Embed Size (px)
Citation preview
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
LMTO
SIESTA
LASTO
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)
LiFSi
Optical spectra calculated by Bathe-Salpeter Eq.
in LASTO basis
•Results similar to LAPW results:
•[Puschnig* and C. Ambrosch-Draxl, PRB 66, 165105 (2002)]
GaAs
AlAs1X1 SL
Exp
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>
•Gs
•The star of G
•Gs
•(001)
•(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)]
H k E
e E E E E
p
ik
xy xx xy zz
, ,
,
' '
' '
2 21
S tra in H am ilton ian
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)( 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.
i
2
3
4
1
Bond-orbital model
[S. Sun,Y. C. Chang, PRB 62, 13631 (2000)]
InAs/GaAs Self assembled quantum dots
GaAs
InAs
Wetting layer
Lattice mismatch 7%
Incident light
Infrared detector
Laser
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
ij
ij
ijk ij ik ij ik
j ki
ij ik
1
4
3
4
1
4
3
43
2
0
22
0
2
0 0
2
0 0
, ,
, , , ,
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
i
2
3
4
1
di1
di2di3
di4
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
PL
IEXC~5000W/cm2
EEXC=2.41eV
InAs/GaAs QDs
3ML PIG
T=7K
Inte
nsit
y (a
rb. u
nits
)
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
Inte
nsit
y (a
rb. u
nits
)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
HH
H1,23
3
Ec
Ev
EWLe
EWLh
1.5
2eV
59meV
26meV1
.45
eV
1.0
62
eV
50meV
32meV
1.1
47
eV
1.2
29
eV
GaAs GaAsQD
InA
s W
L
~310+50meV
~150+50meV
1.1
97eV
1.1
21
eV
?
[Data from A. Madhkar (USC)]
E1
2
4
E
E
HH
H1,23
3
Ec
Ev
EWLe
EWLh
59meV
26meV1
.45
eV
1.0
62eV
50meV
32meV
1.1
47eV
1.2
29eV
~310+50meV
~150+50meV
1.1
97eV
1.1
21eV
E1
2
E
E
3
E4
E5
EWLe
11
0m
eV
16
2m
eV
18
4m
eV
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
Pho
tocurr
ent
(nA
)
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
2
, ,c i cr
. B=200A, h=80A.
Symmetry state i
(Ei(DEE1E1)E
1)
x y z
A1
#2 (0.111)
#3 (0.123)
#4 (0.197)
0
0
0
0
0
0
0.2
57
201
A2
#2 (0.106)
#3 (0.114)
0
0
0
0
28.5
0
B1,B2
#2 (0.109)
#3 (0.138)
#4 (0.201)
0
0
0
0
0
0
15
42
14
A1-B1n
#1 (0.062)
#2 (0.162)
#3 (0.218)
446
0.2
0.4
446
0.2
0.4
0
0
0
B1-A1n
#2(0.049)
#3(0.061)
#4(0.135)
#5(0.161)
536
659
376
10.2
536
659
376
10.2
0
0
0
0
Effective bond-orbital model for QWRs
•(a)
•(b)
•(c)
•(d)
-8
-6
-4
-2
0
2
4
-1 0 1 2
-8
-6
-4
-2
0
2
4
-1 0 1 2
Wave Vector, k
E (
eV)
-1 0 1 2
-8
-6
-4
-2
0
2
4
InAs
KL X
-8
-6
-4
-2
0
2
4
-1 0 1 2
-8
-6
-4
-2
0
2
4
-1 0 1 2
Wave Vector, k
E (
eV)
-1 0 1 2
-8
-6
-4
-2
0
2
4
GaSb
KL X
-8
-6
-4
-2
0
2
4
-1 0 1 2
-8
-6
-4
-2
0
2
4
-1 0 1 2
Wave Vector, k
E (
eV)
-1 0 1 2
-8
-6
-4
-2
0
2
4
GaAs
KL X
-8
-6
-4
-2
0
2
4
-1 0 1 2
-8
-6
-4
-2
0
2
4
-1 0 1 2
Wave Vector, k
E (
eV)
-1 0 1 2
-8
-6
-4
-2
0
2
4
CdTe
KL X
[Y. C. Chang, W. E. Mahmoud, Comp. Phys. Comm., 196, 92 (2015)]
-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)
•(c)
•(a)
•(d)
•(b)
0
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
0
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
0
1
2
3
4
5
6
7
-14
InAs NW
d = 5nm
0
1
2
3
4
5
6
7
0.4 0.8 1.2 1.6 2.0
0
1
2
3
4
5
6
7
0.4 0.8 1.2 1.6 2.0
Photon Energy (eV)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
0.4 0.8 1.2 1.6 2.0
0
1
2
3
4
5
6
7
-14
InAs NW
d = 7nm
0
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
0
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
0
1
2
3
4
5
6
7
-14
GaSb NW
d = 5nm
0
1
2
3
4
5
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
0
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
0
1
2
3
4
5
-14
GaSb NW
d = 7nm
Excitation spectra of colloidal QDs
•r0
•0.65
•2.25 •2.69
•ZnTe
•core
•ZnSe
•shell
•Po
tenti
al (
eV)
•
•0 •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)]
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
ZPXPS
Substrate Substrate Substrate
Tip Tip Tip
in
out
dps EEEz,,
P. Liljeroth et al, Phys. Chem.chem. Phys. 8, 3845 (2006)
1E
2E
L R
(a) No bias (b) Forward bias
FE
SourceDot
Drain
aV
(c) Reverse bias
aV
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,,
ss jj
j nnc
ssss '',','
' )(1 jjjj
j nnNNa
ssss '',','
' 2 jjjj
j nnNNb
ss ''
'
jj
j nnc
'jj
,2,2,,,0
,..,,,,
'54'321
'
5
'
4
'
3
'
2
'
1
jjjj
jjjjjjjjjj
UUUU
acpacpbapabpaap
s,N
Z. Yuan et al., Science, 295, 102 (2002)
•單光子發射器(Single-Photon generator)
0
10
20
30
40
50
60
-27 -25 -23 -21 -19 -17
-Eg (meV)
Inte
nsit
y (
arb
. u
nit
s)
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
/2r
Pe
ak
s
tre
ng
th
(a
rb
. u
nits
)
X
X2
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
0.2
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10 cm
)
0.0 0.1 0.2 0.3 0.4
0.0
0.2
0.4
0.6
0.8
1.0
-14
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)
Ab
so
rpti
on
Co
eff
icie
nt
(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
-14
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)
Ab
so
rpti
on
Co
eff
icie
nt
(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
-14
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10 cm
)
0.0 0.1 0.2 0.3
0.0
0.4
0.8
1.2
1.6
-14
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)]
Quantum well intrasubband photodetector (QWISP)
for far infared and terahertz radiation detection
Quantum well intrasubband photodetector (QWISP)
for far infared and terahertz radiation detection
Submonolayer QD infrared photodetector[Ting et al., APPLIED PHYSICS LETTERS 94, 1 (2009)]
Optical absorption spectra of Si
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
-0.8
-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)
-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)
-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
-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
-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)
•(a)
•(b)
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
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
0
1
2
3
4
5
6
-14
GaAs NW
d = 7nm
0
2
4
6
8
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
0
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
0
2
4
6
8
-14
GaAs NW
d = 5nm
0
2
4
6
8
2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2
0
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2
0
2
4
6
8
-14
ZnSe NW
d = 7nm
0
2
4
6
8
10
2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4
0
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4
0
2
4
6
8
10
-14
ZnSe NW
d = 5nm
0
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
0
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
0
1
2
3
4
5
6
7
-14
CdTe NW
d = 5nm
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
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10
cm
)
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
0
1
2
3
4
5
6
-14
CdTe NW
d = 7nm
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)
Ab
so
rpti
on
Co
eff
icie
nt
(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
-14
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)A
bso
rpti
on
Co
eff
icie
nt
(10 cm
)
0.0 0.1 0.2 0.3 0.4 0.5
0.0
0.5
1.0
1.5
2.0
-14
n-type GaSb NW d = 5nm
d = 7nmd = 14nm
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)
Ab
so
rpti
on
Co
eff
icie
nt
(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
-14
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10 cm
)
0.0 0.1 0.2 0.3 0.4 0.5
0.0
0.4
0.8
1.2
1.6
-14
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)
Ab
so
rpti
on
Co
eff
icie
nt
(10 cm
)
0.0 0.1 0.2 0.3 0.4 0.5
0.0
0.4
0.8
1.2
1.6
-14
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)
Ab
so
rpti
on
Co
eff
icie
nt
(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
-14
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)]
