Sub-micron free-standing metal slabs with dielectric nano-voids of arbitrary shapes embedded beneath atomically-flat surface

Kiang Wei Kho; ZeXiang Shen; Malini Olivo

doi:10.1364/OE.19.010518

1. Introduction

Surface plasmon polaritons (SPPs) are collective oscillation of electron charges bound to a metal-dielectric interface. Their rich features at the nano-scopic scales have rendered SPPs particularly useful for various optical applications such as plasmonic nano-biosensors [1], superlens [2], sub-wavelength waveguides, nano-scale photonic switching devices [3–6], plasmonic-lasers [7], and miniaturized high-speed plasmonic-quantum systems [8–10].

Among the various plasmonic devices, sub-micron thick plasmonic metal slab containing dielectric nano-voids buried just beneath an atomically-flat metal surface - hereby referred to as metal-slab-with-nano-voids or MSWNV – is particularly attractive in both physical as well as technological domains [11–15]. Unique optical properties such as anti-crossing plasmonic responses have been theoretically shown by T. V. Teperik et al. for a MSWNV bearing a 2D hexagonal lattice of spherical nano-cavities, which facilitates electromagnetic couplings between the void-plasmons and the SPPs [11]. G. Lerosey et al., on the other hand, proposed a hypothetical plasmon source capable of generating SPPs with a controllable phase-shift and amplitude by exploiting a Fabry-Perot resonance within a rectangular cavity buried underneath a smooth metal surface [14]. Additionally, a MSWNV is also capable of generating tremendous field enhancements within the embedded voids when excited at the void-plasmon resonance frequency [13,16], permitting mixed “exciton-polariton” states to be generated if the voids are filled with emitters, e.g. quantum dots. This could potentially lead to a high-throughput plasmonic laser [17], or enhanced light source for bio-assay as well as bio-imaging [18]. In the field of quantum computation and quantum information science, an exciton-polariton state could be exploited to facilitate qubit-qubit interactions [8,10,19].

Given the prospect of UV-vis SPPs in scaling down an opto-device owing to their reduced group velocities – and hence more confined SPP fields, extending the operating frequencies of a MSWNV beyond the NIR and into the UV-Vis range (400 nm < λ < 650 nm) is desirable in order to fully unlock the potentials of a MSWNV. Unfortunately, such an endeavor has been plagued by significant perturbations to the propagating SPPs, in the UV-vis, by the surface roughness [20,21]. A reliable method to fabricating a sufficiently-smooth MSWNV, while maintaining the embedded nano-voids (of any shape) in close proximity (< 25 nm) to the planar metal surface, is therefore crucial. However, progress toward this goal has been impeded by the involuntary surface roughness that occurs using conventional fabrication techniques. For instance, metal films with nano-voids encapsulated by electrochemical deposition (ED) exhibit modulated capping surface due to the void template impeding the supply of metal ions from the solution to the growing surface during the deposition process [22]. In this article, we describe a simple and high throughput approach to fabricating a free-standing smooth MSWNV based on a cryogenic-stripping approach. As will be shown later, the current method is versatile and permits encapsulation of sub-500 nm nano-voids of virtually any arbitrary shape, while eliminating major drawbacks suffered by previous fabrication methods. The capping surface of our MSWNV is not only ultra-smooth (δ < 0.55 nm (RMS)), but also remains uncompromised by the harsh cryogenic-stripping procedure as well as by the 3D geometry and size of the underlying nano-voids buried just underneath (< 25 nm) it. To manifest the advantages of our technique, we demonstrate its use in studying the effects of surface roughness on the plasmonic responses of MSWNVs bearing hexagonally-packed nano-voids. First, we solve the Maxwell equation for a rough MSWNV system via first Born approximation in a plane-wave expansion formalism. We then fabricated a series of MSWNVs and investigated changes in the co-polarized angular reflectance spectra measured in the Γ-K and Γ-M directions as the surface of the MSWNVs was gradually and artificially adjusted from ultra-smooth to moderately-rough. Our study concludes the plasmonic performance of a symmetric MSWNV operating in the short SPP wavelength can be extremely sensitive to the surface roughness. In fact, the optimal smoothness is shown to be well below that attainable in similar samples fabricated using traditional techniques (namely electro-deposition). The current technique is thus of primary importance to the preparation of any kind of smooth broadband MSWNV devices.

Figure 1 depicts the current top-down fabrication approach. As shown in the figure, the capping metal surface is formed on a flat template prior to nano-void encapsulation. In this way, the capping surface can be made extremely flat and not affected by the subsequent electro-deposition process during the void-template encapsulation. To achieve this, an initial Au film (I-Au-F) is first deposited onto the ultra-smooth (110) plane of a cleaved mica substrate as shown in step #1 - #2 of Fig. 1. The side of this I-Au-F in contact with the mica template will subsequently become the “capping” metal surface of the final MSWNV once the mica is stripped off (see step #6). Thus, the roughness of the capping surface is entirely determined by the mica template, which is usually at the atomic level. The thickness of the I-Au-F can be precisely tuned (e.g. by adjusting deposition time in the case of e-beam evaporative deposition), which allows the void-to-surface distance (VTSD), and hence the coupling strengths between the void-plasmons and SPPs to be adjusted. In the current study, the I-Au-F thickness was chosen to be 10 nm, which is thick enough to maintain a hole-free continuous film, but thin enough to keep the VTSD to well within the penetration depth (~25 nm) of the SPPs.

Fig. 1 Cryogenic stripping approach to fabricating a nano-void system. 1. Cleaving the mica film to expose the atomically-smooth (110) plane; 2. Deposition of 10-nm Au film; 3. Treating the Au surface with 3- aminopropyltrimethloxisilane (APTMS) to improve wettability; 4. Deposition of a mono-layer of void template; 5. Electro-deposition of Au to encapsulate the nano-voids; 6. Nano-void passivated Au substrate. The final product is flipped over, and the mica strip to reveal the atomically smooth Au surface.

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2. Experimental procedures

2.1 Ar + -Assisted ion beam deposition of Au on an atomically smooth mica substrate

Prior to Au deposition, a thin muscovite mica sheets was freshly cleaved on air to about 1 mm thickness and mounted on a furnace in the vacuum chamber immediately before pump-down. The mica substrate was then heated for about 30 min to 500°C. High purity Au (99.999%) was melted via e-beam bombardment and evaporated onto the substrate at a pressure of 2 × 10-6 Torr. About 10-nm of Au film was deposited at the end of the process.

2.2 Deposition of nano-particle layer to form nano-void template

In order to ensure wide spreading of the nano-particle layer (namely, the nano-void template), the Au-coated mica (Au-mica) was made hydrophilic by incubating it in 180 mM 3- aminopropyltrimethloxisilane (APTMS) solution (prepared in water) for 24 hrs before being thoroughly washed with running distilled water and dried with a dust-blower. This results in the binding of the amino-group of the APTMS toward the Au and exposes the methyl group that was hydrolysable under aqueous condition to give hydroxyl groups. The functionalized Au surface thus become hydrophilic (see step 3 in Fig. 1). The increase in hydrophilicity was verified with a contact-angle test, which showed a decrease in the contact angle of a water droplet from 88 ° to 65 ° upon APTMS treatment [23]. A mono-layer of nano-particles is then deposited via convective self-assembly on the APTMS-treated Au surface, based on the method developed by Dimitory et al [23], and this particle layer subsequently become the nano-void template. Particle concentration required for monolayer formation was experimentally determined according to the particle size.

2.3 Electro-deposition

Au plating solution was prepared by thoroughly mixing 290 ml Techni – Au 25 Makeup ES, 2.5 g TG – 25E stabilizer, 22.5 g sodium sulfite and 5.125 g TG – 25 concentrate in water to a final volume of 500 ml. The solution was then heated and maintained at about 60 °C with constant stirring. pH of the solution was maintained at 7.0. A total plating current of 0.8 mA/cm2 was used. This yielded a deposition rate of about 20 nm/min as judged by FE-SEM analysis. The Au-mica sample was positioned at about 4 cm away from the anode platinum mesh. The plating process proceeded until the nano-sphere array was judged fully covered by Au based on the above estimated deposition rate, before the plated sample was washed with copious amount of distilled water and blow-dried.

2.4 Stripping-off the mica template

A variety of template-stripping methods have been developed for achieving an Au surface with roughness δ < 1 nm (RMS) [24,25]. However, not all are reproducible and many often the stripping process is not ideal, leaving behind thin residual mica shards on the final Au surface. Nonetheless, a clean detachment of the mica can be attained by cryogenically-induced differential contractions between the I-Au-F and the mica template. We therefore soaked the MSWNV sample in liquid N₂ for 2 minutes before peeling off the Au slab either with a tweezer or a scotch tape [26].

Figure 2(a) –2(c) show a piece of free-standing Au slab containing 100-nm nano-voids, while Fig. 2(d) and 2(e) show cross-sectional FE-SEM images of cryogenically-stripped MSWNV (CS-MSWNV) samples containing spherical nano-voids and oblate nano-voids, respectively. To maintain structural integrity, the CS-MSWNVs were glued onto glass substrates before sectioning. We note that the (void-surface distance) VTSD in both samples is about 10 nm, which is in exact agreement with the thickness of the I-Au-F. For comparison, electro-deposited MSWNV obtained with no cryogenic treatment is shown in Fig. 2(f), in which the rough capping metal surface (δ ~7 nm) is clearly evident. Note also the unpredictable VTSD (> 10 nm) in this particular sample.

Fig. 2 FE-SEM images of the thin metal slab. (a), (b) A typical FE-SEM image of a freestanding metal slab bearing embedded nano-voids. (c) “Close-up” view of the metal slab, showing the embedded 100-nm spherical nano-voids. (d) A typical FE-SEM cross-sectional image of N₂-stripped Au surface embedded with spherical nano-voids. (e) FE-SEM cross-sectional image of N₂-stripped Au surface embedded with oblate nano-voids. Note that samples shown in (d) and (e) are prepared by attaching the metal films on a solid substrate via epoxy glue. (f) FE-SEM cross-sectional image of nano-void passivated metal film obtained with mechanical stripping and no cryogenic treatment, showing rough Au surface. Images were taken with JEOL FE-SEM system in SEI mode under 9 × 10⁻⁵ Pa at 12 KV.

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Typical AFM surface scan of the exposed Au surface on a cryogenically-stripped CS-MSWNV sample is shown in the Fig. 3(a) , along with that of an as-stripped (i.e. without cryogenic treatment) sample in Fig. 3(b) for comparison. While these surfaces are generally smooth with an average roughness not exceeding 0.55 nm (RMS), cryogenically prepared surface appears to be cleaner with no mica shards compared to the as-stripped sample. A high-resolution mapping over the Au area with nano-voids buried underneath using a scanning tunneling microscope (STM) at a constant-current mode further reveals the cryogenic-stripped Au surface to be generally hole-defect free as depicted in Fig. 3(c). The surface roughness estimated through STM was found to be 0.45 nm (RMS), which is in agreement with that derived from AFM measurements. The absence of hole-defects in the CS-MSWNV represents another advantage of the current fabrication approach because hole-defects could inevitably couple incident waves into surface plasmons, bringing about undesired plasmonic ring modes, or give rise to radiative loss.

Fig. 3 A typical 3 µm × 3 µm AFM surface mappings of stripped Au substrates containing nano-voids. (a) Cryogenically-stripped sample with no mica residue. RMS roughness = 0.55 nm. (b) Mechanically stripped sample. Mica shards are clearly visible. RMS roughness = 0.75 nm. (c) Scanning Tunneling Microscopy (STM) image of cryogenically-stripped sample. RMS roughness = 0.45 nm.

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3. Mathematical and numerical analysis

We now study the in-plane SPP scatterings at the planar dielectric-metal interface of the MSWNV as a function of surface roughness. To this end, the co-polarized angular reflectance spectra of a MSWNV bearing hexagonally-packed spherical dielectric nano-void are considered. Due to the six-fold angular dispersion in such a nano-void system with hexagonal symmetry, we expect a dependence of the angular reflectance spectra on the sample’s orientation. In particular, we anticipate a resonance dip to occur only along the Γ-M direction if the in-plane SPP scatterings are absent. For this purpose, MSWNVs with encapsulated hexagonally-packed polystyrene nano-spheres (Ø = 400 nm) assembly (see Fig. 4(a) along with the near-field image) was fabricated. This gives Mie void-plasmon resonance frequencies of 2.20 eV and 2.93 eV, which correspond to plasmon modes with orbital quantum numbers l = 1, and l = 2, respectively. Polarized absorbance spectra were measured at 532-nm for different sample orientations and incidence angles. It should be noted that we slightly mismatch the laser line away from the Mie void-plasmon resonance frequencies so that only Bragg plasmons are excited, hence simplifying interpretation of the experimental data. The use of a short excitation wavelength (i.e. < 650 nm) is essential in elucidating the effect of surface topology as in-plane scatterings of SPPs generally increase with decreasing wavelengths for any given surface roughness.

Fig. 4 Angular reflectance profiles for void system with hexagonally-packed 400-nm nano-voids. (a) Different sign conventions used in Eq. (1) and (2). Hexagonally-packed polystyrene nano-particles deposited on I-Au-F, along with the near-field images (the right-most images) of a single nano-void (400 nm) buried 10 nm underneath the Au surface. (b) and (c) show the amplitudes of the p-polarized wave component of $| d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm} 〉$ in the k_x-k_y plane calculated at λ₀ = 532 nm in the positive x-directions with an incident angle of 74 °, and for a = 100 nm and 30 nm respectively, with δ fixed at 1.5 nm. (d) - (g) show theoretical p-polarized reflectivity as a function of ${\overset{⇀}{k}}_{0_| |}$ calculated through Eq. (2) for a = ∞, 100, 30, and 5 nm, respectively. Dielectric constant of Au is derived from the experimental data obtained by Johnson and Christy (Phys. Rev. B 6(12), 4370 (1972)).

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In order to gain insights into the experimental results, we first derive the Maxwell equation for fields scattered from a MSWNV bearing a hexagonally-arranged void array,

\begin{array}{l} {}^{t}{\overset{⇀}{E}} {^{(s)}}^{\pm} = \int d^{2} {\overset{⇀}{k}}_{| |} (α {({\overset{⇀}{k}}_{| |} ↑, {\overset{⇀}{k}}_{o_| |} + ↓, E_{o}^{p}, 0)}^{\pm} | e^{p} {({\overset{⇀}{k}}_{| |} ↑)}^{\pm} 〉 + β {({\overset{⇀}{k}}_{| |} ↑, {\overset{⇀}{k}}_{o_| |} + ↓, E_{o}^{p}, 0)}^{\pm} | e^{s} {({\overset{⇀}{k}}_{| |} ↑)}^{\pm} 〉) + \\ ^{}^{}^{} \int d^{2} {\overset{⇀}{k}}_{| |} (α {({\overset{⇀}{k}}_{| |} ↓, {\overset{⇀}{k}}_{o_| |} + ↓, E_{o}^{p}, 0)}^{\pm} | e^{p} {({\overset{⇀}{k}}_{| |} ↓)}^{\pm} 〉 + β {({\overset{⇀}{k}}_{| |} ↓, {\overset{⇀}{k}}_{o_| |} + ↓, E_{o}^{p}, 0)}^{\pm} | e^{s} {({\overset{⇀}{k}}_{| |} ↓)}^{\pm} 〉) . \end{array}

In Eq. (1), we have denoted an in-plane vector by the subscript ||. Hence,

{\overset{⇀}{k}}_{0_| |}

and

{\overset{⇀}{k}}_{| |}

are the incident in-plane vector (i.e. the projection of the incident vector

{\overset{⇀}{k}}_{0}

onto the Au plane) and the scattered in-plane vector, respectively, and,

\begin{array}{l} j {({\overset{⇀}{k}}_{2} ↑ ↓, {\overset{⇀}{k}}_{1} \pm ↑ ↓, E^{p}, E^{s})}^{\pm} = \sum_{n, m} ({\overset{⇀}{k}}_{2}, {\overset{⇀}{k}}_{1}) f_{p}^{p / s} {({\overset{⇀}{k}}_{2} ↑ ↓ | {\overset{⇀}{k}}_{1} \pm ↑ ↓)}^{\pm} E^{p} + \\ \sum_{n, m} ({\overset{⇀}{k}}_{2}, {\overset{⇀}{k}}_{1}) f_{s}^{p / s} {({\overset{⇀}{k}}_{2} ↑ ↓ | {\overset{⇀}{k}}_{1} \pm ↑ ↓)}^{\pm} E^{s} + \\ \int d^{2} \overset{⇀}{k} (\sum_{n, m} ({\overset{⇀}{k}}_{2}, \overset{⇀}{k}) \sum_{n, m} (\overset{⇀}{k}, {\overset{⇀}{k}}_{1})) (f_{p}^{p / s} {({\overset{⇀}{k}}_{2} ↑ ↓ | \overset{⇀}{k} - ↓)}^{\pm} f_{p}^{p} {(\overset{⇀}{k} ↓ | {\overset{⇀}{k}}_{1} + ↓)}^{-} E^{p} + \\ f_{s}^{p / s} {({\overset{⇀}{k}}_{2} ↑ ↓ | \overset{⇀}{k} - ↓)}^{\pm} f_{p}^{s} {(\overset{⇀}{k} ↓ | {\overset{⇀}{k}}_{1} + ↓)}^{-} E^{p}) + ... \\ \int d^{2} \overset{⇀}{k} (\sum_{n, m} ({\overset{⇀}{k}}_{2}, \overset{⇀}{k}) \sum_{n, m} (\overset{⇀}{k}, {\overset{⇀}{k}}_{1})) (f_{p}^{p / s} {({\overset{⇀}{k}}_{2} ↑ ↓ | \overset{⇀}{k} - ↓)}^{\pm} f_{s}^{p} {(\overset{⇀}{k} ↓ | {\overset{⇀}{k}}_{1} + ↓)}^{-} E^{s} + \\ f_{s}^{p / s} {({\overset{⇀}{k}}_{2} ↑ ↓ | \overset{⇀}{k} - ↓)}^{\pm} f_{s}^{s} {(\overset{⇀}{k} ↓ | {\overset{⇀}{k}}_{1} + ↓)}^{-} E^{s}) + .... \end{array}

in which,

j = α, β

, and

f_{p / s}^{p / s} {({\overset{⇀}{k}}_{| |} ↑ ↓ | \overset{⇀}{k}'_{| |} \pm ↑ ↓)}^{\pm}

is the Fourier scattering coefficient of a single nano-void. Both

{\overset{⇀}{k}}_{| |}

and

\overset{⇀}{k}'_{| |}

define the in-plane directions of the scattered and the incident wave, respectively. The superscript p (s) corresponds to j = α (β).

E^{p}

and

E^{s}

are respectively the p- and s-polarized incident fields, and

\sum_{n, m} ({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o}) = δ ([Δ \overset{⇀}{k} \cdot {\hat{a}}_{⊥}] [{\hat{a}}_{⊥} \cdot \vec{a}] + [Δ \overset{⇀}{k} \cdot {\hat{a}}_{| |}] [{\hat{a}}_{| |} \cdot \vec{a}] - 2 π h) δ ([Δ \overset{⇀}{k} | \vec{b} |] {\hat{a}}_{| |} - 2 π l) .

Δ \vec{k} = {\vec{k}}_{| |} - {\vec{k}}_{o_| |}

;

h, l \in I

;

{\overset{⇀}{a}}_{x}, {\overset{⇀}{a}}_{y}, \vec{a}

and

\vec{b}

are as shown in Fig. 4(a). The + (-) signs indicate the functions are evaluated for the dielectric (metal) medium, while ↑ (↓) specifies an up-warding (down-warding) wave as depicted in Fig. 4(a).

To include the scattered fields arisen from the surface roughness, we modify and re-write Eq. (1), as,

\begin{array}{l} {}^{t}{\overset{⇀}{E}} {^{(s)}}^{\pm} = \int d^{2} {\overset{⇀}{k}}_{| |} (α {({\overset{⇀}{k}}_{| |} ↑, {\overset{⇀}{k}}_{o_| |} + ↓, E_{o}^{p}, 0)}^{\pm} | e^{p} {({\overset{⇀}{k}}_{| |} ↑)}^{\pm} 〉 + β {({\overset{⇀}{k}}_{| |} ↑, {\overset{⇀}{k}}_{o_| |} + ↓, E_{o}^{p}, 0)}^{\pm} | e^{s} {({\overset{⇀}{k}}_{| |} ↑)}^{\pm} 〉) + \\ \int d^{2} {\overset{⇀}{k}}_{| |} (α {({\overset{⇀}{k}}_{| |} ↓, {\overset{⇀}{k}}_{o_| |} + ↓, E_{o}^{p}, 0)}^{\pm} | e^{p} {({\overset{⇀}{k}}_{| |} ↓)}^{\pm} 〉 + β {({\overset{⇀}{k}}_{| |} ↓, {\overset{⇀}{k}}_{o_| |} + ↓, E_{o}^{p}, 0)}^{\pm} | e^{s} {({\overset{⇀}{k}}_{| |} ↓)}^{\pm} 〉) + \\ \int d^{2} {\overset{⇀}{k}}_{| |} [\int_{k'_{| |}} α {({\overset{⇀}{k}}_{| |} ↑, \overset{⇀}{k}'_{| |} - ↓, 〈 e^{p} {(\overset{⇀}{k}'_{| |} ↓)}^{-} | d {\overset{⇀}{E}}^{r (s)} {(\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})}^{-} 〉, 〈 e^{s} {(\overset{⇀}{k}'_{| |} ↓)}^{-} | d {\overset{⇀}{E}}^{r (s)} {(\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})}^{-} 〉)}^{\pm} | e^{p} {({\overset{⇀}{k}}_{| |} ↑)}^{\pm} 〉 + \\ \int_{k'_{| |}} β {({\overset{⇀}{k}}_{| |} ↑, \overset{⇀}{k}'_{| |} - ↓, 〈 e^{p} {(\overset{⇀}{k}'_{| |} ↓)}^{-} | d {\overset{⇀}{E}}^{r (s)} {(\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})}^{-} 〉, 〈 e^{s} {(\overset{⇀}{k}'_{| |} ↓)}^{-} | d {\overset{⇀}{E}}^{r (s)} {(\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})}^{-} 〉)}^{\pm} | e^{s} {({\overset{⇀}{k}}_{| |} ↑)}^{\pm} 〉 + \\ \int_{k'_{| |}} α {({\overset{⇀}{k}}_{| |} ↓, \overset{⇀}{k}'_{| |} - ↓, 〈 e^{p} {(\overset{⇀}{k}'_{| |} ↓)}^{-} | d {\overset{⇀}{E}}^{r (s)} {(\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})}^{-} 〉, 〈 e^{s} {(\overset{⇀}{k}'_{| |} ↓)}^{-} | d {\overset{⇀}{E}}^{r (s)} {(\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})}^{-} 〉)}^{\pm} | e^{p} {({\overset{⇀}{k}}_{| |} ↓)}^{\pm} 〉 + \\ \int_{{\overset{⇀}{k}}_{| |}} β {({\overset{⇀}{k}}_{| |} ↓, \overset{⇀}{k}'_{| |} - ↓, 〈 e^{p} {(\overset{⇀}{k}'_{| |} ↓)}^{-} | d {\overset{⇀}{E}}^{r (s)} {(\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})}^{-} 〉, 〈 e^{s} {(\overset{⇀}{k}'_{| |} ↓)}^{-} | d {\overset{⇀}{E}}^{r (s)} {(\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})}^{-} 〉)}^{\pm} | e^{s} {({\overset{⇀}{k}}_{| |} ↓)}^{\pm} 〉] + .... \end{array}

in which,

d E^{r (s)} (\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})

is the amplitude of an infinitesimal wave component scattered from the rough surface in the direction defined by the in-plane vector,

\overset{⇀}{k}'_{| |}

, for a given

{\overset{⇀}{k}}_{0_| |}

as derived by Millis, D. L., et al [27].

d E^{r (s)} (\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})

can be expressed as,

\begin{array}{l} d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm} = - d^{2} {\overset{⇀}{k}}_{| |} \frac{ω^{2}}{16 π^{3} c^{2}} [ε (ω) - 1] \hat{ξ} ({\overset{⇀}{k}}_{| |} - {\overset{⇀}{k}}_{o_| |}) \sum_{v} \int d z' [d_{μ v} ({\overset{⇀}{k}}_{| |} ω | z^{\pm} z') δ (z') \\ E_{_{v}}^{(0)} ({\overset{⇀}{k}}_{| |}^{(0)} ω | z') e_{μ} {({\overset{⇀}{k}}_{| |})}^{\pm}] . \end{array}

An essential component in Eq. (3) is the Fourier coefficient,

\hat{ξ} ({\overset{⇀}{k}}_{})

, of the surface-profile function

\hat{ξ} (\overset{⇀}{x})

, which dictates the directional dispersion of

d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm}

and can be assumed to be a stationary stochastic process as follows,

\frac{〈 \hat{ξ} (\overset{⇀}{x}) ξ (\overset{⇀}{x}') 〉}{〈 \hat{ξ} {(\overset{⇀}{x})}^{2} 〉} = (ρ_{0} + \sum_{i > 0} ρ_{i} e^{- {| \overset{⇀}{x} - \overset{⇀}{x}' |}^{2} / a_{i}^{2}}) .

or

〈 \hat{ξ} (\overset{⇀}{k}) ξ (\overset{⇀}{k}') 〉 = δ^{2} (ρ_{0} + \sum_{i > 0} ρ_{i} e^{- a_{i}^{2} 4 {| \overset{⇀}{k} - \overset{⇀}{k}' |}^{2}}) .

with a_i being the transverse correlation length, and δ the RMS height of the surface roughness. Here, ρ represents the fractional weight of a particular surface feature (with a given a value) in contributing to the overall scatterings at the metal-dielectric interface.

We note that, in Eq. (2), $d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm}$ acts essentially by “scattering” an incidence ${\overset{⇀}{k}}_{0_| |}$ wave-vector into a distribution of ${\overset{⇀}{k}}_{| |}$ components, which eventually results in the loss of angular symmetry in the void system’s plasmonic responses. To gain insights into the scattering effect of the surface roughness on $d E^{r (s)} (\overset{⇀}{k}'_{| |}, {\overset{⇀}{k}}_{o_| |})$ , we plot the amplitude distribution of the p-polarized scattered wave component of $| d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm} 〉$ in the ${\overset{⇀}{k}}_{| |}$ -plane as shown in Fig. 4(b) and 4(c) with a = 100 nm and 30 nm respectively, and a δ value of 1.5 nm. It is assumed here that the excitation wavelength (λ₀) is 532 nm (i.e. $| {\overset{⇀}{k}}_{0} | = 1.2 \times 10^{7} m^{-1}$ ) and ${\overset{⇀}{k}}_{0_| |}$ = 0.3 × 10⁷ ${\overset{⇀}{a}}_{x}$ m⁻¹, which corresponds to an incident angle of 74 ° (i.e. $| {\overset{⇀}{k}}_{0_| |} | = | {\overset{⇀}{k}}_{0} | \cos (74 °) = 0.3 \times 10^{7} m^{-1}$ ). Only the p-polarized component is considered because of its effectiveness in coupling to SPPs and hence contributions to the overall resonance absorbance. As evident from the graph, the distribution of $| d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm} 〉$ becomes more broadened with decreasing a, indicating increasing electromagnetic scatterings at the interface with increasing roughness. Its effect on the p-polarized reflectance can be illustrated in the polar plots (calculated with Eq. (2) shown in Fig. 4(d)–4(g). In the graph, the light shades indicate plasmon-polariton absorbance dips. For a = ∞, i.e. for a void system with a perfectly smooth surface, the six-fold symmetric absorption feature, which reflects the underlying hexagonally-spaced void lattice, appear sharp and distinct. However, as the a value decreases, as depicted in Fig. 4(e) )–4(g) for a = 100, 30, and 5 nm, respectively, blurring and merging of the resonance “pedal” becomes evident as the effect of scatterings at the rough metal-surface interface becomes more pronounced. This corroborates well with the distribution plot of $| d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm} 〉$ shown in Fig. 4(b)–4(c). We would like to point out that at about a = 5 nm, the scatterings at the roughened interface become so severe that the incident wave become coupled to a broad range of scattered wave-vectors, abolishing the six-fold symmetry in the absorbance profile (see Fig. 4(g)). It is the sensitivity of such a dispersion pattern to the transverse correlation length a (and hence the surface roughness), that a comparison of absorbance spectra acquired along the Γ-K and Γ-M directions could disclose the effects surface roughness had on the SPP scatterings in a MSWNV system.

4. Experimental investigation

To verify the above mathematical model, we fabricated a total of 10 smooth MSWNVs containing periodic arrays of embedded 400-nm dielectric spherical nano-voids. To obtain a long-range periodic nano-avoid array, a hexagonally-packed nano-particle template was formed on the APTMS-treated I-Au-F by the convective self-assembly of 400-nm polystyrene-nanosphere droplet (8.3 × 10⁹ particles/ml). These MSWNVs were then deliberately made roughened by Au sputtering with deposition times ranging from 1 s to 10 s. For each roughened Au sample, several 1 µm × 1 µm AFM images were derived at a 512 × 512 resolution from randomly chosen locations over the area containing encapsulated hexagonally-packed nano-void assembly. An average surface profile was calculated for each sample based on the height profiles obtained from their corresponding AFM mappings. Autocorrelation curves $\frac{〈 \hat{ξ} (\overset{⇀}{x}) ξ (\overset{⇀}{x}') 〉}{〈 \hat{ξ} {(\overset{⇀}{x})}^{2} 〉}$ were then calculated, from which one is able to classify the samples into four different groups as shown in Fig. 5(a) , with Group-I being the smoothest samples, while Group-IV most roughened. The corresponding autocorrelation curves are shown in Fig. 5(b), along with the multi-exponential $(ρ_{0} + \sum_{i > 0} ρ_{i} e^{- a_{i}^{2} 4 {| \overset{⇀}{k} - \overset{⇀}{k}' |}^{2}})$ fitting curves (the dashed curves). The fitted values of the correlation-length a_i for each sample group are displayed in Table 1 . Additionally, we also introduce a parameter, the effective roughness, δ_eff, - defined as ρ × δ - as a means to measure the relative contributions by various nano-scopic features on the Au surface to the overall angular reflectance profile; a particular nano-scopic feature characterizable by a certain a_i value will have insignificant effects on the reflectance spectra if its associated δ_eff value is small, otherwise the contribution is non-negligible.

Fig. 5 AFM images of four different MSWNV sample groups. (a) Roughened metal surface by Au sputtering. (b) Autocorrelation curves.

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Table 1. Fitted values of the correlation-length a_i for each sample group

View Table

The setup for the reflectance measurement is shown in Fig. 6(a) . A 532-nm laser is used as the excitation light source and the laser beam (ø = 2mm) is rendered p-polarized with a polarizer. The sample (i.e. the Au substrate) is placed onto a tiltable mirror mount that is firmly secured to a XYZ-adjustable mount on a rotatable stage (see bottom diagram in Fig. 6). Instead of directly attaching the sample to the mirror mount, it is firmly attached to a standard circular coverglass (see bottom diagram in Fig. 6), which is adhered to the tiltable mirror mount with a thin layer (2 µl) of immersion oil. The stickiness of the oil holds the sample-coverglass in a vertical position while, allowing its orientation to be adjustable. The combination of the XYZ-mount, the tiltable mirror holder and the coverglass ensures the same site on the Au surface can be probed with the laser beam when the substrate is turned about the vertical axis of rotation and at any specific orientation relative to the in-plane vector, ${\overset{⇀}{k}}_{0_| |}$ . Finally, a power meter is used to measure the reflected intensity. An analyzer is placed in front of the meter so that only the p-polarized reflected light is detected. Reflectance (I_refleced/I_incident) is calculated by normalizing the reflected intensity to the incident intensity, which is re-measured (using the same power meter) each time the incident angle is varied. This is to minimize errors brought about by potential laser fluctuations.

Fig. 6 P-polarized angular reflectance measurement. (a) Setup for the reflectance measurement. (b) A circular area containing embedded nano-void assembly appears brownish under the microscope as well as to the naked eye. Hexagonal packing near the edge of the nano-void template assembly.

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Prior to the reflectance measurement, the location of the embedded nano-void layer must be identified. This is accomplished by making use of the fact that the area containing the embedded nano-void assembly appears slightly brownish (see optical image in Fig. 6(b)). Once mounted, the position of the sample is adjusted so that the laser beam is impinging on the edge of the circular nano-void assembly as shown in Fig. 6(a). The reason for such a specific site is the large hexagonal nano-void assembly formed there. Through FE-SEM studies, we have established the Γ-K axis of the hexagonal assembly to be preferentially aligned in tangential to the edge (see FE-SEM image in Fig. 6(b)). Reflectance measurement is first carried out in the Γ- K direction by orienting the ${\overset{⇀}{k}}_{0_| |}$ of the incident beam tangentially to the edge. For the Γ- M measurement, the sample is then re-oriented by 30 °.

Figure 7 illustrates absorbance dips in the typical co-polarized angular reflectance spectra acquired along the Γ-K and Γ-M directions for the various samples. Experimental data (labeled with triangular and square markers) are shown for the two azimuthal directions and are found to generally agree with theoretical predictions (solid lines) calculated using the a parameters shown in Table 1. We found plasmon absorptions in the Γ-K and Γ-M spectra for Group-IV samples to be significantly broadened, while the rest are narrower. This is attributable to the low a values (≤ 30 nm) and the large effective RMS heights, δ_eff, (> 1.5 nm) in this sample group, which leads to significant in-plane scatterings. This can be explained in terms of the scattering terms, $| d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm} 〉$ in Eq. (2). As shown in Fig. 4(b) and 4(c), while the “broadness” of $| d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm} 〉$ is dictated by the transverse correlation length, a, its effect on the angular reflectance profile is also determined by both the δ and the ρ value (in the case where multiple nano-scopic features exist on the Au surface) in Eq. (4). This is evidently reflected in the reflectance spectra for the Group-III samples. As shown in Table. I, the Group-III samples possess multiple surface features with corresponding a values of 14.4, 25, and 3000 nm. Although the a₂ value in Group-III is comparable to those of Group-IV, its effect is diminished by the relatively low δ_eff (ρ × δ) of 0.39. While, on the other hand, the δ_eff values associated with a₃ are large, the corresponding correlation length (i.e. a₃) is also large, which suggests a narrow $| d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm} 〉$ distribution (see Fig. 4(d) and 4(c)). As a consequence, the scattering effects characterized by $| d E_{μ}^{r (s)} {({\overset{⇀}{k}}_{| |}, {\overset{⇀}{k}}_{o_| |})}^{\pm} 〉$ become negligible, and the co-polarized angular reflectance spectra for Group-III samples thus exhibit dips resembling much closer to those theoretically-calculated for a smooth MSWNV (see solid-curves for the Group-I spectra in Fig. 7(a)). Although Group-I and Group-II samples exhibit nano-features with the associated a values in the sub-10 nm range, their low δ_eff values, in comparison to that of Group-IV sample, render their contributions to the in-plane scatterings insignificant.

Fig. 7 Experimental co-polarized angular reflectance spectra derived the MSWNV as well as the electro-deposited samples along the Γ-K and Γ-M directions. Note that $k_{o_| |}$ can be related to the incident angle, θ by $k_{o_| |} = (\frac{2 π}{λ}) \cos θ$ . Each data point is an average of up to 3 measurements.

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On the basis of the theoretical results in Fig. 4(d)–4(g), and the experimental data, we conclude that surface smoothness with an a value of greater than 30 nm and a δ_eff value of less than 1.5 nm is necessary in order to experimentally replicate the theoretical plasmonic responses of a smooth MSWNV possessing structural symmetricity. Such a requirement is not attainable with traditional fabrication techniques as evident in the reflectance spectra derived from Au substrates with nano-voids encapsulated by electro-deposition.

5. Conclusions

We report on the fabrication of an ultra-smooth surface containing buried spherical voids using a “top-down” approach with mica template. The roughness of the resultant substrates was measured to be about 0.55 nm (RMS). Embedding depth of the spherical nano-voids can be easily controlled by adjusting the thickness of the I-Au-F deposited on the mica template at a resolution of a few nano-meters. In the current case, the void depth is about 10 nm beneath the smooth Au surface, which is within the skin-depth of the SPPs. The versatility of our cryogenic-stripping approach also means that one could in principle encapsulated nano-voids of any shape with this particular technique as evident by Fig. 2(d) and 2(e), which shows Au substrates containing oblate nano-voids. The plasmonic responses of our MSWNV were also studied and concluded to be very sensitive to the surface roughness, and a transverse correlation length, a, of less than 30 nm is required in order for the MSWNV to have predictable properties.

Acknowledgments

We would like to thank the Bio-Medical Research Council (BMRC no. 05/1/31/19/397) for the financial support of this project. The principal author would like to thank Singapore Millennium Foundation (SMF) for the award of postgraduate scholarship. Thanks should also be given to Prof. Subodh Mhaisalkar, Ms. Karen Koh Zhen Yu, Ms. Iman Ahmad, and Mr. Chu XinJun for their technical assistances.

References and links

1. S. J. Oldenburg, C. C. Genick, K. A. Clark, and D. A. Schultz, “Base pair mismatch recognition using plasmon resonant particle labels,” Anal. Biochem. 309(1), 109–116 (2002). [PubMed]

2. I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005). [PubMed]

3. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [PubMed]

4. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23(17), 1331–1333 (1998).

5. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B 62(24), R16356–R16359 (2000).

6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [PubMed]

7. N. E. Hecker, R. A. Höpfel, N. Sawaki, T. Maier, and G. Strasser, “Surface plasmon-enhanced photoluminescence from a single quantum well,” Appl. Phys. Lett. 75(11), 1577 (1999).

8. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3(11), 807–812 (2007).

9. T. Xu, Y. Zhao, D. Gan, C. Wang, C. Du, and X. Luo, “Directional excitation of surface plasmons with subwavelength slits,” Appl. Phys. Lett. 92(10), 101501 (2008).

10. E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002). [PubMed]

11. T. V. Teperik, V. V. Popov, F. J. García de Abajo, M. Abdelsalam, P. N. Bartlett, T. A. Kelf, Y. Sugawara, and J. J. Baumberg, “Strong coupling of light to flat metals via a buried nanovoid lattice: the interplay of localized and free plasmons,” Opt. Express 14(5), 1965–1972 (2006). [PubMed]

12. K. Ohtaka, H. Miyazaki, and A. Lucas, “Collective modes of void-surface coupled system,” Phys. Rev. B 21(2), 467–478 (1980).

13. T. V. Teperik, V. Popov, and F. García de Abajo, “Void plamons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71(8), 085408 (2005).

14. G. Lerosey, D. F. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).

15. D. Ballester, M. S. Tame, and M. S. Kim, “Quantum theory of surface plasmon polariton scattering,” Phys. Rev. A 82(1), 012325 (2010).

16. S. Coyle, M. C. Netti, J. J. Baumberg, M. A. Ghanem, P. R. Birkin, P. N. Bartlett, and D. M. Whittaker, “Confined plasmons in metallic nanocavities,” Phys. Rev. Lett. 87(17), 176801 (2001). [PubMed]

17. T. Okamoto, F. H’Dhili, and S. Kawata, “Towards plasmonic band gap laser,” Appl. Phys. Lett. 85(18), 3968–3970 (2004).

18. I. Gryczynski, J. Malicka, W. Jiang, H. Fischer, W. C. Chan, Z. Gryczynski, W. Grudzinski, and J. R. Lakowicz, “Surface-plasmon-coupled emission of quantum dots,” J. Phys. Chem. B 109(3), 1088–1093 (2005).

19. D. E. Chang, A. Sørensen, P. Hemmer, and M. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007).

20. P. Nagpal, N. C. Lindquist, S. H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325(5940), 594–597 (2009). [PubMed]

21. N. C. Lindquist, P. Nagpal, A. Lesuffleur, D. J. Norris, and S. H. Oh, “Three-dimensional plasmonic nanofocusing,” Nano Lett. 10(4), 1369–1373 (2010). [PubMed]

22. P. N. Bartlett, J. J. Baumberg, P. R. Birkin, M. A. Ghanem, and M. C. Netti, “Highly ordered macroscopic gold and platinum films formed by electrochemical deposition through templates assembled from submicron diameter monodisperse polystyrene spheres,” Chem. Mater. 14(5), 2199–2208 (2002).

23. A. S. Dimitrov and K. Nagayama, “Continuous convective assembling of fine particles into two-dimensional arrays on solid surfaces,” Language 12(5), 1303–1311 (1996).

24. P. Wagner, M. Hegner, H.-J. Guentherodt, and G. Semenza, “Formation and in situ modification of monolayers chemisorbed on ultraflat template stripped gold surface,” Language 11(10), 3867–3875 (1995).

25. D. W. Mosley, B. Y. Chow, and J. M. Jacobson, “Solid-state bonding technique for template-stripped ultraflat gold substrates,” Langmuir 22(6), 2437–2440 (2006). [PubMed]

26. J. Mazurkiewicz, F. J. Mearns, D. Losic, L. Weeks, E. R. Waclawik, C. T. Rogers, J. G. Shapter, and J. J. Gooding, “Cryogenic cleavage used in gold substrate production,” J. Vac. Sci. Technol. B 20(6), 2265–2270 (2002).

27. D. L. Mills, “Attenuation of surface polaritons by surface roughness,” Phys. Rev. B 12(10), 4036–4046 (1975).

Sample (δ)	a ₀	a ₁ (δ_eff,1)	a ₂ (δ_eff,2)	a ₃ (δ_eff,3)	a ₄ (δ_eff,4)
I (0.56)	∞	13 (0.12)	-	-	-
II (0.66)	∞	7.6 (0.28)	-	-	-
III (1.2)	-	-	14.4 (0.39)	25 (0.52)	3000 (0.29)
IV (3.0)	∞	4.5 (1.50)	14.5 (1.50)	-	-

Sub-micron free-standing metal slabs with dielectric nano-voids of arbitrary shapes embedded beneath atomically-flat surface

Abstract

1. Introduction

2. Experimental procedures

2.1 Ar + -Assisted ion beam deposition of Au on an atomically smooth mica substrate

2.2 Deposition of nano-particle layer to form nano-void template

2.3 Electro-deposition

2.4 Stripping-off the mica template

3. Mathematical and numerical analysis

4. Experimental investigation

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (7)

Optics Express