Materials interaction with femtosecond lasers : theory and ultra-large-scale simulations of thermal and nonthermal phenomena

This book presents a unified view of the response of materials as a result of femtosecond laser excitation, introducing a general theory that captures both ultrashort-time non-thermal and long-time thermal phenomena. It includes a novel method for performing ultra-large-scale molecular dynamics simulations extending into experimental and technological spatial dimensions with ab-initio precision. For this, it introduces a new class of interatomic potentials, constructed from ab-initio data with the help of a self-learning algorithm, and verified by direct comparison with experiments in two different materials — the semiconductor silicon and the semimetal antimony. In addition to a detailed description of the new concepts introduced, as well as giving a timely review of ultrafast phenomena, the book provides a rigorous introduction to the field of laser–matter interaction and ab-initio description of solids, delivering a complete and self-contained examination of the topic from the very first principles. It explains, step by step from the basic physical principles, the underlying concepts in quantum mechanics, solid-state physics, thermodynamics, statistical mechanics, and electrodynamics, introducing all necessary mathematical theorems as well as their proofs. A collection of appendices provide the reader with an appropriate review of many fundamental mathematical concepts, as well as important analytical and numerical parameters used in the simulations. Foreword Acknowledgements About This Book Contents About the Author Acronyms List of Symbols 1 Introduction References 2 Ab-initio Description of Solids 2.1 Quantum Mechanical Description 2.2 Born-Oppenheimer Approximation 2.2.1 Nuclei Motion in the Harmonic Approximation in Crystalline Systems 2.3 Density Functional Theory 2.3.1 Hohenberg-Kohn Theorems 2.3.2 Kohn–Sham Equations 2.3.3 Approximations to the Exchange Correlation Functional 2.3.4 Bloch Waves in Crystalline Systems 2.3.5 Using a Set of Basis Functions 2.3.6 Solving the Kohn–Sham Equations Self Consistently 2.3.7 Density Mixing to Speed up the Solution of the Kohn–Sham Equations 2.3.8 Pseudopotentials 2.3.9 Electronic Band Structure of Solids 2.4 Te-dependent Density Functional Theory 2.4.1 Basic Considerations of Thermodynamics 2.4.2 Basic Considerations of Statistical Mechanics 2.4.3 Mermin's Theorems 2.4.4 Te-dependent Kohn–Sham Equations 2.5 Summary References 3 Ab-initio Description of a Fs-laser Excitation 3.1 Basic Considerations of Electrodynamics 3.1.1 Maxwell Equations in Vacuum 3.1.2 Radiation of Electromagnetic Waves 3.1.3 Energy in Electromagnetic Fields 3.1.4 Interaction of a Charged Particle with an Electromagnetic Wave 3.2 Basic Considerations of Second Quantization 3.2.1 Second Quantization for Electrons 3.2.2 Second Quantization for Phonons 3.3 Reduced Electron Density Matrices 3.4 Effects of a Fs-laser Interaction on Matter 3.4.1 Effects of the Fs-Laser Field 3.4.2 Electron Relaxation 3.4.3 Electron-Phonon Relaxation 3.4.4 Electron-Phonon Coupling Strength 3.5 Physical Picture of the Fs-laser Excitation 3.6 Code for Highly Excited Valence Electron Systems (CHIVES) 3.7 Summary References 4 Ab-Initio MD Simulations of the Excited Potential Energy Surface 4.1 Molecular Dynamics Simulation Setup 4.1.1 Velocity Verlet Algorithm 4.1.2 Preparation of Initial Conditions 4.2 Calculation of the Diffraction Peak Intensities 4.3 Fs-Laser Induced Thermal Phonon Squeezing and Antisqueezing 4.4 DFT Calculations and MD Simulations of Si at Various Te's 4.4.1 Equilibrium Structure 4.4.2 Cohesive Energies at Various Te's 4.4.3 Phonon Band Structure at Various Te's 4.4.4 MD Simulations of Thermal Phonon Antisqueezing at Moderate Te's 4.4.5 MD Simulations of Non-thermal Melting at High Te's 4.4.6 Behavior of the Electronic Indirect Band Gap 4.4.7 MD Simulations of a Thin-Film at Various Te's 4.4.8 Summary of the Effects Induced by an Increased Te 4.5 DFT Calculations and MD Simulations of Sb at Various Te's 4.5.1 Equilibrium Structure 4.5.2 Cohesive Energies at Various Te's 4.5.3 Potential Energy Surface and Displacive Excitation of the A1g Phonon 4.5.4 Phonon Band Structure at Various Te's 4.5.5 MD Simulations of the A1g-Phonon Excitation at Various Te's 4.5.6 MD Simulations of Thermal Phonon Antisqueezing at Moderate Te's 4.5.7 MD Simulations of Non-thermal Melting at High Te's 4.5.8 MD Simulations of a Thin-Film at Various Te's 4.5.9 Summary of the Effects Induced by an Increased Te 4.6 THz Emission from Coherent Phonon Oscillations in BNNTs 4.6.1 Equilibrium Structure 4.6.2 Displacive Excitation of Coherent Phonons in BNNTs 4.6.3 THz Radiation from Coherent Phonon Oscillations in the (5, 0) Zigzag BNNT 4.7 Summary References 5 Empirical MD Simulations of Laser-Excited Matter 5.1 Interatomic Potentials for Ground State Electrons in Solid State Physics 5.1.1 Classical Analytical Interatomic Potential Models 5.1.2 Determining of Interatomic Potential Parameters 5.1.3 Machine Learning Interatomic Potentials 5.1.4 Performing Large Scale MD Simulations 5.2 Simulation of Laser Excitation via Two Temperatures and Velocity Scaling 5.3 Simulation of Laser Excitation via Bond-Softening in the Tersoff Potential 5.4 Te-Dependent Interatomic Potentials 5.4.1 Si Potential of Shokeen and Schelling 5.4.2 Si Potential of Darkins et al. 5.4.3 MD Simulations with a Te-Dependent Interatomic Potential 5.5 Universal Interatomic Potential Parameter Fitting Program 5.5.1 Construction of Fit Error Function 5.5.2 General Definition of the Analytical Form of the Interatomic Potential 5.5.3 Analytical Expressions for the Interatomic Potential Parameter Derivatives 5.5.4 Efficient and Parallelized Implementation in Fortran 5.6 Summary References 6 Ab-Initio Theory Considering Excited Potential Energy Surface and e–Phonon Coupling 6.1 Usage of Global Temperatures in the Simulation Cell 6.1.1 Implementation in the Velocity Verlet Algorithm 6.1.2 Remarks 6.2 Usage of Local Temperatures in the Simulation Cell 6.2.1 Numerical Implementation 6.2.2 Remarks 6.3 Polynomial Te-Dependent Interatomic Potential Model 6.3.1 Polynomial Functional Form 6.3.2 Fitting of Coefficients 6.3.3 Optimal Polynomial-Degree Combination Selection Procedure 6.3.4 Easy Evaluation via Power Lists 6.3.5 Efficient Evaluation of the Three-Body Term 6.3.6 Efficient Evaluation of the Four-Body Term 6.4 Summary References 7 Study of Femtosecond-Laser Excited Si 7.1 Te-Dependent Interatomic Potential for Si 7.1.1 Ab-Initio Reference Simulations Used for Fitting 7.1.2 Parameter Fitting of Classical Interatomic Potentials 7.1.3 Polynomial Interatomic Potential Φ(Si)(Te) 7.1.4 Physical Properties of Polynomial Φ(Si)(Te) 7.1.5 Thermophysical Properties of Polynomial Φ(Si)(Te) 7.2 MD Simulations of Excited PES and EPC with Polynomial Φ(Si)(Te) 7.2.1 Direct Comparison of the Bragg Peak Intensities with Experiments 7.2.2 MD Simulations of a Femtosecond-Laser Excited Si Film 7.2.3 MD Simulations of Femtosecond-Laser Excited Bulk Si 7.3 Correction of the Melting Temperature 7.3.1 Correction of the 3-Body Potential Coefficients 7.3.2 Melting Temperature and Slope Study on Test Potentials 7.3.3 Correction of the 2-Body and 3-Body Potential Coefficients 7.4 Summary References 8 Study of Femtosecond-Laser Excited Sb 8.1 Te-dependent Interatomic Potential for Sb 8.1.1 Ab-initio Reference Simulations Used for Fitting 8.1.2 Optimization of the Functional Form of the Polynomial Potential 8.1.3 Physical Properties of Polynomial Φ(Sb)(Te) 8.2 Optical Properties of Sb as a Function of the Peierls Parameter 8.3 MD Simulations of Excited PES and EPC with Polynomial Φ(Sb)(Te) 8.3.1 Direct Comparison of the Bragg Peak Intensities with Experiments 8.3.2 Laser-Induced A7 to Sc Transition 8.4 Summary References 9 Summary and Outlook 9.1 Overview 9.1.1 THz Emission from Coherent Phonon Oscillations 9.1.2 Universal Behavior of the Indirect Electronic Band Gap in Laser-Excited Si 9.1.3 Theory Allowing MD Simulations Considering Excited Potential Energy Surface and Electron-Phonon Coupling 9.1.4 Construction of Efficient and Highly Accurate Te-Dependent Interatomic Potentials 9.1.5 Te-Dependent Interatomic Potential Φ(Si)(Te) for Si 9.1.6 Correction of the Melting Temperature of Φ(Si)(Te) to the Experimental Value 9.1.7 MD Simulations of Femtosecond Laser-Pulse Excited Si 9.1.8 Te-Dependent Interatomic Potential Φ(Sb)(Te) for Sb 9.1.9 MD Simulations of Femtosecond Laser-Pulse Excited Sb 9.2 Future Perspectives Reference Appendix A Additional Information and Tables A.1 Review of Vector Calculus A.2 Method of Least Squares and Givens Rotations A.3 Implementation of the e–Phonon Coupling in Velocity Verlet A.4 Calculation of the Pressure in a MD Simulation A.5 Electronic Specific Heat of Si A.6 Adapted Parameters of Classical Potentials to Describe FS-Laser Excited Si A.7 Performance of Reparametrized Classical Potentials for Si A.8 Coefficients of the Polynomial Interatomic Potential Φ(Si)(Te) for Si A.8.1 Modified Coefficients for the Tm-Corrected Interatomic Potential A.9 Coefficients of the Polynomial Interatomic Potential Φ(Sb)(Te) for Sb A.10 Electronic Specific Heat of Sb A.11 Optical Properties of Sb as a Function of the Peierls Parameter A.12 Electron-Phonon Coupling Constant of Sb A.13 Gaussian Basis Sets Used in CHIVES References Index