Epitaxial Growth of Atomically Smooth Aluminum on Silicon and Its

Sep 22, 2016 - ACS Nano , 2016, 10 (11), pp 9852–9860 ... Aluminum (Al) provides an excellent material platform for plasmonic applications in the ul...
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Epitaxial Growth of Atomically Smooth Aluminum on Silicon and Its Intrinsic Optical Properties Fei Cheng,†,§ Ping-Hsiang Su,†,§ Junho Choi,† Shangjr Gwo,‡ Xiaoqin Li,† and Chih-Kang Shih*,† †

Department of Physics, University of Texas at Austin, Austin, Texas 78712 United States Department of Physics, National Tsing-Hua University, Hsinchu 30013, Taiwan

‡

S Supporting Information *

ABSTRACT: Aluminum (Al) provides an excellent material platform for plasmonic applications in the ultraviolet (UV) regime due to its low loss coefficient at UV wavelengths. To fully realize the potential of this material, it is imperative to create nanostructures with minimal defects in order to prevent light scattering and better support plasmonic resonances. In this work, we report the successful development of atomically smooth epitaxial Al films on silicon. These epitaxial Al thin films facilitate the creation of fine plasmonic nanostructures and demonstrate considerable loss reduction in the UV frequency range, in comparison to the polycrystalline Al films based on spectroscopic ellipsometry measurements. Remarkably, our measurements on the epitaxial Al film grown using the two-step method suggest that the intrinsic loss in Al is significantly lower, by up to a factor of 2 in the UV range, with respect to current widely quoted Palik’s values extracted from polycrystalline films. These high-quality epitaxial Al films provide an ideal platform for UV plasmonics. In addition, the availability of intrinsic optical constants will enable more accurate theoretical predictions to guide the device design. KEYWORDS: epitaxial growth, single-crystalline aluminum, intrinsic optical constants, ellipsometry, plasmonic resonances

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plasmonic response over time, limiting long-term device applications. Recently, Al has emerged as the choice of plasmonic material in the UV8,9 and short wavelength visible regime.10,11 Though the interband transition of Al results in a large optical loss at around 800 nm,12 this interband transition probability decreases steadily as the wavelength decreases and the loss is smaller than with Au or Ag in the short wavelength regime. The crossover occurs at ∼420 nm against Au and at ∼310 nm against Ag (see Figure S1 for comparison between Al, Au, and Ag, Supporting Information). As a result, Al is an excellent

oherent oscillations of electrons supported by metallic nanostructures, known as surface plasmons, exhibit remarkable ability to concentrate light to subwavelength volumes and to produce large optical field enhancements.1 These extraordinary properties have enabled numerous applications in areas as diverse as ultrasensitive biosensing,2−4 nonlinear optics,5 photocatalysis,6 and solar energy harvesting.7 Among different metals, Au and Ag have been the most popular choices for plasmonics in the near-infrared and visible wavelength regimes due to their relatively low loss properties. However, the onset of the d-band-related interband transitions leads to significant loss in the short wavelength range. The onset of d-band transitions occurs at 500 nm for Au and 310 nm for Ag. Moreover, unless the surface is well-protected, the oxidation of silver nanostructures severely degrades the © 2016 American Chemical Society

Received: August 17, 2016 Accepted: September 22, 2016 Published: September 22, 2016 9852

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Figure 1. (a,b) RHEED pattern of a well-reconstructed Si(111)-7 × 7 surface and an epitaxially grown Al film (100 ML). (c) XRD 2θ scan pattern of the epitaxially grown Al film. The inset shows the enlarged Al(111) peak with a fwhm of ∼0.5°. (d) AFM image of the epitaxially grown Al film (about 2 nm self-oxidized AlOx capped). (e) AFM scan of a thermally deposited polycrystalline Al film (24 nm). SEM images of slots milled by focused ion beam (FIB) into the two-step epitaxially grown (f) and thermally deposited polycrystalline (g) Al film on a Si substrate. Optimized FIB conditions at 30 kV and 300 pA are applied. Scale bar: 1 μm.

previously32 and has also been used for UV applications;25,31 however, epitaxial Al on Si substrate, in addition to being an excellent choice for plasmonic applications, also provides the attractive feature of being CMOS-compatible. Accurate intrinsic dielectric constant data have been missing for single-crystalline Al. One key reason for this lack of knowledge is that the method to obtain the dielectric constants of optical materials, such as spectroscopic ellipsometry (SE) measurements, is quite challenging to perform on chemically synthesized, singlecrystalline Al NPs.15,21 Our wafer size, flat film geometry provides us with an opportunity to measure the intrinsic optical constants of Al. Such information would be extremely valuable for accurate theoretical and experimental study of the plasmonic responses of nanostructures made from single-crystal aluminum.

plasmonic material in the UV range, evident by several recent demonstrations.9,13−15 For example, the development of Al nanoparticles (NPs) has been employed to serve as plasmonic sensing platforms16−18 and photocatalysts for hydrogen dissociation.19 In addition, a UV plasmonic nanolaser has recently been achieved using an Al film coupled to gallium nitride (GaN) nanowires.20 One interesting observation is that the measured scattering plasmonic resonances of single-crystalline Al NPs are even sharper than the theoretically simulated results,21 indicating that the intrinsic loss might be even lower than the theoretical values being used in the simulation. This may not be surprising, considering that the optical constants used in the current theoretical studies, either Palik’s22 or Rakić’s23 values, are extracted from polycrystalline Al films, whose quality can fluctuate greatly and likely suffer significant structural defects including surface roughness and disordered crystal grain boundaries.24 These structural imperfections cause large ohmic and scattering losses of surface plasmons (SPs) and thus limit the plasmonic performance of Al nanostructures.25,26 The importance of reducing such losses for plasmonic applications has been discussed extensively in the literature.26−29 Recent demonstrations of ultra-low-threshold, continuous-wave operations of plasmonic nanolasers using atomically smooth epitaxial Ag film exemplifies the importance of not only single crystallinity but also surface smoothness.30 Thus, one expects that an epitaxial Al thin film platform would lead to significant advancements for UV plasmonic applications such as lasing.20,31 In this paper, we report the development of epitaxial Al thin films on Si as a plasmonic material platform in the UV range. It is noted that epitaxial growth of Al on GaAs was achieved

RESULTS AND DISCUSSION The epitaxial growth of our film is carried out in a molecular beam epitaxy (MBE) system with a base pressure of 3 × 10−11 Torr. During the growth, the pressure is kept below 1 × 10−10 Torr. Si(111) wafers with a low miscut angle (∼0.2°) are used as substrates, and the surface is cleaned by passing gradually increasing current through the substrate for outgassing (0−2.5 A) and reconstruction (10−17 A). After this cleaning procedure, the surface exhibits the well-known 7 × 7 reconstruction, confirmed by a reflection high-energy electron diffraction (RHEED) pattern shown in Figure 1a. After that, Al is evaporated on the Si substrate followed by a refined two-step growth process similar to the one used previously to grow atomically smooth Ag films on Si.28,30 Al is evaporated using a Knudsen cell, and the deposition rate is controlled precisely by 9853

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Figure 2. (a) RHEED pattern of a bare, untreated Si(111) surface; below is the pattern for the same substrate with an Al film (100 ML) grown on top at RT with a deposition rate of 6.2 Å/min. In the same column, an AFM (rms = 6.4 nm) image, a SEM image of a slot milled by FIB, and XRD 2θ scan pattern of this film are shown. (b) RHEED pattern for a well-reconstructed Si(111)-7 × 7 surface and one with an Al film (100 ML) grown on top at RT with a deposition rate of 4.7 Å/min, AFM (rms = 0.26 nm), SEM image, and XRD pattern. (c) RHEED pattern for Si(111)-7 × 7 and one with an Al film (100 ML) grown on top by the two-step method (first 10 ML, 0.5 A/min) followed by RT deposition (90 ML, 4.7 Å/min), AFM (rms = 0.24 nm), SEM image, and XRD pattern. The Al(111) peak for samples in (b,c) has a fwhm of ∼0.55°, which is 0.05° larger than that of the epitaxial film grown by the two-step method.

terminating native oxide layer on top of the Al film, the sample is transferred without breaking vacuum to another ultra-highvacuum (UHV) chamber to carry out in situ oxidation by exposing the surface to high-purity oxygen gas under low pressure (1 × 10−6 Torr) for 10 min (see Experimental Methods for growth and oxidation details). The surface is then characterized ex situ using AFM (Figure 1d), showing that the atomic smoothness is retained after the oxidation. The stair-like steps reflect the underlying substrate steps, confirming the uniformity of the film using the two-step process. If we assume that the oxidation procedure consumes 2 nm of Al, the resulting metal thickness after the oxidation should be 22 nm. As a comparison, the AFM image of a polycrystalline Al film of similar thickness (24 nm), which was deposited at RT and at a

varying the source temperature. First, a particular amount of aluminum, usually 25 monolayers (ML), is evaporated onto the liquid-nitrogen-cooled Si(111) substrate at around 90 K with a low deposition rate of ∼0.5 Å /min; the sample is then annealed to room temperature (RT) for a few hours (6−8 h). The procedure is repeated until the desired thickness is achieved. During the growth, the surfaces are characterized using RHEED patterns. The post-growth films are then characterized by atomic force microscopy (AFM) and thin film X-ray diffraction (XRD). Shown in Figure 1b is the RHEED pattern, taken in situ for a 100 ML (24 nm) thick epitaxial film grown using the two-step process, confirming the atomic smoothness and single crystallinity. In order to form a high-quality, densified self9854

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RHEED patterns are not able to inform us if fissures or pinholes exist because the electron beam has a finite coherent length. As long as epitaxy is maintained and local flatness is achieved, sharp streaks will be observed in RHEED. Nevertheless, this sequence of film morphology as a function of deposition rate (Figure S2f) might indicate the possibility of achieving atomically flat epitaxial film growth without the need of an elaborate two-step process. In order to further test if the time-saving RT growth method can be applied to get thicker, atomically smooth Al films for plasmonic applications, we deposit two thicker films at RT with relatively higher deposition rate: the first Al film (100 ML) is deposited on Si(111)-7 × 7 surface at RT with a rate (4.7 Å/min) much higher than what is used in the two-step method (0.5 Å/min); the second one is deposited using the two-step method for the first 10 ML (0.5 Å/min) and RT growth for the following 90 ML (4.7 Å/min). For comparison, a third one is constructed entirely at RT on an untreated Si(111) substrate. The RHEED patterns, AFM scans, SEM images of slots milled by FIB, and XRD 2θ scan patterns are shown, respectively, for the three cases in Figure 2. According to the AFM and SEM images, the surface morphology of 100 ML thick Al film grown at RT is as smooth as the one grown by the two-step method provided that the film is deposited on well reconstructed Si(111)-7 × 7 surfaces (rms = 0.24−0.26 nm). Sharp, straight slot edges are observed on the epitaxial Al films (Figure 2b,c). In contrast, the surface morphology examined by AFM and crystalline quality reflected by XRD are much worse for the Al film grown on untreated substrates: the rms value is an order of magnitude larger (rms = 6.4 nm) than Al grown on Si(111)-7 × 7 surfaces, and more diffraction maxima (Al(200) and Al(220)) are observed besides the Al(111) peak, which is much weaker than that of the epitaxial Al films (AFM and XRD panels of Figure 2a). Although fissures are clearly seen on the surface of Al film grown on untreated substrate, interestingly, the slot created by FIB presents sharp, straight edges, showing imperceptible differences with slot edges milled on Al grown on Si(111)-7 × 7 surfaces (SEM panel of Figure 2a). This feature is different from the observation on thermally deposited polycrystalline Al films where irregular milling defects are present on slot edges (Figure 1g). We attribute the difference to the presence of incorporated impurities of the evaporated source and hostile chamber environment of thermal deposition equipment. We also note that the fissures and tiny pinholes observed for the thin films (20 ML) grown at RT show a time-dependent variation when exposed to air. The size of the pinholes enlarges, and the surface roughness increases after the 20 ML thick Al film was taken out of the UHV chamber for 20 days (Figure S3b,c), indicating that further oxidation of the Al advances around the pinholes of the nonuniform Al films grown by the RT method. In comparison, the atomically flat, uniform Al film grown by the two-step method is free of pinholes and fissures, and no deterioration of film surface morphology is observed (Figure S3a,d). The same situation happens for thick films grown using the RT method at higher deposition rates (100 ML, Figure S3e,f). Accordingly, the two-step method remains the best recipe to produce atomically flat, stable epitaxial film. The RT growth method can be utilized to quickly grow relatively smooth epitaxial films with good crystallinity, which is reflected by the sharp streaks observed in the RHEED pattern; however, their plasmonic response is worse than the films grown using the two-step process while still being better than the polycrystalline films grown using conventional methods.

rate of 2 nm/min using a conventional thermal evaporator (Denton Explorer, base pressure around 2.0 × 10−6 Torr), is shown in Figure 1e. The film thickness has a root-mean-square (rms) roughness of 3.4 nm, whereas the epitaxial film presents a rms value (0.23 nm) an order of magnitude smaller. Furthermore, the crystallinity of the epitaxial film was confirmed by XRD analysis, with only one diffraction peak at 39°, arising from the Al(111) crystal plane, observed in the 2θ scan (30−80°), as shown in Figure 1c. Notably, the full width at half-maximum (fwhm) of the Al(111) peak is about 0.5°, suggesting good crystalline quality of the thin metal film. The diffraction peak of Si(111) planes is observed at 28.5° (not shown in Figure 1c) with an intensity about 3 orders of magnitude higher because the sampling depth of the bulk Si is several microns. Interestingly, one also observes a peak around 59° from the Si(222) crystal plane, whose intensity is about one-quarter that of the Al(111). Note that for bulk Si, the (222) diffraction is strictly forbidden. The observation of Si(222) here is likely due to the residual effect of Si(111)-7 × 7 surface reconstruction which causes the atomic arrangement of Si at the top few layers to deviate from the bulk arrangement. We also investigated the performance of the epitaxial film against thermally deposited films in terms of device processing such as plasmonic nanostructures created by focused-ion-beam (FIB) milling. Figure 1f,g shows the representative scanning electron microscope (SEM) images of slot (2 μm wide) edges created by FIB into the epitaxial and polycrystalline Al films. Sharp, straight slot edges are fabricated easily on the epitaxial Al film (Figure 1f). For the thermally deposited polycrystalline film, however, irregular shapes and minor structural defects are present on slot edges even at optimized ion-beam-focusing conditions (Figure 1g); this is due to the fact that randomly oriented crystal grains and rough surfaces introduce variations in the resistance to the ion-beam milling process and thus lead to meandering edges.25 This demonstration suggests that epitaxial, single-crystalline films better facilitate the fabrication of large-area, high-definition plasmonic nanostructures containing fine features. The two-step process described above, while leading to superior quality of epitaxial Al films on Si, is a time-consuming process. In this respect, we also explored a RT growth method (avoiding the need for an anneal process) that is done at higher deposition rates, while retaining the UHV condition and using well-reconstructed Si(111)-7 × 7 surfaces. According to AFM scans, thin Al films (20 ML, ∼4.7 nm) grown on RT substrates at rate of 0.5 Å /min (same as the two-step method) and 1 Å/ min have totally different, rough surface morphologies compared to the atomically flat ones: fissure-like structures can be clearly seen on the metal surfaces (Figure S2a,b), which resemble those observed when a similar method is used to grow Ag films.33 In order to see how the deposition rates further influence the surface morphology, we increase the deposition rate further and find that the surface morphology is gradually improved: the rms roughness of Al films by the RT method decreases with relatively higher deposition rates and presents a similar surface roughness to that of the epitaxial one, though tiny pinholes are observed when the deposition rate is increased to 4.7 and 6.2 Å/min (Figure S2c,d). Interestingly, the RHEED patterns of all the films grown by the RT method under different deposition rates are indistinguishable from those taken of films grown using the two-step process (top panels of Figure S2). The observation of a sharp diffraction pattern indicates that epitaxy is achieved in all of the growth conditions. The 9855

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Figure 3. (a) Layered structure of the Al film sample with a self-oxidized cap. (b) Energy dependence of the real part of the dielectric constant ε1 extracted from the SE measurements on the epitaxial Al film using two-step method (red solid), the one deposited at RT (blue solid), and the one deposited using a two-step method for the first 10 ML and RT growth for the following 90 ML (magenta solid). (c) Energy dependence of the imaginary part of the dielectric constant ε2 extracted from the SE measurements on all three Al films. (b,c) Plotted against data (red dashed) taken from Palik’s handbook of optical constants, and the fitting residues for the epitaxial Al film are plotted below (b,c). The inset of (c) shows the comparison within the UV range (3−5 eV), indicating the energy at which ε2 for the epitaxial Al is approximately only one-half of the value from Palik’s data. The black solid line represents the difference ratio [(ε2,Palik − ε2,Epi)/(ε2,Palik)] of these two data sets for the imaginary part of the dielectric constant.

that in thermal films. Our measurements indeed clearly show substantially lower loss than Palik’s values from ultraviolet to near-infrared range (1.5−5 eV, Figure 3c). The dielectric constants ε2 extracted from the other two Al films deposited at RT (blue and magenta in Figure 3c) are observed to fall between the epitaxial two-step method and Palik’s values, which are due to structural defects (possible voids and pinholes as mentioned above) introduced during the deposition at RT. The fitting residues within the whole spectral region are small and centered around zero, suggesting that our model fits the data very well. In the energy range below 1.5 eV, the errors are relatively large due to reduced detector efficiency. The most interesting observation in the SE measurements resides in the UV range (3−5 eV) where Al outperforms Au and Ag (Figure S1). As indicated by the black solid in the inset of Figure 5c, the intrinsic loss in epitaxially grown Al is ∼2 times smaller than Palik’s values in the UV range, which will improve the plasmonic performance of nanodevices significantly, as demonstrated below. We also confirmed that the extracted dielectric constants are not sensitive to the model of the layer structure chosen. In addition to the simplest model illustrated in Figure 3a with perfectly flat layers, we examine two more structural models which include surface roughness and composition uncertainty of the oxide capping layer (Figure 4a). The maximal difference in retrieved dielectric constants between the three models was less than 2% (Figure 4b), validating the morphology independence of the values presented in Figure 3b,c. In order to evaluate the quality of

This was determined using spectroscopic ellipsometry measurements as we discuss below. Next, we perform SE measurements and analyses28,34,35 of epitaxial Al films (see Experimental Methods for details). We present here the fitted values from three in situ oxidized 100 ML (∼24 nm) epitaxially grown films. The results of epitaxial films are plotted against data taken from Palik’s handbook of optical constants.22 In striking contrast to silver nanostructures, on which a capping layer is a crucial element to prevent the rapid degradation of Ag in ambient conditions (due to bulk oxidation), a compact, native oxide layer forms within a few hours of oxygen exposure and then remains stable on the surface of Al films, acting as a passivation layer preventing further oxidation.14,36 We confirm via SE measurements that, once oxidation is completed, the Al film’s pristine quality and surface smoothness do not show degradation over a period of 6 months. In our fitting, we use a simple capping/Al/Si structural model for the epitaxial films (Figure 3a). The fitted result for both ε1 and ε2 are plotted against those of the thermally deposited film compiled by Palik, as shown in Figure 3b,c. The maximum value around 1.5 eV (∼800 nm) that is shown in Figure 4b,c is a feature of the interband transition (IT) in Al. Outside of the IT band, the contribution to ε2 mainly comes from intraband transitions accompanied by electron scattering, lattice vibrations, (phonons), surface roughness, and grain boundaries inside the bulk.28 As a result, scattering from imperfections within the single-crystalline, epitaxially grown Al film using the two-step method is expected to be lower than 9856

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Figure 4. (a) Two different layered structures modeled in our analysis. The interface of the Al sample is analyzed in two different ways in models 1 and 2. In model 1, the surface roughness comes only from the self-terminating oxide layer (2 nm) with a sawtooth morphology (0.23 nm thick) on the top. In model 2, the same morphology is also presented on the top surface of epi-Al film. (b) Energy dependence of the imaginary part of the dielectric constant ε2 extracted from SE based on the two models (red and blue solid lines) and Palik’s data (black dashed line) are shown for comparison. (c) Uniqueness test of the epitaxial Al film by the two-step method in the main text.

Figure 5. (a) Scattering cross sections for an Al nanocube of edge d = 75 nm on an Al2O3 substrate, calculated with COMSOL Multiphysics. The thick solid line is calculated using tabulated optical constants of epitaxially grown Al film, and the thin dashed line corresponds to that obtained using Palik’s data. (b) Scattering cross sections for an Al nanocube of the same size located at a distance of 10 nm from an aluminum film of thickness t = 100 nm. The schematics depict the geometry used in the simulation.

our fitting procedure, we also conducted a uniqueness test to examine the retrieved dielectric constants by calculating the mean-square-error (mse) values in each fitting iteration (see Experimental Methods for details). The minimum of calculated mse values (Figure 4c) occurs within 1 nm of the film thickness calibrated during the growth process, validating that our fitting model is robust and the retrieved optical constants are valid.

Our measured optical constants suggest improved theoretical limits to the performance of plasmonic devices, which may lead to further advancements in the field of biological research and medical diagnostics based on the Al plasmonic platform.37 By using the retrieved intrinsic optical constants of an epitaxially grown Al film, we performed numerical simulations to predict the performance improvement of a plasmonic nanocavity made of single-crystalline Al. The system we modeled is depicted 9857

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EXPERIMENTAL METHODS

schematically in the insets of Figure 5. It consists of a chemically synthesized Al nanocrystal15,21 (edge size of the nanocube a = 75 nm) on a dielectric (aluminum oxide) or an Al film (thickness t = 100 nm) epitaxially grown on Si substrate. The scattering cross sections of the Al nanocube are modeled using tabulated optical constants from Palik’s handbook and our SE measurements. For a nanoparticle deposited directly on a dielectric (aluminum oxide) substrate, the fundamental, dipolar plasmon resonance is observed at 3.5 eV, and a quadrupolar mode is found around 5 eV (dashed line in Figure 5a, modeled with Palik’s data). In comparison, the spectrum of a single-crystalline Al nanocube is red-shifted with respect to that of a polycrystalline counterpart, and two strikingly sharper resonances, that is, the dipolar mode at 3.2 eV and the quadrupolar mode at 4.6 eV, are observed (solid line in Figure 5a). Different from a nanocube within an isotropic environment, the adjacent dielectric substrate introduces an “image” of the dipolar plasmon resonance and mediates an interaction between the bright dipolar and dark quadrupolar modes of the nanocube.38 That is the reason why a hybridized quadrupolar resonance can be observed in the calculations. In the case of a coupled nanocrystal film system, the Al film beneath the nanocube introduces a stronger interaction of the quadrupolar cube mode with the dipolar cube mode,15,39 resulting in more separated, enhanced double peaks in the scattering spectrum (Figure 5b). It is seen that the epitaxial material platform in both cases reduces the resonance bandwidth and boosts the scattering intensity at both nanocavity resonances. The effects of oxide layer and Al film thickness are also investigated (Figure S4, Supporting Information). We would like to highlight one caveat concerning the simulation results of the above nanocavity: we evaluated the improved spectral response of nanostructures by simply replacing the optical constants from Palik’s data with the intrinsic optical constants extracted from our epitaxial films; however, thermally evaporated or magnetically sputtered polycrystalline films suffer loss significantly higher than that represented by Palik’s data due to the existence of grain boundaries and much worse surface roughness (an order of magnitude larger rms value as shown in the AFM image) that are not taken into account in the simulation by replacing the dielectric constants only. Therefore, the intrinsic optical constants reported here do not capture all advantages of single-crystalline Al films in plasmonic applications.

Sample Growth. The epitaxial Al film presented in this work was grown using a 5 N (99.999%) high-purity aluminum source. A commercial Knudsen cell was used as the evaporator to ensure a highly stable deposition rate and precise thickness control, allowing the total thickness of the film to be determined by the product of time and deposition rate, which was calibrated through a quartz crystal monitor. Before the evaporation, we sent a gradually increasing current (0−16 A) through the substrate for surface cleaning and reconstruction. The total thickness of the Al film is 100 ML and was completed after four growth cycles following a refined two-step growth process that guarantees single-crystalline growth of the film. For each cycle, 25 ML of aluminum was evaporated onto a liquid-nitrogen-cooled, surfacereconstructed Si(111) substrate (∼90 K) with a low deposition rate of ∼0.5 Å/min. After that, the film was naturally annealed to and kept for a while at RT in the UHV chamber. In Situ Oxidation. In order to suppress dewetting and avoid the formation of an uncontrollable oxide layer in an ambient environment, we also developed a procedure for in situ capping of a thin oxide layer. Note that this capping method differs from our previously reported capping methods, such as additional ex situ capping by atomic layer deposition of MgO28 or a low-band-gap semiconductor material, such as germanium,30 which may cause unexpected absorption in the visible wavelength range. Though a self-terminating oxidation naturally occurs once the film is taken out of the UHV chamber, contaminants may be introduced during an uncontrolled ambient environment oxidation process. In order to form a pure, densified native oxide layer with uniform thickness, we transferred the sample to another UHV chamber, while keeping it under UHV, to do in situ oxidation by passing high-purity oxygen gas under low pressure (1 × 10−6 Torr) for 10 min. SE Measurements. The SE measurements were performed using a J.A. Woollam M-2000 spectroscopic ellipsometer. The focusing probe attachments provided an incident spot size of ∼300 μm. Modeling and analysis were performed with the WVASE32 software. We specifically measured the optical constants of a flash-cleaned silicon wafer used in the deposition process to eliminate any discrepancy and uncertainty that may have been introduced by the silicon substrate. These measured silicon optical constants were fixed in the subsequent data fitting procedure during which only the Al parameters were allowed to vary. Al films were measured under three different incident and collection angles (60, 65, and 70°) with respect to the normal of the sample surface. Under each angle, data were collected at three different locations in order to exclude location dependence in the raw data and to verify the spatial homogeneity of our epitaxial Al film. To further verify that the Al film was optically isotropic, we extracted the effective optical constants directly from the raw data before the process of reverse fitting. No angular dependence in the effective optical constants was observed, confirming optical isotropy and suggesting that multiangle analysis contributed no further information in the analysis. In the next step, we performed the reverse fitting process on data taken at 70° without loss of generality. The residues plotted in Figure 4b,c are the differences between the calculated effective optical constant and the experimental effective optical constant. ε2 is obtained via fitting of the SE data based on the structural model and analytical equations for dielectric constants. The values of ε1 can be calculated according to the Kramers−Kronig relations. Due to the finite range of collected data, we modeled the properties outside of the measurement range using one additional effective pole at the low energy (i.e., 0.001 eV). Uniqueness Test. The mse is a critical quantity to evaluate the quality of fit. However, the mse alone is not an absolute quantity to validate the extracted optical constants. If some parameters in the analytical model are strongly correlated, it is possible to provide multiple solutions with similarly low mse values. For absorptive thin films, a strong correlation can exist between the layer thickness and optical constants. We first minimize these correlations by choosing a minimal number of parameters used in the model. In order to verify that the final set of optical constant values is unique, it is essential to

CONCLUSION In summary, we utilize MBE to obtain epitaxially grown, atomically smooth, single-crystalline Al films and then perform SE measurements and analyses to extract their optical constants. The intrinsic loss of epitaxial Al film grown using the two-step method is found to be one-half the value of the widely cited Palik’s value in the UV range. The optical constants reported here (see Table S1 in Supporting Information for a list of values from 1.5 to 5.5 eV) better capture the intrinsic properties of bulk Al, and we suggest that these measured data be incorporated in future theoretical calculations for Al-based optoelectronic and plasmonic devices. We expect that the single-crystalline Al films facilitate the definition of fine plasmonic nanostructures and their optical constants to be applicable in nanostructures or metamaterials constructed by chemically synthesis, single-crystalline Al NPs, nanorods, nanoplatelets, and nanoshells. 9858

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ACS Nano conduct a uniqueness test examining that the final fitting results indeed reach the global minimum as a function of the Al layer thickness. The mse values are calculated in each iteration by fixing the thickness of the Al film in the range of possible values, while the other parameters are allowed to vary during the fitting process. Then the mse values for each iteration are plotted as a function of thickness of the Al film as shown in Figure S5. This uniqueness test indicates that mse reaches a global minimum at the Al layer thickness used in our model, thus validating the extracted optical constants. Numerical Simulations. Numerical simulations were performed with a finite element method (COMSOL Multiphysics, COMSOL Inc.). The far-field scattering cross sections of Al nanocubes can be calculated for different polar and azimuthal angles of incidence. In Figure 5, we show only the case of normal incidence of a linear polarized light with the electric field vector tangential to the surface of the substrate (both polar and azimuthal angles are set to 0°). The 1 scattering cross section is defined as σsc = I ∬ (n ·Ssc)dS , where n is

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0

the outward-facing normal vector from the nanocube, SSC is the relative normal Poynting vector, and I0 is the incident intensity. The integral is taken over the closed surface of the nanocube. The optical constants of polycrystalline Al are taken from the Palik’s handbook of optical constants22 and that of single-crystalline Al from the SE measurement on our epitaxial Al film grown by the two-step method. A two-level approach is adopted in the simulation: the model computes first a background field which is not affected by the nanocube but a superposition of the incident and reflected plane waves from the substrate; then the background field is used to calculate the total field with the scatter present. Floquet conditions are adopted in the first level physical interface, while perfectly matched layers (PMLs) are assumed in the second level interface, which surround the nanocube and were placed far away (≥1 μm) from it. The PML will absorb the scattered field from the nanocube. For both structures in Figure 5, the edge of Al nanocube is 75 nm and fillet corners (radius of curvature = 5 nm) were used to mimic the actual geometry of chemically synthesized nanoparticles.

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b05556. Comparison of optical constants (imaginary part) between Au, Ag, and Al; tabulated optical constants extracted from the epitaxially grown single-crystalline Al film (PDF)

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Author Contributions §

F.C. and P.-H.S. contributed equally.

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was partially supported by the Welch Foundation (F-1672 and F-1662) and by the National Science Foundation (NSF-DMR-1306878, NSF-ECCS-1408302, and NSF-EFMA1542747). S.G., X.Q.L., and C.K.S. also acknowledge support from NT 3.0 program, Ministry of Education, Taiwan. REFERENCES (1) Barnes, W. L.; Dereux, A.; Ebbesen, T. W. Surface Plasmon Subwavelength Optics. Nature 2003, 424, 824−830. 9859

DOI: 10.1021/acsnano.6b05556 ACS Nano 2016, 10, 9852−9860

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DOI: 10.1021/acsnano.6b05556 ACS Nano 2016, 10, 9852−9860