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Abstract
This study investigates the effect of thermal annealing on the surface plasmon resonance properties of gold and silver nanodisk structures fabricated by electron beam lithography. Despite no significant size change due to a nickel adhesion layer, thermal annealing at 500 °C notably altered surface plasmon resonance properties, especially in gold nanodisks, which showed peak blue-shifts and narrowing, indicating improved crystallinity. We fitted the peak shift by using an electromagnetic field analysis and discussed the changes in the dielectric function. The dielectric function of the simple Drude model was adopted, which was fitted to the values of the Lorentz Drude model in a limited wavelength region. While both silver and gold exhibited increased oscillation strength, only gold nanodisk structures showed a decrease in damping frequency. Increased oscillation strength indicated that these structures should be useful for selective enhancement of the light at specific wavelengths by a very simple heat treatment.
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1. Introduction
Localized Surface Plasmon Resonance (LSPR) involves the plasma oscillation of free electrons in metal nanostructures, which resonate with light waves. In recent years, LSPR has been actively studied in various fields, including enhancing the emission efficiency of quantum dots [1–3] and quantum wells [4–6], detecting chiral structures [7–9], gas sensing [10–12] and cell imaging [13–15]. Notably, gold and silver, which exhibit LSPR in the visible light region, can enhance light at various wavelengths through tuning the resonance spectra. Since the resonance spectra can be tuned by changes in size and shape of nanostructures and utilizing dielectric materials, wide variety of structures have been studied including nanoparticles [16,17], nanohemisphere [18,19], nanorod [20,21] and nanodisk [22,23]. Among them, nanostructures fabricated by Electron Beam Lithography (EBL) have periodical structures with precisely controlled size and shape, resulting in sharp LSPR peaks [24,25]. Therefore, they are expected to be applied to selective light enhancement at specific wavelengths or colorimetric sensor. While sharp LSPR peaks with large scattering cross-sections are desirable, they are often compromised by plasmon damping, attributed to evaporation or lithographic process and adhesion layers [26,27]. In our previous study, we annealed nanodisk structures fabricated by EBL to improve the plasmon properties [28]. Significant differences in the LSPR peak shifts were observed between gold and silver even when there were minimal changes in size and shape, due to the presence of Ni adhesion layers. In silver nanodisk structures, the LSPR peak shifted toward short wavelength side while retaining its sharpness. Conversely, gold nanodisk structures exhibited peak narrowing accompanied by a blue shift. This suggested that metal’s quality needed improvement since these LSPR peak shifts could not be solely attributed to changes in size. We investigated the mechanism behind the improvement in crystallinity through thermal annealing, which led to enhanced performance in various devices utilizing LSPRs.
LSPR peaks can be predicted through numerical simulations, such as Finite Difference Time Domain (FDTD) method [17–19], by using the dielectric functions of the metals. The dielectric function has been described in various models including the Drude model [29,30], the Lorentz Drude (LD) model [31,32] and the critical point model [33,34]. In the low-frequency region of the spectrum, the Drude model shows good agreement with experimental data. At the same time, the LD model, consisting of the Drude model and several Lorentz terms, is preferred for energies above the interband transitions [29,31]. The LD model is considered an appropriate model for gold and silver because of the interband transitions at or near visible light region. However, the complex expressions of the formulas negatively impact the peak simulations, leading to longer calculation times and increased processing capacity.
In this study, we employed the Drude model adjusted to the values of the LD model for the dielectric function of gold and silver, focusing on a limited number of spectrum regions. The validity of the model was evaluated by FDTD simulations. Subsequently, we applied the Drude model to fit the LSPR peak shifts induced by thermal annealing and explored the differences in the annealing effects between silver and gold nanodisk structures.
2. Methods
2.1 Material model
First we briefly discuss the models of the dielectric function of metals. The Drude model is derived by solving the equation of motion for a free electron subjected to an oscillating electric field as follows:
LD model is described by the following form, incorporating the Lorentz terms representing interband transitions:
2.2 Calculations
FDTD simulations were conducted with commercial software (Poynting for Optics, Fujitsu, Japan). The periodic boundary condition was set in the X and Y directions, and the absorption boundary condition was set in the Z direction. A pulsed light composed of a differential Gaussian function with a pulse width of 0.3 fs and an electric field of 1 V/m was irradiated under an X-polarized source. The peak position on the spectrum of the excitation pulse was approximately 600 THz (500 nm wavelength). A nonuniform mesh of 0.1–1.5 nm grid size was used for the simulations. The refractive index of the glass was set at 1.5 without dispersion. The dielectric function of Ag and Au was set at the reported values of the LD model [32]. By using the LD model and the Drude model with simply omitted Lorentz terms from the LD model, LSPR peaks of the nanodisk structures were examined in a wide spectrum region. Subsequently, ${\varepsilon _\infty }\; \textrm{and}\,{\varGamma _d}$ of the Drude model were optimized in the visible light region to fit the LD model. Finally, we accurately fitted the LSPR peak shifts of nanodisk structures due to the thermal annealing by employing the adjusted Drude model.
2.3 Experiments
Nanodisk structures were fabricated by EBL and resistance heating evaporation. In this paper, we briefly explain the experimental procedure for fabricating. The cover glasses (No. 3, Matsunami Glass Industry) were ultrasonically cleaned with acetone and ultrapure water, and ZEP 520A (Zeon Corporation) resist was spin-coated onto them followed by baking on a hot plate at 180°C. Subsequently, Espacer 300Z (Showa Denko K.K.), a charge dissipating layer, was spin-coated and baked at 100°C. Electron beam exposure was performed using an EBL system (ELS-7500EX, Elionix) according to the digital pattern of the periodic nanodisk structure created by AutoCAD (Autodesk) with a writing area of 300${\times} $300 µm. After exposure, the sample was soaked in ultrapure water to remove the Espacer 300Z, developed with xylene and rinsed with IPA. After development, Ni was deposited as an adhesion layer followed by Au or Ag by resistance thermal evaporation (SVC-700TM, Sanyu Electron), and lift-off was performed in a 2-butanone, followed by rinse with IPA. Annealing of the samples was performed in an electric furnace under air atmosphere for 10 min. The details are described in our previous report [28]. Extinction spectra were analyzed by an optical microscope (BX51, Olympus) and a xenon lamp (BPS-X150B, Bunkoukeiki), and the surface structure was evaluated by a scanning electron microscope (SEM) (FlexSEM 1000 II, Hitachi High-Tech). The simulation reproduction of the peak shifts induced by thermal annealing was conducted by optimizing the oscillation strength (OS) and damping frequency (DF) in the dielectric function of the Drude model for the nanodisk structures of the same size as the fabricated ones.
3. Results and discussion
3.1 Investigation of the validity of the Drude model
We conducted the FDTD simulations of silver nanodisk structures with a height of 30 nm and a radius of 50 to 90 nm. The model size was set to 200 ${\times} $ 200 nm. Figure 1(a) and (b) show the extinction spectra using the dielectric function of the LD model and the Drude model derived from the LD model by eliminating the Lorentz terms. The variation in the size enabled comprehensive comparison of LSPR peaks over a wide range of the visible light spectrum. Figure 1(c) shows the LSPR peak positions of silver nanodisk structures with a height of 10 to 40 nm and radius of 50 to 90 nm. Simulations using the LD model required a computational time that was 6 to 15 times longer than simulations using the Drude model, depending on the size. There were significant differences in both models over the entire visible light spectrum. The LD model exhibited the broader LSPRs in the longer wavelength side. This indicates that not all electrons can precisely follow the oscillation of the incident electric field since energy loss due to the interband transitions in the ultraviolet spectrum region extends to the visible light. Therefore, we cannot conduct accurate simulations without considering interband transitions even in the absence of such transitions within the visible light range.
Fig. 1. The simulation results of silver nanodisk structures with radius r and height d. Simulated spectra using the LD model (a), using the Drude model derived from the LD model (b), and peak positions varying radius and height (c).
Figure 2(a) shows the real and imaginary parts of the dielectric function of both models. They exhibited significant differences in the entire visible light region. The real part influenced the LSPR peak positions while the imaginary part affected the peak intensity. We optimized ${\varepsilon _\infty }\; \textrm{and}\,{\varGamma _d}$ in the Drude model throughout the visible light region to fit the LD model. Figure 2(b) shows the LSPR peak using the dielectric function of the LD model and the adjusted Drude model. The values ${\varepsilon _\infty } = 3.41,\textrm{ and }{\varGamma _d} = 25.5$ THz were adjusted, while the literature values [32] for ${f_d} = 0.845,\; {\omega _p} = 2.18 \times {10^3}$ THz remained the same. Within the visible light spectrum, both the real and imaginary part exhibit nearly identical values. Figure 2(c) and (d) show simulation results of silver nanodisk structures using the LD model and the adjusted Drude model respectively. The height of the disks was set to 30 nm with a radius of 50 to 90 nm. LSPR peaks calculated by using both the LD model and the adjusted Drude model exhibited remarkable similarity. Consequently, we achieved accurate LSPR peak simulations within the visible light region, significantly reducing the calculation time. In this study, we employed simple disk structures with minimal metal volume. The utilization of larger or more complex metal structures should lead to a reduction in both time and processing capacity by several tens. As a result, it could become feasible to conduct multiple simulations with finer grids simultaneously.
Fig. 2. Dielectric function of silver approximated by the LD and the Drude model before fitting (a), and after fitting (b). ${\varepsilon _1}$ and ${\varepsilon _2}$ represent the real and imaginary parts respectively. The simulated spectra of silver nanodisk structures with height of 30 nm, radius r of 50 to 90 nm using the LD model (c), and using the adjusted Drude model (d).
It is challenging to fit the dielectric function of gold over the entire visible spectrum using the Drude model due to the interband transition in the visible light region. However, restricting the fitting spectrum range enabled successful fitting with the Drude model. Figure 3(a) shows the results of fitting the dielectric function using the same method as for silver. The values ${\varepsilon _\infty } = 5.60,\textrm{ and }{\varGamma _d} = 44.9$ THz were adjusted, while the literature values [32] for ${f_d} = 0.76,\; {\omega _p} = 2.18 \times {10^3}$ THz remained the same. The dielectric function of both models closely matches for about 100 nm around the central wavelength of 700 nm. Figure 3(b) and (c) show the simulation results of gold nanodisk structures using the LD model and the adjusted Drude model respectively. The height of the disks was set to 20 nm with a radius of 50 to 90 nm. From these figures, calculations with the adjusted Drude model are considered to be valid for radius from 50 to 70 nm. Optimizing ${\varepsilon _\infty }\textrm{ and }{\varGamma _d}$ to adjust the central wavelength enables precise simulation of LSPR peaks across a wider range of the spectrum. Therefore, this method would facilitate the use of the Drude model to fit the dielectric functions of other metals, resulting in accurate simulations comparable to the LD model within a considerably short time.
Fig. 3. (a) The dielectric function of gold approximated by the LD model and the Adjusted Drude model. ${\varepsilon _1}$ and ${\varepsilon _2}$ represent the real and imaginary parts respectively. The simulated spectra of gold nanodisk structures with height of 20 nm, radius r of 50 to 90 nm using the LD model (b), and using the Adjusted Drude model (c).
3.2 Annealing effect of nanodisk structures
We previously found that in silver and gold nanodisk structures fabricated by electron beam lithography and deposition, thermal annealing induces a blue-shift in the LSPR peak. The observed peak shifts were attributed to the improved crystallinity since the Ni adhesion layer prevented deformation of the disks. However, nanodisk structures exhibited strong scattering and surface roughness. Even in the case of films, surface irregularities were present after deposition, resulting in the formation of random hemisphere structures by thermal annealing. Evaluating materials with strong scattering or surface roughness is challenging using ellipsometry [35,36]. Instead, we evaluated the annealing effect through the dielectric function with the adjusted Drude model. This simple method allows for the interpretation of the crystallinity by examining the dielectric function changes, even though it can not determine its absolute value.
Figure 4(a) shows the SEM images of silver nanodisk structures with a Ni height of 2 nm and an Ag height of 40 nm before and after annealing. Figure 4(b) also shows the particle size analysis results of SEM images. In the case of silver nanodisk structures, the radius slightly decreased from approximately 55 to 50 nm by thermal annealing. Figure 4(c) and (d) show the extinction spectra in the experiment and in the simulation considering only the size changes respectively. We limited the annealing temperature to 300 °C to prevent significant reduction in the extinction spectrum observed at higher temperatures. In the experiment, the LSPR peak shifted towards the short wavelength side while maintaining its intensity to some extent. This phenomenon was not reproducible in simulations only considering the size or shape changes. Therefore, we optimized the dielectric function of the silver nanodisk structures to fit the LSPR peak shifts. When we assumed that background factors such as electron transitions and effects of electrons that were not focused on remained relatively unchanged, two parameters, OS and DF, could be considered. We know that increasing the OS leads to a blue-shift in the peak, whereas increasing the DF results in the peak broadening while maintaining the peak position. The details are shown in Figure S1. The LSPR peak position and Full Width at Half Maximum (FWHM) can be determined solely by the OS and the DF in the Drude term.
Fig. 4. Experimental results of silver nanodisk structures with Ni height of 2 nm and Ag height of 40 nm. SEM images (a), radius with the error bar representing standard deviation (b) and extinction spectra before and after annealing (c). (d) Simulated spectra with different radii.
Figure 5(a) shows the simulations results considering the size and the dielectric function changes. The slightly higher intensity compared to the experimental results could stem from the absence of certain structures or potential morphological changes. A detailed discussion on morphological changes is presented in Fig. S2 and Fig. S3. Figure 5(b) and (c) respectively show the peak positions and the FWHM, and OS and DF for the simulations. Results using the LD model are also included to exhibit the validity of the adjusted Drude model. Figure 5(c) reveals an increase in OS due to thermal annealing. The improvement of metal quality due to thermal annealing is associated with an increase in OS and a decrease in DF [37,38]. The reduction of the grain boundaries could promote the collective electron oscillations, leading to an increase in OS [37]. However, this effect appeared to be small since the DF was almost unchanged. Considering that the OS is a coefficient of the plasma frequency, these changes in the dielectric function imply an increase in the density of free electrons. In silver nanodisk structures, thermal annealing could induce the reduction of the defects, allowing the previously trapped electrons to participate in the collective oscillation. The enhancement of the OS also means an increase in the real part of the dielectric function. Therefore, thermal annealing could contribute to a significant increase in scattering intensity.
Fig. 5. The reproduction of the LSPR peak shifts of silver nanodisk structures by thermal annealing. Extinction spectra (a), peak positions and FWHM (b), and OS and DF used in the fitting (c).
Figure 6(a) and (b) show the SEM images and extinction spectra of Au nanodisk structures respectively. The radius of the disks was 83 nm with a Ni height of 2 nm and an Au height of 20 nm. Even at an annealing temperature of 500 °C, there were no discernible changes in size due to the effect of the Ni adhesion layer. In contrast to the silver nanodisk structures, thermal annealing resulted in not only a blue-shift but also in the narrowing of the peak with no significant change in size and shape. The peak shifts exhibited the saturation at a heating temperature of 500 °C. We also fitted the peak using the same method as for the silver nanodisk structures. Figure 7(a) and (b) show the results of fitting, the peak positions and the FWHM respectively. Despite the interband transition in the visible spectrum region for gold, the accuracy of peak simulations using the adjusted Drude model was comparable to that of the LD model. Figure 7(c) also exhibits the values of the OS and the DF. In the gold nanodisk structures, thermal annealing resulted in a decrease in DF along with an increase in OS. Considering that DF is the inverse of the relaxation time, a decreased DF indicated an increase in the mean free path of free electrons. We consider that this was due to the reduction of the grain boundaries within the single nanodisk structures by thermal annealing [37,39]. According to the Drude formula, an increase in relaxation time implied an increase in conductivity, but measuring this in a nanodisk was challenging due to its size. Moreover, the substantial increase in OS suggested that, along with the reduction of grain boundaries, the number of defects trapping free electrons was decreased.
Fig. 6. The experimental results of gold nanodisk structures with radius of 83 nm, Ni height of 2 nm and Au height of 20 nm. Extinction spectra (a) and SEM images (b) before and after annealing.
Fig. 7. The reproduction of the LSPR peak shifts of gold nanodisk structures by thermal annealing. Extinction spectra (a), peak positions and FWHM (b), and OS and DF used in the fitting (c).
4. Conclusion
We demonstrated that simulations using the adjusted Drude model were accurate and several times faster than those using the LD model in the limited spectrum region. This method could be used for other metals with interband transitions in the visible spectrum region. We also evaluated the effects of thermal annealing on silver and gold nanodisk structures fabricated by EBL and deposition. By thermal annealing, OS increased in silver nanodisk structures while the DF decreased accompanied by an increased OS in gold nanodisk structures. Thermal annealing had the potential to lead to the reduction of defects in silver and a decrease in both grain boundaries and defects in gold. Considering the decrease in extinction spectrum due to size reductions, annealing temperatures of 300 °C for silver and 500 °C for gold are deemed suitable to efficiently improve plasmonic properties. Without the Ni adhesion layer, in addition to improved plasmonic properties, the blue-shift due to size reduction allows for a wider range of tuning of resonance wavelengths. Thermal annealing-induced tuning of sharp LSPR peaks across a broad range of visible light wavelengths is expected to be applied to various applications, including more efficient emission enhancement for each wavelength and the development of color sensors. Moreover, the enlargement of the scattering-cross section due to the increased OS is particularly advantageous for enhanced emission, offering potential solutions to energy-related issues such as efficient RGB emission enhancement.
Funding
Japan Society for the Promotion of Science (JP20K04521, JP19H05627, JP20H05622).
Acknowledgments
The author wish to thank Prof. K. Tamada of Kyushu University, Prof. Y. Kawakami, and Prof. M. Funato of Kyoto University for valuable discussions and support.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data supporting the findings of this study are available from the corresponding author upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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