Quantum Dot Emission Driven by Mie Resonances in Silicon

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Quantum dot emission driven by Mie resonances in silicon nanostructures Viktoriia Rutckaia, Frank Heyroth, Alexey Novikov, Mikhail Shaleev, Mihail I Petrov, and Joerg Schilling Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b03248 • Publication Date (Web): 02 Oct 2017 Downloaded from http://pubs.acs.org on October 3, 2017

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Quantum dot emission driven by Mie resonances in silicon nanostructures Viktoriia Rutckaia,∗,†,‡ Frank Heyroth,¶ Alexey Novikov,§ Mikhail Shaleev,§ Mihail Petrov,k,⊥ and Joerg Schilling† †Centre for Innovation Competence SiLi-nano® , Martin-Luther-University Halle-Wittenberg, Karl-Freiherr-von-Fritsch-Str. 3, 06120 Halle (Saale), Germany ‡International Max Planck Research School for Science and Technology of Nanostructures, Weinberg 2, 06120 Halle (Saale), Germany ¶Interdisciplinary center of material science, Martin-Luther-University Halle-Wittenberg, Heinrich-Damerow-Str. 4, 06120 Halle (Saale), Germany §Institute for Physics of Microstructures of the Russian Academy of Sciences (IPM RAS), Academicheskaya Str. 7, 603950 Nizhniy Novgorod, Russian Federation kDepartment of Nanophotonics and Metamaterials, ITMO University, St. Petersburg 197101, Russia ⊥Department of Physics and Mathematics, University of Eastern Finland, Yliopistokatu 7, 80101, Joensuu, Finland E-mail: [email protected] Abstract Resonant dielectric nanostructures represent a promising platform for light manipulation at the nanoscale. In this paper, we describe an active photonic system based on Ge(Si) quantum dots coupled to silicon nanodisks. We show that Mie resonances govern the enhancement of the photoluminescent signal from embedded quantum dots due

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to a good spatial overlap of the emitter position with the electric field of Mie modes. We identify the coupling mechanism, which allows for engineering the resonant Mie modes through the interaction of several nanodisks. In particular, the mode hybridization in a nanodisk trimer results in an up to 10-fold enhancement of the luminescent signal due to the excitation of resonant anti-symmetric magnetic and electric dipole modes.

Keywords. silicon nanodisks, quantum emitters, Mie resonances, self-assembled quantum dots, oligomer nanostructures, photoluminescence enhancement Active optical nanoantennas have been recently suggested to enhance and control the quantum source emission through the resonant coupling to localized modes. 1–3 For that metallic nanostructures are considered as preferred systems allowing efficient coupling of radiation with quantum sources due to the existence of surface plasmon resonant modes. The plasmonic modes are characterized by a strong field enhancement near the metal-dielectric interface and high spatial localization of the resonant modes, which allows enhancing spontaneous emission rate 4,5 and resonant fluorescent transfer, 6 manipulating directionality of the emission, 7 and even enabling the strong-coupling regime. 8 Despite the huge progress in this area, plasmonic systems have their intrinsic drawbacks such as high optical losses which can quench spontaneous emission limiting their potential applications. Recently, the resonant all-dielectric photonic nanostructures based on high refractive index materials showed a wide range of applications in nanophotonics and optics. 9,10 They have proved their effectiveness for light scattering manipulation, 11,12 polarization control of light, 13,14 Raman signal enhancement, 15,16 nanoantenna emission directivity control, 17–19 and enabling nonlinear optical effects. 20–24 The interaction of quantum emitters with all-dielectric systems have been actively studied theoretically in the recent years, showing the prospects of all-dielectric systems for emission pattern steering 25 and enhancement of spontaneous emission. 26,27 Nevertheless, there were only a few experimental realizations demonstrating the interaction of quantum sources with all-dielectric structures, which were reported in Ref. 26,28–30 These pa2 ACS Paragon Plus Environment

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pers focus on the luminescence enhancement of colloidal quantum dots (QDs) and fluorescent molecules 31 in the vicinity of all-dielectric nanostructures. By placing the emitters outside of the nanoresonator one opens a way for chemical sensing and imaging applications, but at the same time limits the coupling efficiency with the resonant Mie modes, 26 as their fields are mainly localized inside the nanoresonators. Thus, the integration of emitting materials such as quantum dots, quantum wells, implanted defect-atoms inside the all-dielectric host would be desired to increase the spatial overlap of the mode field with the quantum emitter yielding an enhanced coupling efficiency. Moreover, the incorporation of quantum emitters into silicon nanoresonators would path a way towards applications in active silicon photonics. For that we propose all-dielectric systems based on silicon nanodisks with self-assembled Ge(Si) QDs, showing a broad emission in the 1200-1600 nm range at room temperature. 32–34 These Ge(Si) QDs have already demonstrated their suitability for optoelectronic applications in photonic crystal cavities, 35 LEDs, 36 and NIR photodetectors. 37 In this paper, we demonstrate the interaction of the Ge(Si) QD emission with Mie modes of silicon nanodisk resonators, which results in a strong shaping of the emission spectrum. We elucidate the mechanism of QD coupling to Mie modes of the nanoresonator leading to an enhancement of the observed luminescence. Based on the nanodisk mode engineering we also show that the QD emission can be controlled by forming nanodisk oligomer 38 structures like linear trimers, where three Mie resonators are combined. In particular, we show that the anti-symmetric magnetic and electric modes in such structures can effectively enhance photoluminescence (PL).

Results and discussion Fabrication and characterization Single nanodisks with embedded Ge(Si) QDs were fabricated in several steps using a topdown technique. For this silicon-on-insulator (SOI) substrates with a 3 µm buried oxide layer 3 ACS Paragon Plus Environment

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and 250 nm top Si layer were purchased from SOITEC. An epitaxial structure was grown by molecular beam epitaxy (MBE) at 600 C◦ using the Stranski-Krastanov (SK) growth mode. 39,40 The structure consisted of a 100 nm Si buffer layer, five layers of Ge(Si) QDs separated by 17-nm-thick Si spacers and a 100 nm Si capping layer. In order to check the properties of the Ge(Si) QDs a second structure was grown with the same MBE conditions but without the Si capping layer. The surface of the non-capped structure was probed with an atomic force microscope (AFM) and is shown in Figure 1 A). One can see that Ge(Si) QDs were grown in two structural types: multifaceted domes with the average lateral diameter of 100 nm and square-based pyramids with about 30 nm base size. 41 The lateral density of QDs in the top layer is ∼ 6 · 109 cm−2 . The height of the QDs measured with AFM appear to be 20 nm, but during the high temperature growth of the final Si capping layer Ge diffuses away from the top of the QDs resulting in their reduced final height. 42 Eventually, the smaller height of about 10 nm was observed investigating the cross section of the capped Ge(Si) QDs by high-resolution transmission electron microscopy (HRTEM) (see Supporting Information). The total thickness of all Si and Ge layers above the oxide is 510 nm with QDs placed asymmetrically in the top half of the Si layer (Figure 1 C)). A set of single nanodisk resonators with variable diameters from 280 to 660 nm with a 20 nm step-wise change of diameter was created on the grown epitaxial structure by focused gallium ion beam (FIB) milling using a FEI Versa 3D dual beam system. Figure 1 B) shows a scanning electron microscope (SEM) image of a fabricated 280 nm diameter disk. The area around the disks up to 7 µm in diameter was milled away in order to exclude possible parasitic photoluminescence (PL) from the surroundings of the disk. Ion current adjustment down to 1.5 pA allowed to obtain nearly vertical side walls of small disks on top of the buried oxide (SiO2 ) pedestal. The PL spectra were measured by exciting the disks with a 445 nm laser diode focused on a single nanodisk by a 100x microscope objective lens (see Appendix for the detailed scheme of the setup). The excitation power ∼ 7 mW was focused on a spot with ∼ 2 µm diameter.


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Figure 1: Structure of a substrate and fabricated Mie resonators. a) AFM image of the Ge(Si) QD layer before Si capping. Some characteristic sizes are shown by white dashed lines: average lateral size of a QD is 100 nm, nanodisks have diameters ranging roughly from 300 nm to 600 nm. The color scale represents the height of the structure in growthdirection. During the growth of the capping layer the height of the QDs is reduced from 20 to 10 nm. b) SEM image of a single 280 nm-diameter and 510 nm-height nanodisk milled in the epitaxial structure. c) TEM image of vertically correlated layered Si/Si-Ge QD structure with 5 periods of Ge(Si) QD layers separated by 17 nm Si spacers. The QD emission was collected in the back-scattering geometry using the same objective lens both for PL excitation and collection. The emitted light was focused on the entrance slit of a 0.5-m monochromator Acton SP-2500i and recorded by a liquid nitrogen cooled Ge detector. The grating with 600 grooves/mm and the slit width of 1000 µm provided a spectral resolution of 20 nm. The large removed area around the disks made sure that the detected emission originated only from the QDs inside the disks.

PL emission from single disks. The measured PL spectra for disks of two different diameters are shown in Fig. 2 A) and B). Within the spectral range of QD emission (1200-1600 nm, dotted gray line on Fig. 2 A)) the nanodisks support several Mie resonances. According to a performed multipole decomposition 43 (see Supporting information) the disk with 280 nm diameter exhibits lowest magnetic (MD) and electric (ED) dipole resonances which govern the optical response in this


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Figure 2: A) Experimental RT PL spectrum of as-grown Ge(Si) QDs (gray dotted line) in unstructured sample. Experimental (blue solid line) RT PL spectra of Ge(Si) QDs embedded in a 280 nm diameter disk and electric energy inside the disk (red dashed line) obtained in the scattering calculations. Magnetic (peak E) and electric (peak D) dipole modes are present in the spectra. The red-shaded area denotes the spectral range of reduced sensitivity of the detector. B) Experimental (blue solid line) RT PL spectra of Ge(Si) QDs embedded in a 500 nm diameter disk and electric energy inside the disk (red dashed line) obtained from the scattering calculations show the presence of higher-order Mie resonances. C) Schematic illustration of the numerical model where a x-polarized plane wave is incident on a disk. D) Normalized electric field distribution for the electric dipole mode at 1200 nm and E) magnetic dipole mode at 1390 nm at vertical cross-sections through the disk. region. However, for the electrical dipole mode there are also contributions from quadrupole and toroidal modes, which are spectrally close to the dipole resonance. The larger disks of 500 nm diameter show several pronounced higher order resonances within the considered spectral range. The MD and ED resonances are clearly seen in the PL spectrum detected from 280 nm disk, and a two-fold enhancement compared to the signal from as-grown Ge (Si) QDs


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from non-structured areas of the sample is observed. Note, that this is an underestimated PL enhancement. Since the excitation laser spot is larger than the disks, the number of excited QDs in non-structured area of the sample is higher than in a single disk. In order to characterize the resonant features more thoroughly we performed finite-element simulations of light scattering by nanodisks using COMSOL Multiphysics (Scheme on Fig. 2 C). The spectrum of total electric energy stored inside the disk under normal illumination by a plane wave is shown in Figure 2 A) (dashed line). One can see that the spectral positions of the Mie resonances in the simulations match the positions of the measured PL maxima. The distributions of electric field amplitude for the ED and MD modes are shown in Figure 2 D) and E) respectively corresponding to peaks D and E on figure 2 A). The higher order modes of the disk with larger diameter result in the higher quality factor due to reduced radiation losses of these modes compared to the ED and MD resonances (see Figure 2 B). A comparison of the experimental emission spectra with the calculated scattering spectra shows, that spectral positions of the observed resonances agree well. We summarized the PL emission spectra for different disk diameters and the corresponding electric energy inside the nanodisks obtained from the numerical scattering simulations in Figure 3. With the increasing nanodisk diameter the emission peaks in the PL spectra shift towards the long wavelength region (see Fig. 3 A)) showing at least two higher order resonances. Again, the calculated map of the electric energy stored inside the disk (see Figure 3 B)) shows good agreement with the spectral positions of the PL resonances. The performed calculations show the resonant structure of the silicon nanodisk scattering, but do not directly reflect the mechanism of the QDs coupling with the modes. In order to clarify it, we recall that a quantum emitter interaction with a resonator in the weak coupling regime is governed by the Purcell effect. 44 According to the Fermi’s Golden rule the spontaneous emission (SE) rate Γ of a dipole emitter in a cavity relative to the emission rate Γ0 in free space depends on the interaction strength of the dipole emitter with the cavity mode field: 45


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Figure 4: A) Modeled PL signal from the vertical point dipole placed inside 280 nm-diameter disk for different displacements from the disk axis (dashed lines). Solid line corresponds to the PL signal integrated over the Ge(Si) QDs layer exhibiting maxima at the ED (1200 nm) and MD (1370 nm) resonances. B) Normalized electric field of the ED and c) MD modes and electric field direction (arrows), schematic position and orientation of the point dipole shown with vertical red arrows. B1) Far-field diagrams of the point-dipole emission coupled to the ED and C1) MD resonances in case of different displacements ∆. For ∆ = 0 dipole emission is not coupled to the disk modes resulting in a far-field distribution that corresponds to the dipole in free space. For ∆ = 120 nm dipole emission is efficiently coupled to the Mie modes resulting in the deformed far-field pattern. the identification of the mode volume of a highly radiative mode becomes a complicated problem. Thus, to further elucidate the interaction of QD with the resonant modes we perform additional numerical simulations by placing a dipole emitter inside the nanodisk resonator. For this we have to consider, that stacked QDs have electrons and holes concentrated in the Si spacer and Ge wetting layer respectively, which defines the dipole moment direction ~ perpendicular to the plane of growth d||z . 47 The QD emission can therefore be modeled by placing a vertical oriented oscillating point dipole inside a Si nanodisk resonator and


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integrating the out-flowing Poynting-vector over a surface around the resonator. The oscillating dipole acts as a source of electromagnetic radiation which couples mainly to the Mie resonances of the disk. In Figure 4 A) the emission spectrum is shown for different shifts ∆ of the emitting dipole with respect to the center of the disk (see Fig. 4 B) and C)). The red dense dashed line corresponds to the dipole placed on the axis of the disk (∆ = 0). One can see that it has no maxima in the considered spectral range. This can be easily understood from Fig. 4 B) and C) where the electric field lines of the ED and MD modes are plotted. At the axis of the disk the modes have only horizontal components of the electric field resulting in a vanishing scalar product in Eq. (1). On the other hand dipoles placed closer to the walls of the disk show a clear coupling to the Mie resonances as the vertical component of the mode field becomes larger there. This is confirmed by the increase of the ED and MD peak intensities with increasing displacement ∆ in Fig 4 A). Based on this and assuming homogeneously distributed dipoles in the Ge(Si) QDs layers, we have plotted an integrated theoretical emission spectrum in Figure 4 A) (solid line) whose spectral features match well with the measured PL spectra for the 280 nm disk (Figure 2 A)). Details of the dipole emission calculation are described in the Supporting Information. To determine the impact of Purcell enhancement on the emission into the MD mode from our nanodisks we calculated the ratio of the power outflow for the dipole placed in the nanodisk and in a non-structured Si film. The obtained 1.5-fold theoretical Purcell factor is indeed on the same order as the observed experimental luminescence enhancement in Fig. 2 A). Note, that due to fabrication constraints the spatial position of QDs does not perfectly match with the local electric field maximum of the MD mode resulting in the reduction of the maximum possible Purcell factor. A maximal 3-fold theoretical Purcell factor could be achieved by placing the QDs at the height of 260 nm above the substrate. However, the silicon nanodisk can not only enhance the emission rate through the Purcell effect, but can also out-couple the radiation from Ge(Si) QDs in an upward direction more effectively. The redistribution of emission and reshaping of the emission pattern due to the Mie resonances


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therefore has to be taken into account too. This was studied by the analysis of the far-field emission diagrams shown in Figure 4 B1) and C1) for ED and MD resonances respectively. The emission pattern of a dipole placed at the axis of the disk (∆ = 0) shows a strong similarity with the usual emission of a Hertzian dipole in free space, exhibiting the characteristic zero emission along the direction of dipole oscillation (vertical direction). However, the emission is more concentrated towards the lower half space as the underlying substrate of larger refractive index bends the waves downwards and offers a larger amount of propagating photonic states there. The emission of the displaced dipole (∆ = 120 nm) on the other hand looses the axial symmetry and is strongly modified by the radiation pattern of the resonant Mie mode showing now also emission along the vertical direction, which is detected in the experiment by the microscope objective on top. Thus, the control over the spectral position along with the spatial distribution of the far-field radiation can serve for directive nanoantenna emission. To distinguish experimentally if the observed enhanced emission is mainly caused by an upward redirection of the emission due to the Mie radiation pattern or an overall increased emission due to the Purcell effect, time-resolved PL measurements would be necessary. From the change of the decay rate for non-resonant and resonant coupling the Purcell factor could then be obtained. However, time-resolved measurements in the IR for relatively weak emitters like the Ge(Si) QDs still represent a tough experimental challenge for future studies due to the large detector noises.

Nanodisk trimer In the former paragraphs we have shown the coupling of QDs to the Mie modes of single silicon nanodisks. The effective interaction of the lower dipole modes opens a way for the coupling of QD emission with complex modes of several nanodisks. The interaction of several open resonators leads to their mode hybridization, which allows mode engineering by controlling the design of the oligomer structures consisting of several nanoresonators. This 11 ACS Paragon Plus Environment

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approach has already shown to be effective for enabling a number of important optical properties, such as Fano resonances, 48,49 enhanced Raman scattering, 50 and stimulated nonlinear effects. 51 In order to demonstrate the Mie mode engineering for internal QD luminescence enhancement, we have designed a linear trimer structure shown in the inset of Figure 5 A). Three 280 nm diameter disks are placed in a line (trimer axis) with gaps of about 100 nm in between. The linear trimer has a much stronger field localization inside the nanodisks (see Supporting Information) compared to a simpler dimer system, for instance. This is important for an efficient mode coupling to embedded QDs . Moreover, it has been recently discussed 27 that a linear chain of dielectric disks can give a strong enhancement of fluorescence signal due to localized waveguiding modes. Recently such modes were utilized 28,52 for transfer optical excitation for extremely large distances. The solid black line represents the PL emission of QDs embedded in these resonators. One can see two sharp peaks and an overall one order enhancement of the QD PL signal compared to the single disk (black line with circles) and to the emission from ”free” QDs that are embedded in the non structured substrate (black line with triangles). In order to understand the origin of the observed high-Q modes we have to identify the modal content of the fabricated structures. For that we perform the numerical analysis of a plane wave scattering at the nanodisk trimer in the similar way as for the single disk. The inset in Figure 5 B) shows the scheme of the modeled structure. We have considered the incidence of a plane wave with two distinct orientations of the electric field: perpendicular (transverse) or parallel (longitudinal) to the trimer axis. The calculated spectrum of the energy stored inside the nanodisks is shown in Figure 5 B) for both polarizations. One can see the appearance of two sharp high-Q resonances around 1150 nm (peaks 2 and 3) for both polarizations and another resonance at 1300 nm (peak 1) for the transverse polarized excitation. These resonant modes are formed through the hybridization of magnetic and electric dipole resonances in single nanodisks. The mode decomposition (see Supporting Information) of elastically scattered plane waves shows symmetric and anti-symmetric electric


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Figure 5: A) PL spectra of a trimer (solid black line) shown on the inset having two sharp peaks at 1165 nm and 1302 nm with up to 10-fold intensity enhancement compared to the single disk emission (circles) and to the ”free” Ge(Si) QDs (triangles). B) Modeled energy of the electric field inside the trimer obtained from the scattering of transverse (dashed line) and longitudinal (solid line) polarizations of an incident wave. Disk diameter is 280 nm, gap size is 100 nm. The relative orientation of the magnetic dipoles (forming resonance 1) and electric dipoles (forming resonances 2 and 3) in each disk is shown on the inset. and magnetic modes, that dominate the eigen spectrum of such a trimer. We found that peaks 2 and 3 are formed due to the excitation of anti-symmetric electrical dipole modes (see the Inset on Fig. 5 B)). These modes with x and y polarization of ED moments are spectrally close to each other, but are excited by different polarizations of the incident wave. The important feature of these modes is, that right at the resonant wavelength the electric dipole emission is suppressed due to the destructive interference of the dipole moments in each disk (see Fig. S2 (c,d) in Supporting Information), which decreases the radiation losses of this mode and results in an increased Q-factor. We have also performed an additional extended multipole decomposition in order to identify if higher order modes contribute to the PL enhancement, especially at the point of the electric dipole suppression (see Supporting Information Fig. S3).


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The analysis of the scattered light gives the information about the modal content of the trimer structure. The QDs being randomly distributed inside the nanodisks can couple to modes of different symmetries, and both ED and MD modes contribute to the PL enhancement. The experimentally observed PL peak at 1300 nm is defined by the excitation of the anti-symmetric magnetic mode (peak 1 on Fig. 5 B)), while the peak at 1165 nm corresponds to anti-symmetric ED modes (peaks 2 and 3 Fig. 5 B)). The x and y modes are not resolved due to their small spectral separation. The theoretically possible Purcell enhancement in the case of a trimer structure was obtained in the same way as for a single nanodisk. In particular, we have considered the MD mode (peak 1) at the wavelength 1305 nm where Si luminescence does not contribute and the experimentally collected signal is solely caused by the emission from the QDs. A correct averaging over the QDs spatial distribution in case of the trimer would require extensive numerical simulations as the symmetry of the problem is broken, and the excitation of the resonant modes is strongly dependent on QD positions. We therefore placed the point dipole only in the field maximum of the collective magnetic Mie resonance (peak 1) and obtain a maximum 5.4-fold Purcell enhancement with respect to the emission from the non-structured substrate. The experimentally observed almost 10-fold enhancement of the PL signal compared to non-structured silicon can therefore only partly be explained by the Purcell effect. The efficient redistribution of the radiation in vertical direction also contributes substantially. Overall, the obtained results open a new perspective for developing efficient emitters based on all-dielectric structures using mode engineering in oligomer structures. In particular, it was shown recently that all-dielectric nanoparticle chains 10 can already exhibit a strong Purcell effect in the microwave region for dipole emitters placed outside the resonators. The crucial importance here is, that our QDs emitting in the near IR are placed inside the nanodisk rather than outside. This internal placement of the emitters results in efficient coupling to the resonant modes, as it was already utilized for efficient nonlinear 22–24


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and Raman 15 signal enhancement. In this work we demonstrated that Ge(Si) QDs embedded in Si nanodisks can be effectively coupled to the Mie resonances of the nanodisk. This is observed as a strong modification of the PL spectra of QDs by resonant excitation of lowest MD and ED modes, as well as higher Mie modes. The coupling efficiency was analyzed for different dipole positions of the QDs inside the nanodisk. The numerical analysis of the dipole emission, which took into account the random distribution of QDs, resulted in a good correspondence to the experimental results. Furthermore, the emission pattern and intensity can be significantly changed by engineering dipole modes in nanodisk structures consisting of several nanodisks. Here an up to 10-fold emission enhancement is achieved by exciting anti-symmetric electric and magnetic dipole modes inside the linear trimer. The suppression of the dipole emission increases the quality factor of the resonant modes and paves a way towards a stronger Purcell effect for emitters inside silicon Mie resonators. The results reported in this paper open a way for efficient nanoscale light sources based on resonant structures supporting Mie modes.

Acknowledgement V.R. and J.S. thank the Federal Ministry for Education and Research (Bundesministerium fr Bildung und Forschung, Project N. 03Z2HN12) for their financial support within the Centre for Innovation Competence SiLi-Nano® . V.R. acknowledges International Max Planck Research School for Science and Technology of Nanostructures. In addition we acknowledge Peter Werner from the Max-Planck Institute of Microstructure Physics for the use of the JEOL JEM 4010 microscope. M.P. acknowledges support from Academy of Finland (Grant 310753), Ministry of Education and Science of the Russian Federation (Minobrnauka) (2.2267.2017/4.6) and the Russian Foundation for Basic Research (16-32-60167, 16-02-00684). A.N. and M.S. acknowledge Russian Foundation for Basic Research (15-0205272).


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The authors declare no competing financial interest.

Supporting Information Available Optical response of silicon nanodisk, simulated modes of a trimer, Influence of Si(Ge) QD layers on Mie resonances, microphotoluminescence setup, point dipole in a disk: power outflow averaging, HRTEM of Ge(Si) QDs

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Photoluminescence

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Quantum Dot Emission Driven by Mie Resonances in Silicon

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