Exciton fine structures and energy transfer in single InGaAs quantum-dot molecules

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Phys. Status Solidi C 6, No. 4, 860 – 863 (2009) / DOI 10.1002/pssc.200880623

Exciton fine structures

and energy transfer

in single InGaAs quantum-dot molecules

Hsuan Lin**, 1_{, Sheng-Yun Wang}1_{, Chia-Hsien Lin}1_{, Wen-Hao Chang}*_{, 1}

, Shun-Jen Cheng1_{, Ming-Chih Lee}1_, Wen-Yen Chen2_{, Tzu-Min Hsu}2_{, Tung-Po Hsieh}3_{, and Jen-Inn Chyi}3

1_{Department of Electrophysics, National Chiao Tung University, Hsinchu 300, Taiwan} 2_{Department of Physics, National Central University, Chungli 320, Taiwan}

3_{Department of Electrical Engineering, National Central University, Chungli 320, Taiwan} Received 25 April 2008, revised 1 October 2008, accepted 28 October 2008

Published online 20 January 2009 PACS 71.35.–y, 78.67.Hc, 78.55.Cr

**_{Corresponding author: e-mail}_{[email protected]}_{, Phone: +886-3-5712121, ext: 56111} **_e-mail_{[email protected]}_,_{Phone: +886-3-5712121, ext: 56145, Fax: +886-3-5715230}

1 Introduction The underlying atom-like properties of single isolated semiconductor quantum dots (QDs) have proven to be very useful for the implementation of various quantum information applications, including quantum cryp-tography using single QDs as non-classical light sources [1-4] and quantum gate [5] operation based on exciton excita-tions. Building molecular-like structures with controllable coupling effect provides a possible route for further scal-ability of such applications. Recent experiments have re-vealed that electrical control of tunnel coupling is feasible in single QD molecules (QDMs) formed by a pair of either vertically stacked [6-9] or laterally aligned [10] InGaAs self-assembled QDs. Despite the success in explaining the rich pattern of level anticrossings/crossings in accordance with an applied electric field, the spectral features of a sin-gle QDMs is by far more complicated than their sinsin-gle QD counterparts, since QDMs are usually made of two non-identical dots and the coupling mechanism will also differ with the interdot separation. The directional energy transfer of exciton between the two adjacent dots was observed and

explained in terms of phonon-assisted Förster processes [11, 12]. However, such a directional transfer of carriers could also arise from nonresonant tunneling, which has been re-ported on ensemble of In(Al,Ga)As asymmetric QD pairs [13, 14], and recently on single InP/InGaP QD pairs [15]. Therefore, it is important to clarify whether the Förster transfer or the nonresonant tunneling is responsible for the directional energy transfer in QDMs.

In this work, we present a spectroscopic study of single QDMs formed by two closely stacked In_0.5Ga_0.5As/GaAs QD layers. Fine structures of direct and indirect excitons in QDMs were investigated by power dependent and polari-zation resolved micro-photoluminescence (µ-PL) meas-urements. A directional energy transfer from a direct to an indirect exciton in single QDMs was found as the tempera-ture was increased. This phenomenon is explained in terms of a thermally activated tunneling of the hole between the two adjacent QDs. In this work, we present a spectroscopic study of single QDMs formed by two closely stacked In0.5Ga0.5As/GaAs QD layers [16].

We present a spectroscopic study of single quantum-dot molecules (QDMs) formed by two closely stacked In_0.5Ga_0.5As/GaAs layers. It was found that the interdot cou-pling and directional energy transfer between the two adja-cent dots can be controlled by temperature tuning. Direct and indirect excitons, as well as charged excitons in single QDMs were classified and identified by excitation-power dependent, excitation-energy dependent and polarization-resolved

micro-photoluminescence measurements. With the increasing tem-perature, the direct-exciton intensity decreases while the indi-rect-exciton intensity increases. A rate equation model con-sidering phonon mediated processes has been developed. The directional energy transfer in QDMs is explained in terms of the phonon-assisted tunnelling of hole between the two adja-cent dots.

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2 Experimental Our QDMs samples were grown by

metalorganic chemical vapour deposition (MOCVD), yielding a low QD density of about 108-109 cm-2 by a careful control of the InGaAs coverage [17]. The layer se-quence consists of a 100-nm undoped GaAs buffer layer, followed by a 500-nm Al0.8Ga0.2As layer and a 80-nm GaAs layer grown at 700 °C. The QDMs, formed by a pair vertically stacked In0.5Ga0.5As QD layers, separated by a thin GaAs spacer layer, were then grown at 500 °C. Cross-sectional transmission electron microscopy (TEM) reveals that the InGaAs QDs in each layer is lens-shaped, and about 3 nm in height situated on a 1.8-nm-thick wetting layer (WL) as shown in Fig. 1(a). The two WLs are sepa-rated by a 5-nm-thick GaAs spacer layer, corresponding a tip-to-base distance of only ~2 nm. Individual QDM spec-tra were investigated by a µ-PL setup via an Al metal mask with arrays of nano-apertures. A He-Ne laser beam was fo-cused on the aperture via a microscope objective (N.A. = 0.5, 100×). The PL signals were analyzed by a 0.75 m grat-ing monochromator combined with a liquid-nitrogen-cooled CCD camera, which yields a resolution limited spectral linewidth of ~60 µeV. By using the Lorentzian line-shape fitting, the peak position of emission lines can be determined with an accuracy better than 10 µeV. 3 Results and discussion We have investigated a number of single QDMs to date, and most of which show similar behaviors. Typical µ-PL spectra taken from four different QDMs excited at 1.96 eV under 1 µW are dis-played in Fig. 1(b). Under low excitation conditions, three dominant emission lines (labelled X1, X2, and X3) were in-variably observed. The X1 and X2 lines are separated by an energy varying from 0.3 to 2 meV for different QDMs, while the X3 is invariably present at an energy of about 4.0 ± 0.3 meV below the X1 line.

Power-dependent PL measurements have been per-formed in order to classify these emission lines. A typical spectrum obtained from QDM3 is shown in Fig. 2(a). The dependence of PL intensity (IPL) on the excitation power

(P_ex) for each line can be characterized by I_PL ∝P_exα. As shown in Fig. 2(b), both the X₁ and X₂ intensities increase linearly with P_ex, with exponents of 1.0 and 0.95, respec-tively. We therefore identify X₁ and X₂ as different neutral excitons state in the QDM. The X₃ line shows a superlinear dependence on P_ex, with an exponent of ~1.3, which can be ascribed to the negatively charged exciton (X–). The formation ofX- state is related to the unintentionally doped carbon impurities in the MOCVD grown sample, leading to preferential captures of more electrons into the QDM under nonresonant excitations [18]. Here, it is important to point out that the energy separations between X₁and X₃ are almost the same for different QDMs. Because the binding energy of X- is less sensitive to the dot size, the similar binding energy implies that the X3 line is the negatively charged state of the X1 line in the QDM. Another two peaks marked as 2X1 and 2X2 were also analyzed. Their quadratic and superlinear power dependencies indicate that they are recombinations from of biexciton states.

The X1 and X2 emission lines are unlikely to arise from direct excitons localized in the two different dots of the QDMs, because the inherent size difference of two dots would cause a difference in ground state energy of tens of meV, which cannot account for the variation in X1-X2 separation of only a few meV’s. For QDMs with spacer thickness as thin as 5 nm, theoretical calculations predicted that the lowest lying two electron states hybridize into bonding and anti-bonding orbitals with an energy splitting up to ~50 meV due to the strong interdot tunnel coupling. However, the lowest lying two hole states, which are split by only a few meV, remain essentially uncoupled even in such closely stacked QD pairs, due to the much larger hole

Figure 1 (a) Cross sectional TEM image of the InGaAs QDM structure. (b) PL spectra taken from different QDMs. The energy scale is relative to the X₁ peak energy at 1257.4, 1285.3, 1284.3, and 1283.8 meV from QDM1 to QDM4, respectively.

Figure 2_{Power-dependent µ-PL spectra of QDM3 at excitation}

energy = 1.96 eV. (a) The PL spectrum taken at excitation power = 1 µW. (b) The integrated PL intensity of each emission line as a function of excitation power.

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862 Hsuan Lin et al.: Exciton fine structures and energy transfer in single InGaAs quantum-dot molecules

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effective mass and the interpenetrated strain field [19]. Therefore, we identify the two X1 and X2 lines as the re-combination of the same electron state with two hole states localized in different dots, which can be characterized as a direct and an indirect transitions.

We have performed polarization-resolved PL meas-urements to further examine the direct and indirect natural properties of these emission lines based on the analysis of fine structure splitting (FSS) of exciton states in QDMs. In single dots, because the electron-hole (e-h) exchange inter-action is sensitive to the dot shape symmetry, the neutral exciton line will split into a linearly cross-polarized dou-blet [20]. For a QDM, if a direct exciton is localized in one particular dot of the QDM, the FSS is expected to resemble the single QD case. Furthermore, since the e-h exchange interaction is proportional to the overlap of the electron and hole wavefunctions, the FSS of the indirect exciton would be suppressed due to less wavefunction overlap.

In Fig. 3, linearly polarized spectra of QDM3 along [110] (π_x) and [110] (π_y) directions are displayed. The X₁ line consists of a linearly cross-polarized doublet with a FSS of Δ1~ 30 µeV. The FSS of 2X1 is the same as that of X1, but with a reversed polarization sequence, indicative of a cascade process for the direct exciton and biexciton in the same dot of the QDM. The X3 line does not show any FSS, as expected for an X– state with singlet spin configu-ration of two electrons. In particular, we found that the FSS of the X2 line is virtually zero within our detection limit for all investigated QDMs. This leads us to believe that X2 is the indirect transition.

Temperature-dependent PL measurements have been performed in order to obtain more information about the interdot coupling. The temperature-dependent PL spectra of QDM3 were shown in Fig. 4(a). With the increasing temperature, we found that the X1 intensity (I1) decreases

while the X2 intensity (I2) increases with a crossing in

relative intensities I_1,2/ (I₁+I₂) at about T = 16 K. All the investigated QDMs show a similar behavior as shown in Fig. 4(b), but with different crossing temperatures.

Be-cause X1 and X2 are direct and indirect transitions, the in-tensity crossing indicates a directional transfer of hole be-tween the two adjacent dots.

To understand the underlying transfer processes, a simplified rate-equation model considering an interdot transfer rate γ( )T from X1 to X2 was used. For simplicity, biexcition states are neglected in this model, which is ap-plicable under low-excitation conditions. The thermally ac-tivated transfer rate was phenomenologically assumed to be γ( )T =γ₀exp(−E k T_A/ _B ) , where γ₀ is a pre-exponential factor, E_A is the activation energy for the transfer process. By solving the rate equation in steady state, the relative intensity of X₁ is given by

1 1 1 2 1 2 0 1 / ( ) 1 ( / )exp( A/ B ) I g g g I I γ γ E k T + = + + − , (1)

where g1 and g2 are generation rates of the X1 and X2 states, and γ1 is the recombination rate of the X1 state. The relative intensity of X2 can then be obtain from

1 1 2

1 [ / (− I I +I )]. Fitting parameters are g g1/ 2 , γ γ0/ 1

and E_A, which determine the intensity ratio I I₁/ ₂ at low temperature, the crossing temperature, and the slope of in-tensity variation with temperature. As shown in Fig. 4(b), the simplified model well reproduces our experimental data. Inspections of several QDMs indicated that E_A var-ied in the range of 3-10 meV, without any correlation with their X1-X2 energy separation.

The observed transfer processes are unlikely to arise from resonant tunneling between the two adjacent dots, be-cause the energy levels of nonidentical dots are usually not aligned. However, because excited states of the hole in QDs are less confined, tunnel coupling between hole ex-cited states in the QDM will be more significant. Therefore, it is likely that the observed directional transfer of hole be-tween the two dots is a thermally-activated tunneling, i.e., the hole in one dot first absorbed thermal energy (acoustic phonons) and activated to a higher-lying hole level, then tunneled into another dot, followed by rapid relaxations into the ground hole state to form an indirect exciton X₂.

Figure 4 (a) Temperature dependent PL spectra of QDM3. (b)

The relative intensities of X₁ and X₂ transitions of different QDMs. The dashed lines are fitting curves calculated from the rate-equation model.

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For a square tunneling barrier, the interdot tunneling rate can be approximated by γ_tun∝exp[ 2− d 2m V_hΔ / ]2 , which increases exponentially with the decreasing barrier height ΔV and thickness d . This explains why the inter-dot hole transfer can be considerably enhanced by absorp-tion of thermal energy to available higher-lying levels.

4 Conclusion In summary, we presented a

spectro-scopic study of single QDMs formed by two closely stacked In0.5Ga0.5As QDs. The exciton fine structures as well as direct and indirect excitonic species associated with QDMs were identified by power dependent and polariza-tion resolved micro-photoluminescence measurements. As temperature increasing, a directional energy transfer be-tween the direct and indirect excitons in single QDMs was observed. A rate equation model was developed to explain our data. A thermally-activated tunneling of a hole be-tween the two adjacent dots is responsible for such direc-tional energy transfers in QDMs.

Acknowledgements This works is supported in part by

the program of MOE-ATU and the National Science Council of Taiwan under Grant No. NSC-96-2112-M-009-014.

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