摘要
本篇論文利用緊束模型來探討零奈米石墨在電場下的電子性質與光學性質。我們計算了能態值、能態寬、能隙、電子波函數、狀態密度、聯合態密度、光吸收譜。接著討論這些物理量隨著電場的方向、大小和幾何結構改變的變化，將會發現這些物理量受其影響很大。因為我們已經將懸空鍵去除，所以不討論這些物理量與懸空鍵的關係。隨著電場逐漸增加，將發現能態寬越來越大，而能隙也會隨著改變，最小值約1～7(meV)。最接近費米能狀態之電子波函數在無外加電場時有侷限現象，但隨著電場增加，侷限現象將會消失。且這些物理性質會直接反應在聯合態密度與光吸收譜上。外加電場導致能態分佈有了變化，這使得聯合態密度的吸收峰(absorption peaks)值會有變化，並且吸收峰會有位移(shift)之情形，當然也就會有合併之現象產生。而光吸收譜的吸收峰隨著電場逐漸增加，也會有位移的現象發生，並伴隨著原有的吸收峰可能消失與產生新吸收峰的情形。

Abstract
In this thesis, Tight-binding model is used to study the electronic and optical properties of zero-dimensional nanographites in electric fields. We calculate eigenvalue, width of eigenvalue, energy gap, wave function, density of states, joint density of states and optical absorption. Next, we discuss how rapid these physical properties change with values and directions of external electric fields and the geometric structure of zero-dimensional nanographites. However, the relationship between these physical properties with the dangling bond will not be discussed in the paper because the dangling bond is excluded at the beginning. With the increase of external electric fields, width of eigenvalue increases but energy gap may become very small( about 1～7meV) on some occasions. Wave function of the nearest state to Fermi level will localize on the raising points of the first and final Zigzag line. But, this phenomenon will disappear with the increase of external electric fields. These physical properties would be shown directly on joint density of states and optical absorption. Because external electric fields are able to make distributions of eigenvalue change, amplitudes of absorption peaks of joint density of states will have the alternation as well. In the mean time, absorption peaks will shift, and definitely the two different absorption peaks will combine to form one larger absorption peak. In the end, we will find optical absorption peaks will shift with the increase of external electric fields as well. Then, original optical absorption peaks will disappear and new optical absorption peaks will appear.

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