Multiscale modeling of optical and transport properties of solids … · 2017-03-14 · 0.95 1.00...

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

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

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

SIESTA

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)]

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)]

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:

•BSE (solid line)

•RPA (dashed line)

Optical spectra calculated by Bathe-Salpeter Eq.

in LASTO basis

•Results similar to LAPW results:

•[Puschnig* and C. Ambrosch-Draxl, PRB 66, 165105 (2002)]

AlAs1X1 SL

Optical spectra of GaAs, AlAs & SLs

AlAsGaAs

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

Supercell method in plane-wave basis

•dzt •10

•Symmetrized Plane-wave basis

•Ψ = Σs C(Gs)|Gs>

•The star of G

•(001)

•(010)

•dzt •11

•dzt •12

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)]

Band structure comparison

Comparison between LASTO & WIEN2k

Excitation spectra

Si GaAs

Dielectric functions of InGaAs & InAsP alloys

obtained by TDDFT based on mGGA

[F. Tran and P. Blaha, PRL 102, 226401 (2009)]

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

e E E E E

xy xx xy zz

S tra in H am ilton ian

V D de de

de V D de

de de V D

H xy xz

xy H yz

xz yz H

e ij= ( ij+ ji)/2

V H = (a 1+ a 2)( x x+ y y+ zz)

D 1= b(2 x x- y y- zz)

D 2= b(2 y y- x x- zz)

D 3= b(2 zz- x x- y y)

a 1 , a 2 , b , d = defo rm ation po ten tia ls.

Bond-orbital model

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

InAs/GaAs Self assembled quantum dots

Wetting layer

Lattice mismatch 7%

Incident light

Infrared detector

Area density

211 /10 cm

Bond-orbital model

x (0,0,1)

y (0,1,0)sv’ sv

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

Valence force field (VFF) Model

V d d d

d d d d d d

ij ij ij

ijk ij ik ij ik

, , , ,

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 dijk2 = dijdik

di2di3

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

Theoty

Experiment

Energy (eV)

Island height (A)

Theory

IEXC~5000W/cm2

EEXC=2.41eV

InAs/GaAs QDs

3ML PIG

0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30

EDET=1.062eV

+LO phonon transition

weaker transitions

strongest transitions

Energy (eV)

)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

26meV1

GaAs GaAsQD

~310+50meV

~150+50meV

[Data from A. Madhkar (USC)]

26meV1

~310+50meV

~150+50meV

~310+50meV

2500 2000 1500 1000

184 meV

162 meV

7.62mm

110 meV

11.3mm

Normal incidence

Bias: -0.5 V

tocurr

Wavenumber (cm-1)

Intra-band Transitions

Data from A. Madhkar (USC)

Intra-band Transitions

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

three electron states, 1

, ,c i cr

. B=200A, h=80A.

Symmetry state i

(Ei(DEE1E1)E

#2 (0.111)

#3 (0.123)

#4 (0.197)

#2 (0.106)

#3 (0.114)

#2 (0.109)

#3 (0.138)

#4 (0.201)

A1-B1n

#1 (0.062)

#2 (0.162)

#3 (0.218)

B1-A1n

#2(0.049)

#3(0.061)

#4(0.135)

#5(0.161)

Effective bond-orbital model for QWRs

•(a)

•(b)

•(c)

•(d)

-1 0 1 2

Wave Vector, k

-1 0 1 2

Wave Vector, k

-1 0 1 2

Wave Vector, k

-1 0 1 2

Wave Vector, k

-1 0 1 2

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

0.0 0.5 1.0 1.5 2.0 2.5

Wave Vector, k (nm )

0.0 0.5 1.0 1.5 2.0 2.5

InAs NW VB

d = 5nm

0.0 0.5 1.0 1.5 2.0 2.5

InAs NW CB

d = 5nm

0.0 0.5 1.0 1.5 2.0 2.5

InAs NW CB

d = 7nm

0.0 0.5 1.0 1.5 2.0 2.5

InAs NW VB

d = 7nm

•(a)

•(b)

•(c)

•(d)

•(c)

•(a)

•(d)

•(b)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

Photon Energy (eV)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

InAs NW

d = 5nm

0.4 0.8 1.2 1.6 2.0

Photon Energy (eV)

0.4 0.8 1.2 1.6 2.0

InAs NW

d = 7nm

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

Photon Energy (eV)

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

GaSb NW

d = 5nm

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Photon Energy (eV)

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

GaSb NW

d = 7nm

Excitation spectra of colloidal QDs

•0.65

•2.25 •2.69

•ZnTe

•core

•ZnSe

•shell

•0 •Rb•R

•Figure 1. Schematic bulk band-offset for

•ZnTe/ZnSe CSQD.

•buffer

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

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

Absorption coefficient for ZnTe/ZnSe CSQDs

Transport through nanostructure junctions

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

DFT to Tight-binding conversion

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

Transport characteristics of GaAs ZB/WZ junctions

Normal-incidence conductance

Tunneling current spectroscopy of a nanostructure

junction involving multiple energy levels

Substrate Substrate Substrate

Tip Tip Tip

dps EEEz,,

P. Liljeroth et al, Phys. Chem.chem. Phys. 8, 3845 (2006)

(a) No bias (b) Forward bias

SourceDot

(c) Reverse bias

Energy diagram for STM-QD junction

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)]

M-level case

s ,1 N

ssss jjjj

j nnNNa )(1 ,,

ssss jjjj

j nnNNb 2,,

ssss '',','

' )(1 jjjj

j nnNNa

ssss '',','

' 2 jjjj

j nnNNb

,2,2,,,0

,..,,,,

'54'321

jjjjjjjjjj

acpacpbapabpaap

Z. Yuan et al., Science, 295, 102 (2002)

•單光子發射器(Single-Photon generator)

-27 -25 -23 -21 -19 -17

-Eg (meV)

M. T. Kuo, Y. C. Chang, PRB

0.001 0.01 0.1 1 10

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)]

Thermal rectification properties of QD junctions

ZT=S2GT/k

S=dV/dT

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

Thermoelectric properties of TQD junctions

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

TE behavior of QD array[M. T. Kuo, Y. C. Chang, Nanotechnology 24 175403 (2013) ]

(Fs=0.01)

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)]

DQDSingle QD(Fs=0.1)

• Computation codes were implemented for electronic and optical exciationcalculations 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 exciationcalculations of 1D and 2D materials by using PW-B spline mixed basis.

Summary

DFT with LASTO basis

•dzt •49

•Optical spectra of SiH4 cluster

•dzt •50

•Optical spectra of 1nm Si clusters

Effect of asymmetric tunneling

meVout 1

Shell-filling

Shell-tunneling

meVin 10

meVin 1.0

Comparison with continuum Model

0.0 0.1 0.2 0.3 0.4

Photon Energy (eV)

(10 cm

0.0 0.1 0.2 0.3 0.4

p-type InAs NW

d = 7nm

0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

(10 cm

0.0 0.1 0.2 0.3 0.4 0.5

p-type GaSb NW

d = 7nm

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Photon Energy (eV)

(10 cm

0.0 0.1 0.2 0.3 0.4 0.5 0.6

p-type GaSb NW

d = 5nm

0.0 0.1 0.2 0.3

Photon Energy (eV)

(10 cm

0.0 0.1 0.2 0.3

p-type InAs NW

d = 5nm

polymer semiconductorspolymer semiconductors

Modeling of Quantum Wires

Emission spectrum of QD transistor

Symmetry-adapted basis for large supercells

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:

[(kx2+ky

2 )/mt(E)+z2/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)

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

s-like

d-like

px/py like

pz like

Quantum well intrasubband photodetector (QWISP)

for far infared and terahertz radiation detection

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

Submonolayer QD infrared photodetector[Ting et al., APPLIED PHYSICS LETTERS 94, 1 (2009)]

Optical absorption spectra of Si

•dzt •66

•Comparison in CPU time

•GW approximation for Quasi-particle energy

• ω Integration & plasma pole approximation

•How to obtain symmetrization coefficients

•Ref.

•Evaluating matrix elements

•Symmetry reduction factor ~ nh2

•dzt •71

•Optical spectra of 1nm Si clusters

0.0 0.5 1.0 1.5 2.0 2.5 3.0

GaSb NW VB

d = 5nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

GaSb NW CB

d = 5nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

GaSb NW CB

d = 7nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0-0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0-0.6

GaSb NW VB

d = 7nm

•(c)

•(d)

•(b)

•(a)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

GaAs NW VB

d = 7nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

GaAs NW CB

d = 7nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

GaAs NW CB

d = 5nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

GaAs NW VB

d = 5nm

•(c)

•(a)

•(b)

•(d)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

CdTe NW VB

d = 7nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

CdTe NW VB

d = 5nm

•(c)

•(a)

•(b)

•(d)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

CdTe NW CB

d = 7nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

CdTe NW CB

d = 5nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

ZnSe NW VB

d = 5nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

ZnSe NW CB

d = 5nm

•(c)

•(a)

•(d)

•(b)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

ZnSe NW CB

d = 7nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

ZnSe NW VB

d = 7nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave vector, k (cm )

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Si NW VB

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Wave vector, k (cm )

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Si NW VB

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Ge NW VB

d = 7nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Ge NW VB

d = 5nm

•(c)

•(d)

•(b)

•(a)

•(b)

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Photon Energy (eV)

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

GaAs NW

d = 7nm

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

Photon Energy (eV)

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

GaAs NW

d = 5nm

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2

Photon Energy (eV)

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2

ZnSe NW

d = 7nm

2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

Photon Energy (eV)

2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

ZnSe NW

d = 5nm

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

Photon Energy (eV)

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

CdTe NW

d = 5nm

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Photon Energy (eV)

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

CdTe NW

d = 7nm

0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

(10 cm

0.0 0.1 0.2 0.3 0.4 0.5

n-type InAs NW d = 5nm

d = 7nm

d = 15nm

0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)A

(10 cm

0.0 0.1 0.2 0.3 0.4 0.5

n-type GaSb NW d = 5nm

d = 7nmd = 14nm

0.0 0.2 0.4 0.6 0.8

Photon Energy (eV)

(10 cm

0.0 0.2 0.4 0.6 0.8

p-type Si NW

d = 5nm

0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

(10 cm

0.0 0.1 0.2 0.3 0.4 0.5

p-type Si NW

d = 7nm

0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

(10 cm

0.0 0.1 0.2 0.3 0.4 0.5

p-type Ge NW

d = 7nm

0.0 0.1 0.2 0.3 0.4 0.5

Photon Energy (eV)

(10 cm

0.0 0.1 0.2 0.3 0.4 0.5

p-type Ge NW

d = 5nm

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

Piezoeletric Potential

Supercell calculations in symmetry-adpated LASTO basis

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

Multiscale modeling of optical and transport properties of solids … · 2017-03-14 · 0.95 1.00...

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