Materials by Computational Design A Bottom Up Approach

Materials by Computational Design A Bottom Up Approach Anderson Janotti Department of Materials Science and Engineering University of Delaware Email: janotti@udel.edu Dupont Hall Rm 212 Group members: Dr. Zhigang Gui Dr. Lu Sun Abhishek Sharan Atta Rehman Iflah Laraib Shoaib Khalid Tianshi Wang Wei Li 1

Acknowledgements: Postdoctoral researchers Dr. Zhigang Gui Dr. Lu Sun Computational resources UD HPC (Farber) PhD students Abhishek Sharan Wei Li Tianshi Wang Iflah Laraib Shoaib Khalid Atta Rehman NSF XSEDE (Stampede, Bridges) Funding

Outline Introduction to our research at UD Overview of Density Functional Theory DFT codes VASP Quantum Espresso Applications

Materials Theory at MSEG Oxides: TCOs Complex oxides Mott insulators Transistors Quantum information Spin centers Superconducting qubits Hydrogen impurities multicenter bonds Photovoltaics CIS, CIGS Chalcogenides Perovskites First-principles methods Density Functional Theory Half-Heuslers Topological insulators Weyl semimetals 2D materials MoS2 In2Se3 Rare-earth arsenides IR detectors Thermoelectrics III-V s dilute Bismides

The role of computation Paul Dirac, 1929 The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.

The role of computation Paul Dirac, 1929 The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

The role of computation Emergent Phenomena The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new bevaviors requires research which I think is as fundamental in its nature as any other

First-principles approach Interacting electrons in an external potential (given by the nuclei) Ĥ = X I X i ~ 2 2m e r 2 i ~ 2 2M I r 2 I + 1 2 X i,i X I6=J Z I e 2 r i R I + 1 2 Z I Z J e 2 R I R J X i6=j e 2 r i r j 8

First-principles approach Interacting electrons in an external potential (given by the nuclei) Ĥ = X I X i ~ 2 2m e r 2 i ~ 2 2M I r 2 I + 1 2 X i,i X I6=J Z I e 2 r i R I + 1 2 Z I Z J e 2 R I R J X i6=j e 2 r i r j Ĥ >= E > Many-body Schrödinger equation 9

First-principles approach Interacting electrons in an external potential (given by the nuclei) Ĥ = X I X i ~ 2 2m e r 2 i ~ 2 2M I r 2 I + 1 2 X i,i X I6=J Z I e 2 r i R I + 1 2 Z I Z J e 2 R I R J X i6=j e 2 r i r j Omitting this term, the nuclei are a fixed external potential acting on the electrons Essential for charge neutrality - classical term that is added to the electronic part Ĥ >= E > Easy to write, too difficult to solve 10

Many-body Schrödinger equation 11 From Martijn Marsman

Density functional theory Hohenberg-Kohn (1964) The total energy of the ground-state of a many-body system is a unique functional of the particle density E 0 = E[(r)] The functional has its minimum relative to variations of the particle δn0(r) at the equilibrium density n0(r) E 0 = E[(r)] = min{e[(r)]} E[n(r)] n(r) n(r)=n0 (r) =0 12

Density functional theory The Kohn-Sham Ansatz (1965) n 0 (r) = X X i i (r) 2 Replace original many-body problem with an independent electron problem - that can be solved E KS = 1 2 X X r i 2 + i Z drv ext (r)n(r)+e H [n]+e II + E xc [n] Equations for independent particles - soluble Exchange-Correlation Functional - Exact theory but unknown functional 13

Density functional theory The Kohn-Sham (1965) n 0 (r) = X X i i (r) 2 E KS = 1 2 X X r i 2 + Z drv ext (r)n(r)+e H [n]+e II + E xc [n] i Assuming a form for Exc[n] Minimizing energy (with constraints) -> Kohn-Sham Eqs. E KS i =0 < i 0 i > = i,j, 0 required by the Exclusion principle for independent particles [ 1 2 r2 + V KS (r)] i (r) =" i i (r) 14

Approximations to EXC[n] Local Density Approximation - LDA - Assume the functional is the same as a model problem the homogeneous electron gas E LDA xc [n] = Z E LDA x [n] = 3 4 drn(r)" xc (n) 3 1/3 Z n(r) 4/3 dr E xc = E x + E c - E XC has been calculated as a function of density using quantum Monte Carlo methods Ceperley-Alder (1980) and parameterized by Perdew-Zunger (1981) Generalized Gradient approximation - GGA - Various theoretical improvements for electron density that varies in space E GGA xc [n] = Z drn(r)" xc (n, rn) PBE: J. P. Perdew, K. Burke, and M. Ernzerhof (1996) 15

Self-consistent Kohn-Sham Equations initial guess, density n construct K-S potential V KS (r) =V ext (r)+ E H n(r, ) + E xc n(r, ) = V ext (r)+v H (r)+v xc (r) solve K-S equations [ 1 2 r2 + V KS (r)] i (r) =" i i (r) obtain new density n(r) = X X i i (r) 2 No is n self-consistent? Yes 16 output total energy, forces, eigenvalues,.

N-electron sytems From Martijn Marsman

Take advantage of fast Fourier Transforms From Martijn Marsman

Taking the problem to the k space Plane wave expansion, solve for the planewave coefficients matrix diagonalization techniques

List of quantum chemistry and solid-state physics software https://en.wikipedia.org/wiki/list_of_quantum_chemistry_and_solid-state_physics_software

Our lab Farber - HPC-UD XSEDE - NSF Stampede - TACC Bridges - PSC

Our lab Farber - HPC-UD 120 nodes 2000 cores (20 cores/node) 6.4 TB Allocation: 10 regular nodes 200 cores

Farber at UD

Our lab - Stampede - TACC (NSF XSEDE) Stampede - TACC- Texas 10 PFLOPS (PF) 6400 nodes 16 cores/node 32GB/node

Our lab - Bridges, PSC (NSF XSEDE) Bridges - PSC - Pittsburg https://www.psc.edu/index.php/resources/computing/bridges 3 classes of compute nodes: - 4 Extreme Shared Memory (ESM) nodes, HP Integrity Superdome X servers with 16 Intel Xeon EX-series CPUs and 12TB of RAM; - tens of Large Shared Memory (LSM) nodes, HP DL580 servers with 4 Intel Xeon EX-series CPUs and 3TB of RAM; - hundreds of Regular Shared Memory (RSM) nodes, each with 2 Intel Xeon EP-series CPUs and 128GB of RAM. Current allocation: 2,000,000 cpu hours/year

DFT codes in our lab plane wave codes Vienna ab initio simulation package (VASP) https://www.vasp.at/ Quantum Expresso http://www.quantum-espresso.org/ ABINIT http://www.abinit.org/

Code: Vienna Ab Initio Simulation Package (VASP)

VASP files (fortran)

VASP - Makefile Makefile MPI Intel fortran (algo works with PG and GNU) MKL library Recently has been ported to GPU

largest system we tried on farber pentacene crystal 576 atoms 352 C 224 H 1632 electrons

Scaling tests on stampede (VASP) Ex.: EuTiO3 160 atoms ideal

Applications

Problems that have been addressed using first-principles calculations Point defects, doping Heterostructures N-V center in diamond Defect formation energies, transition levels, optical absorption/emission Surfaces GdTiO3/SrTiO3 superlattices Quantum wells, two-dimensional electron gases, magnetic ordering Interfaces metal-oxide-semiconductor device Surface energies, reconstructions Interface energies, band alignments

Electronic structure - comparison with experiment ZnO - GW band structure vs. Photoemission Comparison between HSE03+G 0 W 0 QP energies (green dots) with soft X-ray angle- resolved photoemission spectroscopy measurements [M. Kobayashi et al (2008)] 34

Doping: Why N cannot lead to p-type ZnO Optical absorption/emission Spin density - unpaired electron Deep acceptor Predicted absorption and emission energies confirmed by experiments Lyons, Janotti, and Van de Walle, APL 95, 252105 (2009) Tarun, Iqbal, and McCluskey, AIP Advances 1, 022105 (2011) Localization of hole on nitrogen atom Axial orientation Explains electron paramagnetic resonance measurements Carlos, Glaser, and Look Physica B 308, 976 (2001) Garces, et al., APL 80, 1334 (2002) 35

Carbon in GaN and the source of yellow luminescence Calculated Lyons, Janotti, and Van de Walle Appl. Phys. Lett. 97, 152108 (2010) CN gives rise to YL Absorption: 2.95 ev Zero-phonon line: 2.60 ev Relaxation energies ~0.4 ev Emission peak: 2.14 ev 36 Photoluminescence GaN 77 K T. Ogino and M. Aoki Jpn. J. Appl. Phys. 19, 2395 (1980)

Luminescence lines shapes - direct comparison with experiments

Complex oxides Bulk SrTiO3 SrTiO3/GdTiO3 heterostructures Kan et al, Nature Materials 4, 816 (2005) Zhang et al, Phys. Rev. B 89, 075140 (2014) Oxygen vacancies as causes of deeplevel luminescence and conductivity? 38 Transition from a 2DEG to insulator as STO thickness decreases?

Sources of deep-level luminescence in STO Kan et al, Nature Materials 4, 816 (2005) Janotti et al, Phys. Rev. B 2014 39

Solution of the Schrödinger-Poisson problem for very large systems using first-principles data as input parameters GdTiO3 SrTiO3 UHB GdTiO3 EC LHB EV Input parameters from first-principles calculations: Effective masses Band offsets Dielectric constants (from exp.) Each interface holds a 2DEG with density of 3.3x10 14 cm -2 = 1/2 electron per interface unit cell

Metal-insulator transition in ultra-thin SrTiO3 QW SrTiO3/GdTiO3 heterostructures Transition from a 2DEG to insulator as STO thickness decreases Zhang et al, Phys. Rev. B 89, 075140 (2014) 41

SrTiO3 quantum well: 6 SrO layers metallic 2DEG charge density on the STO layer 2.5 2.0 Energy Energy (ev) 1.5 1.0 0.5 Fermi level 0-0.5 X Γ M/2 Excess charge uniformly distributed on the SrTiO3 layer Ferromagnetic metal Stoner criterion D(EF)U > 1 High density of states at the Fermi level in the unpolarized system Janotti et al, submitted

SrTiO3 quantum well: 3 SrO layers metallic Energy 2.5 2.0 Energy (ev) 1.5 1.0 0.5 0-0.5 X Γ M/2 1/4 electron per Ti Ferromagnetic metal 100% polarization Janotti et al, submitted

Insulator! SrTiO3 quantum well: 2 SrO layers 2.5 Energy Energy (ev) 2.0 1.5 1.0 0.5 gap 0-0.5 X Γ M/2 1/3 electron per Ti Charge density on STO layer sufficiently high so that on-site repulsion leads to localization Electrons localize at the interface Charge ordering on the TiO2 planes at the interface Empty dispersive band from the middle TiO2 plane Janotti et al, submitted

Insulator! SrTiO3 quantum well: 1 SrO layer 2.5 2.0 Energy 1/2 electron per Ti Energy (ev) 1.5 gap 1.0 0.5 0-0.5 X Γ M/2 Charge density on STO layer sufficiently high so that on-site repulsion leads to localization Charge ordering on the TiO2 planes next to the SrO layer Janotti et al, submitted

Current problems of interest 2D materials In2Se3 InBi MoS2 Complex-oxide heterostructures Memristor materials Neuromorphic computing Half-heusler compounds Materials for solid oxide fuel cells Metal-semiconductor composites