在金屬磊晶成長量子點的問題中，存在著許多的因素，如晶格大小與排列、不配合應變、成長溫度等，都足以影響到長成後量子點的優異，然而，藉由一個原子或分子入射來模擬薄膜之組成機制，在時間上的考量是相當耗時的；在此藉由團簇置於基板上使其自我平衡，觀察其形貌之變遷、動能位能之改變，而晶格不配合、團簇的大小與溫度的考量亦為本文的重點。本文以分子動力學理論，模擬三種金屬團簇與三種元素基板，即銀(Ag)、金(Au)和銅(Cu)，比較其不同配合的情況而加以分析。整個數值方法則採Gear’s五階預測修正來計算奈米系統原子受給定條件後的位置、速度與加速度，並以Verlet鄰近表列與EAM勢能函數的演算法則來處理分子間的作用力。
電腦模擬實驗主要內容分為三種情況：(1)CaseA為團簇半徑為10Å，(2)CaseB為團簇半徑為20Å，(2)CaseC為團簇半徑為30Å，而每種情況又依團簇與基板之組合情形分為實驗一至實驗五。藉由模擬的過程，觀察各種團簇於基板上之組成狀態，有助於了解金屬量子點團簇平衡時之溫度與晶格差異之限制，團簇大小對島狀形成之影響，進而找到量子點團簇之最佳組成環境。最後，做一總結與整理，以期金屬量子點在光電元件、各類相關製程等研究上有些微之貢獻。

About epitaxial crystallization of metal quantum dots, there are many factors among it, such as the lattice’s size and arrangement, the mismatch strain, the growing temperature, etc. That is sufficient to influence the qualities for quantum dots after growing. However, it is quite consume time by means of an incident atom or molecular to simulate thin film’s compositional situation. On this thesis, we let the cluster place on the substrate and let it self-balance. We observe about the transitional shapes, the changed kinetic energy and potential energy. Lattice’s mismatch, cluster’s size and temperature’s consideration are also the key point. In this paper, we simulate three metal clusters and three elementary substrates, the silver, the gold, and the copper. We analyze the different conditions about the mismatch moreover. The Gear’s fifth order predictor-corrector algorithms is adopted in the nanoscopic system to calculate the positions, velocities and accelerations of atoms under displacement condition, while the interactions of atoms are dealt with Verlet’s neighbor lists and EAM’s potential.
These computer simulations contain three parts. The first part is CaseA which cluster’s radius is 10 Å. The second part is CaseB which cluster’s radius is 20 Å. And the third part is CaseC which cluster’s radius is 30 Å. And each part could be divided into Experiment (1) to Experiment (5) by the compositional conditions between the cluster and the substrate. By means of the simulated processes, we can observe the compositional appearance about all kinds of clusters place on certain substrate. It is helpful to understand the balance’s temperature of the cluster in metal quantum dots, the limits in the lattice’s difference, how to influence the island’s shape about cluster’s size. And to find the best compositional environments of quantum dots cluster further. Finally, we make a conclusion and arrangement. To expect the metal quantum dots have a little contribution on the optoeletronic components and all kinds of relative manufacturing processes.

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