李嗣涔臺灣大學：電子工程學研究所張議聰Chang, Yi-TsungYi-TsungChang2007-11-272018-07-102007-11-272018-07-102007http://ntur.lib.ntu.edu.tw//handle/246246/57640本文主要的貢獻是探討光經由金屬/介電質結構上的金屬薄膜挖週期性及隨機分佈孔洞所產生的穿透特性。最近幾年中，光經由金屬薄膜上挖有大面積週期性孔洞陣列的結構，在布拉格散射條件下，因局部表面電漿子交互作用而產生不同表面電荷場強度的效應已被廣泛的研究。但是隨機分佈孔洞結構的表面電漿子模態的穿透尖峰位置、表面電漿子在金屬薄膜上傳輸的長度、色散關係與其所引起的本質阻尼和輻射阻尼並未詳細的探討和研究。因此，為了回答這些問題，本文使用在雙面抛光的矽基板上鍍有鋁金屬薄膜的結構，以黃光技術在鋁金屬薄膜上製作大面積六邊形孔洞的六邊形週期陣列、超週期的微晶胞陣列，隨機分佈的孔洞和隨機分佈的微晶胞陣列。並用傅立葉紅外線穿透儀去量測樣品在不同角度入射光照射下的穿透光譜和表面電漿子的色散關係；並探討表面電漿子的傳輸長度和阻尼特性。經由以上實驗而獲得的結論如下：關於大面積六邊形孔洞的六邊形週期陣列，當孔洞大小接近週期一半時，由穿透光譜和表面電漿子的色散關係可以觀察到 (1,0)-鋁/矽-表面電漿子模態的波峰有愈來愈明顯的分裂（ω+和ω-）。繼續增加入射光的角度，六個退化的(1,0)-鋁/矽-表面電漿子模態會依據樣品上晶格與入射光的對稱性分裂成三個或四個表面電漿子模態；且孔洞直徑變小時，高階的表面電漿子模態可以明確驗證。關於超週期的微晶胞陣列，由穿透光譜和表面電漿子的色散關係可以觀察到表面電漿子是由法布立-比洛(Fabry-Perot)形式波導共振在超單位晶胞內呈現整數階的量化現象。而整數的階數是用超週期結構 p 和N*N 微晶胞 d 的週期比值來決定，其中N = 3、4和5 為獨立孔洞的數目。關於隨機分佈的金屬孔洞，由穿透光譜和表面電漿子的色散關係可以觀察到(1,0)-鋁/矽-表面電漿子模態是由隨機分佈金屬孔洞的最近分佈距離所決定，其峰值的穿透光強度和半高寛是由隨機分佈金屬孔洞的大小和數目所決定；其他分佈距離產生的表面電漿子模態也可以被明確驗證。繼續增加入射光的角度，因為隨機分佈金屬孔洞數目少，所以無法從表面電漿子的色散關係圖觀察到表面電漿子模態退化的情形。關於隨機分佈的微晶胞陣列，由穿透光譜和表面電漿子的色散關係圖可以觀察到當隨機分佈微晶胞陣列的孔洞週期改變時，穿透尖峰也發生改變，它可以用來做成多波段的紅外光選擇器。The main contribution of this thesis is the investigation of the light transmission through a metal/dielectric structure perforated with periodic and random distribution of holes on metallic film. In recent year, the effects of surface electric charge field interacted with the localized surface plasmons under the Bragg scattering condition with the light transmission through a structure of periodic metal holes array are extensively studied. But the transmission peak position of the surface plasmon modes in random structure of holes, the propagation length, dispersion relation, the intrinsic damping and radiation damping of surface plasmon have not yet been investigated in detail. To answer these questions, an aluminum metallic film is evaporated on doubly polished Si substrate, then the hexagonally-ordered holes array, superperiodic micro-cell arrays, random distributed holes and micro-cell arrays on aluminum film are formed by lithography, respectively. The optical transmission properties and dispersion relation of surface plasmon are measured and examined by Fourier Transform Infrared (FTIR) spectrometer. The propagation length and the damping of surface plasmon are calculated and analyzed in details. The dispersion relation of surface plasmon polariton of hexagonally-ordered holes array is measured, it is found that as the light was normally incident onto the sample, the (1,0) Al/Si surface plasmon modes split into two peaks in the transmission spectra, and this effect is most obvious when the diameter of the hole is close to a half of the lattice constant. At larger incident angles, the six degenerate (1,0) Al/Si surface plasmon modes split into three or four modes depending on the symmetry axis, even higher-order surface plasmon modes can be identified for small hole diameters. As to the superperiodic micro-cell arrays, the transmission spectra and dispersion relation of surface plasmon polariton indicated the surface plasmons are generated by Fabry-Perot type waveguide resonances with different integer order. The ratio of periodicity between the super-periodic structure p and the N*N micro-cell d determines the integer order (where N is the number of isolated holes, N= 3, 4 and 5), and suggest that the surface plasmons are Fabry-Perot type resonance within a super unit cell. As to the random distributed holes, the transmission spectra and dispersion relation of surface plasmon polariton suggest that the primary (1,0) Al/Si surface plasmon mode is determined by the nearest neighbor distance in a cluster of random distributed holes, the intensity of transmission peak and the full width at half maximum (FWHM) is determined by the size and number of random distributed holes, and even surface plasmon modes of other distributed distance can be identified as well. When the light incident angle increases, the degenerate surface plasmon mode can not be observed in the dispersion relation, it is owing to the fact that the number of random distributed holes becomes less. As to the micro-cell arrays with random distribution, the transmission spectra and dispersion relation of surface plasmon polariton indicate that as the period of micro-cells is changed, the transmission peaks also changes, it can be exploited to the application of the infrared wavelength-selective devices.Chapter 1 1ntroduction...................................1 Chapter 2 Theory of Surface Plasmons.....................6 2.1 Theory of Surface Plasmons on Smooth surfaces......6 2.2 Theory of Surface Plasmons on the Surface with Periodic Metal Holes Array16 Chapter 3 Experiments...................................23 3.1 Process Flow of Experiments.......................23 3.1.1 Fabrication Processes of Hexagonally Ordered Aluminum Hole Arrays..................23 3.1.2 Fabrication Processes of Superperiodic Micro-cell Arrays...............29 3.1.3 Fabrication Processes of Random Distribution of Aluminum holes....................29 3.1.4 Fabrication Processes of Random Distribution of Micro-cells Arrays.........29 3.2 Measuring Systems............................33 3.2.1 FTIR...................................33 3.2.2 FTIR Measuring System..................36 Chapter 4 Extraordinary Transmission through Hexagonally Ordered Aluminum Holes Array.........................38 4.1 Experiments....................................38 4.2 Results and Discussion.........................39 Chapter 5 Extraordinary Transmission through Superperiodic Micro-cell Arrays....................................49 5.1 Experiments..........................50 5.2 Results and Discussion.......................51 Chapter 6 Extraordinary Transmission through Aluminum Holes with Random Distribution........72 6.1 Experiments...........72 6.2 Results and Discussion............74 Chapter 7 Extraordinary Transmission through Micro-cell Arrays with Random Distribution.........82 7.1 Experiments.......................82 7.2 Results and Discussion............84 Chapter 8 Conclusions...................93 Bibliography............................96 Figure Captions Fig. 2.1 (a) SPs at the interface between a metal/dielectric material. (b) The dispersion relation of SP on a smooth surfaces (solid line)...........7 Fig. 2.2 Skin depth as function of wavelength........15 Fig. 2.3 (a) Definition of the direction of the incident light and sample. (b) Top view of the sample ........19 Fig. 2.4 (a) The dispersion relation of the SP on periodic holes array (solid line). (b) Charge distribution of ω+ and ω- modes in a two-dimensional periodic hole array ...20 Fig. 2.5 The momentum conservation law of SPs on (a) a squared holes array; and (b) a hexagonal holes array. 22 Fig. 3.1 The device fabrication process and measurement procedure..........24 Fig. 3.2 The photograph of the top view of a hexagonally ordered aluminum holes array on Al film. (b) Schematic side view........28 Fig. 3.3 The superperiodic microcell arrays on Al film. Photograph of the top-view and side-view of (a) 3*3 microcell arrays; top view of (b) 4*4 and (c) 5*5 microcell arrays........30 Fig. 3.4 (a) The photograph of the top view of the randomly arranged holes of sub-wavelength on Al film. (b) Schematic side view.........31 Fig. 3.5 The photograph of the top-view of randomly arranged micro-cell arrays of subwavelength holes on Al film. The lattice constants of the micro-cells are (a) 3, (b) 5, (c) 7 and (d) a mixture of (3, 5, 7) um. The radius of each hole is 1um. The Al thickness is 300nm.......32 Fig. 3.6 The principle of Michelson interferometer........34 Fig. 3.7 The setup to measure transmission spectra.......37 Fig. 4.1 For a hexagonally-ordered hole array (a = 5um, r = 0.75, 1, and 2um, Al film thickness t = 300nm), the broad transmission peak comprises two peaks because of Bragg diffraction........40 Fig. 4.2 Transmission spectra obtained by rotating the Al/Si hexagonal hole array (a = 5um and r = 1um) (a) relative to the incident light by rotating the sample by 00 and 900 around the z axis, as displayed in the inset; (b) around the y axis by 300 and then by 00, 450, 2250 and 2750 around the z axis, as displayed in the inset.......42 Fig. 4.3 Zero-order transmission spectra and dispersion relations obtained by rotating the Al/Si sample around the y-axis. The spectra and dispersion relations were obtained in 10 increments to 500 for hexagonally-ordered aluminum hole arrays relative to the incident light, periodicity of sample a = 5um and thickness t = 300nm. (a) Spectra and (b) dispersion relation for the sample r = 2um. (white: Al / Si modes) (c) Spectra and (d) dispersion relation for the sample r = 1um. (white: Al / Si modes) (e) Spectra and (f) dispersion relation for the sample r = 0.75um. (white: Al / Si modes, green: air / Al modes)...........44 Fig. 5.1 (a) Transmission spectra of metal that is perforated with squared hole array. Data are measured with variant incident angle. (Inset: 100nm-thick Ag film on p-type Si wafer with perforated hole array; a = 5um, r = 2um) (b) Dispersion relation of surface plasmon polariton of the metal structure shown in (a)........53 Fig. 5.2 (a) Schematic sample geometries of designed sample. The number in parentheses is the number of the sample in this series. When the period of the 3*3 micro-cell array a is 5um, r is 1um, and the micro-cell array is kept constant for all samples in this series, the superperiod p increases from 16um(sample 1) to 21um (sample 6) in steps of 1 . (b) Transmission spectra of metal/dielectric strucutre perforated with micro-cell arrays........55 Fig. 5.3 Schematically side-view of SPP wave propagated at adjacent microcell structure. r, a and p are radius of hole, period in microcell and period of superperiodic microcell, respectively.........58 Fig. 5.4 Dispersion relation of surface plasmon polariton of 100 -thick Ag film that is perforated with 3 3 micro-cell arrays. The period a of the 3*3 squared micro-cell array is 5um, and the radius of the hole r is 1um. The periods of the larger periodic structure p are (a) 16, (b) 18 and (c) 21um, respectively........60 Fig. 5.5 Transmission spectra of (a) 3*3, (b) 4*4 and (c) 5*5 micro-cell arrays structure.......63 Fig. 5.6 Dispersion relation of surface plasmon polariton of 100 -thick Ag film that is perforated with 3*3, 4*4 and 5*5 micro-cell arrays. The period a of the squared micro-cell array is 5um, and the radius of the hole r is 1um. The periods of the larger periodic structure p are (a) 18, (b) 23 and (c) 28um.........66 Fig. 5.7 Schematic sample geometries of designed sample. The number in parentheses is the number of the sample in this series. When the period of the 3*3 micro-cell array a is 5um, r is 1um, and the micro-cell array is kept constant for all samples in this series, the superperiod p increases from 16um (sample 1), 17um (sample 2) and 19um(sample 3)..........67 Fig. 5.8 Dispersion relation of surface plasmon polariton of 100nm-thick Ag film that is perforated with square holes array (a = 5um, r = 2um). The incident light is (a) unpolarized and (b) x-polarized........68 Fig. 5.9 Dispersion relation of surface plasmon polariton of 100 nm-thick Ag film that is perforated with 3*3 micro-cell arrays. The period a of the squared micro-cell array is 5um, and the radius of the hole r is 1um. The periods of the larger periodic structure p are 16, 17 and 19um. (a), (c) and (e) are measured with incident light of un-polarized; (b), (d) and (f) are measured with incident light of x-polarized light........70 Fig. 6.1 (a) Schematic diagram showing the fabrication processes of random distributed holes. (b) Top view of the Al/Si structure with random distributed holes.........73 Fig. 6.2 The distribution of near neighbor distance of samples (a) A with hole diameter D = 0.5±0.1um, the nearest neighbor distance a = 0.6um, (c) B with D = 1.3±0.1um, a = 1.6um and (e) C with D = 1.5±0.1um, a = 2.8um. The zero-order transmission spectra of samples (b) A, (d) B and (f) C......76 Fig. 6.3 (a) The transmission peak wavelength as a function of the nearest neighbor distance. (b) The damping properties of the SP excitations, by plotting the dependence of peak half-width as a function of resonance wavelength........78 Fig. 6.4 Transmission spectra of perforated metal film with randomly arranged hole. Data are measured in varied incident angle. For samples (a) A with hole diameter D = 0.5±0.1um, the nearest neighbor distance a = 0.6um, (b) B with D = 1.3±0.1 , a = 1.6um and (c) C with D = 1.5±0.1um, a = 2.8um........81 Fig. 7.1 Zero-order transmission spectra of samples (a) A, (b) B, (c) C and (d) D with various hole periods of micro-cells arranged randomly. The lattice constants of the micro-cells are 3, 5, 7 and a (3, 5, 7)um mixture. The radius of each hole is 1um. The Al thickness is 300 nm 85 Fig. 7.2 Transmission spectra of samples (a) A, (b) B and (c) D obtained by rotating sample about the direction of incident radiation.........90 Fig. 7.3 SPP dispersion relations of sample B. (white: Al/Si SP modes).........92 List of Tables Table 3.1 Conditions and purposes of the cleaning solvent........26 Table 3.2 Evaporation conditions.........26 Table 3.3 The photolithography conditions........26 Table 5.1 The theoretical predication and experimental values of the transmission peak wavelengths of the Ag/Si 3 3 superperiodic structure based on quantized surface plasmon model. (unit:um).........57 Table 5.2 The theoretical predication and experimental values of the transmission peak wavelengths of the Ag/Si 4 4 superperiodic structure based on quantized surface plasmon model. (unit:um).........64 Table 5.3 The theoretical predication and experimental values of the transmission peak wavelengths of the Ag/Si 5 5 superperiodic structure based on quantized surface plasmon model. (unit:um).........65 Table 7.1 Structural parameters and position of surface resonance for samples A, B, C and D. (unit:um)....872742264 bytesapplication/pdfen-US表面電漿子微晶胞法布立-比洛 型式共振隨機分佈孔洞surface plasmonmicro-cellFabry-Perot resonancehole of random distributionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/57640/1/ntu-96-D90943016-1.pdf