本論文的目的是要研究一維矽基半導體光子晶體的光子能帶結構特性。我們藉由轉移矩陣法(TMM)來計算結構的頻譜圖，論文有二個主題:

主題一是研究矽基半導體光子晶體的光子能隙，利用air/(AB)^N/air的結構，
A = n-Si、B = air、N=stack number，由於半導體的介電係數可隨載子濃度而改變，所以我們可以藉由調變濃度、n-Si和air的厚度調變光子能隙或位移；另外改變濃度及厚度，可以使部份方向性能隙的寬度及所能達到的角度增加。

主題二則是研究矽基半導體光子晶體的透射特性，利用air/((AB)^N)(A)/air 的結構來研究透射波峰，A = n-Si、B = SiO2，調變層數N會與所產生的透射峰數相等，調變n-Si和SiO2可以使透射峰藍移，調變角度可以使透射峰紅移，若調變偏振TE、TM波則影響較小，綜合以上特性，設計可調式多通道的濾波器。

In this thesis, the photonic band structure in the one-dimensional silicon-based photonic crystals are investigated. Two main topics are involved.
The first part is to investigate silicon-based photonic band gaps. We consider photonic structures of (AB)^N ,in which A is n-Si and B is air, N is the stack number. It is found that the photonic band gaps can be tuned by the variation of carrier density, thickness of A and B .Then we can increase the omnidirectional band gap by tuned carrier density and thickness.
The second part is to investigate the properties of wave transmission. We consider photonic structures of (AB)^N(A) ,in which A is n-Si and B is SiO2. It is found that the number of peaks is equal to the stack number N. The peak positions can be tuned by thickness of A and B, that is, peaks are blue-shifted as the thickness increases. The peak positions are also strongly dependent on the incident angle, but weakly on the polarization of the incident wave. The results suggest that a tunable multichannel filter can be achieved by using such an Si-based photonic crystals.

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