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Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 1, Iss. 3 — Jul. 1, 2011
  • pp: 379–390
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Exciton states of CdTe tetrapod-shaped nanocrystals

Kazuaki Sakoda, Yuanzhao Yao, Takashi Kuroda, Dmitry N. Dirin, and Roman B. Vasiliev  »View Author Affiliations


Optical Materials Express, Vol. 1, Issue 3, pp. 379-390 (2011)
http://dx.doi.org/10.1364/OME.1.000379


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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 A1 exciton. Optical absorption spectra are calculated and compared with available experimental data.

© 2011 OSA

1. Introduction

Since the first report on their chemical synthesis in 2000 [1

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]

], tetrapod-shaped nanocrystals made of II–VI semiconductors have attracted a great deal of attention. Studies on tetrapods made of CdSe [1

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

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]

], CdS [2

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]

], CdTe [2

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

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]

], ZnTe [2

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]

], and their core/shell combinations [11

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

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]

] have been reported. In addition to these synthesis and characterization studies, application to photovoltaic cells, for example, has also been reported [16

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

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]

]. As for theoretical analysis, calculations of one-particle states by the semiempirical pseudopotential method [18

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

, 19

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]

] and exciton states by the Hartree approximation [20

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. 104646–4650 (2010). [CrossRef] [PubMed]

22

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]

] were reported.

Similar to other semiconductor nanostructures, energy levels of electrons and holes in tetrapod-shaped nanocrystals are quantized due to the three-dimensional confinement of their wave functions, and so the tetrapods have discrete absorption and emission bands with an apparent quantum size effect; there is a blue shift of the bands as their size decreases, although the discreteness of the absorption bands in high frequency ranges is often hidden by a large inhomogeneous broadening due to their size distribution. Because of these quantum-confinement properties, we call the tetrapod-shaped nanocrystals “quantum tetrapods” hereafter.

The optical properties of the quantum tetrapods also depend on their shape. In contrast to quantum dots with more or less spherical shapes, ideal quantum tetrapods literally have the shape of a tetrapod. Because the optical properties of quantum nanostructures are crucially influenced by the nature of electron and hole wave functions, which in turn strongly depend on the structural symmetry, it is of fundamental importance to investigate the consequence of the unique tetrapod symmetry.

In this paper, we report on the calculation of their exciton states that are responsible for the absorption and emission bands assuming the ideal tetrahedral symmetry. In order to concentrate on the consequence of their structural symmetry, we deal with the CdTe tetrapod, which is one of the simplest and most investigated structures, and apply the single-band effective-mass approximation for both conduction-band electrons and valence-band (heavy) holes. CdTe has the narrowest energy bandgap (1.5 eV) in the series of cadmium chalcogenides, which is important for photovoltaic applications. We first calculate the one-particle energy levels by the finite element method. Next, we evaluate the matrix elements of the Coulomb and exchange interactions for the electron-hole pair states, and thus obtain the configuration interaction Hamiltonian. We numerically diagonalize it and obtain the wave functions and energy eigenvalues of excitons. We show that the lowest spin-singlet exciton level is of the A 1 symmetry of point group Td, 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.

To the best of our knowledge, this is the first calculation of exciton states of quantum tetrapods by the rigorous diagonalization of the configuration interaction Hamiltonian. This method is superior to the Hartree approximation [20

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. 104646–4650 (2010). [CrossRef] [PubMed]

22

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]

] if sufficiently converged eigenvalues are obtained, because the latter does not take into consideration the full correlation energy.

2. Theory

We deal with the problem of excitons in the CdTe tetrapod by single-band effective-mass approximation. We assume the following forms for the spatial part of electron and hole wave functions:
ψe(re)=φe(re)ue(re),
(1)
ψh(rh)=φh(rh)uh(rh),
(2)
where φe (φh) and ue (uh) 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 ( me*) and heavy hole ( mh*):
eφe(re){h¯2Δe2me*+Ve(re)}φe(re)=Eeφe(re),
(3)
hφh(rh){h¯2Δh2mh*+Vh(rh)}φh(rh)=Ehφh(rh),
(4)
where Δ is the Laplace operator, V is the confinement potential, and E is the energy eigenvalues.

The structural parameters assumed in this study are summerized in Fig. 1. Early experimental studies [3

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

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]

] showed that the four arms of the CdTe tetrapod have a wurzite (WZ) crystal structure, whereas the central region that connects the four arms, which we call the “core” hereafter, has a zinc blende (ZB) structure. In the present study, we follow these observations and assume the band parameters shown in Fig. 1(b).

Fig. 1 (a) Structure of the CdTe tetrapod that consists of four cylindrical arms, which has the wurzite crystal structure, and spherical central region, which has the zinc blende structure. The diameter and length of the arms are denoted by D and L. The diameter of the central region is assumed to be the same as the arms. Three values of D (1.9, 2.2, and 2.5 nm) and L (8.3, 9.0, and 9.7 nm) are used in the numerical calculation. (b) Confinement potential of electron and hole. We assume that the electrons are confined by a potential barrier whose height is equal to the electron affinity of CdTe whereas the holes are confined by an infinite potential barrier [5]. −4.18 eV is assumed for the ZB CdTe electron affinity, which was derived from the XPS experiment [23], whereas 1.5 eV is assumed for the ZB CdTe bandgap [5]. As for the band offset, we use 65 meV for the conduction band and 18 meV for the valence band, which were obtained by theoretical calculation [24]. For effective masses of electron and heavy hole, we assumed me*=0.11×m0 and mh*=0.69×m0, where m 0 is the genuin electron mass. [25]

Table 1. Character table of point group Td. The standard notations for symmetry operations are used: E for the identity operation, Cn for rotation by 360/n degrees, I for inversion, and σd for mirror reflection about a diagonal plane. The numbers in front of the symbols of the symmetry operations denote the number of conjugate operations.

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We calculate the exciton wave functions by exact diagonalization of the configuration interaction Hamiltonian. We solve the following two-body Schrödinger equation based on the expansion of the total wave function Ψ by the linear combination of pair states of electron and hole envelope functions:
XΨ(re,rh)(e+he024πɛ0ɛ|rerh|)Ψ(re,rh)=EXΨ(re,rh),
(6)
Ψ(re,rh)=i,jaijφe(i)(re)φh(j)(rh),
(7)
where 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

25. S. AdachiProperties of Group-IV, III–V and II–VI Semiconductors (Wiley, Chichester, 2005) P.218.

].

Table 2. Symmetry of the electron-hole pair state. The left column shows the individual symmetry of electron and hole envelope functions. The middle column is the character of the pair states. The right column shows the symmetry of the pair states obtained by the reduction procedure.

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It is worth noting that only pair states of the 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:
Io=drφe*(r)φh(r).
(9)

To evaluate the Coulomb term, we should take into consideration the exchange interaction for different spin configurations. For spin-singlet pair states, whose total wave function may be denoted by
|ij(s)=12{|φe(i)φh(j)|ϕe(i)φh(j)},
(10)
the matrix element of the two-body part ( 2) of the exciton Hamiltonian (X) is given by
kl(s)|2|ij(s)=kj|2|il2jk|2|il,
(11)
where
kj|2|il=dr1dr2φh(j)*(r2)φe(k)*(r1)e02ɛ0ɛ|r1r2|φe(i)(r1)φh(l)(r2),
(12)
etc. For spin-triplet pair states
|ij(t)={|φe(i)φh(j),12{|φe(i)φh(j)+|φe(i)φh(j)},|φe(i)φh(j),
(13)
the matrix element of the two-body part only has the Coulomb term:
kl(t)|2|ij(t)=kj|2|il.
(14)
The double integrals in Eq. (12) were calculated by the standard Monte Carlo method.

3. Results and Discussion

3.1. One-particle states

We solved one-particle Schrödinger equations given in Eqs. (3) and (4) by the finite element method with the commercial software COMSOL [27

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]

]. As an example, energy eigenvalues and wave function symmetries for the case of 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.

Table 3. The lowest twenty energy levels of a confined electron and hole in the tetrapod with L = 9.0 nm and D = 2.2 nm. The origin of the energy eigenvalues of the electron (hole) is the bottom of the conduction band (top of the valence band) in the core of the tetrapod with the zinc blende crystal structure.

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Fig. 2 Envelope functions of (a) the lowest and (b) the second lowest A 1 states of electron.

If we regard the localized distributions of the electron in each arm as independent wave functions and denote them by ϕ1 to ϕ4, then the second lowest A 1 state is expressed by the following symmetric combination of ϕ’s:
ϕA1=12(ϕ1+ϕ2+ϕ3+ϕ4).
(15)
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:
ϕT2(1)=12(ϕ1+ϕ2ϕ3ϕ4),
(16)
ϕT2(2)=12(ϕ1ϕ2+ϕ3ϕ4),
(17)
ϕT2(3)=12(ϕ1ϕ2ϕ3+ϕ4).
(18)
It can be confirmed that operation of any R of Td 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 T 2 representation.

For higher 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

Before showing numerical results for the exciton states, let us first give a qualitative prediction by the group theory. When we neglect the Coulomb potential, we have energies and symmetries of excitons, or electron-hole pair states, shown in Table 4, which was obtained by listing the pair states in the ascending order of their energy and assigning their symmetry by consulting Table 2. From Table 4, we may expect that low energy excitons have the A 1 or T 2 symmetry.

Table 4. The lowest 44 electron-hole pair states for L = 9.0 nm and D = 2.2 nm without considering the Coulomb potential energy. Only A 1 states have non-zero transition dipole moments and contribute to the optical transition.

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The exciton states with the Coulomb potential was obtained by numerically diagonalizing the X matrix evaluated with |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 X matrix elements. As shown in Fig. 3, the convergence is fast, and 400 pair states give sufficiently converged results.

Fig. 3 Convergence of the lowest 20 energy eigenvalues of the spin-triplet excitons. (L = 9.0 nm, D = 2.2 nm)

Fig. 4 (a) D and (b) L dependence of the spin-singlet exciton energy. The lowest twenty exciton states are shown, whose symmetries are A 1 or T 2.

As an example, let us describe the case of 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.

Next, Fig. 5 shows the results for the lowest 20 spin-triplet excitons. Again the lowest state is of the 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.

Fig. 5 (a) D and (b) L dependence of the spin-triplet exciton energy. The lowest twenty exciton states are shown, whose symmetries are A 1 or T 2.

Let us give a comment on the exceptionally large binding energy of the lowest A 1 spin-triplet exciton. The averaged value of 1/|r 1r 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.

Since we now know energy eigenvalues and wave functions of excitons, we can calculate their absorption spectra by using Fermi’s golden rule. Figure 6 shows spectra for three different 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.

Fig. 6 Absorption spectra of CdTe tetrapods with different D values, where the lowest eight spin-singlet A 1 excitons are taken into consideration. A spectral width of 60 meV (FWHM) due to size distribution is rather arbitrarily assumed for each exciton transition.

Reference [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]

] and [15

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]

] reported synthesis and optical absorption spectra of CdTe tetrapods. Calculated values in the present study agree with the experimental observation of [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]

] quite well. Their deviation is less than 20 nm. On the other hand, Ref. [15

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]

] reported that the longest peak wavelength of the CdTe tetrapod was 620 nm for the case of 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.

Finally, Fig. 7 shows absorption spectra for three different 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.

Fig. 7 Absorption spectra of CdTe tetrapods with different L values, where the lowest eight spin-singlet A 1 excitons are taken into consideration. A spectral width of 60 meV (FWHM) due to size distribution is rather arbitrarily assumed for each exciton transition.

Generally speaking, for larger variation of the arm length 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.

In this study, we assumed the perfect tetrahedral symmetry for the CdTe tetrapods, although the present method is applicable to tetrapods with broken symmetries as well without an increase in the computational cost. For tetrapods with broken symmetries, localization of wave functions in particular arms and anisotropic emission polarization for individual tetrapods are known [22

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]

]. However, for an ensemble of tetrapods, the inhomogeneously broadened absorption and emission bands are usually isotropic due to the stochastic distribution of the tetrapod orientation. So, the absorption spectrum of the ensemble reflects the nature of the symmetric tetrapod structure.

4. Conclusion

Acknowledgments

This study was supported by Grant-in-Aid for Scientific Research (B) from Japan Society for the Promotion of Science (Grant number 23340090).

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. 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]

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]

4.

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]

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]

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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]

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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]

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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]

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]

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. 7, 2951–2959 (2007). [CrossRef] [PubMed]

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. 9, 3544–3549 (2009). [CrossRef] [PubMed]

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 373, 2287–2290 (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]

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. 104646–4650 (2010). [CrossRef] [PubMed]

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. 52044–2049 (2005). [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]

23.

F. Bechstedt and R. Enderlein, Semiconductor Surfaces and Interfaces: Their Atomic and Electronic Structures (Akademie-Verlag, Berlin, 1988).

24.

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]

25.

S. AdachiProperties of Group-IV, III–V and II–VI Semiconductors (Wiley, Chichester, 2005) P.218.

26.

T. Inui, Y. Tanabe, and Y. Onodera, Group theory and Its Applications in Physics (Springer-Verlag, Berlin1990).

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]

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


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References

  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]
  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]
  4. 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]
  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]
  6. 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]
  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. 89, 094104/1–094104/3 (2006). [CrossRef]
  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. 92, 191905/1–191905/3 (2008). [CrossRef]
  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 4, 2043–2050 (2010). [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]
  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]
  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. 7, 2951–2959 (2007). [CrossRef] [PubMed]
  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. 9, 3544–3549 (2009). [CrossRef] [PubMed]
  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 373, 2287–2290 (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]
  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. 104646–4650 (2010). [CrossRef] [PubMed]
  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. 52044–2049 (2005). [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]
  23. F. Bechstedt and R. Enderlein, Semiconductor Surfaces and Interfaces: Their Atomic and Electronic Structures (Akademie-Verlag, Berlin, 1988).
  24. 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]
  25. S. AdachiProperties of Group-IV, III–V and II–VI Semiconductors (Wiley, Chichester, 2005) P.218.
  26. T. Inui, Y. Tanabe, and Y. Onodera, Group theory and Its Applications in Physics (Springer-Verlag, Berlin1990).
  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]

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