba, Ta, W; diamond cubic lattice metals: Sn; specific cases of Ga, In, Mn, Te and Se; and additionally semimetal graphite and semiconductors Si and Ge. For many materials, we provide the first and so far the only estimation of the electron-phonon coupling at elevated electron temperatures, which can be used in various models simulating ultrafast energy deposition in matter. We also discuss the dependence of the coupling parameter on the atomic mass, temperature and density.
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