numerical study of exciton states of shell cdte ... · • exciton states were investigated as a...
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Numerical study of exciton states of core‐shell CdTe/CdS nanotetrapodsby using COMSOL Multiphysics
Yuanzhao YAO,Kazuaki SAKODA
Quantum Dot Research Center, National Institute for Materials Science
Graduate School of Pure and Applied Sciences, University of Tsukuba
Colloidal quantum dots (QDs)
3D(Bulk)
2D(Quantum Well)
1D(Quantum Wire)
0D(Quantum Dot)
Five different QD solutions are shown excited with the same long-wavelength UV lamp; the size of the nanocrystaldetermines the color.(from HP of “invitrogen” )
Colloidal QDs are synthesized from
precursor compounds
dissolved in solutions.
(Chemical processes)
Application of colloidal QD
Colloidal QDlight‐emitting device pixelsP.O.Anikeeva, et al. (Nano Lett.,9,2532,2009)
• Infrared detector , sensor• QD electroluminescence device• solar cell• luminescent marker
CdSe QDs are injected into a mouse, and fluoresce under UV‐light. Mark the location of cancer tumour.(from National Geographic)
Shape control of colloidal QD
SphericalQD
nanorod nanotetrapod
Colloidal QD
Proposed model of a CdTe tetrapod
L. Manna, et al. Nature materials, vol.2, 382 (2003)
L. Choi, et al., Annu. Rev. Phys. Chem. 61, 369, 2010
CdS
t=CdS shell thickness
CdTeband diagram
R. B. Vasiliev, et al. Mendeleev Commun. 19, 128 (2009)
Type I
Type II
CdTe/CdS core-shell tetrapods
CB
VBE
nerg
y
e
hshell
• With continuously grown CdS shell on CdTe tetrapod , features of type II heterostructures were observed in experiment, e.g. featureless absorption tail @ t=1.2 nm
• Study the influence of CdS shell on the exciton state , consequently the optical properties of core‐shell tetrapod
CdTe(ZB)Core
CdTe(WZ)Arm
CdS shell t
cross-section of one branch
e
h
nice tool for modeling QD
with complicated geometry
Theoretical model
(1)Single particle Schrodinger equation (Effective‐mass approximation)Solved with finite element method by using COMSOL software
(2)Two‐body Schrodinger equationSolved with configuration interaction method
i= e or h
is the envelope function and is the atomic wave function
3D model of CdTe/CdScore‐shell tetrapod
Consider the lowest 20 electron and 20 hole states, whose wave functions only have A1 or T2 symmetry
Same method as: K. Sakoda et al., Opt. Mat. Express 1, 379 (2011).
Lowest electron state(e1) and highest hole state(h1) wave function distribution
t=0(nm) t=0.1 t=0.2 t=0.3 t=0.6 t=0.9 t=1.2
(e1)
(h1)
0.0 0.4 0.8 1.20.4
0.6
0.8
1.0
O
verla
p in
tegr
al
Shell thickness (nm)
Single-particle state e1&h1 overlap integral
e‐h NOT totally separated
type II heterostructureNOT apparent
Shell thickness dependence of exciton energy with A1 and T2 symmetry
0.0 0.2 0.4 0.6 0.8 1.0 1.21.61.71.81.92.02.12.22.3
-0.01
0.00
0.01
0.02
0.03
Exci
ton
ener
gy (e
V)
shell thickness (nm)
A1 T2-1 T2-2 T2-3
Energy difference (eV)
Analytical calculation (1)
two‐body matrix element
In which matrix element
Constructed electron wave function, combination of 4 independent wave function on each branch
@ t=1.2 nm, the order of lowest 4 exciton states NOT change.
Safe to choose only lowest 4 pair states for analytical calculation. (e1h1, e2h1, e3h1, e4h1)
(1)
(2)
(3)
(4)
(5)
(6)
direct Coulomb exchange interaction
1 state
3 degenerated states
t=1.2
Analytical calculation (2)
Diagonal matrix element Off-diagonal matrix element(A) Coulomb integral
same value for 4 diagonal elements
(B) exchange interaction integral (e1h1)
exchange interaction integral (e2h1, e3h1, e4h1)
diagonal element of e1h1(A1) is larger than other three(T2)
(A)direct Coulomb integral
(B) exchange interaction integral
All off‐diagonal elements for exchange interaction integral are zero
All off‐diagonal elements for direct Coulomb integral are zero
Conclusion of analytical calculation:The symmetry of lowest exciton state (t=1.2 nm) is T2
740 760 780 800 8200.00
0.05
0.10
0.15
0.20
0.25
Osc
illat
or st
reng
th (a
rb. u
nit)
Wavelength (nm)740 750 760 770 780 790
0.000.030.060.090.120.150.18
Osc
illat
or st
reng
th (a
rb. u
nit)
Wavelength (nm)
740 745 750 755 760 765 7700.00
0.05
0.10
0.15
0.20
0.25
Osc
illat
or st
reng
th (a
rb. u
nit)
Wavelength (nm)
t=1.2
Symmetry break in core-shell tetrapod
Modification: one thicker armModification: one Arm with thicker shell
For the imperfect cs‐tetrapod, oscillator strength of the lowest‐energy exciton state is NOT zero
t=1.2 t=1.2
Conclusion• The electronic states of core-shell tetrapod with various shell
thickness are calculated. Lowest 20 electron and hole wavefunctions have A1 or T2 symmetry.
• At t=1.2 nm, the carriers separation is not serious, core-shelltetrapod is not apparent type II heterostructure.
• Exciton states were investigated as a function of t. For large t,the lowest exciton state has T2 symmetry, which implysnonluminescence in emission spectrum.
• Core-shell tetrapod with broken symmetry shows non-zerooscillator strength for lowest exciton state.
13
Thank you for your attention!