Quantum Simulations of Nano- Materials for Renewable Energy Zhigang - - PowerPoint PPT Presentation

Quantum Simulations of Nano- Materials for Renewable Energy

Extra Lecture in Modern Physics Class, CSM, 05/04/2010

Zhigang Wu

zhiwu@mines.edu

Department of Physics Colorado School of Mines, Golden, CO 80401

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?

2

“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

What is Renewable Energy?

3

Renewable energy comes from natural resources such as sunlight, wind, tides, biological materials, geothermal heat, etc.

What is Non-Renewable Energy?

4

Fossil fuels: petroleum, coal, natural gas, formed by buried organism through anaerobic decomposition with millions of years.

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: carbon dioxide water vapor methane nitrous oxide Methane, emitted by microbes called methanogens, kept the early earth warm.

5

Sun

Why Do We Care About Renewable Energy?

6

USA Energy Consumption in 2008

7

Is Renewable Energy Enough?

8

There is more energy in sunlight striking on the surface of earth for 1 hour than total global energy consumption per year.

9

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.

10

A Challenge with Solar Energy

20¢ 3-4¢ 3¢ 6-7¢ 5¢

For comparison: the cost of coal/oil/gas is 1-4¢/kWh

Need major improvement in efficiency and cost to take advantage of solar energy: Nanotechnology

There is Plenty Room at the Bottom

11

Richard Feynman (19181988)

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

Why cannot we write the entire 24 volumes

• f the Encyclopedia Brittanica on the head
• f a pin?

Nanoscience and Nanotechnology

12

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. 1 nm = 10-9 m = 10 Å Nanoscale: ~ 1 100 nm Nanomaterials: at least one dimension in the nanoscale. Nanoparticle Ant Motor Speedway

4 nm diameter 4 mm long 4km per lap

http://www.nano.gov

Applications of Nanotechnology

13

$1 trillion market by 2011-2015 (NSF 2004)

. . . nanoscience and nanotechnology will change the nature of almost every human-made object in the next century. —The Interagency Working Group on Nanotechnology, 1999

Michigan Center for Biological Nanotechnology

Anti-cancer drug delivery system Cheap and clean energy

UCSB Bazan Group

Next-generation computer

Quantum Effects at the Nanoscale

http://nanocluster.mit.edu/

UV light

Properties of nanomaterials can be tuned by varying the size.

14

UV light = 729 nm

A bulk material’s properties are fixed.

CdSe

15

Complex Structures of Nanomaterials

Hochbaum et al., Nature 451, 163 (2008)

Rough Si Nanowire

Nature Nanotech. 1, 186 (2006)

Tapered Si Nanowires Smooth Si Nanowire

4nm 3nm

CdSe Thermoelectricity: Good Poor

Properties of nano- materials are affected by their shapes significantly.

• Exp. characterization of

nanomaterials is extremely challenging. Theory and simulations are in critical need for advancing nanotech.

Quantum Mechanical Simulations

First-principles (or ab initio): no experimental input

and start from beginning – solving the many-electron Schrödinger Equation:

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

ˆ H = E

Solving Many-Electron Schrödinger Equation

17

2 2m2( r

1,

r

2,...,

rN ) +V ( r

1,

r

2,...,

rN )( r

1,

r

2,...,

rN ) = E( r

1,

r

2,...,

rN )

Interacting

• Interacting N-

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 104s = 6.1 h N = 100, t = 2.7 1043 s = 8.51035 years! N = 20, t = 4.9 108 s = 15 years

Density Functional Theory

18

Density Functional Theory

• Many-body Schrödinger equation:
• Hohenberg-Kohn (HK) theorem1: ground-state total energy can be

expressed in terms of electron density n(r), instead of wave functions.

• Kohn-Sham (KS) theory2: mapping an interacting many-body system

to a non-interacting single-particle system in a mean field.

19 [1] Phys. Rev. 136, B864 (1964) [2] Phys. Rev. 140, A1133 (1965)

ˆ H = E, where = ( r

1,

r

2,...,

r

N) Intractable 3N-dimentional equation

E0 = E[n( r )]

Interacting Non-interacting

• t eN

ˆ H = where = ( r )

Solvable 3-dimentional equation!

t N 3

KS Single-Particle Equation

20

22 2m + vKS( r )

• i(

r ) = ii( r ) where vKS( r ) = vext( r ) + vH( r ) + vxc( r ) with vH( r ) = n( r ') | r r ' |

• d

r ' vxc( r )= Exc[n( r )] n( r ) and n( r ) = |i( r ) |2

i OCC

• Need approximation,

but simple form works pretty well.

The Triumph of DFT

21

Methanol inside a cage of the zeolite sodalite (Blue: Si; Yellow: Al; Red: O)

N = O (1000)

Clathrate Sr8Ga16Ge30 (Red: Sr; Blue: Ga; white: Ge)

Challenges

22

Nanomaterials are complicated.

CdSe Nano- particle with d = 4 nm ~ 2,000 atoms ~ 20,000 electrons

Solution: better scaling scheme: .

t N

Challenges

23

Accuracy is limited by the approximation for the exchange- correlation energy:

vxc( r )= Exc[n( r )] n( r )

Solution: better Exc guided by results obtained from more accurate methods.

Challenges

24

Excitations: DFT is NOT a theory for excited properties. Band gap problem Si:

Eg

DFT = 0.6 eV

Eg

EXP = 1.2 eV

Solution: go beyond the single-particle method to include the many-body interactions due to excitation.

Quasiparticle

25

• Bare particle

Quasiparticle EQP = E0+

: response of system to the excitation(self-energy) Excitations of many-electron system can often be described in terms of weakly interacting “quasiparticles”. Quasiparticle (QP) = bare particle + polarization clouds.

26

Beyond DFT

Quantum chemistry post-HF methods:

CI, CC, MCSCF, MP2, etc.

Very accurate for small systems But very bad scaling of N5-7

Many-body perturbation methods: GW/BSE

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

Monte Carlo Technique

27

Random numbers can be used to help solve complicated problems in physics.

Diffusion Monte Carlo (DMC)

28

Ref: Foulkes et al., RMP 73, 33 (2001)

How to Perform the Projection?

29

G(R’, R, ) as a Transition Probability

30

H=T+V V=0 V0

Diffusion and Branching

31

A Toy Model: 1D Harmonic Oscillator

32

t DMC ~ O(100 1000) t DFT

DMC is Intrinsic parallel.

33

An Analogy of QM Methods

DFT Post-HF, GW/BSE QMC

Complex-Structured Si Nanowires

34

Wu, Neaton & Grossman, PRL 100, 246804 (2008) Wu, Neaton & Grossman, Nano Lett. 9, 2418 (2009)

35

Tapering in Nanowires

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.

Chan et al., Nature Nanotech. 1, 186 (2006)

36

Tapering in Nanowires

Nature Nanotech. 1, 186 (2006)

Nanowires (NWs) are often tapered rather than straight. Previous theory only considers straight NWs.

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.

GaAs

37

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. Method: DFT with atomic-orbital basis (SIESTA1 code).

Tapered Si NW L = 10 nm d = 1.2 nm 1.4 nm 1.7 nm 1.9 nm 2.2 nm

[1] http://www.icmab.es/siesta/

Linear-scaling code

38

Near-Gap States

Spatial separation of the valence band maximum (VBM) and the conduction band minimum (CBM) states in the tapered nanowire. hole electron

39

Finite-Length Model: Tapered Nanorod

The highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals are separated along axis.

40

A New Route for Solar Cells

No Junction

Type-II Hetero-Junction LUMO HOMO CB VB p-type n-type p-n Junction

Separating charge carriers

Simple and cheap new type of PV

Level-Alignment at Hybrid Interfaces

41

Wu, Kanai & Grossman, PRB 79, 2013(R) (2009)

Level-Alignment at Hybrid Interfaces

42

LUMO HOMO CBM VBM LUMO HOMO CBM VBM LUMO HOMO CBM VBM

Bent Group at Stanford

• Hybrid interface is crucial for

molecular electronics and opto- electronics, e.g. organic PV cells.

• Design interfaces with appropriate

energy-level alignment:

Modify molecular gap Control semiconductor band-gap

by tuning quantum confinement

Si (001)TTF Interface

43

Type-II Junction

1.79 1.91 Interface 0.44

DFT calculation

Tetrathiafulvalence: TTF

Type-II junction is very interesting and useful.

Interface-Type vs. Quantum Confinement

44

4 8 12 16 20 24 28 32 Number of Layers DFT-KS

Type "III"

Type II Type I bulk

LUMO HOMO CBM VBM LUMO HOMO CBM VBM LUMO HOMO CBM VBM

Type III

DFT: This junction can be tuned by quantum confinement.

Many-Body Correction

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.

45

=

QP DFT

is the many-body correction

LUMO HOMO CBM VBM

[1] Walle et al., PRB 35, 8154 (1987) [2] Wei & Zunger, APL 72, 2011 (1998)

VBM CBM VBM CBM

• Bare Particle

Quasiparticle

1.79 1.91 Interface 0.44

Many-Body Corrections to Level-Alignment

46

DFT: Type-II QMC: Type-I LUMO HOMO CBM VBM LUMO HOMO CBM VBM

DFT DFT-KS QMC-DMC 1.79 1.91 Interface 0.44 1.1 0.5 2.5 2.8

Interface-Type vs. Quantum Confinement

47

4 8 12 16 20 24 28 32 Number of Layers DFT-KS

Type "III"

Type II Type I bulk QMC

QMC: The junction type CAN NOT be tuned by quantum confinement.

• DMC

MgH2 Nanoscale Cluster for H Storage

48

Wu, Allendorf & Grossman, JACS 131, 13918, (2009)

Motivation

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

C + O2 = CO2 H2 + O2 = water

Mg and MgH2 Crystal Lattices

50

HCP: P63/mmc Rutile: P42/mnm

Chemical Accuracy for Ed is Required

51

Chemical accuracy: 1 kcal/mol = 4.2 kJ/mol = 0.043 eV

MgH2 Clusters

52

20 40 60 (MgH2)N 50 100 Ed (kJ/mol H2) Expt.: bulk CCSD(T) DMC DFT-LDA DFT-PBE Bulk

Desorption Energy of MgH2 Clusters

53

Desorption Energy of MgH2 Clusters

54

(MgH2)N

Size-Dependent DFT Error

55

Size-Dependent DFT Error

56

20 40 60 (MgH2)N

• 40
• 20

20 Ed

DFT - Ed DMC (kJ/mol H2)

LDA PBE Bulk

Summary

57

Hybrid Nano-Interfaces Hydrogen Storage in Nanoparticles Nanostructured PV Computational Challenges

58

Acknowledgements

Department of Energy (DOE) National Science Foundation (NSF) Molecular Foundry, NERSC, and Teragrid

Thank you very much for your attention!