本文關(guān)鍵詞： 第一性原理研究 四族元素納米管 帶隙標(biāo)度律　出處：《鄭州大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：最近,通過氣相生長方法,成功地在實驗上合成了由錫元素組成的二維單層材料。這也就意味著,在得到石墨烯之后,通過各種各樣的方法,除鉛元素之外的所有四族元素構(gòu)成的單層材料都在實驗上成功被合成,這些單層材料分別命名為硅烯、鍺烯、錫烯。和石墨烯類似,這些二維單層材料的電子性質(zhì)均表現(xiàn)為無質(zhì)量的狄拉克費米子。因此,這些材料都擁有非常高的載流子遷移率,同樣可以實現(xiàn)二維的量子自旋霍爾效應(yīng),量子反�；魻栃�(yīng),以及拓?fù)浣^緣體等特性。與之類似地,在成功的合成這些二維單層之后,這些元素構(gòu)成的納米管的性質(zhì)同樣引發(fā)了人們的關(guān)注。實際上,早在石墨烯出現(xiàn)之前,碳納米管就因為其新奇的電子特性以及廣泛的應(yīng)用引發(fā)了人們的關(guān)注。眾所周知,碳納米管的一個有趣的特性是它可以表現(xiàn)出金屬性或半導(dǎo)體性,這取決于碳納米管的手性。對于硅納米管來說,它擁有齒輪狀的結(jié)構(gòu),或者說褶皺的結(jié)構(gòu)。先前的研究表明,硅納米管的帶隙對納米管的手性與尺寸都非常敏感,armchair型的硅納米管呈現(xiàn)出半導(dǎo)體特性,且?guī)峨S著納米管半徑的增加而減小,zigzag型的硅納米管的帶隙同樣出現(xiàn)以3為周期的震蕩。利用基于密度泛函理論的第一性原理計算,系統(tǒng)地研究了四族元素納米管的能帶特征,發(fā)現(xiàn)納米管第一布里淵區(qū)中的兩個特殊點處的帶隙決定了納米管的帶隙,分別對應(yīng)二維結(jié)構(gòu)中的K點與Γ點。K點與Γ點帶隙隨著納米管半徑的變化遵循兩條不同的標(biāo)度律:K點帶隙遵循1/R的標(biāo)度律,該標(biāo)度律出現(xiàn)在擁有褶皺結(jié)構(gòu)的硅、鍺、錫納米管中,非常重要的是,K點帶隙的標(biāo)度律與納米管的組成元素?zé)o關(guān)而且不受納米管手性的影響;Γ點處帶隙遵循-1/R2+C的標(biāo)度律,C為常數(shù),與納米管的組成元素相關(guān)。兩條標(biāo)度律共同決定了四族元素納米管的帶隙,對于硅納米管與大半徑的鍺、錫納米管,納米管的帶隙由K點帶隙的標(biāo)度律決定,對于小半徑的鍺、錫納米管,帶隙由Γ點帶隙決定。由此,基于兩條標(biāo)度律,可以通過納米管的半徑確定納米管的帶隙。此外,還預(yù)言了鍺、錫armchair型納米管中間接帶隙納米管的存在。
[Abstract]:Recently, two dimensional monolayer materials consisting of tin elements were successfully synthesized experimentally by gas phase growth method, which means that graphene can be obtained by a variety of methods. All four groups of monolayers with the exception of lead were successfully synthesized experimentally. These monolayers were named silicene, germane, stannene, and graphene, respectively. The electronic properties of these two-dimensional monolayers are characterized by massless Dirac fermions. Therefore, these materials have very high carrier mobility and can also realize the two-dimensional quantum spin Hall effect. The properties of quantum anomalous Hall effect and topological insulators. Similarly, after the successful synthesis of these two-dimensional monolayers, the properties of nanotubes formed by these elements have also attracted attention. Long before graphene appeared, carbon nanotubes (CNTs) attracted much attention because of their novel electronic properties and wide applications. One of the interesting properties of carbon nanotubes is that they can exhibit gold or semiconductor properties, depending on the chirality of carbon nanotubes, which have a gear-like structure for silicon nanotubes. Previous studies have shown that the band gap of silicon nanotubes is very sensitive to the chirality and size of nanotubes. And the band gap decreases with the increase of the radius of the nanotubes. The band-gap of the zigzag type silicon nanotubes also oscillates with the period of 3. The first principle calculation based on density functional theory is used. The band-gap at two special points in the first Brillouin region is found to determine the band-gap of the nanotubes. The band gap of K point and 螕 point. K point and 螕 point in two-dimensional structure follow two different scaling laws: K point gap and 螕 point band gap follow the scale law of 1 / R respectively with the change of nanotube radius. The scaling law appears in silicon, germanium and tin nanotubes with fold structure. It is very important that the scaling law of K point gap is independent of the constituent elements of nanotubes and is not affected by the chirality of nanotubes. The band gap at 螕 point follows the scaling law C of -1 / R 2C, which is related to the constituent elements of nanotubes. The two scaling laws together determine the band gap of four groups of elemental nanotubes, and for silicon nanotubes and germanium with large radius. For tin nanotubes, the band gap is determined by the scaling law of K point band gap, and for small radius germanium, tin nanotube, the band gap is determined by 螕 point band gap. Therefore, two scaling laws are used. In addition, the existence of indirect band-gap nanotubes in germanium and tin armchair nanotubes is predicted.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O469

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