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Fine Structure of Biexciton Emission in Symmetric and Asymmetric CdSe ZnSe Single Quantum Dots
V. D. Kulakovskii,* G. Bacher, R. Weigand, T. KÝmmell, and A. Forchel
Technische Physik, UniversitÄt WÝrzburg, 97074 WÝrzburg, Germany

E. Borovitskaya
Institute of Solid State Physics, RAS, 142432 Chernogolovka, Russia

K. Leonardi and D. Hommel
Institut f Ýr FestkÆrperphysik, UniversitÄt Bremen, 28359 Bremen, Germany (Received 12 October 1998) The influence of quantum dot (QD) asymmetry on the emission of single three-dimensionally confined biexcitons in II-VI semiconductor nanostructures has been studied by magnetophotoluminescence spectroscopy. Investigating both the biexciton and the single-exciton transition in the same single QD, we obtain a unified picture of the impact of electron-hole exchange interaction on the fine structure and the polarization properties of optical transitions in QDs. The exchange splitting is demonstrated to have a strong influence on the derivation of the biexciton binding energy, which we determine to be about 17 meV, much less than the separation between exciton and biexciton lines ( 24 meV) in the spectra. [S0031-9007(99)08536-1]
PACS numbers: 78.66. ­ w, 71.35.Cc, 71.70.Gm

In recent years, optical investigations on single semiconductor quantum dots (QDs), often designated as "artificial atoms," opened a new and exciting field of basic physics studies. In contrast to "real" atoms or molecules, a unique feature of solid state quantum dots is the formation of Wannier excitons giving experimental access to both the Coulomb and the electron-hole (e-h) exchange interaction in three-dimensionally confined solid state systems. Therefore, semiconductor QDs with geometries smaller than or comparable to the bulk exciton Bohr radius can be regarded as a model system in order to study the impact of Coulomb and exchange interaction on the optical properties of zero-dimensional excitons and excitonic complexes [1 ­ 5]. Several techniques have been developed to realize semiconductor QDs with high quantum efficiencies. This includes chemically prepared QDs embedded in a matrix [1,6] as well as ensembles of QDs fabricated by means of epitaxy and / or lithography [2,7 ­ 15]. A drawback of such QD arrays is a broadening of the optical transitions due to the size dispersion of the dots, which prevents the investigation of, e.g., the fine structure of exciton states [16,17]. In order to suppress the influence of inhomogeneous broadening effects, spectroscopic techniques with a high spatial resolution have been introduced as a powerful experimental tool. This allows one to investigate single quantum dots (SQDs) by means of photoluminescence (PL) spectroscopy [2 ­ 5,10,14,18]. In II-VI nanostructures, the e-h exchange interaction is significantly enhanced as compared to the (Ga,In)As system [1,6]. This allows studies of the optical transitions of excitons and multiexcitons without any significant mixing of radiative ("bright") and nonradiative ("dark") excitonic states. Therefore, II-VI materials such as, 1780 0031 - 9007 99 82(8) 1780(4) $15.00

e.g., CdSe ZnSe are ideal systems to study the impact of the dot symmetry and the e-h exchange interaction on the fine structure and the polarization properties of excitons and excitonic complexes in SQDs. Until now, the work on e-h exchange interaction in quantum dots has concentrated on single-exciton states, where, e.g., the energy splitting between dark and bright excitons [1,6] or the splitting of the optically allowed singleexciton state into a linearly polarized doublet [2,17] was investigated. To our knowledge, however, there are no studies on the impact of e-h exchange interaction on the emission properties of multiexcitons in QDs until now. However, due to the strong enhancement of the exchange energy expected in low dimensional systems [1,6], a consideration of exchange effects is crucial for, e.g., any spectroscopic determination of multiexciton binding energies in zero-dimensional semiconductors such as, e.g., CdSe ZnSe QDs. In the present paper, we investigate for the first time the influence of e-h exchange interaction (i) on the transition energy, (ii) on the PL polarization, and (iii) on the binding energy of zero-dimensional biexcitons. Both weakly and highly asymmetric SQDs have been investigated without and with magnetic field B parallel to the growth axis z . The study of both, the biexciton as well as the exciton transition in the same SQD, gives a unique opportunity to compare the fine structure of (multi)excitonic states in three-dimensionally confined systems with theoretical predictions. The investigated samples are CdSe ZnSe structures fabricated by migration enhanced epitaxy, embedding three monolayers (ML) of CdSe between ZnSe barriers [12]. RHEED measurements indicate a 3D growth mode © 1999 The American Physical Society


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for a CdSe layer thickness Lz . 2.5 ML. From high resolution transmission electron microscopy data, an estimate of the average QD size has been obtained, yielding a height of about 1.5 ­ 2 nm in growth direction and a lateral extension of 5 ­ 10 nm. To achieve the high spatial resolution required for SQD spectroscopy, we have prepared square mesas with lateral extensions down to 60 nm by electron beam lithography and wet chemical etching [19]. Continuous wave PL studies were carried out in an optical cryostat with a split-coil solenoid in Faraday configuration using the 363.8 nm line of an Ar1 -ion laser for the excitation and a LN2 -cooled CCD camera for the detection of the QD emission. In Fig. 1a, unpolarized PL spectra for two SQDs (QD1 and QD2, respectively) are displayed for different excitation densities. At low excitation densities, the PL spectrum is dominated by the single-exciton transition X . For high excitation, additional features occur in the PL spectrum at about 25 meV lower energy. As will be discussed below in detail, these peaks are due to the recombination of the two-exciton state X2 , the biexciton. Two remarkable features have to be mentioned. First, the energetic difference between the exciton and the biexciton emission is quite large; and, second, the spectral shape of the exciton, which, e.g., is a well resolved doublet for QD2, is exactly reproduced in the PL spectra of the biexciton. To get a more detailed insight into the symmetry of the QD eigenstates and their consequence on the optical properties of excitonic molecules, the polarization dependence of both, the exciton as well as the biexci-

ton transition, is studied. As can be seen in Fig. 1b, the biexciton and the exciton emission consists of a doublet which is linearly polarized along the 110 and ¯ 110 crystal orientation, respectively. The splitting between the two components is small (,0.3 meV) in most (.50%) of the dots investigated (see QD1). However, it changes from one dot to another and, for about 10% of the dots, values of 0.8 meV and larger are obtained (see QD2). Remarkably, the energy sequence of the polarized components is different for the X and X2 transition: While, for the exciton, the px polarized component is the higher energetic one, the situation is exactly the opposite for the biexciton, where the px polarized component forms the low energy part of the doublet. The biexciton ground state is a spin-singlet state (S 0). Thus, both the polarization and the fine structure splitting of the biexciton emission are controlled by the final state of the recombination, i.e., the eigenstates of the single exciton. As schematically depicted in Fig. 2, the ground state of the heavy-hole exciton is expected to be fourfold degenerate, if exchange interaction is neglected. To take into account the influence of exchange interaction on the symmetry and the energy of the exciton eigenstates, we have to discuss the spin Hamiltonian for heavy-hole excitons [16,17,20], which is given by X ^^ ^3 ^ az jh,z se,z 1 bi jh,i se,i , (1) HX
i x ,y ,z

^ with se,i and jh,i as electron and hole spin operators. ^ 61 2 and jz 63 2 for The eigenvalues are sz the electron and the heavy-hole spin, respectively. The e-h spin exchange interaction results in a splitting of the X quartet with the angular momentum component 61, 62. Quantum wells (QWs) as well M sz 1 jz as cylindrical QDs have a D2d point-group symmetry. by and as a consequence the For this symmetry bx

FIG. 1. (a) Unpolarized PL spectra from two QDs for different excitation power. The spectra are taken from a small (diameter of about 100 nm) mesa. X denotes the exciton emission, while X2 corresponds to the recombination of the two-exciton ( biexciton) state. (P0 10 W cm2 ). ( b) Linearly polarized PL spectra from the two QDs.

FIG. 2. Schematic illustration of the exciton and the twoexciton states and the allowed optical transitions in QDs of different symmetry.

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X quartet splits into a radiative doublet j61 and two nonradiative singlets formed by linear combinations of j62 states (see Fig. 2). While in this case the radiative doublet is degenerate, the nonradiative one is split by 3 d2 4 jbx 1 by j. For a lower symmetry, all of the coefficients in Eq. (1) have a different magnitude and the radiative doublet is 3 split by d1 4 jbx 2 by j. In QDs with Lz Ü Lx , Ly , the splitting between bright and dark excitons (d0 27 3 2 az 1 8 bz ) is expected to be much larger than the energy splitting of the bright exciton doublet. Therefore, the mixing of j61 and j62 states is small, and the radiative states are a symmetric and antisymmetric combination of j11 and j21 states, X1 and X2 , respectively. Thus, the optical transitions of both the X and the X2 transitions are expected to be linearly polarized along the principal in¯ plane axes, i.e., the 110 and 110 directions. This is exactly what we observe in our experiments (see Fig. 1b). Moreover, the energy sequence of the px and py polarized components observed in the experiment nicely confirms the theoretical expectation. In order to calculate the energy splitting of the exciton ground state due to exchange interaction, we have applied the theory introduced by Blackwood and Ivchenko [16,17], assuming the simplest form of the exciton envelope function, namely, the full confinement of the exciton in the QD [21]. From our calculations, we find that the exchange splitting between bright exciton states increases with increasing dot asymmetry and decreasing size. For cylindrical QDs (D2d symmetry), the exchange splitting is expected to be zero. Thus, we mainly attribute the variation of the exchange splitting between different dots to a dot dependent deviation from cylindrical shape (i.e., jLx 2 Ly j . 0) [22]. A splitting between the X1 and X2 states of 0.8 meV as obtained, e.g., for QD2 (note that the number of such dots is very small) is possible only in small enough (few nm) and 1.5 nm highly anisotropic QDs. For example, with Lz 10 nm 3 2.5 nm, we obtain d1 d2 and Lx 3 Ly 0.8 meV. In this case, the dark-bright splitting is about 3.2 meV, i.e., significantly enhanced as compared, d0 e.g., to ZnSe ZnCdSe QWs, where a splitting of d0 10 nm [23]. This enhance0.5 meV is found for Lz ment is attributed to quantum confinement effects, in good agreement with results on CdS ZnS nanostructures reported by Woggon et al. [6]. The fine structure of the exciton and the biexciton emission has an important impact on the determination of the biexciton binding energy in QDs. The energetic distance between the emission of the single-exciton and the two-exciton complex, DM , is typically about 23 ­ 25 meV and depends strongly on the PL polarization (see Fig. 1b). In QDs with a large exchange splitting of excitons, however, DM and the biexciton binding energy DM are different entities. As indicated in Fig. 2, the allowed X2 transition corresponds to the transition from 1782

X2 to the excited (j61 ) rather than to the ground (j62 ) X state. Thus, in QDs, DM should be defined by the following equation: DM D
M

2 2d0 7 d1 2 d2 ,

(2)

for px and py polarization, respectively. For example, 24.9 meV (23.3 meV) for px for QD2 we obtain DM (py ) polarization and, with the above estimated values of d0 3.2 meV and d1 d2 0.8 meV, one obtains 16.9 meV, which is significantly smaller than DM . DM Thus, the commonly used energetic difference between the exciton and the biexciton emission results in a strong overestimate of the biexciton binding energy. Nevertheless, the biexciton binding energy determined here including exchange effects is strongly enhanced as compared to II-VI quantum wells, a direct consequence of the threedimensional confinement of the biexciton in the QD. The symmetry and the energy of the dot eigenstates can be systematically varied by applying a magnetic field. For B k z , the Zeeman interaction is given by ^ mB ge,z sz 2 gh,z jz B , ^ (3) HB where ge,h are the electron and hole is the Bohr magneton. The energy the two radiative heavy-hole states corresponding Hamiltonian H HX ge 1 3gh ) p 1 E1,2 d0 6 g1 mB B 2 2 g factors and mB eigenvalues Ei of derived from the 1 HB are (g1
2 1 d1 .

(4)

As shown in Fig. 3a, for the symmetric QD1 the E1 2 E2 , increases almost exciton line splitting, D1 B 1.56. For linearly with B with a g factor of g1 the asymmetric QD2, in contrast, D1 B strongly differs from the linear dependence. This deviation is related to the large zero-field splitting d1 of the radiative exciton state due to e-h exchange interaction. The experimental dependence (symbols) is in excellent agreement with the calculated one using Eq. (4) (solid lines). From these data, we can conclude that both the Zeeman energy as well as the splitting between the bright states

FIG. 3. (a) Energy splitting between the bright exciton states, D1 B , and ( b) degree of circular polarization, I s 1 2 I s2 I s 1 1 I s 2 , of the X2 transition versus magnetic field.


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FIG. 4. s and p polarized PL spectra from SQDs at a magnetic field B 8 T and an excitation power of P0 10 W cm2 .

are much smaller than the dark-bright splitting, d0 . For that reason, a magnetic field in Faraday geometry results in a redistribution of the circular polarized j11 and j21 states between the two bright exciton levels X 1,2 according to (a g1 mB B d1 ) p 1 j11 6 1 1 a 2 7 a j21 1,2 p p jX , (5) p 2 1 1 a2 7 a 1 1 a2 without mixing bright and dark exciton states. As an external magnetic field does not split the biexciton spin-singlet state, both the polarization and the transition energies of the lines X2 are controlled by the energy and the symmetry of the exciton levels. This means that, first, the splitting of the biexciton lines should coincide with that of the exciton emission, in agreement with our experimental data. Second, the linear polarization of both the X and X2 lines at zero magnetic field should transform into a circular one in a high magnetic field. While for the exciton transition the effective exciton temperature and / or the spin flip process between the bright states are expected to influence the polarization degree significantly, the X2 transition should directly reflect the magnetic field induced change of the symmetry of the exciton eigenstates according to Eq. (5). This is shown in Fig. 3b, where the degree of circular polarization of the X2 line is plotted versus magnetic field. Indeed, a very good agreement between the experimental data (symbols) and the theory (lines) is found. In Fig. 4, polarized PL spectra at 8 T are shown. For QD1 (a ¿ 1), the exciton and the biexciton emission consist of two components of s 1 and s 2 polarization, respectively. In contrast, for the asymmetric QD2, the 1). This Zeeman splitting is comparable to d0 (a

results in a degree of linear polarization, which even for B 8 T is still rather large. Most interesting, however, is the change of the polarization sequence of the X2 and the X lines at high magnetic field compared to the zero magnetic field data. As already mentioned, for B 0, the X2 emission has the same magnitude of the fine structure splitting, but the opposite sequence of polarized components than the emission of the exciton (see Fig. 1b). In contrast, at high magnetic fields, the energy sequence of the s 1 and s 2 transitions is the same for excitons and biexcitons, as demonstrated in the magneto PL spectra depicted in Fig. 4. Comparing Figs. 1b and 4, it can be clearly seen that, if the px y components of the line X transform with increasing magnetic field B into the s 1 2 lines, the biexciton emission component px transforms into s 2 and, vice versa, py into s 1 , in full agreement with theory. We gratefully acknowledge the financial support of the Nato Science Program, the Russian Foundation for Basic Research, and the Deutsche Forschungsgemeinschaft.

*Permanent address: Institute of Solid State Physics, RAS, 142432 Chernogolovka, Russia. [1] M. Nirmal et al., Phys. Rev. Lett. 75, 3728 (1995). [2] D. Gammon et al., Phys. Rev. Lett. 76, 3005 (1996). [3] L. Landin et al., Science 280, 262 (1998). [4] E. Dekel et al., Phys. Rev. Lett. 80, 4991 (1998). [5] M. Bayer et al., Phys. Rev. B 58, 4740 (1998). [6] U. Woggon et al., Phys. Status Solidi (a) 164, 505 (1997). [7] A. Zrenner et al., Phys. Rev. Lett. 72, 3382 (1994). [8] S. Fafard et al., Phys. Rev. B 50, 8086 (1994). [9] J. Oshinowo et al., Appl. Phys. Lett. 65, 1421 (1994). [10] M. Grundmann et al., Phys. Rev. Lett. 74, 4043 (1995). [11] S. H. Xin et al., Appl. Phys. Lett. 69, 3884 (1996). [12] K. H. Leonardi et al., Appl. Phys. Lett. 71, 1510 (1997). [13] M. Rabe et al., Phys. Status Solidi ( b) 202, 817 (1997). [14] R. Steffen et al., Phys. Rev. B 54, 1510 (1996). [15] M. Illing et al., Appl. Phys. Lett. 67, 124 (1995). [16] E. Blackwood et al., Phys. Rev. B 50, 14 246 (1994). [17] E. L. Ivchenko et al., Phys. Status Solidi (a) 164, 487 (1997). [18] H. F. Hess et al., Science 264, 1740 (1994). [19] T. KÝmmell et al., Appl. Phys. Lett. 73, 3105 (1998). [20] H. W. van Kesteren et al., Phys. Rev. B 41, 5283 (1990). [21] This approximation is justified by a large confinement potential for both electrons and holes. [22] Because no correlation between the emission wavelength and the bright exciton exchange splitting is found, the influence of the dot size seems to play a minor role for the different exchange splitting observed in our dots. [23] J. Puls and F. Henneberger, Phys. Status Solidi (a) 164, 499 (1997).

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