Letter pubs.acs.org/NanoLett
Terahertz Intersublevel Transitions in Single Self-Assembled InAs Quantum Dots with Variable Electron Numbers Ya Zhang,*,† Kenji Shibata,†,‡ Naomi Nagai,† Camille Ndebeka-Bandou,†,§ Gerald Bastard,†,§ and Kazuhiko Hirakawa*,†,‡ †
Center for Photonics Electronics Convergence, Institute of Industrial Science and ‡Institute for Nano Quantum Information Electronics, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan § Laboratoire Pierre Aigrain, Ecole Normale Superieure, 24 rue Lhomond F75005, Paris, France S Supporting Information *
ABSTRACT: We propose a method for performing terahertz spectroscopy on nanometer (nm)-scale systems by using metal nanogap electrodes. Intersublevel transition spectra of single self-assembled InAs quantum dots (QDs) have been measured with high signal/noise ratios by using a single electron transistor geometry that consists of a QD and nanogap metal electrodes as a terahertz detector. Photocurrent distribution with respect to the Coulomb diamonds indicates that there are two mechanisms for the photocurrent generation. When the p shell was fully occupied, we observed rather simple photocurrent spectra induced by the p → d transitions. However, when the p shell was half-filled, the photocurrent spectra exhibited a markedly different behavior, which we attribute to the fluctuation in electron configuration when the empty p state is filled back from the electrodes. KEYWORDS: Terahertz spectroscopy, nanostructures, intersublevel transitions, quantum dots, nanometer-scale spectroscopy
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standard THz absorption measurements is too small to be detected. These problems generally exist for THz spectroscopy of low-dimensional nanomaterials, such as carbon nanotubes, nanowires, and single molecules. New detection scheme is, therefore, indispensable for THz measurements. In this Letter, we report on the observation of intersublevel transition spectra of single self-assembled InAs QDs measured with high sensitivities. To achieve this, we used a single electron transistor (SET) geometry that consisted of an InAs QD and nanogap metal electrodes as a sensitive THz detector and detected intersublevel transition as a photocurrent induced in the SET. Under a weak, broadband THz radiation, photocurrent was observed in the Coulomb blockaded regions. Photocurrent distribution with respect to the Coulomb diamonds indicates that there are two mechanisms for the photocurrent generation. When the p shell is fully occupied, we observed simple photocurrent spectra induced by the p → d transitions. However, when the p shell is half filled, the photocurrent spectra exhibited a very different behavior as a function the gate voltage, which we attribute to the fluctuation in electron configuration when the empty p state is filled back from the electrode.
elf-assembled InAs quantum dots (QDs) are very attractive materials owing to their discrete energy levels.1 So far, electronic structures of the QDs have been extensively studied mainly by interband luminescence spectroscopy.2−4 Terahertz (THz) intersublevel spectroscopy on self-assembled InAs QDs was first performed on ensembles of QDs.5,6 Later, the intersublevel relaxation process was systematically studied.7,8 However, the THz spectra obtained by the conventional transmission measurements on ensembles of QDs are strongly affected by inhomogeneous broadening, hindering detailed discussions on the physics of intersublevel transitions. THz spectroscopy on single QDs is, therefore, highly desirable. However, if we want to perform single QD spectroscopy we immediately face two serious problems. The first is the problem with the diffraction limit. The typical diameter of InAs QDs is about several tens of nanometers and the energy separations between the zero-dimensional sublevels are typically 10−100 meV;9,10 the corresponding electromagnetic wavelength is about 12−120 μm. This large mismatch between the size of the QDs and the wavelength of the radiation gives extremely small scattering cross sections, making conventional absorption measurements on single QDs extremely difficult. Nevertheless, intersublevel transition measurements on single InAs QDs were performed by using the scanning probe microscopy technique at 300 K.11−13 The observed line widths were, however, of the order of 2.5−10 meV. The second problem is even more serious. Because we typically have only a few electrons in a single QD, the expected signal produced by a single QD in the © XXXX American Chemical Society
Received: November 4, 2014 Revised: January 6, 2015
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DOI: 10.1021/nl5042319 Nano Lett. XXXX, XXX, XXX−XXX
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The light source we used was a globar in a Fourier transform spectrometer. To tightly focus the THz radiation onto the samples, a hyper-hemispherical Si lens was placed on the back surface of the samples. A bow-tie antenna structure was also implemented with the nanogap electrodes,18 as shown in Figure 1a, to concentrate the THz field in the nanogap region.19 It should be noted that, although the THz radiation from a globar is unpolarized, the THz electric field in our samples is always linearly polarized along the direction of the nanogap electrodes. All the measurements were performed at 4.6 K. The spectroscopy was performed using a Fourier transform spectrometer in the step-scan mode. Figure 2a shows the energy band diagram of the SET sample, schematically illustrating a mechanism for photocurrent
The self-assembled InAs QDs were grown by molecular beam epitaxy on (100)-oriented semi-insulating GaAs substrates. After successively growing a 300 nm thick Si-doped GaAs layer, a 100 nm thick undoped Al0.3Ga0.7As barrier layer, and a 200 nm thick undoped GaAs buffer layer, self-assembled InAs QDs were grown by depositing four monolayers of InAs at 480 °C. A pair of Ti(5 nm)/Au(15 nm) electrodes separated by a 20 nm gap were directly placed on an InAs QD with a diameter of about 100 nm and were used as the source and drain electrodes, as shown in the inset of Figure 1a.9,10,14−17
Figure 2. (a) The energy band diagrams for the three-step N ↔ N − 1 photoexcitation process. ΔE and EC denote the energy level separation and the charging energy, respectively. ΓE and ΓR denote the tunnel escape rate and the relaxation rate, respectively. GS and ES stand for the ground and excited states, respectively. (b) The allowed regions for the N ↔ N − 1 photoexcitation process are indicated in pink. (c) The energy band diagrams for the three-step N ↔ N + 1 photoexcitation process. (d) The allowed regions for the N ↔ N + 1 photoexcitation process are indicated in blue.
Figure 1. (a) SEM images of a QD SET sample with a bowtie antenna structure. The QD is marked by a red circle. (b) Coulomb stability diagram of sample A. White solid lines are eyeguides for the Coulomb diamonds. White dashed lines and a red dotted line denotes the excited states. The numbers in the figure denote the numbers of electrons in the dot. VDS at P1 and P2 correspond to the excited state energies for N = 3 (7.8 ± 1 meV) and N = 4 (9.3 ± 1 meV), respectively. P3 shows an excited state that results from electron configurations in the p state for N = 4. Its excited state energy is 2.1 ± 0.5 meV. (c) The linear conductance spectrum of sample A. (d) THzinduced photocurrent as a function of VG measured on sample A. The Roman numbers indicate the positions for spectrum measurements. (e) Coulomb stability diagram of sample B. (f) The linear conductance spectrum of sample B. (g) THz-induced photocurrent as a function of VG measured on sample B. (h) Photocurrent mapping as a function of VG and VDS measured in the N = 6 Coulomb diamond for sample B.
generation. Let us assume that the QD contains N electrons in the ground state. When the QD is irradiated with a broadband THz radiation, an electron in the ground state absorbs a photon and makes a transition to an upper energy state. Then, the photoexcited electron tunnels out to the electrode and the QD returns to the initial state with one electron filling back the lower empty state. Since the electron number changes between N and N − 1 during this photoexcitation process, we call this process the “N ↔ N − 1 excitation”. When VG is increased, the upper energy state eventually goes below the Fermi level and the photoexcited electron cannot tunnel out due to blocking by the electrodes. Therefore, the N ↔ N − 1 excitation process generates a photocurrent in the regions shown in pink in the schematic Coulomb stability diagram of Figure 2b. Figure 1b shows the Coulomb stability diagram of a QD SET (sample A). The numbers shown in the diamonds denote the number of electrons, N, in the QD. As seen in the figure, the Coulomb diamonds for the p and d shells are observed.20 The tunneling current through the s shell was too small to be shown in this diagram. From the stability diagram, we can determine the charging energy, EC, to be around 12 meV. Furthermore,
From the scanning electron microscope observation, the QDs were slightly elongated (∼10%) in the direction of the electrodes. We found that the photocurrent was detectable only when the sample had a high tunnel conductance of the order of 1 μS. Therefore, we chose rather large QDs whose diameters were of the order of 100 nm. It is known that such large QDs are less affected by In−Ga intermixing during crystal growth and have high conductances.10 A backgate voltage, VG, was applied to the Si-doped GaAs buffer layer to change the electrostatic potential in the QD. B
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Thus, we call this process the “N ↔ N + 1 excitation”, which generates a photocurrent in the blue-colored regions shown in Figure 2d. This behavior is indeed consistent with the measured photocurrent distribution for sample B. For the N ↔ N − 1 excitation, the required condition for photocurrent generation is that the tunneling rate, ΓE, of the excited sublevel is much larger than the relaxation rate, ΓR. For the N ↔ N + 1 excitation, it is necessary that the tunneling rate for the empty lower sublevel, ΓG, is larger than ΓR. Figure 3a shows the photocurrent spectra measured on sample B at various VG. As seen in Figure 1g, we could observe
when N = 3, an excited state line touches the diamond from the upper left side (shown by a dashed line) and we can determine the energy of the excited state to be 7.8 ± 1 meV. Similarly, when N = 4, the excited state (shown by a dashed line) is observed at around 9.3 ± 1 meV above the ground state. Figure 1d shows the photocurrent induced by the broadband THz radiation measured as a function of VG by applying a small source-drain voltage (VDS = 0.25 mV). The photocurrent was typically of the order of 1 pA. We would like to point out that, when VG = 300 mV (denoted as “III” in Figure 1d), it is expected that the excited state is below the Fermi levels of the electrodes. However, as seen in Figure 1d, we do have a large photocurrent even in this condition. A similar behavior was observed in another sample. Figure 1e shows the stability diagram of sample B. Photocurrent was observed in the N = 6 Coulomb diamond, as seen in Figure 1g. However, the photocurrent is large in the VG region where the excited state is located below the Fermi levels of the electrodes. Figure 1h shows the photocurrent mapping in the N = 6 Coulomb diamond. The observed photocurrent distribution is contrary to the one expected for the “N ↔ N − 1 excitation process shown in Figure 2b. To explain this, let us look into the total energy of the Nelectron system, U(N). U(N) is expressed within the framework of the constant interaction model21 as U (N ) =
(eN )2 + 2C Σ
N
∑ Ei − eNVext
(1)
i=1
where e is the elementary charge, CΣ ≡ CS + CD + CG, Ei is the orbital energy in the dot, and Vext ≡ (CDVDS + CGVG)/CΣ. CS, CD, and CG are the capacitances between the dot and the source, drain, and gate electrodes, respectively. At the charge degeneracy point VG = VG1, U(N − 1) = U(N) and VDS = 0 holds. By substituting these relationships into eq 1, we can derive αeVG1 =
(2N − 1)e 2 + EN 2C Σ
Figure 3. (a) Photocurrent spectra measured at various VG on sample B. The resolution of the measurement was 0.25 cm−1. The fitting curves correspond to the transitions shown in the same color in (c). (b) Wave function patterns calculated for the s, p, and d shells, assuming that the dot has a two-dimensional disk shape (66L × 60W nm2) that is slightly elongated in the x-direction. The THz field is polarized along the x-axis. (c) Energy band diagram for N = 6. Three possible transitions, that is, p− → d−, p− → 2s, and p+ → d+, are indicated by red, pink, and blue arrows, respectively.
(2)
where α ≡ CG/CΣ. In the N-Coulomb diamond, U(N) < U(N + 1) and the system is stable with N electrons in the dot. However, the situation changes with intersublevel photoexcitation. When an electron absorbs a photon and makes a transition to an upper energy state, the total energy of the photoexcited N-electron system, U′(N), is given by U′(N) = U(N) + ΔE, where ΔE is the orbital energy separation between the initial and the final states. Then, we compare U′(N) and U(N + 1) U ′(N ) − U (N + 1) = αe(VG − VG1) − EC
photocurrent in the N = 6 and 7 Coulomb diamonds. We could perform spectroscopy measurements only in the Coulomb blockaded regions, because shot noise was very large in the single electron tunneling regions. As seen in the figure, a photocurrent peak was observed at around 15 meV. Although complete understanding of the photocurrent spectra is beyond the scope of this paper, we would like to briefly discuss the photocurrent spectra measured at N = 6. When N = 6, the p shell is fully occupied and the electron configuration of the initial state is unique. As shown in Figure 3b,c, the selection rule for the intersublevel transition allows three intersublevel transitions; namely, p− → d−, p− → 2s, and p+ → d+, recalling the fact that the THz electric field is polarized along the direction of nanogap electrodes and using a quasi-cylindrical description of the energy levels (e.g., p− and p+ refer to the two p states whose degeneracies are lifted by the small QD anisotropy, as shown in Figure 3b. We use similar notations also for the d shells.). Having this in mind, we decomposed the observed photocurrent peak into three peaks (red, p− → d−,; pink:, p− → 2s; blue, p+ → d+) by numerical fitting. As seen in
(3)
where EC ≡ e /CΣ is the charging energy. Then, we find 2
U (N + 1) < U ′(N ),
when VG > VG1 +
EC αe
(4)
Equation 4 indicates that, when VG > VG1 + EC/αe, an electron is photoexcited to an upper sublevel and, subsequently, another electron in the electrode can tunnel into the lower empty energy state. Then, all the energy levels are pushed up by EC, as schematically illustrated in Figure 2c, and the photoexcited electron goes above the Fermi levels and tunnels out, producing a photocurrent. During this photoexcitation process, the electron number changes between N and N + 1. C
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configurations B and C also become accessible, appearing as the excited state line seen in the Coulomb stability diagram (red dotted line in Figure 1b). Configuration B has two allowed transitions and produces the broad peak at 12 meV in spectrum III. The transition energies for configuration B are smaller than those for configuration A, because configuration B has a higher total energy due to larger Coulomb repulsion. If we compare the p− → 2s transition energies in configurations A and B, the energy difference is 2.5 meV, as shown in Figure 4a, which reasonably agrees with the excited state energy obtained from the stability diagram (2.1 ± 0.5 meV). Similarly, we expect p+ → d+ transition for configuration C. Let us comment on the complexity of the intersublevel transition spectra measured at N = 4. First, after the THz photoexcitation, the emptied state must be filled by an electron in the electrode. However, when the electron enters the dot, several electron configurations are available, because the energy differences for configurations A−C are of the order of a few meV in our large dots. The time-averaged ratio of the configuration population depends on the tunnel conductance and the relaxation rates between the configurations. Second, the photocurrent mechanism changes from the N ↔ N − 1 excitation to the N ↔ N + 1 excitation as VG is increased. This may also affect the line width of each transition. Another remark is that, when Figures 1b and 4a are compared, the intersublevel transition energies (∼10 meV at N = 3 and 12−14 meV at N = 4) are larger by a few millielectronvolts than the excited state energies (7.8 ± 1 meV at N = 3 and 9.3 ± 1 meV at N = 4) determined from the Coulomb stability diagrams, which calls for further systematic studies. In summary, we have proposed a method for performing terahertz spectroscopy on nanometers-scale systems by using metal nanogap electrodes. Intersublevel transition spectra of single self-assembled InAs QDs have been measured with high sensitivities by using a single electron transistor geometry that consists of a QD and nanogap metal electrodes as a terahertz detector. Photocurrent distribution with respect to the Coulomb diamonds indicates that there exist two mechanisms for the photocurrent generation. When the p shell is fully occupied, the electron configuration is unique and the photocurrent spectra are simple. On the other hand, when the p shell is half occupied, there are three possible electron configurations with different Coulomb energies. The fluctuation in electron configurations results in markedly different photocurrent spectra as a function of the gate voltage. The method we have developed in this work can be applied to THz spectroscopy on various kinds of nanometers-scale systems, such as carbon nanotubes, nanowires, and even single molecules.
Figure 3a, the relative intensities of the three peaks vary with VG, but the peak positions do not shift. The line widths of the spectra are reasonably consistent with the escape time expected from the tunnel conductance of the sample (∼1 μS).22 Note that the effect of intersublevel relaxation is rather minor in our large QDs, because the expected relaxation time is of the order of 100 ps − 1 ns.8 Although the origin of the intensity variation of the three peaks with VG is not clear at present, it is likely that the difference in the charging energy for the three different N + 1 electron configurations gives different threshold VG’s in the N ↔ N + 1 excitation process. By using the wave functions shown in Figure 3b, we can roughly estimate the magnitude of the charging energies for the intermediate states for the N ↔ N + 1 excitation process. We found that because the Coulomb energy for the p− → 2s process is the smallest, this transition becomes allowed at the smallest VG, and the p− → d− and p+ → d+ processes follow (please see Supporting Information 2). Figure 4a shows the photocurrent spectra measured on sample A at various VG. When N = 4, rather complicated
Figure 4. (a) Photocurrent spectra measured at various VG on sample A. I−IV correspond to the bias positions shown in Figure 1d. The fitting curves correspond to the transitions shown in the same color in (b). If we compare the p− → 2s transition energies in configurations A and B, the energy difference is 2.5 meV. (b) Allowed intersublevel transitions are illustrated for three possible electron configurations (A−C) when N = 4.
behavior is observed; with increasing VG, the photocurrent peak at lower energy becomes larger, while the higher energy photocurrent peak become smaller and sharper. Figure 4b shows three available electron configurations in the p shell and the allowed intersublevel transitions. Because the exchange interaction is rather small, we will neglect it in the following discussion. Because the Coulomb energy is minimal in configuration A owing to its small orbital overlap, configuration A is the ground state when VG enters the N = 4 region (VG = 40 mV) from the smaller VG side. In configuration A, three transitions are allowed and produce the broad peak at around 14 meV in spectrum II of Figure 4a. The origin of the sharp peak at 12 meV may be due to configuration fluctuation in the initial state, as will be mentioned later. When VG is increased,
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ASSOCIATED CONTENT
S Supporting Information *
Sample preparation and measurements and effective charging energies in the intersublevel transition process. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail: (Y.Z.)
[email protected]. *E-mail: (K.H.)
[email protected]. D
DOI: 10.1021/nl5042319 Nano Lett. XXXX, XXX, XXX−XXX
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(20) Tarucha, S.; Austing, D. G.; Honda, T.; Van der Hage, R. J.; Kouwenhoven, L. P. Phys. Rev. Lett. 1996, 77, 3613. (21) Beenakker, C. W. J. Phys. Rev. B 1991, 44, 1646−1656. (22) The tunnel conductance of 1 μS at 4.6 K corresponds to the tunneling rate of ∼4 × 1010 s−1 if the source and drain tunnel barriers are symmetric. This tunneling rate gives a line width of about 0.16 meV. However, the tunnel barriers are not symmetric for the source and drain electrodes in the present samples. The tunnel conductance is limited by the thicker tunnel barrier, whereas the line width is govern by the thinner tunnel barrier. Therefore, the line width is even larger than that estimated from tunnel conductance and becomes 0.3 ∼1 meV.
(K.S.) Department of Electronics and Intelligent Systems, Tohoku Institute of Technology, Sendai 982−8577, Japan. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank T. Ando, S. Komiyama, and Y. Arakawa for fruitful discussions. This work was partly supported by CREST-JST, Grants-in-Aid from JSPS (No. 25246004, No. 25600013, and No. 26706002), Project for Developing Innovation Systems of MEXT, and research grants from the Canon Foundation, and the Casio Science Foundation. G.B. gratefully acknowledges IIS, University of Tokyo for support. C.N.-B. and G.B. thank JSPS/CNRS for support. Y.Z. gratefully acknowledges the support from the Yoshida Scholarship Foundation.
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REFERENCES
(1) Petroff, P. M.; Lorke, A.; Imamoglu, A. Phys. Today 2001, 54, 46−52. (2) Marzin, J.-Y.; Gérard, J.-M.; Izrael, A.; Barrier, D.; Bastard, G. Phys. Rev. Lett. 1994, 73, 716−719. (3) Grundmann, M.; Christen, J.; Ledentsov, N. N.; Böhrer, J.; Bimberg, D.; Ruvimov, S. S.; Werner, P.; Richter, U.; Gösele, U.; Heydenreich, J.; Ustinov, V. M.; Egorov, A. Yu.; Zhukov, A. E.; Kop’ev, P. S.; Alferov, Zh. I. Phys. Rev. Lett. 1995, 74, 4043−4046. (4) Dekel, E.; Gershoni, D.; Ehrenfreund, E.; Spektor, D.; García, J. M.; Petroff, P. M. Phys. Rev. Lett. 1998, 80, 4991−4994. (5) Drexler, H.; Leonard, D.; Hansen, W.; Kotthaus, J. P.; Petroff, P. M. Phys. Rev. Lett. 1994, 73, 2252−2255. (6) Hameau, S.; Guldner, Y.; Verzelen, O.; Ferreira, R.; Bastard, G.; Zeman, J.; Lemaitre, A.; Gérard, J. M. Phys. Rev. Lett. 1999, 83, 4152− 4155. (7) Zibik, E. A.; Wilson, L. R.; Green, R. P.; Bastard, G.; Ferreira, R.; Phillips, P. J.; Carder, D. A.; Wells, J-P. R.; Cockburn, J. W.; Skolnick, M. S. Phys. Rev. B 2004, 70, 161305. (8) Zibik, E. A.; Grange, T.; Carpenter, B. A.; Porter, N. E.; Ferreira, R.; Bastard, G.; Stehr, D.; Winnerl, S.; Helm, M.; Liu, H. Y.; Skolnick, M. S.; Wilson, L. R. Nat. Mater. 2009, 8, 803−807. (9) Jung, M.; Machida, T.; Hirakawa, K.; Komiyama, S.; Nakaoka, T.; Ishida, S.; Arakawa, Y. Appl. Phys. Lett. 2005, 87, 203109. (10) Shibata, K.; Jung, M.; Cha, K. M.; Sotome, M.; Hirakawa, K. Appl. Phys. Lett. 2009, 94, 162107. (11) Houel, J.; Sauvage, S.; Boucaud, P.; Dazzi, A.; Prazeres, R.; Glotin, F.; Ortéga, J.-M.; Miard, A.; Lemaître, A. Phys. Rev. Lett. 2007, 99, 217404. (12) Sauvage, S.; Driss, A.; Réveret, F.; Boucaud, P.; Dazzi, A.; Prazeres, R.; Glotin, F.; Ortéga, J.-M.; Miard, A.; Halioua, Y. Phys. Rev. B 2011, 83, 035302. (13) Jacob, R.; Winnerl, S.; Fehrenbacher, M.; Bhattacharyya, J.; Schneider, H.; Wenzel, M. T.; von Ribbeck, H.-G.; Eng, L. M.; Atkinson, P.; Schmidt, O. G.; Helm, M. Nano Lett. 2012, 12, 4336− 4340. (14) Kanai, Y.; Deacon, R. S.; Oiwa, A.; Yoshida, K.; Shibata, K.; Hirakawa, K.; Tarucha, S. Phys. Rev. B 2010, 82, 054512. (15) Takahashi, S.; Deacon, R. S.; Yoshida, K.; Oiwa, A.; Shibata, K.; Hirakawa, K.; Tokura, Y.; Tarucha, S. Phys. Rev. Lett. 2010, 104, 246801. (16) Kanai, Y.; Deacon, R. S.; Takahashi, S.; Oiwa, A.; Yoshida, K.; Shibata, K.; Hirakawa, K.; Tokura, Y.; Tarucha, S. Nat. Nanotechnol. 2011, 6, 511−516. (17) Shibata, K.; Yuan, H. T.; Iwasa, Y.; Hirakawa, K. Nat. Commun. 2013, 4, 2664. (18) Shibata, K.; Umeno, A.; Cha, K. M.; Hirakawa, K. Phys. Rev. Lett. 2012, 109, 077401. (19) We have estimated the enhancement factor for the THz power on a single QD to be in the order of 107∼108. E
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