Slides used in the defense of my dissertation.

1. Ab Initio Simulation and
Analysis of CdS
Nanoparticles
Chad Junkermeier
14 Nov 2008

2. What are nanoparticles?

3. A collection of atoms that bridge the gap between the
classical and quantum worlds.
3

4. A substance with high surface to
volume ratio
Atom-resolved scanning
tunnelling microscope
nano.anl.gov/images/
(STM) image of a 3 nm
highlights/virtualfab1.gif
wide MoS2 cluster.
www.phys.au.dk/camp/.

5. Why should we care
about nanoparticles?

6. Use in Biological/Medical Sciences
In vivo imaging with quantum dots
Injecting QD-micelles into frogs

7. Engineering and Technology
• Quantum Dots in an Optical Transistor -
All optical 1 picosecond performance
• Applications of Quantum Dots to
Telecommunications – Optical
Switching based on EviDots
• Quantum dots in Energy and Lighting
Applications - Tunable band gap
semiconductor
-Technological uses given by Evident Technologies
7

8. Summary of Project
Supplement experimental research of
semiconducting nanocrystal systems by
first understanding highly simplified
systems and then building up to more
complicated systems.

9. Real World Impact
• Experiment often can’t separate
environment and system of interest.
• Experiment can’t give details
concerning individual atoms.
• Experiment can’t show where electrons
reside in a molecule.
• Theory/simulation can do both of these
things, and much more.

10. FIREBALL
Ab-initio tight-binding package
P. Jelinek, et al., Phys. Rev. B 71, 235101 (2005)
J.P. Lewis, et al., Phys. Rev. B 64, 195103 (2001)
• Localized minimal basis set
Fast • Interaction integrals are pre-computed
• Parallel computing, order-N algorithms

11. FIREBALL
Ab-initio tight-binding package
P. Jelinek, et al., Phys. Rev. B 71, 235101 (2005)
J.P. Lewis, et al., Phys. Rev. B 64, 195103 (2001)
Fast

12. FIREBALL
Ab-initio tight-binding package
P. Jelinek, et al., Phys. Rev. B 71, 235101 (2005)
J.P. Lewis, et al., Phys. Rev. B 64, 195103 (2001)
• Based on density functional theory
• Self-consistent charge density
Fast
• Accounts for charge transfer effects
Accurate

13. FIREBALL
Ab-initio tight-binding package
P. Jelinek, et al., Phys. Rev. B 71, 235101 (2005)
J.P. Lewis, et al., Phys. Rev. B 64, 195103 (2001)
Fast
Accurate

14. FIREBALL
Ab-initio tight-binding package
P. Jelinek, et al., Phys. Rev. B 71, 235101 (2005)
J.P. Lewis, et al., Phys. Rev. B 64, 195103 (2001)
Capable
Fast
• Large (nano-scale) systems
Accurate • Electronic properties
• Dynamic simulation

15. Types of MD Simulations
• Relaxation
• Thermodynamic simulation.
13

16. Accomplishments
• Comparing CdS Nanoparticles Against
Bulk Structures
• Band Gap and Gap states of CdS
nanoparticles
• xyzSTATS
• FireballUI
• Ongoing Work

17. Comparing CdS Nanoparticles
Against Bulk Structures
ZB
Or
W
15

18. Comparing CdS Nanoparticles
Against Bulk Structures
Bandaranayake, et al. App. Phys. Let., 67(6):831–833, 1995
ZB Ricolleau, et al. Thin Solid Films, 336:213–217, 1998
Banerjee, et al. J. Phys.: Condens. Mat., 12:10647–10654, 2000
Herron, et al. J. Am. Chem. Soc., 112:1322–1326, 1990
W Murray, et al. J. Am. Chem. Soc., 115:8706–8715, 1993
Bautista-Hernandez, et al. Sol. Energy Mater. Sol. Cel l, 79:539–547, 2003
15

19. Energy Per Atom
Joswig et al., J. Phys. Chem. B, Vol. 104, No. 12, 2000
16

20. Energy Per Atom
Similar Results from other groups
Joswig, et al. J. Phys. Chem., 104:2617–2622, 2000.
Joswig, et al. J. Phys. Chem. B, 107:2897–2902, 2003.
Frenzel, et al. J. Phys. Chem. C, 111:10761–10770,
2007.
Sarkar, et al. Phys. Rev. B, 68:235409:1–7, 2003.
Roy, et al. J. Phys. Chem., 107:2771–2779, 2003.
Pal, et al. J. Chem. Phys., 123:044311:1–9, 2005.
Wen and Melnik. App. Phys. Let., 92:261911, 2008.
Joswig et al., J. Phys. Chem. B, Vol. 104, No. 12, 2000
16

21. Initial Conditions
• CdS Nanoparticles
2.0 to 2.3 nm in
diameter
• Zinc-blende Structure
• (Also used W
structures)
17

22. Regions
0.9 to 1.3 nm
0.5 to 0.9 nm
< 0.5 nm
< 1.3 nm

23. MD Evolutions
• Harris Functional
• 1 fs/time-step
• 10,000 time-steps
• Each took 1-2 months to
run in parallel

24. MD Evolutions
• Harris Functional
• 1 fs/time-step
• 10,000 time-steps
• Each took 1-2 months to
run in parallel

25. Chi-squared Statistic b
5
Two Histograms
0
r < 0.5
−5
−10
Number
Atom Count
10
of Bins
Shells
0.5 < r < 0.9
0
−10
10 −30
0.9 < r < 1.3
0
−10
MD ZB
● ●
−30
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Radius [nm]
Both histograms must have
the same number of bins.

26. Chi-squared Statistic
Chi-squared statistic for
Two Histograms two binned data sets with
differing numbers of data
elements:
Compute Number
Chi-Squared of Bins
Chi-squared goes to
zero as the two
binned sets more
closely equal each
other.

27. Chi-squared Statistic
Two Histograms
Compute Number
Chi-Squared of Bins
Critical
Value
DOF - Degrees of Freedom
DOF = Bins - 1
CV - Critical Value

28. Chi-squared Statistic
Two Histograms
Chi−squared
Compute Number
●
Chi-Squared of Bins
Critical
●
Value
Test 1 test 2 CV
Compare Chi-squared w/ Critical Value YES NO
Histograms
Similar
Yes No

29. Radial Distribution
40
30
r < 0.5
•
20
Computed radial
10
distribution from center of
0
nanoparticle as function of
50
0.5 < r < 0.9
Chi−squared
FALSE
time-step
30
Region [nm]
10
•
0.9 < r < 1.3
20 40 60 80
FALSE
Radial distribution of each
time-step was binned (put
into a histogram)
100 150 200
W ZB
● ●
FALSE
r < 1.3
• binned distribution 50
compared to W and ZB at
CdS281
0 2000 4000 6000 8000 10000
350 K
Time [fs] FALSE
each time-step

30. Radial Distribution
40
30
r < 0.5
•
20
Computed radial
10
distribution from center of
0
nanoparticle as function of
50
0.5 < r < 0.9
Chi−squared
FALSE
time-step
30
Region [nm]
10
•
0.9 < r < 1.3
20 40 60 80
FALSE
Radial distribution of each
time-step was binned (put
into a histogram)
100 150 200
W ZB
● ●
FALSE
W ZB
● ●
r < 1.3
• binned distribution 50
compared to W and ZB at
CdS281
0 2000 4000 6000 8000 10000
350 K
Time [fs] FALSE
each time-step

31. Neighbors
CdS281, r < 1.3, 350 K
CdS281, 0.9 r < 1.3, 350 K
CdS281, 0.5 < r < 0.9, 350 K
CdS281, r < 0.5, 350 K
0.22 0.23 0.24 0.25 0.26 0.27 0.30 0.35 0.40 0.30 0.35 0.40
Radius [nm]

32. Radial Distribution
Function
S. R. Elliot. “Physics of Amorphous Materials. “1990
300 K 300 K 350 K 400 K 300 K
CdS264 CdS281 CdS281 CdS281 CdS357 W ZB
r < 0.5
Count [Arbitary]
0.9 < r < 1.3 0.5 < r < 0.9
Region [nm]
ZB
r < 1.3
0.0 0.6 1.2 0.0 0.6 1.2 0.0 0.6 1.2 0.0 0.6 1.2 0.0 0.6 1.2 0.0 0.6 1.2 0.0 0.6 1.2
Radius [nm]

33. Conclusions
• Amorphous
• Short range order
• Surface of nanoparticles NN distance ~ W

34. Band Gap and Gap states of
CdS nanoparticles
28

35. Motivation
Energy
e
Nanocrystal

36. Motivation
e
Energy
Dangling Bonds

37. Motivation
Energy
e
Bonds Passivated

38. Initial Conditions
• CdS Nanoparticles
2.0 to 2.3 nm in
diameter
• Zinc-blende Structure
• atoms with 4 NN are
assumed to be in a
bulk-like position
32

39. Experimental Procedure
Initial Zinc-Blende Structure
Reconstructed Molecular
Crystal Structure Orbitals
Optimization
Discard Surface Discard Surface
Single Point DOGS Simulation Using
Cd Atoms S Atoms Discard Surface Discard Surface
Calculation Harris Functional
Cd Atoms S Atoms
Single Point Single Point
Single Point
Calculation Calculation Single Point
Optimization
Calculation
Using Harris Using Harris Calculation
Simulation Using
Molecular
Using Harris
Functional Functional Using Harris
DOGS Simulation
Orbitals
Functional Functional
BCB of
TVB of
BCB of
TVB of
zinc-blende
zinc-blende
reconstructed
reconstructed
structure
structure
structure
structure
33

40. Experimental Procedure
Initial Zinc-Blende Structure
Single Point DOGS
Calculation
Molecular
Orbitals
34

41. Experimental Procedure
Initial Zinc-Blende Structure
Single Point DOGS
Calculation
Molecular
Orbitals
35

42. Experimental Procedure
Initial Zinc-Blende Structure
Reconstructed Molecular
Crystal Structure Orbitals
Optimization
Single Point DOGS Simulation Using
Calculation Harris Functional
Optimization
Simulation Using
Molecular
DOGS Simulation
Orbitals
36

43. ZB Relaxed
Relaxation Displacement
264
Initial Zinc-Blende Structure
Reconstructed
Crystal Structure
280
Optimization
Simulation Using
Harris Functional
281
Optimization
Simulation Using
DOGS Simulation
293
264
280
Average Radial Movement [Å]
0 281
293
329
357
-0.5
329
-1
357
-1.5
Cd bulk S bulk Cd surface S surface
37
Cd S

44. Bulk Probability
Each state is plotted twice.
Once for the Cd atoms
Once for the S atoms
38

45. Empirical Tight-Binding
Results
Model
… zinc-blende structure
… sp3s* atomic orbitals
… nearest-neighbor coupling
… spin-orbit coupling
Tight-binding parameters
Energy [eV]
… CdS: Lippens and Lannoo, G.W. Bryant and W. Jaskolski MRS Proceedings
PRB 39, 10935 (1989) 2003 (submitted)
… InAs and GaAs: Vogl,
Hjalmarson, and Dow, J. Phys.
Chem. Solids 44, 365 (1983)
39

46. Passivation by Subtraction
Energy
DB
Cd
S 40

47. Passivation by Subtraction
Energy
DB
Cd
S 41

48. Passivation by Subtraction
Energy
DB
Cd
S 42

49. Experimental Procedure
Initial Zinc-Blende Structure
Reconstructed
Crystal Structure
Optimization
Discard Surface Discard Surface
Simulation Using
Cd Atoms S Atoms Discard Surface Discard Surface
Harris Functional
Cd Atoms S Atoms
Single Point Single Point
Single Point
Calculation Calculation Single Point
Optimization
Calculation
Using Harris Using Harris Calculation
Simulation Using
Using Harris
Functional Functional Using Harris
DOGS Simulation
Functional Functional
BCB of
TVB of
BCB of
TVB of
zinc-blende
zinc-blende
reconstructed
reconstructed
structure
structure
structure
structure
43

50. Passivation by Subtraction
44

51. Experimental Procedure
Initial Zinc-Blende Structure
Reconstructed Molecular
Crystal Structure Orbitals
Optimization
Discard Surface Discard Surface
Single Point DOGS Simulation Using
Cd Atoms S Atoms Discard Surface Discard Surface
Calculation Harris Functional
Cd Atoms S Atoms
Single Point Single Point
Single Point
Calculation Calculation Single Point
Optimization
Calculation
Using Harris Using Harris Calculation
Simulation Using
Molecular
Using Harris
Functional Functional Using Harris
DOGS Simulation
Orbitals
Functional Functional
BCB of
TVB of
BCB of
TVB of
zinc-blende
zinc-blende
reconstructed
reconstructed
structure
structure
structure
structure
45

52. Results
46

53. xyzSTATS
Produce statistical reports of bond lengths, bond
•
angles, and similar data from xyz evolution file.
Produce other types of results that will also use
•
xyz data; ie. GofR, Center of Mass,
COMPARE to reference atomic configurations.
•
Ability to look at only part of the data:
•
1. Choice of groups of atoms.
2. Choice of time-steps.
Modular
•

54. FireballUI

55. Ongoing Work
CdS-ZnS Core-Shell
Electron-Phonon Coupling
in CdS Nanoparticles
3.0
375 K
2.5
2.0
Zeta
1.5
1.0
0.5
0.0
500
400
Ome
300
ga [1
0
200 −1
/cm]
Energy
−2
e
−3
100
[eV]
−4
rgy
Ene
−5
−6
H Atoms

56. Support

57. More Complicated Systems
This is a unit cell of this.

58. Harris-Foulkes Theory
52

59. DOGS
53

60. Innovation
Most
Groups
My
Research
54