单层及有限层石墨体系的扫描隧道显微镜图像模拟与纳米电子器件的理论研究
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摘要
随着硅芯片加工工艺进入30纳米以下,传统的CMOS工艺将日趋极限,基于新材料发展出具有量子效应的电子器件,已成为21世纪科学研究的热点和趋势。2004年单层石墨的发现引领了该领域研究的一场新浪潮。这种标准的二维材料显示出优异的晶体结构及良好的电学性质,基于单层石墨的碳基集成电路有望通过改进的刻蚀技术得以实现。此外单层石墨中的准粒子服从相对论狄拉克方程,而不是传统半导体所遵循的薛定谔方程,这就为利用这种二维平面凝聚态的材料来研究量子电动力学提供了可能。
在第一章中,我们简要介绍了一下现有硅工艺的局限性,碳纳米管的发现及应用,单层石墨的发现及单层石墨中奇特的无质量狄拉克费米子,以及现有制备单层石墨的方案。
在第二章中,我们利用紧束缚近似的模型,解析求解了单层及有限层石墨万轨道的本征态和本征值,进而构造出其相应的传播子(实空间格林函数)。在有效质量的框架下,单层及有限层石墨实空间格林函数可以解析的表达为空间各向同性和空间各向异性两部分的乘积。其中各向同性的部分仅依赖于两个碳原子之间的相对距离,而各向异性部分由正旋和余旋函数决定,具有120°的对称性。利用得到的格林函数的解析表达式,结合Dyson方程,我们模拟了单层石墨上单个杂质和多杂质构成的量子栅栏,双层石墨上单个、多个空位缺陷以及长、短程势的扫描隧道显微镜图像。结果表明当杂质不破坏石墨表面固有的对称性时,其相应的扫描隧道显微镜图像都呈现出120°的对称性。通过研究多层石墨表面电子结构随层数的衍化,我们进一步发现双层石墨的表面电子结构可近似由多层石墨来反映,这就为实验上通过体材料石墨样品来定性研究双层石墨表面电子结构提供了可能。
在第三章中,我们在紧束缚近似的框架下,通过朗道模型研究了单层石墨条带在弹道区的输运性质,并利用新颖的物理现象设计出多种量子器件。我们设计的器件包括:1、Z形的量子点器件。将扶手椅形和锯齿形石墨条带接在一起形成半导体/金属/半导体的异质结,量子点可以被束缚在金属部分。同时该结构具有很好的抗扰动性,不会由于杂质、衬底和边界破损的影响而破坏量子点的存在。2、锯齿形石墨条带的负微分电阻器件。通过掺杂将锯齿形石墨条带分为两部分,选择性的隧穿规则导致其非线性的输运具有负微分特性,并且我们提供了一种描述该选择性规则的一般方案。3、扶手椅形石墨条带的开关器件。利用不同宽度的扶手椅形石墨条带可以是金属、半导体的特性,将不同宽度的部分接在一起,通过调节门电压实现开关的效果。同时我们还发现了一种选择性隧穿,借此可以用来构造可调控的量子点。
As silicon devices scaled down to 30 nanometers, conventional CMOS techniques are fast approaching its physical limitations. The developing of quantum electronic devices based on new materials, therefore, becomes important. Graphene is one of the most promising materials to build nanoelectronics. This novel two-dimensional material has excellent crystal structure and exhibits many interesting electronic properties. Integrated graphene-based circuits can be fabricated by using modern etching techniques. Electrons in conventional semiconducting device are described by the Schrodinger equation, but electrons in graphene are described by the relativistic Dirac equation. This special characteristic provides us a possible way to apply the quantum electrodumamics to study this two dimensional condensed matter material.
In the first chapter of my thesis, I will give a brief introduction about the limitations that current silicon techniques are facing, and discuss the discovery of carbon nanotubes and their applications in nanoelectronics. I will then discuss the property of graphene including the special mass less Dirac fermions in graphene and the fabrication techniques.
In the second chapter, I first introduce the tight binding model and then provide the analytical solution of the eigenstates and eigenvalues ofπorbit in monolayer and multilayer graphenes. I will also discuss how to obtain the corresponding real-space Green's function. Based on the effective mass approximation, I will derive an analytical expression of Green's function in real-space, which is constructed by multiplying the space isotropic and anisotropic functions. Combing with the Dyson equation, I simulate the scanning tunneling microscope image of single impurity and quantum corral on a graphene. I also discuss the effect of single vacancy and double vacancies, long range and short-rang potential on a bilayer graphene. These results exhibit an intrinsic three-fold symmetric pattern on graphene when the impurities do not destroy such symmetry. My further study on multilayer graphene also shows that the surface electronic properties of the bilayer graphene can capture most properties of multilayer graphene. This finding is significant because it indicates that we can use a graphite sample to indirectly study the surface properties of a bilayer graphene.
In the third chapter, I study the ballistic transport properties of graphene nanoribbon using the Landauer model. Under the tight binding framework, I designed several quantum devices that show many novel physical phenomena and they are: 1. Z-shaped quantum-dot device. We connect the armchair and zigzag graphene nanoribbon to form a Z-shaped junction. The quantum dot can be trapped in the center metallic junction region. In addition, the quantum dot is not destroyed by impurities, substrate effect and irregular edge effect. 2. Zigzag graphene nanoribbon negative differential resistance device. The zigzag graphene nanoribbon is divided into two parts with different doping. The selective tunneling rules induce a nonlinear transport behavior in such a device. I provide an easy way to describe this special rule. 3. Armchair graphene nanoribbon switch device. Armchair graphene nanoribbon with different width can be either metalic or semiconducting. By connecting graphene nanoribbon with different width, the resulting device can modulate the gate voltage to achieving switching effect. I also find a selective tunneling effect in this device, which can be used to design the tunable quantum dot.
在第一章中,我们简要介绍了一下现有硅工艺的局限性,碳纳米管的发现及应用,单层石墨的发现及单层石墨中奇特的无质量狄拉克费米子,以及现有制备单层石墨的方案。
在第二章中,我们利用紧束缚近似的模型,解析求解了单层及有限层石墨万轨道的本征态和本征值,进而构造出其相应的传播子(实空间格林函数)。在有效质量的框架下,单层及有限层石墨实空间格林函数可以解析的表达为空间各向同性和空间各向异性两部分的乘积。其中各向同性的部分仅依赖于两个碳原子之间的相对距离,而各向异性部分由正旋和余旋函数决定,具有120°的对称性。利用得到的格林函数的解析表达式,结合Dyson方程,我们模拟了单层石墨上单个杂质和多杂质构成的量子栅栏,双层石墨上单个、多个空位缺陷以及长、短程势的扫描隧道显微镜图像。结果表明当杂质不破坏石墨表面固有的对称性时,其相应的扫描隧道显微镜图像都呈现出120°的对称性。通过研究多层石墨表面电子结构随层数的衍化,我们进一步发现双层石墨的表面电子结构可近似由多层石墨来反映,这就为实验上通过体材料石墨样品来定性研究双层石墨表面电子结构提供了可能。
在第三章中,我们在紧束缚近似的框架下,通过朗道模型研究了单层石墨条带在弹道区的输运性质,并利用新颖的物理现象设计出多种量子器件。我们设计的器件包括:1、Z形的量子点器件。将扶手椅形和锯齿形石墨条带接在一起形成半导体/金属/半导体的异质结,量子点可以被束缚在金属部分。同时该结构具有很好的抗扰动性,不会由于杂质、衬底和边界破损的影响而破坏量子点的存在。2、锯齿形石墨条带的负微分电阻器件。通过掺杂将锯齿形石墨条带分为两部分,选择性的隧穿规则导致其非线性的输运具有负微分特性,并且我们提供了一种描述该选择性规则的一般方案。3、扶手椅形石墨条带的开关器件。利用不同宽度的扶手椅形石墨条带可以是金属、半导体的特性,将不同宽度的部分接在一起,通过调节门电压实现开关的效果。同时我们还发现了一种选择性隧穿,借此可以用来构造可调控的量子点。
As silicon devices scaled down to 30 nanometers, conventional CMOS techniques are fast approaching its physical limitations. The developing of quantum electronic devices based on new materials, therefore, becomes important. Graphene is one of the most promising materials to build nanoelectronics. This novel two-dimensional material has excellent crystal structure and exhibits many interesting electronic properties. Integrated graphene-based circuits can be fabricated by using modern etching techniques. Electrons in conventional semiconducting device are described by the Schrodinger equation, but electrons in graphene are described by the relativistic Dirac equation. This special characteristic provides us a possible way to apply the quantum electrodumamics to study this two dimensional condensed matter material.
In the first chapter of my thesis, I will give a brief introduction about the limitations that current silicon techniques are facing, and discuss the discovery of carbon nanotubes and their applications in nanoelectronics. I will then discuss the property of graphene including the special mass less Dirac fermions in graphene and the fabrication techniques.
In the second chapter, I first introduce the tight binding model and then provide the analytical solution of the eigenstates and eigenvalues ofπorbit in monolayer and multilayer graphenes. I will also discuss how to obtain the corresponding real-space Green's function. Based on the effective mass approximation, I will derive an analytical expression of Green's function in real-space, which is constructed by multiplying the space isotropic and anisotropic functions. Combing with the Dyson equation, I simulate the scanning tunneling microscope image of single impurity and quantum corral on a graphene. I also discuss the effect of single vacancy and double vacancies, long range and short-rang potential on a bilayer graphene. These results exhibit an intrinsic three-fold symmetric pattern on graphene when the impurities do not destroy such symmetry. My further study on multilayer graphene also shows that the surface electronic properties of the bilayer graphene can capture most properties of multilayer graphene. This finding is significant because it indicates that we can use a graphite sample to indirectly study the surface properties of a bilayer graphene.
In the third chapter, I study the ballistic transport properties of graphene nanoribbon using the Landauer model. Under the tight binding framework, I designed several quantum devices that show many novel physical phenomena and they are: 1. Z-shaped quantum-dot device. We connect the armchair and zigzag graphene nanoribbon to form a Z-shaped junction. The quantum dot can be trapped in the center metallic junction region. In addition, the quantum dot is not destroyed by impurities, substrate effect and irregular edge effect. 2. Zigzag graphene nanoribbon negative differential resistance device. The zigzag graphene nanoribbon is divided into two parts with different doping. The selective tunneling rules induce a nonlinear transport behavior in such a device. I provide an easy way to describe this special rule. 3. Armchair graphene nanoribbon switch device. Armchair graphene nanoribbon with different width can be either metalic or semiconducting. By connecting graphene nanoribbon with different width, the resulting device can modulate the gate voltage to achieving switching effect. I also find a selective tunneling effect in this device, which can be used to design the tunable quantum dot.
引文
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