Carrier tunneling in asymmetric coupled quantum dots

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Physica E 21 (2004) 511 – 515 www.elsevier.com/locate/physe

Carrier tunneling in asymmetric coupled quantum dots H. Sasakuraa;∗ , S. Adachia , S. Mutoa , H.Z. Songb , T. Miyazawab , Y. Nakatab a Department

of Applied Physics, Hokkaido University and CREST, Japan Science and Technology Corporation, N13 W8 Kitaku, Sapporo 060-8628, Japan b Fujitsu Laboratories Ltd., 10-1 Morinosato-Wakamiya, Atsugi 243-0197, Japan

Abstract Exciton spin relaxation at low temperatures in InAlAs–InGaAs asymmetric double quantum dots embedded in AlGaAs layers has been investigated as a function of the barrier thickness by the time-resolved photoluminescence measurements. With decreasing the thickness of the AlGaAs layer between the dots, the spin relaxation time change from 3 ns to less than 500 ps. The reduction in the spin relaxation time was considered to originate from the spin-5ip tunneling between the ground state in InAlAs dot and the excited states in InGaAs dot, and the resultant tunneling leads to the spin depolarization of the ground state in InGaAs dot. ? 2003 Elsevier B.V. All rights reserved. PACS: 78.47.+p; 78.67.Hc; 71.35.−y Keywords: Asymmetric quantum dots; Tunneling; Time-resolved photoluminescence

1. Introduction The spin relaxation processes of excitons in semiconductor quantum dots (QDs) are of considerable interest in connection with the search for solid-state implementations for qubit in quantum information technologies [1–3]. One of the key points is to obtain long spin coherence times so that quantum information can be stored and manipulated without losses. Spin relaxation is quite fast in bulk (undoped) semiconductors, typically on the order of a few picoseconds [4]. In quantum wells (QWs), the lifting of valence-band degeneracy due to quantum conBnement leads to a slow

∗ Corresponding author. Tel.: +81-11-706-6670; fax: +81111706-7129. E-mail address: [email protected] (H. Sasakura).

spin relaxation and actually the spin relaxation times are of order of a few 10 –100 ps. [5,6]. Also, the effective spin relaxation mechanisms in QWs have been revealed by intensive experimental and theoretical studies [7–10]. In QDs, several experimental results have been reported [11–15]. The experimental results suggest basically long spin relaxation times of the order of a few nanoseconds to microseconds. To date, however, it is important to know the dependence of the spin relaxation times on system and on parameters in order to refer to the spin relaxation mechanisms and give the guideline to the target system [16] both experimentally and theoretically. In the present work, the exciton spin relaxation at low temperatures in asymmetric double QDs has been studied by the time-resolved polarized photoluminescence (PL) measurements. The used Bve InAlAs– InGaAs QD samples have diHerent AlGaAs-barrier

1386-9477/$ - see front matter ? 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2003.11.076

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thickness between the QDs, which change the tunneling probability between the QDs. The presented data indicate that the carrier tunneling eHects from InAlAs QDs to InGaAs QDs lead to the spin relaxation of the ground state in InGaAs QDs. 2. Experiments and results 2.1. Sample structure We used Bve self-assembled QD samples that consisted of In0:75 Al0:25 As=Al0:3 Ga0:7 As QD and In0:7 Ga0:3 As=Al0:3 Ga0:7 As QD were grown on (0 0 1) GaAs substrate by molecular beam epitaxy as shown schematically in Fig. 1(a). A 200-nm GaAs buHer layer was inserted between the AlGaAs layer and the substrate, and the InGaAs QDs were capped by AlGaAs with a thickness of 25 nm. The nominal thicknesses of the barriers between the InAlAs and InGaAs QDs (from wetting layer to wetting layer) are 9, 10, 11, 13, and 20 nm. Figs. 1(b) and (c) show the cross-sectional TEM images of the QDs with 9 and 13-nm AlGaAs barrier thickness, respectively. The InGaAs QDs are aligned vertically due to the strain generated by the lower InAlAs QDs. In the sample with 20-nm barrier thickness, the QDs are not expected to be aligned because the 20-nm thickness is too large for the strain to aHect the growth of the upper QD layer. Fig. 2 shows the time-integrated PL spectra of the InAlAs QDs and the InGaAs QDs at 10 K. A cw He–Ne laser was used as the excitation source and the PL was detected by a multichannel detector. The excitation power was 10 mW and the laser light was focused on to the sample surface with a diameter of 200 m. Each central emission wavelength from the ground state of InAlAs QDs and InGaAs QDs was found to be around 780 and 960 nm, respectively. The PL intensity of InAlAs QDs decreases with reduction of the barrier thickness between the dots. For QDs with 9-nm barrier thickness, in particular, the PL from the InAlAs QDs is suppressed strongly and the PL peak of InGaAs QDs blue shifts to ∼ 925 nm. In general, wave function coupling between QDs induces the red shift of PL emission for the lower-energy state, which is contrary to the observation. Since, in our growth condition,

Fig. 1. (a) Schematic of the sample structure. (b), (c) Cross-sectional TEM images of InAlAs and InGaAs QDs with 9 nm (b) and 13 nm (c) AlGaAs barrier thickness. Both samples are aligned along the growth direction.

the density of InAlAs QDs is larger than that of InGaAs QDs in each single QD layer sample, the observed blue shift can be reasonably explained as follows. The dots in the upper layer (InGaAs) want to be aligned vertically along the dots in the lower layer (InAlAs) in the case of strong strain coupling which is shown in Fig. 1(b), which means both the dot densities become equal. Therefore, the strain coupling induces a decrease in the average size of InGaAs QDs and causes the blue shift of PL peak in ground state of InGaAs QDs. In the 9-nm barrier sample, the eHect of strain coupling is considered to be stronger than that of wave function coupling.

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Fig. 2. Time-integrated PL spectra of InAlAs and InGaAs QDs having AlGaAs barrier thickness of 9, 10, 11, 13, 20 nm, respectively, at 10 K (excitation wavelength 633 nm).

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sample is excited by the frequency-doubled output of a hand-made mode-locked Ti-doped sapphire laser at a repetition rate of 80 MHz. The excitation density was kept low to avoid many-body eHects. The PL signal was then dispersed by a 250-mm monochromator and was detected by a streak camera (time resolution ∼ 15 ps). As seen in Fig. 3 for InAlAs QDs, the PL gradually decay faster with decreasing AlGaAs barrier thickness. This behavior clearly indicates that the carrier tunnels from InAlAs QDs to InGaAs QDs. On the other hand, the barrier thickness dependence of PL decay times of InGaAs QDs is smaller than that of InAlAs QDs. For a 20-nm barrier sample, since both (wave function and strain) couplings are negligibly small, each PL decay indicates the exciton lifetime in each QDs without carrier tunneling. The exciton lifetime in InAlAs QDs and in InGaAs QDs are estimated to be ∼ 580 and ∼ 550 ps, respectively. In other samples, tunneling times change from 400 ps to 1:2 ns with decreasing AlGaAs barrier thickness. 2.3. Spin relaxation

Fig. 3. Typical time evolution of the PL from both QDs for linearly polarized excitation. The excitation wavelength is 400 nm. The carrier tunneling from InAlAs QDs to InGaAs QDs is clearly observed.

2.2. Carrier tunneling To observe the carrier tunneling between the double QDs at Brst, we have performed the TR–PL measurement using the linearly polarized excitation at 10 K. Fig. 3 shows the typical TR–PL curves at the PL peak energy of each QD. The PL was integrated over the 10-nm thickness around the PL peak wavelength. The

In order to investigate the in5uence of carrier tunneling on the spin relaxation, the excitation light was converted to be circularly polarized by a quarter-wave plate. The laser light entered normal to the sample plane to create the deBnite exciton spin polarization. To avoid the diHerence of the grating diHraction eMciency that depends on the PL polarization, only the vertically linear-polarized PL component always comes into the monochromator using a second quarter-wave plate coupled to an analyzer placed in front of the entrance slit. The spin relaxation time can be estimated from the observed PL signals by changing the excitation pulse from + to − . This procedure means that the polarization combination (excitation, measurement) are (+ ; + ) and (− ; + ), which correspond to the + -PL and − -PL components in the usual polarized PL measurements, respectively. The observed spin relaxation time in InGaAs QDs is plotted as a function of the barrier thickness at 10 K in Fig. 4. The excitation wavelength is 780 nm which is resonant to the ground state of InAlAs QDs (see

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Fig. 4. Barrier thickness dependence of spin relaxation time in InGaAs QDs.

Fig. 2). The population dynamics of spin-polarized carriers can be described by the simple rate equation, dN± =dt = −N± =r ∓ N+ =s ± N− =s , where N± , r , and s are the spin-up (+) and spin-down (−) exciton population, the recombination time, and the spin relaxation time, respectively. In the samples with 10-, 11-, 13-, and 20-nm barrier thickness, a clear diHerence between + -PL and − -PL components was observed. For the 9-nm barrier thickness sample, the signal diHerence is small. As seen in Fig. 4, the faster spin-relaxation time is observed with decreasing barrier thickness. This behavior may be explained by a spin-relaxation process in the individual QD and the carrier tunneling process from the ground state of InAlAs QDs to InGaAs QDs. Although the larger overlap of the wave functions means that the population transfer can occur more easily from the higher-energy state to the lower-energy state via phonon-assisted carrier tunneling while phonons alone do not 5ip spins. However, when phonon scattering connects to the spin–orbit interaction which arises from the coupling between the valence and conduction bands (Elliot–Yafet mechanism) [4], spin-5ip tunneling may occur. In our situation, since the energy difference between the ground states of InAlAs QDs and InGaAs QDs is large enough (220 –270 meV),

the multiple phonon process is needed to satisfy the energy conservation in spin-5ip events during the carrier tunneling between the ground states [17] and the possibility of the case is considered to be signiBcantly small. Instead, the resonant tunneling between the higher-energy states of InGaAs QDs and the ground state of InAlAs QDs is more plausible. In this situation, we consider that the two possible contributions for spin relaxation process may be carrier spin–carrier Elliot– Yafet scattering at the higher-energy states in InGaAs QDs and carrier spin-phonon Elliot–Yafet scattering accompanying the energy relaxation from higher-energy states to the ground state of InGaAs QDs. Another channel for the spin-5ip tunneling arises from the k 3 term [4,18]. Apparently, an electron conBned in QDs has no k-vector. However, the transition from InAlAs QDs to InGaAs QDs involving the diHerent quantum states of lateral conBnement is considered to cause the “eHective” k 3 term such that x kx (ky2 − kz2 ). Whenever the carrier tunneling occurs, this spin-dependent k 3 term always 5ips the carrier spin [18]. Since the hole spin-relaxation time is shorter than the electron spin-relaxation time and the tunneling of the hole is slower than that of the electron, we consider that the observed tendency of Fig. 4 is due to the electron spin-5ip tunneling. Actually, the tunneling rate of hole is two-order smaller than that of the electron. Fig. 5 shows the possible six paths of the carrier tunneling in our experimental situation. In the Bgure, the phonon-assisted tunneling and spin-5ip tunneling due to the k 3 term are indicated by the dashed and solid arrows, respectively. Among these pathways, the spin-5ip tunneling due to the spin-dependent k 3 term is possible for two paths from the ground state of InAlAs QDs (0; 0; g2 ) to the Brst excited states of InGaAs QDs (1; 0; g1 ) and (0; 1; g1 ). For other tunneling pathways, the k 3 term cannot be eHective since the symmetry of the wave functions between the related states is diHerent. The spin-5ip due to the k 3 term has a dependence upon the wave function coupling [18] and needs the carrier tunneling. Therefore, the spin-5ip time decreases faster and barrier thickness becomes narrower, i.e., the spin depolarization is enhanced by the k 3 term.

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Fig. 5. Path of phonon-assisted and spin-5ip tunneling in asymmetric double QDs.

3. Summary We have performed the time-resolved photoluminescence measurements of the exciton spin relaxation at 10 K in InAlAs–InGaAs double QDs embedded in AlGaAs. The spin relaxation times were measured as a function of the barrier thickness and the strong coupling between the excited state in InGaAs QDs and the ground state in InAlAs QDs was considered to lead to the spin depolarization of the ground state in InGaAs QDs. References [1] R.P. Feynman, Opt. News 11 (1985) 11. [2] D. Deutsch, Proc. R. Soc. London A 400 (1985) 95. [3] P.W. Shor, Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, Los Alamitos, CA, IEEE Computer Society Press, New York, 1994, p. 124. [4] F. Meier, B.P. Zakharchenya, Optical Orientation, North-Holland, Amsterdam, 1984.

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