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Abstract
A structured SERS substrate with high uniformity and sensitivity was fabricated orderly by hydrophilizing the monocrystalline silicon substrate, self-assembling a layer of dense polystyrene (PS) microsphere array on the silicon, and depositing a layer (5 nm, 10 nm, 20 nm, 30 nm or 50 nm) of silver film. Rhodamine 6G (R6G) was used as a probe to characterize the performance of Raman enhancement. Experimental results show that our sample with deposition of a 5 nm silver film (PS-Ag-5) can obtain a large number of spatially distributed local electromagnetic field hot spots, with an enhancement factor of over 108, which is several orders of magnitude higher than that of other samples. The sensitivity of PS-Ag-5 to the concentration of probe molecules and the optical enhancement effect of PS microspheres were also analyzed. This novel structured substrate can achieve considerable uniformity, and the calculated relative standard deviation (RSD) of the characteristic peak at 1650 cm-1 is approximately 8%.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface-enhanced Raman scattering (SERS) has been widely used in chemistry, physics, optics, materials science and other fields since its discovery [1]. SERS enhancement mechanism is mainly divided into electromagnetic enhancement (local surface plasmon resonance of precious metal nanoparticles) and chemical enhancement (charge transfer between the molecule to be measured and the surface of metal nanoparticles), and the contribution of electromagnetic field enhancement holds the dominant position [2].
In recent years, researchers have used a variety of methods to improve the Raman enhancement performance of the substrates. In 2007, Tiwari et al. [3] used the solution growth method to prepare triangular AgNPs with better enhancement effects than ordinary AgNPs; in the same year, Chen et al. [4] modified AgNPs by electrochemical deposition. In 2011, two-dimensional single-walled carbon nanotubes was used as the SERS substrate; Cheng et al. [5] prepared gold nanorod-like structures by seed growth method. Wu et al. [6] densely immobilized AuNPs on polymer beads to form core-satellite nanostructures for detecting molecules by SERS and achieved sensitive detection of melamine and sodium thiocyanate in 2017. These methods can obtain high enhancement factors, but the uniformity is relatively poor. Therefore, many periodic nanostructure processing methods have been proposed to improve the uniformity. Lin et al. [7] used focused ion beam and nanoindentation methods to accurately prepare Au nanorod structure SERS substrates of different size and spacing, with an enhancement factor of 107. Liu et al. [8] prepared a new type of wrinkled nanoporous quasi-periodic structure (Au79Ag21) as a highly active SERS substrate with an enhancement factor of 108. Wu et al. [9] used nanoimprint and deposition methods to prepare a gold/silver film modified nano-hemisphere array, with an enhancement factor of 8.51 × 107. Yap et al. [10] used a two-dimensional ordered polyelectron template by self-assembly of polystyrene block poly (2-vinylpyridine) to fabricate nanoparticle cluster arrays, and realized its directed self-assembly on optical fiber. Im et al. [11] prepared Ag film-modified nano-ring cavity array structure using colloidal assembly and etching methods, with an enhancement factor of 108. In 2015, Sivashanmugan et al. [12] used a focused ion beam (Ga+) to obtain a regular array of Au/Ag nanorods. Zao et al. In 2017, Jia et al. [13] used polystyrene microspheres as the framework to prepare giant vesicles with anchored tiny gold nanowires which showed a quantitative SERS analysis in the range of 10−4 to 10−7M and a high reproducibility of SERS signals with the variation of intensities less than 7.6%. Guo et al. [14] successfully designed a kind of multifunctional Fe3O4@mTiO2@noble metal composite NPs as ultrasensitive SERS substrates for trace detection in 2019, with a relative standard deviation of less than 5%. However, the cost of these methods is too high.
At present, there is an urgent need for a technical method that can prepare a high uniformity SERS substrate with a large area and low cost. To this end, we tried to use PS microspheres [15–17] as the framework of nanoparticles, and then thermally vaporized silver of different thicknesses to study the effect of thicknesses of silver film on the SERS performance of the structured substrate.
2. Experiment
2.1 Materials and instruments
The silicon wafer is P-type (100) single-throwing hydrogen peroxide type (1 ∼ 10 Ω·cm), and the thickness of the oxide layer is 300 ± 10 nm (Zhejiang Lijing Optoelectronics Technology Co., Ltd.); monodisperse PS microspheres with a diameter of 600nm (Zhongke Leiming Biomedical Nanotechnology Co.); Rhodamine 6G (Shanghai Aladdin Co., Ltd.). Raman test experiment uses Horiba's LabRAM HR Evolution Confocal Microscope Raman Spectrometer, the excitation wavelength is 532 nm, the power is 5 mW, and the integration time is 2 s. Samples’ geometry characterization uses Quattro S field emission environmental scanning electron microscope (SEM).
2.2 Fabrication of the SERS substrate
The preparation process of the structured SERS substrate is shown in Fig. 1, which mainly undergoes three steps.
Hydrophilic treatment of silicon wafers: Place the silicon wafers in acetone and absolute ethanol for ultrasonic cleaning for 15 minutes to remove the organic solvent impurities on the surface; then put the silicon wafers into concentrated H2SO4/H2O2 [3:1(v/v)] heated in a constant temperature water bath at 90°C for 1 hour; finally, the silicon wafer is rinsed with deionized water 3 to 4 times to remove the acid, and then dried with a nitrogen gun.
PS microsphere array preparation: Use a pipette (5-20 μm) to transfer the PS sphere emulsion to the hydrophilized silicon wafer, and select the multi-stage mode of homogenizer. The first stage is glue dropping, the speed is 500 r/min, and the duration is 15 s; the second stage is homogenization, the speed is 1500 r/min, and the duration is 60 s, Self-assembled monolayer PS microsphere film [18].
Preparation of structured SERS substrate: vacuum evaporation [19] (evaporation speed: 0.1·Å·S-1; control the evaporation time to change the evaporation film thickness). Deposit the silver film on the single-layer PS microsphere array.
In order to study the influence of the morphology of the silver film on the performance of the SERS substrates, we vapor-deposited silver films with five thicknesses of 50 nm, 30 nm, 20 nm, 10 nm, and 5 nm. The SEM characterization is shown in Fig. 2. For samples PS-Ag-50, PS-Ag-30 and PS-Ag-20, the surface of the microspheres was covered by a dense silver film that looks like a helmet. For PS-Ag-10, cracks appeared on the edge of the microsphere surface. And for PS-Ag-5, a large number of AgNPs were formed on the surface of the microspheres.
Fig. 2. SEM images of (a1)-(a2) PS-Ag-50; (b1)-(b2) PS-Ag-30; (c1)-(c2) PS-Ag-20; (d1)-(d2) PS-Ag-10; (e1)-(e2) PS-Ag-5; (f) lateral characterization of the PS-Ag-5, Ag film thickness of 5 nm.
3. Results and discussion
3.1 Effect on samples’ electromagnetic enhancement with different film thicknesses
The three-dimensional finite difference time domain (FDTD) algorithm and COMSOL Multiphysics software were used to simulate the spatial distribution of the electromagnetic field intensity of the sample.
According to the SEM images in Fig. 2, the state of the silver film (PS-Ag-50, PS-Ag-30 and PS-Ag-20) on the surface of the microspheres can be observed. The dense silver film wrapped the upper surface of the microspheres, forming a crown structure with a certain thickness. We used COMSOL for model building and physical field setting. The laser wavelength was 532 nm, the vibration direction and the k direction are shown in the Fig. 3(a), and the incident electric field intensity E0 = 1 V/m.
Fig. 3. (a) Simulation model; (b) COMSOL two-dimensional simulation results; (c) for PS-Ag-50, PS-Ag-30 and PS-Ag-20, the electric field intensity distribution along the arc length direction of the upper surface of the silver film.
Shown in Fig. 3(b), the hot spots were only distributed in the gaps between the microspheres. Because of the close-packed hexagonal structure (HCP) arrangement of the microspheres, each two microspheres were tangent to each other, forming a nano-gap above the tangent, and the electric field strength there was greatly enhanced. The corresponding maximum electric field was 232.3 V/m, 263.6 V/m, 72.8 V/m, shown in Fig. 3(c).
For PS-Ag-50, PS-Ag-30 and PS-Ag-20, because the thickness of the silver film was a little large, the surface of the microsphere array was covered by dense silver, forming a large area periodic and relatively uniform uneven structure. When the thickness was reduced to 10 nm, the situation is different.
The surface area of the spherical cap is calculated by
We imported the SEM image into the FDTD to generate the model (refractive index of PS is 1.59), and the simulation result is shown in Fig. 5. It can be seen that the silver with non-film-forming state on the surface of the microspheres greatly increases the number of hot spots and their distribution is also wider. It can also be seen that the local electric field of the lower AgNPs has a weak enhancement, and this part contributed little to SERS.
Fig. 5. (a) Model of simulation structure; (b) Distribution of electric field intensity on the surface of PS microspheres; (c) lower silver nanoparticles; (d)(e) Electric field distribution in two incident polarization states.
The silver film with a thickness of 5 nm has a very high specific surface area, which will make it have a great tendency to reduce its surface area, so agglomeration occurs at the interface. When the metal film is dewetting, because the spherical structure has the smallest surface area, that is, its surface energy is the smallest, the agglomeration will eventually cause the AgNPs to gradually transform to a hemispherical shape [20,21]. For the contact angle φ [22], it is the result of the entire system adjusting the surface of the silver film, the surface of the microspheres and the grain boundary. Since the system has no elastic strain, the equilibrium state of the AgNPs on the substrate should satisfy Young's relationship [23]:
where φ is the contact angle, γlv is the interface energy between the silver film and the microsphere [24,25], and γsv and γsl are the surface energy of the microsphere and the silver film. Surface energy is also called surface free energy, and its determining formula is as follows: where E(N,2A) is the total energy of the surface model after relaxation, A is the surface area, μ is the chemical potential of the element, N is the total number of effective atoms in the model, P is the pressure, V is the volume, T is the temperature of the system and S stands for entropy. The surface energy per unit area is defined as surface tension, and the surface tension of PS is much smaller than that of silver, so the value of cosφ is negative, that is, φ > 90°. Since the experimental conditions are constant and cosφ is only related to the ratio (γsv - γsl) / γlv, φ can be regarded as a constant. In the simulation model, if the center of Ag spheres is just right on the surface of the PS microsphere, the φ is exactly an obtuse angle. So we set the height to half of the diameter of AgNPs to ensure that φ exceeds 90°.Based on the size and contact angle mentioned above, more simulation is carried on. The simulation model is shown in Figs. 6(a1) and 6(a2), when the diameter of AgNPs was 12 nm, 23 nm and 45 nm (corresponding to Dave/2, Dave and 2Dave), the maximum electric field intensity was 10.2 V/m, 15.7 V/m and 30.1 V/m, which is mainly distributed at the concave corner where AgNPs and microspheres contact. For practical reasons, AgNPs were often not uniform in size and gap between each other, so we abstracted out several special parameters for modeling and simulation.
Fig. 6. Model of AgNPs-PS microsphere structure with (a1) equal particle size and (a2) unequal particle size; (a3) A simulation model with a certain incident angle; (b1)(b2) Distribution of “hot spots” of the two models; (b3) The relationship between incident angle θ and electric field intensity. The light source parameter is set to plane wave with a wavelength of 532 nm, the amplitude value is 1.
According to the results of electromagnetic simulation, we can approximate the electromagnetic enhancement factor of the substrate:
3.2 Influence of the incident angle
In order to explore the influence of the incident angle on the local electric field distribution of the substrate, the simulation model of PS-Ag-5 was set as follows. The K vector of the incident light was changed from vertical downward to deviate from the vertical direction at an angle of θ. The diameter of AgNPs was 23 nm, the gap was 12 nm wide, and the wavelength of light source was 532 nm, the simulation results are shown in Fig. 6(b3). We can see the influence of the incident angle on the electric field intensity. When the incident angle θ reached 20°, the attenuation of the electric field strength was only 7.6%. When θ was greater than 20°, the electric field strength attenuated slowly with a coefficient of -0.192. When the incident angle θ reached 75°, the attenuation of the electric field strength was 61.8%. Due to the three-dimensional distribution of AgNPs, the incident light partially scattered and diffusely reflected by the system can still excite the plasmon resonance at the gap formed by the AgNPs from different angles to form hot spots. It can also be seen that the incidence angle has a weak influence on the distribution of hot spots compared other structures [26,27].
3.3 Optical enhancement effect of the PS microspheres
The PS microsphere itself can form an optical enhancement effect via forming a nano-beam stream under the action of the laser [28]. We carried on simulation, shown in Figs. 7(a) and 7(b).
Fig. 7. (a) Near-field optical enhancement excitation of uncoated PS microsphere array; (b) FDTD simulation result of optical enhancement effect of PS microsphere; (c) experimental Raman signal of empty silicon substrate and PS microsphere.
The results show that after the laser was focused by the near-field of the PS microspheres, the electric field intensity can be increased up to nearly 4 times. The hot spots were distributed on the surface of the silicon wafer and tangent to the PS microspheres. To characterize this enhancement effect of the microspheres, the experimental result is shown in Fig. 7(c). Using a 5 mW 532 nm laser to focus the single-layer PS microsphere array, the Raman spectrum obtained has a characteristic peak at 1002 cm-1 in addition to the characteristic peak at 520 cm-1, which corresponds to the benzene ring breathing vibration. It can be seen that the PS microsphere array can significantly enhance the silicon signal. And the Raman signal of the R6G molecules that settled on the surface of the silicon wafer through the gap between the microspheres can be enhanced. However, due to the extinction of the microspheres, the enhancement factor was less than the theoretical value.
3.4 Raman measurements with different R6G concentrations
Raman enhanced performance tests were performed on PS-Ag-50, PS-Ag-30, PS-Ag-20, PS-Ag-10 and PS-Ag-5. We used a pipette to transfer 4 μL of R6G solution to the prepared samples’ surface. The results are shown in Fig. 8.
Fig. 8. Raman intensities: the concentration of R6G is (a) 10−8 mol/L; (b) 10−8 mol/L; (c) 10−10 mol/L; (d) 10−12 mol/L (PS-Ag-5).
When the concentration of R6G was 10−6 mol/L and 10−8 mol/L, the characteristic peaks of R6G molecules can be detected on substrates with all coating thickness samples. When the concentration of R6G decreased to 10−10 mol/L, the characteristic peak of R6G can still be detected on PS-Ag-5, PS-Ag-10 and PS-Ag-20. When the concentration of R6G reached 10−12 mol/L, the characteristic peak of R6G can only be detected on PS-Ag-5. Through the calculation formula of the experimental enhancement factor EF = ISERS / IR · VSERS / VR · CR / CSERS, the calculated enhancement factors of the substrate with the vapor deposited silver film thickness from small to large were 2.08 × 108, 1.52 × 106, 1.29 × 106, 2.42 × 104 and 4.65 × 104.
The gradient concentration Raman characterization of substrates coated with different thickness of silver film was compared, and the results are as Fig. 9.
Fig. 9. (a) Raman spectra of 10−6 mol/L, 10−8 mol/L and 10−10 mol/L R6G on PS-Ag-5; (b) comparison of the enhancement effects of substrates coated with different silver film thickness. Select the characteristic peak at 1650 cm-1 for calibration.
The PS-Ag-5 has a higher detection limit, and as the concentration of R6G increases, the intensity of the Raman characteristic peak is significantly improved compared to substrates coated with other thickness of silver film. This is because as the number of R6G molecules per unit area increases, R6G molecules gradually fill in numerous hot spots formed by the nanoparticles on the surface of the microsphere. We conducted a qualitative analysis on this. The relationship between the number of molecules contained in the substance and the amount of substance is:
where n is the amount of substance, N is the total number of substance, and NA is the Avogadro constant, which is approximately 6.02 × 1023. The total number of molecules in 4 μL R6G solution with a concentration of 10−10 mol/L is 2.4 × 108. The shape of the droplet in the experiment is approximately an ellipse with a long axis of 4 mm and a short axis of 3 mm, so the approximate area of the droplet is calculated as S = π · a · b ≈ 0.09 cm2. Ignoring the coffee ring effect [29], assuming that the R6G molecules are uniformly distributed in the area of the droplet after the liquid is dried, the diameter of the PS microsphere is 0.6 μm. The projected area of the microsphere on the horizontal plane is S` = 0.28 μm2. The number of molecules present on the surface of the microspheres is N` = N × 0.28 / 0.09 × 108 ≈ 7.46.Compared with AgNPs, the volume of microspheres is too large, and it is difficult for 7 molecules to occupy the hot spots exactly. In practice, the coffee ring effect can’t be ignored. The drying of the droplets is from the outside to the inside. Therefore, the number of molecules on the surface of the microspheres in the central area is less than the theoretical value. Therefore, when the concentration is 10−10 mol/L, the characteristic peak intensity of R6G molecules on PS-Ag-5 is not significantly improved compared to other substrates.
When the concentration of R6G was increased to 10−8 mol/L, even 10−6 mol/L, the number of molecules on the surface of the microspheres also expanded by two orders of magnitude, and more hot spots were occupied by R6G molecules. In contrast, when the thickness of silver film was greater than 5 nm, hot spots only existed in the narrow gaps between microspheres. These strong hot spots occupied only a small volume, so they were difficult to be effectively occupied by R6G molecules. In the Raman experiment, the “10× visible” objective lens was used, and the laser spot diameter was calculated to be 2.59 μm (1.22λ / NA). There were only single-digit gaps between the microspheres in this area. We can explain that when the concentration of R6G is 10−8 mol/L, the performance of PS-Ag-5 is significantly better than that of other substrates. Moreover, the performance of PS-Ag-50 was better than PS-Ag-30 and PS-Ag-20 because the Ag film was thick enough to fill the gap and form a funnel-shaped structure between microspheres.
3.5 Uniformity
In order to verify the uniformity of the Raman enhancement of our sample, a Raman mapping characterization test was performed on PS-Ag-5. The mapping area was set to a rectangular area of 20 μm × 40 μm with a step length of 5 μm. The experimental results (Fig. 10) show that the detection of two concentrations of R6G solution has good uniformity, and the relative standard deviations (RSD) are 8.32% and 7.11%, respectively.
Fig. 10. Raman mapping results on PS-Ag-5, with concentration of R6G of (a1)10−8 mol/L and (b1)10−6 mol/L; (a2), (b2) the corresponding calculated RSD at 1650 cm-1.
4. Conclusion
Structured PS-AgNPs were prepared by self-assembly and vacuum high-temperature evaporation methods. Experiments showed that the substrates coated with 5 nm silver film have better Raman enhancement performance (EF > 108) and uniformity (RSD = 8.32%, 7.11%). This low-cost structured template preparation method can provide effective information for later analysis of large-area SERS substrates, surface roughness of microstructures, and optical effects of structures with sub-wavelength dimensions. High temperature resistant microspheres can be used later to further study the effect of high temperature annealing on the distribution of nanoparticles.
Funding
National Natural Science Foundation of China (61875024); Chongqing Outstanding Youth Fund (cstc2019jcyjjqX0018); Fundamental Research Funds for the Central Universities (CQU2018CDHB1A07).
Acknowledgments
We would like to thank Dr. Gong Xiangnan at Analytical and Testing Centre of Chongqing University for his help in Raman measurement.
Disclosures
The authors declare no conflicts of interest.
References
1. M. Fleischmann, P. J. Hendra, and A. J. Mcquillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974). [CrossRef]
2. S. Y. Ding, J. Yi, J. F. Li, R. Bin, D. Y. Wu, R. Panneerselvam, and Z. Q. Tian, “Nanostructure-based plasmon-enhanced Raman spectroscopy for surface analysis of materials,” Nat. Rev. Mater. 1(6), 16021 (2016). [CrossRef]
3. V. S. Tiwari, T. Oleg, G. K. Darbha, W. Hardy, J. P. Singh, and P. C. Ray, “Non-resonance: SERS effects of silver colloids with different shapes,” Chem. Phys. Lett. 446(1-3), 77–82 (2007). [CrossRef]
4. Y. C. Chen, R. J. Young, J. V. Macpherson, and N. Wilson, “Single-walled carbon nanotube networks decorated with silver nanoparticles: a novel graded SERS substrate,” J. Phys. Chem. C 111(44), 16167–16173 (2007). [CrossRef]
5. C. Jing, G. Lan, X. Bin, and H. Yan, “Investigation of PH effect on gold nanorod synthesis,” J. Chin. Chem. Soc. 58(6), 822–827 (2011). [CrossRef]
6. L. A. Wu, W. E. Li, D. Z. Lin, and Y. F. Chen, “Three-dimensional SERS substrates formed with plasmonic core-satellite nanostructures,” Sci. Rep. 7(1), 13066 (2017). [CrossRef]
7. Y. Y. Lin, J. D. Liao, Y. H. Ju, C. W. Chang, and A. L. Shiau, “Focused ion beam-fabricated Au micro/nanostructures used as a surface enhanced Raman scattering-active substrate for trace detection of molecules and influenza virus,” Nanotechnology 22(18), 185308 (2011). [CrossRef]
8. H. W. Liu, L. Zhang, X. Y. Lang, Y. Yamaguchi, H. Iwasaki, Y. Inouye, Q. K. Xue, and M. W. Chen, “Single molecule detection from a large-scale SERS-active Au79Ag23 substrate,” Sci. Rep. 1(1), 112 (2011). [CrossRef]
9. H. Y. Wu, C. J. Choi, and B. T. Cunningham, “Plasmonic nanogap-enhanced Raman scattering using a resonant nanodome array,” Small 8(18), 2878–2885 (2012). [CrossRef]
10. F. L. Yap, P. Thoniyot, S. Krishnan, and S. Krishnamoorthy, “Nanoparticle Cluster Arrays for High-Performance SERS through Directed Self-Assembly on Flat Substrates and on Optical Fibers,” ACS Nano 6(3), 2056–2070 (2012). [CrossRef]
11. H. Im, K. C. Antz, S. H. Lee, T. W. Johnson, C. L. Haynes, and S. H. Oh, “Self-assembled plasmonic nanoring cavity arrays for SERS and LSPR biosensing,” Adv. Mater. 25(19), 2678–2685 (2013). [CrossRef]
12. K. Sivashanmugan, J. D. Liao, and C. K. Yao, “Elimination of gallium concentration on focused-ion-beam-fabricated Au/Ag nanorod surface to recover its Raman scattering characteristic,” Sens. Actuators, B 206, 415–422 (2015). [CrossRef]
13. Y. Jia, L. Zhang, L. Song, L. Dai, X. Lu, Y. Huang, J. Zhang, Z. Guo, and T. Chen, “Giant vesicles with anchored tiny gold nanowires: fabrication and surface-enhanced Raman scattering,” Langmuir 33(46), 13376–13383 (2017). [CrossRef]
14. H. Guo, A. Zhao, Q. He, P. Chen, Y. Wei, X. Chen, H. Hu, M. Wang, H. Huang, and R. Wang, “Multifunctional Fe3O4@mTiO2@noble metal composite NPs as ultrasensitive SERS substrates for trace detection,” Arabian J. Chem. 12(8), 2017–2027 (2019). [CrossRef]
15. B. Li, G. Niu, Y. Yi, X. W. Zhou, X. D. Liu, X. Ye, and C. Y. Wang, “Fabrication and surface-enhanced Raman scattering research on polystyrene nanospheres arrays,” Spectrosc. Spect. Anal. 36, 2812–2817 (2016). [CrossRef]
16. L. P. Xia, Z. Yang, S. Y. Yin, W. R. Guo, S. H. Li, W. Y. Xie, D. P. Huang, Q. L. Deng, H. F. Shi, H. L. Cui, and C. L. Du, “Surface enhanced Raman scattering substrate with metallic nanogap array fabricated by etching the assembled polystyrene spheres array,” Opt. Express 21(9), 11349–11355 (2013). [CrossRef]
17. M. Z. Cheng, J. Zhang, D. Q. Bao, and X. W. Huang, “Gold surface plasmon crystal structure based-on polystyrene template for biosensor application,” Electrophoresis 40(8), 1135–1139 (2019). [CrossRef]
18. C. Klutse, A. Mayer, J. Wittkamper, and B. M. Cullum, “Applications of self-assembled monolayers in surface-enhanced Raman scattering,” J. Nanotechnol. 2012, 1–10 (2012). [CrossRef]
19. A. Imhof, “Preparation and characterization of titania-coated polystyrene spheres and hollow titania shells,” Langmuir 17(12), 3579–3585 (2001). [CrossRef]
20. D. J. Srolovitz and S. A. Safran, “Capillary instabilities in thin films. I. Energetics,” J. Appl. Phys. 60(1), 247–254 (1986). [CrossRef]
21. L. Liu, Z. Chen, L. Wang, E. Polyakova, T. Taniguchi, K. Watanabe, J. Hone, G. W. Flynn, and L. E. Brus, “Slow gold adatom diffusion on graphene: effect of silicon dioxide and hexagonal boron nitride substrates,” J. Phys. Chem. B 117(16), 4305–4312 (2013). [CrossRef]
22. X. B. Luo, D. Y. Zhu, and L. M. Shi, “Progress in the calculation of solid surface tension based on contact angle method,” Science Technology and Engineering 7(19), 4997–5004 (2007).
23. F. Ruffino, G. Cacciato, and M. G. Grimaldi, “Surface diffusion coefficient of Au atoms on single layer graphene grown on Cu,” J. Appl. Phys. 115(8), 084304 (2014). [CrossRef]
24. Q. Jiang and H. M. Lu, “Size dependent interface energy and its applications,” Surf. Sci. Rep. 63(10), 427–464 (2008). [CrossRef]
25. A. R. Miedema and R. Boom, “Surface tension and electron density of pure liquid metals,” Z METALLKD 69(3), 183–190 (1978).
26. E. C. L. Ru, S. A. Meyer, C. Artur, P. G. Etchegoin, J. Grand, P. Lang, and F. Maurel, “Experimental demonstration of surface selection rules for SERS on flat metallic surfaces,” Chem. Commun. 47(13), 3903–3905 (2011). [CrossRef]
27. B. B. Afeyan and E. A. Williams, “Stimulated Raman sidescattering with the effects of oblique incidence,” Phys. Fluids 28(11), 3397–3408 (1985). [CrossRef]
28. Q. W. Lin, D. Y. Wang, Y. X. Wang, S. Guo, S. Panezai, L. T. Ouyang, L. Rong, and J. Zhao, “Super-resolution quantitative phase-contrast imaging by microsphere-based digital holographic microscopy,” Opt. Eng. 56(3), 034116 (2017). [CrossRef]
29. R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, “Capillary flow as the cause of ring stains from dried liquid drops,” Nature 389(6653), 827–829 (1997). [CrossRef]
