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Multiscale modeling of optical and transport properties of solids - - PowerPoint PPT Presentation

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Multiscale modeling of optical and transport properties of solids and nanostructures Yia-Chung Chang Research Center for Applied Sciences (RCAS) Academia Sinica, Taiwan NTU Colloquium , March 14, 2017 In collaboration with Ming-Ting Kuo, NCU

slide-1
SLIDE 1

Multiscale modeling of optical and transport properties of solids and nanostructures

Yia-Chung Chang Research Center for Applied Sciences (RCAS) Academia Sinica, Taiwan NTU Colloquium , March 14, 2017 In collaboration with Ming-Ting Kuo, NCU

  • S. J. Sun, J. Velev, Gefei Qian, Hye-Jung Kim, UIUC

Zhenhua Ning, Chih-Chieh Chen, UIUC/RCAS Ching-Tang Liang, I-Lin Ho, RCAS

  • J. W. Davenport, R. B. James, BNL
  • T. O. Cheche, U. Burcharest, W. E. Mahmoud
slide-2
SLIDE 2

Outline

  • Optical excitations of solids/nanostructures

modeled by: density-functional theory (DFT), tight-binding (TB), k.p model, and effective bond-orbital model (EBOM)

  • Transport and thermoelectric properties of

nanostructure junctions modeled by non-equilibrium Green function method, including correlation

  • Examples: zincblende/cubic semiconductors,

quantum wires, and QDs and QD tunnel junctions

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SLIDE 3

Flow chart of BSE calculation for excitation spectra

[ G. Onida, L. Reining, A. Rubio

  • Rev. Mod. Phys., 74, 601, (2002)]

Excitation spectra

DFT packages: VASP, CASTEP Abinit WIEN2K LMTO SIESTA LASTO

slide-4
SLIDE 4

Linearized Slater-type orbital (LASTO) method

  • Inside MTs: exact numerical solution (u) & du/dE
  • Outside MTs: Slater-type orbitals, rn-1 e-br Ylm(Ω)
  • Match boundary conditions for each spherical harmonics

[J. W. Davenport, Phys. Rev. B 29, 2896 (1994)]

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SLIDE 5

Symmetry-adapted basis

  • Irreducible

segment

Use of symmetry can reduce the computation effort significantly

  • Symmetry-adapted basis was not

commonly adopted in DFT calculations

  • (For general k, point symmetry is lost)
  • For large supercell calculations, only

k=0 is needed, the use of symmetry- adated basis can be very beneficial

  • Examples:

1. Defects in solids with high point symmetry 2. High-symmetry nanoparticles like C60. 3. Optical excitations of nanoclusters 4. Excitonic excitation of solids with high symmetry

128-atom fcc supercell

[Y.-C. Chang, R. B. James, and J. W. Davenport, PRB 73, 035211 (2006)]

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SLIDE 6

Optically allowed transitions for Td group

  • Only the following 6 (& exch.) out of 100 possible configurations are allowed:
  • Polarization matrix in RPA:
  • Polarization matrix in symmetry-adapted basis:

[Use FFT] Using Wigner-Ekart theorem:

slide-7
SLIDE 7
  • BSE (solid line)
  • RPA (dashed line)

LiF Si

Optical spectra calculated by Bathe-Salpeter Eq. in LASTO basis

  • Results similar to LAPW results:
  • [Puschnig* and C. Ambrosch-Draxl, PRB 66, 165105 (2002)]
slide-8
SLIDE 8

GaAs AlAs 1X1 SL Exp

Optical spectra of GaAs, AlAs & SLs

AlAs GaAs

[Exp. data taken from [M. Garriga et al., Phys. Rev. B 36, 3254 (1987)]

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SLIDE 9

Supercell method in plane-wave basis

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SLIDE 10
  • dzt
  • 10
  • Symmetrized Plane-wave basis
  • Ψ = Σs C(Gs)|Gs>
  • G

s

  • The star of G
  • G

s

  • (001)
  • (001)
  • (010)
slide-11
SLIDE 11
  • dzt
  • 11
slide-12
SLIDE 12
  • dzt
  • 12
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SLIDE 13

The meta-Generalized Gradient Approximation mGGA (TB09) [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)]

Becke-Roussel exchange potential

[A.D. Becke & M.R. Roussel, Phys. Rev. A 39, 3761 (1989)]

TDDFT with mGGA :

[V.U. Nazarov & G. Vignale, PRL 107, 216402(2011)]

slide-14
SLIDE 14

Band structure comparison

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SLIDE 15

Comparison between LASTO & WIEN2k

slide-16
SLIDE 16

Excitation spectra

Si GaAs

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SLIDE 17

Dielectric functions of InGaAs & InAsP alloys

  • btained by TDDFT based on mGGA

[F. Tran and P. Blaha, PRL 102, 226401 (2009)] [V.U. Nazarov and G. Vignale, PRL 107, 216402(2011)]

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SLIDE 18

 

 

 

 

 

H k E e E E E E

p ik xy xx xy zz            

     

, , ,

' ' ' '

 

     

2 2

1

Strain H am iltonian

H V D de de de V D de de de V D

st H xy xz xy H yz xz yz H

                   

1 2 3

3 3 3 3 3 3

e ij=( ij+ ji)/2 V H=(a 1+a 2)( xx+ yy+ zz) D 1=b(2 xx- yy- zz) D 2=b(2 yy- xx- zz) D 3=b(2 zz- xx- yy) a 1, a 2, b, d = deform ation potentials. i 2 3 4 1

Bond-orbital model

[S. Sun,Y. C. Chang, PRB 62, 13631 (2000)]

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SLIDE 19

InAs/GaAs Self assembled quantum dots

GaAs InAs Wetting layer Lattice mismatch 7% Incident light Infrared detector Laser Area density 2 11 /

10 cm

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SLIDE 20

Bond-orbital model

x (0,0,1) y (0,1,0)

sv’ sv

[S. Sun,Y. C. Chang, PRB 62, 13631 (2000)]

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SLIDE 21

Valence force field (VFF) Model

   

V d d d d d d d d d

ij ij ij ij ij ijk ij ik ij ik j k i ij ik

    

  

1 4 3 4 1 4 3 4 3

2 2 2 2 2

 

, , , , , ,

 

i labels atom positions j , k label nearest-neighbors of i dij = bond length joining sites i and j d0,ij is the corresponding equilibrium length ij= bond stretching constants d ijk= bond bending constants We take dijk

2 = dijdik

i 2 3 4 1

di1 di2 di3 di4

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SLIDE 22
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SLIDE 23

UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

Ground Transition Energy Varying With Dot Height (comparing to Experiment)

Dot base length 200Å 20 40 60 80 100 1.04 1.08 1.12 1.16 1.20 1.24

Theoty Experiment

Energy (eV)

Island height (A)

Theory

slide-24
SLIDE 24

PL

IEXC~5000W/cm2 EEXC=2.41eV

InAs/GaAs QDs 3ML PIG T=7K

Intensity (arb. units)

0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30

EDET=1.062eV

PLE

+LO phonon transition weaker transitions strongest transitions Energy (eV) Log of Intensity (arb. units)

PL/PLE Characterization: Electronic Structure

Ground state at 1.062eV Excited states: Strongest at 1.147eV and 1.229eV Weaker at 1.121eV and 1.197eV

E1

2 4

E E

H H H1,2

3 3

Ec Ev EWL

e

EWL

h

1 . 5 2 e V 59meV 26meV 1 . 4 5 e V

1.062eV

50meV 32meV

1.147eV 1.229eV

GaAs GaAs QD

InAs WL

~310+50meV ~150+50meV

1.197eV 1.121eV

?

[Data from A. Madhkar (USC)]

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SLIDE 25

E1

2 4

E E

H H H1,2

3 3

Ec Ev E

WL e

EWL

h

59meV 26meV 1 . 4 5 e V

1 . 6 2 e V

50meV 32meV

1 . 1 4 7 e V 1 . 2 2 9 e V

~310+50meV ~150+50meV

1 . 1 9 7 e V 1 . 1 2 1 e V

E1

2

E E

3

E4 E5 E

WL e

1 1 m e V 1 6 2 m e V 1 8 4 m e V Ec ~310+50meV

2500 2000 1500 1000 0.0 0.1 0.2 0.3 0.4 184 meV 6.7mm 162 meV 7.62mm 110 meV 11.3mm Normal incidence Bias: -0.5 V @77K

Photocurrent (nA) Wavenumber (cm

  • 1)

Intra-band Transitions

Data from A. Madhkar (USC)

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SLIDE 26

Intra-band Transitions

Table 4 Inter-sub band transition matrix elements of ground electron state to upper three electron states,

 

1 2 , , c i c

r 

. B=200A, h=80A. Symmetry state i (Ei(DEE1E1)E x y z A1 #2 (0.111) #3 (0.123) #4 (0.197) 0.2 57 201 A2 #2 (0.106) #3 (0.114) 28.5 B1,B2 #2 (0.109) #3 (0.138) #4 (0.201) 15 42 14 A1-B1n #1 (0.062) #2 (0.162) #3 (0.218) 446 0.2 0.4 446 0.2 0.4 B1-A1n #2(0.049) #3(0.061) #4(0.135) #5(0.161) 536 659 376 10.2 536 659 376 10.2

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SLIDE 27

Effective bond-orbital model for QWRs

  • (

a)

  • (

b)

  • (

c)

  • (

d)

  • 8
  • 6
  • 4
  • 2

2 4

  • 1

1 2

  • 8
  • 6
  • 4
  • 2

2 4

  • 1

1 2

Wave Vector, k E (eV)

  • 1

1 2

  • 8
  • 6
  • 4
  • 2

2 4

InAs   K L X

  • 8
  • 6
  • 4
  • 2

2 4

  • 1

1 2

  • 8
  • 6
  • 4
  • 2

2 4

  • 1

1 2

Wave Vector, k E (eV)

  • 1

1 2

  • 8
  • 6
  • 4
  • 2

2 4

GaSb   K L X

  • 8
  • 6
  • 4
  • 2

2 4

  • 1

1 2

  • 8
  • 6
  • 4
  • 2

2 4

  • 1

1 2

Wave Vector, k E (eV)

  • 1

1 2

  • 8
  • 6
  • 4
  • 2

2 4

GaAs   K L X

  • 8
  • 6
  • 4
  • 2

2 4

  • 1

1 2

  • 8
  • 6
  • 4
  • 2

2 4

  • 1

1 2

Wave Vector, k E (eV)

  • 1

1 2

  • 8
  • 6
  • 4
  • 2

2 4

CdTe   K L X

[Y. C. Chang, W. E. Mahmoud, Comp. Phys. Comm., 196, 92 (2015)]

slide-28
SLIDE 28
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0

InAs NW VB d = 5nm

  • 1

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.5 1.0 1.5 2.0 2.5

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

InAs NW CB d = 5nm

  • 1

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.5 1.0 1.5 2.0 2.5

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

InAs NW CB d = 7nm

  • 1
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

InAs NW VB d = 7nm

  • 1
  • (

a)

  • (

b)

  • (

c)

  • (

d)

slide-29
SLIDE 29
  • (

c)

  • (

a)

  • (

d)

  • (

b)

1 2 3 4 5 6 7 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 1 2 3 4 5 6 7 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

Photon Energy (eV) Absorption Coefficient (10 cm )

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 1 2 3 4 5 6 7

  • 1

4

InAs NW d = 5nm

1 2 3 4 5 6 7 0.4 0.8 1.2 1.6 2.0 1 2 3 4 5 6 7 0.4 0.8 1.2 1.6 2.0

Photon Energy (eV) Absorption Coefficient (10 cm )

0.4 0.8 1.2 1.6 2.0 1 2 3 4 5 6 7

  • 1

4

InAs NW d = 7nm

1 2 3 4 5 6 7 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 1 2 3 4 5 6 7 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

Photon Energy (eV) Absorption Coefficient (10 cm )

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 1 2 3 4 5 6 7

  • 1

4

GaSb NW d = 5nm

1 2 3 4 5 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 1 2 3 4 5 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Photon Energy (eV) Absorption Coefficient (10 cm )

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 1 2 3 4 5

  • 1

4

GaSb NW d = 7nm

slide-30
SLIDE 30

Excitation spectra of colloidal QDs

  • r0
  • 0.65
  • 2.25
  • 2.69
  • ZnTe
  • core
  • ZnSe
  • shell
  • Potential (eV)
  • Rb
  • R
  • Figure 1. Schematic bulk band-offset for
  • ZnTe/ZnSe CSQD.
  • buffer

Te

[8-band or (6+2)-band k.p model]

[Exp. data from S.M. Fairclough et al., J. Phys. Chem. C 116, 26898 (2012)]

slide-31
SLIDE 31

Absorption coefficient for ZnTe/ZnSe CSQDs

slide-32
SLIDE 32

Transport through nanostructure junctions

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SLIDE 33

Green function approach for GMR

[J. Velev and Y.-C. Chang, Phys. Rev. B 63, 184411 (2001)]

Fe4/Cr3/Fe4

trilayer junction

  • A. Fert & P. Grunberg

2007 Nobel Prize (GMR)

(Fe2/CrM/Fe2)N

multiilayer junction

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SLIDE 34

DFT to Tight-binding conversion

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SLIDE 35

GaAs zineblende/wurtzite heterostructure

  • H. Shtrikman et al., Nano Lett., 9, 215 (2009);
  • D. Spirkoska1 et al., https://arxiv.org/ftp/arxiv/papers/0907/0907.1444.pdf
slide-36
SLIDE 36

Transport characteristics of GaAs ZB/WZ junctions

Normal-incidence conductance

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SLIDE 37

Tunneling current spectroscopy of a nanostructure junction involving multiple energy levels

Z

P

X

P

S

Substrate Substrate Substrate Tip Tip Tip in

  • ut

d p s

E E E

z ,

,

  • P. Liljeroth et al, Phys. Chem.chem. Phys. 8, 3845 (2006)
slide-38
SLIDE 38

1

E

2

E

L

R

(a) No bias (b) Forward bias

F

E

Source Dot Drain

a

V

(c) Reverse bias

a

V

Energy diagram for STM-QD junction

slide-39
SLIDE 39

Theory vs. Experiment for STM-QD tunneling spectra

[Data from L. Jdira et al., Phys. Rev. B 73, 115305 (2006)] Reverse bias Forward bias

[M.T. Kuo & Y. C. Chang, PRL, 99, 086803 (2007)]

slide-40
SLIDE 40

M-level case

s 

,

1

N

s s s s  

   

j j j j j

n n N N a ) ( 1

, ,

s s s s   

 

j j j j j

n n N N b 2

, , s s 

j j j

n n c

s s s s  

   

' ' , ' , ' '

) ( 1

j j j j j

n n N N a

s s s s   

 

' ' , ' , ' '

2

j j j j j

n n N N b

s s 

' ' ' j j j

n n c '

j j   

, 2 , 2 , , , ,.. , , , ,

' 5 4 ' 3 2 1 ' 5 ' 4 ' 3 ' 2 ' 1 j j j j j j j j j j j j j j

U U U U a c p a c p b a p a b p a a p

   

              

s  , 

N

slide-41
SLIDE 41
  • Z. Yuan et al., Science, 295, 102 (2002)
  • 單光子發射器(Single-Photon generator)

10 20 30 40 50 60

  • 27
  • 25
  • 23
  • 21
  • 19
  • 17

-Eg (meV) Intensity (arb. units)

X- X X2 X+

  • M. T. Kuo, Y. C. Chang, PRB

1 1.5 2 2.5 3 3.5 4 4.5 5 0.001 0.01 0.1 1 10 /2r Peak strength (arb. units) X X

2

slide-42
SLIDE 42

Quantum interference in triple-QD junction

[C. C. Chen, Y. C. Chang, M. T. Kuo, PCCP, 17, 6606 (2015)] [M. Seo et al., Phys. Rev. Lett.110, 046803 (2013)]

slide-43
SLIDE 43

Thermal rectification properties of QD junctions

ZT=S2GT/k S=dV/dT

[M. T. Kuo, Y. C. Chang, Phys. Rev. B 81, 205321 (2010)]

slide-44
SLIDE 44

Thermoelectric properties of TQD junctions

[C. C. Chen, M. T. Kuo, Y. C. Chang, PCCP, 17, 19386 (2015)]

slide-45
SLIDE 45

TE behavior of QD array

[M. T. Kuo, Y. C. Chang, Nanotechnology 24 175403 (2013) ]

(Fs=0.01)

slide-46
SLIDE 46

Enhancement in TE efficiency of QD junctions dueto increase of level degeneracy

[P. Murphy and J. Moore, Phys. Rev. B 76, 155313 (2007)] [M. T. Kuo, C. C. Chen,Y. C. Chang, Phys. Rev. B 95, 075432 (2017)]

DQD Single QD

(Fs=0.1)

slide-47
SLIDE 47
  • Computation codes were implemented for electronic and optical exciation

calculations by using symmetry adapted PW & LASTO basis.

  • Electronic states and optical linear response of nanoclusters (with high

symmetry) by including the quasi-particle self-energy correction (GW approximation) and the excitonic effects can be calculated efficiently.

  • For high-symmetry (Oh,Td,C3v,D2d) systems, our method improves the

computation efficiency by two-three orders of magnitude.

  • Self-assembled or colloidal QDs can be suitably modeled by VFF model for

strain distribution+EBOM for electronic states

  • Intra-level and inter-level Coulomb interactions play keys roles in the optical

properties

  • Non-equilibrium transport and correlation are important in the analysis of

nanostructure junction devices

  • Computation codes were implemented for electronic and optical exciation

calculations of 1D and 2D materials by using PW-B spline mixed basis.

Summary

slide-48
SLIDE 48

DFT with LASTO basis

slide-49
SLIDE 49
  • dzt
  • 49
  • Optical spectra of SiH4 cluster
slide-50
SLIDE 50
  • dzt
  • 50
  • Optical spectra of 1nm Si

clusters

slide-51
SLIDE 51

Effect of asymmetric tunneling

meV

  • ut

1  

Shell-filling Shell-tunneling

meV

in

10  

meV

in

1 .  

slide-52
SLIDE 52

Comparison with continuum Model

slide-53
SLIDE 53

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.1 0.2 0.3 0.4 0.0 0.2 0.4 0.6 0.8 1.0

  • 1

4

p-type InAs NW d = 7nm

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0

  • 1

4

p-type GaSb NW d = 7nm

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2

  • 1

4

p-type GaSb NW d = 5nm

0.0 0.4 0.8 1.2 1.6 0.0 0.1 0.2 0.3 0.0 0.4 0.8 1.2 1.6 0.0 0.1 0.2 0.3

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.1 0.2 0.3 0.0 0.4 0.8 1.2 1.6

  • 1

4

p-type InAs NW d = 5nm

slide-54
SLIDE 54

polymer semiconductors polymer semiconductors

Modeling of Quantum Wires

slide-55
SLIDE 55
slide-56
SLIDE 56
slide-57
SLIDE 57

Emission spectrum of QD transistor

slide-58
SLIDE 58

Symmetry-adapted basis for large supercells

slide-59
SLIDE 59

Coupled-wave transfer method

  • Energy and wave functions computed using a

stabilized transfer matrix technique by dividing the system into many slices along growth direction.

  • Envelope function approximation with energy-

dependent effective mass is used.

  • Effective-mass Hamiltonian in k-sapce:

[(kx

2+ky 2 )/mt(E)+z 2/ml(E)-E]F(k) +Σk’[V(k,k’)+Vimp(k,k’)]F(k’)=0

is solved via plane-wave expansion in each slice.

  • 14-band k·p effects included perturbatively in optical

matrix elements calculation

  • Dopant effects incorporated as screened Coulomb

potential

  • The technique applies to quantum wells and quantum

dots (or any 2D periodic nanostructures)

slide-60
SLIDE 60

Charge densities of low-lying states in lens-shaped QD

s-like d-like px/py like pz like

slide-61
SLIDE 61

Quantum well intrasubband photodetector (QWISP) for far infared and terahertz radiation detection

[Ting et al., APPLIED PHYSICS LETTERS 91, 073510 (2007)]

slide-62
SLIDE 62

Quantum well intrasubband photodetector (QWISP) for far infared and terahertz radiation detection

slide-63
SLIDE 63

Quantum well intrasubband photodetector (QWISP) for far infared and terahertz radiation detection

slide-64
SLIDE 64

Submonolayer QD infrared photodetector

[Ting et al., APPLIED PHYSICS LETTERS 94, 1 (2009)]

slide-65
SLIDE 65

Optical absorption spectra of Si

Si

slide-66
SLIDE 66
  • dzt
  • 66
  • Comparison in CPU time
slide-67
SLIDE 67
  • GW approximation for Quasi-particle

energy

slide-68
SLIDE 68
  • ω Integration & plasma pole approximation
slide-69
SLIDE 69
  • How to obtain symmetrization coefficients
  • Ref.
slide-70
SLIDE 70
  • Evaluating matrix elements
  • Symmetry reduction factor ~ nh

2

slide-71
SLIDE 71
  • dzt
  • 71
  • Optical spectra of 1nm Si

clusters

slide-72
SLIDE 72
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0

GaSb NW VB d = 5nm

  • 1

1.0 1.2 1.4 1.6 1.8 2.0 2.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.0 1.2 1.4 1.6 1.8 2.0 2.2

GaSb NW CB d = 5nm

  • 1

0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.8 1.0 1.2 1.4 1.6 1.8 2.0

GaSb NW CB d = 7nm

  • 1
  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

GaSb NW VB d = 7nm

  • 1
  • (

c)

  • (

d)

  • (

b)

  • (

a)

slide-73
SLIDE 73
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

GaAs NW VB d = 7nm

  • 1

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

GaAs NW CB d = 7nm

  • 1

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

GaAs NW CB d = 5nm

  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0

GaAs NW VB d = 5nm

  • 1
  • (

c)

  • (

a)

  • (

b)

  • (

d)

slide-74
SLIDE 74
  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

CdTe NW VB d = 7nm

  • 1
  • 1.0
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 1.0
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 1.0
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0

CdTe NW VB d = 5nm

  • 1
  • (

c)

  • (

a)

  • (

b)

  • (

d)

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

CdTe NW CB d = 7nm

  • 1

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

CdTe NW CB d = 5nm

  • 1
slide-75
SLIDE 75
  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

ZnSe NW VB d = 5nm

  • 1

2.8 3.2 3.6 4.0 4.4 0.0 0.5 1.0 1.5 2.0 2.5 3.0 2.8 3.2 3.6 4.0 4.4 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 2.8 3.2 3.6 4.0 4.4

ZnSe NW CB d = 5nm

  • 1
  • (

c)

  • (

a)

  • (

d)

  • (

b)

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

ZnSe NW CB d = 7nm

  • 1
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

ZnSe NW VB d = 7nm

  • 1
slide-76
SLIDE 76
  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave vector, k (cm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

Si NW VB d=5nm

  • 1
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave vector, k (cm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

Si NW VB d=7nm

  • 1
  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.6
  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.0

Ge NW VB d = 7nm

  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave Vector, k (nm ) E (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0

Ge NW VB d = 5nm

  • 1
  • (

c)

  • (

d)

  • (

b)

  • (

a)

slide-77
SLIDE 77
  • (

a)

  • (

b)

1 2 3 4 5 6 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 1 2 3 4 5 6 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Photon Energy (eV) Absorption Coefficient (10 cm )

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 1 2 3 4 5 6

  • 1

4

GaAs NW d = 7nm

2 4 6 8 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 2 4 6 8 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

Photon Energy (eV) Absorption Coefficient (10 cm )

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 2 4 6 8

  • 1

4

GaAs NW d = 5nm

slide-78
SLIDE 78

2 4 6 8 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 2 4 6 8 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2

Photon Energy (eV) Absorption Coefficient (10 cm )

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 2 4 6 8

  • 1

4

ZnSe NW d = 7nm

2 4 6 8 10 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 2 4 6 8 10 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

Photon Energy (eV) Absorption Coefficient (10 cm )

2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 2 4 6 8 10

  • 1

4

ZnSe NW d = 5nm

1 2 3 4 5 6 7 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 1 2 3 4 5 6 7 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

Photon Energy (eV) Absorption Coefficient (10 cm )

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 1 2 3 4 5 6 7

  • 1

4

CdTe NW d = 5nm

1 2 3 4 5 6 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 1 2 3 4 5 6 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Photon Energy (eV) Absorption Coefficient (10 cm )

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 1 2 3 4 5 6

  • 1

4

CdTe NW d = 7nm

slide-79
SLIDE 79

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.5 1.0 1.5 2.0 2.5

  • 1

4

n-type InAs NW

d = 5nm d = 7nm d = 15nm

0.0 0.5 1.0 1.5 2.0 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.5 1.0 1.5 2.0

  • 1

4

n-type GaSb NW

d = 5nm d = 7nm d = 14nm

slide-80
SLIDE 80

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

  • 1

4

p-type Si NW d = 5nm

0.0 0.4 0.8 1.2 1.6 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.4 0.8 1.2 1.6 0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.4 0.8 1.2 1.6

  • 1

4

p-type Si NW d = 7nm

0.0 0.4 0.8 1.2 1.6 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.4 0.8 1.2 1.6 0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.4 0.8 1.2 1.6

  • 1

4

p-type Ge NW d = 7nm

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

Absorption Coefficient (10 cm )

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2

  • 1

4

p-type Ge NW d = 5nm

slide-81
SLIDE 81
slide-82
SLIDE 82

Application to optical excitation of solids & superlattices

  • K =
  • [Puschnig* and C. Ambrosch-Draxl, PRB 66, 165105 (2002)]
  • for k in IBZ
  • Use time-reversal symmetry
slide-83
SLIDE 83

Piezoeletric Potential

slide-84
SLIDE 84

Supercell calculations in symmetry-adpated LASTO basis

[Y.-C. Chang, R. B. James, and J. W. Davenport, PRB 73, 035211 (2006)]