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The low quality factor (Q-factor) of the localized surface plasmon resonance (LSPR) is a significant barrier for further progress of LSPR-based devices. Therefore, we investigate the effect that materials typically used in the nano-fabrication process have on the LSPR wavelength and Q-factor in order to find avenues of improvement. Specifically we investigate the influence of charge dissipation and adhesion layers upon the LSPR of linearly polarizing nano-antennas and show that a simple quasi-static model can be used to describe such systems.
© 2015 Optical Society of America
1. Introduction
Recent advances in the manipulation of electromagnetic fields and light far beyond the diffraction limit have been used to achieve sub-wavelength imaging [1] and spectroscopy of nanometer-sized sample volumes [2, 3]. Such techniques also show promise in the creation of novel chemical sensors [4, 5] and improvements to the light-matter interaction of quantum emitters while preserving their non-classical light emission properties [6, 7]. Central to such manipulation of electromagnetic fields at near infrared and visible frequencies is the surface plasmon and its localized version, the localized surface plasmon (LSP) that can be created in a plasmonic cavity. The plasmon cavity of the simplest geometric configuration is of Fabry-Perot type and resembles a cylinder or rotation ellipsoid, which is well described by Mie theory [8] in the quasi-static regime [9–11]. Other cavity geometries, such as the surface plasmon polariton microdisk whispering gallery mode resonator [12], have also been pioneered.
Though plasmon resonators show great promise for many applications, their performance is limited by their constituent materials. Particularly the plasmonic cavity’s resonance behavior shows a strong dependence on the cavity geometry, the dielectric function of the cavity material and materials in its vicinity. The cavity geometry and in some cases also the metal dielectric function are used as design parameters [13], while the material in the vicinity of the cavity, at best, is used to modify its behavior for sensing applications.
However, the manufacturing process may demand the use of materials that dampen the LSP, such as a thin titanium (Ti) or chromium layer to promote adhesion of gold (Au) or silver (Ag). When using electron beam lithography (EBL) as a means of nano-fabrication on non-conducting samples, one also requires a thin discharge layer to prevent charge buildup. These materials, depending on the further processing steps, may not be removed and their overlap with the cavity field will determine the losses and thus the Q-factor as well as the shift of the LSPR frequency. These limits upon the Q-factor represent a major obstacle for the progress of LSP devices and must be overcome.
In order to improve the performance of LSPR-based devices, it is therefore necessary to understand and predict the influence that device geometry, constituent materials and environmental factors have upon the LSPR. We propose that adhesion and charge dissipation layers, commonly used in the nano-fabrication process, severely impact the Q-factor of the LSPR and require further investigation. In this work, we therefore measure the effect that discharge layers have on the LSPR wavelength λ0 and the Q-factor of linearly polarizing dipole nano-antennas on quartz glass substrate. We choose linearly polarizing nano-antennas for our investigation as they represent a simple form of a plasmonic cavity and our characterization technique requires linearly polarizing structures. We further investigate the effect that a Ti adhesion layer has on antenna performance and will show the increasing deterioration of the LSPR with increasing adhesion layer thickness. The measurement of λ0 and the Q-factor of linearly polarizing Au dipole nano-antennas is carried out by means of rotating polarization spectroscopy (RoPoSpec) [14]. We also apply effective material models to predict the influence these material configurations have upon antenna performance in the quasi-static regime and show good agreement with our measurements.
2. Methods
In this work we focus on Au antennas as they are stable under ambient conditions over long periods of time. The fabrication of these antennas is performed with EBL. To fabricate the antennas, we use clean quartz glass substrates and evaporate 5 nm of Ge on the sample surface to eliminate surface charging and subsequent distortion of the exposed structures. Typically the charge dissipation layer is made by evaporating gold, chrome or aluminum onto the resist stack [15, 16]. We use Ge instead, as it is readily removed with hydrogen peroxide (H2O2) and is most compatible with our process. Furthermore, Ge does not support plasmons in the near infrared and therefore is expected to interfere less with antenna performance when left in the vicinity of the antennas. We also found that by placing the Ge discharge layer beneath instead of above the 150 nm thick resist layer, the resolution of the exposure process was significantly improved. As a consequence, it can be expected that in some processes Ge must be left on the sample and will alter antenna functionality. In order to prevent this, we usually dip the developed sample into a 50:1 mixture of H2O : H2O2 for 10 s. This removes the Ge in the poly(methyl methacrylate) (PMMA) resist openings, leaving a clean glass substrate for the antennas to be fabricated upon.
To promote adhesion, typically a thin layer of Ti is evaporated before the Au evaporation step. To study the effects of Ti on antenna performance, we prepared five samples with 1 to 5 nm thick Ti layers in 1 nm increments. The deposited layer thickness is determined with a piezo evaporation rate sensor placed next to the sample in the evaporation chamber. Once the Ti layer is fabricated, another 40 nm of Au are evaporated at a rate of 0.1 nm/s. Lift-off is carried out in N-ethyl-2-pyrrolidone. This leaves Au antennas surrounded by Ge as shown in Fig. 1(e). The remaining Ge is still useful as it provides a discharge layer when investigating the structure sizes with a scanning electron microscope (SEM). The Ge layer can easily be removed in a final peroxide dip when it is no longer needed. A schematic of the sample fabrication steps can be seen in Fig. 2.
Fig. 1 The schematic of the RoPoSpec setup is shown in (a). The measurement principle relies on placing the individual signal components at different electronic frequencies that are subsequently measured by a lock-in amplifier. The rotating half-wave plate (RHWP) rotates at a frequency ω0 which rotates the polarization angle at ω1 = 4ω0 where the extinction signal Iant is measured. The optical chopper operates at ω2 at which the laser intensity Iref is determined. From these signals, the extinction cross-section of the nano-antennas in the beam’s focus (dFWHM = 1.4 μm) is calculated [14]. The corresponding electronic spectrum, which is measured with the silicon photodiode (Si PD), can be seen in (b). An AFM scan of a typical Au antenna is displayed in (c). Panel (d) shows the calculated resonance Q-factor of prolate ellipsoids in the quasi-static approximation plotted over the corresponding LSPR wavelength λ0 for Au and Ag. The material data were sourced from Johnson and Christy [17]. The Figs. (e) to (h) show the different sample geometries used in the measurements. Panel (f) is representative for the five samples with Ti layer thicknesses varying from 1 to 5 nm. The Au layer is kept constant at 40 nm thickness and the Ge layer is kept at 5 nm. The antennas are designed to be 30 nm wide with varying arm lengths and a constant gap of 20 nm. Arrays of 8 × 8 antennas with a 500 nm pitch were used in all experiments.
Fig. 2 A schematic of the fabrication process used for Au and Ag antennas (a). The main difference between Au and Ag antenna fabrication is depicted in step 3 where the Ge layer must be removed prior to metalization. The resulting metal structure contains 9 antenna arrays with varying arm lengths centered in 10 μm allignment apertures (b). SEM images of typical antenna arrays are shown in panels (c) and (d) while panel (e) shows an atomic force microscope scan of a 1×1 μm field.
To investigate the effect Ge has on antenna performance, we fabricated three further samples. On the first sample Ge is never removed and Au antennas are evaporated directly onto the Ge layer as shown in Fig. 1(f). For the second sample the final peroxide dip is not performed, leaving Au antennas surrounded by a Ge layer resembling Fig. 1(e). The third sample was prepared with both peroxide dips and resembles Fig. 1(g). The five samples containing a Ti adhesion layer are also finalized with a peroxide dip and finally resemble Fig. 1(h). All samples contain antenna arrays with antenna arm lengths L ranging from 120 to 200 nm in 10 nm increments. The antennas’ design height, width and gap are kept at 40 nm, 30 nm and 20 nm respectively. Each array consists of 8 × 8 same-sized antennas spaced 500 nm apart from each other to improve the signal-to-noise ratio of the extinction signal. An AFM scan of a representative antenna is shown in Fig. 1(c).
Finally, a Ag antenna sample was prepared with antenna lengths ranging from 140 nm to 220 nm to compare with Au antennas. The fabrication process of the Ag antennas must be altered such that the Ge is removed before Ag metalization as the H2O2 would oxidize the Ag and thus degrade the antennas. To this end, the exposed but not yet developed sample is placed in 35% H2O2 for 180 s which diffuses through the PMMA [18] and dissolves the Ge. The sample must be carefully rinsed and dried before it can be developed and metalized. An overview of all the used samples is provided in table 1.
Table 1. Listing of the antenna material, adhesion layer (AL), dissipation layer (DL) and environment configuration of all samples used in this work.
The fabricated antenna samples were measured with a RoPoSpec setup. To this end a Spectra Physics S3900 Ti:Sapphire (Ti:S) laser that is tunable from 850 nm to 990 nm is stepped through its spectral range and its linear polarization is rotated by a rotating half-wave plate (RHWP), which is positioned in the beam path just before the objective lens. The polarization is rotated at a frequency of ω1 = 124 Hz. When linearly polarizing antennas are placed in the beam, the beam’s intensity is modulated proportional to the antenna’s extinction cross-section at the frequency ω1 giving Iant. The beam’s intensity Iref is measured by further optically chopping the beam at a frequency ω2 = 318 Hz. From these two amplitudes the extinction cross-section can be quantified. The general measurement scheme as well as the measured electronic spectrum are illustrated in Fig. 1(a) and 1(b). For further details on the RoPoSpec setup we refer to previous work [14].
To understand the impact of the various sample compositions, the measured spectra are least squares fitted with a Lorentzian function to extract λ0 and the full width at half maximum (FWHM) Δλ. Spectra with a λ0 outside the spectral range of the Ti:S laser (850 to 990 nm) as well as spectra with Δλ > 250 nm were excluded as such fits are considered to be unreliable. As the measurements were carried out with a spectral resolution Δλm of 1 and 2 nm, the fitting parameter errors are negligible. The fitting error of the Lorentzian function parameter x ∈ {A, λ0, Δλ} is estimated with [19]
The ratio of the fitted Lorentzian amplitude A and the standard deviation σe of the differences between the measurement data and the fitted function determine the signal-to-noise ratio SN0 = A/σe. The coefficients for calculating the uncertainties SA, Sλ0 and SΔλ are , and as given by [19]. The error for the Q-factor is calculated via error propagation and is plotted where applicable. A larger source of uncertainty stems from the fabrication accuracy which depends on the amount of exposure as well as aliasing errors and EBL resolution. Furthermore, fabrication defects and lift-off of some antennas or parts thereof also cause uncertainty in Δλ and λ0 as well as A. The effect of these uncertainties is reduced by the use of antenna arrays as opposed to single antennas. This, however, broadens the LSPR spectrum which increases the FWHM Δλ and thus effectively lowers the Q-factor.3. Experiment and discussion
As the relationship between the antenna’s arm length L and λ0 is of interest when designing antennas for specific applications and the antenna’s performance is most easily shown by its Q-factor, we measure the spectra of all antenna arrays on the fabricated samples and extract λ0 as well as Δλ for the following analysis.
The measured LSPR peak wavelength λ0 is plotted over the corresponding antenna arm length L to illustrate the scaling red-shift while the Q-factor Q = λ0/Δλ is plotted over corresponding values of λ0 to gain a Q-factor spectrum. Figs. 3(c) and 3(d) show λ0 increasing with L and the Q-factor spectrum for Au on Ge, Au and Ag as well as Au fabricated on Ge after the Ge was stripped. The advantage of Ag over Au is as obvious as its shortcoming is: Ag antennas can be fabricated larger than Au antennas to achieve the same λ0. Unfortunately, Ag also falls far short of the expected Q-factors displayed in Fig. 1(d). This may be due to mask distortions during the Ge oxidation and dissolution process as well as further exposure to ambient oxygen during the post-metalization processing and handling steps. The Q-factor of Au is on average also a factor of two smaller than expected. This is due to fabrication tolerances as well as the surface roughness of the evaporated metal which gives a broadened single-antenna and antenna-array spectrum and thus a lower Q-factor [20].
Fig. 3 (a) and (c) show the change of the LSPR peak wavelength for increasing antenna arm lengths while (b) and (d) show the Q-factor for the corresponding LSPR peak wavelength. (a) and (b) illustrate the shift in LSPR properties when the Ge discharge layer surrounding the Au antennas is removed. The green curve (Au, Ge) represents Fig. 1(e) and the blue curve (Au) represents Fig. 1(g). (c) and (d) show the LSPR behavior for Au on an uninterrupted Ge layer (Au/Ge, fig. 1(f)) and the Au/Ge sample stripped of Ge. Also pure Ag and Au antennas are shown. The error bars in the LSPR over antenna length L curves represent the standard deviation of the measured LSPR peak wavelength over several antenna samples. The error bars in the Q-factor curves represent the fitting errors’ cumulative propagated contributions to the Q-factor.
The Au/Ge curves represent Au antennas on an uninterrupted 5 nm thick Ge discharge layer. The most striking feature of these antennas is the large red-shift in λ0 for same-sized antennas. Due to the strong red-shift, most antennas’ LSPRs were shifted beyond 990 nm and could not be accurately determined. Furthermore, Q-factors for wavelengths below 920 nm could not be determined, as none of the fabricated antennas had a LSPR peak below 920 nm. When the Ge layer is removed by a 60 s dip in 35% concentrated H2O2, the LSPR strongly blue-shifts. However, the original pure Au LSPR is not entirely recovered. This may be due to residual Ge-oxides attached to the bottom of the Au antennas as well as the larger surface roughness of the antennas as they were fabricated on Ge instead of the smoother glass surface – which explains the Q-factors remaining low as well.
Figures 3(a) and 3(b) compare pure Au samples with pure Au samples where the surrounding Ge discharge layer has not yet been removed. As there is no Ge beneath the antennas, their Q-factors are comparable. However, the Ge layer surrounding the antenna represents a modification of the environment and increases the effective ambient permittivity causing a red-shift.
Figures 4(c) and 4(d) illustrate the effect a Ti adhesion layer has on the antennas’ Q-factor and LSPR wavelength. The error bars in the graph represent the standard deviation of the measured Q-factors within the observed spectral window of 850 to 990 nm. The effect the Ti layer has on the Au antennas is different to Ge as it only causes a significant increase in the imaginary component of the permittivity, thus increasing losses and lowering the Q-factor without causing a significant shift to the antenna’s λ0. The measured Q-factors also peak at values of 8 to 10, which indicates an interplay of two limiting effects on the antenna’s Q-factor. For thin Ti layers of up to 3 nm, the Q-factor is limited by the surface roughness of the evaporated Au layer while at 4 nm and above the losses caused by the Ti adhesion layer become dominant.
Fig. 4 (a) shows the calculated average Q-factor of the LSPR for Ti adhesion layer thicknesses of 1 to 5 nm and (b) shows the corresponding calculated LSPR peak wavelength for increasing antenna arm lengths. A clear deterioration of the Q-factor is observed for increasing amounts of Ti while the LSPR peak wavelengths barely change. The error bars show the standard deviation in Q-factor values over the observed spectral window of 850 nm to 990 nm. Pannels (c) and (d) show the measurements corresponding to the calculated curves in panels (a) and (b). The calculations are carried out with the same model used to produce Fig. 5(c) and 5(d).
The behavior of our antenna samples is reproduced by calculations in the quasi-static regime of Mie’s theory with the prolate ellipsoid extension [9]. We use the Maxwell Garnett approximation [21]
for a volume density determined by the ratio of the layer thicknesses of Ge in Au as δ = dGe/dAu to model the antenna’s effective material. A linear combination of vacuum, quartz glass and Ge with respective weighting factors of a = 0.4925, b = 0.4925 and c = 0.015 is used to describe the antenna’s environment [22]. The weighting factors are estimated by the volume proportion of a 250 nm radius sphere composed of vacuum, glass and a 5 nm Ge layer separating the vacuum and glass hemispheres. The sphere roughly approximates the near field region of the antenna. The method as described by Gluodenis and Foss [11] is then used to calculate the LSPR shape with the effective medium data. In the calculation, the antennas are given a constant width of 30 nm and a 30 nm gap while the antenna lengths are increased from 120 to 200 nm. The results are shown in Fig. 5 and qualitatively reproduce the experiment’s results. Numerical data for the dielectric function of Au and Ge were sourced from [17] and [23] respectively. For quartz glass, data from [24] were used.Fig. 5 The individual dielectric functions of Au and Ge are plotted in (a) and (b). The Maxwell Garnett approximation of 40 nm of Au on 5 nm of Ge is illustrated in blue (Au/Ge). (c) and (d) show simulation results for antennas of shape and size similar to the ones measured to produce Fig. 3.
The effective dielectric function of combined Au and Ge, as shown in Fig. 5, exhibits a less negative real component, which causes a strong red-shift of the LSPR. Within the spectral region of 850 and 1000 nm also the imaginary component of the dielectric constant increases, which lowers the Q-factor. It is noteworthy, however, that the imaginary component of the Au/Ge system crosses the pure Au line and exhibits lower losses at wavelengths of 1010 nm and larger. Unfortunately we are not able to probe beyond 990 nm with our system and therefore cannot access this particular cross-over point. The environment of the antenna also plays a role as the Ge layer increases the environment’s real permittivity component while only slightly increasing the imaginary component. This leads to a red-shift of the LSPR for same-sized antennas.
For the uninterrupted Ge layer case, the effective antenna as well as the effective environment media effects must be added, which leads to the observed strong red-shift as well as the lower Q-factor. For the case where Ge is surrounding the antenna, only the effective medium of the environment must be used, thus leading to a less prominent yet noteworthy red-shift of the LSPR. The qualitative behavior of Au/Ti structures is also reproduced by the simulations with this model, however, the predicted Q-factors are better than the measured values for layers thinner than 3 nm. Figures 4(a) and 4(b) illustrate the calculated average Q-factors that result from the Maxwell Garnett approximation of Au/Ti and the corresponding LSPR wavelength shift over antenna arm length. The error bars displayed in the calculated curve in Fig. 4(a) represent the standard deviation of Q-factors within the observable spectral window of our setup. The model reproduces the small redshift for increasing Ti content well. However, a small and increasing difference in the predicted and measured LSPR wavelengths is observed. This error increases as the fabricated antenna sizes approach the limit of the underlying quasi-static model. The calculations were carried out for antennas that are similar in size and shape to the ones measured in Figs. 4(c) and 4(d). For Ti, material data from [25] were used.
4. Conclusion
In this work, we measured the LSPR and Q-factor of pure Au nano-antenna arrays, arrays on uninterrupted Ge discharge layers, arrays surrounded by a Ge discharge layer and the effect of increasing Ti adhesion layer thickness. We found that the strongly red-shifted LSPR of Au antennas fabricated on Ge layers could largely be recovered by rinsing in H2O2. We also found that adhesion layers, which are commonly used in micro- and nano-fabrication, should be avoided to preserve antenna performance. Finally we were able to qualitatively describe the behavior of the nano-antennas with a well-known simple quasi-static Mie model combined with the Maxwell Garnett approximation to describe the effective material of the antenna. Though the Maxwell Garnett model gives good results, its applicability must be investigated further. In our opinion, this model has proven useful as it gives quick and reliable results which are computationally inexpensive to achieve. We expect that the results from the material systems we investigated with the aid of our presented model may be used to estimate the effects that other materials in such geometric configurations will have upon the LSPR.
Acknowledgments
This work was partly supported by the Austrian Science Fund FWF (SFB IR-ON and DK CoQuS). We also want to acknowledge the many fruitful discussions with Juraj Darmo and Vincent Paeder.
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