以第一原理研究扶手椅型石墨烯奈米帶的應變效應

Strain Effects on Armchair Graphene Nanoribbons: A First Principle study

羅曉敏(Loh Siow Mean)

指導教授 ： 梁贊全

國立中正大學/理學院/物理學系/碩士(2014年)

摘要

量子束縛效應(quantum confinement effect)在了解扶手椅型石墨烯奈米帶因應變而產生的能隙變化中扮演了重要的角色。基於第一原理計算及利用相位移模型(phase accumulation model)，我們也探討了不同應變下扶手椅型石墨烯奈米帶在Γ點的相位移。計算結果顯示，雖然相位移的能量色散會被應變所調變，但不同應變下的相位移在費米能階附近大約都為0.75π。除了鋸齒型碳奈米管的相位移為0以外，鋸齒型碳奈米管在圓周方向因週期邊界條件而造成的波向量量化條件與扶手椅型石墨烯奈米帶的相似。利用區域摺疊方法 (zone folding method) ，我們可以利用應變下的石墨烯電子結構及代入0.75 π與0的相位移而分別計算任意應變下的扶手椅型石墨烯奈米帶及鋸齒型碳奈米管的能隙。扶手椅型石墨烯奈米帶隨應變變化的鋸齒型能隙震盪行為非常相似於鋸齒型碳奈米管的結果。此鋸齒型的能隙震盪行為會因相位移的不同而有很明顯的偏移。此外，能隙震盪的峰值與週期都會隨著奈米帶寬度的增加而變小。對於某個寬度的扶手型石墨烯奈米帶而言，能隙震盪的峰值與週期都會隨著應變的增加而變大。所有這些觀察到的結果都可輕易地由區域摺疊方法解釋。另外，我們也探討了應變下扶手椅型石墨烯奈米帶的幾何結構、總能量及功函數。利用區域摺疊方法及考慮偶極能障效應，扶手椅型石墨烯奈米帶的功函數可由應變下的石墨烯電子結構及功函數成功地預測。我們的模型與LDA計算的吻合，證明了我們的模型可提供一個有效且精確的方法來預測任意應變下扶手椅型石墨烯奈米帶的能隙及功函數，並因此提供一個很好了解量子束縛效應在扶手椅型石墨烯奈米帶中所扮演角色的機會。

關鍵字

扶手椅型石墨烯奈米帶 ； 第一原理材料計算 ； 應變效應

並列摘要

Quantum confinement effect may play an important role in the gap modulation of armchair graphene nanoribbons (AGNRs) under strain. Using the phase accumulation model, we investigated the energy dependent phase shift (ε) at the Γ point of AGNRs under various strains using first-principles calculation. The calculation results show that although the energy dispersion of the phase shift is modified by strain, the phase shift near the Fermi level is close to 0.75π for AGNRs under various x-strains. The quantization condition of the wave vector of zigzag carbon nanotubes (ZCNTs) governed by the periodic boundary condition along the circumference direction is similar to that of AGNRs except that the phase shift is equal to zero. Using the zone folding (ZF) method, we can calculate the band gap of any strained AGNR (ZCNT) from the phase shift =0.75π (= 0) and the electronic structure of the strained graphene. The AGNRs show a zigzag behavior in the relationship of band gap to strain which is very similar to the ZCNTs. The zigzag patterns are significantly shifted by different phase shifts. The peak value of the band gap and the period of the pattern both decrease as the width of the ribbon increases. For a given AGNR, the peak value and the period of the pattern both increase as the strain increases. All these observations can be easily understood from our ZF calculations. We also report the geometric structure, total energy and work function of the strained AGNRs. Using the zone folding method with the effect of the dipole barrier, the work function of AGNRs can be estimated successfully based on the electronic structure and work function of strained graphene. The agreement between our model and direct LDA calculations indicates that our model can provide an efficient and accurate method to estimate the band gap and work function of AGNRs under strain, and therefore provide a better understanding of the effect of quantum confinement on the electronic properties of AGNRs.

並列關鍵字

Armchair graphene nanoribbon ； First principle study ； Strain effect

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