可調式隨機雷射與熱膨脹係數之研究

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(1)國立臺灣師範大學光電科技研究所博士論文 Institute of Electro-Optical Science and Technology National Taiwan Normal University. 可調式隨機雷射與熱膨脹係數之研究 Study on flexible random lasers with tunable lasing emissions and thermal expansion coefficients. 指導教授：李亞儒. 博士. 研究生：周俊仰. 中華民國. 一○七. 年七月.

(2) 誌謝光陰似箭，轉眼間博士生涯即將結束。接下來要面對的是更具有挑戰性的社會壓力，故仍應自我鞭策不斷地追求更多專業知識與經驗。不過在這之前，我必須感謝身旁的一些人，因為有他們的鼓勵與指導，才能造就今天的我。本論文得以順利完成，首先感謝指導教授-李亞儒老師，給予學生一個正確的研究方向，在研究的過程中不斷地引發學生對於自身主題的深入思考以及細心指正學生的報告技巧，使學生受益良多，若沒有您的指導我想我的研究之路不會走的如此順遂。亦要感謝口試委員李敏鴻老師與陳正雄老師給與的寶貴意見與琢磨，使我在思考問題上能更加謹慎，深表謝意。另一方面，感謝蔡孟燦老師與黃俊穎老師，在研究上也提供了豐富的研究資源，讓我在自由的環境下盡興地研究。在研究的過程中，不厭其煩的教導影像處理、數值分析等相關的專業知識，當研究遭遇到困難時，老師總能適時的給予幫助，讓學生藉著合作與討論激發出更多的研究方法。最後，感謝我的家人與岳父、岳母，因為他們在生活上全方面的奧援，讓我能夠安心地追求屬於自己的理想與人生目標。此外，深深地感佩我最親愛的內人鈺娟的勇氣與毅力，默默地支持我走過風風雨雨，以及我的寶貝女兒怡昕，你們永遠是支持我最大的力量。有你們.

(3) 相伴，即使面對再大的難關，我也會鼓起勇氣繼續前進。因為有你們的鼓勵與支持，讓我在這段期間能全心全力地投入並且順利地完成我的博士學位。在此向所有關心、協助我的師長、家人及朋友獻上最深的感謝！. 周俊仰謹誌於國立臺灣師範大學光電科技研究所 2018 年 06 月.

(4) 中文摘要本研究分為兩個部分。1.可調式隨機雷射、2.使用光學斷層掃描測定大功率 InGaN 基板發光二極體的熱膨脹係數。. 在研究中，我們通過實驗證明了在聚對苯二甲酸乙二醇酯（PET ）基材上製造的可調式隨機雷射，其雷射發射具有高度的可調性。隨機雷射振盪主要來自增益介質（羅丹明 6G，R6G）發射光子與銀奈米稜鏡（Ag NPRs）的局域表面電漿（LSP）之間的共振耦合，這增加了多光散射的有效截面，從而刺激雷射發射。更重要的是，隨機振蕩波長隨著施加在 PET 基材上彎曲應變的增加而藍移，並且在彎曲應變為 50％時雷射波長實現了約 15nm 的最大偏移施加在 PET 基材上。這種觀察是高度可重複的和可逆的，並且這證明我們可以通過簡單地彎曲用 Ag NPRs 裝飾的可調基底來控制雷射波長。使用顯微鏡測量 AgNPRs 的散射光譜以了解波長漂移對施加的彎曲應變依賴性的機制。因此，我們相信基於顯示結構的可調式雷射發射的實驗性展示，有望開創隨機雷射的新應用領域。. I.

(5) 熱膨脹係數（CTE）是指加熱時材料的熱膨脹值的物理量。對於先進的熱管理，由於對高功率發光二極體（LED）的需求正在增加，所以準確和即時確定包裝材料的 CTE 正變得越來越重要。在這項研究中，我們使用光學相干斷層掃描（OCT）來測量封裝在聚苯乙烯樹脂中的 InGaN 基板（λ= 450 nm）高功率 LED 的 CTE。觀察和記錄 OCT 圖像的各個界面之間的距離，以導出在不同註入電流下封裝 LED 的瞬時 CTE。順向電壓法建立了不同注入電流下的 LED 結溫。因此，測得的聚苯乙烯樹脂的瞬時 CTE 在 25-225℃的結溫範圍內從 5.86×10-5℃-1 變化到 14.10×10-5℃-1，並且在 OCT 掃描區域中呈現均勻分佈 200 微米×200 微米。最重要的是，這項工作證實了 OCT 可以提供一種替代方法來直接和非破壞性地確定封裝 LED 器件的空間分辨 CTE 的假設，並提供了優於傳統 CTE 測量技術的顯著優勢。. 關鍵字：隨機雷射、銀奈米稜鏡、局域表面電漿、彎曲應變、熱膨脹係數、光學相干斷層掃描. II.

(6) Abstract The study is divided into two parts. 1. Flexible random lasers with tunable lasing emissions. 2. Determination on the Coefficient of Thermal Expansion in High-Power InGaN-based Light-emitting Diodes by Optical Coherence Tomography.. In this study, we experimentally demonstrated a flexible random laser fabricated on the polyethylene terephthalate (PET) substrate with a high degree of tunability in lasing emissions. Random lasing oscillation arises mainly from the resonance coupling between the emitted photons of gain medium (Rhodamine 6G, R6G) and the localized surface plasmon (LSP) of silver nanoprisms (Ag NPRs), which increases the effective cross-section for multiple light scattering, thus stimulating the lasing emissions. More importantly, it is found that the random lasing wavelength is blue-shifted monolithically with the increase in bending strains exerted on the PET substrate, and a maximum shift of ~15 nm was achieved in the lasing wavelength, when a 50% bending strain was exerted on the PET substrate. Such observation is highly repeatable and reversible, and this validates that we can control the lasing wavelength by simply bending the flexible substrate decorated with the Ag NPRs. The scattering spectrum of the Ag NPRs is measured using a dark-field microscope to understand the mechanism for the dependence of wavelength shift on the exerted bending strains. As a result, we believe that the experimental demonstration of tunable lasing emissions based on the revealed structure III.

(7) is expected to open up a new application field of random lasers.. The coefficient of thermal expansion (CTE) is a physical quantity that indicates the thermal expansion value of a material upon heating. For advanced. thermal. management,. the. accurate. and. immediate. determination of the CTE of packaging materials is gaining importance because the demand for high-power lighting-emitting diodes (LEDs) is currently increasing. In this study, we used optical coherence tomography (OCT) to measure the CTE of an InGaN-based (λ = 450 nm) high-power LED encapsulated in polystyrene resin. The distances between individual interfaces of the OCT images were observed and recorded to derive the instantaneous CTE of the packaged LED under different injected currents. The LED junction temperature at different injected currents was established with the forward voltage method. Accordingly, the measured instantaneous CTE of polystyrene resin varied from 5.86 × 10 -5 °C-1 to 14.10 × 10-5 °C-1 in the junction temperature range 25–225 °C and exhibited a uniform distribution in an OCT scanning area of 200 μm × 200 μm. Most importantly, this work validates the hypothesis that OCT can provide an alternative way to directly and nondestructively determine the spatially resolved CTE of the packaged LED device, which offers significant advantages over traditional CTE measurement techniques.. Keywords: Random laser; Silver nanoprism; Localized surface plasmon; Bending strain; Coefficient of thermal expansion; Optical coherence tomography. IV.

(8) Contents 中文摘要 ................................................................................................. I Abstract ................................................................................................. III Contents .................................................................................................. V List of figures....................................................................................... VII Chapter 1 Introduction ............................................................................. 1 1-1 Optical properties of random lasers ............................................ 1 1-2 Bending strain of PET substrate ................................................. 6 Chapter 2 Experimental method ............................................................... 9 2-1 Synthesis of silver nanoprisms (Ag NPRs) ................................. 9 2-2 Evolution of the absorption spectrum of Ag NPRs with different synthesis times ............................................................................... 10 2-3 Device fabrication .................................................................... 12 2-4 Characterization of a random laser measurement system ......... 13 Chapter 3 R6G film incoporated with the Ag NPRs ............................... 15 3-1 Plasmonic effect of Ag NPRs on R6G ...................................... 15 3-2 Emission of R6G in methanol for different dye concentrations 21 3-3 Random lasers observed on R6G with the Ag NPRs ................ 24 3-4 FDTD simulations of electric field distribution in the Ag NPRs ....................................................................................................... 36 3-5 Durability test .......................................................................... 38 Chapter 4 The thermal expansion of high power LED ........................... 41. V.

(9) 4-1 Introduction ............................................................................. 41 4-1-1 Thermal management .................................................... 41 4-1-2 The advantages of OCT ................................................ 43 4-2 High-power InGaN-based LEDs .............................................. 46 4-3 Junction temperature of the LEDs ............................................ 49 Chapter 5 Thermal expansion coefficient determined by the OCT ......... 51 5-1 Cross-sectional 2D & 3D OCT images .................................... 51 5-2 Thickness variance vs. injected current .................................... 56 5-3 Spatial distribution of thermal strain & CTE ............................ 61 5-4 Statistical results of CTE value under different injection current ....................................................................................................... 64 Chapter 6 Conclusions ........................................................................... 67 References ............................................................................................. 69. VI.

(10) List of figures Fig. 1.1 Schematic of the design of (a) a conventional laser resonator cavity with its two discrete end mirrors and (b) a random laser based on scattering. Due to their different geometries the lasers exhibit very different characteristics. Green arrows indicate the output laser beam from the devices; red spheres are scattering particles and blue arrows show optical paths. ................................. 2 Fig. 1.2 Advantages of random laser ........................................................ 3 Fig. 2.1 Evolution of the absorption spectrum of the Ag NPRs for the synthesis time from 2 to 10 min. Inset: photograph of a series of Ag NPR solutions with different synthesis times. .............................. 11 Fig. 2.2 Random laser measurement system........................................... 14 Fig. 3.1 (a) SEM image (scale bar = 300 nm) and (b) absorption spectrum of the as-synthesized Ag NPRs. Inset of (a): An enlarged SEM image to identify the edge length of Ag NPRs (scale bar = 50 nm). ..................................................................................................... 17 Fig. 3.2 (a) Absorption (dashed line) and photoluminescence (solid line) spectra of Rhodamine 6G (R6G) dissolved in methanol. Insets: photograph of the fabricated sample illuminated by the green radiation of λ=532 nm (on the right-hand side) and the chemical structure of R6G (on the left-hand side). (b) Normalized PL spectra of R6G films spin-coated on the PET substrate decorated with (red. VII.

(11) line) and without (black line) the Ag NPRs. Inset: PL enhancement ratio as a function of wavelength. ................................................. 19 Fig. 3.3 Normalized PL spectra of R6G dye dissolved in methanol with various R6G concentrations ranging from 10-2 to 10-6 g/ml. ......... 22 Fig. 3.4 Overlap spectra of the PL emission of R6G with the absorption spectrum of the Ag NPRs. ............................................................ 23 Fig. 3.5 Schematics of the R6G film spin-coated on the PET substrate decorated (a) without and (b) with the Ag NPRs. Spectral evolutions of the R6G film spin-coated on the PET substrate decorated (c) without and (d) with the Ag NPRs with the increase in the pump fluence in the range 24.90 − 146.62 μJ and 24.90 − 69.60 μJ, respectively. .................................................................. 26 Fig. 3.6 Homemade tool to control the bending strain exerted on the PET substrate. ...................................................................................... 27 Fig. 3.7 (a) Spectral evolutions of the R6G film decorated with the Ag NPRs with the increase in the pump fluence (24.90 − 69.60 μJ) under different bending strains of 0%, 30%, and 50% (from top to bottom). For comparison, the uppermost panel shows the evolution of the PL spectra of pure R6G film without Ag NPRs. Insets: zoomed-in spectra of the lasing spikes to identify the spacing of laser modes. A schematic presenting the curvature evolution of the fabricated samples that was deformed under different bending strains is also plotted in the figure. (b) Peak intensity of emission VIII.

(12) spectrum vs. pump fluence (L-L curve) for the R6G film decorated with the Ag NPRs under different bending strains of 0%, 30%, and 50% on the PET substrate. The L-L curve of pure R6G film is also plotted in the figure for comparison (the leftmost panel). ............. 30 Fig. 3.8 (a) Scattering spectra of the R6G film with Ag NPR-decorated PET substrate under different bending strains from 0% to 50%. (b) Scattering spectra of pure PET substrate obtained under the same condition as that of (a) for comparison. The curves in both figures shift vertically (i.e., along the y-axis), which results in a more easy identification of any shift in the peak wavelength of the scattering spectra. ......................................................................................... 32 Fig. 3.9 FDTD-simulated scattering spectra of the Ag NPRs with different interparticle distances, d. Inset: a schematic of the simulation geometry. ..................................................................................... 34 Fig. 3.10 Schematic illustration of physical parameters and coordinate system adopted in the FDTD simulation....................................... 35 Fig. 3.11 FDTD simulations of the electric field distribution (Ey) for the Ag NPRs with d =100 nm (left panel) and d = 300 nm (middle panel) at  = 600 nm. Simulated Ey profile of single Ag NPR is plotted in the right panel of the figure. ......................................... 36 Fig. 3.12 FDTD-simulated scattering spectra of the Ag NPRs with different edge lengths ranging from 50 to 70 nm, with an interval of 5 nm. ............................................................................................ 37 IX.

(13) Fig. 3.13 Variation in the threshold of pump fluence as a function of repetitive bending number with (blue square) and without (red square) 50% bending strain on the random laser. [Insets: photographs of the fabricated sample without (left) and with (right) mechanical bending.] ................................................................... 39 Fig. 4.1(a) Photograph of the packaged InGaN-based (λ = 450 nm) high-power LED used in this study. Inset: Microscope top-view image focusing on the center of the packaged LED device. The marked region (dash-line square) represents the chip area of 200 × 200 μm used for the subsequent statistical analysis of the spatial variations of the OCT images. (b) Raman spectrum of polystyrene resin excited by a 532-nm diode-pumped, solid-state laser. Inset: Repeating unit of the chemical structure of polystyrene resin. (c) Light-output power and forward voltage versus forward current for the packaged LED device. Inset: EL spectra of the packaged LED device under different injected currents (from 50 to 500 mA). ..................................................... 48 Fig. 4.2(a) Pulsed calibration measurement (duty cycle = 0.1%, pulse width = 6.5 μs), and (b) measured V f and junction temperature versus injected current of the packaged LED device. Inset: Differential of V f with respect to the temperature (dV f /dT) versus injected current. ........................................................................... 50 Fig. 5.1(a) Schematic diagram of the SS-OCT system. BD: balanced X.

(14) detector,. PC: polarization controller,. C: collimator,. DC:. dispersion compensator, OL: objective lens, M: mirror, and Galva: Galvanometer scanner. (b) Schematic of the configuration of the packaged LED device. (c) Cross-sectional 2D and (d) reconstructed 3D OCT images of the packaged LED device without an injected current. The locations of the Au wires and the LED chip are also labeled in the figures. (e) Top-view 3D OCT image of the polystyrene resin. ................................................... 53 Fig. 5.2(a) Magnified cross-sectional 2D OCT image of the packaged LED device obtained near the LED chip area. (b) Depth-resolved OCT signal curves of the packaged LED device under different injected currents (I = 0/250/500 mA). Magnified images of the first (at 0 μm) and second (at ~1500 μm) peaks are also included in the figure to calculate the corresponding depth position shift under different injected currents. ................................................ 55 Fig. 5.3(a) Thickness variation versus injected current for the polystyrene resin (black squares) and sapphire substrate (blue squares). (b) Thermal strain (εthermal ) and instantaneous CTE versus junction temperature of the packaged LED device for the polystyrene resin. ........................................................................ 59 Fig. 5.4(a) Pure polystyrene resin dispersed on the top surface of the glass substrate as a reference material for the OCT scanning. (b) Instantaneous CTE against operating temperature for the pure XI.

(15) polystyrene resin. ......................................................................... 60 Fig. 5.5 Spatial distribution of ε thermal (a–e) and CTE (f–j) for the polystyrene resin over a specific chip area of 200 × 200 μm [marked in the insert of Fig 4.1 (a)] under different injection current conditions of 100, 200, 300, 400, and 500 mA. .............. 62 Fig. 5.6 Cross-sectional scanning electron microscope (SEM) image of top surface of the InGaN-based LED examined in this work. ....... 63 Fig. 5.7 Statistical results (mean and variance) of (a) εthermal and (b) CTE values versus injected current for the polystyrene resin of the packaged LED device over a specific chip area of 200 × 200 μm [marked in the insert of Fig 4.1 (a)]. ........................................... 65. XII.

(16) Chapter 1 Introduction 1-1 Optical properties of random lasers Conventional laser versus a diffusive random laser(see Fig. 1.1) : While a conventional laser cavity (left) has highly reflecting mirrors that trap light long enough for amplification by the gain medium (light blue) to be efficient, trapping of light in a random laser (right) is not achieved by mirrors, but by multiple scattering between subwavelength-size particles (red dots). In such a random medium, the light emitted by an atom (yellow) can make a roundtrip in an infinite number of loops. In the special case of a diffusive random laser, the scattering is so weak that without gain most of the light would escape before returning to its starting point. Because of this strong damping (leakage), the oscillation frequencies of such a system are not well-defined until lasing sets in and a number of well-defined, sharp oscillation frequencies appear, bearing no straightforward relationship to the strongly damped natural oscillations of the system without gain. (Courtesy of Science Magazine and Robert Tandy).. 1.

(17) Fig. 1.1 Schematic of the design of (a) a conventional laser resonator cavity with its two discrete end mirrors and (b) a random laser based on scattering. Due to their different geometries the lasers exhibit very different characteristics. Green arrows indicate the output laser beam from the devices; red spheres are scattering particles and blue arrows show optical paths.. Compared to traditional lasers which need fixed reflection mirrors to form a cavity, random lasers can be generated by using scattering materials to form cavity-like multiple scattering loop paths. There are several unique advantages of random lasers (see Fig. 1.2), such as simple fabrication process, small size, low cost, multiple lasing wavelengths, broad solid angle of lasing output. In recent years, random lasers have been employed in speckle-free imaging, medical diagnostics, liquid crystal display and illumination system.. 2.

(18) Fig. 1.2 Advantages of random laser. Random lasers, unlike the conventional lasers that assemble rigid optical elements to construct the reflective resonant cavity for achieving an optical feedback, are one of the most unique light sources for which the lasing properties are mainly determined by the interaction between the light scattering and the gain material [1.1-1.5]. The emitted light is trapped. and/or. diffused. into. the. gain. medium. through. the. disorder-induced multiple scatterings similar to the electron transport behavior observed in a defect-containing solid [1.6,1.7], leading to the formation of multiple closed loops for the emitted photons, which is the required optical feedback for lasing actions. In short, the occurrence of random lasing action could be regarded as a combined process of the diffusion of emitted photons and optical amplification. To probe the abundance of fundamental physics and possibly realize the Anderson localization of photons [1.8-1.11], random lasers have been intensely studied over the past decade along with the witness of random lasing actions. in. various. materials 3. such. as. semiconductor.

(19) nanostructures/powders. [1.12,1.13],. dye-doped. liquid. crystals. [1.14,1.15], dye-infiltrated composites [1.16,1.17], and even human tissue [1.18,1.19]. As reflective resonant cavity and additional optical elements are not involved in the lasing process, the random laser devices are of low cost, can easily be fabricated on a large area, and have high flexibility in operation; and the unique optical property of random lasers gives rise to an interesting potential for their applications in environment lighting, remote sensors, and medical diagnostics [1.20-1.22]. However, tunability is an important feature that profoundly affects and determines the application scope of laser devices. The tuning of conventional lasers can be easily achieved by adjusting the resonant frequency (or length) of the resonant cavity to control both the wavelength and optical mode of lasing emissions. However, for a random laser, the lack of both a well-defined resonant cavity and the rigid alignment of optical elements results in a relatively more difficult tuning of random lasing emissions; therefore, considerable attempts have been made by researchers to overcome this issue [1.23-1.30]. To generate tunable random lasing emissions, a specific type of disordered medium, in which the degree/intensity of multiple random scatterings for the emitted photons can be varied to a certain extent, should be incorporated into the random laser system. Liquid crystal materials with the unique anisotropy of birefringence were first proposed and had been widely used as the disordered media to generate random lasers with high tenability [1.20,1.23,1.24]. Because the orientation of liquid crystal molecules can be controlled by applying an electric field or by changing the ambient temperature, it is therefore possible to obtain 4.

(20) different scattering intensities and diffusion constants for the emitted photons, and thus the physical properties of random lasers such as lasing threshold, emission wavelength, and even optical polarization are tunable. Additionally, a novel three-dimensional (3D) disordered structure composed of self-assembled monodisperse polystyrene microspheres, which can spectrally modify the scattering coefficient of emitted photons through the so-called Mie resonances, was recently proposed [1.25-1.27]. The transmission spectrum of such 3D disordered structure can be controlled to match with the gain profile by changing the diameters or the refractive index of polystyrene microspheres. This gives rise to random lasers of preferential emission wavelengths. The utilization of a stretchable substrate is another feasible method to generate tunable random lasers. A disordered medium (e.g., ZnO nanobrushes [1.28,1.29] and silver nanowires [1.30] ) is firs embedded into the stretchable substrate, and then the interplay between the disordered medium and the emitted photons, including the formation of coherent loops and the peak position of plasmonic resonance is then manipulated by mechanically stretching the deformable substrate. All the lasing parameters, for instance, the number of modes, the emission wavelength, and the degree of polarization, can be tunable by this method.. 5.

(21) 1-2 Bending strain of PET substrate In this work, we developed a feasible and reliable approach to generate a random laser with a wide tunable range in the emission wavelength. We experimentally demonstrated that the lasing wavelength is correlated to the bending diameter of the curvature on the flexible PET substrate underneath, and hence, it exhibits a high tunability in accordance with the observed scattering spectrum of the silver nanoprisms (Ag NPRs). Although the generation of random lasing emissions has been well established on flexible substrates and widely reported in the literature [1.31], the aim of this work was to confirm that the optical properties of random lasers could be controlled simply by mechanical bending. Such phenomenon, to our knowledge, has been rarely observed or discussed in the past. However, the incorporation of regular or irregular shaped metallic nanoparticles into optical gain to stimulate random lasing emissions has been reported in the recent years [1.32-1.34]. A high degree of spectral overlap between the localized surface plasmon (LSP) resonance of metallic nanoparticles and the optical profile of gain medium facilitates the random lasing oscillations. A similar mechanism that relies on the surface plasmon effect to stimulate the so-called plasmon nanolaser through the light-matter interactions has been intensively studied as well [1.35-1.37]. Such plasmon nanolaser outperforms the conventional laser because of its extremely small mode volume, large Purcell factor, and slow group velocity to ensure strong exciton/matter coupling. Consequently, as compared to the previous work in which Ag 6.

(22) nanowires were used as the tunable medium [1.30], the proposed strategy in this study directly controls the scattering profile of the Ag NPRs to match with the Rhodamine 6G (R6G) gain by bending the flexible PET substrate that influences the coupling strength and the resonant frequency on the LSP of the Ag NPRs. Because the bending strain mainly affects the interparticle distance in Ag NPRs and barely causes breakages or damages to them, the resultant tuning of lasing wavelength is hence reversible and highly repeatable. It is very difficult to achieve by using the previously described method. Additionally, their claim of lasing emission is closer to the amplified spontaneous emission, rather than the coherent random lasing emission [1.30]. As a result, a maximum shift of ~15 nm was achieved in the lasing wavelength, which is higher than the previously reported value of ~7 nm. This means that we can stimulate a random lasing action with a preferential lasing wavelength within the gain profile of the gain medium, in turn providing a new important feature in the functionality of flexible optoelectronic devices. We expect that this flexible and tunable random laser would be used in a broad range of novel applications such as wearable gadgets for personal healthcare and structural health monitoring of civil infrastructure. Additionally, the fundamental of light-matter interaction and how it affects the transport mean free path of emitted photons at the nanoscale range can also be investigated using such novel structure.. 7.

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(24) Chapter 2 Experimental method 2-1 Synthesis of silver nanoprisms (Ag NPRs) Ag NPRs were synthesized by a soft solution-phase method according to a previously described procedure [2.1]. An aqueous solution of silver nitrate (0.05 M, 50 µL), trisodium citrate (75 mM, 0.50 mL), ethanol (17.5 mM, 0.10 mL), and hydrogen peroxide (35 wt. %, 60 µL) were added into 24.14 mL of DI water and stirred vigorously at room temperature. The total volume of the reaction solution was 25 mL. Sodium borohydride (NaBH4, 100 mM, 70 µL) was then rapidly added into this mixture to initiate the reduction reaction, and this immediately changed the color of chemical solution to light yellow. After approximately 30 s, the colloidal solution turned to deep yellow because of the formation of small Ag nanoparticles. Over the next few minutes, the morphology of Ag particles began to vary and eventually evolved into nanoprism-shaped particles, accompanied with changes in the solution color from deep yellow to red, purple, and blue, indicating that the feature dimensions of nanoprisms increased gradually with time. In general, the entire evolution of Ag NPR morphology takes 2-10 min approximately.. 9.

(25) 2-2 Evolution of the absorption spectrum of Ag NPRs with different synthesis times Fig. 2.1 shows the evolution of the absorption spectrum of Ag NPRs when the synthesis time was increased from 2 to 10 minutes. As mentioned in the experimental section of the article, the addition of NaBH4. into. the. mixed. aqueous. solution. (AgNO3/Na3C6H5O7/C2H6O/H2O2) induces the reduction of silver. This instantly changes the solution color from the original colorless to light yellow and then to deep yellow within ~30 seconds. This indicates the formation of Ag nanoparticles. After that, the morphology of Ag particles started to vary and eventually evolved into nanoprism-shaped particles over the next few minutes (2–10 min), accompanied with the further change in solution color from deep yellow to red, purple, and blue (inset, Fig. 2.1). It should be noted that in this step, we continuously added proper amounts of NaBH4 and stirred incessantly to ensure that the reaction of silver reduction is complete throughout the entire solution. According to Fig. 2.1, the original intensity of the absorption peak at ~408 nm associated with small Ag nanoparticles decreased considerably with the increase in the synthesis time, because of the consumption of small Ag nanoparticles during the reaction. Furthermore, a clear red shift was observed on another dominant absorption peak with an initial peak wavelength of ~514 nm, implying the dimension growth and well formation of Ag NPRs with the increase in synthesis time. In this study, we chose Ag NPRs with a synthesis time in between 3 and 6 min as the resultant LSP peak exhibited high spectral overlapping with the PL 10.

(26) spectrum of R6G gain medium.. Fig. 2.1 Evolution of the absorption spectrum of the Ag NPRs for the synthesis time from 2 to 10 min. Inset: photograph of a series of Ag NPR solutions with different synthesis times.. 11.

(27) 2-3 Device fabrication Ten milliliters of the as-synthesized Ag NPR solution was added in a 25-mL bottle. First, a clean and transparent polyethylene terephthalate (PET) substrate was immersed in the solution for 2 days, which was then removed and dried naturally. Subsequently, the Ag NPRs were randomly distributed and covered over the entire surface of the PET substrate. Furthermore, a mixture of R6G (purchased from Sigma-Aldrich) and methanol at a concentration of 2 g/L was prepared in an ultrasonic bath to ensure a complete dissolution of the R6G dye into the methanol. The dissolved R6G solution and the UV glue were then mixed together under a volume ratio of 2:1. Subsequently, the mixture solution composed of R6G and UV glue (2:1) was spin-coated onto the PET substrate decorated with the Ag NPRs by the two-step spin-coating method (1000 rpm/30 s; 3000 rpm/10 s). Finally, the sample was cured under the UV-light exposure for 1 min and dried in an oven at 65 °C for 2 h. For comparison, we prepared a sample by the same fabrication process, except that the surface of the PET substrate was not decorated with the Ag NPRs, was also prepared.. 12.

(28) 2-4 Characterization of a random laser measurement system The morphology of the synthesized Ag NPRs was characterized using a field emission Scanning Electron Microscope (FE-SEM, JEOL JSM-7600F) (see Fig. 2.2). The optical absorption of the R6G film and the. Ag. NPRs. was. collected. using. a. hitachi. double. beam. spectrophotometer U-2900. Steady-state PL emissions of the fabricated samples were excited by a 532-nm diode-pumped solid-state continuous wave (CW) laser and recorded using a spectrometer equipped with a charge-coupled device (CCD, spectral resolution of 0.25 nm) detector, which was cooled by liquid nitrogen. To stimulate the random lasing emissions in the R6G film decorated with the Ag NPRs on the PET substrate, the fabricated sample was mounted on a stage for 3D adjustment. We then used a frequency-doubled Q-switched Nd:YAG laser as a pump source with a pulse duration of 5 ns, wavelength of 532 nm, and a repetition rate of 10 Hz. The incident laser beam was focused on the central area of the fabricated sample in a strip shape of 50-µ m width and 6.0-mm length by a cylindrical lens at an incidence angle of 45 o with respect to the surface normal. The random lasing emission and/or lasing modes were collected along the strip axis (in the horizontal direction) from the edge of the fabricated sample by an optical fiber to couple with a CCD-equipped grating spectrometer (iHR550 HORIBA JOBIN YVON).. 13.

(29) Fig. 2.2 Random laser measurement system. 14.

(30) Chapter 3 R6G film incoporated with the Ag NPRs 3-1 Plasmonic effect of Ag NPRs on R6G To examine the characteristics of the as-synthesized Ag NPRs, we first used FE-SEM to observe their shape and size and measured the corresponding absorption spectrum. Fig. 3.1 (a) shows the SEM image of the as-synthesized Ag NPRs. The Ag NPRs were composed of large amounts of nanoprisms with edge lengths of ~90 nm and a small amount of irregular nanoparticles with diameters typically less than 50 nm. Furthermore, most of the Ag NPRs had sharp and clear edges, while the edges of some Ag NPRs were truncated. These observed Ag NPRs and irregular nanoparticles were related to the synthesis processes. During the synthesis of the Ag NPRs, smaller nanoparticles first emerged as the nucleation sites, which then gradually increased in dimensions and finally obtained prism-like shapes with the increase in the reaction time [3.1]. However, the irregular shapes observed on the SEM image with diameters less than 50 nm is mainly due to the incomplete reactions during the synthes process of Ag NPRs. As a result, approximately 75% of the Ag nanoparticles was successfully converted into Ag NPRs. The absorption spectrum of the synthesized Ag NPRs exhibited a quite broadband, ranging from 400 to 900 nm with two distinct absorption peaks at λ = 445 nm and λ = 620 nm (Fig. 3.1 (b)). In general, the size, geometric shape, and distribution density of metallic nanoparticles affect the peak position of the LSP situated in the absorption spectrum. The LSP absorption peak shifted toward the longer wavelength region (red shift) 15.

(31) with the increase in dimensions of metallic nanoparticles (see Fig. 2.1). In addition, the structural anisotropy of metallic nanoparticles profoundly affected the corresponding optical characteristics; thus, it would induce more than one LSP resonance peak, determined mainly by their geometric shape. According to the previous studies [3.2,3.3], four discernible absorption peaks associated with dipole and quadrupole polarizations in both in-plane and out-of-plane plasmon resonances were clearly identified at λ = 340 nm (out-of-plane quadrupole), λ = 410 nm (out-of-plane dipole), λ = 470 nm (in-plane quadrupole), and λ = 770 nm (in-plane dipole) for a perfect triangular nanoprism. As a result, the weak absorption peak observed in the range ~400 to ~470 nm, as shown in Fig. 3.1 (b), could be reasonably assigned to a combination of the out-of-plane dipole and the in-plane quadrupole plasmon resonances, whereas the strong and well-defined LSP peak at λ = 620 nm could be merely attributed to the in-plane dipole resonance. The induced polarization along the in-plane dipole resonance is extremely sensitive to the sharpness of the tips of the Ag NPRs [3.3], and its shift from the original LSP peak of 770 to 620 nm was due to the inevitable truncation in the tips of Ag NPRs during the synthesis process.. 16.

(32) Fig. 3.1 (a) SEM image (scale bar = 300 nm) and (b) absorption spectrum of the as-synthesized Ag NPRs. Inset of (a): An enlarged SEM image to identify the edge length of Ag NPRs (scale bar = 50 nm).. Fig. 3.2 (a) shows the absorption and photoluminescence (PL) spectra of R6G dissolved in methanol. Such R6G/methanol solvent was mixed with the UV glue and then spin-coated on the PET substrate to further examine the luminescence properties. Under the illumination of green light (λ = 532 nm), the resulting film glowed nonuniformly as shown in the inset on the right-hand side of Fig. 3.2 (a). This was possibly due to the formation of cracks or the aggregation of R6G molecules after methanol evaporation, which might cause a fluctuation in the refractive index of the R6G film. This in turn induces random refraction that influences the appearance of illuminated color of the R6G film. Additionally, the peak wavelength of PL spectrum (λ P) was determined by the R6G concentration, and λP red-shifted with the increase in concentration because of the aggregation of R6G molecules. Thus, the 3-ring systems (as shown in the left-hand side of Fig. 3.2 (a) inset) are aligned in parallel, modifying the electronic structure of R6G; 17.

(33) consequently, λP can extend into a long-wavelength regime. As shown in Fig. 3.2 (a), we purposely added a high concentration of 10-2 g/ml, so that λP was substantially red-shifted to 562.2 nm in comparison to the low concentration case of 10 -6 g/ml with λP = 550.0 nm (see Fig. 3.3). As a result, it offered a high degree of spectral overlapping with the absorption band of the Ag NPRs (Fig 3.1(b)) for inducing the coupling with the LSP resonances; thus, the PL intensity of the R6G film was enhanced. Yet, the absorption spectrum barely changed with a variation in the R6G concentration, and an extinction peak at λ = 540.0 nm was observed, as shown in the figure. The overlap integral, J(λ), which represents the degree of spectral overlap between the R6G emission and the Ag NPR absorption, can be expressed as follows [3.4,3.5]:. (1). where FD (λ) is the corrected PL emission spectrum of the R6G with the total intensity (area under the curve) normalized to unity and εA (λ) is the extinction coefficient of the Ag NPRs at wavelength λ (in nanometer). In our case (see Fig. 3.4), J(λ) was calculated to be 6.50  1020 nm4 M-1 cm-1, which is quite comparable to the previously reported value (1.22  1021 nm4 M-1 cm-1) obtained by a CW random lasing system, where naturally occurring biocompatible pigments were used as the gain medium [3.4], suggesting that a strong light-matter interaction is hence expected in our random laser system. Fig. 3.2 (b) shows the normalized PL spectra of R6G films decorated with (red line) and without (black 18.

(34) line) the Ag NPRs, which were excited at room temperature by a 532-nm diode-pumped solid-state CW laser with a pumping intensity of 20 mW. The PL enhancement ratio as a function of wavelength, i.e., the PL intensity of the R6G film decorated with the Ag NPRs divided by that without the Ag NPRs, is also shown in the figure inset. Accordingly, the PL intensity of the R6G film decorated with the Ag NPRs was increased by 2.67 folds at λ = 558.3 nm in comparison to that without the Ag NPRs, indicating an efficient resonance coupling between the emitted photons of R6G and the LSP of the Ag NPRs. The largest PL enhancement ratio of 3.23 fold was observed at λ = 564.5 nm, which was slightly red-shifted with respect to the peak wavelength of pure R6G film and was becoming closer to the LSP resonance peak of the Ag NPRs at λ = 620.0 nm. Again, this validates the hypothesis that the interaction between the emitted photons of R6G film and the LSP of the Ag NPRs indeed has an efficient resonance coupling that is likely to increase the effective scattering cross-section of the Ag NPRs, thus prompting the random lasing actions.. Fig. 3.2 (a) Absorption (dashed line) and photoluminescence (solid line) spectra of Rhodamine 6G (R6G) dissolved in methanol. Insets: photograph of the fabricated sample illuminated by the green radiation of λ=532 nm (on the right-hand side) and 19.

(35) the chemical structure of R6G (on the left-hand side). (b) Normalized PL spectra of R6G films spin-coated on the PET substrate decorated with (red line) and without (black line) the Ag NPRs. Inset: PL enhancement ratio as a function of wavelength.. 20.

(36) 3-2 Emission of R6G in methanol for different dye concentrations Fig. 3.3 shows the normalized PL spectra of R6G dye dissolved in methanol with various R6G concentrations ranging from 10-2 to 10-6 g/ml. Accordingly, the peak wavelength of PL spectrum (λ P) is red-shifted with the increase in R6G dye concentration. The R6G with the highest concentration solution (i.e., 10-2 g/ml) emits at λP = 562.2 nm. Dilution of concentration by addition of methanol leads to an obvious blue shift in λP. For the lowest R6G concentration of 10-6 g/ml, λP was at around 550.0 nm, moving away from the LSP peak of the Ag NPRs. λ P does not shift to the longer wavelength range but remains constant at around 562.2 nm when we further increase the R6G concentration to 10 -1 g/ml. Because such high concentration of R6G will cause non-uniformity in the spin coating on the PET substrate, we selected a R6G concentration of 10 -2 g/ml as the treatment condition for the subsequent experiments in this study.. 21.

(37) Fig. 3.3 Normalized PL spectra of R6G dye dissolved in methanol with various R6G concentrations ranging from 10 -2 to 10-6 g/ml.. 22.

(38) Fig. 3.4 shows the overlapping spectra of the PL emission of R6G with the absorption spectrum of the Ag NPRs. In the present work, we purposely used a high concentration of R6G, i.e., 10 -2 g/ml; therefore, λP of the PL emission of R6G was substantially red-shifted to 562.2 nm, and there was a significant spectral overlap between the absorption of Ag NPRs (blue line) and the PL emission spectrum of the R6G (red line). The number of Ag NPRs per milliliter of the solution was calculated by using the equation N = (N0C/1000f) (r/R)3, where N0 is the Avogadro number (~6.02 × 1023), C is the concentration of the silver precursor (0.01 mM), f is the packing fraction of the atoms (f = 0.74), r is the radius of silver atoms (r =1.22 Å ), and R is the average radii of the Ag NPRs. Consequently, the number of Ag NPRs was estimated to be 9.46 × 1013 mL-1, and the corresponding overlap integral according to Eq. (1) was thus estimated to be J(λ) = 6.50  1020 nm4 M-1 cm-1.. Fig. 3.4 Overlap spectra of the PL emission of R6G with the absorption spectrum of the Ag NPRs. 23.

(39) 3-3 Random lasers observed on R6G with the Ag NPRs Fig. 3.5 (a) and Fig. 3.5 (b) show the schematics of the R6G film decorated without and with the Ag NPRs on the PET substrate, respectively. To alleviate the influence of the Fabry-Perot resonance on the discrimination of optical modes in the random lasing emissions, we carefully controlled the thickness of the R6G film to be less than 300 nm by finely tuning the spin-coating conditions. The optical excitation on the fabricated samples was conducted by a frequency-doubled Q-switched Nd:YAG laser (λ = 532 nm) with a repetition rate of 10 Hz, and the results are plotted in Fig. 3.5 (c) and Fig. 3.5 (d) for the R6G films decorated without and with the Ag NPRs, respectively. Owing to the high intensity of Nd:YAG laser at 532 nm, here we display only the spectral range from 540 to 640 nm to prevent the misinterpretation of the emission spectra. Fig. 3.5 (c) exhibits few typical features of the spontaneous emission, i.e., the observed emission peak wavelength (at λ = 560 nm) of the R6G film without the Ag NPRs barely changed with the pump fluence in the range 24.90 − 146.62 μJ, whereas the corresponding PL intensity increased linearly with the increase in the pump fluence. Fig. 3.5 (d) shows that similar spontaneous emissions were observed from the R6G film decorated with the Ag NPRs for the low pump fluences (<41.63 μJ). Furthermore, the peak wavelength of the PL spectrum was red-shifted to λ = 566 nm because of the coupling with the LSP resonance of the Ag NPRs. With further increase in the pump fluence (≥41.63 μJ), several sharp and distinct spikes with a full-width at half maximum of 0.5 nm emerging in the spectral range 586 − 598 nm, an indication of random 24.

(40) lasing oscillation associated with the coherent optical feedback, were clearly observed. In a laser system, the optical loss plays an equally important role as that of the optical gain. Although the photon wavelength of  = 564.5 nm was benefited from the maximum gain profile and supposed to achieve the required optical amplification at this specific wavelength (Fig. 3.2 (b)), it was also subjected to a considerable material loss due to the non-negligible reabsorption of R6G medium, as shown in the absorption spectrum in Fig. 3.2 (a). As a result, the random lasing oscillation mainly emerged in the spectral range 586 − 598 nm because of the trade-off between the optical gain and material loss of the entire random laser system; this was because the system had an acceptable optical gain and a negligible material loss in this spectral range.. 25.

(41) Fig. 3.5 Schematics of the R6G film spin-coated on the PET substrate decorated (a) without and (b) with the Ag NPRs. Spectral evolutions of the R6G film spin-coated on the PET substrate decorated (c) without and (d) with the Ag NPRs with the increase in the pump fluence in the range 24.90 − 146.62 μJ and 24.90 − 69.60 μJ, respectively.. To discuss the effect of the bending of the PET substrate on the random laser spectra, we used a homemade tool to deform the PET substrate into a convex shape with a specific curvature (see Fig. 3.6); Fig. 3.6 shows the homemade tool, which can deform the PET substrate into a convex shape with a specific curvature. The distance between the two parallel acrylic sheets can be controlled by screwing the gears in the center. Thus, the bending diameter of the PET was tunable, 26.

(42) which in turn varied the bending strain exerted on it.. Fig. 3.6 Homemade tool to control the bending strain exerted on the PET substrate.. Therefore, a specific bending strain was exerted on the PET substrate. Fig. 3.7 (a) shows the evolution of the PL spectra of the R6G film decorated with the Ag NPRs with the increase in the pump fluence for the PET substrate that was deformed by different bending strains of 0%, 30%, and 50% (from top to bottom). Here, the degree of bending strain is defined as the ratio of the bending diameter of the curvature to the original length of the PET substrate without exerting any bending strain. In this figure, the evolution of the PL spectra of pure R6G film is also plotted in the uppermost panel for comparison. Random lasing emissions were always observed from the R6G films incorporated with the Ag NPRs, irrespective of the application of bending strain on the PET substrate. Quite interestingly, the emission wavelength of induced random laser blue-shifted as the bending strain was increased, and a maximum shift as high as ~15 nm (from 590 to 575 nm) was achieved for the PET 27.

(43) substrate exerted with a bending strain of 50%. Additionally, the spacing between two individual lasing spikes, called as the spacing of laser modes, was estimated to be Δλ = 0.43−0.50 nm for all the observed random lasing spectra (insets, Fig. 3.7 (a)); this barely changed for different bending strains exerted on the PET substrate. In general, the spacing of laser modes can be expressed as follows [3.6]:.   2. . (n  . dn 1 ) d. (2). 2L. where n is the refractive index, L is the resonant cavity length (which is the closed loop path in the random laser system), and λ is the lasing wavelength. Equation (2) suggests that all the induced random lasers have a similar L although different degrees of bending strains were exerted on the PET substrate. Therefore, the observed blue shift in λ is irrelevant to L, according to the definition of the standing wave equation, i.e., 2nL=mλ [3.6], where m is a positive integer. Alternatively, exerting different bending strains to deform the PET substrate barely affects the closed loop path of the random lasers formed by the multiple light scattering between the Ag NPRs. Another mechanism responsible for the observed blue shift in λ, must exist. Here, it should be noted that we also measured the PL spectra of pure R6G film; however, no blue shift of the PL emission was observed while exerting different bending strains on the PET substrate. This validates that the blue shift in λ is attributed to the introduction of the Ag NPRs. Fig. 3.7 (b) plots the peak intensity of emission spectrum 28.

(44) versus the pump fluence (L-L curve) for the R6G film decorated with the Ag NPRs under different bending strains of 0%, 30%, and 50%. The L-L curve of pure R6G film is also plotted in the figure for comparison (the leftmost panel). Furthermore, the intensity of each emission spectrum was normalized to the maximum peak intensity, i.e., the one for the R6G film decorated with Ag NPRs under 30% bending strain and pump fluence of 69.60 μJ. Accordingly, the peak intensity of PL emission of pure R6G film increased gradually with the increase in pump fluence, which gave rise to a low and static slope in the corresponding L-L curve. For all the R6G films decorated with the Ag NPRs, in contrast, the slopes of their L-L curves increased rapidly above a certain threshold in the pump fluence, confirming the onset of random lasing oscillations. The estimated thresholds of pump fluence were 38.35, 35.08, and 47.46 μJ for 0%, 30%, and 50% bending strains exerted on the PET substrate, respectively. As compared to the earlier reported threshold of pump fluence obtained using the same R6G as the gain medium but incorporated with different nanostructures as scattering media, such as TiO2 nanoparticles (15 mJ), Al nanoparticles (1.2 mJ), and ZnO nanorods (73.8 J) [3.7-3.9], the estimated thresholds of pump fluence herein, which ranged from 35.08 to 47.46 μJ and mainly depended on the bending strains exerted on the PET substrate, are much lower. This suggests that in the present work, the strong light-matter interaction between the emitted photons and the LSP of Ag NPRs can indeed enhance the light scattering, which effectively reduces the threshold of pump fluence required to stimulate the random lasing action.. 29.

(45) Fig. 3.7 (a) Spectral evolutions of the R6G film decorated with the Ag NPRs with the increase in the pump fluence (24.90 − 69.60 μJ) under different bending strains of 0%, 30%, and 50% (from top to bottom). For comparison, the uppermost panel shows the evolution of the PL spectra of pure R6G film without Ag NPRs. Insets: zoomed-in spectra of the lasing spikes to identify the spacing of laser modes. A schematic presenting the curvature evolution of the fabricated samples that was deformed under different bending strains is also plotted in the figure. (b) Peak intensity of emission spectrum vs. pump fluence (L-L curve) for the R6G film decorated with the Ag NPRs under different bending strains of 0%, 30%, and 50% on the PET substrate. The L-L curve of pure R6G film is also plotted in the figure for comparison (the leftmost panel). 30.

(46) To examine the scattering behavior of emitted photons by the synthesized Ag NPRs, and discuss how the different bending strains influence the observed blue shift in random lasing emissions, we obtained the scattering spectrum of the fabricated samples using a dark-field microscope, where the illuminating white light, instead of directly passing through the Ag NPRs, is. obliquely incident on the specimen in. a dark background [3.10]. Hence, most of light striking the Ag NPRs is scattered back into the objective lens of the microscope and then collected by the spectrometer equipped with a CCD to construct the scattering spectrum. Therefore, a spectral measurement by dark-field microscopy provides a direct way to probe the multiple light scattering by the Ag NPRs. For the R6G film decorated with the Ag NPRs as shown in Fig. 3.8 (a), an oscillation phenomenon was observed in the scattering spectrum. One of the oscillation maxima falls into the emission band of random laser, indicating that the coherent optical feedback of random laser is supported by this oscillation maximum. For example, without applying the bending strain on the PET substrate (pink curve), one of the oscillation maxima of scattering spectrum located at 591.59 nm (labeled with a triangle in Fig. 3.8 (a)) is within the emission band (586 – 598 nm) of random laser. This oscillation maximum and other oscillation maximum were blue-shifted gradually with the increase in bending strains exerted on the PET substrate, which drags the random lasing emissions toward the lower wavelength region of the gain profile of the R6G. An ultimate shift as large as 14.54 nm in the peak wavelength of scattering spectrum was measured for a bending strain of 50% exerted on the PET substrate, agreeing well with the observed blue shift amount of 31.

(47) the random lasing emissions as shown in Fig. 3.7 (a). For comparison, we measured the bending strain dependence on the scattering spectrum for pure PET substrate (Fig. 3.8 (b)), which did not show any oscillation in the spectral profile or any shifts in the optical wavelength, entirely because of the absence of the Ag NPRs.. Fig. 3.8 (a) Scattering spectra of the R6G film with Ag NPR-decorated PET substrate under different bending strains from 0% to 50%. (b) Scattering spectra of pure PET substrate obtained under the same condition as that of (a) for comparison. The curves in both figures shift vertically (i.e., along the y-axis), which results in a more easy identification of any shift in the peak wavelength of the scattering spectra. 32.

(48) To understand the blue shift observed in the scattering spectrum of the fabricated sample for different bending strains, we performed the finite-difference. time-domain. (FDTD). simulation. by. using. the. commercially available OptiFDTD software (see Fig. 3.10). Fig. 3.9. shows the calculated scattering spectra of the Ag NPRs (  = 570 – 700 nm) excited by the emitted light with a rectangular wave function for different interparticle distances d, as shown in the inset of Fig. 3.9. Furthermore, each curve is shifted vertically along the y–axis, which confirms the blue shift in the calculated scattering spectrum. We assume that d increases monotonously with the increase in the bending strains exerted on the PET substrate. Except for the oscillation in the spectral profile, most of the scattering spectrum was blue-shifted gradually with the increase d, which qualitatively agrees with the experimental observation (Fig. 3.8 (a)). This suggests that the origin of blue shift in the scattering spectrum is essentially associated with the change in d, which alters the mutual surface plasmon interaction (see Fig. 3.11) and the scattering ability of different emitted photons, altogether leading to a blue shift in the scattering spectrum of the Ag NPRs. From this, the peak position of the scattering spectrum can be manipulated. Because the dimensions and shapes of the Ag NPRs are set to be identical in the FDTD simulation, the absence of oscillation in the spectral profile of calculated scattering spectrum is therefore expected (Fig. 3.12). A similar blue shift was observed for gold nanoparticles, when the interparticle distance between each nanoparticle was increased, which enhanced the surface plasma mutual coupling toward high-frequency resonances [3.11]. However, the FDTD simulation is only an initial step that provides a 33.

(49) qualitative illustration and one possibility for the blue shift in the measured scattering spectrum. Further experiments are necessary before we can conclude the physical rationale for the observed effect.. Fig. 3.9 FDTD-simulated scattering spectra of the Ag NPRs with different interparticle distances, d. Inset: a schematic of the simulation geometry.. Fig. 3.10 shows the schematic for the calculation of the scattering spectrum of the Ag NPRs by using the FDTD simulation (OptiFDTD). For simplicity, the shape of Ag NPRs was set as an equilateral triangle, with an edge length of a = 90 nm and a thickness of h = 50 nm. The unit cell composed of such Ag NPRs is deployed on the y-z plane and arranged in the form of a hexagonal close-packed structure, and the interparticle distance between each Ag NPR is represented as d, which ranges from 100 to 300 nm, with 50-nm intervals. This develops a simulation scenario to reflect the distributed variation in the Ag NPRs when different bending strains were exerted on the PET substrate. We assumed that the interparticle distance between each Ag NPR increases monotonously with the increase in bending strains exerted on the PET 34.

(50) substrate. A light wave of rectangular function ( = 400–700 nm) with a linear polarization (parallel to the y-axis) propagating along the negative x-direction was incident on the Ag NPRs to excite the LPS resonance. This was accompanied by the light scattering in random directions. An observation surface was placed right above the Ag NPRs, and in between them, an opaque object with a slightly smaller blocking area than the observation surface was inserted to block the retro-reflection (or scattering light in the normal direction) by the Ag NPRs. From this configuration of FDTD simulation, the observation surface could mainly detect the scattering light, which was scattered by the Ag NPRs to be inclined in the lateral directions, which is close to our experimental condition for measuring the scattering spectrum by the dark-field microscopy.. Fig. 3.10 Schematic illustration of physical parameters and coordinate system adopted in the FDTD simulation.. 35.

(51) 3-4 FDTD simulations of electric field distribution in the Ag NPRs Fig. 3.11 shows the FDTD simulations of the electric field profile (Ey) for the Ag NPRs with d =100 nm (left panel) and d = 300 nm (middle panel) at  = 600 nm. The simulated Ey profile of single Ag NPR (i.e., equivalent to the case that d is infinity) is plotted in the right panel of Fig. 3.11. For a given optical wavelength, the mutual coupling of surface plasmons between Ag NPRs strongly depends on the interparticle distance d, which in turn affects the scattering degree of the emitted photons. When d was increased, the mutual coupling of surface plasmon between Ag NPRs became weak and tended to disappear, thus altering the scattering ability for the different emitted photon energies. However, the FDTD simulation is only an initial step that provides a qualitative illustration and one possible mechanism for the blue shift in the measured scattering spectrum. Further experiments are necessary before we can conclude the physical rationale for the observed effect.. Fig. 3.11 FDTD simulations of the electric field distribution (Ey) for the Ag NPRs with d =100 nm (left panel) and d = 300 nm (middle panel) at  = 600 nm. Simulated Ey profile of single Ag NPR is plotted in the right panel of the figure.. 36.

(52) Fig. 3.12 shows the FDTD-simulated scattering spectra of the Ag NPRs with different edge lengths ranging from 50 to 70 nm, with a 5-nm interval, whereas the interparticle distance d was kept constant at 300 nm. Accordingly, the position of the spectral maximum of the scattering spectrum strongly depended on the dimension of the Ag NPRs, and this might be one of the possible reasons responsible for the observed oscillation phenomenon in the measured scattering spectra as a dimension variation existed in the Ag NPRs during their synthesis process.. Fig. 3.12 FDTD-simulated scattering spectra of the Ag NPRs with different edge lengths ranging from 50 to 70 nm, with an interval of 5 nm.. 37.

(53) 3-5 Durability test Finally, to examine the stability of fabricated samples, we conducted a mechanical durability test (insets, Fig. 3.13) to repetitively bend the random lasers at a rate of 30 times per minute. After each 100-time bending (the surface faces outward), the fabricated sample was then subjected to excitation using a pump laser to determine the variation in the threshold of pump fluence, and the total bending number of automated cyclic test was set to 1000. Fig. 3.13 shows the variation in the threshold of pump fluence as a function of repetitive bending number with (blue square) and without (red square) 50% bending strain on the random laser. Accordingly, the threshold of pump fluence required to stimulate random lasing emissions barely changed for the random laser with or without 50% bending strain; thus, a high tunability in lasing wavelength was reproduced, even after the 1000-time bending test. This suggests that our random laser system is a reliable and ready to use in various applications that require stable lasing properties after repetitive bending or warping processes.. 38.

(54) Fig. 3.13 Variation in the threshold of pump fluence as a function of repetitive bending number with (blue square) and without (red square) 50% bending strain on the random laser. [Insets: photographs of the fabricated sample without (left) and with (right) mechanical bending.]. 39.

(55) 40.

(56) Chapter 4 The thermal expansion of high power LED 4-1 Introduction 4-1-1 Thermal management The lighting-emitting diode (LED) is a revolutionary, compact, and energy-saving light source. It can directly convert electrical currents into radiative emission through the electroluminescence effect [4.1,4.2] and has been widely used in many commercial applications, such as LCD panel backlighting [4.3-4.5], optical telecommunications [4.6,4.7], and general lighting [4.8-4.10]. As the lighting market has grown rapidly in recent years, the demand for high-power LEDs has become higher than ever. Generally, a high-power LED device includes an LED chip mounted on a ceramic submount for mechanical stability and low thermal resistance, a wire bonding or electrical interconnect layer for the connection of an anode/cathode on the LED chip, and the encapsulant resin for the protection of the LED chip underneath. During the operation of a high-power LED device, one of the most challenging issues is finding appropriate packaging materials for reliable thermal management. The considerable amount of heat produced around the junction area of the LED chip is transferred to the entire device, leading to the thermal expansion of the packaging materials, in particular, the encapsulant resin. This inevitably causes strain due to the large difference of expansion degree between the LED chip and the encapsulant resin, which results in a reliability problem, hindering the output performances and possible applications of high-power LED devices in automotive forward lighting, color sequential projection display, and city environment engineering 41.

(57) [4.11-4.13]. Therefore, proper thermal management and reliable inspection of packaging materials are necessary to ensure high optical outputs and long maintenance times of the high-power LED device. The coefficient of thermal expansion (CTE) is a physical quantity that indicates the thermal expansion value of a material upon heating [4.14,4.15]. When the LED is operated under a high-current condition, the thermal stress becomes a critical issue. Thermally induced stresses caused by the CTE mismatch between the packaging materials and the LED chip (or between the substrate material and the ceramic submount) can lead to fatigue of the wire bond and solder ball on the LED chip and cause delaminations or cracks in the packaged LED device [4.16,4.17]. All these issues limit the reliability and stability performance of the LED device. Therefore, in terms of advanced thermal management, accurate and immediate determination of the CTE of a high-power LED device is extremely important.. 42.

(58) 4-1-2 The advantages of OCT The time-domain OCT (TD-OCT) technique was first invented by D. Huang et al. in 1991 for biomedical applications [4.18]. Based on an interferometer configuration with optical path modulation, the method can acquire depth-resolved information. However, the system sensitivity and the imaging speed of TD-OCT are limited [4.19,4.20]. Hence, Fourier-domain OCT (FD-OCT), including spectral-domain OCT (SD-OCT) [4.21,4.22] and swept-source OCT (SS-OCT) [4.23,4.24] have been developed to overcome the limitations of TD-OCT. Compared to TD-OCT, FD-OCT is able to retrieve depth-resolved information without optical path modulation in the interferometer. Currently, both SD-OCT and SS-OCT systems can provide a frame rate of up to hundreds of frames per second and a system sensitivity of greater than 100 dB. In the past decade, OCT has been widely adopted as an in vivo imaging modality that provides noninvasive, high speed, and three-dimensional (3D) construction mainly in the field of biological specimens, such as gastroenterology,. cardiology,. dermatology,. oral. mucosa,. and. ophthalmology [4.25-4.29]. Typically, OCT can provide high resolutions of 1–10 μm in both the axial and transverse directions and can achieve a penetration depth of ~2 mm. Although OCT has been widely utilized in the above-mentioned biomedical applications, very few studies have employed OCT as an inspection tool in the semiconductor industry [4.30-4.33]. Through the examination of 3D OCT images, the spatial distribution and changes in a sample structure can be identified, allowing optical inspection in many kinds of industrial products. In this study, we examined temperature-dependent and depth-resolved OCT images to 43.

(59) determine the instantaneous CTE of the packaging materials of InGaN-based (λ = 450 nm) high-power LEDs. Typically, the CTE of a material is measured by using a thermomechanical analyzer (TMA) [4.16,4.34], which provides a single value of the CTE based on a specific material undergoing a uniform temperature change. After cooling down to room temperature, the change in the length of the material is measured to determine the CTE. However, the CTE of a packaged LED device is difficult to determine with the traditional method of using a TMA because it comprises many different constituent elements (materials) that must be measured at the same time. Therefore, it is important to develop an inspection tool that is capable of providing the spatial distribution of the measured CTE of the encapsulant materials, as it may have a strong connection with the stability and reliability of the LED device. As revealed in this article, OCT can not only examine the in situ variation of the CTE of packaged LED devices, but also reconstruct the measured CTE values into a two-dimensional (2D) spatial distribution over a given chip area (200 μm × 200 μm). The distances between individual interfaces in the OCT images were observed and recorded to derive the instantaneous CTE of the packaged LED device with different injected currents. The relationship between the junction temperature and the injected current was established using the forward voltage method. The results showed that the measured instantaneous CTE of polystyrene resin varied from 5.86 × 10-5 °C-1 to 14.10 × 10-5 °C-1 in the junction temperature range 25–225 °C, and exhibited a uniform distribution in an OCT scanning area of 200 μm × 200 μm. Most importantly, this work validates the hypothesis that OCT can provide an alternative way to 44.

(60) directly and nondestructively determine the spatially resolved CTE of a packaged LED device, which offers significant advantages over traditional CTE measurement techniques.. 45.

(61) 4-2 High-power InGaN-based LEDs Fig. 4.1 (a) shows an image of the packaged InGaN-based (λ = 450 nm), high-power LED used in this study. A LED chip with dimensions 1.0 mm × 0.5 mm is mounted on a lead frame, and the anode and cathode of the LED chip are connected to the frame through gold wires. The lead frame is soldered on a printed circuit board (star shape) with a metal slug for the supply of injected currents. The inset of Fig. 4.1 (a) shows a microscope top-view image focusing on the center of the packaged LED device. The wire-bonded LED chip mounted on the lead frame is clearly observed in the figure. In this study, polystyrene resin was used to encapsulate the LED chip underneath and form a flat-cavity geometry for its protection. This polymeric encapsulant generally exhibits high transparency, high refractive index, high temperature stability, and good hermeticity [4.35]. Fig. 4.1 (b) shows the Raman spectrum of polystyrene resin excited by a 532-nm diode-pumped, solid-state laser. The repeating unit of the chemical structure of the polystyrene resin is also illustrated in the figure. The polystyrene resin consists of a long-chain hydrocarbon in which alternating carbon centers are attached to phenyl groups. A dominant peak associated with the vibration of aromatic carbon rings in the polystyrene resin appears at approximately 1000 cm-1. In addition, two distinctive peaks, assigned to low carbon-carbon (C-C) and high carbon-hydrogen (C-H) vibrations, are clearly identified at around 600 cm-1 and 3000 cm-1, respectively. We can also observe a vibration of two carbon atoms with double bonds (C=C) that is stronger than that of the C-C single bond in the higher-frequency region of 1600 cm-1. The Raman 46.

(62) spectrum confirms that the encapsulant material of our LED device was primarily composed of polystyrene, as no other dominant peaks are observed in Fig. 4.1 (b). Fig. 4.1 (c) shows plots of the light-output power and the forward voltage versus the forward current of the packaged LED device. The turn-on voltage and series resistance of the packaged LED device were estimated by the Shockley diode equation to be around 2.66 V and 2.40 Ω, respectively [4.36], comparable to that of typical InGaN-based high-power LED chips. The light output power of the LED increases gradually and is saturated at an injected current of approximately I = 400 mA, implying that a considerable dissipation of electrical-input power was induced in the form of unwanted heat. The electroluminescence (EL) spectra of the packaged LED device [inserts of Fig. 4.1 (c)] are slightly blue-shifted (from 454.2 nm to 453.1 nm) at lower injected currents of I < 200 mA owing to the quantum-confined Stark effect, which is generally found in InGaN-based LEDs [4.37]. The EL spectrum exhibits a pronounced red shift (from 454.2 nm to 460.9 nm) at higher injected currents of I > 300 mA, confirming that considerable thermal heat was indeed induced and accumulated inside the LED chip.. 47.

(63) Fig. 4.1(a) Photograph of the packaged InGaN-based (λ = 450 nm) high-power LED used in this study. Inset: Microscope top-view image focusing on the center of the packaged LED device. The marked region (dash-line square) represents the chip area of 200 × 200 μm used for the subsequent statistical analysis of the spatial variations of the OCT images. (b) Raman spectrum of polystyrene resin excited by a 532-nm diode-pumped, solid-state laser. Inset: Repeating unit of the chemical structure of polystyrene resin. (c) Light-output power and forward voltage versus forward current for the packaged LED device. Inset: EL spectra of the packaged LED device under different injected currents (from 50 to 500 mA).. 48.

(64) 4-3 Junction temperature of the LEDs The dominant source of thermal heat is generated close to the active region of the LED chip, determining the operating temperature of the packaged LED device (generally referred to as the junction temperature). In this work, we measured the junction temperature by using the forward voltage (Vf) method. Details about the implementation of the Vf method for the determination of the junction temperature can be found elsewhere [4.25,4.26]. Fig. 4.2 (a) shows the dependence of Vf on the ambient temperature (T = 30–200 oC) of the LED for different current levels (I = 50–500 mA). In this study, the ambient temperature was varied by placing the packaged LED device in a temperature-controlled plate, and the measurement was conducted in the pulse mode (duty cycle = 0.1%, pulse width = 6.5 μs) to minimize any possible thermal perturbation caused by a pulse and ensure that the junction temperature was equivalent to the ambient temperature. The calibration measurement plotted in Fig. 4.2 (a) connects the junction temperature of the packaged LED device to its Vf for a range of currents. Fig. 4.2 (b) shows the Vf of the LED (the left-hand-side primary vertical axis) as a function of DC current in ambient room temperature. The differential of Vf with respect to the temperature for different currents is approximated by a constant dVf / dT = –1.58 mV/K [inset of Fig. 4.2 (b)], which is in agreement with experimental values reported in the literature [4.38,4.39]. The measured Vf and the calibration measurement displayed in Fig. 4.2 (a) can establish the dependence of the junction temperature on different injected (DC) currents, as plotted in the right-hand-side secondary vertical axis in Fig. 49.

(65) 4.2 (b). Accordingly, the junction temperature of the packaged LED device increases rapidly with increasing injected currents and reaches a high value of T = 225 °C at I = 500 mA. Restated, such heat originating from the high junction temperature is likely to cause a serious issue related to the thermal expansion of the packaged LED device.. Fig. 4.2(a) Pulsed calibration measurement (duty cycle = 0.1%, pulse width = 6.5 μs), and (b) measured V f and junction temperature versus injected current of the packaged LED device. Inset: Differential of V f with respect to the temperature (dV f /dT) versus injected current.. 50.