## Exciton states of CdTe tetrapod-shaped nanocrystals |

Optical Materials Express, Vol. 1, Issue 3, pp. 379-390 (2011)

http://dx.doi.org/10.1364/OME.1.000379

Acrobat PDF (3028 KB)

### Abstract

Excitons of CdTe tetrapod-shaped nanocrystals are theoretically analyzed. Individual electron and hole states are calculated by solving one-particle Schrödinger equation by the finite element method with the single-band effective-mass approximation and exciton states are obtained by numerical diagonalization of the configuration interaction Hamiltonian. Spatial symmetries of the exciton states are related to those of the one-particle states by group theory and verified by numerical calculation. It is shown that the lowest exciton state is an optically active *A*_{1} exciton. Optical absorption spectra are calculated and compared with available experimental data.

© 2011 OSA

## 1. Introduction

1. 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]

1. 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]

2. 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]

2. 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]

2. 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]

10. 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]

**131**, 2274–2282 (2009). [CrossRef] [PubMed]

11. 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]

15. 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]

16. 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**, 043101/1–043101/3 (2009). [CrossRef]

17. 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]

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

19. 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,” Nature **430**, 190–195 (2004). [CrossRef] [PubMed]

20. 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. **10**4646–4650 (2010). [CrossRef] [PubMed]

22. 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. B **77**, 153303 (2008). [CrossRef]

*A*

_{1}symmetry of point group

*T*, which contributes to dipole-allowed optical transition to and from the ground state. We also present absorption spectra of the tetrapods assuming several different structural parameters and compare these calculations with available experimental data.

_{d}20. 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. **10**4646–4650 (2010). [CrossRef] [PubMed]

22. 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. B **77**, 153303 (2008). [CrossRef]

## 2. Theory

*φ*(

_{e}*φ*) and

_{h}*u*(

_{e}*u*) are the envelope function and atomic wave function of the conduction band electron (heavy hole), respectively. The envelope functions are obtained by solving the time-independent Schrödinger equation assuming an isotropic effective mass for both the electron (

_{h}*V*is the confinement potential, and

*E*is the energy eigenvalues.

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

5. 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**, 224101/1–224101/3 (2005). [CrossRef]

*R*of point group

*T*. Since the Laplace operator is invariant for

_{d}*R*as well, the single-particle Hamiltonian

*ℋ*commutes with

_{e,h}*R*: Thus, the eigen functions

*φ*and

_{e}*φ*must be irreducible representations of point group

_{h}*T*. It has two one-dimensional representations (

_{d}*A*

_{1}and

*A*

_{2}), one two-dimensional representation (

*E*), and two three-dimensional representations (

*T*

_{1}and

*T*

_{2}). Their characters are listed in Table 1 [26]. In the next section, we will give the results of numerical culculations of the envelope functions by the finite element method and show that each of them is attributed to an irreducible representation in Table 1.

*e*

_{0}denotes the elementary charge,

*ε*

_{0}is the permittivity of free space, and

*ε*(= 10.6) is the dielectric constant of CdTe [25].

*R*of

*T*, the exciton Hamiltonian

_{d}*ℋ*commutes with

_{X}*R*: Thus, the exciton wave function Ψ is an irreducible representation of point group

*T*as well. Since we expand Ψ by pair states

_{d}*φ*(

_{e}**r**

*)*

_{e}*φ*(

_{h}**r**

*), it is convenient to know the symmetry of the pair states in advance. It can be obtained by the standard reduction procedure [26] and is summarized in Table 2, which will be used in the next section.*

_{h}*A*

_{1}symmetry contribute to the dipole-allowed optical transition, since the transition from the valence band to the conduction band is dipole-allowed for CdTe and the following overlap integral (

*I*

_{o}) of the electron and hole envelope functions is non-zero only for the

*A*

_{1}symmetry:

*ℋ*

_{2}) of the exciton Hamiltonian (

*ℋ*) is given by where etc. For spin-triplet pair states the matrix element of the two-body part only has the Coulomb term: The double integrals in Eq. (12) were calculated by the standard Monte Carlo method.

_{X}## 3. Results and Discussion

### 3.1. One-particle states

27. Y. Yao, T. Ochiai, T. Mano, T. Kuroda, T. Noda, N. Koguchi, and K. Sakoda, “Electronic structure of GaAs/AlGaAs quantum double rings in lateral electric field,” Chin. Opt. Lett. **7**, 882–885 (2009). [CrossRef]

*L*= 9.0 nm and

*D*= 2.2 nm are listed in Table 3. Although the effective mass and confinement potential are different between electron and hole, the symmetry of the envelope functions are the same for the two as far as the lowest twenty energy levels are concerned. In this energy range, we only have envelope functions of the

*A*

_{1}and

*T*

_{2}symmetries.

*A*

_{1}states. It is apparent that the lowest

*A*

_{1}state is localized in the core, whereas the second lowest

*A*

_{1}state is distributed equally in the four arms. These features agree with previous calculations for larger CdTe [5

5. 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**, 224101/1–224101/3 (2005). [CrossRef]

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

22. 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. B **77**, 153303 (2008). [CrossRef]

_{1}to ϕ

_{4}, then the second lowest

*A*

_{1}state is expressed by the following symmetric combination of ϕ’s: On the other hand, there are three more independent combinations of the four ϕ’s that give the basis functions of the

*T*

_{2}state: It can be confirmed that operation of any

*R*of

*T*on any one of these three basis functions results in their linear transformation and the trace of the transformation matrix has the property of the

_{d}*T*

_{2}representation.

*A*

_{1}and

*T*

_{2}energy levels listed in Table 3, they have the similar property. The only difference is the number of nodes of the envelope function along the cylinder axis. That is, whereas either the second lowest

*A*

_{1}or the lowest

*T*

_{2}envelope function does not have a node along the cylinder axis, envelope functions of higher energy levels have an increasing number of nodes.

### 3.2. Exciton states

*A*

_{1}or

*T*

_{2}symmetry.

*ℋ*matrix evaluated with |

_{X}*ij*(

*s*)〉 or |

*ij*(

*t*)〉. To check the convergence of the calculation, we examined the variation of energy eigenvalues with respect to the number of basis pair functions to calculate the

*ℋ*matrix elements. As shown in Fig. 3, the convergence is fast, and 400 pair states give sufficiently converged results.

_{X}*D*and

*L*according to observation by electron microscope in Refs. [10

10. 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]

15. 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]

*A*

_{1}symmetry, and so it is optically active. The

*D*dependence is much stronger than the

*L*dependence as far as the analyzed parameter ranges are concerned, which agrees with the results of previous experiments that did not show apparent dependence of absorption peaks on

*L*[10

10. 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]

15. 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]

*A*

_{1}or

*T*

_{2}, which agree well with the group theoretical prediction given in Table 4.

*L*= 9.0 nm and

*D*= 2.2 nm in more detail. The energy eigenvalue of the lowest spin-singlet

*A*

_{1}exciton is 2.234 eV, which mainly (92 %) consists of the lowest

*A*

_{1}electron-hole pair listed in Table 4. The exciton binding energy is 11 meV, if we define it by the energy difference between the absence and presence of the Coulomb attraction in the

*A*

_{1}state. The lowest

*T*

_{2}exciton at 2.254 eV mainly consists of the lowest two

*T*

_{2}electron-hole pairs at 2.286 (86 %) and 2.307 eV (12 %) in Table 4. Since its overlap integral (

*I*

_{o}) is equal to zero by symmetry, it does not contribute to optical transition.

*A*

_{1}symmetry. For the case of

*L*= 9.0 nm and

*D*= 2.2 nm, it mainly (96 %) consists of the lowest

*A*

_{1}electron-hole pair. Its binding energy is 98 meV, so it is much more stabilized than the lowest singlet exciton. The lowest

*T*

_{2}spin-triplet exciton at 2.231 eV mainly consists of the lowest three

*T*

_{2}electron-hole pairs at 2.286 eV (55 %), 2.307 eV (32 %), and 2.341 eV (11 %). Note that optical transition between these spin-triplet excitons and the ground state is, of course, spin-forbidden.

*A*

_{1}spin-triplet exciton. The averaged value of 1/|

**r**

_{1}–

**r**

_{2}| in Eq. (12) is 0.67 × 10

^{−9}[1/m] for the lowest

*A*

_{1}electron-hole pair. If we regard this value as the inverse of the averaged electron-hole distance, the latter is 1.5 nm. Since the wave functions of both the lowest electron and hole states are localized in the core region whose diameter is 2.2 nm, the calculated value of 1.5 nm looks reasonable. The Coulomb matrix element corresponding to this averaged distance is −100 meV. As we mentioned before, the lowest

*A*

_{1}spin-triplet exciton mainly (96 %) consists of the lowest

*A*

_{1}electron-hole pair. So, its binding energy of 98 meV, which is close to 100 meV, is again very reasonable. On the other hand, in the case of the lowest

*A*

_{1}spin-singlet exciton, we have to take into consideration the exchange term whose sign is opposite to the Coulomb term. Thus they nearly cancel out and give a moderate binding energy of 11 meV.

*D*values. The blue shift due to the quantum size effect is clearly observed. In each spectrum, the longer wavelength peak mainly consists of the lowest and the second lowest

*A*

_{1}excitons, whereas the shorter wavelength peak mainly consists of the eighth lowest

*A*

_{1}exciton. Contributions from other

*A*

_{1}excitons are relatively small.

**19**, 126–127 (2009). [CrossRef]

**19**, 128–130 (2009). [CrossRef]

**19**, 126–127 (2009). [CrossRef]

**19**, 128–130 (2009). [CrossRef]

*D*= 2.2 ± 0.3 nm and

*L*= 9.0 ± 0.7 nm, which is appreciably larger than the calculated value. The reason is not necessarily clear, but the specimen may have suffered from aggregation of tetrapods. As for the second longest peak found by the calculation, they were not observed by the experiments presumably due to large inhomogenious broadening of the absorption bands. However, such peaks are frequently observed for larger tetrapods with smaller size distribution. Their detailed comparizon remains to be examined in future works.

*L*values. Since the exciton energy does not depend strongly on

*L*as far as the analyzed parameter range is concerned, the three spectra in Fig. 7 are not so different from each other. The shorter wavelength peak shows a small normal blue shift with decreasing

*L*, whereas the longer wavelength peak shows a slight red shift. The latter, which may look strange at first glance, is actually caused by increased absorption strength of the lowest

*A*

_{1}exciton, which results in the red shift of the center-of-mass of the longer wavelength peak.

*L*, we expect both the larger shift of the absorption peaks, which is caused by the energy shift of one-particle states due to the quantum size effect, and the larger change in the peak height, which is caused by the change in the overlap integral of the electron and hole wave functions. However, although the exciton energy was calculated within a variation of only 15 % of

*L*in the present study, we examined the electron and hole state energies for

*L*= 6 and 12 nm (67 % variation around

*L*= 9 nm) and found only minor variation of energy for the first

*A*

_{1}state (2.3 meV for electron and 0.01 meV for hole) and little bit larger variation for the first

*T*

_{2}state (54 meV for electron and 12 meV for hole). As electron and hole energies constitute the main part of the exciton energy, we may expect the lengthening effect on the low-energy exciton states to be small in this range of

*L*.

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

**77**, 153303 (2008). [CrossRef]

## 4. Conclusion

*A*

_{1}exciton. The culculated absorption spectra showed a good agreement with previous experimental results. Thus we clarified the size effect of the energy bandgap of CdTe tetrapods by this systematic theoretical study.

## Acknowledgments

## References and links

1. | 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. |

2. | 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. |

3. | L. Manna, D. J. Milliron, A. Meisel, E. C. Scher, and A. P. Alivisatos, “Controlled growth of tetrapod-branched inorganic nanocrystals,” Nature Mat. |

4. | M. De Giorgi, D. Tarì, L. Manna, R. Krahne, and R. Cingolani, “Optical properties of colloidal nanocrystal spheres and tetrapods,” Microelectron. J. |

5. | 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. |

6. | S. Malkmus, S. Kudera, L. Manna, W. J. Parak, and M. Braun, “Electron-hole dynamics in CdTe tetrapods,” J. Phys. Chem. B |

7. | 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. |

8. | 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. |

9. | 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 Nano |

10. | R. B. Vasiliev, D. N. Dirin, and A. M. Gaskov, “Temperature effect on the growth of colloidal CdTe nanotetrapods,” Mendeleev Commun. |

11. | 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. |

12. | 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. |

13. | 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. |

14. | 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. A |

15. | 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. |

16. | 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. |

17. | 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. |

18. | J.-B. Li and L.-W. Wang, “Shape effects on electronic states of nanocrystals,” Nano Lett. |

19. | 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,” Nature |

20. | 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. |

21. | J. Müller, J. M. Lupton, P. G. Lagoudakis, F. Schindler, R. Koeppe, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Wave function engineering in elongated semiconductor nanocrystals with heterogeneous carrier confinement,” Nano Lett. |

22. | 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. B |

23. | F. Bechstedt and R. Enderlein, |

24. | S.-H. Wei and S. B. Zhang, “Structure stability and carrier localization in CdX (X=S, Se, Te) semiconductors”, Phys. Rev. B |

25. | S. Adachi |

26. | T. Inui, Y. Tanabe, and Y. Onodera, |

27. | Y. Yao, T. Ochiai, T. Mano, T. Kuroda, T. Noda, N. Koguchi, and K. Sakoda, “Electronic structure of GaAs/AlGaAs quantum double rings in lateral electric field,” Chin. Opt. Lett. |

**OCIS Codes**

(160.6000) Materials : Semiconductor materials

(160.4236) Materials : Nanomaterials

**ToC Category:**

Semiconductors

**History**

Original Manuscript: April 26, 2011

Revised Manuscript: May 20, 2011

Manuscript Accepted: May 30, 2011

Published: June 10, 2011

**Citation**

Kazuaki Sakoda, Yuanzhao Yao, Takashi Kuroda, Dmitry N. Dirin, and Roman B. Vasiliev, "Exciton states of CdTe tetrapod-shaped nanocrystals," Opt. Mater. Express **1**, 379-390 (2011)

http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-1-3-379

Sort: Year | Journal | Reset

### References

- 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]
- 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]
- L. Manna, D. J. Milliron, A. Meisel, E. C. Scher, and A. P. Alivisatos, “Controlled growth of tetrapod-branched inorganic nanocrystals,” Nature Mat. 2, 382–385 (2003). [CrossRef]
- M. De Giorgi, D. Tarì, L. Manna, R. Krahne, and R. Cingolani, “Optical properties of colloidal nanocrystal spheres and tetrapods,” Microelectron. J. 36552–554 (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, 224101/1–224101/3 (2005). [CrossRef]
- S. Malkmus, S. Kudera, L. Manna, W. J. Parak, and M. Braun, “Electron-hole dynamics in CdTe tetrapods,” J. Phys. Chem. B 110, 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, 094104/1–094104/3 (2006). [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, 191905/1–191905/3 (2008). [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 Nano 4, 2043–2050 (2010). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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. A 373, 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, 043101/1–043101/3 (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]
- J.-B. Li and L.-W. Wang, “Shape effects on electronic states of nanocrystals,” Nano Lett. 3, 1357–1363 (2003). [CrossRef]
- 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,” Nature 430, 190–195 (2004). [CrossRef] [PubMed]
- 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]
- J. Müller, J. M. Lupton, P. G. Lagoudakis, F. Schindler, R. Koeppe, A. L. Rogach, J. Feldmann, D. V. Talapin, and H. Weller, “Wave function engineering in elongated semiconductor nanocrystals with heterogeneous carrier confinement,” Nano Lett. 52044–2049 (2005). [CrossRef] [PubMed]
- 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. B 77, 153303 (2008). [CrossRef]
- F. Bechstedt and R. Enderlein, Semiconductor Surfaces and Interfaces: Their Atomic and Electronic Structures (Akademie-Verlag, Berlin, 1988).
- S.-H. Wei and S. B. Zhang, “Structure stability and carrier localization in CdX (X=S, Se, Te) semiconductors”, Phys. Rev. B 62, 6944–6947 (2000). [CrossRef]
- S. AdachiProperties of Group-IV, III–V and II–VI Semiconductors (Wiley, Chichester, 2005) P.218.
- T. Inui, Y. Tanabe, and Y. Onodera, Group theory and Its Applications in Physics (Springer-Verlag, Berlin1990).
- Y. Yao, T. Ochiai, T. Mano, T. Kuroda, T. Noda, N. Koguchi, and K. Sakoda, “Electronic structure of GaAs/AlGaAs quantum double rings in lateral electric field,” Chin. Opt. Lett. 7, 882–885 (2009). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.