Improved emission of SiV diamond color centers embedded into concave plasmonic core-shell nanoresonators

Configuration of three different concave silver core-shell nanoresonators was numerically optimized to enhance the excitation and emission of embedded silicon vacancy (SiV) diamond color centers simultaneously. Conditional optimization was performed to ensure ~20–30–40 and 50% apparent quantum efficiency (cQE) of SiV color centers. The enhancement spectra, as well as the near-field and charge distribution were inspected to uncover the underlying nanophotonical phenomena. The conditionally optimized coupled systems were qualified by the product of the radiative rate enhancements at the excitation and emission, which is nominated as P x factor. The optimized spherical core-shell nanoresonator containing a centralized emitter is capable of enhancing the emission considerably via bonding dipolar resonance. The P x factor is 529-fold with 49.7% cQE at the emission. Decentralization of the emitter leads to appearance of higher order nonradiative multipolar modes. Transversal and longitudinal dipolar resonance of the optimized ellipsoidal core-shell resonator was tuned to the excitation and emission, which results in 6.2∙105 P x factor with 50.6% cQE at the emission. Rod-shaped concave core-shell nanoresonators exploit similar transversal and longitudinal dipolar resonance, moreover they enhance the fluorescence more significantly due to their antenna-like geometry. P x factor indicating 8.34∙105 enhancement is achievable while the cQE is 50.3% at the emission.


Sensitivity study and experimental feasibility
: Optical response of CSCS configuration above the core radius (r 1 )shell thickness (t) parameter space. (a) Purcell factor (b) QE (c) rad excitation R  radiative rate enhancement vs. core radius and shell thickness (d) rad excitation R  radiative rate enhancement vs. core radius and generalized aspect ration (GAR) at SiV excitation wavelength. Insets: projections of the 2D parameter space (aa) Purcell factor vs. shell thickness at optimal core radius [35 nm] and (ab) Purcell factor vs. core radius at optimal shell thickness [5. 96    Only one single resonance and a corresponding Purcell peak appears in the inspected geometrical parameter interval both at the SiV excitation and at the SiV emission wavelengths ( Fig. S1a and S2a). The resonance energy is dependent mainly (exclusively) on the generalized aspect ratio at the excitation (emission) ( Fig. S1d and S2d), only slight deflection is observable on the curve corresponding to the rad emission excitation R /  radiative rate enhancement above the GAR generalized aspect ratio and r 1 core radius parameter space. The cQE corrected quantum efficiency can be high only at radiative resonances (Fig. S2b).
In this study all results are presented with 0.1% accuracy according to the high numerical accuracy of the FEM computations. Via current experimental methodologies such high precision can be just approximated, therefore the effect of geometrical uncertainty on the fluorescence enhancement was inspected. The sensitivity of the P x factor to the geometrical parameters, e.g. core radius, shell thickness, dipole displacement, has been analyzed for the optimized CSCS system (Fig. S3). Figure S3: Dependence of the complete CSCS fluorescence enhancement (P x factor) on geometric parameters: (a) diamond core radius, (b) silver shell thickness and (c) dipole displacement.
The sensitivity study revealed that the P x factor remains in the same order of magnitude, if the core radius is within the +/-2.5 nm interval of the optimal value, while the shell thickness has to be in the +/-0.5 nm interval to meet this criterion. These allowed intervals correspond to 7.1% and 8.4% uncertainty in the core radius and metal shell, respectively. In contrast, the sensitivity to the dipole displacement is significantly smaller, namely only 8.6% P x factor decrease is caused by 30 nm displacement, which corresponds to 85.7% discrepancy from the optimal position. Current nanofabrication methods make possible to prepare nanodiamonds down to the order of 2-5 nm [S1]. Representative experimental results have been already published on successful covering of 200 nm nanodiamonds by a gold shell having a thickness of 20 nm via a modified seed-growth method [S2]. Moreover, it is possible to cover dielectric nanoparticles by silver, e.g. by anchoring 2-4 nm Ag nanocrystals, 2-10 nm reproducible but non-continuous silver layer was coated onto silica surfaces [S3]. Although, discontinuity of the chemically prepared shells could cause discrepancies with respect to the optimized systems, inspection of such non-optimal structures was out of scope of the present study. Based on the previously described experimental procedures and the possibility of nanodiamond surface modifications, silvercoated nanodiamonds can be prepared as well [S2]. It is known that the surface charge of the nanodiamonds strongly influences the type of the reduction process, e.g. negatively charged surface promotes the binding of positively charged silver ions onto the surface [S4, S5]. The reduction of Ag+ ions with hydroxylamine hydrochloride can be carried out in presence of nanodiamonds in aqueous dispersion. Other possible process is the reduction of Ag+ ions using the well-known photoreduction [S6]. The special rod-like particles can be fabricated by evaporating than cutting the diamond nanowires fabricated via e-beam lithography [S7]. Fabrication of ellipsoidal nanodiamond can be realized by etching and ellipsoidal nanoparticles can be also covered by continuous films seeded via metal nanocrystals [S8].
Comparative study on coupled SiV color center -concave nanoresonator systems optimized with different criteria Figure S4: Total fluorescence enhancement (P x factor) of (a) spherical, (b) ellipsoidal and (c) rod-shaped concave core-shell nanoresonators containing a centralized dipole and optimized with 50, 40, 30 and 20% cQE criteria. The P x factor of the optimized configurations consisting of a decentralized dipole corresponding to cQE=50% are also shown by red stars.
The optimization results show that in all optimized configurations at the emission wavelength the rad emission R  radiative rate enhancement of SiV color center decreases by increasing the criterion regarding the corrected quantum efficiency (Fig. S4). In case of CSCS the achievable cQE is governed by the distance between the emitter and the absorbing metal, as well as by the metal shell thickness. Namely, the higher the desired cQE is, the larger is the diamond core radius, and surprisingly the t shell thickness increases as well. As a result, the total spherical core-shell nanoresonator size increases nearly linearly in the quasistatic limit by increasing the cQE criterion (Fig. S5a). The position of the sole visible resonance peak is mainly determined by the GAR aspect ratio of the concave core-shell nanoresonator (Table S1). In all optimized coupled systems the symmetric bonding dipolar mode is tuned to the emission wavelength. Accordingly, the GAR of nanoshells are nearly the same, only a slight GAR decrease is observable as the cQE criterion increases (Fig. S5a). However, the larger core-shell nanoresonator size leads to a weaker resonance as the Purcell factor spectra show (Fig. S5b). As a consequence, the rad emission R  radiative rate enhancement at the emission decreases by increasing the cQE criterion (Fig. S5c). The interdependence of the geometrical parameters and the resonance energy is more complex in case of concave ellipsoidal core-shell nanoresonators. Generally, it can be concluded again that larger cQE requires larger emitter-metal distance (Fig.  S6a). To increase the dipole distance one should increase the short axis of the ellipsoid as well. To maintain the transversal and longitudinal resonances at SiV excitation and emission wavelengths, the ratio of long and short axes should be conserved. Accordingly, the higher the desired cQE is, the larger is the diamond core short and long axis, and surprisingly the t shell thickness increases as well. As a result, the total ellipsoidal core-shell nanoresonator size increases similarly to CSCS. In the GARs corresponding to the short and long axis of nanoshells only a slight decrease is observable, as the cQE criterion increases (Table S1). Moreover, not only the aspect ratio but the axes lengths themselves influence the energies of the resonance peaks. The larger cQE at emission requires larger metal-emitter distance, accordingly larger short and long axis. A slightly smaller long-to-short axis ratio is preferred, as the cQE increases.
Similarly to CSCS nanoresonators, the higher is the cQE, the lower is the Purcell factor and the rad emission excitation R /  radiative decay rate enhancement both at the excitation and emission (Fig. S6b and c). In CECS by decreasing the cQE criterion from 50% through 20%, the relative radiative rate enhancement increase is insignificant at the excitation, while at the emission the increase is more than 2-fold. In case of CRCS the tendencies are the same as in CECS, namely to achieve higher cQE larger dipole distance is required, which implies appropriatley larger short and long axis, and maintainance of the optimal decreasing axis lenght ratio (Fig. S7a). Surprisingly the thickness of the metal shell increases as well. In the GARs corresponding to the short and long axis of nanoshells only a slight decrease is observable. The rod-shaped concave core-shell nanoresonators show a Purcell factor and rad emission excitation R /  radiative rate enhancement characteristics and QE spectra similar to those of CECS ( Fig. S7b and c). Although, their excitation rate enhancements are almost identical, a major difference between CRCS and CECS is that the CRCSs have significantly larger Purcell factor at the emission. Despite the smaller dipole distance from the metal, at the same cQE larger rad emission R  radiative rate enhancement is achieved in case of CRCSs, due to the efficient far-field coupling via rod-shaped nanoantennas. The highest 2.0310 6 fluorescence enhancement among the inspected concave plasmonic nanoresonators was achieved via rod-shaped cores embedded into silver nanoshell, when the criterion regarding the minimum cQE was set to 20%.