Quantum Simulations of NanoMaterials for Renewable Energy
Zhigang Wu
zhiwu@mines.edu
Department of Physics
Colorado School of Mines, Golden, CO 80401
Extra Lecture in Modern Physics
Class, CSM, 05/04/2010
Outline
Introduction
Renewable energy
Nanomaterials and nanotechnology
Quantum Simulation Methods
Density functional theory, Quantum Monte Carlo
Challenges for simulating nanomaterials for energy
My Research Work
Complex-structured silicon nanowires
Energy-level alignment at hybrid nano-interfaces
MgH2 nano-clusters for hydrogen storage
1
Why Do We Care About Renewable Energy?
“The possibilities of renewable energy are limitless…We’ve heard promises
about it in every State of the Union for the last three decades. But each and
every year, we become more, not less, addicted to oil — a 19th-century fossil
fuel.”
—— Barack Obama
2
What is Renewable Energy?
Renewable energy comes from
natural resources such as sunlight,
wind, tides, biological materials,
geothermal heat, etc.
3
What is Non-Renewable Energy?
Fossil fuels: petroleum, coal, natural
gas, formed by buried organism
through anaerobic decomposition with
millions of years.
4
The Greenhouse effect
The greenhouse effect occurs because
windows are transparent in the visible but
absorbing in the mid-IR, where most materials
re-emit. The same is true of the atmosphere.
Greenhouse gases:
Sun
carbon dioxide
water vapor
methane
nitrous oxide
Methane, emitted by
microbes called
methanogens, kept
the early earth warm.
5
Why Do We Care About Renewable Energy?
6
USA Energy Consumption in 2008
7
Is Renewable Energy Enough?
There is more energy in sunlight striking on the surface of earth
for 1 hour than total global energy consumption per year.
8
U.S. Renewable Resources
(100 miles)2 solar
panels (10% efficiency)
in Nevada would
power the U.S.
Turner, Science 285, 687
(1999).
$20 Trillion using
Si solar panels.
9
A Challenge with Solar Energy
For comparison: the cost of coal/oil/gas is 1-4¢/kWh
3-4¢
20¢
3¢
6-7¢
5¢
Need major improvement in efficiency and cost to take
advantage of solar energy: Nanotechnology
10
There is Plenty Room at the Bottom
Why cannot we write the entire 24 volumes
of the Encyclopedia Brittanica on the head
of a pin?
Now, the name of this talk is “There is
Plenty of Room at the Bottom”---not just
“There is Room at the Bottom.” What I
have demonstrated is that there is room--that you can decrease the size of things
in a practical way. I now want to show
that there is plenty of room. I will not now
discuss how we are going to do it, but only
what is possible in principle---in other
words, what is possible according to the
laws of physics. We are not doing it now
simply because we haven't yet gotten
around to it.
Dec. 29, 1959, Annual APS Meeting
Richard Feynman (19181988)
11
Nanoscience and Nanotechnology
1 nm = 10-9 m = 10 Å
Nanoscale: ~ 1 100 nm
Nanomaterials: at least one
dimension in the nanoscale.
Nanoparticle
4 nm diameter
Ant
Motor Speedway
4 mm long
4km per lap
Nanoscience is the study of phenomena and manipulation of nanomaterials.
Nanotechnology is the design, characterization, production and application of
structures, devices and systems by controlling size and shape at nanoscales.
http://www.nano.gov
12
Applications of Nanotechnology
. . . nanoscience and nanotechnology will change the nature of almost every
human-made object in the next century.
—The Interagency Working Group on Nanotechnology, 1999
$1 trillion market by 2011-2015 (NSF 2004)
Anti-cancer drug
delivery system
Cheap and clean
energy
Next-generation
computer
Michigan Center for Biological Nanotechnology
UCSB Bazan Group
13
Quantum Effects at the Nanoscale
= 729 nm
UV
light
UV
light
CdSe
A bulk material’s properties are
fixed.
http://nanocluster.mit.edu/
Properties of nanomaterials can
be tuned by varying the size.
14
Complex Structures of Nanomaterials
Nature Nanotech. 1, 186 (2006)
CdSe
Tapered Si Nanowires
Properties of nanomaterials are affected by
their shapes significantly.
Exp. characterization of
nanomaterials is
extremely challenging.
Thermoelectricity: Good
Poor
Theory and simulations
are in critical need for
advancing nanotech.
Rough Si Nanowire
4nm
Smooth Si Nanowire
3nm
Hochbaum et al., Nature 451, 163 (2008)
15
Quantum Mechanical Simulations
First-principles (or ab initio): no experimental input
and start from beginning – solving the many-electron
Schrödinger Equation:
Hˆ = E
Explain key processes and mechanisms from
fundamental theory.
Empirical models need experimental data.
Materials properties depend strongly on atomistic
details.
Predict new materials with better properties.
16
Solving Many-Electron Schrödinger Equation
2 2 ( r1 , r2 ,..., rN ) + V ( r1 , r2 ,..., rN )( r1 , r2 ,..., rN ) = E( r1 , r2 ,..., rN )
2m
Interacting NInteracting
Electron System
- -
3N-dimensional problem
Exponential wall: the time t needed
to solve this equation is prop. to eN.
N = 1, t = 1 s
N = 2, t = 7 s
N = 10, t = 2.2 104 s = 6.1 h
N = 20, t = 4.9 108 s = 15 years
N = 100, t = 2.7 1043 s
= 8.5 1035 years!
17
Density Functional Theory
18
Density Functional Theory
Many-body Schrödinger equation:
ˆ
H = E, where = ( r1, r2 ,..., rN )
Intractable 3N-dimentional equation
t eN
Hohenberg-Kohn (HK) theorem1: ground-state total energy can be
expressed in terms of electron density n(r), instead of wave functions.
E0 = E[n( r )]
Kohn-Sham (KS) theory2: mapping an interacting many-body system
to a non-interacting single-particle system in a mean field.
Interacting
- - - - -
Non-interacting
-
Ĥ = where = ( r )
Solvable 3-dimentional equation!
t N3
[1] Phys. Rev. 136, B864 (1964)
[2] Phys. Rev. 140, A1133 (1965)
19
KS Single-Particle Equation
2 2
2m + vKS ( r ) i ( r ) = i i ( r )
where vKS ( r ) = vext ( r ) + vH ( r ) + vxc ( r )
n( r ') with vH ( r ) = dr '
|r r'|
Need approximation,
Exc [n( r )]
vxc ( r )=
but simple form
n( r )
works pretty well.
OCC
2
and n( r ) = | i ( r ) |
i
20
The Triumph of DFT
Methanol inside a cage of the zeolite
sodalite (Blue: Si; Yellow: Al; Red: O)
Clathrate Sr8Ga16Ge30
(Red: Sr; Blue: Ga; white: Ge)
N = O (1000)
21
Challenges
Nanomaterials are complicated.
CdSe Nanoparticle with
d = 4 nm
~ 2,000 atoms
~ 20,000 electrons
Solution: better scaling scheme: t N.
22
Challenges
Accuracy is limited by the approximation for the exchange
correlation energy:
Exc [n( r )]
vxc ( r )=
n( r )
Solution: better Exc guided by results obtained
from more accurate methods.
23
Challenges
Excitations: DFT is NOT a theory for excited properties.
Band gap problem
Si: EgDFT = 0.6 eV
EgEXP = 1.2 eV
Solution: go beyond the
single-particle method to
include the many-body
interactions due to
excitation.
24
Quasiparticle
Bare particle
Excitations of many-electron
system can often be described
in terms of weakly interacting
“quasiparticles”.
-
Quasiparticle
-
Quasiparticle (QP) = bare
particle + polarization clouds.
EQP = E0+ : response of system to the
excitation(self-energy)
25
Beyond DFT
Quantum chemistry post-HF methods:
CI, CC, MCSCF, MP2, etc.
Many-body perturbation methods: GW/BSE
Very accurate for small systems
But very bad scaling of N5-7
Accurate for excitations, scaling as N4-7
Quantum Monte Carlo (QMC) methods
Fully-correlated many-body calculation
Stochastic solution to Schrödinger equation
Scaling as N3: most accurate benchmarks for
medium-size systems
26
Monte Carlo Technique
Random numbers can be used to help solve complicated
problems in physics.
27
Diffusion Monte Carlo (DMC)
Ref: Foulkes et al., RMP 73, 33 (2001)
28
How to Perform the Projection?
29
G(R’, R, ) as a Transition Probability
H=T+V
V=0
V0
30
Diffusion and Branching
31
A Toy Model: 1D Harmonic Oscillator
t DMC ~ O(100 1000) t DFT
DMC is Intrinsic parallel.
32
An Analogy of QM Methods
DFT
Post-HF, GW/BSE
QMC
33
Complex-Structured Si Nanowires
Wu, Neaton & Grossman, PRL 100, 246804 (2008)
Wu, Neaton & Grossman, Nano Lett. 9, 2418 (2009)
34
Tapering in Nanowires
Chan et al., Nature Nanotech. 1, 186 (2006)
Nanowires (NWs) are often tapered rather than straight.
The tapering can be as large as 2 nm reduction in d for 10 nm in L.
35
Tapering in Nanowires
GaAs
Nature Nanotech. 1, 186 (2006)
Nanowires (NWs) are often tapered rather than straight.
The tapering can be as large as 2 nm reduction in d for 10 nm in L.
The tapered tip can be grown gradually into a few nm in d.
Previous theory only considers straight NWs.
36
Modeling Tapered Nanowires
Wire axis along [011] direction with periodic boundary
condition.
H-passivation.
More than 1600 atoms or 5000 electrons in the unit-cell.
Tapered Si NW
d = 1.2 nm 1.4 nm
1.7 nm 1.9 nm
2.2 nm
L = 10 nm
Method: DFT with atomic-orbital basis (SIESTA1 code).
Linear-scaling code
[1] http://www.icmab.es/siesta/
37
Near-Gap States
hole
electron
Spatial separation of the valence band maximum (VBM) and the
conduction band minimum (CBM) states in the tapered nanowire.
38
Finite-Length Model: Tapered Nanorod
The highest occupied (HOMO) and lowest unoccupied
(LUMO) molecular orbitals are separated along axis.
39
A New Route for Solar Cells
Separating charge carriers
p-n Junction
n-type
p-type
Type-II Hetero-Junction
CB
No Junction
LUMO
HOMO
Simple and cheap
new type of PV
VB
40
Level-Alignment at Hybrid Interfaces
Wu, Kanai & Grossman, PRB 79, 2013(R) (2009)
41
Level-Alignment at Hybrid Interfaces
LUMO
CBM
VBM
HOMO
Bent Group at Stanford
Hybrid interface is crucial for
molecular electronics and optoelectronics, e.g. organic PV cells.
Design interfaces with appropriate
energy-level alignment:
Modify molecular gap
Control semiconductor band-gap
by tuning quantum confinement
LUMO
CBM
LUMO
CBM
HOMO
HOMO
VBM
VBM
42
Si (001)TTF Interface
DFT calculation
Type-II Junction
Interface
1.91
0.44
1.79
Tetrathiafulvalence: TTF
Type-II junction is very
interesting and useful.
43
Interface-Type vs. Quantum Confinement
DFT-KS
Type "III"
Type III
Type II
LUMO
CBM
Type I
CBM
CBM
VBM
HOMO
HOMO
HOMO
4
LUMO
LUMO
VBM
VBM
8
12
16
20
Number of Layers
24
28
32
bulk
DFT: This junction can be
tuned by quantum confinement.
44
Many-Body Correction
= QP DFT
is the many - body correction
LUMO
CBM
-
HOMO
VBM
-
Quasiparticle
CBM
CBM
VBM
Bare Particle
VBM
DFT has successfully predicted accurate band-offsets at
semiconductor interfaces1,2 due to error cancellation of .
However, for hybrid interfaces composed of two distinct
materials, can be different significantly.
[1] Walle et al., PRB 35, 8154 (1987)
[2] Wei & Zunger, APL 72, 2011 (1998)
45
Many-Body Corrections to Level-Alignment
DFT
DFT-KS
QMC-DMC
Interface
1.1
2.5
1.91
0.44
1.79
2.8
0.5
DFT: Type-II
LUMO
CBM
QMC: Type-I
LUMO
CBM
HOMO
VBM
VBM
HOMO
46
Interface-Type vs. Quantum Confinement
DFT-KS
QMC - DMC
Type "III"
Type II
Type I
4
8
12
16
20
Number of Layers
24
28
32
bulk
QMC: The junction type CAN NOT
be tuned by quantum confinement.
47
MgH2 Nanoscale Cluster for H Storage
Wu, Allendorf & Grossman, JACS 131, 13918, (2009)
48
Motivation
C + O2 = CO2
H2 + O2 = water
Chemical storage: the reversible absorption of H into
another material.
Bulk materials are often too stable.
E.g. MgH2: 7.7wt%, Ed = 75 kJ/mol, Td ~ 300 oC
Desirable Ed = 20 50 kJ/mol
Ed can be tuned by the size of nanoparticles.
49
Mg and MgH2 Crystal Lattices
Rutile: P42/mnm
HCP: P63/mmc
50
Chemical Accuracy for Ed is Required
Chemical accuracy: 1 kcal/mol = 4.2 kJ/mol = 0.043 eV
51
MgH2 Clusters
52
Desorption Energy of MgH2 Clusters
Ed (kJ/mol H2)
100
50
Expt.: bulk
CCSD(T)
DMC
DFT-LDA
DFT-PBE
0
20
40
(MgH2)N
60
Bulk
53
Desorption Energy of MgH2 Clusters
(MgH2)N
54
Size-Dependent DFT Error
55
Size-Dependent DFT Error
0
LDA
PBE
-20
Ed
DFT
- Ed
DMC
(kJ/mol H2)
20
-40
0
20
40
(MgH2)N
60
Bulk
56
Summary
Nanostructured PV
Hydrogen
Storage in
Nanoparticles
Hybrid Nano-Interfaces
Computational
Challenges
57
Acknowledgements
Department of Energy (DOE)
National Science Foundation (NSF)
Molecular Foundry, NERSC, and Teragrid
Thank you very much for your attention!
58