Superlinear Photoluminescence Dynamics in PlasmonâQuantum-Dot

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Superlinear Photoluminescence Dynamics in Plasmon--Quantum-Dot Coupling Systems Masanobu Iwanaga, Takaaki Mano, and Naoki Ikeda ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b01142 • Publication Date (Web): 04 Dec 2017 Downloaded from http://pubs.acs.org on December 11, 2017

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Superlinear Photoluminescence Dynamics in Plasmon–Quantum-Dot Coupling Systems Masanobu Iwanaga,∗ Takaaki Mano, and Naoki Ikeda National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba 305-0044, Japan E-mail: [email protected] Abstract Light–matter interaction exploiting plasmons is attracting great interest in terms of a new twist, hot electrons. We designed a basic configuration to couple plasmonic metasurfaces with a layer of quantum dots (QDs) embedded in semiconductors and experimentally investigated the photoluminescence (PL) dynamics in the coupled systems of III-V semiconductor QDs with plasmonic metasurfaces. The QDs of InAs, which emit luminescence at telecom wavelengths near 1300 nm, were grown on GaAs substrates with a molecular-beam-epitaxy technique. The plasmonic metasurfaces were fabricated on top of the GaInAs substrates, using a numerical design for single-layer Au metasurfaces. Here we show that the PL responses through the plasmonic metasurface becomes more active in the coupled systems than those in the QDs without the plasmonic metasurfaces, being superlinear with respect to the excitation laser intensity, even under weak continuous-wave excitation. The superlinear responses are successfully described in a general theoretical model, incorporating hot-electron contributions by the plasmonic metasurfaces to the PL processes. We examined the PL responses at room temperature and a low temperature of 9 K, and found that the hot electrons mainly contribute to superlinear PL responses at room temperature, whereas induced transitions between the excitonic levels in the QDs are significant at 9 K. Thus, our

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systematic study enables discrimination of the origins of the nonobvious PL responses. In particular, this study provides a new insight for the active contributions by hot electrons to photoexcited processes at room temperature.

Keywords Photoluminescence, Superlinear Response, Quantum Dot, Semiconductor, Plasmonic Metasurface, Hot Electron

The manipulation of optical transitions in materials is one of the goals in plasmonics. At the early stage, electric-field enhancement was dominantly, perhaps excessively, stressed and led the numerous trials on surface-enhanced Raman scattering, 1–5 fluorescence-enhanced spectroscopy, 6–11 and so on. As the studies advanced, the simple scheme relying only on electricfield enhancement becomes insufficient to describe experimental results reported recently. For example, the artificially selective control of enhanced optical transition in fluorescence molecules has been demonstrated. 12–15 Additionally, it has been found that plasmons exit the purely classical framework and metallic nanostructures can be sources to generate so-called hot electrons. Hot electrons have been extensively investigated in many plasmonic platforms for photocatalysis and photovoltaic applications. 16–21 In these applications, the efficient extraction of the hot electrons is the main issue. However, there are few reports that address the active contributions of hot electrons to photoluminescence (PL). This is probably because it is generally difficult to discriminate the hot-electron contributions from others. Still, PL is one of the fundamental optical processes in materials. It is therefore highly desirable to demonstrate the active roles of hot electrons in PL processes. Here, we experimentally examine a series of configurations composed of plasmonic meta2


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surfaces and InAs quantum dots (QDs) grown on GaAs substrates. The configurations are fundamental in terms of current-drivable light emitting devices, compared with the configuration using colloidal QDs such as CdS 22 that are grown in chemically wet processes and are electrically isolated. We intend to realize single-photon emitting devices in the near future and address the sparsely distributed QDs. This setting is in contrast to the denseQD devices 23,24 and the so-called SPASERs (surface-plasmon-amplified stimulated emission resonators) that have been realized employing gain semiconductor materials of substantial volumes and placing the gain materials on or near smooth noble-metal surfaces. 25–29 (a)

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Figure 1: (a) Schematic of the present experimental configuration. (b) AFM image of InAs QDs, whose one side is 500 nm. (c) Top-view SEM image of the Au-mesh metasurface of 330 nm periodicity, which was fabricated on the GaInAs sample. The white scale bar indicates 1 µm. Figure 1a illustrates the experimental configuration addressed in this article. The Aumesh-shaped metasurface was fabricated on the outermost surface of InAs-QD-grown GaAs substrate; the QDs were covered by barrier and capping layers, and embedded at a depth of 50 or 22 nm from the outermost surface in the experiment. PL of the QDs is induced by excitation light and measured through the barrier/capping layer and the metasurface. Figure 1b shows an atomic-force-microscopy (AFM) image of the InAs QDs in a tilted 3


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manner, whose side corresponds to 500 nm. The planar density of the QDs was approximately 40 µm−2 and a QD typically had 30 nm diameter and 12 nm height. Figure 1c shows a scanning-electron-microscopy (SEM) image, taken in a top-view configuration, of a Au-mesh metasurface with periodic length 330 nm. The white scale bar indicates 1 µm.

Experimental Sample preparation The InAs QDs were grown with a solid-source molecular-beam epitaxy (MBE) technique. The substrates were n+ -GaAs (100) wafers.

The layer structures grown on the GaAs

wafers were as follows, where we note the order of the growth procedure: GaAs buffer (500 nm)/Al0.3 Ga0.7 As barrier (50 nm)/GaAs (50nm)/InAs QDs/GaAs (20 or 10 nm)/Al0.3 Ga0.7 As barrier (20 or 10 nm)/GaAs of outermost capping layer (10 or 2 nm). We prepared barrier/capping layers over the InAs-QD layer of two thicknesses: 50 and 22 nm. To form the InAs QDs, InAs of two monolayers (MLs) was supplied at 0.005ML/s and 500 ◦ C. Apart from the InAs QDs and the single succeeding GaAs layer, the other layers were grown at 580 ◦ C. The resultant QDs were quite uniform in shape. A typical AFM image is shown in Figure 1b, which was taken at the step just after the growth of the InAs QDs and GaAs layer. The QD density was approximately 4 × 109 cm−2 . The plasmonic metasurfaces were fabricated directly on the MBE-grown samples. The nanopatterning of the metasurfaces was conducted by electron-beam (EB) drawing. Based on the numerical designs noted below, we adopted a mesh-shaped design in Figure 1a; the periodic length was set to 330, 352, and 374 nm in order to tune the plasmonic resonance to the QD-PL emission wavelengths. After the development of the EB resist, metals of 1-nm Ti and 30-nm Au were normally deposited on the developed nanopatterns. The thin Ti layer was introduced as an adhesion layer between GaAs and Au. Removing the nanopatterned EB resist resulted in the mesh-shaped metasurfaces, one of which is shown in Figure 1c. The 4


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typical size of the metasurfaces was 1 × 1 mm2 . It is noted that the mesh-shaped metals form Schottky contact to the GaInAs samples.

Numerical methods and designs To design plasmonic metasurfaces, which are definitely resonant at the PL wavelengths of the InAs QDs and have rather simple single-layer structures, we employed a numerical method of rigorous coupled-wave analysis (RCWA), 30 which was coded compatibly with the scattering(S)-matrix algorithm. 31 The RCWA incorporating the S-matrix algorithm is suitable to numerically calculate the optical spectra of arbitrary periodic structures, including metals. After many computational trials, we selected the Au-mesh metasurfaces, as illustrated in Figure 1. For the selection, we emphasized the spectral contrast at the resonance and the localized distribution of the resonant electromagnetic field. The Au-mesh metasurfaces exhibited a change of reflection efficiency of approximate 20%, which was the only detectable optical quantity in the configuration of single-layer plasmonic metasurface on the bulk GaAs. The spectral contrast is a signature for large light absorption by metasurfaces. The numerical results for the Au-mesh metasurface of various periodic length are shown in the Supporting Information (Figure S1). We note that other structures such as nanoantenna showed less spectral contrast. Besides, grating couplers had a disadvantage in the localization of the resonant field. When large light-absorbing metasurfaces were successfully prepared, 32,33 it was demonstrated that fluorescence on the metasurfaces becomes highly enhanced, 12–14 due to the reciprocity connecting the large light absorption to high emittance of the metasurfaces. 34 From the success in fluorescence enhancement, we adopted the selection criterion for the metasurfaces in this study. The metasurfaces were fabricated on bulk GaAs substrates, so that it is difficult to evaluate light absorption by the metasurfaces because transmissive light is absorbed in the bulk 5


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crystals. As an alternative way, we evaluated light absorption of the Au-mesh metasurface on a GaAs slab, which is optically thin. We consequently found that the Au-mesh metasurface has discrete resonances in the wavelength from 850 to 1300 nm and that one of the resonances corresponds to the minimum of reflection efficiency. These data are shown in the Supporting Information (Figure S2). Although the MBE-grown layer structures consist of GaAs, GaInAs, and AlGaAs, we simply assume, in the computation, that they have nearly the same complex permittivity as GaAs. Indeed, in the near infrared range of present interest, the difference was not prominent. 35 In addition, the total thickness was relatively small. Consequently, we numerically evaluated the electromagnetic field distributions under this assumption. The complex permittivities of Au and Ti were taken from the literature, 36 and that of air was set to 1.00054.

Optical experiment The PL of the InAs QDs was measured in illumination-and-collection setups at room temperature and 9 K. Excitation light of wavelength 532 nm was emitted from continuous-wave lasers and illuminated on the sample surface with a focus spot of approximately 100 µm diameter. To suppress undesired laser-light scattering in measuring the PL, we inserted high-optical-density laser-light cut filters at the collecting path. Also, a short-wavelength pass filter was inserted at the illuminating path to avoid unexpected long-wavelength light from the laser. The collected PL was transferred to a monochromator and measured by a liquid-nitrogen-cooled InGaAs detector. Reflectance (R) spectra were measured at room temperature using a spectrometer. The incident angle was set to 5◦ , i.e., nearly normal. At this incident condition, the measured R spectra are almost independent of polarization. We also note that the R spectra are assumed to be nearly independent of temperature because the complex permittivities of Au, Ti, and GaAs are hardly affected by temperature in the wavelength range around 1300 nm; therefore, we use the R spectra as reference spectra at low temperature. 6


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Results and discussion Superlinear PL responses

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Figure 2: Measured PL and reflectance (R) spectra of InAs QDs, measured at room temperature. (a)–(c) Series of PL (red) and R (purple) spectra of the as-grown InAs QDs, a = 330 metasurface(MSF)-covering QDs, and a = 352 MSF-covering QDs, respectively. The PL spectra in each panel depend on the excitation-laser power. The right axes indicate the R spectra. (d)–(f) The PL intensities at the two peak positions of 1288 ± 1 and 1208 ± 1 nm in (a)–(c), respectively, which are shown with closed red and blue circles in the log-log scale. The black and magenta solid curves are derived from the theoretical model described in Section . Figure 2 shows a series of PL (red curves) and R spectra (purple curves) measured at room temperature; in Figure 2a, the PL spectra of the InAs QDs for several excitation powers and the R spectrum of the GaInAs substrate are shown, and, in Figure 2b,c, the PL and R spectra of the GaInAs substrates with Au-mesh metasurfaces of periodic length 330 and 352 7


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nm, respectively, as shown. The troughs of the R spectra correspond to resonances of the metasurfaces. The metasurface of periodic length a = 330 nm in Figure 2 has a resonance at the PL wavelengths including 1200 and 1300 nm, and the metasurface of a = 352 nm in Figure 3 has a resonance tuned only to the PL band at 1300 nm. As for the PL spectra in Figure 2a–c, we observed main three peaks at 1290, 1200, and 1140 nm. The longest-wavelength (i.e., lowest-energy) PL peak is ascribed to the lowest excitons in the InAs QDs. The other peaks presumably come from higher excitons of n ≥ 2 where n is principal quantum number because of the fairly large energy splitting from the lowest exciton, of the room temperature measurement, and of the excitation-power dependence examined later. These conditions are likely to deny possibilities of LO-phonon replica 37 and biexcitons. Note that multiple excitons are easily created in each QD under fairly large excitation power. In addition, the PL band of the lowest exciton at 1290 nm in Figure 2a–c exhibits two peaks at 1288(±1) and 1302(±1) nm, being likely to comprise small several peaks. This property probably comes from InAs QDs of different monolayer height; indeed, it was frequently reported that the III-V semiconductor QDs of different monolayer height show excitonic PL bands of several small peaks. 38,39 The different monolayer height affects the confined exciton energy, resulting in the different PL wavelengths. We note that the measured PL spectra represent the ensemble within the focal spot of excitation light. Figure 2d–f shows the PL intensities at the two main peaks (closed circles), dependent on the excitation-laser power on the sample surfaces. The PL intensities were collected from the PL spectra as shown in Figure 2a–c. The solid curves reproducing the measured PL intensities are described later (Section “Theoretical model for the superlinear PL response”). To understand the nontrivial excitation-power dependence, let us briefly mention the results using a simple power function before introducing a theoretical model. The dependence of PL intensity IPL on excitation power P can be fitted using an equation such as IPL = a · P α + b (a and b: constants) in divided subranges. For example, as for the InAs QDs

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without any metasurface in Figure 2d, the lowest exciton peak (red circles) is almost linear (i.e., α = 1.0) in the power range below 1 mW and the second peak (blue circles) is slightly superlinear, such as α = 1.15, in the same range; the lowest peak shows a clearly sublinear dependence, such as α = 0.3, in the power range above 1 mW. As for the InAs QDs associated with the plasmonic metasurfaces, the lowest peak is superlinear with respect to the excitation power, such as α = 1.4–1.7, and the second peak is also superlinear, such as α = 1.5–1.8, in the power range below 1 mW. The fitted results can be seen in the Supporting Information (Figure S3). Thus, it is experimentally evident that the plasmonic metasurfaces contribute to the more active PL responses, although the mechanism thereof has not been clarified so far. We also examined a specimen of plasmonic metasurface of a = 374 nm though the measured data are not shown here. In that case, the resonance of the plasmonic metasurface is located at a longer wavelength than the metasurface of a = 352 nm and is off-resonant to the PL of the InAs QDs. The PL responses to the excitation power were similar to those shown in Figure 2f. We mention the PL responses later (Section “Implications by the theoretical model”). Figure 3 shows PL (red solid curves) spectra measured at a low temperature of 9 K and reference R (purple dashed curves) spectra that are the same as those in Figure 2. As the temperature decreases, the peak wavelengths of the PL spectra move toward shorter wavelengths; for example, the lowest exciton peak of 1288 nm at room temperature (Figure 2) moves to approximately 1200 nm at 9 K (Figure 3). Figure 3a shows the PL spectra of the InAs QDs at 9 K, dependent on the excitation-laser power. Obviously, as the excitation power increases, the second PL peak at 1121 nm becomes larger than the lowest exciton peak at 1200 nm. As for the line width of each PL peak, it is relatively narrower than that at room temperature (Figure 2a); as a result, multiple peaks observed in the lowest-exciton peak at room temperature become deeply overlapped at 9 K and probably are not seen in Figure 3a.

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Figure 3: PL spectra measured at 9 K and reference R spectra. (a) PL spectra (red) of the InAs QDs. (b) and (c) PL spectra (red) of the QDs covered by the metasurfaces of periodic length 330 and 352 nm, respectively. The R spectra (purple dashed curves) are also shown, indicated by the right axes. (d)–(f) Excitation-power-dependent PL intensities at the two main peaks of 1200 ± 2 and 1121 ± 1 nm in the PL spectra (a)–(c), respectively, plotted in the log-log scale. The black and magenta solid curves and lines come from the theoretical model in Section .

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Figure 3b,c shows the PL spectra measured through the plasmonic metasurfaces of periodic length a = 330 and 352 nm, respectively. The R spectra are shown with dashed purple curves, which are the same as those in Figure 2b,c and indicated by the right axes. The resonance of the metasurface of a = 330 nm is tuned to the lowest exciton, whereas that of the metasurface of a = 352 nm is off-resonant to the PL wavelengths from 1050 to 1200 nm. Accordingly, a definite resonant effect is observed; when the PL of the lowest exciton is on resonance (Figure 3b), the ratio of PL-peak intensities at 1200 and 1120 nm is approximately 1.5 at the largest excitation power; in contrast, when the PL of the lowest exciton is off resonance (Figure 3c), the ratio is approximately 0.9; thus, there is certainly a resonant enhancement effect. Figure 3d–f shows the PL intensities of the two main peaks of 1200 ± 2 (red closed circles) and 1121 ± 1 nm (blue closed circles), plotted with respect to the excitation-laser power. Under a weak-excitation range less than 1 mW, the PL intensities of the InAs QDs, IPL , which are not associated with any plasmonic metasurface are almost linear for the lowest exciton peak and superlinear for the second exciton peak (i.e., α = 1.7). However, in the same excitation range, the PL intensities detected through the plasmonic metasurfaces are slightly superlinear for the lowest exciton peak and superlinear (i.e., α = 1.6–2.2) for the second peak. The fitted results are shown in the Supporting Information (Figure S4). Because the resonant of the plasmonic metasurface is tuned to the lowest exciton peak, we can attribute the increase in the superlinearity to the resonance matching. The nonobvious dependence on the excitation power in the measured range is successfully reproduced by the solid curves that are derived from a theoretical model described in the next subsection. We also experimentally examined GaInAs substrates with a barrier/capping layer of 20 nm thickness. The PL from InAs QDs was quite similar to that shown in Figure 2 with/without plasmonic metasurfaces. The difference in the thickness of barrier/capping layer did not result in a prominent difference in the PL data. We show the results in the Supporting Information (Figure S5).

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At the end of this subsection, we refer to a spectral property of the measured PL. We have used the PL-peak intensities in the plots for excitation power. If substantial spectral broadening or narrowing takes place in a PL band, integrated PL intensity is suitable for the plot. However, such spectral change were not observed in each PL band; therefore, the PL-peak intensities are almost proportional to the integrated PL intensities in this study. The verification is shown in the Supporting Information (Figure S6). Thus, the plots in Figure 2d–f and 3d–f are reasonable.

Theoretical model for the superlinear PL responses Here, we introduce a reasonable theoretical model for describing the PL responses in Figures 2 and 3. We moreover derive the functions to reproduce the measured PL responses for the excitation power. Figure 4 shows a schematic illustration of energy diagrams in the GaInAs crystals including the InAs QDs, which are weakly coupled with plasmons in the metasurfaces. Under the weak coupling, the main structures of energy levels in the QDs and the plasmonic metasurfaces are maintained, and the interplay between the QDs and metasurfaces is incorporated. Concretely, we assume only one that hot electrons transfer to the excitonic levels (ex1 and ex2) in the QDs, as indicated by the dotted arrows. As suggested in Figures 2 and 3, the plasmonic metasurfaces enable the more active PL responses; accordingly, we introduce the interplay as a possible origin of the PL responses. In Figure 4, the excitation light of wavelength 532 nm is partially absorbed by Au in the plasmonic metasurfaces and also by the GaInAs substrate; that is, it simultaneously induces interband transitions in the Au forming the metasurfaces 40 and in the GaAs substrate. 41 This situation was also confirmed in the Supporting Information (Figure S2). After the interband photoexcitations, the excited carriers relax into lower energy levels through nonradiative processes, as indicated by dashed arrows; when there is no coupling between the GaInAs substrates and the plasmonic metasurfaces, a substantial portion of the excited carriers in the 12


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Plasmonic metasurface

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Figure 4: Schematic of energy diagrams in the weakly coupled system of the InAs-QDembedded GaAs crystal (GaInAs) with the plasmonic metasurfaces. GaInAs substrate relaxes into the excitonic levels and the excited electrons in the Au forming the plasmonic metasurfaces mostly relax into the ground state. These are ordinary relaxation processes. We also note that the main two excitonic levels ex1 and ex2 are incorporated in this diagram because we intend to clarify the main features in the present coupling systems. However, it is possible to extend the present model to the excitonic states of more levels in a straightfoward way. In accordance with the energy diagram in Figure 4, we can write down the following rate equations for the PL processes: dnex1 = r1 nc + δ1 ne − γ1 nex1 − BU (ω)nex1 dt dnex2 = r2 nc + δ2 ne − γ2 nex2 + BU (ω)nex1 dt

(1) (2)

where nex1 and nex2 denote number of the excitons at levels ex1 and ex2, respectively, nc represents the number of states at the excited continuum, ri (i = 1, 2) are the nonradiative relaxation coefficients from the continuum to the excitons, δi (i = 1, 2) are the transfer rates of the hot electrons from the plasmonic metasurfaces, ne are the number of states of the hot 13


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electrons, γi (i = 1, 2) are the radiative decay rates from levels ex1 and ex2, respectively, B is the so-called Einstein’s B coefficient representing the induced transitions between levels ex1 and ex2, and U is the distribution of photons at frequency ω. We note that level ex1 is the lowest excitonic state in the QDs and level ex2 represents a higher excitonic state in the QDs, corresponding to the second PL peak. Under the experimental condition, the continuous-wave excitation leads to balanced input–output states, i.e., dnex1 dnex2 = = 0. dt dt

(3)

When eq 3 holds, eqs 1 and 2 are solved for nex1 and nex2 as follows. r1 n c + δ 1 n e , γ1 + BU (ω) r1 n c + δ 1 n e 1 r2 n c + δ 2 n e + BU (ω) . = γ2 γ1 + BU (ω)

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First, let us mention a simpler case than the present experiment, i.e., a case without the plasmonic metasurfaces; then, the hot-electron contribution δi in eqs 4 and 5 is assumed to be δi = 0 (i = 1, 2). The number of photoexcited states nc is proportional to excitationlight power Pexc under the experimental condition (Section “Optical experiment”), which is expressed as nc = CPexc , where C is constant. As for the photon distribution U (ω), there has been no established theory to describe it under thermal nonequilibrium balanced states as in the present experiment; nevertheless, the distribution U is assumed to increase in the excitation-light power; therefore, we can express it in a general form as U ∝ Pxexc (x > 0) ˜ x . Thus, eqs 4 and 5 are explicitly written, dependent on Pxexc , as and write BU (ω) = BP exc follows: r1 C Pexc , ˜ ˜ B γ1 /B + Pxexc r2 C r1 P1+x exc = Pexc + . ˜ + Px γ2 r2 γ 1 / B exc

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(7)

14


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Equations 6 and 7 are power laws of the populations of the PL states for the excitation-light power. These equations are applicable to the PL responses from the InAs QDs because the nex1 and nex2 are proportional to the resultant PL intensities; indeed, the equations have reproduced the measured data, as shown by the solid curves in Figures 2d and 3d. Thus, the nonlinear PL responses from the InAs QDs are described using eqs 6 and 7. Note that the coefficient r1 /r2 in eq 7 represents the contribution of induced transition to the population nex2 . If the coefficient r1 /r2 should be negligible, the nex2 in eq 7 would be simply proportional to the excitation power Pexc . However, the experimental results show nonlinear responses of the ex2 state in Figures 2d and 3d. Second, let us come back the present experimental situation incorporating the plasmonic metasurfaces. The differences of the equations for nexi appear only in the hot-electron terms δi ne (i = 1, 2). Although, to our knowledge, no general hot-electron theory applicable to this experiment has been established, it is possible to evaluate the contribution by phenomenologically assuming δi ne = Di Pyexc (y > 0 and Di is constant). Note that the power index y is assumed to approximate a finite range of the excitation power. Then, from eqs 4 and 5, the number states nexi are explicitly expressed such that r1 C Pexc + (D1 /(r1 C))Pyexc , ˜ ˜ + Px B γ 1 /B exc r2 C D2 y r1 Pexc + (D1 /(r1 C))Pyexc x = Pexc + Pexc . P + ˜ + Pxexc γ2 r2 C exc r2 γ 1 /B

nex1 =

(8)

nex2

(9)

Equations 8 and 9 represent the excitation-power dependence of the number states, indicating that the dependence is not as simple as linear response. By incorporating the hot-electron contribution, the term (Di /(ri C))Pyexc (i = 1, 2) appears in eqs 8 and 9. The coefficient Di /(ri C) is an index to show the contribution of hot electrons to the population nexi , and the power index y represents nonlinearity of the hot-electron transfer process when y 6= 1. As shown in Figures 2 and 3, the nonobvious PL responses in the coupling systems are reproduced using eqs 8 and 9. In Figure 2, we examined a two-order excitation-power range

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Table 1: Parameters in the theoretical model for the PL data measured at room temperature (Figure 2). The symbols MSF and a denote metasurface and periodic length, respectively. For example, sample a = 330 nm denotes the MSF of a = 330 nm. Samples no MSF a = 330 nm a = 352 nm a = 374 nm

x y 0.8 — 1.0 1.5 1.0 1.5 1.1 1.6

D1 /(r1 C) 0 15 15 14

D2 /(r2 C) 0 0.7 0.9 0.5

r1 /r2 1.4 ∼ 0.01 ∼ 0.01 ∼ 0.01

above 0.1 mW.

Implications by the theoretical model Here, we briefly summarize the parameters in the theoretical model (Section “Theoretical model for the superlinear PL responses”) and discuss the implications for the superlinear PL processes in the present coupling systems. Table 1 lists the key parameters in eqs 8 and 9, which reproduced the PL data at room temperature as the solid curves in Figure 2. Note that we include the result for the metasurface of a = 374 nm. The PL data was measured at room temperature. The indices x and y are the power indices such that U ∝ Pxexc and δi ne = Di Pyexc (i = 1, 2), respectively. The values of x were found to be close to 1 for the four cases in Table 1. This means that photon distribution U is almost proportional to the excitation power. In contrast, the values of y are approximately 1.5, indicate nonlinear (or superlinear) contributions of the hot electrons to the excitons, and is found to be the origin of the superlinear PL responses. The value y also implies that the hot-electron transfer is efficient at room temperature and that the Au-mesh metasurfaces are working as an electrode supplying electrons. We also point out that the coefficient D1 /(r1 C) is substantially larger than D2 /(r2 C), which means that the hot electrons mostly transfer to the ex1 state. This selective transfer probably reflects a general tendency in relaxation processes; that is, excited states tend to relax into lower energy states as possible when there are multi-relaxation levels. Still, the D2 /(r2 C) play a role in the superlinear PL responses of the ex2 states because it has finite 16


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Table 2: Parameters in the theoretical model for the PL data measured at 9 K (Figure 3). The symbols are the same as those in Table 1. Samples no MSF a = 330 nm a = 352 nm a = 374 nm

x y 1.0 — 1.0 1.1 1.0 1.1 1.1 1.0

D1 /(r1 C) 0 33 11 43

D2 /(r2 C) 0 ∼0 ∼0 ∼0

r1 /r2 40 1.2 1.5 0.5

values and is not 0. Note that in the case without any metasurface, the hot-electron transfer is exactly 0 (i.e., Di = 0) and y does not appear at all in the analysis (see eqs 6 and 7). The coefficient r1 /r2 indicates the degree of the contribution of the induced transition from the ex1 to ex2 states. It takes a definite value of 1.4 in the case without any metasurface whereas it is quite small (∼ 0.01) in the cases with the metasurfaces. Indeed, we found that r1 /r2 can be practically replaced with 0 in case with the metasurfaces; this result for r1 /r2 strongly suggests that the population of the ex2 state hardly increases owing to the B-factor induced transition. Thus, the superlinear PL responses of the higher exciton at room temperature are mainly attributable to the hot electrons generated in the plasmonic metasurfaces. Table 2 lists the parameters that are the same as those in Table 1. The parameters reproduce the PL data as the solid curves in Figure 3. The PL data were measured at a low temperature of 9 K. As for the power index x, it is similar to the result at room temperature (Table 1), whereas the index y is close to 1, which implies that hot-electron transfer at 9 K is less efficient than at room temperature. In particular, we point out that the hot-electron transfer to the ex2 states is virtually 0 (i.e., D2 ∼ 0). This is distinct from the results at room temperature. In addition, the coefficient r1 /r2 in Table 2 is in the order of 1, which is also distinct from the room-temperature results. The parameters suggest the following: (i) the induced transition between the ex1 and ex2 levels takes place in an efficient manner (i.e., r1 /r2 ∼ 1), and (ii) the hot electrons selectively transfer to the lowest exciton, ex1 (i.e, D2 ∼ 0). As for the coefficients D1 /(r1 C) and r1 /r2 , we find a qualitative correlation; when D1 /(r1 C) 17


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becomes large (or small), r1 /r2 becomes small (or large). This correlation suggests that a coupling system of more efficient hot-electron transfer tends to have less efficient induced transition between ex1 and ex2. Thus, the present analysis enables to provide the insight for the coupling systems. Let us consider the difference at room temperature and 9 K. The energy difference between the ex1 and ex2 states is 71 meV and the thermal energy kB × 300 K (kB : Boltzmann constant) is 26 meV at room temperature, whereas at 9 K the energy difference is 73 meV and the thermal energy is 0.77 meV. Accounting for these thermal energy factors, thermal fluctuations between the levels ex1 and ex2 are substantially suppressed at 9 K and probably the well-defined induced transition becomes possible at 9 K; on the other hand, at room temperature, the induced transition most likely becomes an obscure transition due to the thermal fluctuations. Overall, the dynamical processes involving the ex1 and ex2 states becomes distinct at room temperature and 9 K, giving rise to the superlinear PL responses in different ways. Next, we show other results derived from different parameters to confirm the allowance in this model analysis. Figure 5a shows plots of nex2 , derived from eq 9 for the metasurface of a = 352 nm; the PL data for the higher exciton (blue closed circles) and the reproduced curve (magenta) are taken from Figure 2f. As shown in Table 1, the parameters y and r1 /r2 represent the main features. Therefore, we changed only the values of y or r1 /r2 , and evaluated the theoretical curves using eq 9. When y deviates from the optimal value of 1.5 as indicated in the panel, the theoretical curves (orange and purple) deviate from the PL data. When r1 /r2 becomes larger than 0.01, the theoretical curves (green and black) appear far below the PL data. Note that the curves are shown as to have equivalent maxima. Thus, it is unlikely that there are other parameters different from Table 1 and capable of reproducing the PL data. Figure 5b shows the PL data for the lowest exciton (red closed circles) and the reproduced theoretical curve (black), which are taken from Figure 3e. We compare other curves evaluated

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(a) Room temperature, MSF of a=352 nm


10

6

PL at 1207.4 nm nex2 10

10

10

5

y = 0.5 y = 1.0 4

3

r1/r2 = 1 r1/r2 = 10 10

2 2

4 6

2

0.1

4 6

2

1

4 6

2

10

Excitation Power (mW) (b) 9 K, MSF of a=330 nm 10


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10

10

10

6


5

4

(1.5,1.1) (1.2,1.1) (0.7,1.1) (0.5,1.1) (1.0,0.7) (1.0,1.5)

3

2

10 0.01

0.1

1

10

100


Figure 5: Comparison of the PL-data-reproducing curve with curves of different parameters in the theoretical model. (a) The PL data for a higher exciton peak (blue closed circles) measured at room temperature and the theoretical curve (magenta) are taken from Figure 2f. The parameters y or r1 /r2 were changed, as indicated in the panel, and the four theoretical curves (orange, purple, green, and black) were evaluated using eq 9. Note that the curves were adjusted to have the same maxima. (b) The PL data for the lowest exciton (red closed circles) measured at 9 K and the theoretical curve (black) are taken from Figure 3e. The parameters (x, y) are changed as indicated in the panel. The dashed curves (orange, ocher, green, and light blue) were evaluated by changing y and the solid curves (magenta and purple) are based on different x.

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by eq 8 with different parameters. As for nex1 , because the set of power indices (x, y) mainly determines the shape of the curves (eq 8), we changed only the set (x, y) as indicated in the panel. The x-changed results are shown with dashed curves (orange, ocher, green, and light blue), and the y-changed results are shown with solid curves (magenta and purple). It is confirmed that a small change in x or y can result in a large deviation from the PL data. Thus, the allowance for (x, y) turns out to be small. At the end of this section, we stress that this analytical consequence is obtained in quite a general setting of the energy levels in the QDs coupling weakly with the plasmonic metasurfaces; therefore, similar power laws will be found in many plasmon–quantum-dot coupling systems.

Electric-field and Poynting-field distributions Here, we show numerically evaluated electric-field distributions around the plasmonic metasurfaces. Additionally, we estimate effective transmission efficiency of the PL emitted by the QDs to the detection region. Figure 6a,b shows the numerically calculated snapshots of the electric-field component Ex around a typical plasmonic metasurface of periodicity of 360 nm. The xz-section views are shown; as for the x direction, the length is set to two unit-cell lengths, and the xzsection goes through the center of the square apertures of the Au meshes. The incidence was set to normally illuminate the metasurface from the air side and to be x-polarized with an absolute value |Ex | = 1.0. The incident wavelengths are 532 and 1280 nm in Figures 6a and 6b, respectively; the former is the excitation wavelength and the latter is the PL-emission wavelength. In addition, the PL wavelength is resonant to the resonance of the plasmonic metasurface. It is verified that the incidence gradually decays in the GaAs and that the electric-field component is particularly enhanced and strongly localized at the sidewall of the Au-mesh structure. The QD position is indicated by dashed lines, located at z = −50 nm. Therefore, it is also verified that electric-field enhancement of the QDs is not expected in 20


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(a) z

1.3

Au

air x

Au

GaAs

-1.3

QDs (b) 2.5

air

GaAs

-2.5

(c) z = -50 nm

(d) z = 81 nm

0

y -0.29

x (e) 0.0

-0.1

Sz

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ACS Photonics

From bulk GaAs to air Sz: fwd comp only Sz: fwd&bwd average through the MSF

-0.2 air

-0.3 -100

-50

GaAs

0

50

100

z (nm)

Figure 6: Simulated resonant electric fields and Poynting flux. (a) and (b) Snapshots of electric-field component Ex at the excitation wavelength of 532 nm and PL-emission wavelength, respectively. The xz -section views are shown. (c) and (d) The z component of Poynting vector Sz at the xy sections of z = −50 and 81 nm, respectively; the z = 0 position was defined at the air/GaAs interface and the Poynting flux was set to propagate from bulk GaAs to air. The color bar and the coordinate setting are in common to (c) and (d). White dotted lines denote projection of the Au mesh onto the xy domain. (e) Profiles of the Sz components. Black solid line shows the forward-component Sz profile without any plasmonic metasurface. Light blue broken line shows the total Sz profile containing forward and backward components. Red dot indicates the averaged value of Sz through the metasurface.

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this experimental configuration. Let us estimate effective transmission efficiency of PL emitted by the QDs located at z = −50 nm. We set the incidence of the PL wavelength of 1280 nm, which propagates along +z direction in the bulk GaAs. The coordinate is set to be the same as that in Figure 6a; then, the position of z = 0 is assigned to the interface of air and bulk GaAs. Figure 6c,d shows the xy-section views of the forward Sz components at z = −50 and 81 nm, respectively, where Sz denotes the z component of Poynting vector. Note that the forward component moves for −z direction; accordingly, the color bar in common with Figure 6c,d takes negative values. The sections correspond to an xy-unit cell of the plasmonic metasurface. Figure 6c represents the incident component and Figure 6d displays the transmitted Sz patterns in air, which come from the Au-mesh metasurface structure; the projection of the Au mesh onto the xy-section is indicated by the white dotted lines. Figure 6e shows the profiles of the Sz components; the black solid line shows the forward Sz component without any metasurface, the light blue broken line shows the total Sz component containing the forward and backward components, and the red dot indicates the Sz value with the plasmonic metasurface, which was averaged over an xy-unit cell. From the Sz components, the transmittance without any metasurface is estimated to be 69.7% and that with the metasurface is 51.3%. Thus, the metasurface is found to reduce the transmission efficiency of the PL emitted by the QDs to the air region. This is probably due to the excitation of the plasmonic resonance in the metasurface. These estimations are consistent with the experimental PL data in Figures 2 and 3. Thus, the metasurfaces do not significantly increase the PL-extraction efficiency, whereas we did not observe any drastic quenching of the PL intensity. Therefore, there seems to be scope to search for a metasurface with better PL-extraction efficiency. Overall, the metasurfaces are sources of hot electrons for the InAs QDs at room temperature. In this sense, the metasurfaces play an active role as an electrode, having a potential to serve as an element in current-driven light emitting devices.

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Conclusions We have experimentally examined the PL responses from the coupling systems of MBEgrown InAs QDs and plasmonic metasurfaces. The InAs QDs emit telecom-wavelength PL at room temperature and the plasmonic metasurfaces were numerically designed for the PL wavelengths. Superlinear PL responses were experimentally found and the mechanism has been investigated based on a transition model for the weak coupling systems. Consequently, we clarified that the superlinear responses mainly come from the hot-electron transfer at room temperature and originate from the induced transitions between the exciton levels in the QDs at the low temperature of 9 K. It is worth stressing that the hot electrons in plasmonic metasurfaces play a substantial role in the PL processes at room temperature.

Acknowledgement This study was partially supported by JSPS KAKENHI Grant (Number JP17H01066) from the Japan Society for Promotion of Science, by HPCI system research project (ID: hp170134) through the Cyberscience Center of Tohoku University, and by the 4th mid-term research project in NIMS. The nanofabrication was conducted at Namiki Foundry and NanoIntegrated Platform in NIMS.

Supporting Information Available The following figures are available free of charge. S1: Numerical R spectra of the plasmonic metasurfaces of various periodic length, and the dependence on incident angles and polarizations; S2: Estimation for light absorption by the plasmonic metasurfaces; S3: PL intensities at room temperature that are simply fitted by a power function; S4: PL intensities at 9 K that are simply fitted by a power function; S5: Sets of PL data and the analyzed results for the GaInAs substrates of a barrier/capping

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layer of 20 nm thickness.

Author Information Corresponding Author *E-mail: [email protected] Author Contributions M.I arranged the whole plan of this study, designed the metasurfaces, and analyzed the experimental data. T.M. conducted the growth of InAs QDs. N.I. collaborated nanofabrication with M.I. Optical measurement was conducted by M.I. and T.M. All the authors contributed to discussion and writing this paper. Notes The authors declare no competing financial interests.

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Graphical TOC Entry QD

1000

PL

Normalized PL Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

100

QDs

10

1

With metasurface 0.1

Metasurface

1

10

Excitation Power

29


Superlinear Photoluminescence Dynamics in PlasmonâQuantum-Dot

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