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Materials by Computational Design – A Bottom Up Approach
Anderson Janotti
Department of Materials Science and EngineeringUniversity of Delaware
Group members:Dr. Zhigang GuiDr. Lu Sun
1
Email: [email protected] Hall Rm 212
Abhishek SharanAtta RehmanIflah Laraib
Shoaib KhalidTianshi WangWei Li
Acknowledgements:
Dr. Zhigang GuiDr. Lu Sun
Abhishek SharanWei Li Tianshi Wang
Iflah Laraib Shoaib KhalidAtta Rehman
Postdoctoral researchers PhD students
Computational resources
UD HPC (Farber)
NSF XSEDE (Stampede, Bridges)
Funding
Outline
Introduction to our research at UD
Overview of Density Functional Theory
DFT codes
VASPQuantum Espresso
Applications
Materials Theory at MSEG
Oxides:TCOs
Complex oxidesMott insulators
Transistors
PhotovoltaicsCIS, CIGS
Chalcogenides Perovskites
Half-HeuslersTopological insulators
Weyl semimetals
Rare-earth arsenides
IR detectorsThermoelectrics
III-V’s dilute
Bismides
Hydrogen impurities multicenter
bonds
2D materials MoS2 In2Se3
First-principles methods
Density Functional Theory
Quantum information Spin centers
Superconducting qubits
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”
Interacting electrons in an external potential (given by the nuclei)
H = �X
i
~22me
r2i �
X
i,I
ZIe2
|ri �RI|+
1
2
X
i 6=j
e2
|ri � rj|
�X
I
~22MI
r2I +
1
2
X
I 6=J
ZIZJe2
|RI �RJ|
First-principles approach
8
Interacting electrons in an external potential (given by the nuclei)
H = �X
i
~22me
r2i �
X
i,I
ZIe2
|ri �RI|+
1
2
X
i 6=j
e2
|ri � rj|
�X
I
~22MI
r2I +
1
2
X
I 6=J
ZIZJe2
|RI �RJ|
H| >= E| >
9
Many-body Schrödinger equation
First-principles approach
Interacting electrons in an external potential (given by the nuclei)
H = �X
i
~22me
r2i �
X
i,I
ZIe2
|ri �RI|+
1
2
X
i 6=j
e2
|ri � rj|
�X
I
~22MI
r2I +
1
2
X
I 6=J
ZIZJe2
|RI �RJ|
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
Easy to write, too difficult to solve H| >= E| >10
First-principles approach
Many-body Schrödinger equation
11 From Martijn Marsman
Density functional theoryHohenberg-Kohn (1964)
The total energy of the ground-state of a many-body system is a unique functional of the particle density
E0 = E[(r)]
The functional has its minimum relative to variations of theparticle 𝛿n0(r) at the equilibrium density n0(r)
E0 = E[(r)] = min{E[(r)]}
�E[n(r)]
�n(r)|n(r)=n0(r) = 0
12
n0(r) =X
�
X
i
|��i (r)|2
Density functional theory
The Kohn-Sham Ansatz (1965)
Replace original many-body problem with an independent electron problem - that can be solved
Exchange-CorrelationFunctional - Exact theory but unknown functional
EKS =1
2
X
�
X
i
|r��i |2 +
ZdrVext(r)n(r) + EH [n] + EII + Exc[n]
Equations for independentparticles - soluble
13
n0(r) =X
�
X
i
|��i (r)|2
�EKS
���⇤i
= 0 <��i |��0
i > = �i,j��,�0
Density functional theory
EKS =1
2
X
�
X
i
|r��i |2 +
ZdrVext(r)n(r) + EH [n] + EII + Exc[n]
Assuming a form for Exc[n] Minimizing energy (with constraints) -> Kohn-Sham Eqs.
The Kohn-Sham (1965)
required by the Exclusion principle for independent particles
[�1
2r2 + 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
• Generalized Gradient approximation - GGA- Various theoretical improvements for electron density that varies in space
Exc
= Ex
+ Ec
ELDAx
[n] = �3
4
✓3
⇡
◆1/3 Zn(r)4/3dr
- EXC has been calculated as a function of density using quantum Monte Carlo methods Ceperley-Alder (1980) and parameterized by Perdew-Zunger (1981)
ELDAxc
[n] =
Zdrn(r)"
xc
(n)
EGGAxc
[n] =
Zdrn(r)"
xc
(n,rn)
PBE: J. P. Perdew, K. Burke, and M. Ernzerhof (1996)15
Self-consistent Kohn-Sham Equations
[�1
2r2 + V �
KS(r)]��i (r) = "�i �
�i (r)
initial guess, density n
construct K-S potential
solve K-S equations
V �KS(r) = Vext(r) +
�EH
�n(r,�)+
�Exc
�n(r,�)
= Vext(r) + VH(r) + V �xc(r)
is n self-consistent?
obtain new density n(r) =X
�
X
i
|��i (r)|2
No
Yes output total energy, forces, eigenvalues, ….16
N-electron sytems
From Martijn Marsman
From Martijn MarsmanTake advantage of fast Fourier Transforms
Plane wave expansion, solve for the planewave coefficients
Taking the problem to the k space
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
120 nodes2000 cores (20 cores/node)6.4 TB
Allocation: 10 regular nodes200 cores
Farber - HPC-UD
Farber at UD
Our lab - Stampede - TACC (NSF XSEDE)
Stampede - TACC- Texas
10 PFLOPS (PF)6400 nodes16 cores/node32GB/node
Our lab - Bridges, PSC (NSF XSEDE)
Current allocation: 2,000,000 cpu hours/year
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.
DFT codes in our lab
Vienna ab initio simulation package (VASP)
Quantum Expresso
ABINIT
https://www.vasp.at/
http://www.quantum-espresso.org/
plane wave codes
http://www.abinit.org/
Code: Vienna Ab Initio Simulation Package (VASP)
VASP files (fortran)
VASP - Makefile
Makefile
MPIIntel fortran(algo works with PG and GNU)MKL library
Recently has been ported toGPU
largest system we tried on farber
pentacene crystal
576 atoms352 C224 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
Surfaces
Defect formation energies, transition levels, optical absorption/emission
Interface energies, band alignmentsSurface energies, reconstructions
N-V center in diamondGdTiO3/SrTiO3 superlattices
metal-oxide-semiconductor device
Interfaces
Quantum wells, two-dimensional electron gases,magnetic ordering
Electronic structure - comparison with experiment
Comparison between HSE03+G0W0 QP energies (green dots) with soft X-ray angle- resolved photoemission spectroscopy measurements [M. Kobayashi et al (2008)]
ZnO - GW band structure vs. Photoemission
34
Doping: Why N cannot lead to p-type ZnO
35
Spin density - unpaired electron
• 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)
Lyons, Janotti, and Van de Walle, APL 95, 252105 (2009)
• Deep acceptor
• Predicted absorption and emission energies confirmed by experiments
Optical absorption/emission
Tarun, Iqbal, and McCluskey, AIP Advances 1, 022105 (2011)
Carbon in GaN and the source of yellow luminescence
36
Lyons, Janotti, and Van de Walle Appl. Phys. Lett. 97, 152108 (2010)
Calculated
T. Ogino and M. Aoki Jpn. J. Appl. Phys. 19, 2395 (1980)
• Emission peak: 2.14 eV
CN gives rise to YL
•Absorption: 2.95 eV
• Zero-phonon line: 2.60 eV
•Relaxation energies ~0.4 eV
PhotoluminescenceGaN 77 K
Luminescence lines shapes - direct comparison with experiments
Complex oxides
38
Kan et al, Nature Materials 4, 816 (2005)
Bulk SrTiO3
Oxygen vacancies as causes of deep-level luminescence and conductivity?
SrTiO3/GdTiO3 heterostructures
Zhang et al, Phys. Rev. B 89, 075140 (2014)
Transition from a 2DEG to insulator as STO thickness decreases?
Sources of deep-level luminescence in STO
39
Kan et al, Nature Materials 4, 816 (2005)
Janotti et al, Phys. Rev. B 2014
Solution of the Schrödinger-Poisson problem for very large systems using first-principles data as input parameters
SrTiO3 GdTiO3GdTiO3
LHB
UHB
EV
EC
Input parameters from first-principles calculations:Effective massesBand offsetsDielectric constants (from exp.)
Each interface holds a 2DEG with density of 3.3x1014 cm-2
= 1/2 electron per interface unit cell
Metal-insulator transition in ultra-thin SrTiO3 QW
41
SrTiO3/GdTiO3 heterostructures
Zhang et al, Phys. Rev. B 89, 075140 (2014)
Transition from a 2DEG to insulator as STO thickness decreases
SrTiO3 quantum well: 6 SrO layers
Ferromagnetic metal
Stoner criterion D(EF)U > 1
Energy
Excess charge uniformly distributed on the SrTiO3 layer
charge density on the STO layer
-0.5
0
0.5
1.0
1.5
2.0
2.5
X Γ M/2
Ener
gy (e
V)
Fermilevel
High density of states at the Fermi level in the unpolarized system
2DEGmetallic
Janotti et al, submitted
-0.5
0
0.5
1.0
1.5
2.0
2.5
X Γ M/2
Ener
gy (e
V)
SrTiO3 quantum well: 3 SrO layers
Ferromagnetic metal
Energy
1/4 electron per Ti
100% polarization
metallic
Janotti et al, submitted
SrTiO3 quantum well: 2 SrO layers
-0.5
0
0.5
1.0
1.5
2.0
2.5
X Γ M/2
Ener
gy (e
V)
Insulator!
Charge density on STO layer sufficiently high so that on-site repulsion leads to localization
gap
Energy
1/3 electron per Ti
Electrons localize at the interface
Empty dispersive band from the middle TiO2 plane
Charge ordering on the TiO2planes at the interface
Janotti et al, submitted
SrTiO3 quantum well: 1 SrO layer
-0.5
0
0.5
1.0
1.5
2.0
2.5
X Γ M/2
Ener
gy (e
V)
Insulator!Energy
Charge density on STO layer sufficiently high so that on-site repulsion leads to localization
1/2 electron per Ti
gap
Charge ordering on the TiO2planes next to the SrO layer
Janotti et al, submitted
Current problems of interest
2D materialsIn2Se3 InBiMoS2
Memristor materialsNeuromorphic computing
Complex-oxide heterostructures
Half-heusler compounds
Materials for solid oxide fuel cells
Metal-semiconductor composites
…
