Probing of sub-picometer vertical differential resolutions using cavity plasmons

Plasmon rulers can be used for resolving ultrasmall environmental, dimensional, and material changes owing to their high sensitivity associated with a light-scattering spectral shift in response to changes in the separation between plasmonic nanostructures. Here, we show, in several experimental setups, how cavity plasmons in a metal nanowire-on-mirror setup can be used to probe vertical dimensional changes with sub-picometer differential resolutions using two carefully chosen material systems. Specifically, we monitor the dielectric layer thickness changes in response to growth using atomic-layer deposition and to thermal expansion, demonstrating a sensitivity of 14-nm spectral shift per Ångström thickness change and 0.58 pm of vertical differential resolution, respectively. The findings confirm theoretical predictions and highlight the potential use of cavity plasmons in some ultrasensitive sensing applications.

Averaged root mean square (RMS) roughness from AFM images of the ultrasmooth gold film with the Al2O3 coating vary from 0.5 nm to 5 nm and the conventional gold film, respectively.
Every error bar represents the standard deviation from five samples.

Supplementary Figure 6 | Quantum damping of the cavity plasmon in Au-NWOM.
Dark field scattering spectra of a 0.5 nm thick CTAB coated AuNW over a gold film system with and without a 0.5 nm thick Al2O3 spacer. The former with a 1 nm gap distance is still free from quenching, while quantum tunneling effects 2 occur by further decreasing the gap thickness down to about 0.5 nm (with only the CTAB layer, red line). This is agree with the results of a theoretical study of quantum tunneling effects in a dimer with flat shape terminals 3 , which shows that the cavity plasmon would disappear at a ~0.4 nm separation rather than broadening and shifting to shorter wavelengths, as is typical for radiative dipole antenna modes. Thus, for our optical setup, the limit-of-detection, which is defined as the 3-fold standard deviation of the spectral peak positions 4 , is about 0.01 nm (3.72 × 10 -5 eV).

Supplementary Note 1. Impact of the surface roughness effect on the NWOM nanocavity
To demonstrate the impact of the surface roughness effect on the NWOM nanocavity for the cavity plasmons, we built two PVP covered Ag-NWOM systems. The mirrors are the ultrasmooth gold film and the conventional thermal deposition gold film, respectively ( Supplementary Fig. 4a, b). Here, the real gold film can serve as a perfect plane combines with an air layer. The thickness of the air layer gair shown in Supplementary Fig. 4b depends on the roughness of the gold film, which can be defined as the distance between the maximum height and the average height of the gold film from the area beneath the nanowire. The gair for the ultrasmooth gold film and the conventional gold film are about 0.3 nm and 2 nm, respectively, where the former down to the atomic level ( Supplementary Fig. 4c-f). The lattice of the nanowire is clearly shown in the TEM image in Supplementary Fig. 1. The planar surfaces of nanowires are the Au/Ag (100) crystalline arrangement 6 , whose roughness we assume here to be negligible compared with that of the gold film. The total effective gap distance gtotal = gair + gPVP, where gPVP is the thickness of the PVP spacer. In comparison to the ultrasmooth goldbased NWOM cavity, the conventional gold-based NWOM cavity brings an additional 1.7 nm of effective distance (given that the gPVP is the same), which limits its maximum available sensitivity.
We perform dark field scattering measurements of 2.3 nm thick PVP covered AgNWs on the ultrasmooth gold film and on the conventional thermal deposition gold film ( Supplementary   Fig. 4g), respectively. The results suggest that a higher roughness of the cavity surface leads to a larger full width at half maximum of the far field cavity plasmon resonance. This can be explained by the superimposed effect of the local cavity plasmon resonances with different wavelengths in the micro scale area (collection area of the spectrometer). The wavelength difference comes from the roughness of the gold film and depends on its averaged root mean square. This peak broadening effect decreases the figure-of-merit of the NWOM system, thereby reducing the sensitivity of the conventional gold-based NWOM system.

Supplementary Note 2. Analysis of the vertical differential resolution and its uncertainty of the NWOM systems
For our NWOM sensor, the gap distance dependent resonance energy of the cavity plasmon EM follows the universal function in a form of: where g is the gap distance, E0 is the plasmon energy for infinite gap distance (an isolated nanowire), A is the amplitude constant, and τ is the exponential decay length. The differential sensitivity at g can be obtained by the absolute value of first-order derivative of the EM(g), and the vertical resolution limit GM is given by: where ELOD is the limit-of-detection of the optical measurement setup. By using this equation, we can obtain the vertical resolution limit of the measured Al2O3 spaced Au-NWOM system (Fig. 2 in the main text) and the simulated PVP spaced Au-NWOM system (Fig. 4 in the main text), respectively. These are plotted in Supplementary Fig. 9a. The ELOD is chosen from the result of our optical setup, which is 3.72 × 10 -5 eV (0.010 nm at 578.595 nm). For the measured Au-NWOM system, the gap distance g is chosen as the total effective gap distance gtotal = gALD + gCTAB + gair, where gALD is the Al2O3 thickness; gCTAB = 0.5 nm is the CTAB thickness; and gair is the effective air thickness induced by the surface roughness of the gold mirror (Supplementary Note 1), set as 0.3 nm here. The result (red curve in Supplementary Fig. 9a) suggests that the vertical differential resolution is better than one picometer when the gap distance is smaller than ~ 4 nm (namely, 3.2 nm Al2O3 thickness).
The uncertainty of the vertical differential resolution ΔG originates from the uncertainty of the gap distance Δg. The error transfer from the gap distance to the vertical differential resolution depends on equation (2), whose transfer function is defined as: By applying this formula, we can get the corresponding vertical differential resolution deviation ΔG of the measured Au-NWOM system and the simulated Ag-NWOM system, respectively ( Supplementary Fig. 9b). The results show that the ΔG depends almost linearly on the Δg as the Δg is smaller than the τ, where the τ of the measured Au-NWOM system and the simulated Ag-NWOM system are 1.396 nm and 2.702 nm, respectively. A larger exponential decay length τ (a higher sensitivity), results in a lower uncertainty of the vertical differential resolution. In our two measured NWOM systems, the Δg mainly comes from the thickness error of the organic molecule layers (CTAB and PVP), which is estimated as ~0.3 nm by the TEM characterization (Methods and Supplementary Fig. 1). The thickness error of the Al2O3 layer grown by ALD method is smaller than 5%, which is negligible compared with the above factor. By applying Δg = 0.3 nm into equation (3), we estimated that the uncertainties of the vertical differential resolution are ±21.7% (0.071±0.016 pm for 0.5 nm Al2O3 thickness) and about ±11.1% for the measured Au-NWOM and simulated Ag-NWOM systems, respectively.

Supplementary Note 3. Gas sensing application of PVP spaced Au-NWOM
We fabricate a PVP spaced Au-NWOM system to realize an in-situ gas sensing application with ultrahigh sensitivity. The single Au-NWOM consists of a 0.5 nm thick CTAB covered AuNW placed on a ~2 nm thick PVP stabilized gold microplate surface (inset of the Supplementary Fig. 10b). The gold microplate has a single crystalline Au (111) surface 7 , with a roughness that is better than that of the ultrasmooth gold film. The thickness of the PVP spacer will increase (decrease) slightly after the adsorption (desorption) of water molecules from the environment. This can be monitored by the NWOM system. As the relative humidity (RH) increases, water molecules can be 'inserted (released)' into the ~2 nm thick PVP spacer, thereby increasing the gap and changing the NWOM cavity plasmon resonance to a shorter (longer) wavelength. The sample is put into a chamber with a tunable density of water molecules around the NWOM. Before the RH sensing experiment, the sample is baked at 323 K for 1 hour to make sure the water density inside the PVP is lower than the lowest water density used in the chamber. During the experiment, the temperature of the sample is stabilized at 295 K to avoid the thermal expansion effect of the PVP. Then we change the RH with a sequence of 7% → 68% → 7% 3 times, measuring the RH dependent dark field scattering spectra of three Au-NWOM. It takes about 30 min to a form new equilibrium state of the sample after each change of the RH environment. The results indicate that all the Au-NWOMs show a reversible ~16 nm red (blue) spectral shift as the RH decrease (increase), which demonstrates the reliability of our experimental system.
Dark field scattering measurements are performed on the three Au-NWOMs as the RH changes from 7% to 65% with several smaller humidity steps, one of those results is shown in Supplementary Fig. 10a. Supplementary Figure 10b shows the RH dependent peak shift averaged from the three Au-NWOMs. The best fit is a two-phase exponential decay function in the form of λ(φ) = λ0 -29.9×exp(-φ/219.6)-22×exp(-φ/7.3), where λ(φ) (nm) is the amount of blue shift and φ (%) is the RH. By calculating the slope of this fitting curve at 7% RH, we obtain the maximum RH differential sensitivity, which can reach 1.28 nm per % RH. This result is higher than the recent records of 0.19 and 0.57 nm per % RH in a single nanoparticle based sensor 8,9 . The sensitivity reduces as the RH increases, which could be a combination of factors. First, as we have demonstrated (Fig. 2 in the main text) the vertical differential resolution of the Au-NWOM decreases as the thickness of the PVP spacer (gap distance) increases due to the water adsorption. Second, as the RH increases, water absorption of the PVP is gradually saturated: it becomes increasingly difficult to 'insert' more water molecules into the ~2 nm thick PVP spacer.

Supplementary Note 4. Vertical differential sensitivity of the nonparallel NWOM nanocavity
To clarify what happens when the surface of the analyte spacer film inside the NWOM is irregular, we simulate the gap distance dependent cavity plasmon resonance of a Au-NWOM with respect to the nanocavity tilt angle θ ( Supplementary Fig. 11). In Supplementary Fig. 11b, the gap distance is defined as gMin ( Supplementary Fig. 11a), which is the minimum value of the gap distance between the nanowire and the mirror. The results suggest that the nonparallel nanocavity can also support the cavity plasmons but shows lower vertical differential sensitivity, and the larger the tilt angle θ the lower the sensitivity. The sensitivity reduction effect originates from the increase in the average gap distance gAvg as the tilt angle θ increases, where gAvg is defined as the distance between the center of the nanowire bottom surface and the mirror ( Supplementary Fig. 11a). If gMin is replaced by gAvg, as shown in Supplementary Fig. 11c, the conclusions are the opposite: the larger the tilt angle θ, the higher the sensitivity, while the minimum value of the average gap distance also becomes larger. In general, for a small tilt angle θ (smaller than 5°), the nonparallel geometry will not have any significant influence on the sensitivity. For a large tilt angle θ (significantly larger than 5°), the effective gap distance between the two non-parallel surfaces is large compared with the parallel case, given that the minimum value of the gap distance is fixed. This prevents a non-parallel NWOM configuration from working in the small gap region and therefore limits the maximum possible sensitivity.