石墨烯/氮化硼层状复合材料的理论研究
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摘要
自石墨烯发现以来,对于层状材料的研究在不断地发展,人们对于层状材料的认识与设想也在逐步的深化。在所有的层状材料中,石墨烯仍然是人们研究的中心,其他的层状材料都或多或少与其存在一定的联系。自石墨烯开始,人们将层状材料延伸到了其他的类石墨烯结构的材料如六方氮化硼,硅烯,锗烯,二硫化钨等,也通过改变C-C键的分布来构造各式各样的同素异形体。人们所期望的是通过调控层状材料的结构来得到具有独特的电学,磁学,光学性质的材料。石墨烯独特的狄拉克锥状的零带隙能带结构,限制了它在纳米电子器件领域中的应用。为了解决这一问题,人们一直在探索调控石墨烯能带的方法。在众多方法之中,通过基底材料对石墨烯能带进行调控的设想具有多个优点：(1)不需要施加额外的电场,(2)不会对石墨烯的层状结构造成破坏,(3)结构简单,没有杂质的掺杂等。同时六方氮化硼与石墨烯的晶格失配只有1.8%,模型简单,也成为了理论研究的热点。
本论文主要从密度泛函理论出发,对石墨烯／六方氮化硼复合材料的界面相互作用能以及能带结构随它们之间的相对滑移和旋转的变化规律进行了理论研究,并将计算结果与实验进行了对比,主要的研究内容和研究结果如下：
(1)考虑到石墨烯和氮化硼之间的堆叠方式的多样性,特别是由于小的晶格失配所造成的长周期的摩尔结构中所包含的复杂的堆叠方式。本论文采用晶格匹配的模型,模拟了石墨烯在氮化硼上发生连续滑移所形成的堆叠方式的变化对两者之间的相互作用以及电子结构的影响,得到了滑移过程中势能面和带隙的分布,清晰地揭示了全局能量最低的堆叠方式以及滑移的最低势垒。在此基础上预言了长周期摩尔结构存在的可能性。通过对滑移过程中能带变化进行分析,我们发现大多数的堆叠方式可以在石墨烯的狄拉克点处打开一个带隙,不同堆叠方式的带隙大小不同。值得注意的是,在带隙分布图中,存在着带隙为零的堆叠方式。这是在以前的文献中从未报道的。进一步的研究表明,在这些零带隙的堆叠方式处,石墨烯的狄拉克锥的特征得到很好的保持。此外我们还采用了一种完全从几何出发的Rl(Rigistry Index)方法,给出了滑移过程中的势能面,证明该方式能反映第一性原理的计算结果的主要特征。紧束缚模型可以给出带隙变化的主要特征,但无法反映零带隙的堆叠方式。上述结果对于理解由于晶格失配形成的长周期的摩尔结构的电子结构具有重要的意义。
(2)石墨烯和氮化硼衬底之间的相对旋转也会导致形成摩尔结构,其周期与两者之间的旋转角度有关。我们通过对旋转不同角度所形成的摩尔结构的电子结构进行计算,我们发现在不同的旋转角度下,其能带始终保持着单层石墨烯的狄拉克锥的特征,而且狄拉克点仍然位于K点处,并且费米速度随角度的变化不明显。当旋转角度从5°增加到30°左右时,其电子和空穴的费米速度相对于石墨烯费米速度的比值仅从0.97增加到了0.99。
Since the discovery of graphene, the study of two-dimensional materials has become a topic of growing interest. Now graphene remains the focus of the research of layered materials since most of the other layered materials have more or less relationship with graphene. The research of layered materials has extended to the graphene-like materials such as hexagonal boron nitride (h-BN), silicene, germanene and WS2. Different carbon allotropes have been proposed by changing the framework or the bonding features of carbon atoms. Revealing the relationship between the unique properties and the atomic structures of these layered materials becomes the aim of recent theoretical and experimental works. Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point. Substrate materials that offer mechanical support to graphene without interfering with its electrical properties are quite crucial for achieving such applications, because the disorder arising from the substrate will leave the graphene with local microscopic electron and hole puddles which reduces the device performance. The source of the disorder includes corrugation effects of graphene, charge traps, and dangling bonds. Recent works showed that hexagonal boron nitride (h-BN) is a promising substrate material yielding high-quality graphene devices. This BN polymorph has much in common with graphite:(1) They have the same atomic arrangement but h-BN has a lattice constant slightly longer (~1.8%) than graphite.(2) Weak van der Waals interactions hold the sheets together, allowing layers to cleave readily. The electronic properties, however, exhibit clear differences. Due to the ionic characteristics of the B-N bonds, h-BN is a wide-band-gap (6.0eV) electric isolator. Therefore, the planar structure of h-BN cleaves into an ultra-flat surface and the ionic bonding of h-BN should leave it free from dangling bonds and charge traps at the surface. This reduces the disorder and charge inhomogeneity of the graphene on h-BN substrate.
In this thesis we mainly studied the energy landscape and band structure variation during the interlayer movement of G/BN by the first principle calculations method based on the density functional theory (DFT). Then we analyzed the result of the calculations and compared the result with the experiment data. The main content of the study is as followings:
(1) We studied the landscapes of sliding energy surface and energy band gap of graphene on BN substrate within a lattice-matched approximation from first-principles calculations. We show that the sliding energy surface is rather smooth with the AA and AB stacking modes being the global maximum and minimum in energy, respectively. The energy difference between the two modes is only22.5meV/cell. There is a saddle point that joins two AB stacking modes together, corresponding to an energy barrier of15.6meV/cell. Such features can be well reproduced using a registry index (R1) method, implying the capability of the simple geometric model in capturing the essence of the interlayer-interaction-related properties of more complex systems. For most stacking patterns, the interlayer interactions open a band gap at the Dirac point of graphene. Most interestingly, there are special stacking patterns that preserve the Dirac cones of graphene, which can be ascribed to the charge redistribution during the sliding process. The existence of zero-band-gap stacking modes hints the complexity of the electronic structures of the long periodic graphene-BN moire structure arising from small lattice mismatch. These first-principles landscapes of sliding energy surface and band gap offer not only benchmarks for developing empirical strategies dealing with long-periodic graphene-h-BN moire structures but also useful pictures for understanding the morphology and electronic properties of graphene on BN substrate.
(2)The Moire structure of graphene on h-BN substrate can also be generated by the rotation between the two lattices. The periodicity of the Moire pattern is closely related to rotation angle. The Dirac cone feature of graphene monolayer is well preserved in these Moire patterns regardless of rotation angle. The Fermi velocities isolated graphene monolayer. This theoretical result is in good agreement with experimental findings.
本论文主要从密度泛函理论出发,对石墨烯／六方氮化硼复合材料的界面相互作用能以及能带结构随它们之间的相对滑移和旋转的变化规律进行了理论研究,并将计算结果与实验进行了对比,主要的研究内容和研究结果如下：
(1)考虑到石墨烯和氮化硼之间的堆叠方式的多样性,特别是由于小的晶格失配所造成的长周期的摩尔结构中所包含的复杂的堆叠方式。本论文采用晶格匹配的模型,模拟了石墨烯在氮化硼上发生连续滑移所形成的堆叠方式的变化对两者之间的相互作用以及电子结构的影响,得到了滑移过程中势能面和带隙的分布,清晰地揭示了全局能量最低的堆叠方式以及滑移的最低势垒。在此基础上预言了长周期摩尔结构存在的可能性。通过对滑移过程中能带变化进行分析,我们发现大多数的堆叠方式可以在石墨烯的狄拉克点处打开一个带隙,不同堆叠方式的带隙大小不同。值得注意的是,在带隙分布图中,存在着带隙为零的堆叠方式。这是在以前的文献中从未报道的。进一步的研究表明,在这些零带隙的堆叠方式处,石墨烯的狄拉克锥的特征得到很好的保持。此外我们还采用了一种完全从几何出发的Rl(Rigistry Index)方法,给出了滑移过程中的势能面,证明该方式能反映第一性原理的计算结果的主要特征。紧束缚模型可以给出带隙变化的主要特征,但无法反映零带隙的堆叠方式。上述结果对于理解由于晶格失配形成的长周期的摩尔结构的电子结构具有重要的意义。
(2)石墨烯和氮化硼衬底之间的相对旋转也会导致形成摩尔结构,其周期与两者之间的旋转角度有关。我们通过对旋转不同角度所形成的摩尔结构的电子结构进行计算,我们发现在不同的旋转角度下,其能带始终保持着单层石墨烯的狄拉克锥的特征,而且狄拉克点仍然位于K点处,并且费米速度随角度的变化不明显。当旋转角度从5°增加到30°左右时,其电子和空穴的费米速度相对于石墨烯费米速度的比值仅从0.97增加到了0.99。
Since the discovery of graphene, the study of two-dimensional materials has become a topic of growing interest. Now graphene remains the focus of the research of layered materials since most of the other layered materials have more or less relationship with graphene. The research of layered materials has extended to the graphene-like materials such as hexagonal boron nitride (h-BN), silicene, germanene and WS2. Different carbon allotropes have been proposed by changing the framework or the bonding features of carbon atoms. Revealing the relationship between the unique properties and the atomic structures of these layered materials becomes the aim of recent theoretical and experimental works. Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point. Substrate materials that offer mechanical support to graphene without interfering with its electrical properties are quite crucial for achieving such applications, because the disorder arising from the substrate will leave the graphene with local microscopic electron and hole puddles which reduces the device performance. The source of the disorder includes corrugation effects of graphene, charge traps, and dangling bonds. Recent works showed that hexagonal boron nitride (h-BN) is a promising substrate material yielding high-quality graphene devices. This BN polymorph has much in common with graphite:(1) They have the same atomic arrangement but h-BN has a lattice constant slightly longer (~1.8%) than graphite.(2) Weak van der Waals interactions hold the sheets together, allowing layers to cleave readily. The electronic properties, however, exhibit clear differences. Due to the ionic characteristics of the B-N bonds, h-BN is a wide-band-gap (6.0eV) electric isolator. Therefore, the planar structure of h-BN cleaves into an ultra-flat surface and the ionic bonding of h-BN should leave it free from dangling bonds and charge traps at the surface. This reduces the disorder and charge inhomogeneity of the graphene on h-BN substrate.
In this thesis we mainly studied the energy landscape and band structure variation during the interlayer movement of G/BN by the first principle calculations method based on the density functional theory (DFT). Then we analyzed the result of the calculations and compared the result with the experiment data. The main content of the study is as followings:
(1) We studied the landscapes of sliding energy surface and energy band gap of graphene on BN substrate within a lattice-matched approximation from first-principles calculations. We show that the sliding energy surface is rather smooth with the AA and AB stacking modes being the global maximum and minimum in energy, respectively. The energy difference between the two modes is only22.5meV/cell. There is a saddle point that joins two AB stacking modes together, corresponding to an energy barrier of15.6meV/cell. Such features can be well reproduced using a registry index (R1) method, implying the capability of the simple geometric model in capturing the essence of the interlayer-interaction-related properties of more complex systems. For most stacking patterns, the interlayer interactions open a band gap at the Dirac point of graphene. Most interestingly, there are special stacking patterns that preserve the Dirac cones of graphene, which can be ascribed to the charge redistribution during the sliding process. The existence of zero-band-gap stacking modes hints the complexity of the electronic structures of the long periodic graphene-BN moire structure arising from small lattice mismatch. These first-principles landscapes of sliding energy surface and band gap offer not only benchmarks for developing empirical strategies dealing with long-periodic graphene-h-BN moire structures but also useful pictures for understanding the morphology and electronic properties of graphene on BN substrate.
(2)The Moire structure of graphene on h-BN substrate can also be generated by the rotation between the two lattices. The periodicity of the Moire pattern is closely related to rotation angle. The Dirac cone feature of graphene monolayer is well preserved in these Moire patterns regardless of rotation angle. The Fermi velocities isolated graphene monolayer. This theoretical result is in good agreement with experimental findings.
引文
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