圓柱光量子井及特殊多層膜結構之光學特性的探討

Abstract

本論文主要分兩大主題，第一個主題是探討光量子井結構應用於圓柱光子晶體時對於光子能隙的影響。第二個主題是針對漸變折射率抗反射層之變化程度對反射頻譜的影響作分析研究。 首先，我們單純探討單一介面與單一殼層反射頻譜與圓柱柱心半徑的關係。藉由改變圓柱柱心半徑及方位角模態，研究對於反射頻譜的影響。接著，我們將光量子井結構運用於圓柱對稱系統的光子晶體上。利用光子能隙與通帶之間的不完美匹配製造出量子化的極窄通帶，並配合使用液晶的雙折射特性研究不同方位角模態及不同偏振態之間反射頻譜的差異，最後發現，在圓柱對稱系統下圓柱柱心的尺寸對於反射頻譜有相當明顯的影響力。 第二個主題探討的是漸變折射率抗反射層之變化程度對反射頻譜的影響。我們針對當substrate是silicon時作分析，目的是希望能找出一個適合silicon solar cell的antireflection coating (ARC) profile。首先，我們對模擬的條件做一些限制，目的是為了減少使用折射率過低的材料，而這種針對矽太陽能電池設置侷限的條件尋找最佳化的抗反射層條件，於目前文獻中並沒有其他研究提及。我們利用refractive angle以及differential refractive angle去驗證linear以及parabolic兩個profile的折射率變化程度，最後證明對於矽太陽能電池而言是比較適合的ARC profile。接著，我們將兩種profile離散化，並比較兩種profile在不同層數時反射頻譜的表現。經比較得知，離散化後的linear profile會隨著層數的增加反射率會明顯的下降。而parabolic profile則對於層數增加並沒有明顯的變化，但反射率都能一直維持於0.1~0.2%左右，對於製程來說，能以少層數達到低反射率是最好的結果，所以我們認為五層近似拋物線漸變折射率ARC對於silicon solar cell是合適的，其平均反射率約R=0.2285%，與目前業界常用的ARC相比約降低了20倍左右。

This dissertation mainly focuses on simulate 1D photonic crystals, to explore their properties and investigate the effects of special structures and materials on the band gap. The transfer matrix method (TMM) is employed in this dissertation to calculate the band gaps of photonic crystals. First, we studied the reflectance responses of EM wave propagate in a cylindrical multilayer structure for two model structures, single cylindrical interface and single cylindrical slab. In a single cylindrical interface case, the reflection responses in both polarizations are strongly dependent on the starting radius as well as the azimuthal mode number. In H-polarization, there exists a Brewster radius at which the reflectance attains a minimum. This Brewster radius will increase as the azimuthal mode number increases. On the other hand, it will decrease by increasing the difference in the refractive indices of the two media. In the single cylindrical slab model, the wavelength-dependent reflectance can be divided into the oscillating and nonoscillating regions. The ranges of these two regions are strongly dependent on the starting radius. In the thickness domain, it is found that the reflectance has an oscillating behavior. This oscillation is then smeared out at a high value of azimuthal mode number. Then, we introduced PQW structure into the cylindrical symmetry system to broaden the PBGs. The calculated results demonstrated that the PBG is widened successfully not only for mode order m = 0 but also for m = 1. Moreover, we used the property of LCs to create a narrow pass-band. An external electric field is applied to the CPQW structure which is used to control the refractive index of the LCs in the simulation. In the calculations, there are four pass-bands at = 489nm, 505nm, 527nm and 548nm. When the electric field was applied, the narrow pass-bands will shift to shorter wavelength and the reflectance will change simultaneously. After that, we changed the azimuth mode from m = 0 to m = 1, all of the narrow pass-band are located at same wavelength as m = 0. However, the result was reversed when the state of LCs are changed from pseudo-isotropic to homeotropic state. When the external electric field is turned on, the reflectance of second pass-bands decreases in the TE and increases in the TM mode when the azimuthal mode number m = 1. The result of azimuth mode number m = 1 is contrary to m = 0. This novel feature will become insignificant when the starting radius is increased. Therefore, this phenomenon is caused by the effect of small starting radius. Finally, we proposed the design of an antireflection coating (ARC) to improve the conversion efficiency of silicon solar cells. A method of constraining the refractive index within a certain range in the parabolic index profile to optimize the ARC for wide incident angles is proposed for silicon solar cells. Results indicate that a five-layered quasi-parabolic ARC performs well over a wide range of wavelengths and incident angles. The average reflectance at normal incidence is 0.2282% in both transverse electric (TE) field and transverse magnetic (TM) field modes. As the incident angle is increased from 0° to 60°, the average of angle-averaged reflectance in the TE mode is 0.7225%, and that in the TM mode is 0.2087%. These quasi-parabolic ARCs can suppress undesired interfacial Fresnel reflection and assist the collection of solar energy over a wide angle more effectively than can conventional coatings.