Emission and Förster Resonance Energy Transfer Behaviors of Colloidal Quantum Dots in a Metal Nanohole

Emission and Förster Resonance Energy Transfer Behaviors of Colloidal Quantum Dots in a Metal Nanohole | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Emission and Förster Resonance Energy Transfer Behaviors of Colloidal Quantum Dots in a Metal Nanohole Shaobo Yang, Yueh-Chi Lee, Yu-Sheng Lin, Li-Ping Liang, Yang Kuo, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4367418/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract The reduction of the photoluminescence (PL) decay time of a colloidal quantum dot (QD) inserted into an Ag or Au surface nanohole and the efficiency enhancement of the Förster resonance energy transfer (FRET) from a green-emitting QD into a red-emitting QD are first experimentally demonstrated. Besides the factor of metal dissipation in the induced surface plasmon (SP) coupling process, the reduced PL decay time is attributed to the QD emission efficiency increase caused by the SP-coupling involved nanoscale-cavity effect. Numerical simulation studies are undertaken to confirm the feasible enhancements of QD emission, FRET, and color conversion efficiencies. In particular, by artificially changing the dielectric constant of Ag based on the Drude model, the effects of cavity resonance and SP coupling in producing the enhanced radiated power peaks can be differentiated. Such a peak can be formed when both conditions of cavity resonance and SP resonance are satisfied. In the case of a weaker (stronger) SP resonance, the combined resonance can lead to a stronger and sharper (weaker and broader) radiated power peak. The results in this paper indicate that a nanoscale metal cavity can be used for enhancing the emission and color conversion efficiencies of inserted light emitters. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1. Introduction As predicted by Purcell, the emission behavior of a light emitter is influenced by the scattered field of its own radiation, which is scattered back from the surrounding structure [ 1 ]. Either the far- or near-field portion of the scattered field can produce the Purcell effect. When we place a light emitter inside a cavity not extremely small, the built cavity resonance field can couple with the light emitter to enhance its emission. In the case of locating a light emitter inside a small cavity, the near-field version of the Purcell effect can also increase its emission efficiency. Experimental and numerical studies have demonstrated the emission efficiency enhancements of colloidal quantum dots (QDs) when they are inserted into nanoscale cavities, such as a surface nanohole (NH) and a subsurface porous structure [ 2 – 4 ]. Such an emission enhancement was generally referred to as the nanoscale-cavity effect. A theoretical study has also predicted that such an enhancement is stronger when the contrast of dielectric constant between the cavity material and interior medium is higher [ 5 ]. Because the real-part magnitude of the dielectric constant of Ag or Au in the visible range is large even though it is negative [ 6 ], it is expected that the nanoscale-cavity effect in such a metal nanocavity can be stronger than that in a dielectric counterpart. Meanwhile, the metal nanostructure in a metallic nanocavity can induce a surface plasmon (SP) coupling effect, which can further enhance the emission efficiency of a light emitter inside a metal nanocavity. For the two reasons above, the study of the emission behavior of a colloidal QD in an Ag or Au nanocavity is important for expanding the application of a QD. Besides the emission efficiency of a single QD, the enhancement of the Förster resonance energy transfer (FRET) from a QD donor into a QD acceptor has been demonstrated when both donor and acceptor are located inside a nanocavity [ 2 – 5 ]. FRET is a non-radiative near-field energy transfer process [ 7 ], which is an effective mechanism for implementing photon color conversion [ 8 – 10 ]. The color conversion efficiency relies on two factors, including the efficiency of the energy transfer from donor into acceptor and that of acceptor emission [ 2 , 11 , 12 ]. The former can be quite high if an FRET process is utilized. It is proportional to the field intensity at the position of the acceptor produced by the donor. When both donor and acceptor are placed inside a metal nanocavity, the field intensity of the donor is expected to be enhanced, leading to a stronger FRET process. Therefore, the color conversion efficiency in a metal nanocavity can be improved. This issue also deserves a careful investigation. A light emitter can couple with an SP resonance mode of a metal nanostructure for changing its emission behavior. In such a coupling process, the energies of the light emitter and SP resonance mode can coherently exchange to form a coupled resonance system. In many situations, it can lead to the enhancement of emission efficiency [ 13 – 15 ]. As mentioned earlier, in a metal nanocavity, besides the cavity effect of either far-field cavity resonance or near-field induced emission enhancement, SP resonance can be excited on the sidewall of the metal nanocavity for generating the SP coupling with the light emitter. Such a light emission phenomenon of mixing the mechanisms of the cavity effect and SP coupling has not been well studied yet. In particular, the differentiation between the effects of individual mechanisms is useful for us to further understand the emission behavior. In this paper, we first demonstrate the experimental results of QD-filled Ag and Au surface NHs, which are fabricated by coating metal onto the sidewall and bottom of a GaN surface NH. The time-resolved photoluminescence (TRPL) behaviors of the inserted QDs are shown. Then, a numerical study is undertaken for understanding the dipole emission and FRET behaviors in a metal surface NH structure with the hole morphology simulating that obtained in experiment. Also, the structure of a cylindrical metal NH is used for numerically studying the interplay between the aforementioned two mechanisms of cavity effect and SP coupling. In section 2 of this paper, the sample structure, fabrication procedures, and TRPL results in the experimental study are shown. Then, the simulation results of the dipole emission and FRET behaviors in a metal NH are presented in section 3. Next, in section 4, the numerical results of the interplay between the two mechanisms of cavity effect and SP coupling are reported. Further discussions about the experimental and simulation results are made in section 5. Finally, conclusions are drawn in section 6. 2. Experimental study In the experimental study, we fabricate metal NH arrays on a 2-µm thick GaN template, which is grown on a double-polished sapphire substrate with metalorganic chemical vapor deposition at 1043 o C in temperature. To fabricate a metal NH array, we first prepare a surface NH array on the GaN template through the processes of nano-imprint lithography, inductively coupled plasma reactive ion etching (ICPRIE), and wet etching with AZ400K [ 4 , 16 ]. Figures 1 (a) and 1(b) show the plane-view and cross-sectional scanning electron microscopy (SEM) images, respectively, of the fabricated GaN NH array. The dimension of a hexagonal-shaped hole on the surface is ~ 200 nm. The hole depth is ~ 320 nm. A metal NH array is implemented by depositing metal onto the top surface of the GaN NH array. In this situation, metal can attach onto the sidewall and bottom of a GaN NH to form a metal nanocavity. Figure 1 (c) [1(d)] shows the plane-view SEM image after an Ag (Au) layer of 80 nm in thickness is deposited onto a GaN NH array. Figure 2 (a) [2(b)] shows the cross-sectional SEM image of the Ag (Au) NH array sample, corresponding to that in Fig. 1 (c) [1(d)]. Here, one can clearly see a vase-shaped metal NH in either sample. The width of such a metal NH at the bottom is ~ 90 (~ 80) nm in the Ag (Au) NH sample. The hole depth in either sample is around 320 nm. In other words, the metal deposition thicknesses inside and outside NHs are roughly the same. Next, the photoresist solutions of colloidal QDs are inserted into the fabricated metal NHs. The used green- (530 nm in wavelength) and red-emitting (625 nm in wavelength) CdZnSeS/ZnS colloidal QDs, which are referred to as GQD and RQD, respectively, are purchased from Taiwan Nanocrystals Inc. Tainan, Taiwan. Those QDs are capped with poly(isobutylene-alt-maleic anhydride). Both GQD and RQD are negatively charged with the zeta potentials at -28.3 and − 25.6 mV, respectively [ 17 ]. The size of the amphiphilic polymer capped GQD or RQD ranges from 8 to 10 nm. The procedures for uniformly immersing QDs in the used photoresist (SU-8) have been reported in earlier publications of ours [ 4 , 16 ]. Three photoresist solutions of different QD combinations are prepared, including GQD, RQD, and GQD plus RQD. The total QD weight concentrations in those three solutions are the same. After drop-casting a photoresist solution onto a metal NH sample, the solution can flow into and fill up the NHs. Then, a cotton swab is used to sweep the sample for cleaning the top surface. After a photoresist solidification process, the fabrication of a QD-filled metal NH sample is completed. Those samples with the Ag (Au) NHs filled with the photoresist solutions of GQD, RQD, and GQD plus RQD are designated as samples NH/XX-GQD, NH/XX-RQD, and NH/XX-GQD + RQD, respectively, with XX = Ag (Au). For comparison, other sample groups with the same QD combinations are also prepared, including the samples of filling GaN NHs (i.e., no metal deposition) with the photoresist solutions of QD and those of drop-casting the solutions onto the flat surfaces of GaN templates. The former group includes samples NH/GN-GQD, NH/GN-RQD, and NH/GN-GQD + RQD. Those in the latter group are designated as samples S-GQD, S-RQD, and S-GQD + RQD. Figures 2 (c) and 2(d) show the plane-view SEM images of samples NH/Ag-GQD and NH/Au-GQD, respectively. After the application of the photoresist solutions to those samples, the SEM images become blurred due to the low conductivity of the photoresist. The emission behaviors of the QDs in those samples are characterized with TRPL measurement. The TRPL measurement is excited by the second-harmonic of a femtosecond Ti:sapphire laser (MIRA 900, pumped by VERDI-8W, Coherent) with the pulse repetition rate at 76 MHz. The wavelength and power used for QD excitation are 390 nm and ~ 1.5 mW, respectively. The time-dependent signals are detected by a photon-counting system (the time-correlated single photon-counting solution, Becker & Hickl). Its temporal resolution is higher than 100 ps. The procedure for calibrating the decay time of a photoluminescence (PL) decay profile has been reported in detail before [ 18 ]. Figure 3 shows the normalized green-light PL decay profiles of all those samples with GQD. Here, the decay profiles can be classified into two groups, including those samples with and without metal deposition. With metal deposition, the PL decay rates are significantly higher. In each sample structure (S-, NH/GN-, NH/Ag-, or NH/Au-), with the combination of GQD and RQD, the green-light decay rate is higher, when compared to that with GQD only. This variation trend is caused by the FRET process from GQD into RQD. Figure 4 shows the normalized red-light PL decay profiles of all those samples with RQD. Here, the decay profiles can also be classified into the two groups of samples with and without metal deposition. Again, with metal deposition, the PL decay rates are significantly higher. For red light, the decay rate in a sample with GQD + RQD is always lower than that with RQD only of the same structure that again is caused by the FRET process. Table 1 shows the PL decay times of all the samples calibrated from the decay profiles in Figs. 3 and 4 . Here, the numbers inside the parentheses show the efficiencies of the corresponding FRET processes from GQD into RQD. The FRET efficiency, η, is defined as η = 1- τ DA /τ D [ 19 ]. Here, τ DA (τ D ) is the PL decay time of the energy donor, i.e., GQD, when the acceptor, i.e., RQD, is present (absent). In the surface samples, the green-light decay time reduces from 5.874 ns in sample S-GQD to 5.672 ns in sample S-GQD + RQD due to the FRET process from GQD into RQD with the FRET efficiency at 3.44%. For the same reason, the red-light decay time increases from 10.388 ns in sample S-RQD to 11.786 ns in sample S-GQD + RQD. Then, in the samples with QDs inserted into GaN NHs, all the decay times are reduced from the corresponding values in the surface samples. Such reductions are attributed to the enhancements of QD emission efficiencies caused by the nanoscale-cavity effect [ 3 – 5 ]. In sample NH/GN-GQD + RQD, the green-light decay time further decreases due to the FRET process. That for red light is also reduced due to the nanoscale-cavity effect even though RQD receives energy from GQD through the FRET process. In this situation, the FRET efficiency increases to 7.19%. Then, as shown in column 5 of Table 1 , in the samples of Ag NHs, all the decay times are further reduced significantly. Among those Ag-NH samples with different photoresist solutions, the relative PL decay times of green and red lights are similar to those among surface or GaN NH samples. The significantly shorter PL decay times in those Ag NH samples are caused by two key factors. First, the nanoscale-cavity effect, particularly with SP coupling, can enhance the QD emission efficiency and hence reduce its PL decay time. The nanoscale-cavity effect here is expected to be even stronger, when compared with that in a GaN NH sample, due to the metal cavity wall and smaller cavity size [see Fig. 2 (a)]. Second, the metal dissipation in the SP coupling process produces the energy loss of the coupled system that can also reduce the PL decay time. In this situation, the nanoscale-cavity effect can still enhance the FRET from GQD into RQD and hence the FRET efficiency is further increased to 15.84%. As shown in column 6 of Table 1 , the behaviors of PL decay time in the Au NH samples are similar to those in Ag NH samples even though the decay time values are slightly different. The SP coupling effect with Au is expected to be weaker than that with Ag. Therefore, the nanoscale-cavity effect involving SP coupling in an Au NH sample must be weaker than that in an Ag NH sample. The FRET efficiency in sample NH/Au-GQD + RQD is 10.83%, which is significantly lower than that in sample NH/Ag-GQD + RQD (15.84%). Table 1 PL decay times of all those experimental samples. The numbers inside the parentheses show the efficiencies of the corresponding FRET processes from GQD into RQD. Sample XXX = S-XXX (ns) NH/GN-XXX (ns) NH/Ag-XXX (ns) NH/Au-XXX (ns) GQD green 5.874 5.553 1.506 1.477 RQD red 10.388 7.155 2.854 3.284 GQD + RQD green 5.672 (3.44%) 5.154 (7.19%) 1.268 (15.84%) 1.317 (10.83%) red 11.786 10.972 3.477 3.534 3. Numerical simulation study To confirm the enhancements of QD emission and FRET efficiencies when QDs are inserted into a metal NH, simulation studies are undertaken with the sample structures illustrated in Figs. 5 (a)-5(d). As illustrated in Fig. 5 (a), we design a metal NH simulating the experimental NH structures shown in Figs. 2 (a) and 2(b). This metal NH structure is designated as NH-XX/GaN with XX = Ag or Au. The NH is designed as a semi-ellipsoid with its long axis coinciding with the axis of the cylindrical GaN NH. The semi-major axis of the ellipsoid is equal to d, which is the depth of the GaN NH. The semi-minor axis is b/2 - w, where b is width of the GaN NH. The semi-ellipsoid NH is filled with the photoresist of 1.577 in refractive index. Ag or Au is deposited in the space between the GaN wall and the photoresist-filled semi-ellipsoid NH. The thickness of metal deposition at the center of the GaN NH bottom is t. Therefore, it is assumed that on the top surface of a sample, a metal layer of t in thickness is also deposited. Two QDs or radiating dipoles are placed inside the metal NH at its semi-major axis, one serves as the donor and the other serves as the acceptor in an FRET process. The origin of the coordinate system is set at the center of the GaN NH bottom. In Fig. 5 (b), the reference sample of the NH-GaN structure is illustrated for comparing the QD emission and FRET efficiencies between the cases with and without metal deposition. Figure 5 (c) shows the structure of homogeneous photoresist (structure R), which is used as the normalization base in numerical computations. Figure 5 (d) illustrates a cylindrical metal NH structure (NH-Ag) for understanding the cavity resonance effect in a metal NH, as to be further discussed in the next section. For simulation studies, the dielectric constant, \(\epsilon = {\epsilon }^{{\prime }}+i\epsilon "\) , of the used metal needs to be assigned first. Figures 6 (a) and 6(b) show the real and imaginary parts ( e’ and e” ), respectively, of the wavelength-dependent dielectric constants we use for simulation studies. For simulating the experimental conditions, we use the experimental data of dielectric constant for Ag and Au, as labeled by Exp. (Ag) [ 20 ] and Exp. (Au) [ 21 ] in Figs. 6 (a) and 6(b). To understand the SP coupling effect in cavity resonance behavior, we also consider the dielectric constants of Ag based on the Drude model, as to be discussed in section 4. Here, a negative value of the real part of dielectric constant implies the possible excitation of SP resonance and hence SP coupling in the visible range. We can see that the magnitude (negative value) of the real part of the dielectric constant in Au is smaller than that of Ag. Also, the imaginary part of Au is smaller (larger) than that of Ag for a wavelength longer (shorter) than 600 nm in the visible range. The high peak of the imaginary part of Au around 400 nm in wavelength is caused by the electron interband transition between the lower d band and the higher s band. The method for the numerical simulation studies has been described in a few earlier publications of ours [ 22 , 23 ]. It is based on the exact electromagnetic theory. This method includes the feedback effect from the scattered field on the radiation behavior of the source dipole. In other words, the Purcell effect, either near- or far-field portion, is taken into account [ 22 , 23 ]. To numerically demonstrate the simulation results, we fix the GaN NH depth, d, at 320 nm and consider the following two sets of GaN NH width and two conditions of metal deposition thickness. In a wider (narrower) GaN NH, which is denoted by the symbol “W” (“N”), the GaN NH width, b, is 280 (200) nm. In the case of a larger (smaller) metal deposition thickness, which is denoted by the symbol “L” (“S”), t = 80 (40) nm, w = 40 (20) nm, the donor coordinates at (0, 0, 200 nm) [(0, 0, 160 nm)], and the acceptor coordinates at (0, 0, 230 nm) [(0, 0, 190 nm)]. Therefore, we have four combinations in total, including the cases of W/L, W/S, N/L, and N/S. In all cases, the distance between the donor and acceptor is kept at 30 nm. For comparison, we also consider the structures of NH-GaN with b = 200 (N) and 280 (W) nm. In either case, the coordinates of the donor and acceptor are (0, 0, 120 nm) and (0, 0, 150 nm), respectively. Figures 7 (a) and 7(b) show the normalized radiated power spectra of the acceptor as an x- and z-dipole, respectively, in an Ag NH shown in Fig. 5 (a). Besides the aforementioned four cases of Ag NH, the results of the narrow and wide GaN NHs are shown. As shown in Fig. 7 (a) for an x-dipole, in the case of either narrower or wider NH, the radiated power shows a sharper peak when metal deposition is thicker. With a thinner metal deposition, the radiated power is weaker and shows a two-peak spectrum. When the GaN NH is narrower and hence the metal NH becomes smaller, the spectral peaks are blue-shifted and become sharper. In the cases of GaN NH, slowly increasing radiated power spectra can be observed. The difference between the narrower and wider GaN NHs is small. In this figure, we can see that in a large spectral range, an Ag NH sample can lead to a stronger radiated power, when compared with that of a GaN NH sample. The vertical dashed line in Fig. 7 (a) indicates the wavelength of RQD emission (625 nm). At this wavelength, except case N/L, the radiated powers are all enhanced (normalized radiated power > 1), when compared with that in structure R. However, except case W/S, the radiated powers in samples Ag NH are lower than those of samples GaN NH. We believe that the sidewall metal deposition in experiment is thinner than that designated in simulation such that the curve of N/S is red-shifted. In this situation, the radiated power in the N/S case of an Ag NH sample becomes higher than that of a GaN NH sample. As shown in Fig. 7 (b) for a z-dipole, in the cases of narrower NH, the major portions of the radiated power peaks fall into the ultraviolet range. In the cases of wider NH, the radiated power peaks are quite sharp and located far away from the RQD emission wavelength. At this wavelength, the normalized radiated powers in all cases are lower than unity, indicating that it is unlikely for a z-dipole to contribute to QD emission enhancement in either an Ag NH or a GaN NH sample. Such contributions originate mainly from the x- and y-dipole. Figures 8 (a) and 8(b) show the normalized field intensity spectra at the position of the acceptor produced by an x- and a z-dipole donors, respectively. Generally speaking, with a narrower NH, the spectral peak of the donor intensity is located at a shorter wavelength. Also, with a thicker Ag deposition, the donor peak intensity is higher. At the GQD emission wavelength, as indicated by the vertical green dashed line, the normalized donor intensities produced by an x-dipole under all the sample conditions, including the NH-GaN structures, are larger than unity, i.e., enhanced. However, those produced by a z-dipole are not significantly enhanced except the case of W/S. The donor intensity enhancements at the emission wavelength of GQD imply the increased energy absorption of the acceptor (RQD) and hence the improvement of the efficiency of the FRET from GQD into RQD. Figures 9 (a) and 9(b) show the spectra of the normalized radiated power of the acceptor and the normalized field intensity at the position of the acceptor produced by the donor, respectively, in the samples of Au NH with the structure shown in Fig. 5 (a). Both results of an x- and a z-dipole are shown in either Fig. 9 (a) or 9(b). The geometries used for the Au NH samples are the same as those for the Ag NH samples. Here, only the cases of N/S and N/L are considered. Two strong peaks of radiated power produced by an x-dipole acceptor can be seen in Fig. 9 (a). In the concerned wavelength range, the radiated power produced by a z-dipole acceptor is quite low. Fano-like oscillations can be observed around 550 nm in wavelength for donor intensity in all cases, as shown in Fig. 9 (b). The intensity peak levels produced by an x-dipole donor are higher than those produced by a z-dipole donor. The emission wavelengths of RQD and GQD are also indicated by the vertical dashed lines in Figs. 9 (a) and 9(b), respectively. Table 2 shows the normalized field intensity at the position of the acceptor produced by the donor (abbreviated by “donor intensity”), the normalized acceptor radiated power, and the color conversion factor, which is the product of the last two values, excited by x- and z-oriented dipoles under various metal and GaN NH conditions. The energy absorbed by the acceptor or the transferred energy in an FRET process is proportional to the donor intensity at the position of the acceptor. Hence, the enhancement of donor intensity can be regarded as the increment of FRET efficiency. Therefore, the product of the normalized donor intensity and normalized acceptor radiated power represents the improvement factor of color conversion. In Table 2 , we can see that in most cases of z-dipole, either donor intensity or acceptor radiated power is suppressed or weakly enhanced. However, in most cases of x-dipole, either donor intensity or acceptor radiated power is enhanced, leading to the increase of the color conversion factor. These variation trends are true for both metal and GaN NH samples. However, the increments of the color conversion factors in the metal NH samples are generally larger than those in the GaN NH sample, indicating the stronger nanoscale-cavity effect in a metal NH. In the N/S case, the Au NH sample results in a higher color conversion factor, when compared with the corresponding Ag NH sample. However, this variation trend cannot be regarded as a general rule in the comparison between the Au and Ag NH samples. A change of metal deposition or NH geometry condition can reverse the relative color conversion factors between the samples of the two metals. Table 2 Normalized field intensity at the position of the acceptor produced by the donor (donor intensity), the normalized acceptor radiated power, and the color conversion factor, which is the product of the last two values, excited by x- and z-oriented dipoles under various metal and GaN NH conditions. Donor intensity Acceptor radiated power Color conversion factor x-dipole z-dipole x-dipole z-dipole x-dipole z-dipole Ag-N/S 1.135 0.864 1.688 0.056 1.916 0.048 Au-N/S 1.719 1.122 3.543 0.087 6.090 0.098 Ag-N/L 0.025 0.878 0.114 0.013 0.003 0.011 Au-N/L 2.126 1.123 0.385 0.024 0.819 0.027 Ag-W/S 1.869 1.476 5.433 0.103 10.154 0.152 Ag-W/L 4.228 0.945 1.193 0.008 5.044 0.008 GaN, N 1.582 1.032 1.720 0.708 2.721 0.731 GaN, W 1.449 0.919 1.845 0.452 2.673 0.415 4. Resonance behavior in a metal nanohole In Fig. 7 (b), one can see a sharp peak for the radiated power in the W/L case. Due to its lossy resonance behavior, an SP-involved resonance peak usually shows a broad spectrum. The sharp peak in Fig. 7 (b) implies the existence of a cavity resonance feature in such an SP-involved metal NH. Here, we study such a cavity resonance feature in a cylindrical metal NH, as illustrated in Fig. 5 (d), in which an NH is fabricated on a half-space Ag body. Although the fabrication of such a metal NH sample can be practically difficult, it can be regarded as a simplified structure of that shown in Fig. 5 (a) when metal deposition is very thick, and can provide us with fruitful simulation study results. Again, the NH is filled with the photoresist of 1.577 in refractive index. A radiation dipole is placed at the center of the NH, i.e., with the coordinates at (0, 0, d/2). In numerical computations, d and b are again set at 320 and 200 nm, respectively. Figure 10 (a) shows the normalized radiated power spectra of an x-dipole under various assumptions of dielectric constant. Based on the experimental dielectric constant of Ag shown in Figs. 6 (a) and 6(b), we obtain the normalized radiated power spectrum of the dipole labeled by Exp in Fig. 10 (a). This spectrum consists of a major peak at 682 nm, a minor peak at 576 nm, and an even smaller peak at 457 nm. This radiated power behavior may involve the two factors of cavity resonance and SP coupling. The SP coupling effect is controlled by the behavior of dielectric constant. To understand the SP coupling effect, we use the Drude model to replace the experimental data of dielectric constant as $$\varepsilon (\omega )={\varepsilon _\infty } - \frac{{\omega _{p}^{2}}}{{\omega \left( {\omega - i\Gamma } \right)}}$$ 1 . Here, w p is the plasma frequency, G is the damping frequency, and \({\varepsilon _\infty }\) is the dielectric constant at infinitely large frequency. For Ag, we set \({\varepsilon _\infty }\) = 5, w p = w p0 = 1.3521 x 10 16 rad/s, and G = 5.6 x 10 13 rad/s [ 24 ]. The real and imaginary parts of the dielectric constant based on the Drude model are shown as the curves labeled by “Drude, w p0 ” in Figs. 6 (a) and 6(b), respectively. The parameters for the Drude model are assigned for fitting the real part of the experimental dielectric constant. In Fig. 6 (a), one can see that the Drude model fits the experimental data of Ag quite well. However, as shown in Fig. 6 (b), the imaginary part based on the Drude model is significantly smaller than that of the experimental data. In Fig. 10 (a), we also show the result of normalized radiated power by using the Ag dielectric constant based on the Drude model, as labeled by “Drude, w p0 ”. The major spectral peak positions of radiated power with dielectric constants based on the experimental data and Drude model are about the same. However, the peak intensities based on the Drude model are significantly higher that is due to the smaller imaginary part of its dielectric constant. The reason for us to consider the Drude model is to artificially change the dielectric constant and hence SP coupling behavior for understanding the role of SP coupling in QD emission. For this purpose, we change the plasma frequency w p in the Drude model shown in Eq. ( 1 ). In Figs. 6 (a) and 6(b), we also show the real and imaginary parts of the dielectric constants based on the modified Drude models with w p = 0.7 w p0 , 0.8 w p0 , and 0.9 w p0 ( \({\varepsilon _\infty }\) and G fixed). In Fig. 6 (a), we can see that the magnitude of the negative e’ decreases with decreasing w p , implying that the SP resonance peak will red shift when such a modified Drude model is used. Although the G value in the Drude model is unchanged, the e” value also decreases with decreasing w p . In Fig. 10 (a), we also show the normalized radiated power spectra when those modified Drude models are employed. Here, one can see that the spectra profiles for different w p values are about the same except that such a profile red shifts as w p decreases. In Fig. 10 (a), we also show the radiated power spectrum by assuming that the metal is a perfect conductor, as labeled by “PEC”. Based on this assumption, the major peak of the spectrum becomes very sharp and is significantly blue shifted. In this extreme case of a perfect conductor, no SP resonance behavior can be observed. Therefore, this spectral curve represents the condition of cavity resonance without SP coupling. It is noted that the excitation of an SP polariton (localized SP) resonance requires the condition of matching the negative real part of the dielectric constant in the metal with (two times) the positive real part of that in the surrounding dielectric medium. If the dielectric constant is assumed to be infinity like that in a perfect conductor, such an SP resonance condition can never be satisfied. Therefore, the spectrum labeled by PEC in Fig. 10 (a) shows the result of cavity resonance only. With the finite dielectric constants of negative real parts, the cavity resonance condition is changed. Other radiated power spectra, including those cases of experimental and Drude-model dielectric constants, in Fig. 10 (a) can be produced when both conditions of cavity resonance and SP resonance are simultaneously satisfied. Because of the low quality factor of the metal cavity (due to the opening at the top and metal dissipation) and the lossy SP resonance, the spectral features of radiated power become broader. In Fig. 10 (a), for comparison, the normalized radiated power of an x-dipole in a GaN NH structure is also shown. It is a smooth curve without a clear peak feature. Figure 10 (b) shows the spectra of the normalized radiated power of a z-dipole located at the center of structure NH-Ag with the assumed dielectric constants the same as those for the results in Fig. 10 (a). The general variation trend of the radiated power spectra among different dielectric constant assumptions in Fig. 10 (b) is similar to that in Fig. 10 (a). However, certain major peaks in Fig. 10 (b) are significantly sharper. The sharper peaks produced by a z-dipole can be attributed to the higher quality factors in the excited cavity resonance modes and the weaker SP coupling effects along the z polarization. A weaker SP coupling process can lead to a narrower resonance peak and a stronger radiated power. In this situation, if the emission wavelength of a QD coincides well with the resonance peak, a strong emission enhancement of the QD can be achieved. On the other hand, a stronger SP coupling process results in a broader resonance spectrum, which can more easily cover the emission wavelength of a QD even though the emission enhancement can be relatively weaker. In Fig. 10 (b), we also show the z-dipole result of the NH-GaN structure. Again, it shows a weak spectral dependence. Figures 11 (a)-11(c) show the charge distributions on the Ag surface of structure NH-Ag at the wavelengths of the three peaks, i.e., 457, 576, and 682 nm, respectively, when an x-dipole is placed at the NH center, as indicated by the arrows. Figure 11 (d) shows the similar result at 471.5 nm when a z-dipole is placed at the NH center. The experimental data of Ag dielectric constant are used for obtaining those simulation results. As shown in Fig. 11 (c) for the major peak of the x-dipole radiation, the charge distribution manifests a dipole resonance along either x- or z-direction (covering the NH sidewall and bottom). As shown in Figs. 11 (a) or 11(b) for either minor peak, the charge distribution also illustrates a dipole resonance along the x-direction. However, higher-order resonance modes are excited along the z-direction. On the other hand, as shown in Fig. 11 (d) for the major peak of the z-dipole radiation, the circularly uniform charge distribution varies along the z-direction to form a quadrupole resonance. Here, we can see that the surface charge densities in Figs. 11 (a) and 11(d) are significantly higher, when compared with those in Figs. 11 (b) and 11(c). However, the corresponding emission intensities of the resonance modes shown in Figs. 11 (a) and 11(d) are significantly weaker than those shown in Figs. 11 (b) and 11(c). In other words, a higher surface charge density corresponds to a lower overall radiation intensity. Theoretically, a higher surface charge density implies a condition of a stronger SP coupling process. However, a stronger SP coupling does not necessarily lead to a stronger emission intensity, particularly in the current situation with the cavity resonance in a metal NH. Here, two factors can be involved. First, a stronger SP coupling results in a higher energy loss due to metal dissipation and hence a relatively lower radiation efficiency. Second, although a higher quality factor in such a metal NH can lead to a stronger cavity resonance mode for producing a stronger intensity inside the cavity, it can limit the escape of energy from the cavity to contribute to the radiated power. The low cavity output coupling results in more energy loss through metal dissipation. In the designated metal NH geometry, a radiation peak is produced through the combination of the cavity resonance and SP coupling conditions. When the SP coupling is stronger, the induced metal dissipation leads to a lower overall radiation power. In the extreme case of no SP resonance, such as that of a perfect conductor, the radiated power peak becomes extremely sharp and strong. In another extreme case of no cavity resonance, such as that in an open structure or in an even smaller cavity structure, a stronger SP coupling process normally leads to a surface charge distribution of a higher density and also a stronger radiated power. Figures 12 (a1)-12(d1) show the field strength (norm) distributions of the four resonance modes shown in Figs. 11 (a)-11(d), respectively. Here, the boundaries between the yellow and reddish regions correspond to the border of Ag. The strengths of the field distributions outside NHs are generally consistent with the radiated power intensities shown in Figs. 10 (a) and 10(b). Figures 12 (a2)-12(d2) show the magnified field strength distributions inside the metal NHs in the cases shown in Figs. 12 (a1)-12(d1), respectively. Here, in each part, the radiating dipole is located at the center of the central circular white region. Generally speaking, for those modes with stronger field distributions near the cavity opening (the upper edge of a figure), the overall radiated power is stronger. 5. Discussions As shown in columns 5 and 6 of Table 1 , the green-light PL decay time in sample NH/Au-GQD is shorter than that in sample NH/Ag-GQD. However, the red-light PL decay time in sample NH/Au-RQD is longer than that in sample NH/Ag-GQD. This behavior can be attributed to the larger (smaller) e” in Au in the visible wavelength range of 600) nm, when compared with that in Ag, as shown in Fig. 6 (b) (see the experimental data). A larger (smaller) e” leads to a stronger (weaker) dissipation in the sample with Au and hence a relatively shorter (longer) PL decay time for GQD (RQD), when compared to that with Ag. Also, the smaller magnitude of the negative real part of the dielectric constant in Au when compared with Ag, as shown in Fig. 6 (a), leads to a lower FRET efficiency in the sample with Au (see Table 1 ). Therefore, the green-light PL decay time is longer in sample NH/Au-GQD + RQD, when compared to that in sample NH/Ag-GQD + RQD, due to the less energy transfer from GQD into RQD. Meanwhile, the lower FRET efficiency is expected to result in a shorter red-light PL decay time in sample NH/Au-GQD + RQD, when compared to that in sample NH/Ag-GQD + RQD. However, the smaller e” of Au in the visible range of > 600 nm leads to a longer red-light PL decay time in sample NH/Au-GQD + RQD, as shown in Table 1 . The behavior of PL decay time is affected by the enhancements of QD emission and FRET efficiencies. It is also influenced by the metal dissipation level at the concerned wavelength. It is noted that as shown in Figs. 2 (a) and 2(b), the top surface of either metal NH sample is not flat. Therefore, it is difficult to remove those QDs settled in the shallow depressions on the top surface during surface cleaning. Those QDs are weakly influenced by the metallic nanoscale-cavity effect. Their emission contribution to the total radiated power can effectively reduce the overall efficiency enhancements of QD emission and FRET. It is also noted that with the same NH geometry under study, cavity resonance can occur in structure NH-Ag (a metal NH), as illustrated in Fig. 5 (d), but not in structure NH-GaN (a dielectric NH), as illustrated in Fig. 5 (b). However, the nanoscale-cavity effect in structure NH-GaN can still lead to the enhancements of QD emission and FRET efficiencies. Meanwhile, although strong cavity resonances can be observed in structure NH-Ag, as shown in Figs. 10 (a) and 10(b), in the smaller metal NH of structure NH-Ag/GaN [see Fig. 5 (a)], cavity resonance may not exist. In this situation, the enhancements of dipole radiation and FRET can be mainly attributed to the near-field version of the nanoscale-cavity effect. From the simulation results shown in Table 2 , one can see that the dipole emission, FRET, and color conversion are enhanced only in part of the cases of different metal NH geometries and polarizations. In particular, in most of the cases with a z-dipole, the efficiencies of dipole emission, FRET, or color conversion are reduced. Such numerical results can still be used for confirming the enhancements of the dipole emission, FRET, and color conversion in experiment. This claim is made based on two reasons. First, either emission polarization can be excited in a QD. As long as the emission in one polarization is enhanced, the absorbed energy of a QD will be used mainly for the emission in this polarization. Second, QDs are distributed in different corners of the metal NH, at which the spectral peaks of radiation enhancement are different, leading to an effectively broad spectral range of emission enhancement. Such a broad spectral range can easily cover a concerned QD emission wavelength. In practice, the GaN NH geometry and metal deposition thickness can be optimized for maximizing the efficiencies of QD emission and FRET. From Figs. 7 – 10 , one can see that the peaks of the acceptor radiated powers or donor intensities produced by an x-dipole are generally higher than the counterparts produced by a z-dipole, particularly in the cases of narrower NHs. This general trend can be further understood by considering the image dipoles induced in the metal sidewalls. For an x- (z-) oriented source dipole, the image dipole is in-phase (out-of-phase) with respect to the source dipole. When the distance between the source dipole and metal sidewall is small (in a narrow NH), the image and source dipoles produce constructive-like (destructive-like) interference and hence a relatively stronger (weaker) radiated power or field intensity under the excitation of an x- (z-) dipole. 6. Conclusions In summary, we have first experimentally demonstrated that the PL decay time of a colloidal QD inserted into an Ag or Au NH was reduced and the FRET efficiency from GQD into RQD was increased. The reduced PL decay time was attributed to the QD emission efficiency enhancement, which was caused by the SP-coupling involved nanoscale-cavity effect, and the metal dissipation in the induced SP coupling. Numerical simulation studies confirmed the feasible enhancements of QD emission, FRET, and color conversion efficiencies. In particular, by artificially changing the dielectric constant of the used metal in a relatively larger metal NH, we could differentiate the effects of cavity resonance and SP coupling in producing the enhanced radiated power peaks. In practice, such a peak was formed when both conditions of cavity resonance and SP resonance were satisfied. With a weaker (stronger) SP resonance, the combined resonance could lead to a stronger and sharper (weaker and broader) radiated power peak. A nanoscale metal cavity has great potential for enhancing the emission and color conversion efficiencies of inserted light emitters. Declarations Funding This research was supported by National Science and Technology Council, Taiwan, the Republic of China, under the grants of NSTC 112-2221-E-002-104 and MOST 111-2221-E-002-073 . Author Contributions Shaobo Yang: Epitaxial growth, sample process, optical characterization; Yueh-Chi Lee: Sample process; Yu-Sheng Lin: Time-resolved photoluminescence measurement; Li-Ping Liang: Numerical computation; Yang Kuo: Numerical algorithm preparation; C. C. (Chih-Chung) Yang: Concept proposing, data interpretations, writing. Data Availability All data included in this paper are available upon request by contacting with the corresponding author. Conflicts of interest/Competing interests Availability of data and material The authors declare that they have no conflict of interest. Ethical Approval This submission includes semiconductor growth, process, and numerical studies on the metallic nanoscale-cavity effects. Consent to Participate This submission includes experimental and numerical studies of the metallic nanoscale-cavity effects on quantum dot emission, Förster resonance energy transfer, and surface plasmon coupling. Consent for Publication All authors of this paper agree to publish the research results. References Purcell EM (1946) Spontaneous emission probabilities at radio frequencies. Phys Rev 69 :681-681 Kuo Y, Lu YJ, Shih CY, Yang CC (2021) Simulation study on the enhancement of resonance energy transfer through surface plasmon coupling in a GaN porous structure. 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Phys Rev B 6 (12):4370-4379 Förster T (1946) Energy transport and fluorescence. Naturwissenschaften 33 :166-175 Chanyawadee S, Lagoudakis PG, Harley RT, Charlton MDB, Talapin DV, Huang HW, Lin CH (2010) Increased color-conversion efficiency in hybrid light-emitting diodes utilizing non-radiative energy transfer. Adv Mater 22 (5):602-606 Demira HV, Nizamoglub S, Erdemb T, Mutluguna E, Gaponikc N, Eychmuller A (2011) Quantum dot integrated LEDs using photonic and excitonic color conversion. Nano Today 6 (6):632-647 Ni CC, Kuo SY, Li ZH, Wu SH, Wu RN, Chen CY, Yang CC (2021) Förster resonance energy transfer in surface plasmon coupled color conversion processes of colloidal quantum dots. Opt Express 29 (3):4067-4081 Lin CH, Chiang HC, Wang YT, Yao YF, Chen CC, Tse WF, Wu RN, Chang WY, Kuo Y, Kiang YW, Yang CC (2018) Efficiency enhancement of light color conversion through surface plasmon coupling. Opt Express 26 (18):23629-23640 Chang WY, Kuo Y, Kiang YW, Yang CC (2019) Simulation study on light color conversion enhancement through surface plasmon coupling. Opt Express 27 (12):A629-A642 Kwon MK, Kim JY, Kim BH, Park IK, Cho CY, Byeon CC, Park SJ (2008) Surface-plasmon-enhanced light-emitting diodes. Adv Mater 20 (7):1253-1257 Sun G, Khurgin JB, Soref RA (2007) Practicable enhancement of spontaneous emission using surface plasmons. Appl Phys Lett 90 (11):111107 Lin CH, Su CY, Yao YF, Su MY, Chiang HC, Tsai MC, Liu WH, Tu CG, Kiang YW, Yang CC, Huang FW, Lee CL, Hsu TC (2018) Further emission efficiency improvement of a commercial-quality light-emitting diode through surface Plasmon coupling. Opt Lett 43 (22):5631-5634 Huang YY, Li ZH, Lai YC, Chen JC, Wu SH, Yang S, Kuo Y, Yang CC, Hsu TC, Lee CL (2022) Nanoscale-cavity enhancement of color conversion with colloidal quantum dots embedded in the surface nano-holes of a blue-emitting light-emitting diode. Opt Express 30 (17):31322-31335 Lin CAJ, Sperling RA, Li JK, Yang TA, Li PY, Zanella M, Chang WH, Parak W J (2008) Design of an amphiphilic polymer for nanoparticle coating and functionalization. Small 4 (3):334-341 Chen CY, Ni CC, Wu RN, Kuo SY, Li CH, Kiang YW, Yang CC (2021) Surface plasmon coupling effects on the Förster resonance energy transfer from quantum dot into rhodamine 6G. Nanotechnology 32 (29):295202 Ghenuche P, Mivelle M, de Torres J, Moparthi SB, Rigneault H, Hulst NFV, Parajó MFG, Wenger J (2015) Matching nanoantenna field confinement to FRET distances enhances Förster energy transfer rates. Nano Lett 15 (9):6193–6201 Ferrera M, Magnozzi M, Bisio F, Canepa M (2019) Temperature-dependent permittivity of silver and implications for thermoplasmonics. Phys Rev Mater 3 (10):105201 Magnozzi M, Ferrera M, Mattera L, Canepa M, Bisio F (2019) Plasmonics of Au nanoparticles in a hot thermodynamic bath. Nanoscale 11 (3):1140-1146 Kuo Y, Ting SY, Liao CH, Huang JJ, Chen CY, Hsieh C, Lu YC, Chen CY, Shen KC, Lu CF, Yeh DM, Wang JY, Chuang WH, Kiang YW, Yang CC (2011) Surface plasmon coupling with radiating dipole for enhancing the emission efficiency of a light emitting diode. Opt Express 19 (14):A914-A929 Kuo Y, Chang WY, Lin CH, Yang CC, Kiang YW (2015) Evaluating the blue-shift behaviors of the surface plasmon coupling of an embedded light emitter with a surface Ag nanoparticle by adding a dielectric interlayer or coating. Opt Express 23 (24):30709-30720 Yang HU, D’Archangel J, Sundheimer ML, Tucker E, Boreman GD, Raschke MB (2015) Optical dielectric function of silver. Phys Rev B 91 (23):235137 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 05 Jun, 2024 Reviews received at journal 24 May, 2024 Reviews received at journal 23 May, 2024 Reviewers agreed at journal 14 May, 2024 Reviewers agreed at journal 14 May, 2024 Reviewers invited by journal 14 May, 2024 Submission checks completed at journal 06 May, 2024 Editor assigned by journal 06 May, 2024 First submitted to journal 04 May, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4367418","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":304191325,"identity":"570d5661-ba93-4d4e-9cc0-3a667b1a99b7","order_by":0,"name":"Shaobo Yang","email":"","orcid":"","institution":"National Taiwan University","correspondingAuthor":false,"prefix":"","firstName":"Shaobo","middleName":"","lastName":"Yang","suffix":""},{"id":304191326,"identity":"3767a31c-224e-4faf-bcad-9cb8bcf50290","order_by":1,"name":"Yueh-Chi Lee","email":"","orcid":"","institution":"National Taiwan University","correspondingAuthor":false,"prefix":"","firstName":"Yueh-Chi","middleName":"","lastName":"Lee","suffix":""},{"id":304191327,"identity":"8c6348c6-dcfb-42aa-aca2-4c053e9d4431","order_by":2,"name":"Yu-Sheng Lin","email":"","orcid":"","institution":"National Taiwan University","correspondingAuthor":false,"prefix":"","firstName":"Yu-Sheng","middleName":"","lastName":"Lin","suffix":""},{"id":304191328,"identity":"c73365a9-25aa-4f10-bb3b-a2255d564b6e","order_by":3,"name":"Li-Ping Liang","email":"","orcid":"","institution":"National Taiwan University","correspondingAuthor":false,"prefix":"","firstName":"Li-Ping","middleName":"","lastName":"Liang","suffix":""},{"id":304191329,"identity":"f5848cb5-3f89-4f0d-9479-a970e04e7866","order_by":4,"name":"Yang Kuo","email":"","orcid":"","institution":"National Taiwan University","correspondingAuthor":false,"prefix":"","firstName":"Yang","middleName":"","lastName":"Kuo","suffix":""},{"id":304191330,"identity":"038d9508-bca6-45af-88c1-51324ccfc57e","order_by":5,"name":"C. C. (Chih-Chung) Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsUlEQVRIiWNgGAWjYNCCCgglQYKWMxDVQMKASB2MbaRo4W8/Y/jh57w7dQYHmA/e5mH4k9hASIvEmRxjyd5tzyQMDrAlW/MwGBDWYiDBY8bMuO0wUAuPmTRQSy6RWuaAtPB/I0VLA9gWNuK0SJxJK5bsOXZYcuZhNmPLOQbG9QS18Lcf3vjhR81hfr7jzQ9vvKmQMyakAwg4oFHBDHYnERoYGNgfEKVsFIyCUTAKRjAAAJ75NEhCyojzAAAAAElFTkSuQmCC","orcid":"","institution":"National Taiwan University","correspondingAuthor":true,"prefix":"","firstName":"C.","middleName":"C. (Chih-Chung)","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2024-05-04 08:15:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4367418/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4367418/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":57290550,"identity":"2a31389a-43c0-4855-ba65-130932e63a01","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":44528,"visible":true,"origin":"","legend":"\u003cp\u003e(a) and (b): Plane-view and cross-sectional SEM images, respectively, of the fabricated GaN NH array. (c): [(d):] Plane-view SEM image after an Ag (Au) layer of 80 nm in thickness is deposited onto a GaN NH array.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/174aaa36e90acd4a6c67731d.jpg"},{"id":57290551,"identity":"aae3b0d8-7dab-4266-a5fa-091b0519dcf1","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":45958,"visible":true,"origin":"","legend":"\u003cp\u003e(a): [(b):] Cross-sectional SEM image of the Ag (Au) NH array sample, corresponding to that in Fig. 1(c) [1(d)]. (c) and (d): Plane-view SEM images of samples NH/Ag-GQD and NH/Au-GQD, respectively.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/05f123a5a9947d1049aaa3f6.jpg"},{"id":57290554,"identity":"634e36fd-5eb1-4056-88f8-8758b8f8d505","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":76042,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized green-light PL decay profiles of all the experimental samples with GQD.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/58ed3fe98ef6cd73084dddaf.jpg"},{"id":57290556,"identity":"61fce370-1c0e-4c57-987c-c266519d6306","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":70835,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized red-light PL decay profiles of all the experimental samples with RQD.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/5511b4b3f3cbbec9b81a33d6.jpg"},{"id":57290552,"identity":"427b21ff-f00f-41db-8d27-36fcb6100259","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":59563,"visible":true,"origin":"","legend":"\u003cp\u003e(a): Schematic illustration of a metal NH simulating the experimental NH structures shown in Figs. 2(a) and 2(b) for the numerical study. Two radiating dipoles are placed inside the metal NH at its semi-major axis to serve as the donor and acceptor in an FRET process. (b): Schematic illustration of the NH-GaN structure for the simulation study. (c): Schematic illustration of the structure of homogeneous photoresist (structure R). (d): Schematic illustration of a cylindrical Ag NH structure (NH-Ag).\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/122361f6dae3795822243914.jpg"},{"id":57292450,"identity":"57676324-25fe-49ce-8a7f-094e9d26f500","added_by":"auto","created_at":"2024-05-28 18:04:55","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":74132,"visible":true,"origin":"","legend":"\u003cp\u003e(a) and (b): Real and imaginary parts (\u003cem\u003ee’\u003c/em\u003e and \u003cem\u003ee”\u003c/em\u003e), respectively, of the wavelength-dependent dielectric constants used for simulation studies, including those for Ag and Au based on experimental data and those of various Drude models.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/d27cbf57086978974b3300f5.jpg"},{"id":57290558,"identity":"844f4e38-bc56-4ecc-a67b-28ecaf751730","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":72161,"visible":true,"origin":"","legend":"\u003cp\u003e(a) and (b): Normalized radiated power spectra of the acceptor as an x- and z-dipole, respectively, based on simulation when Ag is used for forming a metal NH. Besides the four Ag NH cases of different NH widths (N and W) and metal deposition thicknesses (S and L), the results of the narrow and wide GaN NHs (N and W) are shown.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/f3e150c4b240a0bda032717f.jpg"},{"id":57290557,"identity":"22d80c85-7eb7-4cda-8601-432734514122","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":60705,"visible":true,"origin":"","legend":"\u003cp\u003e(a) and (b): Normalized field intensity spectra at the position of the acceptor produced by the donor for an x- and z-dipole, respectively, based on simulation in those cases shown in Figs 7(a) and 7(b).\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/392b83b4cfdba462cc58c9b2.jpg"},{"id":57290559,"identity":"74c14d63-f905-4abf-b03b-792adf692891","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":58258,"visible":true,"origin":"","legend":"\u003cp\u003e(a) and (b): Normalized radiated power of the acceptor and the normalized field intensity at the position of the acceptor produced by the donor, respectively, with an x- and a z-dipole in sample NH-Au/GaN.\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/d84ae92d7017d5a54cfa7428.jpg"},{"id":57290560,"identity":"7c6eba8a-f81b-4f24-8535-a6c4e49cffe2","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":76781,"visible":true,"origin":"","legend":"\u003cp\u003e(a): Normalized radiated powers of an x-dipole located at the center of the NH in structure NH-Ag shown in Fig. 5(d) under various assumptions of dielectric constant. (b): Normalized radiated powers of a z-dipole corresponding to the cases shown in part (a).\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/9c6a356dab680b3db984d0b2.jpg"},{"id":57290561,"identity":"4d73c6bf-df0d-4d35-bc10-0d1b7a7d6b6d","added_by":"auto","created_at":"2024-05-28 17:56:55","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":42136,"visible":true,"origin":"","legend":"\u003cp\u003e(a)-(c): Charge distributions on the Ag surface of structure NH-Ag at the wavelengths of the three peaks, i.e., 457, 576, and 682 nm, respectively, when an x-dipole is placed at the NH center, as indicated by the arrows. (d): Charge distribution at 471.5 nm when a z-dipole is placed at the NH center.\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/e1aef862d684cc77132025bc.jpg"},{"id":57292449,"identity":"41390486-0de5-4cf4-ba50-3bb60ed316f7","added_by":"auto","created_at":"2024-05-28 18:04:55","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":71197,"visible":true,"origin":"","legend":"\u003cp\u003e(a1)-(d1): Field strength (norm) distributions of the four resonance modes shown in Figs. 11(a)-11(d), respectively. (a2)-(d2): Magnified field strength distributions inside the NHs in the cases shown in parts (a1)-(d1), respectively.\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/ec69ca86ab2473cf07ba7cc9.jpg"},{"id":57292451,"identity":"faa46c30-a421-403d-aed0-3dc7bbe9db07","added_by":"auto","created_at":"2024-05-28 18:05:00","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1302055,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4367418/v1/e75c4780-4924-4c90-9f61-adbe9014685f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Emission and Förster Resonance Energy Transfer Behaviors of Colloidal Quantum Dots in a Metal Nanohole","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eAs predicted by Purcell, the emission behavior of a light emitter is influenced by the scattered field of its own radiation, which is scattered back from the surrounding structure [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Either the far- or near-field portion of the scattered field can produce the Purcell effect. When we place a light emitter inside a cavity not extremely small, the built cavity resonance field can couple with the light emitter to enhance its emission. In the case of locating a light emitter inside a small cavity, the near-field version of the Purcell effect can also increase its emission efficiency. Experimental and numerical studies have demonstrated the emission efficiency enhancements of colloidal quantum dots (QDs) when they are inserted into nanoscale cavities, such as a surface nanohole (NH) and a subsurface porous structure [\u003cspan additionalcitationids=\"CR3\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Such an emission enhancement was generally referred to as the nanoscale-cavity effect. A theoretical study has also predicted that such an enhancement is stronger when the contrast of dielectric constant between the cavity material and interior medium is higher [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Because the real-part magnitude of the dielectric constant of Ag or Au in the visible range is large even though it is negative [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], it is expected that the nanoscale-cavity effect in such a metal nanocavity can be stronger than that in a dielectric counterpart. Meanwhile, the metal nanostructure in a metallic nanocavity can induce a surface plasmon (SP) coupling effect, which can further enhance the emission efficiency of a light emitter inside a metal nanocavity. For the two reasons above, the study of the emission behavior of a colloidal QD in an Ag or Au nanocavity is important for expanding the application of a QD. Besides the emission efficiency of a single QD, the enhancement of the F\u0026ouml;rster resonance energy transfer (FRET) from a QD donor into a QD acceptor has been demonstrated when both donor and acceptor are located inside a nanocavity [\u003cspan additionalcitationids=\"CR3 CR4\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. FRET is a non-radiative near-field energy transfer process [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], which is an effective mechanism for implementing photon color conversion [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The color conversion efficiency relies on two factors, including the efficiency of the energy transfer from donor into acceptor and that of acceptor emission [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The former can be quite high if an FRET process is utilized. It is proportional to the field intensity at the position of the acceptor produced by the donor. When both donor and acceptor are placed inside a metal nanocavity, the field intensity of the donor is expected to be enhanced, leading to a stronger FRET process. Therefore, the color conversion efficiency in a metal nanocavity can be improved. This issue also deserves a careful investigation.\u003c/p\u003e \u003cp\u003eA light emitter can couple with an SP resonance mode of a metal nanostructure for changing its emission behavior. In such a coupling process, the energies of the light emitter and SP resonance mode can coherently exchange to form a coupled resonance system. In many situations, it can lead to the enhancement of emission efficiency [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. As mentioned earlier, in a metal nanocavity, besides the cavity effect of either far-field cavity resonance or near-field induced emission enhancement, SP resonance can be excited on the sidewall of the metal nanocavity for generating the SP coupling with the light emitter. Such a light emission phenomenon of mixing the mechanisms of the cavity effect and SP coupling has not been well studied yet. In particular, the differentiation between the effects of individual mechanisms is useful for us to further understand the emission behavior. In this paper, we first demonstrate the experimental results of QD-filled Ag and Au surface NHs, which are fabricated by coating metal onto the sidewall and bottom of a GaN surface NH. The time-resolved photoluminescence (TRPL) behaviors of the inserted QDs are shown. Then, a numerical study is undertaken for understanding the dipole emission and FRET behaviors in a metal surface NH structure with the hole morphology simulating that obtained in experiment. Also, the structure of a cylindrical metal NH is used for numerically studying the interplay between the aforementioned two mechanisms of cavity effect and SP coupling. In section 2 of this paper, the sample structure, fabrication procedures, and TRPL results in the experimental study are shown. Then, the simulation results of the dipole emission and FRET behaviors in a metal NH are presented in section 3. Next, in section 4, the numerical results of the interplay between the two mechanisms of cavity effect and SP coupling are reported. Further discussions about the experimental and simulation results are made in section 5. Finally, conclusions are drawn in section 6.\u003c/p\u003e"},{"header":"2. Experimental study","content":"\u003cp\u003eIn the experimental study, we fabricate metal NH arrays on a 2-\u0026micro;m thick GaN template, which is grown on a double-polished sapphire substrate with metalorganic chemical vapor deposition at 1043 \u003csup\u003eo\u003c/sup\u003eC in temperature. To fabricate a metal NH array, we first prepare a surface NH array on the GaN template through the processes of nano-imprint lithography, inductively coupled plasma reactive ion etching (ICPRIE), and wet etching with AZ400K [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Figures\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) and 1(b) show the plane-view and cross-sectional scanning electron microscopy (SEM) images, respectively, of the fabricated GaN NH array. The dimension of a hexagonal-shaped hole on the surface is ~\u0026thinsp;200 nm. The hole depth is ~\u0026thinsp;320 nm. A metal NH array is implemented by depositing metal onto the top surface of the GaN NH array. In this situation, metal can attach onto the sidewall and bottom of a GaN NH to form a metal nanocavity. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c) [1(d)] shows the plane-view SEM image after an Ag (Au) layer of 80 nm in thickness is deposited onto a GaN NH array. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) [2(b)] shows the cross-sectional SEM image of the Ag (Au) NH array sample, corresponding to that in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c) [1(d)]. Here, one can clearly see a vase-shaped metal NH in either sample. The width of such a metal NH at the bottom is ~\u0026thinsp;90 (~\u0026thinsp;80) nm in the Ag (Au) NH sample. The hole depth in either sample is around 320 nm. In other words, the metal deposition thicknesses inside and outside NHs are roughly the same. Next, the photoresist solutions of colloidal QDs are inserted into the fabricated metal NHs. The used green- (530 nm in wavelength) and red-emitting (625 nm in wavelength) CdZnSeS/ZnS colloidal QDs, which are referred to as GQD and RQD, respectively, are purchased from Taiwan Nanocrystals Inc. Tainan, Taiwan. Those QDs are capped with poly(isobutylene-alt-maleic anhydride). Both GQD and RQD are negatively charged with the zeta potentials at -28.3 and \u0026minus;\u0026thinsp;25.6 mV, respectively [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. The size of the amphiphilic polymer capped GQD or RQD ranges from 8 to 10 nm. The procedures for uniformly immersing QDs in the used photoresist (SU-8) have been reported in earlier publications of ours [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Three photoresist solutions of different QD combinations are prepared, including GQD, RQD, and GQD plus RQD. The total QD weight concentrations in those three solutions are the same. After drop-casting a photoresist solution onto a metal NH sample, the solution can flow into and fill up the NHs. Then, a cotton swab is used to sweep the sample for cleaning the top surface. After a photoresist solidification process, the fabrication of a QD-filled metal NH sample is completed. Those samples with the Ag (Au) NHs filled with the photoresist solutions of GQD, RQD, and GQD plus RQD are designated as samples NH/XX-GQD, NH/XX-RQD, and NH/XX-GQD\u0026thinsp;+\u0026thinsp;RQD, respectively, with XX\u0026thinsp;=\u0026thinsp;Ag (Au). For comparison, other sample groups with the same QD combinations are also prepared, including the samples of filling GaN NHs (i.e., no metal deposition) with the photoresist solutions of QD and those of drop-casting the solutions onto the flat surfaces of GaN templates. The former group includes samples NH/GN-GQD, NH/GN-RQD, and NH/GN-GQD\u0026thinsp;+\u0026thinsp;RQD. Those in the latter group are designated as samples S-GQD, S-RQD, and S-GQD\u0026thinsp;+\u0026thinsp;RQD. Figures\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c) and 2(d) show the plane-view SEM images of samples NH/Ag-GQD and NH/Au-GQD, respectively. After the application of the photoresist solutions to those samples, the SEM images become blurred due to the low conductivity of the photoresist.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe emission behaviors of the QDs in those samples are characterized with TRPL measurement. The TRPL measurement is excited by the second-harmonic of a femtosecond Ti:sapphire laser (MIRA 900, pumped by VERDI-8W, Coherent) with the pulse repetition rate at 76 MHz. The wavelength and power used for QD excitation are 390 nm and ~\u0026thinsp;1.5 mW, respectively. The time-dependent signals are detected by a photon-counting system (the time-correlated single photon-counting solution, Becker \u0026amp; Hickl). Its temporal resolution is higher than 100 ps. The procedure for calibrating the decay time of a photoluminescence (PL) decay profile has been reported in detail before [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the normalized green-light PL decay profiles of all those samples with GQD. Here, the decay profiles can be classified into two groups, including those samples with and without metal deposition. With metal deposition, the PL decay rates are significantly higher. In each sample structure (S-, NH/GN-, NH/Ag-, or NH/Au-), with the combination of GQD and RQD, the green-light decay rate is higher, when compared to that with GQD only. This variation trend is caused by the FRET process from GQD into RQD. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the normalized red-light PL decay profiles of all those samples with RQD. Here, the decay profiles can also be classified into the two groups of samples with and without metal deposition. Again, with metal deposition, the PL decay rates are significantly higher. For red light, the decay rate in a sample with GQD\u0026thinsp;+\u0026thinsp;RQD is always lower than that with RQD only of the same structure that again is caused by the FRET process.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the PL decay times of all the samples calibrated from the decay profiles in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Here, the numbers inside the parentheses show the efficiencies of the corresponding FRET processes from GQD into RQD. The FRET efficiency, η, is defined as η\u0026thinsp;=\u0026thinsp;1- τ\u003csub\u003eDA\u003c/sub\u003e/τ\u003csub\u003eD\u003c/sub\u003e [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Here, τ\u003csub\u003eDA\u003c/sub\u003e (τ\u003csub\u003eD\u003c/sub\u003e) is the PL decay time of the energy donor, i.e., GQD, when the acceptor, i.e., RQD, is present (absent). In the surface samples, the green-light decay time reduces from 5.874 ns in sample S-GQD to 5.672 ns in sample S-GQD\u0026thinsp;+\u0026thinsp;RQD due to the FRET process from GQD into RQD with the FRET efficiency at 3.44%. For the same reason, the red-light decay time increases from 10.388 ns in sample S-RQD to 11.786 ns in sample S-GQD\u0026thinsp;+\u0026thinsp;RQD. Then, in the samples with QDs inserted into GaN NHs, all the decay times are reduced from the corresponding values in the surface samples. Such reductions are attributed to the enhancements of QD emission efficiencies caused by the nanoscale-cavity effect [\u003cspan additionalcitationids=\"CR4\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. In sample NH/GN-GQD\u0026thinsp;+\u0026thinsp;RQD, the green-light decay time further decreases due to the FRET process. That for red light is also reduced due to the nanoscale-cavity effect even though RQD receives energy from GQD through the FRET process. In this situation, the FRET efficiency increases to 7.19%. Then, as shown in column 5 of Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, in the samples of Ag NHs, all the decay times are further reduced significantly. Among those Ag-NH samples with different photoresist solutions, the relative PL decay times of green and red lights are similar to those among surface or GaN NH samples. The significantly shorter PL decay times in those Ag NH samples are caused by two key factors. First, the nanoscale-cavity effect, particularly with SP coupling, can enhance the QD emission efficiency and hence reduce its PL decay time. The nanoscale-cavity effect here is expected to be even stronger, when compared with that in a GaN NH sample, due to the metal cavity wall and smaller cavity size [see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a)]. Second, the metal dissipation in the SP coupling process produces the energy loss of the coupled system that can also reduce the PL decay time. In this situation, the nanoscale-cavity effect can still enhance the FRET from GQD into RQD and hence the FRET efficiency is further increased to 15.84%. As shown in column 6 of Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the behaviors of PL decay time in the Au NH samples are similar to those in Ag NH samples even though the decay time values are slightly different. The SP coupling effect with Au is expected to be weaker than that with Ag. Therefore, the nanoscale-cavity effect involving SP coupling in an Au NH sample must be weaker than that in an Ag NH sample. The FRET efficiency in sample NH/Au-GQD\u0026thinsp;+\u0026thinsp;RQD is 10.83%, which is significantly lower than that in sample NH/Ag-GQD\u0026thinsp;+\u0026thinsp;RQD (15.84%).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePL decay times of all those experimental samples. The numbers inside the parentheses show the efficiencies of the corresponding FRET processes from GQD into RQD.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample XXX =\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eS-XXX\u003c/p\u003e \u003cp\u003e(ns)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNH/GN-XXX (ns)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNH/Ag-XXX (ns)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNH/Au-XXX (ns)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGQD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003egreen\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.874\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.553\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.506\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.477\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRQD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ered\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.388\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.854\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.284\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGQD\u0026thinsp;+\u0026thinsp;RQD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003egreen\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.672\u003c/p\u003e \u003cp\u003e(3.44%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.154\u003c/p\u003e \u003cp\u003e(7.19%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.268\u003c/p\u003e \u003cp\u003e(15.84%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.317\u003c/p\u003e \u003cp\u003e(10.83%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ered\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.786\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.972\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.477\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.534\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"3. Numerical simulation study","content":"\u003cp\u003eTo confirm the enhancements of QD emission and FRET efficiencies when QDs are inserted into a metal NH, simulation studies are undertaken with the sample structures illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a)-5(d). As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a), we design a metal NH simulating the experimental NH structures shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) and 2(b). This metal NH structure is designated as NH-XX/GaN with XX\u0026thinsp;=\u0026thinsp;Ag or Au. The NH is designed as a semi-ellipsoid with its long axis coinciding with the axis of the cylindrical GaN NH. The semi-major axis of the ellipsoid is equal to d, which is the depth of the GaN NH. The semi-minor axis is b/2 - w, where b is width of the GaN NH. The semi-ellipsoid NH is filled with the photoresist of 1.577 in refractive index. Ag or Au is deposited in the space between the GaN wall and the photoresist-filled semi-ellipsoid NH. The thickness of metal deposition at the center of the GaN NH bottom is t. Therefore, it is assumed that on the top surface of a sample, a metal layer of t in thickness is also deposited. Two QDs or radiating dipoles are placed inside the metal NH at its semi-major axis, one serves as the donor and the other serves as the acceptor in an FRET process. The origin of the coordinate system is set at the center of the GaN NH bottom. In Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b), the reference sample of the NH-GaN structure is illustrated for comparing the QD emission and FRET efficiencies between the cases with and without metal deposition. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(c) shows the structure of homogeneous photoresist (structure R), which is used as the normalization base in numerical computations. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d) illustrates a cylindrical metal NH structure (NH-Ag) for understanding the cavity resonance effect in a metal NH, as to be further discussed in the next section.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor simulation studies, the dielectric constant, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\epsilon = {\\epsilon }^{{\\prime }}+i\\epsilon \u0026quot;\\)\u003c/span\u003e\u003c/span\u003e, of the used metal needs to be assigned first. Figures\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) and 6(b) show the real and imaginary parts (\u003cem\u003ee\u0026rsquo;\u003c/em\u003e and \u003cem\u003ee\u0026rdquo;\u003c/em\u003e), respectively, of the wavelength-dependent dielectric constants we use for simulation studies. For simulating the experimental conditions, we use the experimental data of dielectric constant for Ag and Au, as labeled by Exp. (Ag) [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] and Exp. (Au) [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) and 6(b). To understand the SP coupling effect in cavity resonance behavior, we also consider the dielectric constants of Ag based on the Drude model, as to be discussed in section 4. Here, a negative value of the real part of dielectric constant implies the possible excitation of SP resonance and hence SP coupling in the visible range. We can see that the magnitude (negative value) of the real part of the dielectric constant in Au is smaller than that of Ag. Also, the imaginary part of Au is smaller (larger) than that of Ag for a wavelength longer (shorter) than 600 nm in the visible range. The high peak of the imaginary part of Au around 400 nm in wavelength is caused by the electron interband transition between the lower d band and the higher s band. The method for the numerical simulation studies has been described in a few earlier publications of ours [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. It is based on the exact electromagnetic theory. This method includes the feedback effect from the scattered field on the radiation behavior of the source dipole. In other words, the Purcell effect, either near- or far-field portion, is taken into account [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo numerically demonstrate the simulation results, we fix the GaN NH depth, d, at 320 nm and consider the following two sets of GaN NH width and two conditions of metal deposition thickness. In a wider (narrower) GaN NH, which is denoted by the symbol \u0026ldquo;W\u0026rdquo; (\u0026ldquo;N\u0026rdquo;), the GaN NH width, b, is 280 (200) nm. In the case of a larger (smaller) metal deposition thickness, which is denoted by the symbol \u0026ldquo;L\u0026rdquo; (\u0026ldquo;S\u0026rdquo;), t\u0026thinsp;=\u0026thinsp;80 (40) nm, w\u0026thinsp;=\u0026thinsp;40 (20) nm, the donor coordinates at (0, 0, 200 nm) [(0, 0, 160 nm)], and the acceptor coordinates at (0, 0, 230 nm) [(0, 0, 190 nm)]. Therefore, we have four combinations in total, including the cases of W/L, W/S, N/L, and N/S. In all cases, the distance between the donor and acceptor is kept at 30 nm. For comparison, we also consider the structures of NH-GaN with b\u0026thinsp;=\u0026thinsp;200 (N) and 280 (W) nm. In either case, the coordinates of the donor and acceptor are (0, 0, 120 nm) and (0, 0, 150 nm), respectively. Figures\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) and 7(b) show the normalized radiated power spectra of the acceptor as an x- and z-dipole, respectively, in an Ag NH shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a). Besides the aforementioned four cases of Ag NH, the results of the narrow and wide GaN NHs are shown. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) for an x-dipole, in the case of either narrower or wider NH, the radiated power shows a sharper peak when metal deposition is thicker. With a thinner metal deposition, the radiated power is weaker and shows a two-peak spectrum. When the GaN NH is narrower and hence the metal NH becomes smaller, the spectral peaks are blue-shifted and become sharper. In the cases of GaN NH, slowly increasing radiated power spectra can be observed. The difference between the narrower and wider GaN NHs is small. In this figure, we can see that in a large spectral range, an Ag NH sample can lead to a stronger radiated power, when compared with that of a GaN NH sample. The vertical dashed line in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) indicates the wavelength of RQD emission (625 nm). At this wavelength, except case N/L, the radiated powers are all enhanced (normalized radiated power\u0026thinsp;\u0026gt;\u0026thinsp;1), when compared with that in structure R. However, except case W/S, the radiated powers in samples Ag NH are lower than those of samples GaN NH. We believe that the sidewall metal deposition in experiment is thinner than that designated in simulation such that the curve of N/S is red-shifted. In this situation, the radiated power in the N/S case of an Ag NH sample becomes higher than that of a GaN NH sample. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b) for a z-dipole, in the cases of narrower NH, the major portions of the radiated power peaks fall into the ultraviolet range. In the cases of wider NH, the radiated power peaks are quite sharp and located far away from the RQD emission wavelength. At this wavelength, the normalized radiated powers in all cases are lower than unity, indicating that it is unlikely for a z-dipole to contribute to QD emission enhancement in either an Ag NH or a GaN NH sample. Such contributions originate mainly from the x- and y-dipole. Figures\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(a) and 8(b) show the normalized field intensity spectra at the position of the acceptor produced by an x- and a z-dipole donors, respectively. Generally speaking, with a narrower NH, the spectral peak of the donor intensity is located at a shorter wavelength. Also, with a thicker Ag deposition, the donor peak intensity is higher. At the GQD emission wavelength, as indicated by the vertical green dashed line, the normalized donor intensities produced by an x-dipole under all the sample conditions, including the NH-GaN structures, are larger than unity, i.e., enhanced. However, those produced by a z-dipole are not significantly enhanced except the case of W/S. The donor intensity enhancements at the emission wavelength of GQD imply the increased energy absorption of the acceptor (RQD) and hence the improvement of the efficiency of the FRET from GQD into RQD.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(a) and 9(b) show the spectra of the normalized radiated power of the acceptor and the normalized field intensity at the position of the acceptor produced by the donor, respectively, in the samples of Au NH with the structure shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a). Both results of an x- and a z-dipole are shown in either Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(a) or 9(b). The geometries used for the Au NH samples are the same as those for the Ag NH samples. Here, only the cases of N/S and N/L are considered. Two strong peaks of radiated power produced by an x-dipole acceptor can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(a). In the concerned wavelength range, the radiated power produced by a z-dipole acceptor is quite low. Fano-like oscillations can be observed around 550 nm in wavelength for donor intensity in all cases, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(b). The intensity peak levels produced by an x-dipole donor are higher than those produced by a z-dipole donor. The emission wavelengths of RQD and GQD are also indicated by the vertical dashed lines in Figs.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(a) and 9(b), respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the normalized field intensity at the position of the acceptor produced by the donor (abbreviated by \u0026ldquo;donor intensity\u0026rdquo;), the normalized acceptor radiated power, and the color conversion factor, which is the product of the last two values, excited by x- and z-oriented dipoles under various metal and GaN NH conditions. The energy absorbed by the acceptor or the transferred energy in an FRET process is proportional to the donor intensity at the position of the acceptor. Hence, the enhancement of donor intensity can be regarded as the increment of FRET efficiency. Therefore, the product of the normalized donor intensity and normalized acceptor radiated power represents the improvement factor of color conversion. In Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, we can see that in most cases of z-dipole, either donor intensity or acceptor radiated power is suppressed or weakly enhanced. However, in most cases of x-dipole, either donor intensity or acceptor radiated power is enhanced, leading to the increase of the color conversion factor. These variation trends are true for both metal and GaN NH samples. However, the increments of the color conversion factors in the metal NH samples are generally larger than those in the GaN NH sample, indicating the stronger nanoscale-cavity effect in a metal NH. In the N/S case, the Au NH sample results in a higher color conversion factor, when compared with the corresponding Ag NH sample. However, this variation trend cannot be regarded as a general rule in the comparison between the Au and Ag NH samples. A change of metal deposition or NH geometry condition can reverse the relative color conversion factors between the samples of the two metals.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNormalized field intensity at the position of the acceptor produced by the donor (donor intensity), the normalized acceptor radiated power, and the color conversion factor, which is the product of the last two values, excited by x- and z-oriented dipoles under various metal and GaN NH conditions.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eDonor intensity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eAcceptor radiated power\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eColor conversion factor\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ex-dipole\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ez-dipole\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ex-dipole\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ez-dipole\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ex-dipole\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ez-dipole\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAg-N/S\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.864\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.688\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.056\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.916\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.048\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAu-N/S\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.719\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.122\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.543\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.087\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.090\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.098\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAg-N/L\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.878\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.114\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAu-N/L\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.126\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.123\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.385\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.819\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.027\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAg-W/S\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.869\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.476\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.433\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.103\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e10.154\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.152\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAg-W/L\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.228\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.945\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.193\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.044\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGaN, N\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.582\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.720\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.708\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.721\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.731\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGaN, W\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.919\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.845\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.452\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.673\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.415\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4. Resonance behavior in a metal nanohole","content":"\u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b), one can see a sharp peak for the radiated power in the W/L case. Due to its lossy resonance behavior, an SP-involved resonance peak usually shows a broad spectrum. The sharp peak in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b) implies the existence of a cavity resonance feature in such an SP-involved metal NH. Here, we study such a cavity resonance feature in a cylindrical metal NH, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d), in which an NH is fabricated on a half-space Ag body. Although the fabrication of such a metal NH sample can be practically difficult, it can be regarded as a simplified structure of that shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a) when metal deposition is very thick, and can provide us with fruitful simulation study results. Again, the NH is filled with the photoresist of 1.577 in refractive index. A radiation dipole is placed at the center of the NH, i.e., with the coordinates at (0, 0, d/2). In numerical computations, d and b are again set at 320 and 200 nm, respectively. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a) shows the normalized radiated power spectra of an x-dipole under various assumptions of dielectric constant. Based on the experimental dielectric constant of Ag shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) and 6(b), we obtain the normalized radiated power spectrum of the dipole labeled by Exp in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a). This spectrum consists of a major peak at 682 nm, a minor peak at 576 nm, and an even smaller peak at 457 nm. This radiated power behavior may involve the two factors of cavity resonance and SP coupling. The SP coupling effect is controlled by the behavior of dielectric constant. To understand the SP coupling effect, we use the Drude model to replace the experimental data of dielectric constant as\u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\varepsilon (\\omega )={\\varepsilon _\\infty } - \\frac{{\\omega _{p}^{2}}}{{\\omega \\left( {\\omega - i\\Gamma } \\right)}}$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e.\u003c/p\u003e \u003cp\u003eHere, \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e is the plasma frequency, G is the damping frequency, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varepsilon _\\infty }\\)\u003c/span\u003e\u003c/span\u003e is the dielectric constant at infinitely large frequency. For Ag, we set \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varepsilon _\\infty }\\)\u003c/span\u003e\u003c/span\u003e= 5, \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep0\u003c/em\u003e\u003c/sub\u003e = 1.3521 x 10\u003csup\u003e16\u003c/sup\u003e rad/s, and G\u0026thinsp;=\u0026thinsp;5.6 x 10\u003csup\u003e13\u003c/sup\u003e rad/s [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The real and imaginary parts of the dielectric constant based on the Drude model are shown as the curves labeled by \u0026ldquo;Drude, \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep0\u003c/em\u003e\u003c/sub\u003e\u0026rdquo; in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) and 6(b), respectively. The parameters for the Drude model are assigned for fitting the real part of the experimental dielectric constant. In Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a), one can see that the Drude model fits the experimental data of Ag quite well. However, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b), the imaginary part based on the Drude model is significantly smaller than that of the experimental data. In Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a), we also show the result of normalized radiated power by using the Ag dielectric constant based on the Drude model, as labeled by \u0026ldquo;Drude, \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep0\u003c/em\u003e\u003c/sub\u003e\u0026rdquo;. The major spectral peak positions of radiated power with dielectric constants based on the experimental data and Drude model are about the same. However, the peak intensities based on the Drude model are significantly higher that is due to the smaller imaginary part of its dielectric constant. The reason for us to consider the Drude model is to artificially change the dielectric constant and hence SP coupling behavior for understanding the role of SP coupling in QD emission. For this purpose, we change the plasma frequency \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e in the Drude model shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) and 6(b), we also show the real and imaginary parts of the dielectric constants based on the modified Drude models with \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 0.7\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep0\u003c/em\u003e\u003c/sub\u003e, 0.8\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep0\u003c/em\u003e\u003c/sub\u003e, and 0.9\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep0\u003c/em\u003e\u003c/sub\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varepsilon _\\infty }\\)\u003c/span\u003e\u003c/span\u003eand G fixed). In Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a), we can see that the magnitude of the negative \u003cem\u003ee\u0026rsquo;\u003c/em\u003e decreases with decreasing \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e, implying that the SP resonance peak will red shift when such a modified Drude model is used. Although the G value in the Drude model is unchanged, the \u003cem\u003ee\u0026rdquo;\u003c/em\u003e value also decreases with decreasing \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e. In Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a), we also show the normalized radiated power spectra when those modified Drude models are employed. Here, one can see that the spectra profiles for different \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e values are about the same except that such a profile red shifts as \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e decreases. In Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a), we also show the radiated power spectrum by assuming that the metal is a perfect conductor, as labeled by \u0026ldquo;PEC\u0026rdquo;. Based on this assumption, the major peak of the spectrum becomes very sharp and is significantly blue shifted. In this extreme case of a perfect conductor, no SP resonance behavior can be observed. Therefore, this spectral curve represents the condition of cavity resonance without SP coupling. It is noted that the excitation of an SP polariton (localized SP) resonance requires the condition of matching the negative real part of the dielectric constant in the metal with (two times) the positive real part of that in the surrounding dielectric medium. If the dielectric constant is assumed to be infinity like that in a perfect conductor, such an SP resonance condition can never be satisfied. Therefore, the spectrum labeled by PEC in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a) shows the result of cavity resonance only. With the finite dielectric constants of negative real parts, the cavity resonance condition is changed. Other radiated power spectra, including those cases of experimental and Drude-model dielectric constants, in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a) can be produced when both conditions of cavity resonance and SP resonance are simultaneously satisfied. Because of the low quality factor of the metal cavity (due to the opening at the top and metal dissipation) and the lossy SP resonance, the spectral features of radiated power become broader. In Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a), for comparison, the normalized radiated power of an x-dipole in a GaN NH structure is also shown. It is a smooth curve without a clear peak feature. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(b) shows the spectra of the normalized radiated power of a z-dipole located at the center of structure NH-Ag with the assumed dielectric constants the same as those for the results in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a). The general variation trend of the radiated power spectra among different dielectric constant assumptions in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(b) is similar to that in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a). However, certain major peaks in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(b) are significantly sharper. The sharper peaks produced by a z-dipole can be attributed to the higher quality factors in the excited cavity resonance modes and the weaker SP coupling effects along the z polarization. A weaker SP coupling process can lead to a narrower resonance peak and a stronger radiated power. In this situation, if the emission wavelength of a QD coincides well with the resonance peak, a strong emission enhancement of the QD can be achieved. On the other hand, a stronger SP coupling process results in a broader resonance spectrum, which can more easily cover the emission wavelength of a QD even though the emission enhancement can be relatively weaker. In Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(b), we also show the z-dipole result of the NH-GaN structure. Again, it shows a weak spectral dependence.\u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(a)-11(c) show the charge distributions on the Ag surface of structure NH-Ag at the wavelengths of the three peaks, i.e., 457, 576, and 682 nm, respectively, when an x-dipole is placed at the NH center, as indicated by the arrows. Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(d) shows the similar result at 471.5 nm when a z-dipole is placed at the NH center. The experimental data of Ag dielectric constant are used for obtaining those simulation results. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(c) for the major peak of the x-dipole radiation, the charge distribution manifests a dipole resonance along either x- or z-direction (covering the NH sidewall and bottom). As shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(a) or 11(b) for either minor peak, the charge distribution also illustrates a dipole resonance along the x-direction. However, higher-order resonance modes are excited along the z-direction. On the other hand, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(d) for the major peak of the z-dipole radiation, the circularly uniform charge distribution varies along the z-direction to form a quadrupole resonance. Here, we can see that the surface charge densities in Figs.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(a) and 11(d) are significantly higher, when compared with those in Figs.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(b) and 11(c). However, the corresponding emission intensities of the resonance modes shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(a) and 11(d) are significantly weaker than those shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(b) and 11(c). In other words, a higher surface charge density corresponds to a lower overall radiation intensity. Theoretically, a higher surface charge density implies a condition of a stronger SP coupling process. However, a stronger SP coupling does not necessarily lead to a stronger emission intensity, particularly in the current situation with the cavity resonance in a metal NH. Here, two factors can be involved. First, a stronger SP coupling results in a higher energy loss due to metal dissipation and hence a relatively lower radiation efficiency. Second, although a higher quality factor in such a metal NH can lead to a stronger cavity resonance mode for producing a stronger intensity inside the cavity, it can limit the escape of energy from the cavity to contribute to the radiated power. The low cavity output coupling results in more energy loss through metal dissipation. In the designated metal NH geometry, a radiation peak is produced through the combination of the cavity resonance and SP coupling conditions. When the SP coupling is stronger, the induced metal dissipation leads to a lower overall radiation power. In the extreme case of no SP resonance, such as that of a perfect conductor, the radiated power peak becomes extremely sharp and strong. In another extreme case of no cavity resonance, such as that in an open structure or in an even smaller cavity structure, a stronger SP coupling process normally leads to a surface charge distribution of a higher density and also a stronger radiated power. Figures\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e(a1)-12(d1) show the field strength (norm) distributions of the four resonance modes shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(a)-11(d), respectively. Here, the boundaries between the yellow and reddish regions correspond to the border of Ag. The strengths of the field distributions outside NHs are generally consistent with the radiated power intensities shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a) and 10(b). Figures\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e(a2)-12(d2) show the magnified field strength distributions inside the metal NHs in the cases shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e(a1)-12(d1), respectively. Here, in each part, the radiating dipole is located at the center of the central circular white region. Generally speaking, for those modes with stronger field distributions near the cavity opening (the upper edge of a figure), the overall radiated power is stronger.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Discussions","content":"\u003cp\u003eAs shown in columns 5 and 6 of Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the green-light PL decay time in sample NH/Au-GQD is shorter than that in sample NH/Ag-GQD. However, the red-light PL decay time in sample NH/Au-RQD is longer than that in sample NH/Ag-GQD. This behavior can be attributed to the larger (smaller) \u003cem\u003ee\u0026rdquo;\u003c/em\u003e in Au in the visible wavelength range of \u0026lt;\u0026thinsp;600 (\u0026gt;\u0026thinsp;600) nm, when compared with that in Ag, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b) (see the experimental data). A larger (smaller) \u003cem\u003ee\u0026rdquo;\u003c/em\u003e leads to a stronger (weaker) dissipation in the sample with Au and hence a relatively shorter (longer) PL decay time for GQD (RQD), when compared to that with Ag. Also, the smaller magnitude of the negative real part of the dielectric constant in Au when compared with Ag, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a), leads to a lower FRET efficiency in the sample with Au (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Therefore, the green-light PL decay time is longer in sample NH/Au-GQD\u0026thinsp;+\u0026thinsp;RQD, when compared to that in sample NH/Ag-GQD\u0026thinsp;+\u0026thinsp;RQD, due to the less energy transfer from GQD into RQD. Meanwhile, the lower FRET efficiency is expected to result in a shorter red-light PL decay time in sample NH/Au-GQD\u0026thinsp;+\u0026thinsp;RQD, when compared to that in sample NH/Ag-GQD\u0026thinsp;+\u0026thinsp;RQD. However, the smaller \u003cem\u003ee\u0026rdquo;\u003c/em\u003e of Au in the visible range of \u0026gt;\u0026thinsp;600 nm leads to a longer red-light PL decay time in sample NH/Au-GQD\u0026thinsp;+\u0026thinsp;RQD, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The behavior of PL decay time is affected by the enhancements of QD emission and FRET efficiencies. It is also influenced by the metal dissipation level at the concerned wavelength.\u003c/p\u003e \u003cp\u003eIt is noted that as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) and 2(b), the top surface of either metal NH sample is not flat. Therefore, it is difficult to remove those QDs settled in the shallow depressions on the top surface during surface cleaning. Those QDs are weakly influenced by the metallic nanoscale-cavity effect. Their emission contribution to the total radiated power can effectively reduce the overall efficiency enhancements of QD emission and FRET. It is also noted that with the same NH geometry under study, cavity resonance can occur in structure NH-Ag (a metal NH), as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d), but not in structure NH-GaN (a dielectric NH), as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b). However, the nanoscale-cavity effect in structure NH-GaN can still lead to the enhancements of QD emission and FRET efficiencies. Meanwhile, although strong cavity resonances can be observed in structure NH-Ag, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a) and 10(b), in the smaller metal NH of structure NH-Ag/GaN [see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a)], cavity resonance may not exist. In this situation, the enhancements of dipole radiation and FRET can be mainly attributed to the near-field version of the nanoscale-cavity effect.\u003c/p\u003e \u003cp\u003eFrom the simulation results shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, one can see that the dipole emission, FRET, and color conversion are enhanced only in part of the cases of different metal NH geometries and polarizations. In particular, in most of the cases with a z-dipole, the efficiencies of dipole emission, FRET, or color conversion are reduced. Such numerical results can still be used for confirming the enhancements of the dipole emission, FRET, and color conversion in experiment. This claim is made based on two reasons. First, either emission polarization can be excited in a QD. As long as the emission in one polarization is enhanced, the absorbed energy of a QD will be used mainly for the emission in this polarization. Second, QDs are distributed in different corners of the metal NH, at which the spectral peaks of radiation enhancement are different, leading to an effectively broad spectral range of emission enhancement. Such a broad spectral range can easily cover a concerned QD emission wavelength. In practice, the GaN NH geometry and metal deposition thickness can be optimized for maximizing the efficiencies of QD emission and FRET.\u003c/p\u003e \u003cp\u003eFrom Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, one can see that the peaks of the acceptor radiated powers or donor intensities produced by an x-dipole are generally higher than the counterparts produced by a z-dipole, particularly in the cases of narrower NHs. This general trend can be further understood by considering the image dipoles induced in the metal sidewalls. For an x- (z-) oriented source dipole, the image dipole is in-phase (out-of-phase) with respect to the source dipole. When the distance between the source dipole and metal sidewall is small (in a narrow NH), the image and source dipoles produce constructive-like (destructive-like) interference and hence a relatively stronger (weaker) radiated power or field intensity under the excitation of an x- (z-) dipole.\u003c/p\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eIn summary, we have first experimentally demonstrated that the PL decay time of a colloidal QD inserted into an Ag or Au NH was reduced and the FRET efficiency from GQD into RQD was increased. The reduced PL decay time was attributed to the QD emission efficiency enhancement, which was caused by the SP-coupling involved nanoscale-cavity effect, and the metal dissipation in the induced SP coupling. Numerical simulation studies confirmed the feasible enhancements of QD emission, FRET, and color conversion efficiencies. In particular, by artificially changing the dielectric constant of the used metal in a relatively larger metal NH, we could differentiate the effects of cavity resonance and SP coupling in producing the enhanced radiated power peaks. In practice, such a peak was formed when both conditions of cavity resonance and SP resonance were satisfied. With a weaker (stronger) SP resonance, the combined resonance could lead to a stronger and sharper (weaker and broader) radiated power peak. A nanoscale metal cavity has great potential for enhancing the emission and color conversion efficiencies of inserted light emitters.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was supported by National Science and Technology Council, Taiwan, the Republic of China, under the grants of NSTC \u003cstrong\u003e112-2221-E-002-104\u003c/strong\u003e and \u003cstrong\u003eMOST 111-2221-E-002-073\u003c/strong\u003e. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eShaobo Yang: Epitaxial growth, sample process, optical characterization; Yueh-Chi Lee: Sample process; Yu-Sheng Lin: Time-resolved photoluminescence measurement; Li-Ping Liang: Numerical computation;\u0026nbsp;Yang Kuo: Numerical algorithm preparation; C. C. (Chih-Chung) Yang: Concept proposing, data interpretations, writing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAll data included in this paper are available upon request by contacting with the corresponding author.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest/Competing interests Availability of data and\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ematerial\u003c/strong\u003eThe authors declare that they have no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval\u0026nbsp;\u003c/strong\u003eThis submission includes semiconductor growth, process, and numerical studies on the metallic nanoscale-cavity effects.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Participate\u003c/strong\u003e This submission includes experimental and numerical studies of the metallic nanoscale-cavity effects on quantum dot emission, F\u0026ouml;rster resonance energy transfer, and surface plasmon coupling.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for Publication\u003c/strong\u003e All authors of this paper agree to publish the research results.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003ePurcell EM (1946) Spontaneous emission probabilities at radio frequencies. 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Phys Rev B \u003cstrong\u003e91\u003c/strong\u003e(23):235137\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"plasmonics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"plas","sideBox":"Learn more about [Plasmonics](https://www.springer.com/journal/11468)","snPcode":"11468","submissionUrl":"https://submission.nature.com/new-submission/11468/3","title":"Plasmonics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4367418/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4367418/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe reduction of the photoluminescence (PL) decay time of a colloidal quantum dot (QD) inserted into an Ag or Au surface nanohole and the efficiency enhancement of the F\u0026ouml;rster resonance energy transfer (FRET) from a green-emitting QD into a red-emitting QD are first experimentally demonstrated. Besides the factor of metal dissipation in the induced surface plasmon (SP) coupling process, the reduced PL decay time is attributed to the QD emission efficiency increase caused by the SP-coupling involved nanoscale-cavity effect. Numerical simulation studies are undertaken to confirm the feasible enhancements of QD emission, FRET, and color conversion efficiencies. In particular, by artificially changing the dielectric constant of Ag based on the Drude model, the effects of cavity resonance and SP coupling in producing the enhanced radiated power peaks can be differentiated. Such a peak can be formed when both conditions of cavity resonance and SP resonance are satisfied. In the case of a weaker (stronger) SP resonance, the combined resonance can lead to a stronger and sharper (weaker and broader) radiated power peak. The results in this paper indicate that a nanoscale metal cavity can be used for enhancing the emission and color conversion efficiencies of inserted light emitters.\u003c/p\u003e","manuscriptTitle":"Emission and Förster Resonance Energy Transfer Behaviors of Colloidal Quantum Dots in a Metal Nanohole","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-28 17:56:50","doi":"10.21203/rs.3.rs-4367418/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-06-05T11:11:32+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-05-24T07:17:03+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-05-23T12:39:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"288702236502260705759577204490915792155","date":"2024-05-14T13:09:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"77849567640916403987261134282352311049","date":"2024-05-14T10:50:30+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-05-14T10:20:04+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-05-06T07:55:20+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-05-06T07:55:20+00:00","index":"","fulltext":""},{"type":"submitted","content":"Plasmonics","date":"2024-05-04T08:13:59+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"plasmonics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"plas","sideBox":"Learn more about [Plasmonics](https://www.springer.com/journal/11468)","snPcode":"11468","submissionUrl":"https://submission.nature.com/new-submission/11468/3","title":"Plasmonics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"cbc663df-8e6b-49bc-87a0-f128fe2d1fd1","owner":[],"postedDate":"May 28th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-06-18T11:45:59+00:00","versionOfRecord":[],"versionCreatedAt":"2024-05-28 17:56:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4367418","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4367418","identity":"rs-4367418","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}