Quantum Simulations of Nano- Materials for Renewable Energy

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edu Department of Physics Colorado School of Mines,

1 Quantum Simulations of Nano- Materials for Renewable Energy Zhigang Wu Department of Physics Colorado School of Mines, Golden, CO Extra Lecture in Modern Physics Class, CSM, 05/04/2010

2 Introduction Outline 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 MgH 2 nano-clusters for hydrogen storage 1

3 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

4 What is Renewable Energy? Renewable energy comes from natural resources such as sunlight, wind, tides, biological materials, geothermal heat, etc. 3

5 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.

6 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. Sun Greenhouse gases: carbon dioxide water vapor methane nitrous oxide Methane, emitted by microbes called methanogens, kept the early earth warm. 5

7 Why Do We Care About Renewable Energy? 6

8 USA Energy Consumption in

9 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

10 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

11 A Challenge with Solar Energy 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 10

12 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. Richard Feynman ( ) Dec. 29, 1959, Annual APS Meeting 11

Nanoscience and Nanotechnology 1 nm = 10-9 m = 10 Å Nanoscale: ~ 1 100 nm Nanomaterials: at least one dimension in the nanoscale.

13 Nanoscience and Nanotechnology 1 nm = 10-9 m = 10 Å Nanoscale: ~ nm Nanomaterials: at least one dimension in the nanoscale. Nanoparticle Ant Motor Speedway 4 nm diameter 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. 12

almost every human-made object in the next century.

trillion market by 2011-2015 (NSF 2004) Anti-cancer drug

14 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 (NSF 2004) Anti-cancer drug delivery system Cheap and clean energy Next-generation computer Michigan Center for Biological Nanotechnology UCSB Bazan Group 13

15 Quantum Effects at the Nanoscale = 729 nm UV light UV light CdSe A bulk material s properties are fixed. Properties of nanomaterials can be tuned by varying the size. 14

Complex Structures of Nanomaterials Properties of nanomaterials are

Thermoelectricity: Good Poor Theory and simulations are in critical

16 Complex Structures of Nanomaterials Properties of nanomaterials are affected by their shapes significantly. CdSe Nature Nanotech. 1, 186 (2006) Tapered Si Nanowires 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

17 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. H ˆ = E Materials properties depend strongly on atomistic details. Predict new materials with better properties. 16

18 Solving Many-Electron Schrödinger Equation 2 2m 2 ( r 1, r 2,..., r N ) + V ( r 1, r 2,..., r N ) ( r 1, r 2,..., r N ) = E ( r 1, r 2,..., r N ) Interacting N- Electron System N-dimensional problem Exponential wall: the time t needed to solve this equation is prop. to e N. N = 1, t = 1 s N = 2, t = 7 s N = 10, t = s = 6.1 h N = 20, t = s = 15 years N = 100, t = s = years! 17

19 Density Functional Theory 18

20 Density Functional Theory Many-body Schrödinger equation: H ˆ = E, where = ( r 1, r 2,..., r N ) Intractable 3N-dimentional equation t e N Hohenberg-Kohn (HK) theorem 1 : ground-state total energy can be expressed in terms of electron density n(r), instead of wave functions. E 0 = E[n( r )] Kohn-Sham (KS) theory 2 : 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 N 3 [1] Phys. Rev. 136, B864 (1964) [2] Phys. Rev. 140, A1133 (1965) 19

21 KS Single-Particle Equation 2 2 2m + v ( r ) KS ( r ) = i i i ( r ) where v KS ( r ) = v ext ( r ) + v H ( r ) + v xc ( r ) with v H ( r ) = n( r ') r r dr ' ' v xc ( r )= E xc [n( r )] n( r ) OCC i and n( r ) = i ( r ) 2 Need approximation, but simple form works pretty well. 20

22 The Triumph of DFT Methanol inside a cage of the zeolite sodalite (Blue: Si; Yellow: Al; Red: O) Clathrate Sr 8 Ga 16 Ge 30 (Red: Sr; Blue: Ga; white: Ge) N = O (1000) 21

23 Challenges Nanomaterials are complicated. CdSe Nanoparticle with d = 4 nm ~ 2,000 atoms ~ 20,000 electrons Solution: better scaling scheme: t N. 22

24 Challenges Accuracy is limited by the approximation for the exchangecorrelation energy: v xc ( r )= E xc [n( r )] n( r ) Solution: better E xc guided by results obtained from more accurate methods. 23

25 Challenges Excitations: DFT is NOT a theory for excited properties. Band gap problem Si: E g DFT = 0.6 ev E g EXP = 1.2 ev Solution: go beyond the single-particle method to include the many-body interactions due to excitation. 24

26 Quasiparticle Bare particle Quasiparticle Excitations of many-electron system can often be described in terms of weakly interacting quasiparticles. - - Quasiparticle (QP) = bare particle + polarization clouds. E QP = E 0 + : response of system to the excitation(self-energy) 25

27 Beyond DFT Quantum chemistry post-hf methods: CI, CC, MCSCF, MP2, etc. Very accurate for small systems But very bad scaling of N 5-7 Many-body perturbation methods: GW/BSE Accurate for excitations, scaling as N 4-7 Quantum Monte Carlo (QMC) methods Fully-correlated many-body calculation Stochastic solution to Schrödinger equation Scaling as N 3 : most accurate benchmarks for medium-size systems 26

28 Monte Carlo Technique Random numbers can be used to help solve complicated problems in physics. 27

29 Diffusion Monte Carlo (DMC) Ref: Foulkes et al., RMP 73, 33 (2001) 28

30 How to Perform the Projection? 29

31 G(R, R, ) as a Transition Probability H=T+V V=0 V 0 30

32 Diffusion and Branching 31

33 A Toy Model: 1D Harmonic Oscillator t DMC ~ O( ) t DFT DMC is Intrinsic parallel. 32

34 An Analogy of QM Methods DFT Post-HF, GW/BSE QMC 33

35 Complex-Structured Si Nanowires Wu, Neaton & Grossman, PRL 100, (2008) Wu, Neaton & Grossman, Nano Lett. 9, 2418 (2009) 34

36 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

The tapering can be as large as 2 nm reduction in d for 10 nm in L.

37 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.

38 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 (SIESTA 1 code). Linear-scaling code [1] 37

39 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

40 Finite-Length Model: Tapered Nanorod The highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals are separated along axis. 39

41 A New Route for Solar Cells Separating charge carriers p-n Junction Type-II Hetero-Junction No Junction n-type p-type CB LUMO VB HOMO Simple and cheap new type of PV 40

42 Level-Alignment at Hybrid Interfaces Wu, Kanai & Grossman, PRB 79, 2013(R) (2009) 41

43 Level-Alignment at Hybrid Interfaces CBM LUMO VBM HOMO Bent Group at Stanford Hybrid interface is crucial for molecular electronics and optoelectronics, e.g. organic PV cells. CBM LUMO CBM LUMO Design interfaces with appropriate energy-level alignment: Modify molecular gap Control semiconductor band-gap by tuning quantum confinement VBM HOMO VBM HOMO 42

Si (001) TTF Interface DFT calculation Type-II Junction Interface 1.79 0.44 1.

44 Si (001) TTF Interface DFT calculation Type-II Junction Interface Tetrathiafulvalence: TTF Type-II junction is very interesting and useful. 43

45 Interface-Type vs. Quantum Confinement DFT-KS Type "III" Type II Type I CBM VBM LUMO HOMO CBM VBM LUMO HOMO Type III LUMO CBM HOMO VBM bulk 32 Number of Layers DFT: This junction can be tuned by quantum confinement. 44

Many-Body Correction = QP DFT is the many- body correction Bare Particle Quasiparticle CBM LUMO - - CBM CBM VBM VBM VBM HOMO DFT has successfully predicted accurate band-offsets at semiconductor

46 Many-Body Correction = QP DFT is the many- body correction Bare Particle Quasiparticle CBM LUMO - - CBM CBM VBM VBM VBM HOMO DFT has successfully predicted accurate band-offsets at semiconductor interfaces 1,2 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

47 Many-Body Corrections to Level-Alignment DFT-KS QMC-DMC Interface DFT: Type-II CBM LUMO QMC: Type-I CBM LUMO VBM HOMO VBM HOMO 46

48 Interface-Type vs. Quantum Confinement Type "III" DFT-KS QMC- DMC Type II Type I bulk 32 Number of Layers QMC: The junction type CAN NOT be tuned by quantum confinement. 47

49 MgH 2 Nanoscale Cluster for H Storage Wu, Allendorf & Grossman, JACS 131, 13918, (2009) 48

50 Motivation C + O 2 = CO 2 H 2 + O 2 = water Chemical storage: the reversible absorption of H into another material. Bulk materials are often too stable. E.g. MgH 2 : 7.7wt%, E d = 75 kj/mol, T d ~ 300 o C Desirable E d = kj/mol E d can be tuned by the size of nanoparticles. 49

51 Mg and MgH 2 Crystal Lattices HCP: P6 3 /mmc Rutile: P4 2 /mnm 50

52 Chemical Accuracy for E d is Required Chemical accuracy: 1 kcal/mol = 4.2 kj/mol = ev 51

53 MgH 2 Clusters 52

54 Desorption Energy of MgH 2 Clusters 100 E d (kj/mol H 2 ) 50 0 Expt.: bulk CCSD(T) DMC DFT-LDA DFT-PBE (MgH 2 ) N Bulk 53

55 Desorption Energy of MgH 2 Clusters (MgH 2 ) N 54

56 Size-Dependent DFT Error 55

57 Size-Dependent DFT Error 20 E d DFT - Ed DMC (kj/mol H2 ) LDA PBE (MgH 2 ) N Bulk 56

58 Summary Nanostructured PV Hybrid Nano-Interfaces Hydrogen Storage in Nanoparticles Computational Challenges 57

59 Acknowledgements Department of Energy (DOE) National Science Foundation (NSF) Molecular Foundry, NERSC, and Teragrid Thank you very much for your attention! 58

André Schleife Department of Materials Science and Engineering

André Schleife Department of Materials Science and Engineering Yesterday you (should have) learned this: http://upload.wikimedia.org/wikipedia/commons/e/ea/ Simple_Harmonic_Motion_Orbit.gif 1. deterministic