Advanced Computation& Modeling

張亞中 (Yia-Chung Chang) –Nanostructure electronics & photonics

馬尚德 (Alec Maassen van den Brink)– Quantum computing

關肇正 (Chao-Cheng Kaun)– Ab initio transport

謝東翰 (Tung-Han Hsieh) – Web computing

Vladimir Nazarov-CDFT

New Hire: Shu-Wei Chang

-Nanophotonics

Missions

To carry out theoretical modeling in targeted areas of importance in applied sciences, including:

1) Nanostructure optoelectronic devices 2) Quantum information devices 3) Optical metrology and nanophotonics Provide theoretical guidance and analysis to

experimental groups within RCAS

Progress in Nanophotonics• Efficiency Enhancement of GaAs Photovoltaics Employing Antireflective Indium

Tin Oxide Nanocolumns, (with P. Yu, NCTU) [ Adv. Mater., 20, 1–4 (2008); Y. Z. Hsu Scientific Paper Award, 2010] 

• Aspect-ratio-dependent ultra-low reflection and luminescence of dry-etched Si nanopillars on Si substrate [Nanotechnology, 20, 035303, (2009)]

• Spatial filtering by using cascading plasmonic gratings [Optics Express 17, 6218 (2009).]

• Effective dielectric properties of biological cells: Generalization of the spectral density function approach [J. Phys. Chem. B 113 (29), 9924–9931 (2009)]

• Dielectric response of AlSb from 0.7 to 5.0 eV determined by in situ ellipsometry [Appl. Phys. Lett. 94, 231913 (2009)]

• T-shaped plasmonic array as a narrow-band thermal emitter or biosensor [Optics Exp. 17, 13526-31 (2009)]

• Interband transitions of InAsxSb1−x alloy films [Appl. Phys. Lett. 95,111902 (2009)]

• Manipulative depolarization and reflectance spectra of morphologically controlled nano-pillars and nano-rods [Optics Exp., 17, 20824-32 (2009)]

• Optical metrology of randomly-distributed Au colloids on a multilayer film [Optics Exp. 18, 1310-15 (2010)]

• Plasmon-polariton band structures of asymmetric T-shaped plasmonic gratings [Optics Exp. 18, 2509-14 (2010)]

• Surface plasmon resonance ellipsometry based sensor for studying biomolecular interaction [Biosensors and Bioelectronics 25, 2633 (2010)]

Research progress in nanoelectronics

Superconducting nanowires ： Interplay of discrete transverse modes with supercurrent (Kaun)[Phys. Rev. B 80, 024513 (2009)]

Submonolayer quantum dot infrared photodetector [Appl. Phys. Lett. 94, 1 (2009)]

Bistable states of quantum dot array junctions for high-density memory [Jpn. J. Appl. Phys., 48, 104504 (2009)]

Cesium doped and undoped ZnO Nanocrystalline thin films: a comparative study of structural and Micro-Raman investigation of optical phonons, R. Thangavel [J. Ram. Spect. DOI 10.1002/jrs.2599 (2010)]

Surface States/Modes in One-Dimensional Semi-infinite Crystals, [Annals of Physics 325, 937-947 (2010)]

Thermoelectric and thermal rectification properties of quantum dot junctions, [Phys. Rev. B 81, 205321 (2010)]

Progress in DFT & quantum structures Exact dynamical exchange-correlation kernel of a weakly inhomogeneous

electron gas [Phys. Rev. Lett., 102, 113001 (2009)] Open a way for interpolation between low- and high frequency behavior of

the xc kernel of an arbitrary system by expressing it in the high-frequency limit through a few ground-state properties. (Nazarov) [Phys. Rev. B 81, 245101 (2010)]

On the relation between the scalar and tensor exchange-correlation kernels of the time-dependent density-functional theory [J. Chem. Phys.. in press (2010)

Enhancement factor, electrostatic force and emission current in nanoneedle emitter [Euro Phys. Lett. 85, 17001 (2009) ]

Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle [Ultramicroscopy 109, 373 (2009)]

Van der Waals interaction between two crossed carbon nanotubes [ACS nano, in press (2010)]

Corrected field enhancement factor for the floating sphere model of carbon nanotube emitter [J. Appl. Phys., in press (2010)]

Development of GPU computing environment and Investigation of the novel "Adaptive Thick Restart Lanczos Algorithm" for low-lying eigenmode projection for large sparse Hermition matrix. (TH Hsieh)

Optical nanometrologyNanometrology allows optical inspection of the geometry of nanostructures down to 10nm scale.

It uses a best fit to the measured ellipsometric spectra via theoretical simulation (with efficient software) to determine the critical dimension.

If done correctly, one can reconstruct images of nm resolution by using an optical instrument (with wavelengths 100nm-1000nm).

It is noninvasive and capable of probing buried structures and biological systems

SEM of Au Nanoparticles of different sizes

d = 20nm

d = 40nm

d = 60nm

d = 80nm

Ellipsometry Results – Au NP@60o

1 2 3 4 5 6 7 8

0

10

20

30

40

50

60

70

80

10 nm 20 nm 40 nm 60 nm 80 nm

Au NP, 60o

(d

egre

e)

Photon energy (eV)1 2 3 4 5 6 7 8

4

6

8

10

12

14

16

18

10 nm

40 nm

20 nm

80 nm

60 nm

Au NP, 60o

(d

egre

e)

Photon energy (eV)

Ellipsometry Measurement vs. simulation

Au nanoparticles: 20, 40, 60, 80 nm angle of incidence: 60º

1 2 3 4 5 6 7 84

6

8

10

12

14

16

18

20

22

24

26

20 nm 40 nm 60 nm 80 nm

Au NP, 60o

(d

egre

e)

Photon energy (eV)

1 2 3 4 5 6 7 8 94

6

8

10

12

14

16

18

20

22

24

26

20 nm 40 nm 60 nm 80 nm

AuNP, 60o

(d

egre

e)

Photon energy (eV)

Fitting by a lattice model

Effects of Site Disorder

f

∫

Simplified model for structure factor

S(g) = 1 + f ∑j≠0 exp{i (k-k0) ∙Rj}

= 1+ f 2π ∫a

L rdr J0(gr) /Ac

= 1 + f [Nδk,k0 – 2π(a2/Ac)J1(ga) /ga],

f = similarity factor

N= total number of atoms considered,

g = k - k0

Ac = average cell volume

[S.-H. Hsu, Y.-C. Chang*, Y.-C. Chen, P.-K. Wei, Y. D. Kim, Optics Exp. 18, 1310 (2010)]

Au NP 20~60 nm, random (without clusters)

1 2 3 4 5 6 7 82

4

6

8

10

12

14

16

1 2 3 4 5 6 7 82

4

6

8

10

12

14

16experiment

(d

egre

e)

Photon energy (eV)

20 nm: 55o 60o

40 nm: 55o 60o 60 nm: 55o 60o

model

Photon energy (eV)

(d

egre

e)

Au NP 20~60 nm, random (without clusters)

1 2 3 4 5 6 7 8

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8

0

20

40

60

80

100

120

140

160

180

experiment

(d

egre

e)

Photon energy (eV)

20 nm: 55o 60o

40 nm: 55o 60o

60 nm: 55o 60o

model

Photon energy (eV)

(d

egre

e)

GF results (random, no clusters)substrate: glass slide coated with a buffer layer ( = 2.0)

parameters: m = 7 isur = 1

nominal size

radial k

meshslices particle size sk0 pitch

buffer thicknes

sMSE

20 nm 35 1518 16 nm 0.9 42 nm

2 nm11.75

18 16 nm 1.0 42 nm 11.64

40 nm 37 1942 32 nm 0.9 140 nm

2 nm27.54

40 36 nm 1.0 155 nm 24.28

60 nm 39 2360 55 nm 0.8 170 nm 2 nm 32.00

60 57 nm 0.9 180 nm 0 nm 31.62

cc = 1.0 gst = 2

Comparison of modeling based on random and periodic distributions

Nominal size (nm)

SEM estimation Random distribution Periodic distribution

Average distance (nm)

Average distance (nm) MSEa

Periodicity (nm) MSEa

20 40 - 42 42 12.2 (11.0) 80 13.1 (12.5)

40 135 - 140 140 26.4 (14.7) 200 25.6 (15.7)

60 156 - 175 175 35.6 (18.7) 220 35.1 (23.3)

80 210 - 249 235 31.6 (17.2) 300 32.2 (23.2)aValues in parentheses are for fitting in the 2-9 eV range.

Effects of clustering

2

Modeling potential for clusters

V2

V3

V4

Au NP 40 & 60 nm, random (with clusters)

1 2 3 4 5 6 7 82

4

6

8

10

12

14

16

1 2 3 4 5 6 7 82

4

6

8

10

12

14

16experiment

(d

egre

e)

Photon energy (eV)

40 nm: 55o 60o

60 nm: 55o 60o

model

Photon energy (eV)

(d

egre

e)

Au NP 40 & 60 nm, random (with clusters)

1 2 3 4 5 6 7 8

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8

0

20

40

60

80

100

120

140

160

180

experiment

(d

egre

e)

Photon energy (eV)

40 nm: 55o 60o

60 nm: 55o 60o

model

Photon energy (eV)

(d

egre

e)

GF (random, with clustering)angle of incidence: 55º, 60ºsubstrate: pseudo-dielectric constants from APTES w/o BSC modelingcommon parameters:

m = 8 radial k mesh = 45 ns = 4

size (nm)

slices p fc fv Dc ds

MSE (1~9 eV)

MSE (2~9 eV)

42 36 19 145 nm0.04

0.30 90 1513.20 11.07

0.045

13.11 11.52

60 57 23 180 nm 0.05 0.30 12520 21.44 18.17

15 21.51 17.93

80 72 25235 nm 0.05

0.45 160 2021.24 17.27

230 nm 0.04 21.28 16.96

sk0 = gst = 1 cc = 1.0 isurf = 1

Samples with different sizes of Gold nanoparticles immobilized on

a glass substrate are investigated by variable-angle spectroscopic

ellipsometry (VASE) in the UV to near IR region.

Both the Green’s function method and rigorous coupled-wave

analysis (RCWA) were used to model the ellipsometric spectra

GF method is 10 – 100 times more efficient than RCWA in most

cases for lattice model calculation.

For random scattering problem, only GF method is used, and it is

faster by another order of magnitude.

Our model calculations show reasonable agreement with the

ellipsometric measurements.

This demonstrates that the spectroscopic ellipsometry could be a

useful tool to provide information about the size and distribution of

nanoparticles deposited on insulating substrate.

The technique can be extended to inspect buried nanostructures

Summary

Microscopic imaging ellipsometer

original capabilities single-wavelength measurement

variable-angle ellipsometry/reflectance (spatial resolution: ~ mm)

imagine ellipsometry (spatial resolution: 5~10 m)

Ongoing upgrades intense white-light source + monochromator

spectroscopic measurement

in-house software

scatterometry (scattering-type ellipsometry/reflectance)

atomic force microscope (AFM)

increased spatial resolution (100 nm), tip-enhanced measurement

projected-field electromagnet

magnetism-related studies

Multiskop

• Measures polarization change (ψ and Δ) when light reflects from a surface.

p

s

R tanΨ = and

R p s p

s

R tanΨ = and

R p s

Introduction

Source: J. A. Woollam Co., Inc.

Film ThicknessRefractive Index

Surface Roughness Interfacial Regions

AnisotropyUniformity

CompositionCrystallinityBiosensing

Properties of Interest:

Figure (a) Ellipsometry measurement showing light reflected from sample surface parallel to the sample stage.(b) SPR ellipsometry showing light reflected from sample surface perpendicular to the sample stage.

Sample preparation process

Gold(40nm)

Ti(5nm)

SiO2(~4nm)

AuNPs(13nm)

1min 1min

5min 5min

Gold nanoparticle on gold substrate

SPR dip with different surface coverage of Gold nanoparticles on Gold film

EMA layer

Gold=40nmTi

Glass

Gold=40nmTi

Glass

AuNP1st EMA

2nd EMA or Au thin layer

3rd EMA

Gold nanoparticle is slice into 2EMA layers- 5 and 10 minutes

3EMA layers - 20, 60 and 120 minutes

Non-uniform medium

Metal substrate

Image dipole, multipole effect

Bulk sensitivity measurement for bare Gold film and Gold nanoparticles coated on Gold film

Bare gold filmBare gold film

AuNPs/ gold film (1min)AuNPs/ gold film (1min)

Dynamic measurement

BSA / Anti-BSA interaction

Bare gold substrate After attachment of BSA + anti-BSA

Ti Gold

Glass slide Ti/Glass slideAu/Ti/Glass

slide

BSA

anti-BSA

Bare 13nm AuNPS

After attachment of BSA + anti-BSA

Current study on BSA / Anti-BSA interaction

Surface mass density of BSA adsorption on gold surface

Solutions Fitting Paramete

r An

Fitting Parameter Bn

Mean Square Error

(MSE)

Thickness (nm)

PBS 1.340 0.000235

6.978

BSA 1.338 0.01 1.715 6.9

Anti-BSA 1.342 0.01 1.655 22.2

Dynamic measurement on various samples for BSA / Anti-BSA interaction

Dynamic measurement on bare gold film for BSA / Anti-BSA interaction

A comparison on biomolecular interaction study

Comparison on sensitivity of various samples for BSA / Anti-BSA interaction

Conclusion– A very simple and promising technique is presented and

further extended its potential application to investigate both spectroscopic and real time response of bio-molecular interaction based on the ellipsometry optical signals.

– Surface Plasmon Resonance(SPR) of the gold film can be tune with various distribution of AuNPs coated on gold film.

– Bulk refractive indices measurement shows that more densely packed AuNPs on gold film give higher refractive index (RI) resolution.

– However, local refractive index change corresponding to the adsorption of BSA and subsequent attachment of anti-BSA measurement shows that sample dipped in AuNPs for 1 minute shows better sensitivity as compare to other dipping time as well as bare gold film.

– Hence, direct correlation on sensitivity from bulk to local refractive index change is trivial and need further investigation.

– SPR ellipsometry does make a unique tool to investigate various challenging issues in terms high affinity bio-detection with sub-nanometer thickness resolution.

Application software development

• LED/light scattering Simulator:Optical simulation for LED devices and optical

metrology.• LASTO package:

An abinitio computation package based on Linear Augmented Slater-Type Orbitals basis.

• Nanostructure Simulator: Effective bond-orbital method for microsopic

strain distribution, electronic states, and optical properties of semiconductor nanostructures computatio

• GPU software development (Hsieh)

Future goals of ACM group

Development of multiscale modeling package for future generation nanoscale optoelectronic devices (combining modeling techniques for electron transport, interface characteristics, optical properties and heat dissipation.

Couple theoretical modeling with experimental studies for development of novel nanometrology technology.

Modeling for spintronics, quantum information, and magnetic RAM.