本論文針對含有摻雜半導體的半導-介電光子晶體(SDPC)作理論性的研究。以轉移矩陣法來運算GaAs光子晶體的透射率。
在半導-介電光子晶體，介電係數和半導體內的溫度、壓力、載子密度有強相關，可以藉由這些因素來調整介電係數由正值到負值。
第一個部分是研究溫度、壓力、載子密度對1維GaAs/air光子晶體產生的能隙影響。
第二個部分是研究負介電係數在N層的1維GaAs/air光子晶體的情形，可發現在能隙上有N-1個頻道可通過。
第三個部分是研究以GaAs為缺陷之Si/SiO2光子晶體的光子能隙，可發現此缺陷有多個通過峰值出現在能隙上。

This dissertation is theoretically devoted to the studies of photonic properties in the semiconductor-dielectric photonic crystal (SDPC) containing a doped semiconductor. The theoretical simulation results obtained by transfer-matrix method (TMM) are to show the transmittance in GaAs-based photonic crystal structure.
In SDPC, the permittivity of semiconductor is strongly dependent on temperature, pressure, and density of free carrier. These dependences can cause the permittivity to be either positive or negative at a certain frequency range. The first topic is to study pressure, temperature and plasma frequency effects on the band structure of 1D semiconductor photonic crystal made of alternating layers of air and GaAs. The second topic is to study the negative permittivity in 1D finite semiconductor photonic crystal made of alternating layers of air and GaAs with N being the number of periods. It is found the number of channels in the pass band of photonic crystal is equal to N-1. The third topic is to study the properties of photonic band gaps in Si/SiO2 photonic crystals and the photonic defect modes in the Si/SiO2 photonic structures with GaAs defects. It is found that there are multiple transmission peaks within the photonic band gap (PBG) as the defects.

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