以化學能分析鍺量子點成長於孔洞陣列的矽基板

量子點是目前理論上與實驗上熱門的議題，因三個維度的尺寸均小於電子費米波長，內部電子在各方向上的運動都受到侷限，所以量子侷限效應特別顯著。而自我聚集的方式形成鍺量子點能在短時間處理大量的材料，相當符合奈米製造的需求，其製程多樣性、簡便、低成本更具競爭優勢。但欲將鍺量子點應用於電子與光學元件上時，鍺量子點的精準定位是必須，因此利用奈米結構的矽基板來達到鍺量子點的定位，是一個不錯的方式。本篇論文致力於研究鍺量子點成長於矽基板的過程中，矽鍺介面中的化學能對鍺量子點的定位將產生何種影響，因此將先定性探討矽鍺介面化學能的來源與其物理意義，並進一步定量描述化學能的影響，進而對一維的陣列結構探模擬其化學能的分佈，發現當一維陣列結構的凹槽寬度改變時將會影響凹槽內部的化學能低點數目；接著引進數學上處理二維曲面中曲率的概念，將一維的化學能模擬推廣至二維系統，再對二維的孔洞陣列結構探討不同表面形貌下其化學能的分布情形，發現製程過程中的同步熱處理時間、孔洞陣列的大小、週期、形狀與孔洞陣列的側壁形貌，都對化學能的分佈產生微妙的影響。而根據化學能的模擬結果，可以推論在縮小孔洞陣列週期並使孔洞側壁平緩，可有效降低圍繞孔洞的化學能障，使鍺量子點定位於孔洞陣列內部；而縮小孔洞尺寸及縮短長晶前之同步熱處理時間，可有效地使孔洞內部形成唯一化學能低點，達成鍺量子點成長於孔洞內部的正中央。另外在實驗上，我們實際利用電子束微影系統，配合超高真空化學氣相沉積儀器，針對各項參數所實際製作出樣品的結果，也能與利用理論上化學能模擬之結果互相吻合，驗證根據化學能模擬的推論能準確的預測鍺量子點於奈米結構之矽基板上之定位。

關鍵字

化學能模型；表面能；應變能；自聚性量子點； S-K成長模型

並列摘要

The theory and experiment of quantum dot are currently an interesting issue. Since its size of the three dimensions is less than the electron wavelength, electron movement is restricted in all direction, and the quantum confinement effect is more significantly. There are many advantages on the fabrication of germanium quantum dots by the self-assembly method, diversity, simplicity and low cost in fabrication procedure. The precise positioning of the quantum dots is required for its application on electronic and optical devices. So using the silicon patterned substrates to control the position of germanium quantum dots is the best choice. This thesis made an effort to study what the impact of the chemical potential in the Si/Ge interfacial system on the germanium dots’ growth mechanism on the silicon patterned substrate. First, I studied the physical meaning of the chemical potential, and then I gave a quantitative description for chemical potential. Next I fabricated the one-dimensional grating and simulated it by the chemical potential model. We found out that the width of the trench will affect the distribution of the chemical potential in grating structure. And then I introduced the mathematical concept of how to tackle the curvature in two-dimensional case, so our simulation can be extended to two-dimensional system. Then I simulated the two-dimensional hole array structure and found that the period of the in-situ heat treatment in the fabrication process, the hole size, pitch, shape and the sidewall of the hole array will influence the distribution of the chemical potential. Based on the simulation result of the chemical potential, I can get a conclusion that the decreasing of the pitch and the smoothen of the sidewall of the hole array will lower the chemical potential barrier around the hole. The germanium dots will locate inside the hole. Decreasing the hole size and the period of the in-situ heat treatment before the epitaxy will get an only one chemical potential minimum inside the hole. The germanium dots will position in the hole center. Besides, I used the electron beam lithography system and the ultra high vacuum chemical vapor deposition system in experiment to fabricate the samples according to the above conditions. The result in the experiment is agreed to the chemical potential simulation. So the simulation by the chemical potential model can precisely predict the position of the germanium quantum dots on the silicon patterned substrate.

並列關鍵字

Chemical potential model ； surface energy ； strain energy ； self-assembled quantum dots ； S-K growth model

參考文獻

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以化學能分析鍺量子點成長於孔洞陣列的矽基板

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