本研究的主題是屬於光子晶體波導的應用與設計。一般來說光偵測器的吸收波段在波長1.6微米以上的吸收效率都不太好，因此我們將把光子晶體其中一種很有用的物理現象，稱作慢光，他的意思就是要利用光子晶體的週期性結構對光造成的影響把光的群速度給慢下來，再利用單晶的鍺晶棒增加對光的吸收。首先我們會先介紹快速熔融成長 ( RMG ) 的製程，它的好處是製程簡單而且速度快，而我們將會利用它在設計出來的光子晶體波導上成長單晶的鍺晶棒。二微光子晶體在光電領域已經慢慢在工程上被拿來應用，因為它在傳導電磁波時會產生一些很有用的物理特性，在製程上也比較好做。我們設計出來的光子晶體慢光波導，從 MODE solution 計算出來的光子晶體能帶結構圖上可以找到一條慢光模態，其波段範圍大概有8奈米，並以不同波導距離下量到的功率去計算出來的吸收係數大約在 0.04 ~ 0.06 dB/microns，把這結果和以量子力學的一階能量修正項推導出的解析解作比較，我們可以發現結果大致上是符合的。但我們在元件的應用上會希望慢光這個現象能用在比較寬的波段，而不是只有8奈米，因此接下來我們可以藉由調整光子晶體波導結構的週期、波導的間距與鍺的寬度大小去改變光子能帶結構的能隙寬度與位置，最後可以把慢光波段的範圍擴大到現在通訊常用的波段與吸收較差的波段。

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