CDT in New and Sustainable Photovoltaics (2018) Materials Modelling: From Atoms to Solar Cells Prof. Aron Walsh Department of Materials Imperial College London https://wmd-group.github.io @lonepair

2018 Module Team Aron Walsh Professor at Imperial College London Daniel Davies PhD Student in CDT for Sustainable Chemical Technologies at Bath

Solar Minerology Developing sustainable energy technologies: from minerals to devices Kesterite Mineral Cu2 ZnSnS4 Solar Panel

Kesterite

Herzenbergite

Perovskite

Matlockite

Enargite, Stephanite, Bournonite

Session Aim Background: Materials modelling is widely used as a tool for characterisation and prediction in materials science. There is an expanding literature on solar energy (e.g. active layers, interfaces, transparent conducting oxides). Aim: A basic understanding of terms and concepts, with the ability to critically assess results from research papers in your field.

Modelling Solar Cells © Materials Research Society

Modelling Solar Cells Active Layer • Electronic structure • Optical properties • Electron transport • Defect states Front Contact • Band offsets • Interfacial states • Interfacial dipoles • Modification layers Back Contact • Band offsets • Ion diffusion • Interfacial reactions • Modification layers Device Modelling • Carrier collection • J–V response • Efficiency losses • Layer optimisation

Session Outline Materials Modelling Part 1 Fundamentals (AW) Equations, codes, databases Part 2 Advanced (DD) High-throughput and machine learning

Relevant Textbooks General Specialist

Lecture Outline Materials Modelling 1. Theory: What Equations to Solve 2. Practice: Codes & Supercomputers 3. Interactive: Databases 4. Application: Halide Perovskites

Multi-Scale Simulation Toolbox

First-Principles Materials Modelling What? Simulate the properties of materials using the Schrödinger equation and chemical composition as the sole input Why? Accurate, unbiased, and predictive When? If such calculations are feasible and meaningful How? Digital computers, clever algorithms, common sense, and scientific rigor Source: http://stefano.baroni.me/presentations/

First-Principles Workflow Structure Properties Input: Output: William Hamilton (Dublin, 1805) Hamiltonian (ions and electrons) William Bragg (Wigton, 1862) X-ray Diffraction (unit cells) Physical Chemistry (stimuli) Neville Mott (Leeds, 1905)

Quantum Mechanics ˆ HΨ = EΨ Kinetic and Potential Energy Operators ˆ H = ˆ T + ˆ V Non Relativistic Relativistic Schrödinger (1887, Vienna) Dirac (1902, Bristol) Extra terms: scalar relativistic spin-orbit coupling

Electronic Structure Techniques E[Ψ] → E[ρ] Density based quantum mechanics Wavefunction based quantum mechanics Methods Hartree-Fock Møller–Plesset Configuration Interaction Methods Thomas–Fermi Density Functional Dynamical Mean Field

Density Functional Theory (DFT) Source: F. Bechstedt – Many-body Approach to Electronic Excitations (2015) Hohenberg-Kohn (1964); Kohn-Sham (1965)

Kohn-Sham DFT (1965) Use one-electron Ψ i that reproduce interacting ρ Core Electrons all-electron pseudopotential frozen-core Hamiltonian non-relativistic scalar-relativistic spin-orbit coupling Periodicity 0D (molecules) 1D (wires) 2D (surfaces) 3D (crystals) Electron Spin restricted unrestricted non-collinear Basis Set plane waves numerical orbitals analytical functions Functional beyond…….. hybrid-GGA meta-GGA GGA LDA QMC GW RPA TD-DFT

Materials Modelling with DFT Input Chemical Structure or Composition Output Total Energy + Electronic Structure Structure atomic forces equilibrium coordinates atomic vibrations phonons elastic constants Thermodynamics internal energy (U) enthalpy (H) free energy (G) activation energies (ΔE) Electron Energies density of states band structure effective mass tensors electron distribution magnetism Excitations transition intensities absorption spectra dielectric functions spectroscopy

Exact (Analytical) Wavefunctions

From Atoms to Molecules

From Molecules to 1D Chain 1D Chain of Atoms ! !*

From 1D Chain to 2D Lattice 2D Lattice ! !*

Learn from a Laureate

Bloch Waves Felix Bloch (1928) Periodic Electronic Wavefunctions Crystal wavefunction Periodic cell potential Plane waves 4.3. DENSITY-FUNCTIONAL THEORY: IMPLEMENTATION 55 Bloch waves describe local (intra unit cell) and long-range (inter unit cell) interactions in a crystal

Bloch Waves Felix Bloch (1928) Periodic Electronic Wavefunctions Crystal wavefunction Periodic cell potential Plane waves 4.3. DENSITY-FUNCTIONAL THEORY: IMPLEMENTATION 55 λ=2π/k k-point Electron wavevector Crystal momentum

Band Structure: GaAs Fundamentals of Semiconductors Yu and Cardona (Springer, 1995) Koster Notation (group theory) Brillouin Zone Unit Cell

Band Structure: Halide Perovskite Relativistic GW Theory Physical Review B 89, 155204 (2014) CH3 NH3 PbI3 Conduction Band Valence Band Electronic Configuration: PbII [5d106s26p0]; I-I [5p6]

Lecture Outline Materials Modelling 1. Theory: What Equations to Solve 2. Practice: Codes & Supercomputers 3. Interactive: Databases 4. Application: Halide Perovskites

2018 Supercomputers (1017 FLOPS) Top500.org Ranking

National Supercomputer Usage Archer: Cray XC30 with 118,080 cores http://www.archer.ac.uk/status/codes/

Same Method, Same Result

Some Popular DFT Packages • CASTEP (Plane wave basis set) • CP2K (Mixed Gaussian/plane waves) • FHI-AIMS (Numeric orbitals) • GPAW (Numeric orbitals) • QUANTUM-ESPRESSO (Plane waves) • SIESTA (Numeric orbitals) • VASP (Plane waves) • WIEN2K (Augmented plane waves) [Open Source] [Open Source] [Open Source] [Open Source]

GPAW: Open Source and Python https://wiki.fysik.dtu.dk/gpaw/ Large community of researchers. Free and open source! • Links to Atomistic Simulation Environment • Written in C and Python • Easy to use • pip install gpaw

Vienna Ab Initio Simulation Package Widely used FORTRAN code from Austria (Prof. Georg Kresse) • License fee ~€5000 (small academic group) • Site: http://www.vasp.at • Forum: http://cms.mpi.univie.ac.at/vasp-forum • Wiki: http://cms.mpi.univie.ac.at/wiki • Many pre- and post-processing tools • Visualisation: http://jp-minerals.org/vesta A popular package because of reliable pseudopotentials for periodic table (benchmarked against all-electron methods)

Compiling Scientific Codes General Requirements: Program source code (e.g. x.f, x.f90, x.c); Makefile or configure script; Math libraries; Fortran or C compiler Common Compilers: Intel Fortran (ifort); Portland Group (pgf90); Gnu-Fortran (gfortran); Pathscale (pathf90); Generic links (f77 or f90) Common Libraries: LAPACK (Linear algebra - diagonalisation) - ScaLAPACK (Distributed memory version) BLAS (Linear algebra – vector / matrix multiplication) BLACS (Linear algebra communication subprograms) Examples: MKL (Intel); ACML (AMD); GotoBLAS

VASP Input Files • POSCAR (“Position Card”) • POTCAR (“Potential Card”) • INCAR (“Input Card”) • KPOINTS (k-point Sampling) All four files should be in the same directory for VASP to run successfully Caution: The order of the elements in POTCAR must be the same as POSCAR

VASP Output Files • OUTCAR (“Output Card”) • CONTCAR (“Continue [Positions] Card”) • CHGCAR (“Charge Density Card”) • vasprun.xml (Auxiliary output as xml) A number of additional files that are generated depending on flags set in INCAR Caution: If NSW > 0, a number of the properties are averaged over past structures (rerun with NSW=0 at end)

Step 1: Structure Generate crystal structure by hand, from supplementary information, or from a database (e.g. ICSD)

Step 1: Structure Check POSCAR

Step 2: Input Files cat ./C/POTCAR ./N/POTCAR ./H/POTCAR ./Pb_d/POTCAR ./I/POTCAR > POTCAR INCAR (Partial) KPOINTS

Step 3: Run VASP INCAR (Partial) KPOINTS Let’s see…

Choice of Exc Takes Experience INCAR (Partial) KPOINTS Recommended: PBEsol (GGA for solids) & HSE06 (screened hybrid GGA) Journal of Chemical Physics 123, 174101 (2005) Often a (computational) cost vs accuracy tradeoff

Electronic Spectroscopy INCAR (Partial) KPOINTS Source: Patrick Rinks (FHI-AIMS Workshop 2011) Electronic band gap ≠ Optical band gap N-1 quasi-particle N+1 quasi-particle (electron + interaction with environment) N excitation (e-h interaction)

Electronic Spectroscopy: HgO INCAR (Partial) KPOINTS Chemical Physics Letters 399, 98 (2004) [1st Publication!] XPS (weighted DOS) O K XES (O 2p DOS)

Electronic vs Optical: In2 O3 INCAR (Partial) KPOINTS Physical Review Letters 100, 167402 (2008) Large difference in optical and electronic band gap is one reason why it is a high performance TCO

Lecture Outline Materials Modelling 1. Theory: What Equations to Solve 2. Practice: Codes & Supercomputers 3. Interactive: Databases 4. Application: Halide Perovskites

Past: Local Optimisation INPUT OUTPUT Structure Properties

Future: Materials Design INPUT OUTPUT Property Composition Structure

New Paradigm in Science Global Movement Associated with Databases, #OpenData and #OpenScience Agrawal and Choudhary, APL Materials 4, 053208 (2016)

Computational Property Databases • http://aflowlib.org • https://materialsproject.org • http://repository.nomad-coe.eu • http://materials.nrel.gov • http://oqmd.org • http://phonondb.mtl.kyoto-u.ac.jp • http://www.tedesignlab.org Popular databases include:

Materials Project

Materials Project

Materials Project Code (Open Source)

Crystal Structure Task What is the shortest Cu–S bond length in CuGaS2 ? 1. Log on to: https://materialsproject.org 2. Download the most stable crystal structure of CuGaS2 3. Open in VESTA (http://jp-minerals.org/vesta/en/) and draw bonds [EDIT: BONDS]

Lecture Outline Materials Modelling 1. Theory: What Equations to Solve 2. Practice: Codes & Supercomputers 3. Interactive: Databases 4. Application: Halide Perovskites

Hybrid Organic–Inorganic Perovskites Brief History (1958) – Photoconductivity in CsPbI3 (Møller) (1978) – Synthesis of CH3 NH3 PbI3 (Weber) (1994) – Metallic transition in CH3 NH3 SnI3 (Mitzi) (2009) – Perovskite dye cell (Miyasaka) (2012) – Planar thin-film solar cell (Snaith) Inorganic CsPbI3 Hybrid CH3 NH3 PbI3 or MAPI

Why Halide Perovskites? Essentials for Solar Cells • Strong optical absorption (Eg ~ 1.6 eV) • Light electron and hole masses (conductive) • Easy to synthesise (cheap and scalable) Advanced Features • Dielectric screening: carrier separation (weak excitons) and transport (low scattering rates) • Slow e-h recombination: low losses, large VOC o Relativistic effects – spin-orbit coupling o Polar domains – dynamic fluctuations o Phonon scattering – non-radiative limits

Perovskites: Model vs Reality Plastic crystal behaviour probed by Quasi-Elastic Neutron Scattering (P. Barnes, DOI: 10.1038/ncomms8124); 2D IR Spectroscopy (A. Bakulin, DOI: 10.1021/acs.jpclett.5b01555); Inelastic X-ray Scattering (S. Billinge, DOI: 10.1021/acsenergylett.6b00381) with simulations

Dynamic Processes in Perovskites Faster (fs) Slower (s) Electrons and Holes Effective semiconductors Lattice Vibrations Symmetry breaking and carrier separation Molecular Rotations Large static dielectric constant Ions and Charged Defects “Self healing” and hysteresis J. M. Frost and A. Walsh, Acc. Chem. Res. 49, 528 (2016)

Dielectric Response Standard Inorganic Dielectric Organic-Inorganic Dielectrics Microstructure Conductivity Contacts Lattice dynamics Optical response Stat. mechanics Sum of:

Dielectric Response High-frequency from QSGW theory Low-frequency from harmonic phonons (DFT/PBEsol)

“Giant Dielectric Constant” JPCM 20, 191001 (2008) JPCL 5, 2390 (2014) J. M. Frost and A. Walsh, Acc. Chem. Res. 49, 528 (2016)

“Giant Dielectric Constant” JPCM 20, 191001 (2008) JPCL 5, 2390 (2014) J. M. Frost and A. Walsh, Acc. Chem. Res. 49, 528 (2016)

Bananas are Lossy Dielectrics J. F. Scott, J. Phys. Conden. Matter 20, 2 (2007)

Mixed Ion–Electron Conductors Evidence and Consequences • Current-voltage hysteresis [Snaith et al, JPCL (2014); Unger et al, EES (2014)] • Rapid chemical conversion between halides [Pellet et al, CM (2015); Eperon et al, MH (2015)] • Photoinduced phase separation [Hoke et al, CS (2015); Yoon et al, ACS-EL (2016)] • Electric field induced phase separation [Xiao et al, NatM (2015); Yuan et al, AEM (2016)]

Hot Polaron Cooling Long-lived hot carriers upon photoexcitation [Phonon Bottleneck] Science 356, 59 (2017); Science 353, 1309 (2016); Nat. Photonics 10, 53 (2016); Nat. Commun. 6, 8420 (2015)

Key Factor: Thermal Conductivity Whalley, Skelton, Frost, Walsh, Physical Review B 94, 220301(R) (2016) T = 300K GaAs 38 (calculated) 45 (measured) CdTe 9 (calculated) 7 (measured) MAPI 0.05 (calculated) ~0.5 (measured) Calculated lattice thermal conductivity (3-phonon scattering) 46,800 DFT calculations!

Hot Polaron Cooling Rate Excess energy contained in polaron, with slow exchange to the bulk crystal Frost, Whalley, Walsh, ACS Energy Letters 2, 2647 (2017) Low Density n < 1018 cm-3 High Density n > 1018 cm-3 (Laser source) Notebooks: https://github.com/WMD- group/hot-carrier-cooling

Reproducible Analysis https://github.com/WMD-group/hot-carrier-cooling

Conclusions • Many materials modeling approaches for different length and time scales • First-principles techniques can accurately predict structure and properties • Materials data and reproducibility is becoming increasingly important Slides: https://speakerdeck.com/aronwalsh news & views e spoiled for urally occurring iodic table give y compounds ry compounds ompounds, each element inations exceed nent system. the number of ALS uest for new functionality tanding of the chemical bond, advances in synthetic chemistry, and large-scale computation, ow become a reality. From a pool of 400 unknown compositions, 15 new compounds have pt the expected structures and properties. Structural prediction Property simulation Targeted synthesis Chemical input Figure 1 | A modular materials design procedure, where an initial selection of chemical elements is subject to a series of optimization and screening steps. Each step may involve prediction of the crystal Future: