Abstract

Excitons of tetrapod-shaped nanocrystals made of CdTe, CdS, CdSe, ZnTe, and ZnSe were investigated systematically by numerical diagonalization of configuration interaction Hamiltonian based on single-particle states obtained by finite-element method. Both one-particle and exciton wave functions have high spatial symmetries due to the tetrahedral symmetry of the nanocrystals, which leads to a distinct selection rule for optical absorption and emission. The absorption spectra thus calculated were compared with available experimental data and good agreement was found.

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (2)

E. J. Tyrrell and J. M. Smith, “Effective mass modeling of excitons in type-II quantum dot heterostructures,” Phys. Rev. B84, 165328 (2011).
[CrossRef]

K. Sakoda, Y. Yao, T. Kuroda, D. N. Dirin, and R. B. Vasiliev, “Exciton states of CdTe tetrapod-shaped nanocrystals,” Opt. Mater. Express1, 379–390 (2011).
[CrossRef]

2010 (6)

A. A. Lutich, C. Mauser, E. Da Como, J. Huang, A. Vaneski, D. V. Talapin, A. L. Rogach, and J. Feldmann, “Multiexcitonic dual emission in CdSe/CdS tetrapods and nanorods,” Nano Lett.104646–4650 (2010).
[CrossRef] [PubMed]

C. Mauser, E. D. Como, J. Baldauf, A. L. Rogach, J. Huang, D. V. Talapin, and J. Feldmann, “Spatio-temporal dynamics of coupled electrons and holes in nanosize CdSe-CdS semiconductor tetrapods,” Phys. Rev. B82, 081306/1–081306/4(2010).
[CrossRef]

W. Y. Ko, H. G. Bagaria, S. Asokan, K. Lin, and M. S. Wong, “CdSe tetrapod synthesis using cetyltrimethylammonium bromide and heat transfer fluids,”J. Mater. Chem.20, 2474–2478 (2010).
[CrossRef]

M. D. Goodman, L. Zhao, K. A. DeRocher, J. Wang, S. K. Mallapragada, and Z. Lin, “Self-assembly of CdTe tetrapods into network monolayers at the air/water interface,” ACS Nano4, 2043–2050 (2010).
[CrossRef] [PubMed]

F. Jiang, Y. Li, M. Ye, L. Fan, Y. Ding, and Y. Li, “Ligand-tuned shape control, oriented assembly, and electrochemical characterization of colloidal ZnTe nanocrystals,” Chem. Mater.22, 4632–4641 (2010).
[CrossRef]

H. Shen, J. Niu, H. Wang, X. Li, L. Li, and X. Chen, “Size-and shape-controlled synthesis of ZnSe nanocrystals using SeO2as selenium precursor,” Dalton Trans.39, 11432–11438 (2010).
[CrossRef] [PubMed]

2009 (7)

R. B. Vasiliev, D. N. Dirin, and A. M. Gaskov, “Temperature effect on the growth of colloidal CdTe nanotetrapods,” Mendeleev Commun.19, 126–127 (2009).
[CrossRef]

A. Fiore, R. Mastria, M. G. Lupo, G. Lanzani, C. Giannini, E. Carlino, G. Morello, M. De Giorgi, Y. Li, R. Cingolani, and L. Manna, “Tetrapod-shaped colloidal nanocrystals of II–VI semiconductors prepared by seeded growth,” J. Am. Chem. Soc.131, 2274–2282 (2009).
[CrossRef] [PubMed]

C. L. Choi, K. J. Koski, S. Sivasankar, and A. P. Alivisatos, “Strain-dependent photoluminescence behavior of CdSe/CdS nanocrystals with spherical, linear, and branched topologies,” Nano Lett.9, 3544–3549 (2009).
[CrossRef] [PubMed]

A. G. Vitukhnovsky, A. S. Shul’ga, S. A. Ambrozevich, E. M. Khokhlov, R. B. Vasiliev, D. N. Dirin, and V. I. Yudson, “Effect of branching of tetrapod-shaped CdTe/CdSe nanocrystal heterostructures on their luminescence,” Phys. Lett. A373, 2287–2290 (2009).
[CrossRef]

R. B. Vasiliev, D. N. Dirin, M. S. Sokolikova, S. G. Dorofeev, A. G. Vitukhnovskyc, and A. M. Gaskovb, “Growth of near-IR luminescent colloidal CdTe/CdS nanoheterostructures based on CdTe tetrapods,” Mendeleev Commun.19, 128–130 (2009).
[CrossRef]

Y. Li, R. Mastria, K. Li, A. Fiore, Y. Wang, R. Cingolani, L. Manna, and G. Gigli, “Improved photovoltaic performance of bilayer heterojunction photovoltaic cells by triplet materials and tetrapod-shaped colloidal nanocrystals doping,” Appl. Phys. Lett.95, 043101 (2009).
[CrossRef]

Y. Li, R. Mastria, A. Fiore, C. Nobile, L. Yin, M. Biasiucci, G. Cheng, A. M. Cucolo, R. Cingolani, L. Manna, and G. Gigli, “Improved photovoltaic performance of heterostructured tetrapod-shaped CdSe/CdTe nanocrystals using C60 interlayer,” Adv. Mater.21, 4461–4466 (2009).
[CrossRef]

2008 (3)

C. Mauser, T. Limmer, E. Da Como, K. Becker, A. L. Rogach, J. Feldmann, and D. V. Talapin, “Anisotropic optical emission of single CdSe/CdS tetrapod heterostructures: Evidence for a wavefunction symmetry breaking,” Phys. Rev. B77, 153303 (2008).
[CrossRef]

J. W. Cho, H. S. Kim, Y. J. Kim, S. Y. Jang, J. Park, J. Kim, Y. Kim, and E. H. Cha, “Phase-tuned tetrapod-shaped CdTe nanocrystals by ligand effect,” Chem. Mater.20, 5600–5609 (2008).
[CrossRef]

G. Morello, D. Tarì, L. Carbone, L. Manna, R. Cingolani, and M. De Giorgi, “Radiative recombination dynamics in tetrapod-shaped CdTe nanocrystals: Evidence for a photoinduced screening of the internal electric field,” Appl. Phys. Lett.92, 191905 (2008).
[CrossRef]

2007 (3)

D. V. Talapin, J. H. Nelson, E. V. Shevchenko, S. Aloni, B. Sadtler, and A. P. Alivisatos, “Seeded growth of highly luminescent CdSe/CdS nanoheterostructures with rod and tetrapod morphologies,” Nano Lett.7, 2951–2959 (2007).
[CrossRef] [PubMed]

S. Asokan, K. M. Krueger, V. L. Colvin, and M. S. Wong, “Shape-controlled synthesis of CdSe tetrapods using cationic surfactant ligands,” Small3, 1164–1169 (2007).
[CrossRef] [PubMed]

K. Yong, Y. Sahoo, M. T. Swihart, and P. N. Prasad, “Shape control of CdS nanocrystals in one-pot synthesis,” J. Phys. Chem. C111, 2447–2458 (2007).
[CrossRef]

2006 (4)

S. Malkmus, S. Kudera, L. Manna, W. J. Parak, and M. Braun, “Electron-hole dynamics in CdTe tetrapods,” J. Phys. Chem. B110, 17334–17338 (2006).
[CrossRef] [PubMed]

D. Tarì, M. De Giorgi, P. P. Pompa, L. Carbone, L. Manna, S. Kudera, and R. Cingolani, “Exciton transitions in tetrapod-shaped CdTe nanocrystals investigated by photomodulated transmittance spectroscopy,” Appl. Phys. Lett.89, 094104 (2006).
[CrossRef]

Y. Zhou, Y. Li, H. Zhong, J. Hou, Y. Ding, C. Yang, and Y. Li, “Hybrid nanocrystal/polymer solar cells based on tetrapod-shaped CdSexTe1−xnanocrystals,” Nanotechnology17, 4041–4047 (2006).
[CrossRef] [PubMed]

I. Gur, N. A. Fromer, and A. P. Alivisatos, “Controlled assembly of hybrid bulk-heterojunction solar cells by sequential deposition,” J. Phys. Chem. B110, 25543–25546 (2006).
[CrossRef] [PubMed]

2005 (6)

Y. Cui, U. Banin, M. T. Bjork, and A. P. Alivisatos, “Electrical transport through a single nanoscale semiconductor branch point,” Nano Lett.5, 1519–1523 (2005).
[CrossRef]

L. Wang, “Charging effect in a CdSe nanotetrapod,” J. Phys. Chem. B109, 23330–23335 (2005).
[CrossRef] [PubMed]

P. Peng, D. J. Milliron, S. M. Hughes, J. C. Johnson, A. P. Alivisatos, and R. J. Saykally, “Femtosecond spectroscopy of carrier relaxation dynamics in type II CdSe/CdTe tetrapod heteronanostructures,” Nano Lett.5, 1809–1813 (2005).
[CrossRef] [PubMed]

M. De Giorgi, D. Tarì, L. Manna, R. Krahne, and R. Cingolani, “Optical properties of colloidal nanocrystal spheres and tetrapods,” Microelectron. J.36, 552–554 (2005).
[CrossRef]

D. Tarì, M. De Giorgi, F. Della Sala, L. Carbone, R. Krahne, L. Manna, R. Cingolani, S. Kudera, and W. J. Parak, “Optical properties of tetrapod-shaped CdTe nanocrystals,” Appl. Phys. Lett.87, 224101 (2005).
[CrossRef]

Q. Pang, L. Zhao, Y. Cai, D. P. Nguyen, N. Regnault, and N. Wang, “CdSe nano-tetrapods: controllable synthesis, structure analysis, and electronic and optical properties,” Chem. Mater.17, 5263–5267 (2005).
[CrossRef]

2004 (1)

D. J. Milliron, S. M. Hughes, Y. Cui, L. Manna, J. Li, L.-W. Wang, and P. Alivisatos, “Colloidal nanocrystal heterostructures with linear and branched topology,” Nature430, 190–195 (2004).
[CrossRef] [PubMed]

2003 (3)

L. Manna, D. J. Milliron, A. Meisel, E. C. Scher, and A. P. Alivisatos, “Controlled growth of tetrapod-branched inorganic nanocrystals,” Nature Mater.2, 382–385 (2003).
[CrossRef]

B. Sun, E. Marx, and N. C. Greenham, “Photovoltaic devices using blends of branched CdSe nanoparticles and conjugated polymers,” Nano. Lett.3, 961–963 (2003).
[CrossRef]

J.-B. Li and L.-W. Wang, “Shape effects on electronic states of nanocrystals,” Nano Lett.3, 1357–1363 (2003).
[CrossRef]

2000 (2)

S. H. Wei and S. B. Zhang, “Structure stability and carrier localization in CdX(X= S, Se, Te) semiconductors,” Phys. Rev. B62, 6944–6947 (2000).
[CrossRef]

L. Manna, E. C. Scher, and A. P. Alivisatos, “Synthesis of soluble and processable rod-, arrow-, teardrop-, and tetrapod-shaped CdSe nanocrystals,” J. Am. Chem. Soc.122, 12700–12706 (2000).
[CrossRef]

1999 (1)

R. Pässler, E. Griebl, H. Riepl, G. Lautner, S. Bauer, H. Preis, W. Gebhardt, B. Buda, D. J. As, D. Schlkora, K. Lischka, K. Papagelis, and S. Ves, “Temperature dependence of exciton peak energies in ZnS, ZnSe, and ZnTe,” J. Appl. Phys.86, 4403–4411 (1999).
[CrossRef]

1997 (1)

F. Long, W. E. Hagston, P. Harrison, and T. Stirner, “The structural dependence of the effective mass and Luttinger parameters in semiconductor quantum wells,” J. Appl. Phys.82, 3414–3421 (1997).
[CrossRef]

1995 (1)

S. Ninomiya and S. Adachi, “Optical properties of cubic and hexagonal CdSe,” J. Appl. Phys.78, 4681–4689 (1995).
[CrossRef]

1984 (1)

L. E. Brus, “Electron-electron and electron-hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state,” J. Chem. Phys.80, 4403–4409 (1984).
[CrossRef]

1979 (1)

B. Clerjaud, A. Gelineau, D. Galland, and K. Saminadayar, “Cyclotron resonance from photoexcited electrons in ZnTe,” Phys. Rev. B19, 2056–2058 (1979).
[CrossRef]

1977 (1)

M. Sondergeld, “Two-photon absorption by envelope-hole coupled exciton states in Cubic ZnSe,” Phys. Status Solidi B81, 253–262 (1977).
[CrossRef]

1971 (1)

R. Dalven, “Calculation of effective masses in cubic CdS and CdSe,” Phys. Status Solidi B48, K23–K26 (1971).
[CrossRef]

1967 (1)

R. K. Swank, “Surface properties of II–VI compounds,” Phys. Rev.153, 844–849 (1967).
[CrossRef]

1965 (1)

M. Cardona, M. Weinstein, and G. A. Wolff, “Ultraviolet reflection spectrum of cubic CdS,” Phys. Rev.140, A633–A637 (1965).
[CrossRef]

1964 (1)

D. Marple, “Electron effective mass in ZnSe,” J. Appl. Phys.35, 1879–1882 (1964).
[CrossRef]

1963 (1)

M. Aven and B. Segall, “Carrier mobility and shallow impurity states in ZnSe and ZnTe,” Phys. Rev.130, 81–91 (1963).
[CrossRef]

1962 (1)

R. G. Wheeler and J. O. Dimmock, “Exciton structure and Zeeman effects in cadmium selenide,” Phys. Rev.125, 1805–1815 (1962).
[CrossRef]

1961 (2)

J. J. Hopfield and D. G. Thomas, “Fine structure and magneto-optic effects in the exciton spectrum of cadmium sulfide,” Phys. Rev.122, 35–52 (1961).
[CrossRef]

M. Cardona, “Fundamental reflectivity spectrum of semiconductors with zinc-blende structure,” J. Appl. Phys.32, 2151–2155 (1961).
[CrossRef]

Adachi, S.

S. Ninomiya and S. Adachi, “Optical properties of cubic and hexagonal CdSe,” J. Appl. Phys.78, 4681–4689 (1995).
[CrossRef]

S. Adachi, Properties of Group-IV, III–V and II–VI Semiconductors(Wiley, 2005).

Alivisatos, A. P.

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[CrossRef] [PubMed]

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Nanotechnology (1)

Y. Zhou, Y. Li, H. Zhong, J. Hou, Y. Ding, C. Yang, and Y. Li, “Hybrid nanocrystal/polymer solar cells based on tetrapod-shaped CdSexTe1−xnanocrystals,” Nanotechnology17, 4041–4047 (2006).
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Figures (6)

Fig. 1
Fig. 1

(a) Structure and (b) band diagram of quantum tetrapods. We assume the perfect tetrahedral symmetry for their structure, which consists of a spherical central core and four cylindrical arms. We denote the diameter and length of the arms by D and L, respectively. The diameter of the central core is assumed to be the same as D. In the band diagram, we generally assume different energy values for the core and arm, since early experimental studies revealed that the core had a zinc blende structure whereas the arms had a wurtzite structure. The confinement potential height of the conduction band is assumed to be the same as the electron affinity (χe), while an infinite potential barrier is assumed for the valence band. The band gap is denoted by Eg and the band offsets between the arm and core are denoted by ΔECB and ΔEVB for the conduction and valence bands, respectively.

Fig. 2
Fig. 2

The D dependence of the spin-singlet exciton energy of quantum tetrapods made of (a) CdTe, (b) CdS, (c) CdSe, (d) ZnTe, and (e) ZnSe. (f) Spin-triplet exciton energy of the CdTe quantum tetrapod.

Fig. 3
Fig. 3

The D dependence of the binding energy of the lowest spin-triplet exciton.

Fig. 4
Fig. 4

The D dependence of the absorption spectrum of the CdTe tetrapod.

Fig. 5
Fig. 5

The material dependence of absorption spectra. D was assumed to be 3 nm.

Fig. 6
Fig. 6

(a) The D dependence of the peak energy of the lowest (black square) and second lowest (white square) absorption bands calculated for CdTe quantum tetrapods and the lowest absorption peak energy observed in Ref. [14] (exp1, circle), Ref. [9] (exp2, triangle), and Ref. [8] (exp3, diamond). (b) The peak energy of the lowest absorption band of CdSe quantum tetrapods: calculation (black square) and observation in Ref. [5] (exp1, circle), Ref. [3] (exp2, triangle), and Ref. [4] (exp3, diamond). (c) The lowest absorption peak energy calculated for CdS, ZnTe, and ZnSe quantum tetrapods (square) and observed for ZnSe (Ref. [17], circle).

Tables (1)

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Table 1 Parameters used in the present calculation*

Equations (16)

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ψ e ( r e ) = φ e ( r e ) u e ( r e ) ,
ψ h ( r h ) = φ h ( r h ) u h ( r h ) ,
e φ e ( r e ) { h ¯ 2 Δ e 2 m e * + V e ( r e ) } φ e ( r e ) = E e φ e ( r e ) ,
h φ h ( r h ) { h ¯ 2 Δ h 2 m h * + V h ( r h ) } φ h ( r h ) = E h φ h ( r h ) ,
R e , h R 1 = e , h ( R T d ) .
X Ψ ( r e , r h ) ( e + h e 0 2 4 π ε 0 ε | r e r h | ) Ψ ( r e , r h ) = E X Ψ ( r e , r h ) ,
Ψ ( r e , r h ) = i , j a i j φ e ( i ) ( r e ) φ h ( j ) ( r h ) ,
R X R 1 = X ( R T d ) .
I o = d r φ e * ( r ) φ h ( r ) .
k l ( s ) | 2 | i j ( s ) = k j | H 2 | i l 2 j k | H 2 | i l ,
k j | H 2 | i l = d r 1 d r 2 φ h ( j ) * ( r 2 ) φ e ( k ) * ( r 1 ) e 0 2 ε 0 ε | r 1 r 2 | φ e ( i ) ( r 1 ) φ h ( l ) ( r 2 ) ,
k l ( t ) | 2 | i j ( t ) = k j | H 2 | i l .
ϕ A 1 = 1 2 ( ϕ 1 + ϕ 2 + ϕ 3 + ϕ 4 ) .
ϕ T 2 ( 1 ) = 1 2 ( ϕ 1 + ϕ 2 ϕ 3 ϕ 4 ) ,
ϕ T 2 ( 2 ) = 1 2 ( ϕ 1 ϕ 2 + ϕ 3 ϕ 4 ) ,
ϕ T 2 ( 3 ) = 1 2 ( ϕ 1 ϕ 2 ϕ 3 + ϕ 4 ) .

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