原子力显微镜在二维材料力学性能测试中的应用综述1)

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高扬^,²⁾

浙江大学工程力学系, 杭州 310027

REVIEW OF THE APPLICATION OF ATOMIC FORCE MICROSCOPY IN TESTING THE MECHANICAL PROPERTIES OF TWO-DIMENSIONAL MATERIALS¹⁾

Gao Yang^,²⁾

Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China

通讯作者: 2)高扬, 研究员, 主要研究方向: 微纳米力学、极端力学、二维材料力学. E-mail:ygao96@zju.edu.cn

收稿日期:2020-10-13接受日期:2021-01-2网络出版日期:2021-04-08

基金资助:

1)浙江大学****资助项目.188020*194222002/035/008

Received:2020-10-13Accepted:2021-01-2Online:2021-04-08
作者简介 About authors

摘要
以石墨稀为代表, 二维材料有着诸多优异的性质, 在下一代电子器件等领域拥有广阔的应用前景. 目前绝大多数关于二维材料的研究都集中在其电子学和光学的性质和应用, 对于其力学性质的研究则相对欠缺, 而力学性质在二维材料的研究和应用中都有着至关重要的意义. 原子力显微镜是低维材料力学性质表征的主要手段, 例如基于原子力显微镜的纳米压痕技术. 本文首先简要介绍了二维材料的基本背景以及原子力显微镜的工作原理. 进一步展示了纳米压痕技术的工作原理和理论背景, 并回顾了利用纳米压痕技术研究二维材料面内力学性质的相关实验和理论工作, 同时探讨了原子力显微镜在表征二维材料力学性能中存在的测量误差及来源. 由于二维材料展现出强烈的各向异性, 纳米压痕技术在能够很好地测量二维材料面内力学性质的同时, 对于二维材料层间力学性质表征等方面存在明显的局限性. 第三部分介绍了一种全新的基于原子力显微镜的埃(Å)压痕技术, 该技术能够将形变尺度控制在0.1 nm以内, 从而精确地表征和调控二维材料的层间范德华作用力, 即层间力学性质. 作者在第三部分介绍了通过埃压痕技术表征和调控的石墨烯、氧化石墨烯等二维材料的层间力学性质. 最后简要介绍了范德华异质结材料的基本性质, 探讨了埃压痕技术在该材料力学性质研究中的潜在应用.
关键词： 二维材料;石墨烯;原子力显微镜;纳米压痕技术;埃压痕技术;范德华异质结

Abstract
Graphene and other two-dimensional (2D) materials possess various excellent properties and hold great promises for next generation of electronic devices and other applications. The mechanical properties are of fundamental importance in the research and application of 2D materials. Despite the fact that 2D materials have been extensively investigated in the past two decades, efforts on the mechanical properties are strikingly lacking and vastly needed. Atomic force microscopy (AFM) is one of the most widely used tools for the mechanical characterizations of low-dimensional materials. Particularly, the AFM-based nano-indentation technique has been extensively employed to explore the mechanical properties of 2D materials. In this review, we first introduce the basic backgrounds of 2D materials and atomic force microscopy. The mechanism and theoretical background of AFM-based nano-indentation are then demonstrated. In the second part, we review the research work by employing nano-indentation on studying the in-plane mechanical properties of 2D materials. The measurement errors of AFM-based nano-indentation and their origins are also discussed. Nano-indentation is perfectly suitable for the in-plane/intralayer mechanical measurement but also greatly limited in probing the out-of-plane/interlayer elasticity, due to the extreme anisotropy of 2D materials. Therefore, in the third part, we introduce an unconventional AFM-based technique - Angstrom-indentation which allows for sub-nm deformation on 2D materials. With such a shallow indentation depth comparable to the interlayer spacing of 2D materials, Angstrom-indentation is capable of measuring and tuning the interlayer van der Waals interactions in 2D materials. The interlayer elasticities of graphene and graphene oxide measured by Angstrom-indentation are discussed as examples in the third part. In the final part, we give a quick overview of a new type of 2D material - van der Waals heterostructure and its novel mechanical properties. We also discuss the potential application of Å-indentation in the investigation of the mechanical properties of van der Waals heterostructures.
Keywords：two-dimensional material;graphene;atomic force microscopy;nano-indentation;angstrom-indentation;van der Waals heterostructure

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本文引用格式
高扬. 原子力显微镜在二维材料力学性能测试中的应用综述¹⁾. 力学学报[J], 2021, 53(4): 929-943 DOI:10.6052/0459-1879-20-354
Gao Yang. REVIEW OF THE APPLICATION OF ATOMIC FORCE MICROSCOPY IN TESTING THE MECHANICAL PROPERTIES OF TWO-DIMENSIONAL MATERIALS¹⁾. Chinese Journal of Theoretical and Applied Mechanics[J], 2021, 53(4): 929-943 DOI:10.6052/0459-1879-20-354

1 引言

1.1 二维材料及其力学表征

二维材料是指仅仅由单原子层构成的平面材料^[1-3]. 石墨烯是最早被发现的二维材料, 由英国曼彻斯特大学Geim和Novoselov^[4]在2004年通过透明胶带机械剥离石墨所得到. 另外值得注意的是, 同年美国佐治亚理工学院的de Heer^[5]也通过碳化硅表面外延生长的方式得到了单层石墨结构并进行了细致的表征. 但是"石墨烯"的概念确是由Geim首先提出的, Geim和Novoselov也在2010年获得了诺贝尔物理学奖. 二维材料之所以受到极大的关注, 一方面是长久以来统计力学中"非零温情况下不存在理想的二维晶体"这个大家认可的共识被石墨烯打破; 另一方面, 以石墨烯为代表的二维材料本身也展现出了迥异于其对应的块体材料的优异性质^[2-9]. 例如石墨烯的迁移率高达10$^{4}$ cm$^{2}$/(V $\cdot$ s), 电子在狄拉克点附近呈现线性色散关系, 同时在石墨烯中观测到了半整数量子霍尔效应, 这些都是石墨所不具备的新颖物理现象^[4,8-9]. 除了石墨烯, 以二硫化钼MoS$_{2}$为代表的二维过渡金属硫族化合物(TMDC)由于天然的空间反演对称性破缺, 与石墨烯零带隙的结构不同, 单层时直接带隙大小普遍在1 $\sim$ 2 eV之间^[10-11]. 以单层MoS$_{2}$为原材料制备得到的二维场效应晶体管的开关比在常温时高达10$^{8}$, 达到甚至超过了传统硅基逻辑芯片的标准, 被认为是下一代集成电路芯片材料的有力候选^[12]. 如果说石墨烯和二硫化钼分别代表了二维材料的第一和第二波热潮, 那么以磷烯phosphorene (或者黑磷black phosphorus)为代表的其他非碳二维材料可以被认为是二维材料研究的第三波热潮^[13-16]. 磷原子最外层有5个价电子, 能够与近邻的3个磷原子形成sp$^{3}$杂化键, 因此不同于平坦的石墨烯, 磷烯的表面褶皱起伏同时还展现出明显的平面内各向异性^[17-18]. 不过值得注意的是, 目前大多数关于二维材料的研究和报道主要聚焦于其电学、光学和磁学性质及其相关应用, 对其力学性质的研究则相对缺乏^[19]. 而作为材料科学中的最基本的物理性质之一, 对于二维材料力学性质的探索除了基础研究的需要, 另外一方面也是二维材料从实验室走向具体应用中不可或缺的重要步骤. 例如柔性电子器件对二维材料对拉伸、弯曲等外界载荷的响应提出了新的要求, 而航空航天和军事领域则要求对二维材料在极端力学环境(如高压、冲击、爆炸、超高温)中的相变行为或者性质变化有清晰的认知^[20].

当前对二维材料力学性质的研究主要集中于弹性模量、泊松比、断裂强度、摩擦润滑、吸附力、高压相变等方向^[19,21-22]. 微纳压痕技术(micro/nano-indentation)是传统的表征宏观块体材料力学性质的重要测量手段^[23-27]. 通过控制正压力的大小, 可以使材料发生相应的弹性/塑性形变, 从而得到对应的力学参数. 原子力显微镜的针尖半径一般小于100 nm, 压电陶瓷可以将压印形变控制到10 nm以下, 因此很自然的被研究人员用于测量纳米级二维材料的力学性能^[28]. 在引言的第二小节, 简单介绍了原子力显微镜的工作原理和发展历史; 在第二部分中将进一步阐述基于原子力显微镜的纳米压痕技术的工作原理和具体实例, 并讨论测量中可能存在的误差与来源.

狭义的二维材料正如本文开始所提到的, 特指仅仅由单原子层组成的晶体. 但是研究人员发现多层的二维材料往往也具有和单层二维材料相似的性质. 特别的是, 多层二维材料在某些方面甚至具有单层二维材料不具备的特性, 其根源便在于层间的范德华作用力. 通过调节层间范德华作用力来调控二维材料的各种性质已经成为当下热门研究课题. 二维材料又被称为范德华材料, 其层间距普遍小于1 nm(例如石墨烯是0.34 nm, 二硫化钼是0.65 nm), 因此若要精确地测量范德华材料的层间力学性质而不受面内弹性模量的干扰, 则要求压印形变小于范德华材料的层间距, 对此通过纳米压痕技术来实现较为困难. 为了解决这个问题, 最近研究人员开发了同样基于原子力显微镜的埃(Å)压痕技术(angstrom-indentation), 通过间接测量$+$积分的方式, 巧妙地将压印形变降低到了1 nm以下, 精度达到了0.1 Å, 完美适用于测量范德华材料的层间力学性质^[29]. 在本文的第三部分中, 作者将详细阐述埃压痕技术的原理和应用. 最后, 简要介绍了一种新型的范德华材料-范德华异质结, 即不同的二维材料通过层间范德华作用力实现的垂直堆叠. 同时简要讨论了埃压痕技术在范德华异质结力学性质研究中的潜在应用.

1.2 原子力显微镜

原子力显微镜(atomic force microscopy, AFM)是在扫描隧道显微镜(scanning tunneling microscopy, STM)的基础上由IBM在1986年发明的, 原子力显微镜和扫描隧道显微镜被合称为扫描探针显微镜(scanning probe microscopy, SPM)^[30]. 原子力显微镜的基本结构如图1(a)所示, 核心结构是由悬臂梁和针尖组成的探针, 探针的运动通过压电陶瓷来控制. 激光束照射在悬臂梁的背面并反射到由光敏二极管阵列组成的激光探测器上, 因此悬臂梁的微小弯曲通过光路实现了放大和接收. 原子力显微镜最基础的测量模式是"接触模式". 在接触模式的实际测量过程中, 针尖接触样品表面并且水平移动, 样品表面的高低起伏引起的悬臂梁弯曲程度的变化被激光探测器检测到, 控制器内部的反馈系统会自动调节压电陶瓷的电流从而升高或降低悬臂梁和样品的相对位置使悬臂梁的弯曲(即激光光斑在探测器上的位置)一直保持在预设值, 压电陶瓷的压缩或伸张就蕴含了样品表面形貌的具体信息. 纳米压痕技术和埃压痕技术都是基于原子力显微镜的接触工作模式, 因此原子力显微镜的其他工作模式(例如"敲击模式")在此不做赘述.

图1

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图1原子力显微镜

Fig.1Atomic force microscopy

2 纳米压痕技术和二维材料面内力学性质

2.1 悬空二维材料的面内拉伸测量

为了实现足够大的拉伸应变, 在纳米压痕实验中, 二维材料一般被置于悬空基底上, 如图2所示. 最早利用原子力显微镜测量二维材料力学性质是在2007年, 2 $\sim$ 8 nm厚的若干层石墨烯被置于宽度为1 $\mu$m的长方形沟槽上, 原子力显微镜的探针在石墨烯中间施加正压力, 产生垂直位移, 从而引起面内拉伸^[33]. 利用这种方式得到的若干层石墨烯的弹性模量为500 GPa, 明显低于理论预测值^[34]. 美国哥伦比亚大学的Lee等^[35]对悬空石墨烯纳米压痕实验做出改进, 将单层石墨烯置于圆形孔洞上, 针尖在二维薄膜中心施加点载荷, 从而提供了相比长方形沟槽更对称的应变分布, 如图2(c)所示. 此后大多数二维材料的弹性力学测量都是基于相似的实验装置. 通过控制针尖的位移, 可以精确控制二维薄膜的形变, 同时将激光探测器得到的光斑偏转信号乘以探针悬臂梁的弹簧常数得到施加的正压力, 最终得到压力-位移曲线, 如图3(a)所示. 由于基底侧壁与二维材料之间的范德华力的吸附作用, 纳米压痕实验一般被视为边缘固定薄圆板在中心点载荷作用下弯曲的过程, 连续介质力学理论给出压力和位移的本构关系^[35-37]

(1)$\begin{eqnarray} \label{eq1} F=(\sigma_{0}^{2D} )\delta +\left(E^{2D}\frac{q^{3}}{r^{2}}\right)\delta^{3} \end{eqnarray} $

其中, $F$是针尖作用于二维材料薄膜正压力, $\delta$是二维材料薄膜中心被针尖下压的位移, $r$是圆孔的半径, $q$是一个与二维材料的泊松比$v$相关的无量纲常数 $1/(1.05-0.15v-0.16v^{2})$. $\sigma _{0}^{2D} $和$E^{2D}$是二维材料的二维预应力和二维弹性模量. 将式(1)对纳米压痕得到的压力-位移曲线进行拟合, 便可得到二维材料的二维预应力和二维弹性模量. 如果将二维材料简单认为是各向同性的, 那么将二维弹性模量除以二维材料的厚度, 便得到等效三维弹性模量. 如果持续增大正压力直到二维薄膜破裂, 还可以得到二维材料的二维断裂强度$\sigma_{m}$

(2)$\begin{eqnarray} \sigma_{m}^{2D} =\left(\frac{FE^{2D}}{4\pi R}\right)^{1/2} \end{eqnarray} $

其中, $F$是二维材料破裂时的正压力, $E^{2D}$是二维材料的二维弹性模量, $R$是原子力显微镜针尖的曲率半径.

图2

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图2二维材料纳米压痕实验示意图

Fig.2AFM-based nano-indentation on 2D materials

图3

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图3单层石墨烯的面内力学性质

Fig.3Transverse/in-plane elasticity of graphene

2.1.1 石墨烯面内弹性模量

图3(a)是悬空单层石墨烯的压力-位移曲线和对应式(1)的拟合, 拟合曲线与实验结果十分接近. 在多次重复纳米压痕实验之后可得到如3(b)所示的二维弹性模量的统计直方图, 单层石墨烯的二维弹性模量约为(342 $\pm$ 30) N/m. 假设单层石墨烯的厚度为0.34 nm, Lee等^[35,38]得到单层石墨烯的三维等效弹性模量约为(1.0 $\pm$ 0.1) TPa, 二维断裂强度约为 55 N/m. 1.0 TPa的弹性模量与金刚石接近, 基本达到了固体材料刚度(stiffness)的上限. 值得注意的是, 目前所有关于无支撑二维材料的力学性质的实验工作都把二维材料简单地视作连续的各向同性材料, 然而二维材料具有明显的各向异性, 其面内和层间的力学性质是完全不同的. 更严谨的表达是: 此处所谓的 "等效三维弹性模量" 实质上是面内弹性模量$E_{||}$, 对应的是石墨烯层内碳原子之间的sp$^{2}$杂化键的强度, 因此石墨烯超高的面内弹性模量是结构稳定并且键能极高的碳碳sp$^{2}$键的结果. 考虑到石墨烯和其他大多数二维材料在面内具有很高的对称性, 我们可以在不失严谨性的前提下认为二维材料面内是近似各向同性的, 因此二维材料又可以被视为面内各向同性材料(transversely isotropic materials). 面内各向同性材料的应力张量 $\sigma $和应变张量$\varepsilon $的关系可表达成

(3)$\begin{eqnarray} \left[ {\begin{array}{l} \sigma_{xx} \\[.5mm] \sigma_{yy} \\[.5mm] \sigma_{zz} \\[.5mm] \sigma_{yz} \\[.5mm] \sigma_{xz} \\[.5mm] \sigma_{xy} \\[.5mm] \end{array}} \right]=\left[\begin{array}{ccccl} C_{11} & C_{12} & C_{13} & & \\[.5mm] C_{12} & C_{22} & C_{23} & & \\[.5mm] C_{13} & C_{23} & C_{33} & & \\[.5mm] & & & C_{44} & \\[.5mm] &&&& C_{44} \\[.5mm] &&&&(C_{11} -C_{12})/2\\[.5mm] \end{array} \right]\left[ {\begin{array}{l} \varepsilon_{xx} \\[.5mm] \varepsilon_{yy} \\[.5mm] \varepsilon_{zz} \\[.5mm] \varepsilon_{yz} \\[.5mm] \varepsilon_{xz} \\[.5mm] \varepsilon_{xy} \\[.5mm] \end{array}} \right] \end{eqnarray} $

决定面内各向同性材料的弹性性质的主要有5个独立参量, 分别是

(4)$\begin{eqnarray} \label{eq4} \left.\begin{array}{l} E_{\parallel } =(C_{11} -C_{12} )(C_{11} C_{13} +C_{12} C_{33} -2C_{13} C_{13} )/\\\qquad (C_{11} C_{33} -C_{13} C_{13} ) \\[.5mm] E_{\bot } =C_{33} -2C_{13} C_{13} /(C_{11} +C_{12} ) \\[.5mm] G_{xy} =(C_{11} -C_{12} )/2 \\[.5mm] \nu_{xz} =\nu_{yz} =C_{13} /(C_{11} +C_{12} ) \\[.5mm] G_{yz} =G_{xz} =C_{44} \\[.5mm] \end{array}\right\} \end{eqnarray} $

其中$E_{||}$即二维材料的面内弹性模量, 即纳米压痕实验中得到的"等效三维弹性模量", $v$是材料的泊松比, $E_{\bot}$是二维材料的层间弹性模量, 对应二维材料的层间范德华作用力的强度, $G_{yz}(G_{xz}$, C$_{44})$即二维材料的层间剪切模量, 代表了二维材料抵抗层间滑移的能力, 又被称为层间吸附强度. 层间剪切模量的来源与层间弹性模量相同, 即范德华作用^[39-40]. 在本文第三部分将具体介绍用于测量二维材料层间弹性模量的方法和技术.

2.1.2 二硫化钼面内弹性模量

和石墨烯相似, 二硫化钼也具有六方蜂巢晶格结构; 不同的是二硫化钼是化合物, 由硫和钼两种元素组成, 并且硫和钼原子在层内不处于同一个平面, 两层硫原子之间夹着一层钼原子, 如图4(a)所示. 二硫化钼由于其较弱的层间剪切模量($C_{44})$, 在工业上一直被广泛地用作润滑剂. 块体二硫化钼是间接带隙半导体, 而单层二硫化钼则是直接带隙半导体, 带隙约为1.8 eV, 对应波长处于可见光范围内, 因此二硫化钼被认为在光电材料领域有着诱人的应用前景. 图4(b)是机械剥离在多孔硅基底上的单层二硫化钼, 纳米压痕实验的过程与石墨烯完全相同, 在此不再赘述. 纳米压痕实验发现, 单层二硫化钼面内弹性模量约为270 GPa^[41-43].

图4

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图4二硫化钼

Fig.4MoS$_{2}$

2.1.3 其他二维材料面内弹性模量

自石墨烯和二硫化钼之后, 二维材料家族迅速扩大, 大量新型二维材料被发现和合成. 例如有"白石墨烯"之称的六方氮化硼(hexagonal boron nitride, h-BN)的面内弹性模量达到了900 GPa^[44]; 此外国际上多个课题组对其他过渡金属硫族化合物(例如WS$_{2}$, WSe$_{2}$和MoTe$_{2}$等)和其他新型非碳二维材料 (例如磷烯、GaS, Bi$_{2}$Te$_{3}$, WN等)的面内力学性质也做了广泛而深入的研究^[45-52]. 文献[50]中总结并展示了若干有代表性的报道, 如图5所示.

图5

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图5部分二维材料面内弹性模量总结^[50]

Fig.5In-plane Young's moduli of representative 2D materials^[50]

2.2 带柔性可延展基底的二维材料的面内拉伸测量

二维材料在其他实验和实际应用中往往会置于基底上, 而基底会影响二维材料的力学性能. 尤其是在柔性电子器件和可穿戴设备等情形下, 二维材料往往要承受很大的应变^[53-55]. 因此对带柔性可延展基底的二维材料的面内拉伸性质的研究至关重要. Xiong等^[53-54]通过AFM纳米压痕实验和有限元计算分析发现, 粘附在PDMS (polydimethylsiloxane)上的单层石墨烯的弹性模量和断裂强度和悬空的情形类似, 如图6所示. PDMS在石墨烯的保护下, 可以抵抗更大的形变.

图6

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图6石墨烯/PDMS结构纳米压痕实验

Fig.6Nano-indentation on graphene/PDMS

2.3 原子力显微镜在纳米压痕实验中的测量误差与来源

原子力显微镜在悬空二维材料面内力学性能测量中有独到的优势, 同时也不可避免地带来一些测量误差. 目前大多数关于悬空二维材料力学性能的研究都是基于连续介质力学假设: 单层二维材料被视为连续的、各向同性的弹性薄膜; 并且AFM探针的尺寸忽略不计, 压力被视为点载荷. 然而二维材料的厚度是原子级别的, 并且二维材料与AFM探针之间的范德华作用力不能忽略, 因此上述假设并不完全适用于二维材料. Cao等^[56-58]通过molecular mechanics(MM)模拟发现, 当AFM探针靠近悬空二维材料时, 探针与二维材料之间的范德华作用会产生应力与应变的不同步(phase lag), 即在真正接触发生之前(应力依然为零), 二维薄膜已产生一个不可忽略的预应变, 如图7(a)所示. 因此在实际测量时, 针尖的位移和二维材料的中心处的位移并不完全相同. 随着二维薄膜形变的增大, 范德华作用的影响迅速减弱, 当面内应变$>2.5$${\%}$时, 范德华作用可以忽略不计, 如图7(c)所示. 此外理论计算发现, 二维材料与基底侧壁之间的范德华作用力不足以强大到在中心载荷作用下完全固定住二维薄膜. 相反的, 二维薄膜与基底侧壁之间的吸附边界(adhesive boundary)会在压力作用下发生剥落, 如图7(b)所示. 因此悬空二维材料的纳米压痕实验更接近于边界不固定的纯弯曲模型, 而非大多数实验工作中使用的边缘固定薄圆板的弯曲模型^[34]. Cao等^[34,58]通过理论与计算, 发现纯弯曲模型给出的应力-应变本构关系与实验结果更为符合, 很好地解释二维材料纳米压痕实验中得到的弹性模量普遍偏低的问题. Cao等^[56-57]还对AFM探针的尺寸对纳米压痕实验的影响进行了计算, 发现只有当悬空二维薄膜的尺寸与压头尺寸的比值足够大于时($>$ $\sim$ 30), 压头的尺寸对测量的影响方可忽略不计, 如图7(c)所示.

图7

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图7纳米压痕实验可能误差来源

Fig.7Possible error analysis of nano-indentation on suspended 2D materials

3 埃压痕技术和二维材料层间力学性质

基于原子力显微镜的纳米压痕技术可以准确地表征二维材料的面内弹性模量$E_{||}$, 而为了完整地描述二维材料的力学性质, 范德华作用力对应的层间弹性模量$E_{\bot}$是不可或缺的. 一直以来, 研究人员都是利用理论计算或者拉曼光谱等间接手段表征二维材料的层间范德华作用力^[59-65], 如何精确地直接测量二维材料的$E_{\bot}$是困扰材料力学领域的一大难题. 而为了解决这个难题, 美国佐治亚理工学院的科研人员开发了一套同样是基于原子力显微镜的"埃压痕技术"^[29,31,66]. 顾名思义, 埃压痕技术的压印形变(indentation depth)在1 nm以下, 对应的形变精度可达到0.1 Å. 如此微小的压印形变与二维材料的层间距十分接近, 因此能够比较准确地"感知"层间的范德华作用力. 此外, 为了尽可能消除面内的共价键对的埃压痕测量的影响, 埃压痕实验中的二维材料都需要被放置在一个相对坚硬的基底(例如碳化硅)上, 这样二维材料的面内形变相对于层间形变可忽略不计, 针尖施加的正向压力基本被范德华作用力所承担.

3.1 基本原理

埃压痕技术中的一大难点便是如何精确地控制并且测量二维材料的微弱形变. 埃压痕要求形变在1 nm以下, 由于原子力显微镜自身压电陶瓷的热漂移以及环境因素的存在, 直接进行Å级别的位移测量得到的误差较大. 开发者并没有拘泥于纳米压痕技术的直接测量形变的思路, 而是创造性地采用了"间接"测量的方式, 即先测量压力-形变曲线的斜率再对压力(压力可通过原子力显微镜精确测量)做积分来间接得到压力-形变曲线.

埃压痕技术的基本仪器配置如图8所示. 通过锁相放大器对原子力显微镜的压电陶瓷在原有的直流信号$V_{0}$的基础上施加一个额外的小幅低频正弦信号$\Delta V(\omega t)$, 那么此时压电陶瓷形变则在是直流信号对应的形变$z_{0}$的基础上叠加了一个小幅正弦振动$\Delta z_{piezo}(\omega t)$, 该小幅振动一般控制在1 Å以下. $\Delta z_{piezo}(\omega t)$远小于$z_{0}$ (4 $\sim$ 6 nm). 在探针十分靠近材料表面时, 针尖和材料之间的范德华作用会产生一个"snap in"效应, 针尖会被迅速吸附到材料表面. 若在进针过程中进行埃压痕测量, 这个吸附力(adhesive force)可以被视为一个额外负压力, 在探针与二维材料未接触时产生一个预应变, 不利于埃压痕测量. 因此埃压痕测量是在退针过程中进行的. AFM探针先与被测样品以30 $\sim$ 100 nN的压力接触, 此时可认为针尖与样品已完全接触. 此时压电陶瓷的形变$z_{piezo}$

(5)$\begin{eqnarray} \label{eq5} z_{piezo} =z_{0} +\Delta z_{piezo} (\omega t) \end{eqnarray} $

$\Delta z_{piezo}(\omega t)$对应的正压力$F_{0}$的小幅振动$\Delta F(\omega t)$可以被激光探测器接收, 但是由于信号过于微弱, 一般通过锁相放大器过滤掉噪音信号. 压力-形变曲线的斜率为

(6)$\begin{eqnarray} \label{eq6} k_{0} =\frac{\Delta F(\omega t)}{\Delta z_{piezo} (\omega t)} \end{eqnarray} $

图8

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图8埃压痕技术示意图^[66]

Fig.8Schematic of angstrom-indentation^[66]

但是此时压电陶瓷的形变并不等于材料和针尖接触处的形变, 而是等于接触形变$\Delta z_{indent}$(或者$\Delta z_{contact}$)和悬臂梁弯曲形变$\Delta z_{cantilever}$的总和

(7)$\begin{eqnarray} \label{eq7} \left.\begin{array}{l} z_{piezo} =z_{cantilever} +z_{indent} \\ \Delta z_{piezo} =\Delta z_{cantilever} +\Delta z_{indent} \\ \end{array}\right\} \end{eqnarray} $

因此可以将接触处视作一个和悬臂梁串联的弹簧, 弹簧常数分别为$k_{contact}$和$k_{cantilever}$, 如图9(a)所示. 将式(7)和式(6)联立便可得到

(8)$\begin{eqnarray} \label{eq8} \frac{1}{k_{0} }=\frac{1}{k_{cantilever} }+\frac{1}{k_{contact} } \end{eqnarray} $

式中$k_{contact}$便是针尖-材料接触处形变曲线对应的斜率. 我们缓慢地减小正压力$F_{0}$并且记录每个$F_{0}$对应的$k_{contact}$直至针尖与材料表面脱离接触, 再做式(9)中的积分便可得到材料的$F$$-$$z$曲线, 如图9(b)和图9(c)所示. 值得注意的是, 即使经过锁相放大器过滤, 得到的斜率数据依然存在噪音, 如图9(b)所示. 对斜率的积分在不失数据有效性的前提下, 巧妙地从客观上对力-位移曲线实现了一次平滑处理, 如图9(c)所示

(9)$\begin{eqnarray} \label{eq9} z=\int_{F_{pull\mbox{-}off} }\frac{\Delta F}{k_{contact} (F)} \end{eqnarray} $

当针尖与样品表面分离时, 根据接触力学中适用于变形较小、弹性模量较大情形的Derjaguin-Muller-Toporov (DMT)模型, 针尖和样品之间的吸附力可以被简单视为一个额外的负压力$F_{pull\mbox{-}off}$ (由于是吸引力, $F_{pull\mbox{-}off}$为负)

(10)$\begin{eqnarray} \label{eq10} F-F_{pull\mbox{-}off} =\frac{4}{3}E^{\ast }R^{1/2}z^{3/2} \end{eqnarray} $

式中, $E^{\ast }$是接触处等效弹性模量, $R$是针尖曲率半径. 因此埃压痕技术通过反向退针测量, 将针尖与样品之间的范德华作用简单等效成一个额外负压力. 接触力学中的Johnson-Kendall-Roberts (JKR)模型相较于DMT模型, 更适用于变形较大、弹性模量较小的情形. 在文献[29,31]中作者对DMT模型和JKR模型根据实验数据做了详细比较, 发现对于石墨烯等二维材料的埃压痕实验数据, DMT模型符合得更好, 但两者差别不大. 因此在不失有效性的前提下, 一般使用数学形式更为简洁的DMT模型即式(10)对$F$$-$$z$曲线进行拟合, 得到等效接触弹性模量$E^{\ast }$

(11)$\begin{eqnarray} \label{eq11} \frac{1}{E^{\ast }}=\frac{1-\nu_{1}^{2} }{E_{1} }+\frac{1-\nu_{2}^{2} }{E_{2} } \end{eqnarray} $

图9

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图9埃压痕技术的弹性力学模型

Fig.9Elastic mechanics modelling of Angstrom-indentation

其中$E_{1}$, $\nu_{1}$和$E_{2}$, $\nu_{2}$分别是针尖和材料的弹性模量和泊松比. 联立式(9) $\sim\!$式(11)便可得到被测样品的弹性模量. 值得注意的是, 埃压痕技术的目标对象并不限于二维材料, 亦可用于表征其他材料的弹性力学性质, 例如碳纳米管的径向弹性系数和超硬材料的弹性模量^[67-71].

3.2 可能影响埃压痕测量的因素

埃压痕技术要求二维材料表面尽可能的平整, 褶皱或者其他非常规几何结构会严重影响二维材料力学性能测量^[72]. 例如CVD石墨烯的褶皱一般在几纳米左右, 远远大于埃压痕的压印形变^[73-74], 所以对于埃压痕测量来说, 石墨烯相当于是"悬空的", 即便能够得到低噪音的应力应变曲线, 它必然包含了面内和层间弹性模量复合信息, 很难从中分离出单纯的层间弹性模量相关信息. 因此埃压痕测量时需要尽量避免不平整区域. 通常在埃压痕测量开始之前, 会先进行样品表面形貌的扫描, 寻找到一块平整区域进行测量. 由于埃压痕测量时探针位置保持不动, 并且接触半径仅仅为几十纳米, 所以二维材料在3 $\mu$m左右大小的区域内足够平整即可.

当二维材料层数很少时(例如两层), 埃压痕测量将不可避免地受到基底的影响. 一方面探针施加的压力会压缩二维材料与基底之间的距离, 使二维材料与基底之间的范德华作用发生变化, 增加了受力分析的复杂性. 另一方面, 即使不考虑二维材料和基底之间的范德华力, 施加在二维材料表面的压力也会使基底发生微小形变. 二维材料越厚, 以上两个方面的影响就越弱. 理论计算和实验发现, 当形变与二维材料总体厚度的比例小于10${\%}$时, 基底的作用可忽略不计, 具体讨论也可见文献[29]中"semi-analytical-methods"和"supplementary information"部分.

由于形变很小, 因此AFM针尖的尺寸和形状对埃压痕测量的影响十分巨大. 接触力学中的Hertz模型、DMT模型和JKR模型的公式中均包含压头曲率半径, 例如式(10). 因此在埃压痕实验开始前, 一般会对AFM探针进行扫描电子显微镜(SEM)观测得到探针曲率半径. 亦可对诸如碳化硅、氧化锌等已知其弹性模量的近似各向同性材料作为基准材料进行埃压痕测量, 利用DMT模型对力-位移曲线进行拟合得到探针半径, 并和SEM得到的半径进行比对. 此外, 在埃压痕测量结束之后, 也需要对探针进行SEM的观测: 若针尖半径或者针尖形状出现明显变化(例如破损、污染), 则该次埃压痕测量的数据便不可信.

3.3 石墨烯和氧化石墨烯层间弹性模量的直接测量

Gao等利用埃压痕技术首次直接测量了碳化硅上生长的外延石墨烯的层间弹性模量, 发现其约为33 GPa, 与理论预测值十分接近^[29]. 氧化石墨烯(graphene oxide)的反应活性优于石墨烯, 可用于制备具有优异力学性能的复合材料^[75]. Gao等^[29]系统地研究了氧化石墨烯层间弹性模量和层间插层水分子之间的定量关系. 层间插层水分子可以显著的改变氧化石墨烯的层间距, 从而改变其电导率、热导率、掺杂等多种性质. 通过控制密闭腔内部的相对湿度, Gao等^[29]实现了层间插层水分子数量的动态控制. 埃压痕实验表明, 氧化石墨烯的层间弹性模量随着湿度增大从10${\%}$湿度下的20 GPa增大到了25${\%}$湿度时的35 GPa, 此后湿度的增大反而降低了氧化石墨烯的层间弹性模量, 最终在50${\%}$左右的湿度时层间弹性模量回落到了最初的20 GPa左右. 该现象的可能机理为: 在低湿度时, 层间插层水分子增加了氧化石墨烯的层间距从而减弱了范德华吸引力, 同时水分子亦会减弱氧化石墨烯之间的接触, 因此此时层间弹性模量低于石墨烯的层间弹性模量. 随着湿度的增大, 插层水分子逐渐填满了氧化石墨烯的层间空间, 并且形成一层氢键网络, 水分子层可被视为"额外"的一层氧化石墨烯, 反过来加强了氧化石墨烯系统的层间范德华作用力, 此时层间弹性模量会增大到和石墨烯接近的35 GPa. 随着水分子数量持续增大, 第二层水分子开始形成, 层间距再次扩大, 同时在水分子流动性的作用下, 层间弹性模量开始降低. 具体的数据展示在图10中.

图10

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图10氧化石墨烯的层间力学性质

Fig.10Out-of-plane elasticity of graphene oxide

3.4 双层石墨烯-单层金刚石相变

石墨和金刚石是自然界中最常见的碳的同素异形体. 通过对石墨施加高温高压的是工业上常用的人工合成金刚石的手段. 自从石墨烯被发现之后, 科研人员一直致力于合成超薄甚至单层的金刚石的结构^[76-79]. Gao等^[80-81]发现在常温下利用原子力显微镜施加10 GPa左右的局域压强可以驱使碳化硅上的双层外延石墨烯转化为单层金刚石结构, 如图11(a)所示. 他们同时利用原位埃压痕技术直接测量了单层金刚石结构的弹性模量, 发现其约为1 TPa, 与天然块体金刚石接近. 埃压痕测量的结果如图11(b)所示. 硬度测量从侧面佐证了相变的发生: 在同等压力下, 多层石墨烯和碳化硅都发生了塑性形变, 而双层石墨烯则完好如初, 如图12所示^[80]. 该工作充分地展现了原子力显微镜和埃压痕技术的强大功能.

图11

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图11双层石墨烯-单层金刚石相变

Fig.11Bilayer graphene-monolayer diamond phase transition

图12

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图12单层金刚石、碳化硅、多层石墨烯的硬度测量^[80]

Fig.12Hardness of monolayer diamond, SiC and multilayer graphene^[80]

4 范德华异质结

当将几种不同的二维材料垂直堆叠起来时, 由于层间范德华作用力, 可形成许多新奇的异质结构^[82-87]. 范德华异质结"任意搭配"的特性可以把这些单独的二维材料像乐高积木一样结合到一起, 如图13(a)所示, 在仍保持超薄的厚度的基础上呈现出令人惊奇的物理性质. 例如把双层石墨烯轻微旋转约1.1$^\circ$ (所谓的"魔角 (magic angle)"), 狄拉克点附近电子能带变得十分扁平, 杂化的层间电子在狄拉克点的费米速度趋近于零, 电子有效质量急剧增大^[88]; 并且当导带或者价带处于半满(half-filling)状态时, 本应呈现金属特性的"魔角"石墨烯却表现出反常的莫特绝缘体性质; 如果使费米能级稍微偏离半满态, "魔角"石墨烯甚至能变成超导体^[89]. 然而目前大多数关于范德华异质结的研究聚焦于其电学和光学性质, 对其潜在的可能奇异的力学性质的研究则有所欠缺. Liu等^[43]发现MoS$_{2}$/WS$_{2}$双层异质结构的二维弹性模量低于其单体结构二维弹性模量的总和, 但与相应的双层单一材料结构相似, 如图13(b)所示. 范德华异质结之所以不同于普通单体二维材料, 其根源便在于二维材料的层间范德华耦合, 因此精确表征和调控层间作用力对范德华异质结的基础认知和未来应用有着十分重大的意义. 由于埃压痕技术的独特的施加Å级形变的能力, 可能是范德华异质结层间力学性质测量难题的可行的解决方案. 例如用于研究不同材料、不同层数、不同角度组成的范德华异质结材料的等效层间弹性模量; 也可利用埃压痕技术施加微小形变, 同时进行原位电输运测量, 研究范德华作用力对电子学性质的影响.

图13

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图13范德华异质结示意图及其力学性质

Fig.13Schematic of van der Waals heterostructures and their elastic properties

5 总结与展望

原子力显微镜能够在纳米甚至埃尺度上施加压力和测量形变, 在二维材料及其异质结构的弹性力学性质的研究方面展示了强大的功能, 是目前最常用的纳米材料力学性质的研究手段. 基于原子力显微镜的纳米压痕技术可用于表征无支撑二维材料及其异质结构的面内力学性质. 而同样基于原子力显微镜的埃压痕技术在垂直表面形变的精度上比纳米压痕技术提高了一个数量级, 达到了埃级别, 完美适用于测量范德华材料的层间力学性质, 很好地填补了纳米压痕技术在这方面的不足.

随着前沿科学和新技术的不断发展, 对工程材料与结构的超常规尺度、硬度、刚度等极端性能以及在超常规压强等极端服役环境中的力学响应规律的研究, 既是力学发展和研究的需要, 更是与关乎国计民生的重大科研与工程项目密切相关^[20]. 新型材料在微纳尺度上展现出的极端性能和在超高压强等极端外界条件的力学性能, 也许是实现其在重大工程(例如航空航天、关键装备等)和民用(例如可穿戴柔性设备)等领域具体应用的一个可能的突破口^[90]. 因此对于二维材料力学性能的研究, 无论在力学基础研究领域还是工程应用领域都有重大意义, 基于原子力显微镜的力学测量手段在未来无疑将发挥更大的作用.

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, Xiong

. Fracture behavior of graphene mounted on stretchable substrate
Carbon, 2016,109:852-859

[本文引用: 2]

[54]

Niu

, Cao

, Xiong

. Indentation behavior of the stiffest membrane mounted on a very compliant substrate: Graphene on PDMS
International Journal of Solids and Structures, 2018, 132-133:1-8

[本文引用: 1]

[55]

Chen

, Guo

, Tang

, et al. Nanomechanical properties of graphene on poly(ethylene terephthalate) substrate
Carbon, 2013,55:144-150

[本文引用: 1]

[56]

Zhou

, Wang

, Cao

. Van der waals effect on the nanoindentation response of free standing monolayer graphene
Carbon, 2013,57:357-362

[本文引用: 2]

[57]

Zhou

, Xue

, Wang

, et al. Molecular mechanics simulations of the deformation mechanism of graphene monolayer under free standing indentation
Carbon, 2013,63:117-134

[本文引用: 1]

[58]

Zhou

, Wang

, Cao

. Boundary condition and pre-strain effects on the free standing indentation response of graphene monolayer
Journal of Physics$:$ Condensed Matter, 2013,25:475303

URL PMID [本文引用: 2]

[59]

Bj?rkman

, Gulans

, Krasheninnikov

, et al. Van der waals bonding in layered compounds from advanced density-functional first-principles calculations
Physical Review Letters, 2012,108(23):235502

DOI URL PMID [本文引用: 1]

Although the precise microscopic knowledge of van der Waals interactions is crucial for understanding bonding in weakly bonded layered compounds, very little quantitative information on the strength of interlayer interaction in these materials is available, either from experiments or simulations. Here, using many-body perturbation and advanced density-functional theory techniques, we calculate the interlayer binding and exfoliation energies for a large number of layered compounds and show that, independent of the electronic structure of the material, the energies for most systems are around 20 meV/A2. This universality explains the successful exfoliation of a wide class of layered materials to produce two-dimensional systems, and furthers our understanding the properties of layered compounds in general.

[60]

Fan

, Zhu

, Ke

, et al. Vibrational spectrum renormalization by enforced coupling across the van der waals gap between MoS$_{2}$ and WS$_{2}$ monolayers
Physical Review B, 2015,92(24):241408

[61]

Wang

, Zhou

, Jin

, et al. Strain-dependent Raman analysis of the G* band in graphene
Physical Review B, 2019,100:241407

[62]

Zhang

, Zhang

, Wang

, et al. Crack propagation and fracture toughness of graphene probed by raman spectroscopy
ACS Nano, 2019,13:10327-10332

DOI URL PMID

Fracture behaves as one of the most fundamental issues for solid materials. As a one-atom-thick crystal, many aspects in fracture mechanics of graphene are of high significance, such as the crack propagation and its fracture toughness. Here we present a method to study the fracture characteristics of graphene using Raman spectroscopy and designed chemical-vapor-deposited monolayer graphene with preset cracks. The dynamic fracture process of graphene was experimentally observed, and its fracture toughness was obtained using Griffith's criterion based on the strain distribution derived from the frequency shifts of Raman bands. The fracture toughness of Kc = 6.1 +/- 0.6 MPa[Formula: see text] and Gc = 37.4 +/- 6.7 J/m(2) are comparable with the previously reported theoretical and experimental values, and we believe that this simple and easy-to-operate approach of characterizing the fracture of graphene using Raman spectroscopy can also be extended to other two-dimensional materials.

[63]

Wang

, Wang

, Xu

, et al. Domain-boundary independency of Raman spectra for strained graphene at strong interfaces
Carbon, 2018,134:37-42

[64]

Lin

, Chen

, Lu

, et al. Identifying the stacking order of multilayer graphene grown by chemical vapor deposition via Raman spectroscopy
Journal of Raman Spectroscopy, 2018,49:46-53

[65]

, Zhang

, Das

, et al. Step-by-step monitoring of CVD-graphene during wet transfer by Raman spectroscopy
RSC Advances, 2019,9:41447-41452

[本文引用: 1]

[66]

Cellini

, Gao

, Riedo

. Å-indentation for non-destructive elastic moduli measurements of supported ultra-hard ultra-thin films and nanostructures
Scientific Reports, 2019,9(1):4075

DOI URL PMID [本文引用: 3]

During conventional nanoindentation measurements, the indentation depths are usually larger than 1-10 nm, which hinders the ability to study ultra-thin films (<10 nm) and supported atomically thin two-dimensional (2D) materials. Here, we discuss the development of modulated A-indentation to achieve sub-A indentations depths during force-indentation measurements while also imaging materials with nanoscale resolution. Modulated nanoindentation (MoNI) was originally invented to measure the radial elasticity of multi-walled nanotubes. Now, by using extremely small amplitude oscillations (<<1 A) at high frequency, and stiff cantilevers, we show how modulated nano/A-indentation (MoNI/AI) enables non-destructive measurements of the contact stiffness and indentation modulus of ultra-thin ultra-stiff films, including CVD diamond films (~1000 GPa stiffness), as well as the transverse modulus of 2D materials. Our analysis demonstrates that in presence of a standard laboratory noise floor, the signal to noise ratio of MoNI/AI implemented with a commercial atomic force microscope (AFM) is such that a dynamic range of 80 dB -- achievable with commercial Lock-in amplifiers -- is sufficient to observe superior indentation curves, having indentation depths as small as 0.3 A, resolution in indentation <0.05 A, and in normal load <0.5 nN. Being implemented on a standard AFM, this method has the potential for a broad applicability.

[67]

Song

, Wang

, Riedo

, et al. Elastic property of vertically aligned nanowires
Nano Letters, 2005,5(10):1954-1958

[本文引用: 1]

[68]

Palaci

, Fedrigo

, Brune

, et al. Radial elasticity of multiwalled carbon nanotubes
Physical Review Letters, 2005,94(17):175502

URL PMID

[69]

Lucas

, Mai

, Yang

, et al. Aspect ratio dependence of the elastic properties of ZnO nanobelts
Nano Letters, 2007,7(5):1314-1317

DOI URL PMID

The Young's modulus of ZnO nanobelts was measured with an atomic force microscope by means of the modulated nanoindentation method. The elastic modulus was found to depend strongly on the width-to-thickness ratio of the nanobelt, decreasing from about 100 to 10 GPa, as the width-to-thickness ratio increases from 1.2 to 10.3. This surprising behavior is explained by a growth-direction-dependent aspect ratio and the presence of stacking faults in nanobelts growing along particular directions.

[70]

Lucas

, Leach

, McDowell

, et al. Plastic deformation of pentagonal silver nanowires: comparison between AFM nanoindentation and atomistic simulations
Physical Review B, 2008,77(24):245420

[71]

Narayan

, Gupta

, Bhaumik

, et al. Q-carbon harder than diamond
MRS Communications, 2018,8(2):428-436

[本文引用: 1]

[72]

任云鹏, 曹国鑫. 褶皱与晶界偶合作用对石墨烯断裂行为的影响
力学学报, 2019,51(5):1381-1392

[本文引用: 1]

(Ren

Yunpeng

, Cao

Guoxin

. Coupling effects of wrinkles and grain boundary on the fracture of graphene
Chinese Journal of Theoretical and Applied Mechanics, 2019,51(5):1381-1392 (in Chinese))

[本文引用: 1]

[73]

Lin

, Jing

, Zhou

, et al. Stretch-induced stiffness enhancement of graphene grown by chemical vapor deposition
ACS Nano, 2013 7(2):1171-1177

DOI URL PMID [本文引用: 1]

The mechanical properties of ultrathin membranes have attracted considerable attention recently. Nanoindentation based on atomic force microscopy is commonly employed to study mechanical properties. We find that the data processing procedures in previous studies are nice approximations, but it is difficult for them to illustrate the mechanical properties precisely. Accordingly, we develop a revised numerical method to describe the force curve properly, by which the intrinsic mechanical properties of these membranes can be acquired. Combining the nanoindentation measurements with the revised numerical method, we demonstrate that loading-unloading cycles under large load can lead to a pronounced improvement in stiffness of graphene grown by chemical vapor deposition (CVD). The Young's moduli of the stretched CVD graphene membranes can be improved to approximately 1 TPa, closing to the value of the pristine graphene. Our findings demonstrate a possible way to recover the exceptional elastic properties of CVD graphene from the softened stiffness caused by wrinkles.

[74]

Ren

, Cao

. Adhesive boundary effect on free-standing indentation characterization of chemical vapor deposition graphene
Carbon, 2019,153:438-446

[本文引用: 1]

[75]

李东波, 刘秦龙, 张鸿驰等. 基于分子动力学的氧化石墨烯拉伸断裂行为与力学性能研究
力学学报, 2019,51(5):1393-1402

[本文引用: 1]

(Li

Dongbo

, Liu

Qinlong

, Zhang

Hongchi

, et al. Study on tensile fracture behavior and mechanical properties of GO based on molecular dynamics method
Chinese Journal of Theoretical and Applied Mechanics, 2019,51(5):1393-1402 (in Chinese))

[本文引用: 1]

[76]

Rajasekaran

, Abild-Pedersen

, Ogasawara

, et al. Interlayer carbon bond formation induced by hydrogen adsorption in few-layer supported graphene
Physical Review Letters, 2013,111(8):085503

URL PMID [本文引用: 1]

[77]

Kvashnin

, Chernozatonskii

, Yakobson

, et al. Phase diagram of quasi-two-dimensional carbon, from graphene to diamond
Nano Letters, 2014,14(2):676-681

DOI URL PMID

We explore how a few-layer graphene can undergo phase transformation into thin diamond film under reduced or no pressure, if the process is facilitated by hydrogenation of the surfaces. Such a

[78]

Martins

LGP

, Matos

MJS

, Paschoal

, et al. Raman evidence for pressure-induced formation of diamondene
Nature Communications, 2017,8(1):96

DOI URL PMID

Despite the advanced stage of diamond thin-film technology, with applications ranging from superconductivity to biosensing, the realization of a stable and atomically thick two-dimensional diamond material, named here as diamondene, is still forthcoming. Adding to the outstanding properties of its bulk and thin-film counterparts, diamondene is predicted to be a ferromagnetic semiconductor with spin polarized bands. Here, we provide spectroscopic evidence for the formation of diamondene by performing Raman spectroscopy of double-layer graphene under high pressure. The results are explained in terms of a breakdown in the Kohn anomaly associated with the finite size of the remaining graphene sites surrounded by the diamondene matrix. Ab initio calculations and molecular dynamics simulations are employed to clarify the mechanism of diamondene formation, which requires two or more layers of graphene subjected to high pressures in the presence of specific chemical groups such as hydroxyl groups or hydrogens.The synthesis of two-dimensional diamond is the ultimate goal of diamond thin-film technology. Here, the authors perform Raman spectroscopy of bilayer graphene under pressure, and obtain spectroscopic evidence of formation of diamondene, an atomically thin form of diamond.

[79]

Bakharev

, Huang

, Saxena

, et al. Chemically induced transformation of chemical vapour deposition grown bilayer graphene into fluorinated single-layer diamond
Nature Nanotechnology, 2020,15(1):59-66

URL PMID [本文引用: 1]

[80]

Gao

, Cao

, Cellini

, et al. Ultrahard carbon film from epitaxial two-layer graphene
Nature Nanotechnology, 2018,13(2):133-138

DOI URL PMID [本文引用: 4]

Atomically thin graphene exhibits fascinating mechanical properties, although its hardness and transverse stiffness are inferior to those of diamond. So far, there has been no practical demonstration of the transformation of multilayer graphene into diamond-like ultrahard structures. Here we show that at room temperature and after nano-indentation, two-layer graphene on SiC(0001) exhibits a transverse stiffness and hardness comparable to diamond, is resistant to perforation with a diamond indenter and shows a reversible drop in electrical conductivity upon indentation. Density functional theory calculations suggest that, upon compression, the two-layer graphene film transforms into a diamond-like film, producing both elastic deformations and sp (2) to sp (3) chemical changes. Experiments and calculations show that this reversible phase change is not observed for a single buffer layer on SiC or graphene films thicker than three to five layers. Indeed, calculations show that whereas in two-layer graphene layer-stacking configuration controls the conformation of the diamond-like film, in a multilayer film it hinders the phase transformation.

[81]

Cellini

, Lavini

, Cao

, et al. Epitaxial two-layer graphene under pressure: diamene stiffer than diamond
Flat Chem, 2018,10:8-13

[本文引用: 1]

[82]

Dean

, Young

, Meric

, et al. Boron nitride substrates for high-quality graphene electronics
Nature Nanotechnology, 2010,5(10):722-726

[本文引用: 1]

[83]

Ponomarenko

, Gorbachev

, Yu

, et al. Cloning of Dirac fermions in graphene superlattices
Nature, 2013,497(7451):594-597

URL PMID

[84]

Geim

, Grigorieva

, Van der Waals

heterostructures

. Nature, 2013,499(7459):419-425

DOI URL PMID

Research on graphene and other two-dimensional atomic crystals is intense and is likely to remain one of the leading topics in condensed matter physics and materials science for many years. Looking beyond this field, isolated atomic planes can also be reassembled into designer heterostructures made layer by layer in a precisely chosen sequence. The first, already remarkably complex, such heterostructures (often referred to as 'van der Waals') have recently been fabricated and investigated, revealing unusual properties and new phenomena. Here we review this emerging research area and identify possible future directions. With steady improvement in fabrication techniques and using graphene's springboard, van der Waals heterostructures should develop into a large field of their own.

[85]

Liu

, Weiss

, Duan

, et al. Van der Waals heterostructures and devices
Nature Reviews Materials, 2016,1(9):16042

[86]

Yankowitz

, Ma

, Jarillo-Herrero

, et al. Van der waals heterostructures combining graphene and hexagonal boron nitride
Nature Reviews Physics, 2019,1(2):112-125

[87]

Jin

, Regan

, Yan

, et al. Observation of moiré excitons in WSe$_{2}$/WS$_{2}$ heterostructure superlattices
Nature, 2019,567(7746):76-80

DOI URL PMID [本文引用: 1]

Moire superlattices enable the generation of new quantum phenomena in two-dimensional heterostructures, in which the interactions between the atomically thin layers qualitatively change the electronic band structure of the superlattice. For example, mini-Dirac points, tunable Mott insulator states and the Hofstadter butterfly pattern can emerge in different types of graphene/boron nitride moire superlattices, whereas correlated insulating states and superconductivity have been reported in twisted bilayer graphene moire superlattices(1-12). In addition to their pronounced effects on single-particle states, moire superlattices have recently been predicted to host excited states such as moire exciton bands(13-15). Here we report the observation of moire superlattice exciton states in tungsten diselenide/tungsten disulfide (WSe2/WS2) heterostructures in which the layers are closely aligned. These moire exciton states manifest as multiple emergent peaks around the original WSe2 A exciton resonance in the absorption spectra, and they exhibit gate dependences that are distinct from that of the A exciton in WSe2 monolayers and in WSe2/WS2 heterostructures with large twist angles. These phenomena can be described by a theoretical model in which the periodic moire potential is much stronger than the exciton kinetic energy and generates multiple flat exciton minibands. The moire exciton bands provide an attractive platform from which to explore and control excited states of matter, such as topological excitons and a correlated exciton Hubbard model, in transition-metal dichalcogenides.

[88]

Cao

, Fatemi

, Demir

, et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
Nature, 2018,556(7699):80-84

DOI URL PMID [本文引用: 1]

A van der Waals heterostructure is a type of metamaterial that consists of vertically stacked two-dimensional building blocks held together by the van der Waals forces between the layers. This design means that the properties of van der Waals heterostructures can be engineered precisely, even more so than those of two-dimensional materials. One such property is the 'twist' angle between different layers in the heterostructure. This angle has a crucial role in the electronic properties of van der Waals heterostructures, but does not have a direct analogue in other types of heterostructure, such as semiconductors grown using molecular beam epitaxy. For small twist angles, the moire pattern that is produced by the lattice misorientation between the two-dimensional layers creates long-range modulation of the stacking order. So far, studies of the effects of the twist angle in van der Waals heterostructures have concentrated mostly on heterostructures consisting of monolayer graphene on top of hexagonal boron nitride, which exhibit relatively weak interlayer interaction owing to the large bandgap in hexagonal boron nitride. Here we study a heterostructure consisting of bilayer graphene, in which the two graphene layers are twisted relative to each other by a certain angle. We show experimentally that, as predicted theoretically, when this angle is close to the 'magic' angle the electronic band structure near zero Fermi energy becomes flat, owing to strong interlayer coupling. These flat bands exhibit insulating states at half-filling, which are not expected in the absence of correlations between electrons. We show that these correlated states at half-filling are consistent with Mott-like insulator states, which can arise from electrons being localized in the superlattice that is induced by the moire pattern. These properties of magic-angle-twisted bilayer graphene heterostructures suggest that these materials could be used to study other exotic many-body quantum phases in two dimensions in the absence of a magnetic field. The accessibility of the flat bands through electrical tunability and the bandwidth tunability through the twist angle could pave the way towards more exotic correlated systems, such as unconventional superconductors and quantum spin liquids.

[89]

Cao

, Fatemi

, Fang

, et al. Unconventional superconductivity in magic-angle graphene superlattices
Nature, 2018,556(7699):43-50

URL PMID [本文引用: 1]

[90]

李正, 杨庆生, 尚军军等. 面内随机堆叠石墨烯复合材料压阻传感机理与压阻性能
力学学报, 2020,52(6):1700-1708

[本文引用: 1]

(Li

Zheng

, Yang

Qingsheng

, Shang

Junjun

, et al. Piezoresistive sensing mechanism and piezoresistive performance of in-plane random stacked graphene composites
Chinese Journal of Theoretical and Applied Mechanics, 2020,52(6):1700-1708 (in Chinese))

[本文引用: 1]