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Abstract
Metal-insulator-metal tunnel junctions (MIM-TJs) can electrically excite surface plasmon polaritons (SPPs) well below the diffraction limit. When inelastically tunneling electrons traverse the tunnel barrier under applied external voltage, a highly confined cavity mode (MIM-SPP) is excited, which further out-couples from the MIM-TJ to photons and single-interface SPPs via multiple pathways. In this work we control the out-coupling pathways of the MIM-SPP mode by engineering the geometry of the MIM-TJ. We fabricated MIM-TJs with tunneling directions oriented vertical or lateral with respect to the directly integrated plasmonic strip waveguides. With control over the tunneling direction, preferential out-coupling of the MIM-SPP mode to SPPs or photons is achieved. Based on the wavevector distribution of the single-interface SPPs or photons in the far-field emission intensity obtained from back focal plane (BFP) imaging, we estimate the out-coupling efficiency of the MIM-SPP mode to multiple out-coupling pathways. We show that in the vertical-MIM-TJs the MIM-SPP mode preferentially out-couples to single-interface SPPs along the strip waveguides while in the lateral-MIM-TJs photon out-coupling to the far-field is more efficient.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Plasmonics has attracted great interest over the past decade because of its potential as a complementary technology in applications ranging from catalysis [1–3], sensing [4–7], to nano-optoelectronics [8–12]. For these applications it is desirable to have access to electrical sources of SPPs and, in this context, SPP excitation via quantum mechanical tunneling in metal-insulator-metal tunnel junctions (MIM-TJs) is of interest [13–16] because of the non-diffraction limited nature of SPPs. In MIM-TJs, tunneling charge carriers that tunnel inelastically can couple to the local density of optical states (LDOS) [17,18], mainly exciting the highly confined cavity mode (MIM-SPP mode) [19,20], which then out-couples to all available SPP modes and to photons.
Inelastic electron tunneling in MIM-TJs is well approximated by a dipole oscillating normal to the TJ [21], exciting the MIM-SPP mode, which is highly confined within the MIM-TJ where the insulator is typically around 1-3 nm thick. The electron tunneling direction dictates the resultant MIM-SPP wavevector and concomitant out-coupling of the MIM-SPP mode to free-space photons or lower-momentum SPPs. However, the large momentum mismatch between the MIM-SPP mode and single-interface SPPs or photons makes the direct out-coupling process highly inefficient. Nevertheless, in large area planar junctions where the MIM-SPP mode is mostly confined within the MIM-TJ area, scattering of the MIM-SPP mode off of the surface roughness (pathway 1 in Fig. 1) of the MIM-TJ interfaces provides sufficient momentum to facilitate the mode overlap between the MIM-SPP mode and the single-interface SPPs or photons, enhancing the out-coupling efficiency by 3-4 orders of magnitude [13,20,22–28] as compared to MIM-TJs with flat interfaces [19,29,30]. Moreover, as recently demonstrated by Makarenko et al. [20], by reducing the thickness of the top and bottom electrodes, electromagnetic screening of the metal electrodes to the mode overlap can be minimized to enhance the out-coupling efficiency of the MIM-SPP mode to single-interface SPPs [pathway 2 in Fig. 1(a)], at either the metal-glass or metal-air interfaces, or to photons [20,31].
Fig. 1. Schematic representation of (a) vertical and (b) lateral-MIM-TJs connected to Al and Au waveguides, showing the out-coupling of the MIM-SPP mode (red) to single-interface SPPs (dark blue) and photons (green arrows). The MIM-SPP out-coupling pathways are indicated as: pathway 1 – photon emission from scattering off the MIM-TJ surface roughness, pathway 2 – mode overlap of the MIM-SPP with the single-interface SPPs through the metal electrodes, pathway 3 – coupling to single-interface SPPs at the junction edge. On the top left side of each schematic, we indicate the electron tunneling direction with respect to the surface normal of the glass substrate. On the top right side of each schematic we indicate the relative orientation of the momenta of the MIM-SPP mode and the single-interface SPPs.
Given the large bandwidth of excitation [24] and the presence of multiple decay channels for the MIM-SPP mode, gaining control over the out-coupling pathways is equally relevant as achieving better out-coupling efficiencies in MIM-TJs. In particular, preferential out-coupling of the MIM-SPP mode to SPPs or photons is critical in most of the practical applications mentioned above. Out-coupling of the MIM-SPP mode to photons has been demonstrated in the past in planar MIM-TJ designs based on nanoparticle-coupled junctions [32–35] and nanoscale break junctions [36,37] with an in-plane (lateral) direction of tunneling directly mediating the out-coupling process. The dipolar nature of the inelastic tunneling can also be utilized to control the out-coupling of the MIM-SPP to photons with carefully designed nanoscale antennas [38] or with molecular junctions [39]. In contrast, in planar MIM-TJs dominated with out-of-plane (vertical) direction of tunneling, controlling the out-coupling pathways is non-trivial and requires either specific grating/nano-patch antenna designs [40,41] or a local excitation source like the tip of a scanning tunneling microscope [42,43] to improve, or control, SPP/photon out-coupling.
Here we demonstrate how the electron tunneling in the vertical [along z; Fig. 1(a)] and lateral [normal to z; Fig. 1(b)] direction affects the out-coupling efficiency of the MIM-SPP mode to SPPs and photons in MIM-TJs. We fabricated vertical and lateral Al-AlOx- Cr-Au TJs (Fig. 1) and the far-field emission due to photon or SPP out-coupling from the biased TJs was collected via leakage radiation microscopy. However, due to the broadband nature of the excitation and the complex geometry of the MIM-TJs (Fig. 1), experimentally collected far-field emission intensity in the real plane is intricate [20] with intensity contributions from photon/SPP scattering [36] and SPP leakage, [40] including 1D-SPP modes [44]. Since these contributions are manifested separately in the back focal plane (BFP) of the leakage radiation according to their effective mode index, we performed a detailed BFP intensity analysis to calculate the out-coupling efficiency associated with each pathway. Finite-difference time-domain (FDTD) simulations were also performed to theoretically calculate the out-coupling efficiency for the vertical and lateral-MIM-TJs. Both experimental and theoretical results show that in the vertical-MIM-TJ, the MIM-SPP mode out-couples preferentially to the single-interface SPPs, with an out-coupling efficiency a factor of 5 higher than in the lateral-MIM-TJ, whereas in the lateral-MIM-TJ the MIM-SPP mode out-couples preferentially to photons due to the scattering corners [pathway 1 in Fig. 1(b)] present in the structure. These results give us new insights into the tunneling-direction dependence of the out-coupling mechanisms of the highly confined junction modes.
2. Results and discussions
2.1 Design of the junctions
In this work, we fabricated Al-AlOx-Cr-Au MIM-TJs as they have been well-characterized in literature [13,20,40,45,46]. The vertical [Fig. 1(a)] and lateral [Fig. 1(b)] MIM-TJs were fabricated on borosilicate coverslips through patterning by electron beam lithography, thermal evaporation of the Al electrode, oxidation of the Al layer to grow the native oxide and thermal evaporation of the Au electrode, with 1 nm Cr as an adhesion layer. During the fabrication process, we kept all the deposition methods and evaporation rates the same to ensure the surface roughness variation was minimal across all devices. Section 1 in the Supplement 1 gives all the fabrication details.
Figure 1(a) shows the schematic of a vertical-MIM-TJ, where the MIM-SPP mode can out-couple directly to photons via scattering off the surface roughness of the bottom electrode (pathway 1). The in-plane momentum of the MIM-SPP in this case can also lead to coupling to the single-interface SPPs due to the scattering of the MIM-SPP at protrusions caused by surface roughness or at the junction edges. Specifically, it can out-couple to the SPPAu-glass, SPPAl-glass, SPPAu-air and SPPAl-air modes (shown in Fig. S4) via mode overlap through the Au and Al electrodes (pathway 2), aided by surface roughness [23,28,47]. Figure 1(b) shows that in the lateral-MIM-TJ, the MIM-SPP can out-couple to SPPAl-glass, SPPAu-air and SPPAu-glass at the corner of the junction (pathway 3) or directly scatter to photons at the corners where the MIM cavity is in direct contact with the glass substrate or with air (pathway 1). Even though the momentum of the MIM-SPP mode is orthogonal to that of the SPPAu-air, the presence of these corners in the structure aids in the momentum matching between the MIM-SPP mode and the single-interface SPPs.
For the vertical-MIM-TJ, we chose the thickness of the top and bottom electrodes to be twice the skin depth of Au/Al (∼ 40 nm) [28] so that the signatures of the SPP features from pathway 2 are clearly visible in the BFP image without getting over-saturated by the photonic contributions from pathway 1. In the case of the lateral-MIM-TJ, we chose a thickness of ∼100 nm for the Al electrode which gives a large thickness difference between the Al and the Au electrodes (∼60 nm, indicated in Section 2, Fig. S3 in the Supplement 1) that allows the formation of a lateral stack of electrode materials (as shown in Supplement 1, Fig. S1 and Fig. S3).
2.2 Characterization of the junctions
Figures 2(a)–2(b) show the atomic force microscopy (AFM) images of the vertical and lateral-MIM-TJs, respectively. We determined a root-mean-squared (rms) surface roughness of 7 ${\pm} \; $1.5 nm for Al and 1.1 ${\pm} $ 0.2 nm for Au, measured over a 1 × 1 µm2 area. We also extracted the thicknesses of the metallic electrodes from the AFM images. The vertical-MIM-TJ has a 40$\; \pm $ 5 nm thick Al bottom electrode, and a 45 ${\pm} $ 3 nm thick Au top electrode, while the lateral-MIM-TJ has a 100 ${\pm} $ 5 nm thick Al electrode and 35 ${\pm} $ 3 nm Au electrode.
Fig. 2. Atomic force microscopy images of the (a) vertical and (b) lateral-MIM-TJs. (c) IV-characteristics and (d) differential conductance dI/dV, corresponding to the vertical (black) and lateral (red) MIM-TJs. The error bars represent the standard deviation of the current and conductance, respectively, for five different junctions in each geometry.
Before the optical characterization, we recorded the IV-characteristics for all devices to ensure that the charge transport mechanism in the fabricated Al-AlOx-Cr-Au junctions was dominated by tunneling [Fig. 2(c)]. During the measurements, we grounded the Au electrode and biased the Al electrode. As we have previously shown, the Al-AlOx-Cr-Au MIM-TJs have a lower break down voltage at positive bias [13] than at negative bias. Therefore, we applied an external bias between +1.0 V and −1.6 V to avoid breakdown at large positive bias. According to Rowell’s criteria [48,49], the exponential behavior of the IV curves along with the positive parabolic shape of the differential conductance (dI/dV) [Fig. 2(d)] are signatures that the MIM-TJs are dominated by direct tunneling and do not suffer from pinholes. These observed device characteristics of the vertical- and lateral-MIM-TJs are in agreement with previous findings [13,20,40].
2.3 Optical Properties of the Junctions
We recorded the optical characteristics of the MIM-TJs using a 100${\times} $ oil immersion objective with a numerical aperture (NA) of 1.49 in an inverted optical microscope equipped with an electron multiplying charge-coupled device (EMCCD) camera and a spectrometer (with a spectral range 400-1100 nm). The light emission from these devices was collected beneath the glass substrate while applying a bias across the MIM-TJ. Figure 3(a) shows the real plane EMCCD image of the vertical-MIM-TJ. The intensity distribution in the real plane image is dominated by the light emission from the direct scattering of the MIM-SPP mode off of the surface roughness from the MIM-TJ area (pathway 1). We also observe light emission from the truncated end of the Au (-x direction) and Al (+y direction) waveguides in Fig. 3(a). These represent the single-interface SPPs, out-coupled from the MIM-TJ via pathway 2, propagating along the waveguides and scattering to photons because of the momentum imparted by the discontinuity at the end of the waveguide [indicated in Fig. 1(a) and Fig. 3(a) as SPP pathway 2]. Figure 3(b) shows the real plane image of the lateral-MIM-TJ. Also, here light emission is dominated by pathway 1 as well as the scattering of the SPPs at the end of the waveguides is clearly visible, which in this geometry corresponds to the out-coupling of the MIM-SPP mode via pathway 3.
Fig. 3. Real plane EMCCD images of the (a) vertical and (b) lateral-MIM-TJs, recorded at −1.5 V. (c)-(d) BFP images of the corresponding MIM-TJs, recorded at −1.5 V. The inner dashed lines in the BFP images represent the critical angle of the total internal reflection at the air-glass interface (k/k0 = 1.0) and the outer dashed lines indicate the maximum angle of the collected light limited by the NA of the objective (k/k0 = 1.49).
2.4 Back focal plane imaging
To investigate the emission intensity contributions from various out-coupling pathways, we recorded the BFP images of the light emitted by the devices. As mentioned before, since the angular distribution of these contributions render in the BFP according to their effective mode index, mode assignments and the out-coupling efficiency estimation is straightforward from the BFP analysis. We assigned all features observed in the experimental BFP images [Figs. 3(c) and 3(d)] with the aid of FDTD numerical simulations (Lumerical software [50]). Figures 3(c)–3(d) show the distribution of the light intensity in the BFP as a function of the normalized wavenumber k/k0 for vertical- and lateral-MIM-TJs respectively, where k0 is the free-space wavenumber. Here, the inner dashed circle refers to the critical angle of the total internal reflection at the air-glass interface (k/k0 = 1.0), and the outer dashed circle indicates the maximum angle of the collected light limited by the NA of the objective (k/k0 = 1.49).
The BFP images show the contributions of the scattered MIM-SPP mode (pathway 1) and those of the individual single-interface SPP modes, excited via pathway 2 [Fig. 3(c)] or pathway 3 [Fig. 3(d)], as discussed in the previous section. Roughness-induced scattering of the MIM-SPP mode contributes mainly to the region corresponding to k/k0 < 1 due to the broad spatial extent of the scattering centers, resulting in the far-field interference and dominates the central disc demarcated in the BFP [51]. The contribution of the single-interface SPP modes can be detected in the k-space region confined by the two green rings demarcated in the figure, where 1< k/k0 < 1.49. To extract the individual contribution of each out-coupling pathway, we analyzed the experimental BFP images [Figs. 3(c)–3(d)] as described in the Supplement 1 Section 4 and Table 1, which collectively summarize the values obtained for the integrated intensity/pixel corresponding to each pathway. Table 1 shows that the intensity of the SPP signatures in the lateral-MIM-TJ is 3 times smaller than that of the vertical-MIM-TJ. This is due to the low out-coupling efficiency of the MIM-SPP mode to the SPPAu-glass mode due to the orthogonality of the momenta of the two modes [as shown in Fig. 1(b)]. Considering that in the vertical-MIM-TJs the SPPs are excited via pathway 2, whereas in the lateral-MIM-TJ the SPPs are excited via pathway 3, we conclude that SPP out-coupling via pathway 2 is 3 times more efficient than via pathway 3. Moreover, when we compare the photonic contributions in the two geometries, we note that pathway 1 is 3 times more intense in the lateral than in the vertical-MIM-TJ, indicating that the MIM-SPP mode out-couples preferentially to photons in the lateral-MIM-TJ.
Table 1. Integrated intensity/pixel for individual out-coupling pathways.
To assign the features observed in the experimental BFP images, we carried out FDTD simulations for the plasmonic response of the vertical and lateral-MIM-TJs and obtained simulated BFP images for comparison. In FDTD, a total simulation domain volume of $\; 16\; \mu $m ${\times}\; 16\; \mu $m ${\times}\; 2\; \mu $m is used. Figures 4(a)–4(b) show the 2D cross-section of the simulation domain in the $xy$ plane, corresponding to the vertical and lateral-MIM-TJs, respectively. We used a uniform dipole distribution within the MIM-TJ [Figs. 4(a)–4(b)] to represent the MIM-SPP mode excitation sources, assuming that the current flows homogeneously across the MIM-TJs [52]. Within the 2 nm thick AlOx insulator layer, the electromagnetic field changes rapidly and therefore we used a mesh size of 0.25 nm in all three dimensions. The broadband nature of the MIM-SPP mode excitation with a spectral peak ∼ 900 nm is represented by the dipole spectrum spanning from 800 nm to 1000 nm. We recorded the electric field on a $xy$ plane placed at 500 nm below the substrate in the glass medium and this $xy$ plane collects the emission into the glass substrate from the whole simulation domain. A near- to far-field transformation is applied to the recorded electric field to obtain the far-field radiation/scattering pattern. Finally, we account for any apodization effects due to the collection lens and obtain the BFP intensity distribution. In the simulations we consider the individual dipoles as non-interacting and therefore the contribution from each dipole is calculated separately, with all contributions then integrated together to obtain the overall intensity distribution of the MIM-TJs in the BFP. The experimentally observed BFP features are well reproduced in the simulated BFP images [Figs. 4(c) and 4(d)].
Fig. 4. FDTD simulations of the BFP images of the junctions. (a) Placement of the nine dipoles in the vertical-MIM-TJ and (b) five dipoles in the lateral-MIM-TJ. All of the dipoles are placed 10 nm away from the scattering edges. (c)-(d) Simulated BFP images of the structures in panels (a) and (b), respectively.
Based on the simulation results we analyze the features observed in the experimental BFP images and justify the mode assignments adopted in Figs. 3(c)–3(d). As noted before (Fig. 1), the MIM-SPP mode out-couples to single-interface SPPs at the metal-air and metal-glass interfaces via pathway 2. The metal-glass SPPs (SPPAu-glass and SPPAl-glass) are in general bound to the metal surface because of the high effective index (k/k0 ∼1.52) as compared to the free-space photons and mainly out-couple to the far-field via scattering at the end of the waveguide. For the vertical-MIM-TJs, the BFP feature represented as SPPAu-glass [Fig. 3(c) and Fig. 4(c)], which is asymmetric with respect to the ${k_y}$ axis, arises from the scattering of SPPAu-glass mode from the truncated Au waveguide, which extends 2 $\mu $m from the MIM-TJ in the $- x$ direction [Fig. 3(a) and Fig. 4(a)]. In the $+ x $ direction, the Au waveguide is long enough (20 $\mu $m) to effectively absorb the SPPAu-glass modes traveling along the waveguide and therefore the scattering contributions are absent in $+ {k_x}$ direction in the BFP [Fig. 3(c) and Fig. 4(c)]. Similarly, the contribution from the SPPAl-glass scattering from the truncated-end of the Al waveguide [$+ y$ direction, Figs. 3(a) and 4(a)] is weak compared to the SPPAu-glass scattering and does not give rise to distinct BFP features. This observation can be explained by the low out-coupling efficiency of the MIM-SPP mode to the SPPAl-glass mode and the high losses associated with the Al waveguide.
The metal-air SPPs (SPPAu-air and SPPAl-air) excited via pathway 2 have a lower effective index k/k0 than those SPP modes propagating along the glass substrate (n = 1.515) and can leak through the substrate at specific angles [53]. This manifests as a ring feature in the BFP close to k/k0 = 1.0 with a narrow angular distribution [Fig. 3(c)]. The width of the angular distribution is directly related to the propagation losses of the metal-air SPP modes [53]. For the vertical-MIM-TJs, we also observe the MIM-SPP scattering contributions, predominantly in the ${\pm} {k_y}$ direction [Fig. 3(c)] due to the exposed junction edges (pathway 3) to the air medium. However, from the simulated BFP [Fig. 4(c)] we observe a combined effect of both SPPAu-air/Al-air leakage and MIM-SPP scattering as a single intensity band since both the contributions are located very close to $k/{k_0}\; \sim 1$ and the angular emission is dominated by the MIM-SPP scattering.
In contrast to its vertical counterpart, BFP intensity distributions in the lateral-MIM-TJs are dominated by the direct scattering of the MIM-SPP to photons. The bright circular band observed in Fig. 3(d) and Fig. 4(d) close to k/k0 ∼1 represents this contribution and the dominance of the scattering observed in the $+ {k_x}$ direction can be attributed to the MIM-TJ material asymmetry close to glass substrate, at the interface between the 100 nm thick Al and the 35 nm Au waveguides. The direct scattering of the MIM-SPP here is similar to the case of a laterally oscillating dipolar emitter (see Fig. 1 and Fig. S8 in the Supplement 1) located in the close proximity of a glass substrate and these observations are consistent with the simulated BFP image [Fig. 4(d)]. For the lateral-MIM-TJs, the single-interface SPP leakage/scattering contributions are too weak to be distinctly observed in the BFP images as the emission intensity is dominated by the photon out-coupling from the MIM-SPP scattering.
In Fig. 3(d) we note some specific features in the wavevector range 1$\le $ k/k0 $\le $1.49, for which the circular symmetry is lacking as compared to the angular intensity distribution in Fig. 3(c). A prominent feature, distributed along the ${\pm} {k_y}$ direction, tangent at $- {k_x}/{k_0}$ ∼ 1 to the bright circular band, is observed and is labelled as the edge-SPP mode in Fig. 3(d). It can be understood from the distribution of the feature along ${\pm} {k_y} $ with a constant ${k_x} $ value that the feature represents an SPP mode confined and propagating along the $|x |$-direction [Fig. 3(b)] as a 1D-SPP mode. We ascribe this feature to the light emanating due to the edge diffraction of the SPPAl-air mode from the two edges [54] of the 100 nm thick Al waveguide, oriented along the -$x$-direction [Fig. 3(b)]. Since the Al-air SPP modes confined along the discontinuity of the Al waveguide give rise to the observed edge-SPPs, the effective index of these modes closely follows the mode index of the SPPAl-air mode $(|{k_x}/{k_0}|\sim 1).$ We also observe similar features distributed in the ${\pm} {k_x}\; $ direction, tangent at ${\pm} {k_y}/{k_0}$ ∼ 1 to the bright circular band, representing the edge diffraction of the SPPAu-air modes along the edges of the Au waveguide, oriented in the $y$-direction [Figs. 3(b) and 3(d)]. We note that there is a 35 nm thick Au nanostrip overlapping with the 100 nm thick Al electrode, however the nanostrip is disconnected from the rest of the Au waveguide (as it lies at ∼60 nm height difference from the top of the Au waveguide, as shown in Supplement 1 Section 2). Given the positioning of the small nanostrip, the SPP modes that are excited in the MIM-TJ would be absorbed by the Al electrode or scattered to photons before reaching the Au nanostrip, hence we attribute the horizontal segments in the BFP to edge-SPP modes supported by the Au edges connected to the MIM-TJ, as shown in Fig. 3(b). The simulated BFP images shown in Fig. 4(d) corroborate the existence of edge-SPP modes supported by the waveguide edges in the lateral-MIM-TJ [54].
2.5 Out-coupling efficiency evaluation
Figures 5(a)–5(b) show the electromagnetic field distribution from the FDTD simulations representing the SPP modes that are excited in the vertical- [Fig. 5(a)] and lateral-MIM-TJs [Fig. 5(b)]. Visualization 1 and Visualization 2 show the time evolution of the SPPAu-air and SPPAu-glass electromagnetic fields for the vertical and lateral-MIM-TJs respectively. We quantify the out-coupling efficiencies of the MIM-SPP mode to photons and SPPs as follows. From the FDTD simulations we calculate the total time averaged power flow, ${P_{net}}$, across the surface of a cube of volume $1\; \mu {\textrm{m}^3}$ enclosing the MIM-TJ, with the dipole-source located at the center of the cube. ${P_{net}}$ includes contributions from both SPPs and photons out-coupled from the MIM-TJ. The MIM-SPP mode excited by the dipole will be completely absorbed within the enclosed volume due to the small propagation length (${\ll} 1\; \mu \textrm{m}$) and will not contribute to ${P_{net}}$. The total photonic power flow contribution ${P_{ph}}$ is separately estimated by calculating the radiated power through two designated $xy$ planes, in glass (at $z ={-} 1\; \mu $m) and in air ($z = 1\; \mu $m), below and above the MIM-TJ respectively. From ${P_{net}}$ and ${P_{ph}}$, the SPP power flow contribution ${P_{spp}}$ can be obtained as:
Total power dissipation of the dipole ${P_T}$, which is directly proportional to the LDOS and comprises ${P_{ph}}$, ${P_{spp}}$ and energy absorbed by the electrodes, can be directly calculated from the FDTD simulations and ${P_T}$ distributed into all decay channels is conserved and equals the power radiated by the source dipole. From ${P_T},$ ${P_{ph}}$ and ${P_{spp}}$ we estimate the theoretical out-coupling efficiencies to photons (${\eta _{ph}})$ and SPP (${\eta _{spp}}$) as:
Figure 5(c) shows the out-coupling efficiencies obtained from Eqs. (2) and (3) for the vertical and the lateral-MIM-TJs and are plotted as a function of energy. As observed from the intensity analysis of the experimental BFP images (Table 1), theoretical results also show that the MIM-SPP mode out-couples preferentially to photons rather than to SPPs in the lateral-MIM-TJ, whereas in the vertical-MIM-TJ it out-couples preferentially to the single-interface SPPs. To meaningfully compare the out-coupling efficiencies of each geometry, we calculate the theoretical fractional out-coupling efficiency $\delta \eta $ given by:
which can be compared to the experimental fractional out-coupling intensity $\delta I$ which is calculated analogously to Eq. (4) by:In Table 2 we show the comparison between the fractional theoretical [calculated from Eq. (4) and using values from Fig. 5] and experimental out-coupling efficiencies [using the values from Table 1 and substituting in Eq. (5)] at an energy of 1.5 eV (826 nm wavelength) which corresponds to the bias we applied when we recorded the experimental images. When we compare the fractional theoretical and experimental out-coupling efficiencies of the MIM-SPP mode to photons and to SPPs in the vertical and lateral-MIM-TJs, we observe a similar trend. It is clear that theoretically the vertical-MIM-TJs out-couple more efficiently to SPPs by a factor of 9, and experimentally this is reproduced although with a smaller margin of 54% to SPPs and 46% to photons. The lateral-MIM-TJs out-couple more efficiently to photons on the other hand, where both theoretical and experimental efficiencies indicate a factor of 5 conversion to photons over SPPs.
Fig. 5. Simulated near-field ${E_z}$ distributions showing the excitation of both SPPAu-air and SPPAu-glass for (a) vertical [with dipole located at position 6; Fig. 4(a)] and (b) lateral [with dipole located at dipole position 3; Fig. 4(b)] MIM-TJs for excitation wavelength of 900 nm. (c) The out-coupling efficiency of the MIM-SPP mode to SPPs (dotted lines) and photons (solid lines) in vertical (black) and lateral (red) MIM-TJs.
Table 2. Theoretical and experimental fractional out-coupling efficiencies.
From the results presented in Table 2 we note that the theoretical and experimental fractional out-coupling efficiencies in lateral-MIM-TJs are similar, however there is a discrepancy for the vertical-MIM-TJs. We explain the smaller margin between the experimentally observed SPP (54%) and photon (46%) fractional out-coupling efficiency in vertical-MIM-TJs by the surface roughness and the losses associated with the inverted microscope measurement system. The far-field emission intensity from the vertical-MIM-TJs depends strongly on the surface roughness of the metallic electrodes which enhances the background photon scattering contributions in the experimental BFP. However, the effect of the surface roughness was not taken into account in the FDTD modelling. Effectively, this results in a net lower $\delta {\eta _{ph}}$ ( = 0.1) from theory as compared to the experimental $\delta {I_{ph}}$ ( = 0.46). On the other hand, we detect the single-interface SPPs in an inverted microscope system, imaging from below the MIM-TJ and the glass substrate. In this setup, we collect the radiation emitted in the lower half-space (below the MIM-TJ) and lose the contributions emitted in the upper half-space (above the MIM-TJ). However, in the numerical calculations we assessed the total power flow both below and above the MIM-TJ, resulting in a higher theoretically predicted $\delta {\eta _{spp}}$ ( = 0.9) as compared to the experimentally calculated $\delta {I_{spp}}$ ( = 0.54). Altogether, these factors lead to a smaller margin between the experimental out-coupling efficiencies for SPPs and photons in the vertical-MIM-TJ as compared to theoretical calculations.
3. Conclusions
This study quantitatively explores the optimal out-coupling pathway for photons or SPPs associated with the tunneling direction for a given MIM-TJ. The theoretical and the experimental results presented here emphasize the significance of the geometric control over the excited MIM-SPP and the subsequent out-coupling to daughter modes. We show that it is possible to control the tunneling direction with respect to the SPP propagation direction along the plasmonic waveguide, which directly affects the out-coupling efficiencies of the highly confined MIM-SPP mode to all available decay channels. Using BFP imaging supported by numerical calculations, we isolate and distinguish the contributions of each pathway in the out-coupling of the MIM-SPP mode. In the lateral-MIM-TJs, the MIM-SPP mode out-couples preferentially to photons by a factor of 5 while in vertical-MIM-TJs the MIM-SPP mode preferentially out-couples to single-interface SPPs by a factor of 9 in theory but by a factor of 1.2 experimentally due to roughness in the electrode materials. This difference comes from the orientation of the momenta of the MIM-SPP mode and the single-interface SPPs with respect to each other. In the lateral-MIM-TJ, the momenta of the MIM-SPP and the single-interface SPPs are orthogonal, leading to a lower coupling efficiency to single-interface SPPs. On the other hand, the out-coupling of the MIM-SPP to photons via scattering off the surface roughness (pathway 1) is present in both designs, where photon out-coupling in the lateral-MIM-TJ is 3 times higher than in the vertical-MIM-TJ. Additionally, in the lateral-MIM-TJs, the in-plane direction of tunneling leads to the edge diffraction of the metal-air SPP modes, readily exciting the 1D-SPP modes confined along the edges of the plasmonic waveguides. This study also demonstrates the versatility of the BFP imaging technique, supported by the FDTD simulations, in explicitly identifying the plasmonic modes associated with the waveguides of finite physical dimensions and in estimating their far-field intensity contributions based on the effective mode index. Our results also indicate that it is important to develop methods enabling the fabrication of MIM-TJs with atomically flat electrodes to eliminate adverse effects of surface roughness which, as we have shown here, lowers control over the out-coupling pathways. From this work we work towards increased optimization of MIM-TJs as efficient, electrically excited, on-chip SPP sources and demonstrate that, by rational design of the device, out-coupling directions can be controlled.
4. Methods
Sample fabrication. The detailed fabrication flow is provided in Supplement 1 Section 1. The Al-AlOx-Cr-Au MIM-TJs were fabricated on borosilicate coverslips (Paul Marienfeld GmbH, 22 × 22 mm, 0.16 - 0.19 mm thick, refractive index 1.515). The contact pads were fabricated via optical lithography (Microtech, LW405B), with a double-layer photoresist stack with a total resist thickness of ∼1.3 µm (LOR3A and S1805). The photoresist was exposed with a 405 nm beam at 320 mJ/cm2. The metallic electrodes of Al and Au were patterned using electron-beam lithography (JEOL, JBX-6300FS system) with a writing current of 5 nA at 100 kV acceleration voltage on PMMA 950 A4 resist. All the metals were deposited via thermal evaporation (Kurt J. Lesker, NANO 36).
Electrical characterization. We recorded current-voltage, I(V), curves using two Signatone micromanipulators with tungsten probes. We used a source meter (Keithley 6430, Keithley Instruments) and a homemade LabView program to operate the source meter and record the I(V) curves. During measurements, we grounded the Au electrode and biased the Al electrode.
Optical characterization. We recorded the optical characteristics of the MIM-TJs in an inverted optical microscope (Nikon Eclipse Ti-E) equipped with an Andor spectrometer (Shamrock 122 303i) for spectral characterization and an electron multiplying CCD (EMCCD, iXon Ultra 897) for the real and back focal plane imaging. The signal was measured from the glass (back) side using a 100× oil objective (Numerical Aperture, NA=1.49). The EMCCD images (both real and back focal plane) were recorded with a 2 min integration time and 300 EM gain.
Funding
National Research Foundation Singapore (NRF-CRP17-2017-08).
Acknowledgments
The authors acknowledge the National Research Foundation (NRF) for supporting this research under the Prime Minister’s Office, Singapore, under its Medium Sized Centre Programme and the Competitive Research Programme (CRP) (NRF-CRP17-2017-08). The authors also thank the Centre for Advanced 2D Materials (CA2DM) for the provided facilities. H.S.C and T.X.H acknowledge the support of the A*STAR Computational Resource Centre through access to high-performance computing facilities.
Disclosures
The authors declare no conflicts of interest.
Supplemental document
See Supplement 1 for supporting content.
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