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Excited state process in perovskites

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Excited state process in perovskites

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Content EXCITED STATE PROCESS IN PEROVSKITES by Carlos Mora Perez A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CHEMISTRY) May 2024 Copyright 2024 Carlos Mora Perez iii ACKNOWLEDGEMENTS I am immensely grateful for the support, guidance, and encouragement I have received throughout my time at USC. I am pleased to express my sincerest appreciation to those who have contributed to my academic and personal growth. My deepest gratitude goes to my USC graduate advisor, Dr. Oleg Prezhdo, and my mentor at Los Alamos National Laboratory (LANL), Dr. Amanda Neukirch. Their invaluable advice and guidance and the endless opportunities they provided have been instrumental in the success of my career. They have been a constant source of inspiration, and I thank them for their boundless patience. Their support has been indispensable. Special thanks also go to Dr. Dibyajyoti Ghosh, Dr. Aaron Forde, and Dr. Sergei Tretiak. Their collaboration, guidance, and insights on numerous projects have enriched my LANL experience. Working alongside them has been a privilege. To my experimental collaborators, your willingness to share your expertise and provide growth opportunities has been invaluable. The collaborative spirit within our research community has been a constant source of inspiration and encouragement. My family deserves a notable mention for their unwavering support and encouragement. Their faith in me has been a constant source of strength throughout this journey. To my wife, Wendy Mora, I owe a debt of gratitude for her endless love, support, and understanding. Wendy, your presence has been a beacon of light during challenging times, and your unwavering support has been my foundation. Thank you for being by my side, for your sacrifices, and for making our shared dreams a reality. I also thank my qualifying exam committee, Dr. Jahan Dawlaty, Dr. Alexander Benderskii, Dr. Megan Fieser, and Dr. Susumu Takahashi, for their time. I especially thank my defense committee, Dr. Jahan Dawlaty, and Dr. Paulo Sergio Branicio. iv This chapter in my life has been one of my most extraordinary moments of growth, learning, and fulfilling opportunities. Thank you to everyone who has been a part of this adventure! v TABLE OF CONTENTS ACKNOWLEDGEMENTS..................................................................................................... iii LIST OF TABLES.................................................................................................................. vii LIST OF FIGURES ............................................................................................................... viii ABSTRACT............................................................................................................................ xii Chapter 1 Introduction ...............................................................................................................1 Perovskites............................................................................................................................1 Nonadiabatic Molecular Dynamics.......................................................................................4 Time-dependent Schrödinger equation .................................................................................5 Surface hopping ....................................................................................................................6 Chapter 2 Defects In 2D Perovskites.........................................................................................8 Introduction...........................................................................................................................8 Computational Methodology ..............................................................................................11 Results & Discussion ..........................................................................................................12 Conclusion ..........................................................................................................................22 Chapter 3 Defects In Perovskite Quantum Dots......................................................................24 Introduction.........................................................................................................................24 Computational Methodology ..............................................................................................26 Results & Discussion ..........................................................................................................28 Conclusion ..........................................................................................................................37 UV-Vis plots.......................................................................................................................38 Density of state (DOS) plots...............................................................................................40 Natural transition orbitals and molecular orbitals for high perturbing systems..................42 Chapter 4 Auger Process In Perovskite Quantum Dots...........................................................50 Introduction.........................................................................................................................50 vi Computational Methodology ..............................................................................................51 Experimental Evidence .......................................................................................................52 Results & Discussion ..........................................................................................................57 Density of state (DOS) plots...............................................................................................60 Conclusions.........................................................................................................................61 Chapter 5 Machine Learning Analysis On Vacancy Ordered Perovskites..............................63 Introduction.........................................................................................................................63 Computational Methodology ..............................................................................................66 Results & Discussion ..........................................................................................................69 Mutual Information Tables .................................................................................................80 Conclusion ..........................................................................................................................82 Chapter 6 Conclusion and future directions.............................................................................84 REFERENCES ........................................................................................................................86 vii LIST OF TABLES Table 2.1: List of defects studied with expected low formation energies. ................................... 10 Table 3.1. Modeled defect types and their location on the CsPbBr3 nanocluster......................... 29 Table 5.1. Mutual information of the bandgap and the structure features.................................... 80 Table 5.2: Mutual information of the CBM and the structure features. ....................................... 80 Table 5.3. Mutual information of the VBM and the structure features. ....................................... 81 Table 5.4. Mutual information of the NAC and the structure features. ........................................ 81 Table 5.5. Description of all the featured data.............................................................................. 82 viii LIST OF FIGURES Figure 1.1. The number of perovskite papers published in the last 24 years.................................. 1 Figure 1.2. (a) ABX3 perovskite structure showing BX6 octahedral (Reprinted from Ref 1 ) (b) Unit cell of cubic MAPbI3 perovskite (Reprinted from Ref 1 ) (c) Illustration of “materiallevel” low-dimensional perovskites and 3D perovskite (Reprinted from Ref 5 ). (d) Illustration of “structure-level” low-dimensional perovskites and perovskite bulk materials (Reprinted from Ref 5 ). ..................................................................................................................................... 2 Figure 1.3. Schematic of photophysical processes in pristine α-CsPbI3 (left), and α-CsPbI3 with dynamic defects, including iodine interstitial (middle) and cesium-iodine switch (right). (Reprinted from Ref 22)................................................................................................................... 4 Figure 2.1 The optimized geometry (0 K) primitive cell of pristine 2D-perovskite = 1; 2 − 13 + 1 model (BA = butylammonium), composed of 1×1×1-unit cells, with chemical formula H96C32N8Pb4I16 (156 atoms in a cell)......................................................... 8 Figure 2.2. A cartoon rendition of all studies defect location on the n=1 2D-perovskite BA2Pb1I4 system of the in-plane side view................................................................................. 12 Figure 2.3. Projected density of states (PDOS) with band decomposed charge densities of the band edge states for the Γ point and band structure along the high symmetry k-points of the pristine 2D-perovskite with = 1;ℎ ℎ 2 − 13 + 1 model, composed of 2×1×2-unit cells, for the optimal geometry (0 K): The valence band maximum (VBM) originates from I orbitals, with minor contributions of Pb orbitals, whereas the conduction band minimum (CBM) is primarily formed by Pb orbitals........................................ 12 Figure 2.4. Projected density of states (PDOS) for all systems with the defects at the optimized geometries (0K), composed of 2×1×2-unit cells: (a) BA vacancy (VBA), (b) BA + I Vacancy (VBAI), (c) Pb + I2 Vacancy (VPbI2), (d) I (out-of-plane) Vacancy (VI1), (e) I (Inplane) Vacancy (VI2), (f) I (out-of-plane) Vacancy (iI1) and (g) I (In-plane) Vacancy (iI2). Point defects breaking electron pairs and containing a halogen introduce defects near the band edges. Specifically, halogen vacancies create defects near the CBM, while iodine interstitials create defects near the VBM. ..................................................................................... 14 Figure 2.5. Projected density of states (PDOS) for the systems with the defects at the optimal geometries for the Γ point, composed of 2×1×2-unit cells: (a) Iodine vacancy in-plane (VI2). (b) Iodine interstitial in-plane (II2), (c) Iodine interstitial out-of-plane (II1). Halogen vacancies create defects near the CBM, while iodine interstitials create defects near the VBM.................. 15 Figure 2.6. Projected density of states (PDOS) and band structure of high symmetry k-points near the Γ-point including spin-orbit coupling (SOC), composed of 2×1×2-unit cells: (a) pristine (b) Iodine vacancy in-plane (VI2). (c) Iodine interstitial in-plane (iI2), (d) Iodine interstitial out-of-plane (iI1). Halogen vacancies create defects near the CBM, while iodine interstitials create defects near the VBM. ..................................................................................... 18 Figure 2.7. Projected density of states (PDOS) for the pristine system during the NVE MD trajectory at (a) 500 fs, (b) 1500 fs, and (c) 2000 fs. .................................................................... 20 ix Figure 2.8. Projected density of states (PDOS) for iodine vacancy system during the NVE MD trajectory at (a) 500 fs, (b) 1500 fs, and (c) 2000 fs. .................................................................... 20 Figure 2.9. Projected density of states (PDOS) for iodine interstitial (out-of-plane) system during the NVE MD trajectory at (a) 500 fs, (b) 1500 fs, and (c) 2000 fs. .................................. 20 Figure 2.10. Projected density of states (PDOS) for iodine interstitial (in-plane) system during the NVE MD trajectory at (a) 500 fs, (b) 1500 fs, and (c) 2000 fs............................................... 20 Figure 2.11. Projected density of states (PDOS) and band structure of high symmetry k-points for Iodine vacancy in-plane (VI2) at various depths of unit cells. (a) 2×1×2-unit cells, (b) 1×1×1-unit cells, (c) 1×2×1-unit cells, and (d) 1×3×1-unit cells. ................................................ 21 Figure 2.12. Projected density of states (PDOS) and band structure of high symmetry k-points for I (out-of-plane) Interstitial (iI1) at various depths of unit cells. (a) 2×1×2-unit cells, (b) 1×1×1-unit cells, (c) 1×2×1-unit cells, and (d) 1×3×1-unit cells. ................................................ 22 Figure 2.13. Projected density of states (PDOS) and band structure of high symmetry k-points for I (in-plane) Interstitial (iI2) at various depths of unit cells. (a) 2×1×2-unit cells, (b) 1×1×1- unit cells, (c) 1×2×1-unit cells, and (d) 1×3×1-unit cells. ............................................................ 22 Figure 3.1. (a) Charge neutral pristine CsPbBr3 nanocluster (3×3×3; 27-unit cell system), with Cs and Br terminated surface. (b) Unique surfaces of a cluster. Uneven surface natively contains a Cs vacancy. .................................................................................................................. 28 Figure 3.2. (a) Simulated UV-Vis spectra of the pristine CsPbBr3 nanocluster representing 15 singlet transitions. The oscillator strengths for the transitions are shown as black sticks caped with a cross (left scale). The resulting absorption profile is shown in blue, with the max peaks highlighted by a vertical dashed line (4.78 and 4.80 eV) (right scale). (b) The density of states (DOS) of the pristine system highlights contributing atom types (the vertical dash line represents the HOMO level). ........................................................................................................ 31 Figure 3.3. Simulated UV-Vis spectra of the CsPbBr3 nanocluster with defects calculated from the 15 lowest-energy singlet transitions. (a) Cs defects, (b) Pb defects, (c) Br defects. Here “E” represents a defect from the even surface, and “U” represents a defect from the uneven surface (see Table 3.1 for defect locations)...................................................................... 33 Figure 3.4. (a) UV-VIS spectra comparison between the charged defects, (b) the DOS of the positively charged defect (resulting LUMO shown), (c) the DOS of the negatively charged defect (resulting HOMO shown). ................................................................................................. 35 Figure 3.5. UV-Vis spectra of first 15 excited states for the pristine and high perturbance defects; (a) pristine, (b) positively charged, (c) negatively charged, (d) Br vacancy on the even surface, and (e) Br vacancy on the uneven surface. The oscillator strengths for the transitions are seen in black and caped with a cross (left scale). The Absorption is seen in the blue (right scale). ............................................................................................................................................ 38 Figure 3.6. UV-Vis spectra of first 15 excited states for the low perturbance defects; (a) Pb vacancy on the even surface, (b) Cs vacancy on the even surface, (c) Pb vacancy on the center of the cluster “bulk-like,” (d) Cs vacancy on the uneven surface near existing Cs vacancy, (e) Pb vacancy on the uneven surface, and (f) Cs vacancy on the uneven surface far from existing Cs vacancy. The oscillator strengths for the transitions are seen in black and caped with a cross (left scale). The Absorption is seen in the blue (right scale). .............................................. 39 x Figure 3.7. DOS of the pristine and high perturbance defects: (a) pristine, (b) positively charged, (c) negatively charged, (d) Br vacancy on the even surface, and (e) Br vacancy on the uneven surface. Here the vertical dash line indicates the HOMO level. The FWHM was set to 1.0 eV. ................................................................................................................................. 40 Figure 3.8. DOS of the low perturbance defects; (a) Pb vacancy on the even surface, (b) Cs vacancy on the even surface, (c) Pb vacancy on the center of the cluster “bulk-like,” (d) Cs vacancy on the uneven surface near existing Cs vacancy, (e) Pb vacancy on the uneven surface, and (f) Cs vacancy on the uneven surface far from existing Cs vacancy. Here the vertical dash line indicates the HOMO level. The FWHM was set to 1.0 eV.............................. 41 Figure 3.9. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the pristine system. The percent contribution is given for each NTO pair. ......................................................................... 42 Figure 3.10. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the Br uneven defect. The percent contribution is given for each NTO pair................................................................... 43 Figure 3.11. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the Br even defect. The percent contribution is given for each NTO pair. ......................................................................... 44 Figure 3.12. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the negative charge system. The percent contribution is given for each NTO pair...................................................... 45 Figure 3.13. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the positive charge system. The percent contribution is given for each NTO pair...................................................... 46 Figure 3.14. Spin orbitals from HOMO-3 to LUMO+3 for comparing the charged systems against the pristine system. ........................................................................................................... 47 Figure 3.15. Molecular orbitals from HOMO-3 to LUMO+3 were used to compare Br defects with those of pristine systems....................................................................................................... 48 Figure 3.16. Comparison between NTO pairs and a localized hole-electron analysis................. 49 Figure 4.1. Time dependent survival probabilities of both electrons and holes are reflected by the ΔΔOD transients, probed at the band edge bleach (electrons) and the excited state absorption sub-resonant to the band edge (holes). a) ΔΔOD transient, representing the survival probability of electrons, in CsPbBr3 (light red), fit to a varying rate model (dark red) and how these rates vary (purple line). Cartoon shows electron cooling. b) The same as a) but for FAPbBr3. c,d) ΔΔOD transient, representing hole survival probabilities, in CsPbBr3 (c, red) and FAPbBr3(d, blue). Darker lines are a biexponential fit as a guide to the eye. Cartoons in c,d) show initial electron cooling through Auger heating (c), followed by hole cooling (d). The carrier density is <N> = 1 per NC, corresponding to a density of 3.0 x 1017 cm-3. ............ 53 Figure 4.2. SRPP spectra under high fluence conditions with band edge pumping (left) and 3.1 eV pumping (right). The yellow curves are to guide the eye. Here, <N> = 5, corresponding to a density of 1.5 x 1018 cm-3 . t-PL spectra at low and high fluence, with energy resolved pumping in order to directly test slow relaxation at high density. a) t-PL spectrum at low xi fluence with 3.1 eV pumping. Here, <N> = 0.015, corresponding to a density of 4.5 x 10-15 cm-3 . b) t-PL spectrum at high fluence with 3.1 eV pumping. Here, <N> = 7.4, corresponding to a density of 2.2 x 1018 cm-3 . c) t-PL spectrum at low fluence with 2.6 eV pumping. Here, <N> = 0.017, corresponding to a density of 5.1 x 1015 cm-3 . d) t-PL spectrum at high fluence with 2.6 eV pumping. Here, <N> = 4.2, corresponding to a density of 1.3 x 10-18 cm-3 .............. 56 Figure 4.3. Comparison of electron cooling for single (SE) and double (DE) electron excitations in a) CsPbBr3 and b) FAPbBr3. DEs are slightly faster than SEs because DEs have more channels for energy relaxation. The canonically averaged DOS is included for each system, together with a structure cell. Charge densities of the band edge and excitation orbitals are shown in Figure S5. Comparison of electron SE and hole cooling (HC) for c) CsPbBr3 and d) FAPbBr3............................................................................................................. 57 Figure 4.4. Canonically averaged absolute nonadiabatic (NAC) coupling for a) CsPbBr3 and b) FAPbBr3. The NAC is larger in the valence band (VB) than conduction band (CB) because the VB DOS is higher than the CB DOS, Figure 4.6. The VB NAC is larger for FAPbBr3 than CsPbBr3 rationalizing why holes relax faster in the former, Figure 4.3c,d of the main text. ...... 58 Figure 4.5. Canonically averaged charge densities of the valence band maximum (VBM), conduction band minimum (CBM), and initial hole and electron excitation orbitals for a) CsPbBr3 and b) FAPbBr3. The holes are supported primarily by Br atoms, while the electrons are localized on Pb atoms, in agreement with the DOS, Figure 4.6. ............................................ 59 Figure 4.6. Canonically averaged projected density of states (DOS) for a) CsPbBr3 and b) FAPbBr3. The DOS is larger in the valence band (VB) than the conduction band (CB). As a result, a larger part of the pump energy is deposited into electrons than holes because more hole states are closer to the band edge. Also, the nonadiabatic coupling (NAC) is larger in the VB than CB, Figure 4.4, because energy level spacings are smaller, and hole-vibrational relaxation is faster than electron-vibrational relaxation................................................................ 60 Figure 4.7. The DOS across the MD trajectory for CsPbBr3 at time step a) 1 fs, b) 500 fs, c) 1000 fs, d) 1500 fs, e) 2000 fs, f) 2500 fs, g) 3000 fs. ................................................................. 60 Figure 4.8. The DOS across the MD trajectory for FAPbBr3 at time step a) 1 fs, b) 500 fs, c) 1000 fs, d) 1500 fs, e) 2000 fs, f) 2500 fs, g) 3000 fs. ................................................................. 61 Figure 5.1. Electronic structures fluctuate over a 5ps (5000 snapshots) time window for all three VOHPs at 300K. The histogram plots for (a) band gaps and (b) the VBM and CBM state energies along the AIMD trajectories of corresponding VOHPs. (c) The mutual information of bandgap with vital structural features. .......................................................................................... 69 Figure 5.2: The excited state charge carrier dynamics in VOHPs at ambient conditions. (a) The population of nonradiatively recombined electron-hole over time in VOHPs. (b) The absolute NAC value between VBM and CBM energy states for a 5ps time window at ambient conditions. (c) The mutual information of NAC with considered key structural features. .......... 74 Figure 5.3. The mutual information of VBM with considered key structural features. ............... 77 Figure 5.4. The mutual information of CBM with considered key structural features................. 77 xii ABSTRACT This thesis presents a comprehensive investigation into the optoelectronic properties of perovskite quantum dots (QDs) and two-dimensional Ruddlesden–Popper (RP) halide perovskites, with a particular focus on defect tolerance, the nature of electronic excitations, and the dynamics of hot phonon and quantum phonon bottlenecks. Through the application of timedependent density functional theory, we analyze the ground and excited states of CsPbBr3 QDs, highlighting their defect tolerance and the critical need to avoid bromine vacancies that result in trap states detrimental to light-emitting diode (LED) performance. Further exploration into the electronic structure of RP perovskites reveals their general defect tolerance. Still, it identifies donor/acceptor defects as potential threats to electronic performance, advocating for strategies to mitigate halide vacancies and interstitial defects. This insight is crucial for enhancing the efficiency of devices based on 2D halide perovskites. Additionally, we address the debated concept of phonon bottlenecks in perovskite nanocrystals through experimental techniques like state-resolved pump/probe and time-resolved photoluminescence spectroscopy. Our findings challenge the prevailing assumption of inherent phonon bottlenecks, demonstrating an absence of such bottlenecks in CsPbBr3 and FAPbBr3 nanocrystals and suggesting efficient Auger processes as a mechanism for rapid cooling and relaxation of hot excitons. This work contributes to the fundamental understanding of defect and phonon dynamics in perovskite materials, providing insights that can guide the design and optimization of perovskite-based optoelectronic devices. By integrating theoretical and experimental approaches, we offer strategies for overcoming challenges related to defects and light interactions, paving the way for advancing perovskite technology. 1 Chapter 1 Introduction Perovskites Figure 1.1. The number of perovskite papers published in the last 24 years. The data in red represents publication years during my Ph.D. Perovskite research has existed for several years but has recently gained massive attention, as seen in Figure 2.1. The general composition for a perovskite takes the form of ABX3, where A is a cation (typically a small molecule such as methylammonium (MA) or inorganic atom such as cesium (Cs), B is a secondary cation (typically lead (Pb)), and X is an anion (typically a halogen), see Figure 1.2a&b 1 for a visual representation. The most popular prototype is the hybrid organic-inorganic perovskite MAPbI3, which has remarkable optoelectronic properties.2-5 Perovskites have been used for various applications for all aspects of light interaction: solar cells,6 light emitting diodes (LEDs),7-9 photocatalysts,10 lasers,11 and x-ray detectors.12-14 Aside from their vast usage, they come in many different flavors: 3D (bulk crystals), 2D (layered), 1D (nanowires/nanorods), and 0D (quantum dots), see illustrations in Figure 1.2c&d.5 Besides their immense application range, perovskites have remarkable 2 optoelectronic properties: high power conversion efficiency, direct bandgap, long carrier lifetimes, small exciton binding energy, and high defect tolerance. Figure 1.2. (a) ABX3 perovskite structure showing BX6 octahedral (Reprinted from Ref 1) (b) Unit cell of cubic MAPbI3 perovskite (Reprinted from Ref 1) (c) Illustration of “material-level” low-dimensional perovskites and 3D perovskite (Reprinted from Ref 5). (d) Illustration of “structure-level” low-dimensional perovskites and perovskite bulk materials (Reprinted from Ref 5). Metal halide perovskites (MHP) have been the leading configurations between perovskites. Most of the attention has been on lead (Pb) variants due to their increased performance and thermal stability. However, the harmful effects of lead (Pb) in perovskite 3 devices significantly hinder their commercialization as we move towards safer environmental options.15 Additionally, progress has been made to investigate the effects of defects on perovskites to increase device performance via defect engineering.16,17 Defects in solids are classified as either intrinsic or extrinsic defects. Extrinsic defects are characterized as interface defects and grain boundaries. This thesis focuses on intrinsic defects, specifically point defects, such as atom vacancies (Schottky defects, ions missing from their regular sites) and atom interstitial (Frenkel defects, ions leave their regular sites and occupy additional sites). Perovskites are hailed for their high defect tolerance. However, it has been determined that in the case of MHPs, halide defects are typically detrimental and perturbed its electronic structure, which must be mitigated to enhance device performance.18-21 These defects create deep level trap states that open up the system to nonadiabatic pathways which reduce performance, an example of such a photophysical processes can be seen in Figure 1.3. 22 4 Figure 1.3. Schematic of photophysical processes in pristine α-CsPbI3 (left), and α-CsPbI3 with dynamic defects, including iodine interstitial (middle) and cesium-iodine switch (right). (Reprinted from Ref 22). Nonadiabatic Molecular Dynamics Nonadiabatic molecular dynamics (NAMD)23-42 is a computational tool for atomistic time-domain modeling of out-of-equilibrium processes in molecular, condensed matter, nanoscale and biological systems. Justified by the mass and timescale separation, a system's faster, typically electronic part is treated quantum mechanically. In contrast, the slower vibrational part is modeled classically or semi-classically. NAMD originated from quantum mechanics. Ehrenfest43 considered equations of motion for quantum-mechanical expectation values and showed that they have the same form as the classical equations of motion, allowing the coupling of classical variables to quantum-mechanical averages. This gave rise to the quantum-classical mean-field approximation, the Ehrenfest approach. Additionally, Landau44 and Zener45 investigated transitions between quantum electronic states induced by a classical atomic motion and derived semiclassical transition probabilities. Notably, a family of trajectory surface hopping (SH) approaches was originated by Tully.46,47 5 Time-dependent Schrödinger equation Consider quantum electrons r⃗ that couple to classical nuclear coordinates R⃗⃗, with the quantum-classical Hamiltonian H = P⃗⃗2 2m + He(r⃗, R⃗⃗) 1.1 The time-dependent Schrödinger equation gives the evolution of the electron iℏ ∂Ψ(r⃗⃗,R⃗⃗) ∂t = H(r⃗, R⃗⃗)Ψ(r⃗, R⃗⃗) 1.2 Expanding the time-dependent wavefunction in an orthonormal basis, φj(r⃗, R⃗⃗), typically formed by eigenfunctions of the Hamiltonian H(r⃗, R⃗⃗) Ψ(r⃗, R⃗⃗) = ∑j cjφj(r⃗, R⃗⃗) 1.3 and expanding into iℏ ∂Ψ(r⃗⃗,R⃗⃗) ∂t = H(r⃗, R⃗⃗)Ψ(r⃗, R⃗⃗) 1.2 gives an equation of motion for the expansion coefficients iℏċ i = ∑ cj (Hij − iℏR⃗⃗ ̇ ⋅ ⃗d⃗ j ij) 1.4 If eigenfunctions of H form the basis, then the electronic Hamiltonian is diagonal, = . The nonadiabatic, or derivative, coupling ⃗d⃗ ij = ⟨φi |∇R⃗⃗ |φj ⟩ = ⟨φi |∇R⃗⃗H|φj ⟩ Ej−Ei 1.5 arises by the application of the chain rule d dt = ∇R⃗⃗ dR⃗⃗ dt. These equations can be used in ab-initio density functional theory (DFT). DFT is typically formulated in the Kohn-Sham (KS) representation.48 Where the wavefunction is a slater determinate 6 Φ(r1, r2, ⋯ , rN) = 1 √N! | ϕ1 (r1 ) ϕ2 (r1 ) ⋯ ϕN(r1 ) ϕ1 (r2 ) ϕ2 (r2 ) ⋯ ϕN(r2 ) ⋮ ⋮ ⋱ ⋮ ϕ1 (rN) ϕ2 (rN) ⋯ ϕN(rN) | 1.6 of time-dependent single electron KS orbitals ϕ(), and the many-body NA coupling is a product of NA couplings between corresponding KS orbitals.49,50 −iℏ ⟨Φi | ∂ ∂t |Φj ⟩ = −iℏ ⟨∏ ϕik (k) N k=1 | ∂ ∂t | ∏ ϕj k ′ (k ′ ) N k ′=1 ⟩ 1.7 = ∑ −iℏ ⟨ϕi k ′ (k ′ )| ∂ ∂t ϕj k ′ (k ′ )⟩ N k ′=1 ∏ δi k ′′j k ′′ N k ′=1,k ′′≠ k ′ 1.8 where −iℏ ⟨ϕi k ′ (k ′ )| ∂ ∂t ϕj k ′ (k ′ )⟩ is the nonadiabatic coupling between KS orbitals i and j, and k, k' refer to electron number. If one uses the Slater determinant basis to perform the NAMD simulations, then Coulomb interactions ⟨|⟩ = 2 2 ∫ r1r2ϕ ∗ (r1 )ϕ ∗ (r2 )12 −1ϕ (r1 )ϕ (r2 ) 1.9 enter as off-diagonal electronic matrix elements,51 Hij, enables one to consider explicitly chargecharge scattering, resulting in Auger-type energy exchange between charges. Surface hopping Tully-originated trajectory surface hopping (SH) approaches.46,47 Tully's algorithm is suitable for modeling condensed phase systems in which quantum transitions can occur over extended timescales, known as fewest switches surface hopping (FSSH), which utilizes probability flux rather than the probability itself to induce hops. First, we define a density matrix, aij = cicj ∗ , which time dependence is deduced from iℏċ i = ∑ cj (Hij − iℏR⃗⃗ ̇ ⋅ ⃗d⃗ j ij) as ȧ ij = ∑j≠i bij 1.10 Where 7 bij = 2ℏ −1 Im(aij ∗ Vij) − 2Re (aij ∗ R⃗⃗ ̇ ⋅ ⃗d⃗ ij) 1.11 The probability of a hop from the current active state i to any other state j over the time interval dt is computed as gij = max { −dt⋅bij aii , 0} 1.12 The classical degrees of freedom are evolved on the potential energy surface corresponding to the active state i: M d 2R⃗⃗ dt2 = −⟨φi |∇H|φi ⟩ 1.13 8 Chapter 2 Defects In 2D Perovskites The material in this chapter is adapted from: Perez, C. M.; Ghosh, D.; Prezhdo, O.; Nie, W.; Tretiak, S.; Neukirch, A., Point Defects in 2D Ruddlesden-Popper Perovskites Explored with ab initio Calculations. The Journal of Physical Chemistry Letters 2022, 13, 23, 5213–5219 Introduction Figure 2.1 The optimized geometry (0 K) primitive cell of pristine 2D-perovskite = 1; 2−13+1 model (BA = butylammonium), composed of 1×1×1-unit cells, with chemical formula H96C32N8Pb4I16 (156 atoms in a cell). Halide perovskites have emerged as unique materials for several applications such as light-emitting diodes (LEDs)52,53, photodetectors53,54, solar cells55-57, and thin-film field-effect transistors (FET)58,59 because of their facile synthesis60,61, convenient solution-based processing, and low fabrication cost55,62,63. Specifically, lead halide perovskites (LHP) have excellent physical and electronic properties, including narrow full width at half-maximum emission lines, high photoluminescence quantum yield, and tunable band gaps64. Although 3D-LHP has shown great promise in its applications, recent investigations focus on low-dimensional materials due to similar optoelectronic properties and superior structural stability and tunability. 9 Thus, significant effort was put into the development and characterization of these lowdimensional materials, including two-dimensional (2D), one-dimensional (1D), and zerodimensional (0D) systems19,65-73. Specifically, 2D Ruddlesden–Popper (RP) perovskites have been the focus of extensive investigations. The general composition of RP perovskite is (RNH3)2(A)n-1BnX3n+1, where R is an alkyl chain or an aromatic ligand that is used as a separating layer between the inorganic planes, A is a monovalent cation (typically Cesium (Cs+ ) or methylammonium (MA, CH3NH3 + ), B is a divalent metal cation (typically lead (Pb2+) or tin (Sn 2+), X is a halogen ion (typically iodine (I- ) or bromine (Br- ), and "n" represents the number of monolayer sheets in between the insulating RNH3 organic layer. These 2D perovskites retain not only excellent optoelectronic properties similar to their bulk countertypes but also include exciting properties such as large exciton binding energy74-76, strong quantum confinement effect73,77,78, and additional bandgap tunability from the thickness of layers (via tuned “n” value, that controls the number of monolayers)70,71. The variation in the number of monolayers leads to changes in stoichiometric proportions, thus tuning the strength of quantum confinement. Due to these changes in quantum conferment between the inorganic layer (serving as potential wells) and the organic layers (serving as potential walls), they resemble multiple quantum wells (MQW)79 . Additionally, heavy atoms, such as lead (Pb), result in large spin-orbit coupling (SOC) within the 2D RP. The SOC causes spin-splitting of the continuum bands (referred to as "Rashba splitting") when the structure undergoes symmetry breaking (typically caused by structural defects). Significant spin-splitting makes these materials promising for spintronic and spinrelated optoelectronic applications80-82 . 10 Table 2.1: List of defects studied with expected low formation energies. Benign Defects Detrimental Defects BA Vacancy (VBA) Iodine Vacancy Iodine Interstitial BA + I Vacancy (VBAI) I (out-of-plane) Vacancy (VI1) I (out-of-plane) Interstitial (II1) Pb + I2 Vacancy (VPbI2) I (In-plane) Vacancy (VI2) I (In-plane) Interstitial (II2) Furthermore, given that the choice of organic layer influences the electronic properties of the inorganic layer by distorting the soft inorganic framework, various combinations of organicinorganic layers have already been characterized. 83,84 However, a robust ab-initio examination of the ground state electronic structure of novel 2D-RP perovskite BA2MAn−1PbnI3n+1 (BA=butylammonium) with the n=1 thickness, the effect of common defects is still mostly lacking, even though perovskites have been widely experimentally characterized. 67,83,85-87 In this study, we employ density functional theory (DFT) on the BA2PbI4 metal halide perovskite (the composition in question is illustrated in Figure 2.1), and examine the ground state electronic structure of several low-formation energy defects commonly seen in this material, listed in Table 2.1. Defects are unavoidable in solution-processed single-crystalline and polycrystalline films, and thus, they frequently present in lower-dimensional (0D - 2D) and 3D bulk perovskites. Therefore, a fundamental understanding of an interplay between defects and optoelectronic properties of 2D halide perovskites is critical. Defects that facilitate charge carrier localization of a hole or an electron, increase their spatial overlap, or create midgap trap states within the CBM/VBM levels in the electronic structure have a negative impact on the charge carrier lifetimes and consequently, the performance of perovskite-based devices88-94. However, congruent with the high-defect tolerance widely associated with many perovskites, most defects investigated were classified as benign, which cause only negligible perturbations to the electronic structure and optoelectronic properties95-99. Except for halogen defects that break the electron spin pairing (i.e., donor/acceptor type defects that result in an unpaired electron), I vacancies (a single missing I atom) or I intestinal (a single additional I atom) lead to localized 11 trap states. Thus, all I defects considered severely affect the electronic structure. Therefore, fabricating such material in moderate I conditions is imperative, thereby mitigating detrimental halide defects. Computational Methodology The pristine 2D-RP perovskite BA2MAn-1PbnI(3n+1) (BA=butylammonium) for the n=1 layer, perovskite composition is seen in Figure 2.1. 100 And was built as a 2×1×2 supercell system (4-unit primitive cells). The supercell was designed to minimize defect-defect interactions within the layers while maximizing computational efficiency. However, to verify a sufficiently large model that captures defects' effects on the electronic structure, we compare model cell sizes of 2×1×2, 1×1×1, 1×2×1, and 1×3×1 (PDOS and band structures of the three detrimental defects shown in Figure 2.11-Figure 2.13). Defect concentration reported experimentally is difficult and impractical to reproduce computationally. Defects are visualized with their relative layer location in Figure 2.2. All calculations were performed at the Density Functional Theory (DFT)48,101,102 level with the projector-augmented-wave (PAW) potentials103,104 and a generalized gradient approximation (GGA)105 functional, PBE106. All calculations were done within the Vienna Ab initio Simulation Package (VASP)107-110. The POTCAR versions included the following PAW PBE per species: PAW_PBE C 08Apr2002, PAW_PBE N 08Apr2002, PAW_PBE H 15Jun2001, PAW_PBE Pb_d 06Sep2000, PAW_PBE I 08Apr2002, PAW_PBE C 08Apr200. We utilized a large ENCUT of 520 eV for both spin-nonpolarized and spin-polarized when appropriate due to an odd number of electrons. We set the KPOINTS along the high-symmetry k-path of Γ-X-U-Z- Γ to accurately probe the electronic structure. Furthermore, to confirm that the localization and formation of the observed trap states in our defect systems were not an artifact of basic PBE calculations, an addition calculational with spin-orbit coupling (SOC) was 12 conducted. In this SOC case, we used a smaller k-path around the k-point location of VBMCBM, as Z-Γ-X, due to the large computation cost associated with SOC calculations. Results & Discussion Figure 2.2. A cartoon rendition of all studies defect location on the n=1 2D-perovskite BA2Pb1I4 system of the in-plane side view. Figure 2.3. Projected density of states (PDOS) with band decomposed charge densities of the band edge states for the Γ point and band structure along the high symmetry k-points of the pristine 2D-perovskite with = 1;ℎ ℎ 2−13+1 model, composed of 2×1×2-unit cells, for the optimal geometry (0 K): The valence band maximum (VBM) originates from I orbitals, with minor contributions of Pb orbitals, whereas the conduction band minimum (CBM) is primarily formed by Pb orbitals. 13 For ab initio investigations, a sufficiently large supercell is required, limiting unphysical defect-defect interactions while keeping the computational cost within reach. Thus, a 2×1×2-unit supercell is chosen for all systems. Nevertheless, to verify if this model captures defects effects on the electronic structure, we compare cell sizes of 2×1×2, 1×1×1, 1×2×1, and 1×3×1 (projected density of states, PDOS, and band structures of the three different defects are shown in Figure 2.11-Figure 2.13). This comparison reveals that trap states formed are not affected by the layer thickness (within 1-3 layers) or defect concentration in x/y plane (2×1×2 (1:624, defect to atom ratio) vs. 1×1×1 (1:156, defect to atom ratio)). Given that experimental defect concentrations (>1015cm3 ) 111 are difficult and mainly impractical to reproduce computationally91, the size comparison illustrates that a 2×1×2 supercell is sufficient for our defect study. First, the characterization of a defect-free "pristine" system serves as a baseline for comparison with defect systems. To this end, the PDOS and band structure along the high symmetry k-points of the pristine system with its optimal geometry is illustrated in Figure 2.3. In a defect-free perovskite system, the valence band maximum (VBM) originates from I orbitals, with minor contributions of Pb orbitals. In contrast, the conduction band minimum (CBM) is primarily formed by Pb orbitals51100. This orbital contribution scheme is consistent with our results, as shown by the PDOS and emphasized by the delocalized nature of the band decomposed charge densities of the VBM and CBM orbitals. Furthermore, the band structure along the high symmetry k-points (Γ→X→U→Z→ Γ) reveals a direct (Γ→Γ) bandgap of 2.11 eV, in agreement with a previous study100 . To characterize the extent of perturbation that point defects cause on the electronic structure of BA2PbI4 2D-perovskite, a wide selection of common low-formation energy defects, was chosen70,94. These defects are listed in Table 2.1 and schematically depicted in Figure 2.2. 14 Defects in question include acceptor-type defects, such as out-of-plane and in-plane iodine interstitial (II1 and II2); donor-type defects, such as out-of-plane and in-plane iodine vacancies (VI1 and VI2); and neutral-type defects, such as BA vacancy (VBA), BA + I Vacancy (VBAI), and Pb + I2 Vacancy (VPbI2). Among these, we have identified neutral-type defects as benign. They do not significantly influence the electronic structure, emphasized by the lack of deep trap state formation within the bandgap, as illustrated in Figure 2.2a-c. Due to the geometry of a monolayer, some defects can exist in the out-of-plane configuration (orientated along the organic-inorganic interface) and in-plane configuration (embedded within the inorganic framework). Figure 2.4. Projected density of states (PDOS) for all systems with the defects at the optimized geometries (0K), composed of 2×1×2-unit cells: (a) BA vacancy (VBA), (b) BA + I Vacancy (VBAI), (c) Pb + I2 Vacancy (VPbI2), (d) I (out-of-plane) Vacancy (VI1), (e) I (In-plane) Vacancy (VI2), (f) I (out-of-plane) Vacancy (iI1) and (g) I (In-plane) Vacancy (iI2). Point defects breaking electron pairs and containing a halogen introduce defects near the band edges. Specifically, 15 halogen vacancies create defects near the CBM, while iodine interstitials create defects near the VBM. Figure 2.5. Projected density of states (PDOS) for the systems with the defects at the optimal geometries for the Γ point, composed of 2×1×2-unit cells: (a) Iodine vacancy in-plane (VI2). (b) Iodine interstitial in-plane (II2), (c) Iodine interstitial out-of-plane (II1). Halogen vacancies create defects near the CBM, while iodine interstitials create defects near the VBM. In contrast, acceptor and donor-type defects significantly influence the electronic structure, resulting in an unpaired electron and breaking the degeneracy of the spin-orbitals. The unpaired electrons occupy a trap state formed within the bandgap, reducing charge carrier lifetimes and mobility111-113. These defects introduce various trap states, as shown in the PDOS 16 plotted in Figure 2.5. Specifically, the halide (donor-type) vacancies result in n-type defects forming shallow trap states near the CBM, and the charge densities of the CBM and VBM are localized to the Pb-I layer containing the vacancy. The halide (acceptor-type) interstitials also result in p-type defects forming deep trap states near the VBM and highly localizing the charge density to the extra iodine atom impurity. Moreover, the simultaneous presence of multiple defects brings the possibility of effective passivation in the defect pair, which are in proximity. For example, suppose a defect introducing a trap state near the top of the VB (i.e., an acceptor-type defect) is combined with a defect creating a trap state near the bottom of the CB (i.e., a donor-type defect). In that case, the resulting neutral-type configuration may leave the overall electronic structure unperturbed. These neutral-type defects (such as BA vacancy (VBA), BA + I Vacancy (VBAI), and Pb + I2 Vacancy (VPbI2).) are benign (see Figure 2.4 a-c) and further emphasize, in part, the persistent defect tolerance ubiquitous in perovskites as we investigate novel 2D materials. In Figure 2.5, we highlight the PDOS of (a) in-plane iodine vacancy due to its higher stability, lower ground state energy, and a deeper trap state position than that of its out-of-plane configuration (see Figure 2.4 d&e) and both (b) in-plane and (c) out-of-plane iodine interstitials leading to the formation of highly localized trap states. Since the degeneracy of the spin-orbitals is broken, spin-polarized calculations are required (i.e., treating the alpha and beta spin components individually). Here, the PDOS shows both spin components. Furthermore, the pristine system contains band edge states delocalized across every Pb-I in-plane layer, leading to the band dispersion of those states (see Figure 2.3). In contrast, for the VI2 defect, while the bands show dispersion and signify delocalization when we examine the charge density of the 17 band edge states, their density is only present on the Pb-I layer containing the vacancy. (see Figure 2.5).” Interstitial iodine defects introduce deep and highly localized trap states for both spin components, while the iodine vacancies are more shallow and less localized within a single spin component. These differences in spin components caused by the various defects can lead to spinpolarized carriers and undergo spin-dependent charge transport, including a preferential spininjection mechanism. 82,114,115 Our results suggest an interesting avenue of research is to investigate iodine-rich systems for spin-injection applications. 2D RP perovskites containing MQWs hold promises for spin-related optoelectronic applications, including spin-LED devices115 , optical spin injection114, and spin-valve devices82. Furthermore, MQWs with tunable bandgaps exhibit quantum-confined carrier transitions and suppress hot-carrier cooling rates.116 These properties of MQWs make 2D-perovskite materials desirable for nanoscale bandgap engineering, creating a unique charge carrier distribution in a particular material. Thus, defect characterization and facile fabrication of 2D-halide perovskite would resolve common bottlenecks that currently limit the expansion of semiconductor heterostructure technologies. 18 Figure 2.6. Projected density of states (PDOS) and band structure of high symmetry k-points near the Γ-point including spin-orbit coupling (SOC), composed of 2×1×2-unit cells: (a) pristine (b) Iodine vacancy in-plane (VI2). (c) Iodine interstitial in-plane (iI2), (d) Iodine interstitial outof-plane (iI1). Halogen vacancies create defects near the CBM, while iodine interstitials create defects near the VBM. 19 Furthermore, to confirm that the localization and formation of the observed trap states in our defect systems are not an artifact of basic DFT calculations, additional calculations with spin-orbit coupling (SOC) corrections are conducted. With the caveat that due to the significant increase in computational cost, only the k-path surrounding the Γ point (the origin of the direct bandgap) was chosen (Z→ Γ→X) for an improved accuracy treatment. The PDOS and band structure of the SOC calculations shown in Figure 2.6 reinforce that interstitial iodine defects (Figure 2.6 c&d) introduce two deep-level trap states (as seen by the two energy-separated peaks) near the VBM, which are highly localized (as seen by the two flat bands across all kpoints, emphasizing a heavy effective mass for electron/holes trapped in those states). Additionally, in the case of excess iodine (both in-plane and out-of-plane interstitial iodine defects), our collinear and non-collinear spin calculations with SOC suggest no fundamental changes in the electronic structure to the energetics of the defect state due to SOC. Thus, by comparing the PDOS and band structure (collinear spin-polarized calculations (Figure 2.12 a & Figure 2.13 a) vs. non-collinear spin calculations (Figure 2.6 c&d)), the deep-level trap states remain unique and present with flat bands, highlighting their continued highly localizing nature. Although the iodine vacancy does not produce flat bands across the k-path, the charge density of the band edge states remains localized to the Pb-I layer containing the vacancy. Unmistakably, trap states introduced by the various defects will lead to broadband emission and decreased performance of this perovskite in LED applications, corroborated by previous studies of similar materials and defects. 19 Thus, a future investigation into defect charge carrier dynamics could probe the extent of decreased performance of these novel 2D-perovskites. 20 Figure 2.7. Projected density of states (PDOS) for the pristine system during the NVE MD trajectory at (a) 500 fs, (b) 1500 fs, and (c) 2000 fs. Figure 2.8. Projected density of states (PDOS) for iodine vacancy system during the NVE MD trajectory at (a) 500 fs, (b) 1500 fs, and (c) 2000 fs. Figure 2.9. Projected density of states (PDOS) for iodine interstitial (out-of-plane) system during the NVE MD trajectory at (a) 500 fs, (b) 1500 fs, and (c) 2000 fs. Figure 2.10. Projected density of states (PDOS) for iodine interstitial (in-plane) system during the NVE MD trajectory at (a) 500 fs, (b) 1500 fs, and (c) 2000 fs. 21 At room temperature (300K), the motion of the atoms causes localized trap states to fluctuate even deeper in and out of the band edge as atoms surrounding the point defect shift. Therefore, charge carrier dynamics must understand whether defect-induced trap states are shortlived or persist under ambient conditions. Molecular dynamic (MD) simulations allow tracking these trap states through their trajectory. Figure 2.7-Figure 2.10 shows the PDOS at various snapshots (500, 1500, and 2000 fs) along the representative MD trajectory. These figures illustrate that the discussed defect states observed for the optimal structures persist at room temperature and thus remain detrimental to 2D RP perovskites. Figure 2.11. Projected density of states (PDOS) and band structure of high symmetry k-points for Iodine vacancy in-plane (VI2) at various depths of unit cells. (a) 2×1×2-unit cells, (b) 1×1×1-unit cells, (c) 1×2×1-unit cells, and (d) 1×3×1-unit cells. 22 Figure 2.12. Projected density of states (PDOS) and band structure of high symmetry k-points for I (out-of-plane) Interstitial (iI1) at various depths of unit cells. (a) 2×1×2-unit cells, (b) 1×1×1- unit cells, (c) 1×2×1-unit cells, and (d) 1×3×1-unit cells. Figure 2.13. Projected density of states (PDOS) and band structure of high symmetry k-points for I (in-plane) Interstitial (iI2) at various depths of unit cells. (a) 2×1×2-unit cells, (b) 1×1×1-unit cells, (c) 1×2×1-unit cells, and (d) 1×3×1-unit cells. Conclusion Our ab-initio calculations provide a detailed description of electronic structure modifications due to the presence of common point defects in 2−13+1 2D- 23 perovskite with n=1 thickness. The results demonstrate that the defect-chemistry in this material is subjugated to the typical iodine redox chemistry observed in other (including 3D and 2D-RP) perovskites, as highlighted by the defect properties of iodine interstitials and vacancies for both in-plane and out-of-plane configurations. Therefore, such materials should be synthesized in Imoderate conditions to mitigate the formation of both iodine interstitials and vacancies above other low-formation energy point defects. Localization of spin states with iodine defects suggests further investigations into Iodine rich systems for spin-injection applications. Although our results highlight no alteration to the energetics of the defect state due to SOC, when considering these materials for potential spin-injection applications, additional simulations with SOC, such as a spin-polarized framework, need to be performed. The detrimental defects, which result in trap states, lead to a broadband emission and potentially poor performance of this perovskite in LED applications. Our modeling demonstrates the origin of trap states and their control over the optical properties that can be mitigated by utilizing appropriate crystal growth conditions. The effect on charge carrier dynamics caused by the formation of the trap states will be further investigated in a separate publication, providing insights into their underlining effects on charge carrier lifetimes as we explore non-adiabatic molecular dynamics (NAMD) and the relaxation of excited electrons and holes. 24 Chapter 3 Defects In Perovskite Quantum Dots The material in this chapter is adapted from: Perez, C. M.; Ghosh, D.; Prezhdo, O.; Tretiak, S.; Neukirch, A., Excited-State Properties of Defected Halide Perovskite Quantum Dots: Insights from Computation. The Journal of Physical Chemistry Letters 2021, 12, 3, 1005–1011 Introduction Lead halide perovskites (LHPs) have emerged as a unique material for various applications such as light-emitting diodes (LEDs), 117 photodetector, 118 and solar cells119,120 due to their facile synthesis, 121,122 convenient solution-based processing, and low fabrication cost.123-126 More specifically, perovskite solar cells have undergone an 11% increase in cell efficiencies in only six years, reaching a remarkable 25.2% power conversion efficiency.119,120 Meanwhile, perovskite LEDs have increased to a photoluminescence quantum yield (PLQY) of ~20% in four years,127-130 further substantiating their promise as a possible candidate for high-performance optoelectronic devices. The general composition for a halide perovskite takes the form of ABX3, where A is a cation (typically a small molecule such as methylammonium (MA) or inorganic cesium (Cs) atom, B is a secondary cation (typically lead (Pb) or tin (Sn)), and X is a halogen (typically iodine (I), bromine (Br), or chlorine (Cl)). The most popular prototype is the hybrid organic-inorganic perovskite MAPbI3, which has remarkable optoelectronic properties.2-4 However, more recently, all-inorganic cesium LHP materials CsPbX3(X=Cl, Br, I) have taken center stage due to their higher thermal stability and lower degradation rate when exposed to air, compared to that for hybrid perovskites.89,131-138 Given the promise shown by 3D bulk LHPs through extensive studies, the focus has eventually shifted to low-dimensional materials, including two-dimensional (2D), onedimensional (1D), and zero-dimensional (0D) systems.139-145 Currently, significant effort has 25 gone into the development and characterization of LHP quantum dots (QDs) (0D systems) with simple solution-based synthesis routes for LHP, such as CsPbX3. 146,147 Similar to their 3D counterparts, LHP QDs have beneficial optoelectronic properties, such as narrow full width at half maximum (FWHM) emission lines, high PLQY, and tunable band gaps.148-150 These sustained properties allow for continued promising applications in solar cells (~ 17% power conversion efficiency), LEDs (~20% quantum yield), lasers, and displays.151-154 Compared to its hybrid counterpart MAPbX3, CsPbX3 QDs have a more controllable diameter and can easily achieve full-spectrum light emission in the visible spectrum range and a high fluorescence quantum efficiency.147,150,154 LHP LED devices are also boasted due to high mobility and increased color purity.155,156 However, these QDs still suffer from the double edge sword of solution-based synthesis: it allows for rapid and facile synthesis, yet unfortunately, it results in unavoidable point defects.157,158 Thus, it is critical to study defects' effects on the excited-state properties of perovskite QDs. CsPbBr3 stands out as a favorable model for a QDs study due to a high PLQY (~90%) with narrow FWHM superior to traditional CdSe‐based QDs, enhanced color purity, excellent batch-to-batch reproducibility, and improvable thermal stability.159-162 Although progress has been made in the characterizations of LHP QDs,100,117-119, a thorough ab-initio computational investigation into the ground and excited-state properties of CsPbBr3 QDs is still lacking. In these low-dimension materials, photoluminescence (PL) is expected to originate from excitation recombination rather than bimolecular recombination.163 Thus, understanding the nature of optical excitations and electronic structure can help guide the optoelectronic properties' tunability. This Time-Dependent Density Functional Theory (TDDFT) investigation focuses on CsPbBr3 QDs in the presence of common low formation energy defects such as Cs, Br, and Pb vacancies, as well as its charge states (+1, -1). Our systems 26 retained high defect tolerance for most of the modeled defects. However, Br vacancies break this trend and severely affect the electronic structure, and thus, it is imperative to avoid Br-deficient conditions, thereby mitigating Br vacancies. Moreover, charge build-up will likely continue the blinking effect observed in other QD systems. Computational Methodology The pristine CsPbBr3 perovskite nanocluster model is visualized in Figure 3.1a. It was built as a 3×3×3 supercell system (27-unit primitive cells). The cluster was designed to preserve charged neutrally with the chemical formula Cs54Pb27Br108 (189 atoms) and has a singlet spin state. A similar approach to model hybrid perovskite clusters has been reported previously.164-166 Experimentally, such clusters have been shown to have Cs/Br terminated surfaces.167 Replicating the Cs/Br terminated surfaces and preserving charge neutrally result in two unique surfaces caused by two Cs vacancies, as seen in Figure 3.1b. An “even” distribution of Cs atoms (12 Cs atoms on the surface layer) and an “uneven” distribution of Cs atoms with a Cs vacancy (11 Cs atoms on the surface layer). There is an unequal distribution of the two surfaces on the pristine system, 4 “uneven” and 2 “even” surfaces. Nevertheless, the geometry is symmetric, allowing for an inversion center along with the opposing Cs vacancy sites. Due to the small size of our model with side lengths of 1.8×1.8 nm, it is expected to observe significant quantum confinement effects in the electronic structure of the perovskite nanocluster (i.e., the small size results in a larger energy gap, and thus blue-shifted spectra when compared to experiment done on larger systems).168,169 The geometry optimization and molecular orbital calculations were performed at the Density Functional Theory (DFT) level. In contrast, excited states and absorption spectra derived from vertical excitations were computed using the Time-Dependent DFT (TD-DFT) method. 27 CAM-B3LYP hybrid functional and LANL2DZ basis set level of theory was employed for all structures170,171 through the Gaussian16 software package.172 CAM-B3LYP best-balanced localized and delocalized states during geometry optimizations and excited state calculations. A conductor polarizable continuum model (C-PCM) with water (ε=78.3553) solvation was employed to mimic dielectric environment effects and mitigate the dangling bonds in perovskites.173 This solvation method is in the range of the static dielectric constant at room temperature for perovskite materials.174,175 While an equilibrium solvation model was used during the geometry optimization, a non-equilibrium solvation model (vertical excitations) was employed for the excited state calculations. A different symmetry between the ground and excited states causes several optically forbidden (dark) transitions. The pristine system is assigned the Ci point group symmetry; thus, the ground state (S0) possesses the Ag symmetry. Only excited states with Au symmetry would be symmetry allowed (i.e., Ag →Au would be bright states). For example, S1 and S2 states have Ag symmetry and thus are symmetry-forbidden transitions from the S0 state and, consequently, are dark states (oscillator strength=0). The symmetry of the excited states provides quick insight into expected bright and dark transition states. Notably, these symmetry rules get relaxed due to, for example, thermal fluctuations and spin-orbit coupling effects. The overlap of the contributing electronic wavefunctions is another major factor of the oscillator strength for symmetry-allowed transitions. The more substantial the spatial overlap of the orbitals involved, the larger the resulting oscillator strength of that transition. The strength in this overlap is supported by the plotted natural transition orbitals (NTOs) shown in Figure 3.9-Figure 3.16. NTO analysis is used to avoid inspecting many MOs when discussing electron excitation. Typically, NTOs provide a single dominant pair that highlights the electronic distribution of 28 excitation. When there is still no single NTO pair with a dominating contribution, an alternative electron excitation analysis should be used. One such method is the representation of the hole and electron distribution.176 Figure 3.16 compares the visual representation of the first and third electrons between the NTO and “hole-electron” analysis. Both methods capture the qualitative tends of localization to the model's edges. Therefore, the NTO is enough to describe the general trends of the electron excitations for all modeled systems. Additionally, the NTO analysis preserves orbital phase information, which is lost in the electron-hole analysis. Results & Discussion Figure 3.1. (a) Charge neutral pristine CsPbBr3 nanocluster (3×3×3; 27-unit cell system), with Cs and Br terminated surface. (b) Unique surfaces of a cluster. Uneven surface natively contains a Cs vacancy. 29 The charge-neutral pristine CsPbBr3 perovskite nanocluster model under consideration is visualized in Figure 3.1a, with two unique terminated surfaces shown in Figure 3.1b. In comparison, our model system is smaller than experimentally investigated species due to the numerical cost involved in modeling large systems. However, we expect to have qualitatively similar excited state features of both pristine QD and its defected counterparts.177 We aim for a comprehensive computational investigation of this nanocrystal in the presence of various defects. Only charged vacancy defects are considered here to give a spin-multiplicity of 1 required for spin-allowed singlet-singlet transitions. Table 2.1 provides a complete list of defects that we have considered in this study. These defects are chosen for their common appearance and low formation energy in bulk CsPbBr3 perovskite material.99,157,178 Specifically, halide defects have been shown repeatedly as the most readily produced defect with the lowest formation energy, which has the strongest effect on the electronic properties of CsPbX3 perovskites.99,157,178 Furthermore, we have also investigated charged systems in the form of a singly positively charged (+1) and negatively charged (-1) version of the neutral CsPbBr3 QD as a way to probe the blinking effect commonly observed in semiconductor QDs.179-181 This large array of defects allows us to review expected optical phenomena in perovskite QDs properly. Table 3.1. Modeled defect types and their location on the CsPbBr3 nanocluster. 30 Type Location Cs+1 Even Surface Uneven Surface near-native Cs vacancy Uneven Surface far from native Cs vacancy Pb+2 Even Surface Uneven Surface Center “Bulk like” Br-1 Even Surface Uneven Surface +1 [Cs54Pb27Br108] +1 -1 [Cs54Pb27Br108] -1 31 Figure 3.2. (a) Simulated UV-Vis spectra of the pristine CsPbBr3 nanocluster representing 15 singlet transitions. The oscillator strengths for the transitions are shown as black sticks caped with a cross (left scale). The resulting absorption profile is shown in blue, with the max peaks highlighted by a vertical dashed line (4.78 and 4.80 eV) (right scale). (b) The density of states (DOS) of the pristine system highlights contributing atom types (the vertical dash line represents the HOMO level). A common experimental method for probing low-lying energy states, such as the band gap, is ultraviolet-visible spectroscopy (UV-Vis). The lowest energy peak (i.e., the band edge) observed in the UV-Vis spectrum of a material can be approximated by the calculated energy gap (EHL) being a difference between the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO).182 However, a more accurate representation would come from excited-state calculations typically done via TD-DFT methodology using hybrid functionals accounting for excitonic effects.182,183 The Methods section outlines computational methodologies used in this work. The first step is to analyze optically allowed transitions. Given that the pristine and all vacancy-containing QDs have a singlet ground state, here we focus only on singlet-singlet transitions, assuming singlet to triplet transitions are optically forbidden (when neglecting spin-orbit interactions). The UV-VIS profile for the pristine CsPbBr3 nanocluster comprised of the first 15 singlet transitions is shown in Figure 3.2a, with calculated band peaks at 4.78 and 4.80 eV. Experimental band gaps for a 4nm highly stable and reproducible QD are around 2.75 eV.168,169 32 Additionally, the smallest reported CsPbBr3-based QDs are ~1.1nm with a more pronounced blue-shifted bandgap of ~2.86 eV.184 Our nanoclusters have a cubic sidelength of ~1.8 nm and are within experimentally viable sizes. The higher energy band gaps we report here are due to enhanced quantum confinement effects, given that considered nanoclusters are smaller than most experimentally stable sizes (> half in size) and our functional choice. The perturbative methods such as ACD(2)/CC(2) may be employed to check the functional dependence of the band gap. However, uncertainty on real improvement over TD-DFT and significantly higher computational costs for these methods currently prohibit us from exploring such options. Note that the quantum confinement effect appears as the QDs become smaller than the exciton Bohr radius of the material. The CsPbBr3 QDs have a reported excitation Bohr radius of ~7nm.168,184-186 Thus, the considered small sizes QDs would be expected to have a strong quantum confinement effect, resulting in substantial blue-shifts in the bandgap. Although macro tuning of the bandgap is generally achieved from compositional engineering of the perovskite (i.e., changing the halide ion), the ability to fine-tune the bandgap with cluster size is a positive feature of LHP QDs for blue LED candidates.160,184,187 33 Figure 3.3. Simulated UV-Vis spectra of the CsPbBr3 nanocluster with defects calculated from the 15 lowest-energy singlet transitions. (a) Cs defects, (b) Pb defects, (c) Br defects. Here “E” represents a defect from the even surface, and “U” represents a defect from the uneven surface (see Table 3.1 for defect locations). Computed UV-Vis profiles of the vacancy defect for Cs+1, Pb2+, and Br-1 are shown in Figure 3.3. The various Cs defects perturbed the spectra to a similar extent as seen by the overlapping UV-Vis profiles, which are red-shifted when compared to the first peak in the pristine system, Cseven (Δ=-3.09 meV), Csfar uneven (Δ=-0.71 meV) Csnear uneven ( Δ=-3.41 meV). Although the individual transition peaks and oscillator strengths vary (see Figure 3.5-Figure 3.6), the overall profile remains unchanged. However, the break in the symmetry caused by the vacancies results in the oscillator strengths being controlled by the orbital overlap to a greater extent.188 Pb defects have a more pronounced effect on the UV-Vis profile, where the initial 34 peaks differ as follows: Pbeven (Δ=-63.77 meV), Pbuneven (Δ=-54.90 meV), PbCenter (Δ=-39.14 meV) (Figure 3.3b). The Pb vacancy on an even surface introduces the largest perturbation to the system, as seen by the large redshift in the initial band peak and by the absorption peak, two times larger than that of the pristine system. The largest change to the UV-Vis profile is due to Br vacancies on either surface. There is a large redshift in the first band peak, Breven (Δ=-566 meV) and Bruneven (Δ=-582 meV) (Figure 3.3c). This is due to the lowering of the energy of the LUMO level caused by a strong spatial localization on the vacancy site (see NTO/MO in the SI Section 4). Additionally, the Br vacancy creates shallow LUMO defects consistent with experimental bulk studies where halide vacancies create trap states near the conduction band.99,157,178 As a continued testament to the extensively reported defect tolerance of CsPbX3 perovskite materials,99,157 the various vacancy defects have a minimal effect on the electronic properties of the systems, apart from the Br vacancies. Given the trap states caused by the Br vacancies and lack of effect from Cs vacancies, it is best to synthesize these QDs materials in a Br rich/Cs poor environment to reduce undesirable halide vacancies and promote increased performance.99 Trap states allow non-radiative pathways to dominate excitation decay and reduce performance.89 Although some modeled defects cause trap states, their effect on the nonadiabatic charge-phonon coupling and dephasing times has yet to be predicted. Thus, the non-radiative decay rates cannot be accurately determined for the various modeled defects. However, nonadiabatic molecular dynamic studies have been previously conducted on the parent CsPbBr3 QD, which discusses methods for controlling electron-hole recombination.189-192 The optimal conditions of the bulk CsPbBr3 and the formation energy of defects have been previously reported and completely align with our present 35 results.99,157 This alludes to the expected high performance of perovskite QDs for various photoluminescent applications. Figure 3.4. (a) UV-VIS spectra comparison between the charged defects, (b) the DOS of the positively charged defect (resulting LUMO shown), (c) the DOS of the negatively charged defect (resulting HOMO shown). Quantum dots as a class have been reported to provide a degraded performance when experiencing a blinking phenomenon, a fluctuation of photoluminescence (i.e., switching between active and dark states).193-195 Blinking has been explained through the charging model in which the fluctuation is caused by photoionization and neutralization (i.e., a buildup of either positive or negative charge causes reduced photoluminescence).193-195 This blinking effect can be probed by modeling an ionic system (i.e., a system with a single positive or negative charge) to provide insight into its continued impact on the newer perovskite QDs. The UV-Vis profile comparison between the charge-neutral (pristine) and singly charged systems (positive & negatively charged ion system) is shown in Figure 3.4a. As expected, a charge buildup in the 36 system causes lower oscillator strengths in the observed transitions; see individual transitions for charged systems in Figure 3.5-Figure 3.6. The UV-Vis profiles of the charged systems are oneto-two orders of magnitude lower than that of the neutral system, with the negative charge underperforming by a factor of 80 and the positive by a factor of 15. Note that both charged system spectra are significantly red-shifted compared to the pristine system. This can be attributed to the MO localization into the system's center, as seen in Figure 3.4b&c. For the positively charged system, the LUMO is a localized defect state and thus destabilizes the orbital, which raises in energy when compared to the HOMO of the pristine system. In the negatively charged system, the HOMO is a localized defect state and thus stabilizes the orbital, which lowers the energy when compared to the LUMO of the pristine system. This localization and energy reordering of the orbitals results in a lower HOMO-LUMO gap of the charged states, see Figure 3.4b&c, which affects the calculated UV-Vis spectra. As the LUMO in the positive system is destabilized by 2.35 eV, while the HOMO in the negative system is stabilized by 4.28 eV, the positive system has a greater overall redshift in the absorption profile. Thus, it is reasonable to expect blinking phenomena to be observed in the photoluminescence of perovskite quantum dots unless charge stabilization is achieved by, for instance, an appropriate shell of surface agents. Thus, implementing conventional mitigation strategies to reduce system charging of traditional QDs will continue to benefit the new LHP QDs.196-198 Note that recent spectroscopic studies have extensively studied the excited state charge distribution and dynamics.199,200 These studies strongly indicate that perovskite QDs' charging can adversely affect their absorption and emission profile. As discussed here, our simulations provide in-depth reasoning of the charging-effect at an atomistic level. 37 Conclusion We have modeled several low energy formation defects and charge build-up in the model LHP CsPbBr3 nanocluster. True to its perovskite nature, our quantum dot retained defect tolerance, except for Br and charge defects. Therefore, defects that create localized electronic states resulting in shallow or deep-level trap states open the system to non-radiative relaxation pathways.163,194,195 These non-radiative pathways dictate the “on/off” behavior and lower photoluminescence. Consequently, it is vital to mitigate the low formation energy defects that cause the considered trap states in the material to optimize device performance. Notably, one should avoid halide vacancies, which can be reduced during synthesis in a halide-rich and/or Cspoor environment. Alternatively, several methods of surface passivation have improved charge carrier delocalization198,201,202 and other methods that minimize vacancy concentration.203,204 More generally, our results highlight properties of defects that can affect the performance of devices containing CsPbBr3 nanoparticles. 38 UV-Vis plots Pristine Positive Charge Negative Charge Br Vacancy on Even Surface Br Vacancy on Uneven Surface Figure 3.5. UV-Vis spectra of first 15 excited states for the pristine and high perturbance defects; (a) pristine, (b) positively charged, (c) negatively charged, (d) Br vacancy on the even surface, and (e) Br vacancy on the uneven surface. The oscillator strengths for the transitions are seen in black and caped with a cross (left scale). The Absorption is seen in the blue (right scale). (a) (b) (c) (d) (e) 39 Pb Vacancy on Even Surface Cs Vacancy on Even Surface Pb Vacancy on center bulk Cs Vacancy on Close Uneven Surface Pb Vacancy on Uneven Surface Cs Vacancy on Far Uneven Surface Figure 3.6. UV-Vis spectra of first 15 excited states for the low perturbance defects; (a) Pb vacancy on the even surface, (b) Cs vacancy on the even surface, (c) Pb vacancy on the center of the cluster “bulk-like,” (d) Cs vacancy on the uneven surface near existing Cs vacancy, (e) Pb vacancy on the uneven surface, and (f) Cs vacancy on the uneven surface far from existing Cs vacancy. The oscillator strengths for the transitions are seen in black and caped with a cross (left scale). The Absorption is seen in the blue (right scale). (a) (b) (c) (d) (e) (f) 40 Density of state (DOS) plots Pristine Positive Charge Negative Charge Br Vacancy on Even Surface Br Vacancy on Uneven Surface Figure 3.7. DOS of the pristine and high perturbance defects: (a) pristine, (b) positively charged, (c) negatively charged, (d) Br vacancy on the even surface, and (e) Br vacancy on the uneven surface. Here the vertical dash line indicates the HOMO level. The FWHM was set to 1.0 eV. LUMO HOMO (a) (b) (c) (d) (e) 41 Pb Vacancy on Even Surface Cs Vacancy on Even Surface Pb Vacancy on center bulk Cs Vacancy on Close Uneven Surface Pb Vacancy on Uneven Surface Cs Vacancy on Far Uneven Surface Figure 3.8. DOS of the low perturbance defects; (a) Pb vacancy on the even surface, (b) Cs vacancy on the even surface, (c) Pb vacancy on the center of the cluster “bulk-like,” (d) Cs vacancy on the uneven surface near existing Cs vacancy, (e) Pb vacancy on the uneven surface, and (f) Cs vacancy on the uneven surface far from existing Cs vacancy. Here the vertical dash line indicates the HOMO level. The FWHM was set to 1.0 eV. (a) (b) (c) (d) (e) (f) 42 Natural transition orbitals and molecular orbitals for high perturbing systems. Pristine Excited State Transition Energy (eV) Oscillator Strength Primary Dominate NTO pair Secondary NTO Pair “hole” “electron” “hole” “electron” 1 4.7384 0.0000 25.0% 21.5% 2 4.7509 0.0000 25.5% 16.8% 3 4.7607 1.0708 31.7% 30.7% 7 4.7791 1.2606 25.3% 22.6% 10 4.7867 1.3535 24.0% 21.7% Figure 3.9. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the pristine system. The percent contribution is given for each NTO pair. 43 Br Uneven Excited State Transition Energy (eV)Oscillator Strength Primary Dominate NTO pair Secondary NTO Pair “hole” “electron” “hole” “electron” 1 4.2026 0.1903 97.0% 2.2% 2 4.5357 0.2216 91.6% 5.6% 3 4.6721 0.0041 97.1% 0.6% 8 4.7601 0.4865 22.0% 17.5% 9 4.7619 0.6270 24.1% 16.2% Figure 3.10. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the Br uneven defect. The percent contribution is given for each NTO pair. 44 Br Even Excited State Transitio n Energy (eV) Oscillat or Strengt h Primary Dominate NTO pair Secondary NTO Pair “hole” “electron” “hole” “electron” 1 4.2192 0.1634 97.4% 1.8% 2 4.5459 0.2174 92.3% 4.9% 3 4.6940 0.0725 90.1% 3.5% 8 4.7609 1.3689 36.6% 30.4% 9 4.7700 0.2965 28.6% 18.1% Figure 3.11. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the Br even defect. The percent contribution is given for each NTO pair. 45 Negative Charge Excited State Transition Energy (eV) Oscillator Strength Primary Dominate NTO pair Secondary NTO Pair “hole” “electron” “hole” “electron” 1 1.5229 0.0000 99.91% 0.04% 2 1.5691 0.0000 99.90% 0.04% 3 3.1304 0.0089 99.73% 0.09% 6 3.1847 0.0040 99.82% 0.11% 10 3.2546 0.0023 99.46% 0.43% Figure 3.12. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the negative charge system. The percent contribution is given for each NTO pair. 46 Positive Charge Excited State Transition Energy (eV)Oscillator Strength Primary Dominate NTO pair Secondary NTO Pair “hole” “electron” “hole” “electron” 1 1.2688 0.0000 99.15% 0.39% 2 1.3065 0.0000 99.02% 0.51% 3 1.3416 0.0000 99.04% 0.35% 6 1.4489 0.1040 99.33% 0.24% 7 1.4583 0.0989 99.28% 0.32% Figure 3.13. Natural transition orbitals pairs of the first three electronic transitions and the two with the strongest oscillator strength within the first ten transitions for the positive charge system. The percent contribution is given for each NTO pair. 47 Orbital Pristine (eV) Negative (eV) Positive (eV) LUMO+3 -0.496 -0.471 -0.537 LUMO+2 -0.514 -0.473 -0.557 LUMO+1 -0.534 -0.492 -0.564 LUMO -0.546 -0.518 -4.631 HOMO -6.986 -4.835 -7.034 HOMO-1 -7.199 -6.992 -7.091 HOMO-2 -7.207 -6.998 -7.226 HOMO-3 -7.216 -7.169 -7.231 Figure 3.14. Spin orbitals from HOMO-3 to LUMO+3 for comparing the charged systems against the pristine system. 48 Orbital Pristine (eV) Br Even (eV) Br Uneven (eV) LUMO+3 -0.496 -0.535 -0.535 LUMO+2 -0.514 -0.653 -0.633 LUMO+1 -0.534 -0.691 -0.673 LUMO -0.546 -1.290 -1.286 HOMO -6.986 -7.023 -7.025 HOMO-1 -7.199 -7.218 -7.227 HOMO-2 -7.207 -7.234 -7.228 HOMO-3 -7.216 -7.246 -7.246 Figure 3.15. Molecular orbitals from HOMO-3 to LUMO+3 were used to compare Br defects with those of pristine systems. 49 Pristine NTO Excited State Transition Energy (eV) Oscillator Strength Primary Dominate NTO pair Secondary NTO Pair “hole” “electron” “hole” “electron” 1 4.7384 0.0000 25.0% 21.5% 3 4.7607 1.0708 31.7% 30.7% Pristine hole-electron analysis Excited State Transition Energy (eV) Oscillator Strength “Hole” “Electron” 1 4.7384 0.0000 3 4.7607 1.0708 Figure 3.16. Comparison between NTO pairs and a localized hole-electron analysis 50 Chapter 4 Auger Process in Perovskite Quantum Dots The material in this chapter is adapted from: Baker, H.; Perez, C. M.; Sonnichsen, C.; Strandell, D.; Prezhdo, O.; Kambhampati, P., Breaking phonon bottlenecks through efficient auger processes in perovskite nanocrystals. ACS Nano 2023, 17, 4, 3913–3920 Introduction Metal halide perovskite nanocrystals (PNCs) have been shown to possess promising optoelectronic properties for use in devices such as high-performance solar panels and lightemitting diodes.141,160,205,206 Thus, understanding the fundamental behavior of photoexcited carriers is crucial for producing efficient devices.207,208 Importantly, the carrier dynamics in PNCs have been shown to exhibit liquid-like behavior due to their dynamic, ionic lattices.209-212 This liquid-like behavior results in polaron formation and protection of charge carriers from trapping. 209,213-215 The protection from trapping plays a particularly important role for hot carriers, which could be used in hot-carrier solar cells to break the Shockley-Queisser limit.208,216 The simple but fundamental question arises of the time-scales and pathways of carrier relaxation or thermalization. Many studies on PNCs, both strongly and weakly confined, have shown that relaxation occurs on time-scales of multiple picoseconds at high excitation densities.215,217-219. The same results are observed in perovskite films; the result is general to perovskites. These slow cooling rates have been attributed to an initially fast redistribution of energy through coupling to the longitudinal optical (LO) phonon, followed by a slower process due to total occupation of this phonon mode, a phenomenon known as the “hot phonon bottleneck”.217-221 Further to this, Auger heating processes have also been identified as a mechanism for extending hot carrier lifetimes.218,222 The point is that one expects to see hot carriers on the ten ps time-scale at high densities. 51 Though many studies have suggested the observation of the hot phonon bottleneck and slow cooling in PNCs, others have found much faster cooling rates on the order of 100s of femtoseconds in quantum dot (QD) versions of the PNC.223-226 In QD PNCs, the fast relaxation is attributed to processes usually associated with the electronic structure of quantum-confined systems for which a “quantum phonon bottleneck” becomes relevant. In quantum confined systems such as quantum dots (QD), there are Auger energy transfer and multi-phonon emission, rather than the expected bulk mechanisms, thereby breaking the quantum phonon bottleneck.225,227 Furthermore, for strongly confined PNCs at low excitation densities, the observed fast carrier cooling rates and breaking of the quantum phonon bottleneck have been attributed to non-adiabatic coupling to surface ligands, similar to that of holes in CdSe.228,229. A wide variety of results have emerged regarding the basic process of hot carrier thermalization in semiconductor perovskites. Hence, the fundamental question of time-scales and hot carrier relaxation pathways in the bulk PNC model system remains controversial. The basic questions remain ambiguous about whether there is a hot phonon bottleneck under high carried densities and whether the quantum phonon bottleneck is relevant for bulk systems. Computational Methodology Density functional theory (DFT)48,101,102 ab-initio molecular dynamics (AIMD) with the projector-augmented-wave (PAW) potentials103,104 and the Perdew-Burke-Ernzehof (PBE) functional under the generalized gradient approximation105,106 was employed for all systems. The electronic structure and AIMD calculations were performed within the Vienna Ab-initio Simulation Package (VASP)107,109,110 The PAW PBE versions included in the POTCAR files for each species were PAW_PBE Cs_sv 08Apr2002, PAW_PBE Pb 08Apr2002, and PAW_PBE Br 06Sep2000. During the VASP calculations, we utilized a sizeable plane-wave basis energy cutoff (ENCUT) of 520 eV, and a 1×1×1 Γ centered k-point mesh to sample the Brillouin zone. The 52 simulation cells were constructed as 2×2×3 supercells containing 12 formula units of APbBr3 (A= FA or Cs). We included van der Waals (vdW) dispersion interactions within the DFT-D3 method for all the simulations.230 The mixed quantum-classical nonadiabatic molecular dynamics (NAMD) simulations were performed using Tully’s fewest switches surface hopping (FSSH),231 implemented within real-time time-dependent DFT.232 The classical path approximation was applied to FSSH,50,233 as implemented in the PYthon eXtension for Ab Initio Dynamics (PYXAID) code. 50,233 The Coulomb interactions between electrons and holes were included into the simulations to model simultaneously the electron-vibrational and Auger energy relaxation channels.51 The AIMD simulations were conducted with a 1×1×1 Γ centered k-point mesh and a time step of 1 fs. All systems were slowly heated from geometry optimized 0K structures to 300 K using repeated velocity rescaling for 3 ps, followed by a thermal equilibrium calculation for 3 ps under the canonical ensemble (NVT). Lastly, the 3 ps production run trajectories were generated in the microcanonical ensemble (NVE). The entire 3 ps NVE trajectories were utilized to compute the nonadiabatic and Coulomb coupling matrix elements. During the NAMD simulations, every 150th geometry throughout the 3 ps trajectory has been considered as the initial geometry, giving 20 initial conditions. We modeled the FSSH process with 300 stochastic realizations for each initial condition. Experimental Evidence All spectroscopic experiments were conducted by the Kambhampati group. 53 Figure 4.1. Time dependent survival probabilities of both electrons and holes are reflected by the ΔΔOD transients, probed at the band edge bleach (electrons) and the excited state absorption sub-resonant to the band edge (holes). a) ΔΔOD transient, representing the survival probability of electrons, in CsPbBr3 (light red), fit to a varying rate model (dark red) and how these rates vary (purple line). Cartoon shows electron cooling. b) The same as a) but for FAPbBr3. c,d) ΔΔOD transient, representing hole survival probabilities, in CsPbBr3 (c, red) and FAPbBr3(d, blue). Darker lines are a biexponential fit as a guide to the eye. Cartoons in c,d) show initial electron cooling through Auger heating (c), followed by hole cooling (d). The carrier density is <N> = 1 per NC, corresponding to a density of 3.0 x 1017 cm-3. The bleach dynamics for each sample are shown in Figure 4.1. Upon 3.1 eV excitation (blue), an attenuated bleach response is observed in both types of P NC, building up over the first picosecond after excitation. With band-edge excitation (green), an instrument response limited bleach is observed with a fast recovery after the first 200 fs. The difference spectra are OD, in which the band edge pump signal is subtracted from the 3.1 eV pump signal to reveal hot carrier processes directly. An energetic or initial state-resolved method and suitable time-frequency resolution are required to separate electronically state-to-state transitions and disentangle carrierspecific dynamics. Here, the energetic or quantum state is controlled by subtracting the pumpprobe signal with band-edge excitation from that obtained at 3.1 eV. Carrier specificity is obtained by changing the energy the pump-probe signal is monitored. Electron dynamics are reflected through monitoring of the band edge bleach, whereas hole dynamics are reflected in the 54 PIA dynamics.229,234,235 This method, yielding a ΔΔOD transient, directly follows the difference between carriers with excess energy (hot carriers) and those already completely cooled (bandedge carriers). Importantly, the combination of time and initially pumped state enable measurement of dynamics with ten fs precision, thereby making this analysis possible. The resulting transient represents the time-dependent survival probability of hot carriers specific to either electrons or holes. The ΔΔOD transients for electron thermalization in Cs and FA PNCs are shown in Figure 4.2. In both cases, the electron relaxes rapidly over a time scale of ~400 fs, qualitatively faster than the rate extracted from the tail-fitting method. Notably, by the first picosecond, there is almost no difference in carriers excited to the continuum and the band-edge. The timescales upon which this occurs are an order of magnitude faster than those extracted from the tail fitting, indicating the absence of a quantum phonon bottleneck in these materials. This observation of a breaking of the expected phonon bottleneck raises the question of the mechanism, given these are bulk nanocrystals. Relaxation from the continuum occurs through complex channels, including the occupation of phonon modes and Auger processes, following quantum dynamics. Here, a simple model is proposed to describe these complex processes; the initial electron relaxation occurs through a dense manifold of states in the continuum, which becomes sparser as the electron approaches the band edge. Full details of this model can be found in the Supplement. It is noted that other models have been proposed in the literature.236,237 In both cases, this quantum dynamic model returns the qualitative behavior of the experimental data at an initially fast rate, decaying rapidly over ~400fs, followed by a significantly slower rate after this time. More important than 55 the fit quality is that the quantum dynamical model rationalizes the observations regarding simple theory that can be tested. Further evidence of quantum effects arising during the thermalization process can be seen in the hole dynamics shown in Figure 4.1. The aim is to see if some electron-to-hole type of energy transfer process might be resolvable by a buildup in a hole signal. In both cases, a rise time of ~200 fs is observed, followed by a slower cooling process. The growth observed is a signature of electron-hole energy transfer through intra-band Auger relaxation, as is seen in traditional II-VI semiconducting NCs such as CdSe, followed by a phonon-mediated cooling process.28,42 Different to CdSe and other semiconducting nanocrystals, PNCs show a delay before the onset of hole heating through Auger processes, beginning roughly 200 fs after photoexcitation. To evaluate the hot phonon bottleneck that is more commonly discussed in perovskites than the quantum phonon bottleneck, we also perform experiments at high carrier concentrations. Figure 4.2 shows the SRPP and t-PL data with both band edge pumping and 3.1 eV pumping at high excitation densities. In the low-density case, <N> = 1, whereas in the high-density cases, <N> = 5, corresponding to a density of 1.5 x 1018 cm-3 . At these excitation densities, hot phonon bottlenecks are assumed to arise from the prior TA measurements. The SRPP measurements at high fluence reveal 1 – 10 ps timescale dynamics. However, the same dynamics are seen with band edge pumping into cold carriers with no excess energy, as in the case of 3.1 eV pumping into hot carriers. If the 1 – 10 ps dynamics in TA measurements are due to hot carrier cooling, why is there the same cooling process when there is no excess energy? These experiments reveal complexities in the nonlinear spectroscopy of perovskite NC that need to be better understood, and they are currently obfuscating the evaluation of the hot phonon bottleneck. 56 We directly measure the presence of hot carriers at high concentration and perform t-PL measurements with three ps time resolution and selective pumping into both the band edge and at 3.1 eV. At low carrier concentrations of <N> = 1, no hot PL is observed at either pump photon energy. At high carrier concentrations of <N>~5, once again, there is no hot PL observed. Since the time resolution of the t-PL is 3 ps, the 10 ps dynamics in TA experiments should be easily visible. Even 1 ps hot PL should be observable with this time resolution, albeit within the instrument response function. The complete absence of hot PL at a 3.1 eV pump at high carrier density is proof that there is no hot phonon bottleneck in these bulk perovskite NC. Figure 4.2. SRPP spectra under high fluence conditions with band edge pumping (left) and 3.1 eV pumping (right). The yellow curves are to guide the eye. Here, <N> = 5, corresponding to a density of 1.5 x 1018 cm-3 . t-PL spectra at low and high fluence, with energy resolved pumping in order to directly test slow relaxation at high density. a) t-PL spectrum at low fluence with 3.1 eV pumping. Here, <N> = 0.015, corresponding to a density of 4.5 x 10-15 cm-3 . b) t-PL spectrum at 57 high fluence with 3.1 eV pumping. Here, <N> = 7.4, corresponding to a density of 2.2 x 1018 cm3 . c) t-PL spectrum at low fluence with 2.6 eV pumping. Here, <N> = 0.017, corresponding to a density of 5.1 x 1015 cm-3 . d) t-PL spectrum at high fluence with 2.6 eV pumping. Here, <N> = 4.2, corresponding to a density of 1.3 x 10-18 cm-3 . Results & Discussion Figure 4.3. Comparison of electron cooling for single (SE) and double (DE) electron excitations in a) CsPbBr3 and b) FAPbBr3. DEs are slightly faster than SEs because DEs have more channels for energy relaxation. The canonically averaged DOS is included for each system, together with a structure cell. Charge densities of the band edge and excitation orbitals are shown in Figure S5. Comparison of electron SE and hole cooling (HC) for c) CsPbBr3 and d) FAPbBr3. We perform ab initio quantum dynamics calculations, to investigate the impact of Auger and electron-vibrational relaxation processes on electron cooling in CsPbBr3 and FAPbBr3. The modeled systems are composed of 2×2×3 supercells containing 12 formula units of APbBr3 (A=Cs or FA), as shown in the inserts of Figure 4.3. The density of states (DOS) of both systems is asymmetric, with the valence band (VB) rising faster than the conduction band (CB). This indicates that the pump energy is distributed unevenly between electrons and holes, with 58 electrons gaining more energy than holes because there are more hole states close to the band edge. Subsequently, the energy is transferred from electrons to holes via the Auger mechanism. The higher VB DOS also indicates that energy spacings are smaller in the VB than the CB, and hence, the non-adiabatic coupling (NAC) is stronger for holes than electrons, as shown in Figure 4.4. As established previously, the stronger NAC results in faster hole-vibrational relaxation than electron-vibrational relaxation.21,238-241 Finally, the DOS is slightly higher in CsPbBr3 than FAPbBr3, in particular in the VB. The higher VB DOS provides a larger density of hole states, accelerating Auger energy transfer from electrons to holes in CsPbBr3 relative to FAPbBr3. Figure 4.4. Canonically averaged absolute nonadiabatic (NAC) coupling for a) CsPbBr3 and b) FAPbBr3. The NAC is larger in the valence band (VB) than conduction band (CB) because the VB DOS is higher than the CB DOS, Figure 4.6. The VB NAC is larger for FAPbBr3 than CsPbBr3 rationalizing why holes relax faster in the former, Figure 4.3c,d of the main text. Panels a and b of Figure 4.3 present the relaxation of electrons in CsPbBr3 and FAPbBr3 following either a single excitation (SE) or a double excitation (DE). Two representative initial conditions are chosen in each case. Auger energy transfer from electrons to holes, and electronvibrational relaxation take place simultaneously. However, the Auger mechanism dominates, resulting in sub-100 fs relaxation timescales. The relaxation is faster in CsPbBr3 than in FAPbBr3 because of the higher VB DOS in the former. The calculated timescales agree with the experimental data, Figure 4.1a&b and are somewhat faster because the simulated systems are 59 small due to computational limitations, the charges are close to each other, and the Coulomb interactions are enhanced. The relaxation of electrons is purely due to coupling to phonons, which occurs on a much longer picosecond timescale, as established in the earlier calculations. 21,238-241 Panels a and b of Figure 4.3also show the relaxation of electrons following a double excitation (DE). Relaxation is also dominated by energy transfer to holes rather than by the electron-vibrational mechanism. Notably, the relaxation of electrons following a DE proceeds on the same timescale and is even slightly faster than the relaxation following a SE, and no phonon bottleneck is observed. The DE leads to a slightly faster relaxation than the SE because of a larger number of relaxation pathways available with two excited electrons. Finally, parts c and d of Figure 4.3 present hole cooling (HC) due to coupling to phonons. The HC takes several hundred femtoseconds and is slightly faster in CsPbBr3 than FAPbBr3 due to a higher VB DOS and stronger NAC, Figure 4.4. This is in agreement with the experimental results, Figure 4.1c&d and prior quantum dynamics calculations.21,238-241 Figure 4.5. Canonically averaged charge densities of the valence band maximum (VBM), conduction band minimum (CBM), and initial hole and electron excitation orbitals for a) CsPbBr3 and b) FAPbBr3. The holes are supported primarily by Br atoms, while the electrons are localized on Pb atoms, in agreement with the DOS, Figure 4.6. 60 Density of state (DOS) plots Figure 4.6. Canonically averaged projected density of states (DOS) for a) CsPbBr3 and b) FAPbBr3. The DOS is larger in the valence band (VB) than the conduction band (CB). As a result, a larger part of the pump energy is deposited into electrons than holes because more hole states are closer to the band edge. Also, the nonadiabatic coupling (NAC) is larger in the VB than CB, Figure 4.4, because energy level spacings are smaller, and hole-vibrational relaxation is faster than electron-vibrational relaxation. Figure 4.7. The DOS across the MD trajectory for CsPbBr3 at time step a) 1 fs, b) 500 fs, c) 1000 fs, d) 1500 fs, e) 2000 fs, f) 2500 fs, g) 3000 fs. 61 Figure 4.8. The DOS across the MD trajectory for FAPbBr3 at time step a) 1 fs, b) 500 fs, c) 1000 fs, d) 1500 fs, e) 2000 fs, f) 2500 fs, g) 3000 fs. Conclusions State-resolved pump/probe spectroscopy and time-resolved PL were performed on two classes of bulk perovskite nanocrystals, which reveal qualitatively different behavior from the past decade of literature. The pump/probe spectroscopy at low carrier concentration reveals a breaking of the quantum phonon bottleneck via electron-to-hole energy transfer that is missed in generic transient absorption analysis. The pump/probe spectroscopy at high carrier concentration can be interpreted as revealing a hot phonon bottleneck, but the signals were misinterpreted in the past. Even pumping with zero excess energy gives the illusion of a hot carrier bottleneck. Hence, t-PL experiments were performed to unambiguously resolve the timescale of energy dissipation. The t-PL measurements conclusively show no hot phonon bottleneck in these bulk perovskite NC. Ab initio molecular dynamics rationalized the experimental observation in light of efficient Auger processes. These experiments provide an accurate view of hot carrier 62 processes in perovskites, which can be exploited to advance their use in optoelectronic devices related to hot carrier thermalization processes. 63 Chapter 5 Machine Learning Analysis on Vacancy Ordered Perovskites The material in this chapter is adapted from: Kumar Nayak, P.; Perez, C.; Liu, D.; Prezhdo, O.; Ghosh, D.; A-Cation-Dependent Excited State Charge Carrier Dynamics in Vacancy-Ordered Halide Perovskites: Insights from Computational and Machine Learning Models Chem. Mater. 2024, XXXX, XXX, XXX-XXX Introduction Metal halide perovskites (MHPs) have fascinated the optoelectronics community due to their compositional and structural variety, which result in a wide range of functional applications, including solar cells,242,243 light emitting diodes (LED),244,245 photocatalysis,246,247 and photodetection.248,249 These materials exhibit attractive properties such as high absorption coefficient, tunable band gap, defect tolerance, and long carrier diffusion length.RW.ERROR - Unable to find reference:doc:6618050feb51e80606204ce9 Despite the promising optoelectronic properties of the halide perovskites, the toxicity of lead and the long-term material stability have remained the bottleneck for their commercialization as next-generation optoelectronic devices.251-254 In this regard, vacancy-ordered halide perovskites (VOHPs) are capturing unprecedented attention due to their structural and chemical stability, compositional diversity, and promising photoactivity.255-257 The prototype of the VOHP structure, A2B¢X6 (A: Monovalent (in)organic cation, B: divalent metal cation, X: halide anion), can be constructed by eliminating alternate metal-sites of conventional ABX3 MHP in all three dimensions. Such structural engineering leads to doubling the oxidation state of B-site metal cation, +4, opening new chemical space for finding potential alternatives to toxic Pb2+ atoms. The stable tetravalent (+4) oxidation state of various transition and nontransition metal cations can further tune the optoelectronics of VOHPs through materials screening. In the conventional ABX3 with B = Sn, Ge encounters severe auto-oxidation of B2+ cations to B4+, eventually decomposing the crystal structure.258,259 For such systems, the 64 vacancy-ordered form exhibits much higher stability as B remains at the tetravalent state, effectively resolving the issue of auto-oxidation-induced materials instability.256,257,260 The A2BX6 perovskites family attributes distinctive physical and electronic features such as high compressibility,261 reduced electronic band gap,262 and highly tunable emission properties.255,263 These attractive optoelectronic properties have already demonstrated promising applications of VOHPs in photovoltaics256,260 white-light emission264, thermoelectric265, and photocatalysis.257,266 Lee et al. have demonstrated Cs2SnI6 as an efficient hole transport layer in dye-sensitized solar cell devices in ambient conditions.256 The defect tolerance of compositionally mixed Sn/Te-based VOHPs has been explored by Maughan et al.267 Promising structural stability with a suitable band gap range (1.25-1.30 eV) demonstrates the possibility of fabricating optoelectronic devices from VOHPs. In recent work, some of us have computationally depicted the stable photocatalytic activity of MA2SnBr6 (MA: methylammonium) that has been synthesized successfully. 266 The strategic doping of VOHPs has successfully demonstrated widely tunable bright emission properties, indicating their applications in the display industry.263,264 Though the initial reports are encouraging, the optoelectronic devices from VOHPs are yet to be significantly optimized for efficient performance. The lack of chemically connected metal halide octahedra in VOHPs gives rise to intrinsic structural confinement, mitigating conventional charge carrier pathways.268 Furthermore, the isolated metal halide octahedra exhibits more lattice dynamical activity than traditional MHPs, resulting in unique electron-phonon interactions in VOHPs.269 The lattice dynamics at ambient conditions play a crucial role in determining the functional properties of MHPs, including carrier transport,270 emission efficiency,271 thermal conductivity, 272 and ferroelectricity.273 In this regard, 65 A-cations that stack the isolated octahedra can indirectly influence the optoelectronics and transport properties of VOHPs.269 Specifically, the A-cations typically reside distant from the electronic band edge states in these perovskites. However, the dynamic coupling of those with inorganic octahedra can substantially impact photophysics. Maughan et al. report the anharmonic rattling of A-site cations at ambient conditions, inducing dynamic tilting in stand-alone SnBr6 octahedra. 269The A-cation size and its dynamic non-covalent interactions with octahedra modify the close-packed arrangement of halogen, impacting the electronic dispersions and carrier transport through the band edge states.274 Moreover, several detailed studies have shown that the dynamic coupling between A-cations and inorganic octahedra in MHPs influences the electronphonon interactions, ultimately impacting the excited state properties such as carrier recombination processes and carrier lifetime. 269,274,275 Despite the substantial impact of these cations on the overall vibrational and excited-state properties of VOHPs, an in-depth understanding of the correlation among structural dynamics, transient electronic structures, and carrier recombination properties is still largely missing. Such insights are essential to propose fundamental design principles for VOHPs with efficient optoelectronic properties. ML models can be utilized to develop strategic design principles and reveal underlying physical phenomena inside halide perovskites.276-278 Here, we combine state-of-the-art atomistic modeling and unsupervised ML models to reveal the detailed impact of A-cations on the dynamic electronic and excited state properties of VOHPs. The current study considers three VOHPs, A2SnBr6, where A= Rb, Cs, methylammonium (MA), where the A-site cations have varying cationic sizes and non-bonding interaction patterns with metal bromide octahedra. The computed structural dynamics show that the A-cations significantly impact the geometric fluctuations and coupling with electronic states at ambient conditions. The nonadiabatic 66 molecular dynamics (NAMD) simulations further depict that charge carriers' nonradiative recombination rate strongly depends on the A-cations in VOHPs. The ML-based analyses highlight the detailed dynamic geometry-optoelectronic property relationships by illustrating the correlation between transient electronic properties and different structural features. We emphasize the importance of strategically choosing appropriate A-cations to design efficient VOHPs with exceptional optoelectronic characteristics. Computational Methodology All the DFT-based calculations, along with ab initio molecular dynamics (AIMD) simulation, were performed using the Vienna Ab Initio Simulation Package (VASP) with a Projected Augmented Wave (PAW) approach to describe the interaction of ion and valence electrons.103,107-110 The cut-off energy of 520 eV was considered for the plane wave basis set to relax the vacancy-ordered perovskite structures. The energy convergence criterion was set to 10-6 eV, and the geometry was relaxed until the Hellmann Feynman force between ions reached less than 0.01 eV/Å. Moreover, geometry relaxation was done where coordinates of atoms, cell shape, and volume were allowed to relax (setting ISIF = 3 in VASP INCAR). For exchangecorrelation interaction, the semi-local Generalized Gradient Approximation (GGA) functional in the form of Perdew-Burke-Ernzerhof (PBE) has been considered for geometry optimization simulations.106 We have taken Γ-centred 3x3x3 Monkhorst-Pack k-point mesh and included dispersion correction DFT-D3 as Grimme et al. prescribed for these simulations.230,279 Screened hybrid functionals of Heyd–Scuseria–Ernzerhof (HSE06) and the spin-orbit coupling (SOC) effects were considered to calculate the electronic structures up to reasonable accuracy. We have used SUMO to analyze the electronic properties of these halide perovskites.280 Moreover, 67 VESTA and VMD software have been used for static and dynamic structural bond-parameter calculatio.281,282 The combination of classical and quantum elements in NAMD simulations, specifically using the Decoherence-Induced Surface Hopping (DISH) method, has been applied to explore the excited state charge carrier behavior. In this approach, electrons are treated quantummechanically, while the behavior of nuclei is approached classically. In our simulations for Ab Initio Molecular Dynamics (AIMD), we considered the conventional cell containing four formula units and 4 Sn-vacancy and a total of 36 and 92 atoms for (Cs/Rb)2SnBr6 and MA2SnBr6 respectively. To handle the quantum aspects, we used a 2×2×2 Monkhorst-Pack k-point mesh, a small time step of 1 femtosecond (fs), and a cut-off energy of 400 eV for plane-wave calculations. We incorporated the PBE-GGA exchange-correlation functionals and DFT-D3 corrections230 for accuracy, given the unfeasibly high computational expense associated with the HSE06 hybrid functional. These computational methods are widely applied for modeling charge carrier dynamics in halide perovskites using NAMD simulations. In AIMD, our simulations began with a structure optimized using DFT and then gradually heated to 300 K over 4 picoseconds (ps). We equilibrated the system for an additional 4 ps using the canonical ensemble to ensure the system reached thermal equilibrium. Finally, we conducted 13.5 ps trajectories in the microcanonical ensemble and used 5 ps of these trajectories (with a 1fs timestep) for calculations involving nonadiabatic coupling at the Γ-point. To investigate the process of electron-hole recombination using the PYXAID code, we considered all 5000 snapshots along the trajectories and ran 500 stochastic simulations of the DISH process for each geometry.50,233 To manage the computational load, we iterated the nonadiabatic Hamiltonian computed over the 5 ps trajectory to simulate the charge recombination dynamics occurring over a much longer 68 timescale (12 ps). Our focus lies on the electron-hole recombination occurring across the band gap, emphasizing the dynamical structural features conducive to electron-phonon interactions and limiting carrier lifetime. The fitting function f(t) = 1- exp[-t/t] has been used to calculate the recombination lifetime. The pure dephasing function is the destruction of quantum coherence due to elastic electron-phonon scattering, which the 2nd-order approximation of optical response formalism can evaluate.283 () = exp{− 1 ℏ ∫ ′ 0 ∫ ′′ ′ 0 (′′)} Cij(t) is the unnormalized auto-correlation function of the fundamental energy gap; Cij (t) = < ()(0) >, where () = () − < > is the fluctuation of the energy gap between ith and jth states from the canonical ensemble average value. We estimated the decoherence time by applying the concept of pure-dephasing time, as defined in optical response theory and implemented in PYXAID. Gaussian fit is used to calculate the dephasing time for VOHP materials. The calculated radiative carrier lifetime is the inverse of the Einstein co-efficient. The Einstein coefficient for spontaneous emission, , between states, i and j relates the oscillator strength, , and the frequency () of the specified transition: = 8 2 2 2 3 And , , , and are the fundamental constants. The state degeneracies are = = 1 in the current system because it has no symmetry due to thermal atomic fluctuations. The mutual information (MI) is defined as: (, ) = ∬ p(, ) log p(, ) p() p() 69 Where the marginal densities of X and Y are p() and p(), respectively, and the joint probability is given as p(, ). The MI calculations used k=3 for the k-nearest-neighbors distances, which provides a balance between limited noise and overestimation bias.284 We used this non-parametric entropy estimator method to gauge the correlation between structure properties (see SI Table S8 for a complete list of properties tested) and electronic properties (bandgap, VBM, CBM, and NAC). A higher MI value signifies a stronger correlation between the two data sets (structure features vs electronic properties).18 The MI-based analysis has previously been employed to extract the noncollinear structure-property relationships.285 A 5ps trajectory was used for these calculations, and the MI correlation was taken as an average for a given feature over this same trajectory. Results & Discussion Figure 5.1. Electronic structures fluctuate over a 5ps (5000 snapshots) time window for all three VOHPs at 300K. The histogram plots for (a) band gaps and (b) the VBM and CBM state 70 energies along the AIMD trajectories of corresponding VOHPs. (c) The mutual information of bandgap with vital structural features. We compute the electronic structure of VOHPs over time to reveal the impact of structural dynamics on their photophysical properties. The band gap distributions are presented as the histogram plots in Figure 5.1a. The band gap distributions are evident in the dominant role of structural dynamics on the overall electronic structures of VOHPs. The more dynamic lattice of MA2SnBr6 has widely fluctuating band gaps with an SD of 0.19 eV. On the contrary, Cs2SnBr6, which has the least dynamic structure, exhibits the most narrowly (SD: 0.11 eV) distributed time-dependent band gap values (Figure 5.1a). We further investigate the variation in the individual band edge positions due to geometric fluctuations in these VOHPs. The rapid change in the VBM and CBM positions can modify the transient band alignment, ultimately impacting the charge carrier collection and transport in photovoltaic devices.286 In Figure 5.1b, we plot the distributions of relative energetic positions of the band edges over time. Since the SnBr framework dominantly contributes to the band-edge states, the dynamic band-edge position over the 5 ps timeframe mainly depends upon the A-cation-induced Sn-Br fluctuation. The Sn-Br sub-lattice of Cs2SnBr6 is less dynamic than Rb2SnBr6 and MA2SnBr6, indicating a more confined band-edge distribution (Figure 5.1b). Further, the CBM state fluctuates more drastically (SD: Rb2SnBr6, 0.12 eV; Cs2SnBr6, 0.10 eV; MA2SnBr6, 0.18 eV), resulting in a wider distribution than that of the VBM state (SD: Rb2SnBr6, 0.054 eV; Cs2SnBr6, 0.047 eV; MA2SnBr6, 0.099 eV) for all VOHPs. Thus, the phonon modes are strongly coupled to the CBM state at ambient conditions, changing their position rapidly in the femtosecond timescale. Among VOHPs, MA2SnBr6 exhibits the broadest distribution of varied band edge positions over time, reiterating the close dynamic structure – electronic property relationships. 71 The highly dynamic crystal lattices indicate the presence of several active phonon modes that can influence the transient electronic structure of VOHPs. Consequently, it becomes considerably challenging to identify the relevant features that impact optoelectronics most. In this regard, we compute the mutual information (MI) that efficiently captures hard-to-find nonlinear correlations and provides features that dominantly control the electronic structure fluctuations. As detailed in previous works, these nontrivial correlations are revealed using the unsupervised ML algorithm of non-parametric entropy estimators.18,285 To include diverse structural parameters, we track several geometric features such as RMSF of atoms, intra- and inter-octahedral bond distances and angles, and dihedral angles throughout the simulation time and find the correlation with bandgaps. In the heatmap, Figure 5.1c, a few common trends emerge from these MI analyses. The band gaps of these VOHPs share considerable mutual information with intra- and inter-octahedral Br-Br distances (DBrBr_intra/inter). As the band edge states remain delocalized over the SnBr6 octahedra, the high MI between intra-octahedral Br-Br distances and band gap is expected and discussed further in Section S4 (SI). However, since these VOHPs have isolated octahedra, the high correlation between inter-octahedral Br-Br distances and bandgap is nontrivial. This insight emphasizes the through-space dynamic electronic coupling among the halogen orbitals of the neighboring octahedra, which controls the VBM-CBM energy gap. The features involving metal halide octahedra, such as Sn-Sn-Br tilting angles (∠Sn-Sn-Br), Sn-Br distances (DSn-Br), and Sn-Sn shortest distances (DSn-Sn), also exhibit relatively high correlation with bandgap values. Note that these features primarily differ from the feature set that exhibits high MI with the band gap in traditional MHPs.112,285 Thus, VOHPs have a substantially dissimilar dynamic structureproperty relationship compared to MHPs. The presence of multiple inter-octahedral features 72 illustrates that even though SnBr6 octahedra are not chemically connected, their mutual dynamics significantly influence the band gap values of VOHPs. Further analysis identifies several structural features with high MI with band gap only for MA2SnBr6. Specifically, the features for A-cation dynamics, such as A-A distance (DA-A) and RMSF of A (RMSFA), exhibit more correlation with the band gap in MA-based perovskites than the inorganic ones. As A cations do not contribute directly to the band edge states, the high MI for these features is somewhat unexpected. We realize that the significant influence of the rattling motion of MA cations to the band edge states gives rise to such high MI values. The quantified MI between structural features and individual band edges further reveals that the VBM state correlates more to the A-cation dynamics. The evaluated nonlinear correlations indicate that a more dynamic lattice of MA2SnBr6 results in a more significant number of structural factors that modify the band gap values over time. The thermal lattice fluctuations in MHPs substantially influence the photoexcited charge carrier dynamics activating nonradiative carrier recombination processes, which can reliably be modeled by combining the nonadiabatic molecular dynamics (NA-MD) with time-dependent density functional theory (TD-DFT).21,143,287 The recombined carrier population along the NAMD trajectories illustrates a faster nonradiative band-to-band charge recombination rate in MA2SnBr6 compared to inorganic VOHPs (Figure 5.2a). Furthermore, Cs2SnBr6 has a lower nonradiative recombination rate compared to Rb2SnBr6, depicting the subtle impact of A-cations on charge carrier dynamics. Employing the short-time linear approximation to the exponential function, we evaluate the nonradiative carrier lifetimes as 21.12 ns, 32.38 ns, and 16.43 ns for Rb2SnBr6, Cs2SnBr6, and MA2SnBr6, respectively. Thus, the nonradiative carrier lifetime can be elongated two times while completely substituting MA with Cs in A2SnBr6 perovskites. The 73 nanosecond timescale for computed carrier lifetimes in MHPs closely agrees with experimental reports.288,289 Our findings emphasize the pivotal role of A-cation in tuning the excited state carrier dynamics of VOHPs, indicating a strategic approach for enhancing their efficiency for photovoltaics and LED applications. Nonradiative recombination serves as the predominant pathway for the dissipation of charges and energy, thereby constraining the efficiency of photon-to-electron conversion in perovskite solar cells. We computationally simulate radiative lifetimes to discern whether carrier lifetimes are constrained by nonradiative or radiative decay. The emission lifetime stands as the reciprocal of the Einstein coefficient. Our computed radiative recombination times for Rb2SnBr6, Cs2SnBr6, and MA2SnBr6 perovskites are 184.59, 157.01, and 147.61 nanoseconds, respectively. Notably, these timescales exceed the corresponding nonradiative electron-hole recombination times. These findings reveal that the harvested electronic energy by photoexcitation dissipates to phonon modes at a much faster rate than the radiative process,241,290,291 resulting in poor emission in pristine VOHPs. 292,293 74 Figure 5.2: The excited state charge carrier dynamics in VOHPs at ambient conditions. (a) The population of nonradiatively recombined electron-hole over time in VOHPs. (b) The absolute NAC value between VBM and CBM energy states for a 5ps time window at ambient conditions. (c) The mutual information of NAC with considered key structural features. The dynamic interplay between electronic and lattice degrees of freedom exerts a dominant influence on nonradiative charge relaxation and recombination processes, significantly impacting the operational device efficacy of optoelectronic devices.294,295 During nonradiative recombination, the excess energy of excited electrons dissipates through various active inelastic electron-phonon scattering processes. In contrast, the elastic electron-phonon modes can slow down nonradiative decay by hampering the coherence between engaged states. The inelastic electron-phonon interaction that frequently plays a key role is quantified as nonadiabatic coupling (NAC).296 We compute the NAC constants between the band edges along the simulated trajectories for evaluating instantaneous inelastic scattering strength. Conceptually, a heightened NAC value denotes a more robust coupling between electronic and lattice degrees of freedom, indicating accelerated nonradiative charge recombination in the material.297 In Figure 5.2b, the (a) (b) (c) 75 NAC strengths along the MD trajectories highlight a few crucial factors: (a) MA2SnBr6 exhibits high instantaneous NAC values (>0.5 meV) more frequently than the inorganic ones, and (b) the NAC values fluctuate much faster in time for hybrid VOHP. The high instantaneous NAC values indicate more regular opening of nonadiabatic channels, giving rise to a faster rate of nonradiative band-to-band carrier recombination in MA2SnBr6. Moreover, the Fourier transformation (FTs) of NACs over time illustrates a broader range of frequencies for MA2SnBr6, emphasizing its more active inelastic electron-phonon interaction processes. The large number of peaks in the FT plot also indicates that various phonon modes couple to the band edge states, impacting the instantaneous NAC strengths. In this regard, Rb2SnBr6 exhibits several higher frequencies but much less than the MA-based VOHP. We thus rationalize that the strength and variation of NACs over time have dominant control on the nonradiative charge carrier recombination rates in VOHPs. Due to their significant influence on the excited state carrier dynamics, we further evaluate the shared information between NACs and several dynamical structural parameters regarding MI. Figure 5.2c and Table 5.4 shows that MI values are much smaller for MA2SnBr6 than inorganic VOHPs, indicating weaker correlations between structural features and NAC values. The drastic fluctuations of instantaneous NACs and structural features over time collectively reduce the shared information in this dynamic system. Considering several features, the NAC appears to be most correlated with the ∠Sn-Sn-Br for all VOHPs (see Table 5.5 for a detailed description of considered key structural features). The Br-Sn-Sn-Br dihedral angles (∠Br-Sn-Sn-Br) in inorganic VOHPs also share considerably adequate information with the instantaneous NACs. The entropy correlation between inter-octahedral features and NACs emphasizes the dominant impact of collective tilting motions in chemically disconnected SnBr6 76 on electron-phonon interaction strengths. The octahedral tilting motion also shows a higher correlation with NAC in 3D MHPs.18,165 Other inter-octahedral distance features, such as DA-A and DSn-Sn, correlate with NACs in Cs and Br-based perovskites. Note that the A-cation-related features (DA-A and RMSFA) illustrate a decrease in MI moving from Cs to Rb to MA as A-site in VOHPs. Thus, more fluctuation of A-site cations results in a weaker correlation between these features and NAC values. Machine learning (ML) for the analysis of nonadiabatic molecular dynamics (NAMD) simulations has emerged as a potential strategy for elucidating the intricate relationship between structural and electronic properties and the dynamics of excited states. These state-of-the-art techniques can be used to draw insights about the A-site cation coupled thermal motion of structurally confined isolated octahedra and substantial active electron-phonon interactions. Thus, we implemented the machine learning approach to explicitly study the correlation between key structural parameters (called features) that significantly impact specific dynamic electronic properties and nonradiative coupling (called properties). We established correlations between fundamental structure-property relationships using non-parametric entropy estimators’ unsupervised machine learning algorithm. The electronic properties were chosen as 1) bandgap, 2) CBM, 3) VBM, and 4) NAC to highlight fundamental tunable (A-site cations) properties for charge carrier recombination. The complete list of structure properties examined is shown in Table 5.1-Table 5.4. As mentioned in the computational methods. 77 Figure 5.3. The mutual information of VBM with considered key structural features. See Table 5.5 for detailed descriptions of structural properties. Figure 5.4. The mutual information of CBM with considered key structural features. See Table 5.5 for detailed descriptions of structural properties. 78 The VBM and CBM states of VOHPs remain delocalized over SnBr6 units where Br 4p orbitals participate dominantly. In this regard, the overall electronic properties of VOHPs are sensitive to non-covalent orbital interactions between Br atoms (1) that are in the same SnBr6 octahedron and (2) in neighboring octahedra. We track these interactions by calculating dynamic intra-octahedral and inter-octahedral Br…Br distances. Thus, we realize relatively strong correlations between DBr-Br and electronic bandgaps. Furthermore, the NAC between the VBM and CBM states depends on the wave function of these states and the nuclear motions of contributing atoms. As Br atoms contribute to these band edge states, the distance between anions controlling the orbital interactions correlates to the NAC values. In the case of MA2SnBr6, the A-cation possesses a comparatively expansive spatial environment, wherein the MA cation’s dynamic motion significantly influences the Br sublattice’s vibrational behavior via non-covalent interactions. Conversely, in (Cs/Rb)2SnBr6 structures, the Br sublattice is arranged compactly, resulting in a lower ensemble average of dynamic Br-Br distances across these inorganic VOHPs. The higher correlation between Br-Br distances (DBrBr_Intra and DBr-Br_Inter) and band edge properties and NAC is attributed to the relatively lower fluctuations on those dynamic bonds in Cs/Rb-based VOHPs. While comparing Cs and Rb-based perovskites, we find a similar trend. The narrower inter and intra-octahedral Br…Br distances in Rb2SnBr6 result in their higher entropy correlations (1.5, 1.23) with the bandgap compared to that for Cs2SnBr6 (1.09, 1.12) (Figure 5.1c). For NAC, however, the entropy correlation values are the same for both inorganic VOHPs (Figure 5.2c). We find that the marginally higher nuclear motion of Br atoms in Rb2SnBr6 than in Cs-based ones counterbalances the opposite trend in DBr-Br. The dynamic structure – NAC relationships are 79 generally more complicated due to inherent complexity in phonon-induced nonadiabatic processes. The VBM possesses a much narrower distribution in values when compared to the CBM (Figure 5.1b). Yet, it strongly correlates to the A-A site distance (DA-A), with a weak correlation to the intra-octahedral Br-Br bond distance (DBr-Br_Intra). Indicating that the CBM position controls the bandgap value while the VBM sets the magnitude. This is an unexpected feature of the perovskite system; the DOS shows that Br defines the VBM while the Sn and Br atoms define the CBM. The DOS does not show a substantial contribution from the A-site cation to the VBM or CBM, yet the A-A site distance correlated strongly to the VBM. The CBM is highly correlated to Sn-Br (DSn-Br) and Br-Br (DBr-Br_Intra and DBr-Br_Inter), which illustrates that the closepacked arrangement of Br-sublattice indeed affects the CBM significantly. To clarify the disparity of elevated dynamic bandgap and band edge fluctuation of MA2SnBr6 (Figure 3b), we closely investigate other important structural features and evaluated that inter-octahedral Sn-SnBr tilt (∠Sn-Sn-Br), inter-octahedral Br-Sn-Sn-Br dihedral angle (∠Br-Sn-Sn-Br) are relatively more correlated to CBM (Figure 5.4) in presence of MA than its inorganic counterpart in VOHPs. The A-A distance and RMSF of A are most correlated for MA2SnBr6 as compared to (Cs/Rb)2SnBr6, indicating the maximum influence of the rattling of A-site cation towards dynamic bandgap among three VOHPs. Further, the perpendicular ∠Br-Sn-Br angle (∠Br-SnBr90) is relatively more correlated to the CBM for MA2SnBr6 than the other two VOHPs. Relatively higher MI values of almost all structural features of MA2SnBr6, unlike inorganic VOHPs, reveal enhanced dynamical correlation for CBM. These enhanced thermal fluctuations of individual atoms with higher MI correlation to CBM play a significant role in varied CBM of MA2SnBr6 in ambient conditions. Further, features like RMSF of A/Sn/Br follow the same 80 correlation trend for CBM (Figure 5.4 and Table 5.2) as that of bandgap (Table 5.1). This indicates the significant thermal fluctuation of the overall lattice of MA2SnBr6 makes almost all features equivalently correlated with the bandgap and loses the influence of any specific feature. Thus, it is evident that the A-cation impacts the extent of correlation of both highly and minutely correlated structural features on dynamical electronic properties in VOHPs. Mutual Information Tables Table 5.1. Mutual information of the bandgap and the structure features. The features are written according to the ascending order of MI of Rb2SnBr6 for convenience. See Table 5.5 for detailed descriptions of structural properties. Features Rb2SnBr6 Cs2SnBr6 MA2SnBr6 DBr-Br_Inter 1.50 1.09 1.00 DBr-Br_Intra 1.23 1.12 1.04 ∠Sn-Sn-Br 1.19 0.94 1.32 DSn-Br 1.18 1.14 1.10 DSn-Sn 0.97 1.06 1.21 DA-A 0.84 0.78 1.01 RMSFBr 0.83 0.74 1.02 ∠Br-Sn-Sn-Br 0.83 0.77 1.08 RMSFA 0.70 0.78 0.87 RMSFSn 0.64 0.77 1.09 ∠Br-Sn-Br180 0.60 0.52 0.72 ∠Br-Sn-Br90 0.51 0.58 0.75 Table 5.2: Mutual information of the CBM and the structure features. The features are written according to the ascending order of MI of Rb2SnBr6 for convenience. See Table 5.5 for detailed descriptions of structural properties. Features Rb2SnBr6 Cs2SnBr6 MA2SnBr6 DSn-Br 2.18 1.53 1.90 DBr-Br_Intra 1.86 1.06 1.47 DBr-Br_Inter 1.74 1.30 1.68 ∠Sn-Sn-Br 1.10 0.93 1.36 ∠Br-Sn-Sn-Br 0.79 0.59 0.97 DSn-Sn 0.77 0.90 1.16 DA-A 0.68 0.61 0.96 RMSFBr 0.60 0.55 0.95 RMSFA 0.58 0.56 0.79 81 ∠Br-Sn-Br180 0.52 0.40 0.58 RMSFSn 0.48 0.57 1.00 ∠Br-Sn-Br90 0.38 0.42 0.72 Table 5.3. Mutual information of the VBM and the structure features. The features are written according to the ascending order of MI of Rb2SnBr6 for convenience. See Table 5.5 for detailed descriptions of structural properties. Features Rb2SnBr6 Cs2SnBr6 MA2SnBr6 RMSFBr 1.18 1.03 1.04 DA-A 1.17 1.26 1.02 RMSFA 1.13 1.18 0.88 DSn-Sn 1.11 1.16 1.24 ∠Sn-Sn-Br 1.00 0.68 1.02 DBr-Br_Inter 0.80 0.76 0.76 ∠Br-Sn-Br90 0.80 0.72 0.77 RMSF Sn 0.76 1.07 1.13 ∠Br-Sn-Sn-Br 0.74 0.49 0.71 DBr-Br_Intra 0.69 0.63 0.71 DSn-Br 0.57 0.54 0.59 ∠Br-Sn-Br180 0.48 0.47 0.48 Table 5.4. Mutual information of the NAC and the structure features. The features are written according to the ascending order of MI of Rb2SnBr6 for convenience. See Table 5.5 for detailed descriptions of structural properties. Features Rb2SnBr6 Cs2SnBr6 MA2SnBr6 ∠Sn-Sn-Br 0.76 0.82 0.35 ∠Br-Sn-Sn-Br 0.68 0.61 0.32 DSn-Sn 0.49 0.65 0.19 RMSFBr 0.47 0.33 0.17 DA-A 0.46 0.57 0.13 RMSFA 0.38 0.53 0.16 ∠Br-Sn-Br180 0.37 0.48 0.14 RMSFSn 0.33 0.44 0.17 ∠Br-Sn-Br90 0.30 0.32 0.12 DBr-Br_Inter 0.23 0.23 0.09 DSn-Br 0.21 0.14 0.12 DBr-Br_Intra 0.20 0.20 0.12 82 Table 5.5. A clear description of all the featured data has been mentioned in the table for better understanding of readers. Features Name Representation in VOHPs ∠Sn-Sn-Br Sn’ …Sn-Br angle tilt where Sn-Br is the from an SnBr6 octahedron and Sn’ is the periodic replication of Sn outside the cell boundary ∠Br-Sn-Sn-Br inter-octahedral Br-Sn-Sn*-Br* dihedral angle (Data name: ∠Br-SnSn-Br), inter-octahedral Sn-Sn* distance (Data name: DSn-Sn); where ‘*’ represents the atom(s) corresponds to neighboring octahedra DSn-Sn Shortest distance between neighboring two Sn RMSFBr Root mean square fluctuation of bromine (Br) DA-A Shortest distance between two neighboring A-site cations RMSFA Root mean square fluctuation of A-site cation (In case of MA, the mid-point of C-N bond has been considered for RMSF calculation) ∠Br-Sn-Br180 Intra-octahedral Br-Sn-Br angle corresponding ~180 degree RMSFSn Root mean square fluctuation of tin (Sn) ∠Br-Sn-Br90 Intra-octahedral Br-Sn-Br angle corresponding ~90 degree DBr-Br_Inter Nearest inter-octahedral distance between two Br atoms DSn-Br Bond distance of intra-octahedral Sn-Br bond DBr-Br_Intra Nearest distance of intra-octahedral Br atoms Conclusion Our extensive study unambiguously identifies the decisive impact of A-cation dynamics on the excited state charge carrier dynamics in VOHPs. The initial static structure and electronic properties illustrate a negligible impact from the A-cations. However, the AIMD simulations show the significant impact of A-cations on the dynamic structural and optoelectronic characteristics of these VOHPs. The detailed unsupervised ML analyses efficiently establish the complex nonlinear correlations between dynamic structural features and material properties like bandgap and NACs. Though these VOHPs contain isolated SnBr6 octahedra, the inter-octahedral dynamical features like tilting, dihedral angles, and Sn-Sn distances exhibit high MI values with bandgap and NACs. These insights firmly state that initial attempts to understand the optoelectronics and emission from VOHPs by focusing only on the individual octahedra are insufficient. The MA cations that activate several phonon modes in MA2SnBr6 give rise to large 83 instantaneous NACs, ultimately accelerating the nonradiative charge carrier recombination processes. From this work, we suggest considering inorganic elemental monocations like Cs+ to realize high-performance VOHPs for optoelectronic applications. The elaborate understanding of the complex and non-colinear structure-property relationships can provide strategic design principles for further improvement of the photophysical properties of MHPs. 84 Chapter 6 Conclusion and future directions This thesis comprehensively investigates the defect chemistry and charge carrier dynamics of various perovskite materials and employs advanced theoretical techniques to expand our understanding of their potential in optoelectronic applications. Across the four chapters, we have explained the complex interactions between structural defects, electronic properties, and carrier dynamics in perovskites. In Chapter 1, we highlight the significance of controlling iodine chemistry in 2D perovskites to mitigate the formation of detrimental defects that induce trap states, adversely affecting optoelectronic device performance, such as in LEDs. It underscores the necessity of moderate iodine conditions during synthesis and points towards further investigations into spininjection applications by considering spin-orbit coupling effects in future simulations. Chapter 2 explores the defect tolerance of CsPbBr3 quantum dots and emphasizes the importance of avoiding halide defects charge localization that leads to nonradiative decay pathways, thereby diminishing photoluminescence and overall device efficiency. Surface passivation techniques should be used to improve charge carrier delocalization, suggesting a strategic approach to optimize the material synthesis and treatment processes to enhance device performance. Chapter 3 provides new insights into carrier dynamics in perovskite nanocrystals, challenging previous interpretations of hot phonon bottlenecks with evidence from our novel experimental measurements and NAMD simulations. These findings advocate for a revised understanding of energy dissipation in these materials, promoting their potential in highefficiency optoelectronic devices. Chapter 4 reveals the critical influence of A-cation dynamics on the optoelectronic properties of VOHPs, showing that dynamic interactions within the crystal structure profoundly 85 affect electronic characteristics such as the bandgap and nonadiabatic couplings. The results call for an innovative material design, suggesting the use of inorganic monocations to enhance performance and highlighting the importance of machine learning in uncovering nonlinear structural-property relationships. Future research should strongly consider advancing simulation techniques to optimize perovskite materials for optoelectronic applications, particularly by integrating spin-orbit coupling (SOC) into computational frameworks. This will enable a deeper exploration of spinrelated phenomena, crucial for applications such as spintronic devices and quantum computing. Using machine learning algorithms to decode complex, nonlinear relationships between structural dynamics and electronic properties can lead to a deeper understanding of unique interactions. These advanced computational methods will facilitate the design of materials with tailored properties, allowing for the predictive modeling of perovskites under various environmental and operational conditions. Additionally, the continued development of nonadiabatic molecular dynamics (NAMD) across different perovskite systems could provide profound insights into the relaxation processes of excited charge carriers and the possible mechanisms. 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Abstract (if available)

Abstract This thesis presents a comprehensive investigation into the optoelectronic properties of perovskite quantum dots (QDs) and two-dimensional Ruddlesden–Popper (RP) halide perovskites, with a particular focus on defect tolerance, the nature of electronic excitations, and the dynamics of hot phonon and quantum phonon bottlenecks. Through the application of time-dependent density functional theory, we analyze the ground and excited states of CsPbBr3 QDs, highlighting their defect tolerance and the critical need to avoid bromine vacancies that result in trap states detrimental to light-emitting diode (LED) performance. Further exploration into the electronic structure of RP perovskites reveals their general defect tolerance. Still, it identifies donor/acceptor defects as potential threats to electronic performance, advocating for strategies to mitigate halide vacancies and interstitial defects. This insight is crucial for enhancing the efficiency of devices based on 2D halide perovskites. Additionally, we address the debated concept of phonon bottlenecks in perovskite nanocrystals through experimental techniques like state-resolved pump/probe and time-resolved photoluminescence spectroscopy. Our findings challenge the prevailing assumption of inherent phonon bottlenecks, demonstrating an absence of such bottlenecks in CsPbBr3 and FAPbBr3 nanocrystals and suggesting efficient Auger processes as a mechanism for rapid cooling and relaxation of hot excitons. This work contributes to the fundamental understanding of defect and phonon dynamics in perovskite materials, providing insights that can guide the design and optimization of perovskite-based optoelectronic devices. By integrating theoretical and experimental approaches, we offer strategies for overcoming challenges related to defects and light interactions, paving the way for advancing perovskite technology.

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Creator Mora Perez, Carlos (author)

Core Title Excited state process in perovskites

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Degree Conferral Date 2024-05

Publication Date 05/17/2024

Defense Date 04/29/2024

Publisher Los Angeles, California (original), University of Southern California (original), University of Southern California. Libraries (digital)

Tag 0D,2D,defects,NAMD,OAI-PMH Harvest,perovskite,quantum dots

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Prezhdo, Oleg (committee chair), Branicio, Paulo (committee member), Dawlaty, Jahan (committee member)

Creator Email morapere@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113940236

Unique identifier UC113940236

Identifier etd-MoraPerezC-12957.pdf (filename)

Legacy Identifier etd-MoraPerezC-12957

Document Type Dissertation

Format theses (aat)

Rights Mora Perez, Carlos

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Source 20240517-usctheses-batch-1155 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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