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Computational Protocol for Material Optical Properties During Pump-Probe Experiments and in Nanostructures Irradiated with Ultrashort Pulses

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Computational Protocol for Material Optical Properties During Pump-Probe Experiments and in Nanostructures Irradiated with Ultrashort Pulses DELIVERABLE REPORT WP9 JRA4 – Research on Time-resolved ultrafast probes on nanosystems D9.7 Computational protocol for material optical properties during pump-probe experiments and in nanostructures irradiated with ultrashort pulses Expected date M40 NFFA-Europe has received funding from the EU's H2020 framework programme for research and innovation under grant agreement n. 654360 PROJECT DETAILS PROJECT ACRONYM PROJECT TITLE NFFA-Europe NANOSCIENCE FOUNDRIES AND FINE ANALYSIS - EUROPE GRANT AGREEMENT NO: FUNDING SCHEME 654360 RIA - Research and Innovation action START DATE 01/09/2015 WP DETAILS WORK PACKAGE ID WORK PACKAGE TITLE WP9 JRA4 – Research on Time-resolved ultrafast probes on nanosystems WORK PACKAGE LEADER Emmanuel Stratakis (FORTH) DELIVERABLE DETAILS DELIVERABLE ID DELIVERABLE TITLE D9.7 Computational protocol for material optical properties during pump- probe experiments and in nanostructures irradiated with ultrashort pulses DELIVERABLE DESCRIPTION A short description of the theoretical framework that was developed to describe laser matter interaction with nanosctructures that can be used to assist fundamental mechanism understanding as well as appropriate design protocols in pump-probe experimental set ups. EXPECTED DATE ESTIMATED INDICATIVE PERSONMONTHS 31/12/2018 16 AUTHORS Emmanuel Stratakis (FORTH), George Tsibidis (FORTH), Leonidas Mouchliadis (FORTH), Andrea Marini (CNR), Paolo Umari (CNR) PERSON RESPONSIBLE FOR THE DELIVERABLE Emmanuel Stratakis (FORTH) NATURE R - Report DISSEMINATION LEVEL ☒ P - Public ☐ PP - Restricted to other programme participants & EC: (Specify) ☐ RE - Restricted to a group (Specify) ☐ CO - Confidential, only for members of the consortium 2 REPORT DETAILS ACTUAL SUBMISSION DATE NUMBER OF PAGES 21/12/2018 14 FOR MORE INFO PLEASE CONTACT Emmanuel Stratakis (FORTH) Tel. +30-2810-391274 Email: [email protected] Description / Reason for Version Date Author(s) Status modification 1 18/12/2018 Emmanuel Stratakis, Final George Tsibidis, Leonidas Mouchliadis, Andrea Marini, Paolo Umari Choose an item. Contents Executive Summary 4 1. Concept –Theoretical framework 4 1.1 DFT and BSE+GW calculations 5 GW calculations 5 Bethe-Salpeter equations 6 1.2 Relaxation Processes 7 2. Design specification 7 2.1 Yambo Code/Quantum Espresso 9 Simulation 9 Initialization 9 Input file generation and command line options 9 Hartree-Fock and GW calculation 9 2.2 Two Temperature Model module/Phase transition Module 10 3. Simulation Results for 6H-SiC 10 4. Conclusions and perspectives 13 Publications in which NFFA is acknowledged 14 3 Executive Summary To design appropriate efficient pump-probe experiments and evaluate the response of nanostructured materials to ultrashort-pulsed laser irradiation, it is important to understand the underlying physical mechanisms that characterise laser-matter interaction. To this end, a computational protocol is developed to describe the multiscale analysis of all physical processes that are involved following irradiation with very short pulses. To efficiently quantify the optical response of the material in the first stages after the irradiation, a quantum mechanical approach is followed through the synergy of Quantum Espresso and Yambo Code that are coupled with revised versions of the Two Temperature Model (TTM) to eventually describe relaxation processes and/or morphological changes. To test the computational code, 6H-SiC is used as a test material for which the damage threshold fluence (i.e. minimum temperature at which the material melts) is being calculated. The reason for which this material is used is because there are existing experimental protocols designed by groups in the consortium. 1. Concept –Theoretical framework Laser-matter interaction with intense (ultrashort) pulsed lasers triggers a variety of time-scale dependent processes influenced by the applied conditions (i.e. fluence, pulse duration, number of pulses, etc). Determining the material’s response characteristics changes at longer time scales has been hampered by the absence of a direct correlation between the conditions applied and the interdependence of the intermediate mechanisms at all time-scales. In brief, a consistent theoretical approach to describe the multiscale analysis of the response of the irradiated material should comprise the following components: (i) a term that describes energy absorption through a precise estimate of the optical properties, (ii) a term that describes electron excitation and all relevant interactions (electron-electron and electron-phonon collisions, etc.), (iii) a heat transfer component that accounts for electron-lattice thermalisation through particle dynamics and heat conduction and carrier-phonon coupling, and/or (iv) a hydrodynamics component that describes fluid dynamics followed by a mass removal and re-solidification process in areas where a phase transition occurs. In principle, the processes start after some fs, they continue to mechanisms that complete after some picoseconds (ps) while others require more time and they last up to the nanosecond (ns) regime. One very important aspect that requires a thorough investigation is the absorption of laser energy by the irradiated material. A critical parameter is the computation of the optical properties (reflectivity, absorption coefficient) while a detailed analysis of the propagation of the beam inside the irradiated material allows the computation of the spatio-temporal distribution of the absorbed laser energy. There are various models that have been used to simulate the dielectric constant of the material (and therefore the optical properties) as a function of the laser beam wavelength while solution of Maxwell equations can yield the energy distribution. One classical (approximate) approach that has been used to simulate the dielectric constant of the material as a function of the laser beam wavelength is by means of modified versions of the Lorentz-Drude model the interaction of intense laser pulses with an extensive variety of solids giving rise to surface modifications as well as changes in optical properties, has been the subject of intensive research during recent years. However, many of the expressions used to estimate the optical properties, firstly, are valid at low temperatures while they do not take into account their possible variation during the laser pulse (i.e. 4 for extremely short pulses). Therefore an imprecise calculation of the optical properties is derived that potentially may lead to an inaccurate determination of the absorbed energy; the latter is, then, expected to produce erroneous estimation of the thermal response of the system. Therefore, a first principle analysis of the laser interaction with matter was based on the fundamental quantum mechanical-based processes. Simulations (DFT Calculations, etc) were performed in various conditions in Tasks 9.2 of JRA4 to provide precisely the reflectivity and absorption coefficient of the irradiated material and results were used as a feedback to compute the thermal response of the material. 1.1 DFT and BSE+GW calculations GW calculations The aim of a GW calculation is to obtain the quasiparticle correction to energy levels using many- body perturbation theory (MBPT). The general non-linear quasiparticle equation reads: As a first step we evaluate the self-energy Σ entering in the quasiparticle equation. In the GW approach the self-energy can be separated into two components: a static term called the exchange self-energy (Σx), and a dynamical term (energy dependent) called the correlation self-energy (Σc): We treat these two terms separately and find the most important variables for calculating each term. In practice we compute the quasi-particle corrections to the one particle Kohn-Sham eigenvalues obtained through a DFT calculation. The steps are the following: Step 1. The Exchange Self Energy or HF quasi-particle correction: We start by evaluating the exchange Self-Energy and the corresponding Quasiparticle energies (Hartree-Fock energies). Step 2. The Correlation Self-Energy and Quasiparticle Energies Once we have calculated the exchange part, we next turn our attention to the more demanding dynamical part. The correlation part of the self-energy in a plane wave representation reads: In the expression for the correlation self energy, Σc, we have (1) a summation over bands, (2) an integral over the Brillouin Zone, and (3) a sum over the G vectors. In contrast with the case of Σx, the summation over bands extends over all bands (including the unoccupied ones), and so convergence tests are needed. Another important difference is that the Coulomb interaction is now screened so a fundamental ingredient is the evaluation of the dynamical dielectric matrix. In the calculation, we use two ways to take into account the dynamical effects. First, we set the proper parameters to obtain a model dielectric function based on a widely used approximation, which models the energy dependence of each component of the dielectric matrix with a single pole function. Secondly, we perform calculations by evaluating the dielectric matrix on a regular grid of frequencies. Once the correlation part of the self-energy is calculated, we will check the convergence of the different parameters with respect to some final quantity, such as the gap. After computing the frequency dependent self-energy, we observe that in order to solve the quasiparticle equation we need to know its value at the value of the quasiparticle itself. We therefore solve the non-linear
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