本研究通過分析化學氣相沉積過程中與層間和層內相互作用相關的因素，探究了扭轉雙層石墨烯的生長機制。生長過程發生在銅基底上，形成亞毫米級的單晶石墨烯晶粒，並在下方形成多個合併的附屬層晶粒。生長動力學包括協同成核，並利用銅基底中殘餘碳雜質和氣態碳氫化合物作為碳源。採用計算機算法和微米激光拉曼技術研究了石墨烯的扭轉角分佈。根據統計數據，在考慮單個成核中心的雙層區域中，除了熱力學穩定的AB堆疊或分離雙層石墨烯，沒有形成具有特定扭轉角（3°至8°，8°至13°和11°至15°）的扭轉雙層石墨烯。 扭轉雙層石墨烯形成的概率受到合併附屬層晶粒的取向失配的影響，層間和層內相互作用在決定扭轉角方面起著關鍵作用。層間相互作用涉及熱膨脹差異引起的變形和層與基底之間的分離，導致扭轉角的範圍受到限制。對相關變形的高度分析以及銅基底上石墨烯的能帶結構顯示出層間僅存在輕微的不匹配。 扭轉雙層石墨烯的發生還與生長速率變化有關，同位素標記實驗導致拉曼特徵峰的偏移。通過考察附屬層晶粒之間的相互作用並考慮在合併過程中發生的生長速率變化，分析了扭轉雙層石墨烯的生長機制。提出了與使用不同邊緣的合併配置相關的新模型，改善了我們對扭轉雙層石墨烯的生長機制的理解。生長速率和一系列合併配置都會影響TBLG的概率和面積占比。極端的生長條件，特別是高梯度的碳源和較短的成核距離，已被發現能夠有效地提高扭轉雙層石墨烯的生長速率並增加其面積占比。

This research investigates the growth mechanism of twisted bilayer graphene (TBLG) by analyzing the factors related to interlayer and intralayer interactions during chemical vapor deposition (CVD). The growth process occurs on a copper substrate, resulting in the formation of sub-millimeter-sized single crystalline graphene grains with merged adlayer grains beneath. The growth dynamics involve synergistic nucleation and utilize carbon sources from residual carbon impurities in the copper substrate as well as gaseous hydrocarbons (CHx). The distribution of twist angles in the graphene is studied using a computer algorithm and micro-Raman mapping. Based on the statistical, apart from the thermodynamically stable AB-stacking (AB-BLG) or decoupled bilayer graphene (DC-BLG), there is no formation of twisted bilayer graphene (TBLG) with specific twist angles ranging from 3° to 8°, 8° to 13°, and 11° to 15° when considering bilayer regions with a single nucleation center. The probability of TBLG formation is influenced by the orientation mismatch of merging adlayer grains, and the interlayer and intralayer interactions play a crucial role in determining the twist angle. The interlayer interaction involves deformation resulting from thermal expansion differences and decoupling between layers and the substrate, resulting in a confined range of twist angles. Height analysis of the associated deformation, as well as the band structure of graphene on the copper substrate, indicate only a small mismatch at the interlayer. The occurrence of TBLG is also related to the growth rate variation, as evidenced by the use of isotopic labelling, which induces peak shifts in Raman characteristics. The growth mechanism of twisted bilayer graphene (TBLG) is analyzed by examining the interactions between adlayer grains and taking into account the variations in growth rate that occur during the merging process. Novel modules associated with merging configurations employing distinct edges are proposed, improving our understanding of the growth mechanism of TBLG. The probability and areal fraction of TBLG are influenced by both growth rate and a series of merging configurations. Extreme growth conditions, characterized by high source gradients and short nucleation distances, have been found to effectively increase the growth rate of TBLG and enhance its areal fraction.

[1] Y. Zhang et al., “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature, vol. 459, p. 820, Jun. 2009.
[2] Y. Cao et al., “Unconventional superconductivity in magic-angle graphene superlattices,” Nature, vol. 556, no. 7699, pp. 43–50, Mar. 2018.
[3] F. Schwierz, “Graphene transistors,” Nat. Nanotechnol., vol. 5, p. 487, May 2010.
[4] F. Xia, D. B. Farmer, Y. Lin, and P. Avouris, “Graphene Field-Effect Transistors with High On/Off Current Ratio and Large Transport Band Gap at Room Temperature,” Nano Lett., vol. 10, no. 2, pp. 715–718, Feb. 2010.
[5] Y. Cao et al., “Correlated insulator behaviour at half-filling in magic-angle graphene superlattices,” Nature, vol. 556, p. 80, Mar. 2018.
[6] N. Yang, K. Choi, J. Robertson, and H. G. Park, “Layer-selective synthesis of bilayer graphene via chemical vapor deposition,” 2D Mater., vol. 4, no. 3, p. 035023, Aug. 2017.
[7] I. Vlassiouk et al., “Role of Hydrogen in Chemical Vapor Deposition Growth of Large Single-Crystal Graphene,” ACS Nano, vol. 5, no. 7, pp. 6069–6076, Jul. 2011.
[8] J. M. Raimond, M. Brune, Q. Computation, F. De Martini, and C. Monroe, “Electric Field Effect in Atomically Thin Carbon Films,” vol. 306, no. October, pp. 666–670, 2004.
[9] K. I. Bolotin et al., “Ultrahigh electron mobility in suspended graphene,” Solid State Commun., vol. 146, no. 9, pp. 351–355, 2008.
[10] A. A. Balandin et al., “Superior Thermal Conductivity of Single-Layer Graphene,” Nano Lett., vol. 8, no. 3, pp. 902–907, Mar. 2008.
[11] L. Lindsay, D. A. Broido, and N. Mingo, “Flexural phonons and thermal transport in multilayer graphene and graphite,” Phys. Rev. B, vol. 83, no. 23, p. 235428, Jun. 2011.
[12] C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene,” Science (80-. )., vol. 321, no. 5887, pp. 385–388, Jul. 2008.
[13] J. S. Bunch et al., “Impermeable Atomic Membranes from Graphene Sheets,” Nano Lett., vol. 8, no. 8, pp. 2458–2462, Aug. 2008.
[14] J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, “The structure of suspended graphene sheets,” Nature, vol. 446, no. 7131, pp. 60–63, 2007.
[15] R. R. Nair et al., “Fine Structure Constant Defines Visual Transparency of Graphene,” Science (80-. )., vol. 320, no. 5881, p. 1308, Jun. 2008.
[16] M. Liu et al., “A graphene-based broadband optical modulator,” Nature, vol. 474, no. 7349, pp. 64–67, 2011.
[17] X. Li et al., “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science (80-. )., vol. 324, no. 5932, pp. 1312 LP – 1314, Jun. 2009.
[18] L. Gao et al., “Repeated growth and bubbling transfer of graphene with millimetre-size single-crystal grains using platinum,” Nat. Commun., vol. 3, no. 1, p. 699, 2012.
[19] G. Yang, L. Li, W. B. Lee, and M. C. Ng, “Structure of graphene and its disorders: a review,” Sci. Technol. Adv. Mater., vol. 19, no. 1, pp. 613–648, 2018.
[20] Z. Z. Alisultanov, L. S. Paixão, and M. S. Reis, “Oscillating magnetocaloric effect of a multilayer graphene,” Appl. Phys. Lett., vol. 105, no. 23, p. 232406, Dec. 2014.
[21] L. G. Can\ifmmode \mbox\cc\else ç\fiado, M. A. Pimenta, B. R. A. Neves, M. S. S. Dantas, and A. Jorio, “Influence of the Atomic Structure on the Raman Spectra of Graphite Edges,” Phys. Rev. Lett., vol. 93, no. 24, p. 247401, 2004.
[22] A. C. Ferrari et al., “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett., vol. 97, no. 18, pp. 1–4, 2006.
[23] A. Das et al., “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol., vol. 3, p. 210, Mar. 2008.
[24] T. M. G. Mohiuddin et al., “Uniaxial strain in graphene by Raman spectroscopy: $G$ peak splitting, Grüneisen parameters, and sample orientation,” Phys. Rev. B, vol. 79, no. 20, p. 205433, 2009.
[25] M. M. Lucchese et al., “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon N. Y., vol. 48, no. 5, pp. 1592–1597, 2010.
[26] A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mater., vol. 10, p. 569, Jul. 2011.
[27] V. Carozo, C. M. Almeida, E. H. M. Ferreira, L. G. Cançado, C. A. Achete, and A. Jorio, “Raman Signature of Graphene Superlattices,” Nano Lett., vol. 11, no. 11, pp. 4527–4534, Nov. 2011.
[28] J. Dong, D. Geng, F. Liu, and F. Ding, “Formation of Twinned Graphene Polycrystals,” Angew. Chemie Int. Ed., vol. 58, no. 23, pp. 7723–7727, Jun. 2019.
[29] G. Heo, Y. S. Kim, S.-H. Chun, and M.-J. Seong, “Polarized Raman spectroscopy with differing angles of laser incidence on single-layer graphene,” Nanoscale Res. Lett., vol. 10, no. 1, p. 45, 2015.
[30] L. G. Cançado et al., “Quantifying Defects in Graphene via Raman Spectroscopy at Different Excitation Energies,” Nano Lett., vol. 11, no. 8, pp. 3190–3196, Aug. 2011.
[31] W.-J. Huang and W.-Y. Woon, “Ion implantation of graphene with keV carbon ions: Defect types, evolution and substrate effects,” Vacuum, vol. 166, pp. 72–78, 2019.
[32] P. Lespade, A. Marchand, M. Couzi, and F. Cruege, “Caracterisation de materiaux carbones par microspectrometrie Raman,” Carbon N. Y., vol. 22, no. 4, pp. 375–385, 1984.
[33] C. H. Lui et al., “Observation of Layer-Breathing Mode Vibrations in Few-Layer Graphene through Combination Raman Scattering,” Nano Lett., vol. 12, no. 11, pp. 5539–5544, Nov. 2012.
[34] R. P. Vidano, D. B. Fischbach, L. J. Willis, and T. M. Loehr, “Observation of Raman band shifting with excitation wavelength for carbons and graphites,” Solid State Commun., vol. 39, no. 2, pp. 341–344, 1981.
[35] R. He et al., “Observation of Low Energy Raman Modes in Twisted Bilayer Graphene,” Nano Lett., vol. 13, no. 8, pp. 3594–3601, Aug. 2013.
[36] R. W. Havener, H. Zhuang, L. Brown, R. G. Hennig, and J. Park, “Angle-Resolved Raman Imaging of Interlayer Rotations and Interactions in Twisted Bilayer Graphene,” Nano Lett., vol. 12, no. 6, pp. 3162–3167, Jun. 2012.
[37] C.-M. Chu and W.-Y. Woon, “Growth of twisted bilayer graphene through two-stage chemical vapor deposition,” Nanotechnology, vol. 31, no. 43, p. 435603, Oct. 2020.
[38] K. Kim et al., “Raman Spectroscopy Study of Rotated Double-Layer Graphene: Misorientation-Angle Dependence of Electronic Structure,” Phys. Rev. Lett., vol. 108, no. 24, p. 246103, Jun. 2012.
[39] Z. Ni et al., “$G$-band Raman double resonance in twisted bilayer graphene: Evidence of band splitting and folding,” Phys. Rev. B, vol. 80, no. 12, p. 125404, Sep. 2009.
[40] J. Campos-Delgado, L. G. Cançado, C. A. Achete, A. Jorio, and J.-P. Raskin, “Raman scattering study of the phonon dispersion in twisted bilayer graphene,” Nano Res., vol. 6, no. 4, pp. 269–274, Apr. 2013.
[41] L. Brown, R. Hovden, P. Huang, M. Wojcik, D. A. Muller, and J. Park, “Twinning and Twisting of Tri- and Bilayer Graphene,” Nano Lett., vol. 12, no. 3, pp. 1609–1615, Mar. 2012.
[42] K.-D. Park, M. B. Raschke, J. M. Atkin, Y. H. Lee, and M. S. Jeong, “Probing Bilayer Grain Boundaries in Large-Area Graphene with Tip-Enhanced Raman Spectroscopy,” Adv. Mater., vol. 29, no. 7, p. 1603601, Feb. 2017.
[43] A. Zangwill, Physics at Surfaces. Cambridge: Cambridge University Press, 1988.
[44] J. W. Robinson, E. S. Frame, and G. M. Frame II, “Undergraduate Instrumental Analysis,” Undergrad. Instrum. Anal., 2014.
[45] G. J. Bullen, R. Mason, and P. Pauling, “Pyrolytic Carbon Formation from Carbon Suboxide,” Nature, vol. 189, pp. 291–292, 1961.
[46] J. Coraux, A. T. N‘Diaye, C. Busse, and T. Michely, “Structural Coherency of Graphene on Ir(111),” Nano Lett., vol. 8, no. 2, pp. 565–570, Feb. 2008.
[47] P. W. Sutter, J.-I. Flege, and E. A. Sutter, “Epitaxial graphene on ruthenium,” Nat. Mater., vol. 7, p. 406, Apr. 2008.
[48] L. Baraton et al., “On the mechanisms of precipitation of graphene on nickel thin films,” EPL (Europhysics Lett., vol. 96, no. 4, p. 46003, 2011.
[49] A. N. Obraztsov, E. A. Obraztsova, A. V. Tyurnina, and A. A. Zolotukhin, “Chemical vapor deposition of thin graphite films of nanometer thickness,” Carbon N. Y., 2007.
[50] B. M. Singleton and P. Nash, “The C-Ni ( Carbon-Nickel ) System,” Bull. Alloy Phase Diagrams, vol. 10, no. 2, pp. 121–122, 1989.
[51] G. A. López and E. J. Mittemeijer, “The solubility of C in solid Cu,” Scr. Mater., vol. 51, no. 1, pp. 1–5, 2004.
[52] T. Bligaard and J. K. Nørskov, “Scaling Properties of Adsorption Energies for Hydrogen-Containing Molecules on Transition-Metal Surfaces,” Phys. Rev. Lett., vol. 016105, no. July, pp. 4–7, 2007.
[53] H. Shu, X. Tao, and F. Ding, “What are the active carbon species during graphene chemical vapor deposition growth ?,” Nanoscale, vol. 7, pp. 1627–1634, 2015.
[54] C. G. de Walle and J. Neugebauer, “First-Principles Surface Phase Diagram for Hydrogen on GaN Surfaces,” Phys. Rev. Lett., vol. 88, no. 6, p. 66103, 2002.
[55] Y. Kangawa, T. Ito, A. Taguchi, K. Shiraishi, and T. Ohachi, “A new theoretical approach to adsorption–desorption behavior of Ga on GaAs surfaces,” Surf. Sci., vol. 493, no. 1, pp. 178–181, 2001.
[56] P. Koskinen, S. Malola, and H. Häkkinen, “Evidence for graphene edges beyond zigzag and armchair,” Phys. Rev. B, vol. 80, no. 7, p. 73401, Aug. 2009.
[57] T. Ma et al., “Edge-controlled growth and kinetics of single-crystal graphene domains by chemical vapor deposition,” Proc. Natl. Acad. Sci., vol. 110, no. 51, pp. 20386–20391, Dec. 2013.
[58] D. Geng et al., “Controlled Growth of Single-Crystal Twelve-Pointed Graphene Grains on a Liquid Cu Surface,” Adv. Mater., vol. 26, no. 37, pp. 6423–6429, Oct. 2014.
[59] W. Guo et al., “Governing Rule for Dynamic Formation of Grain Boundaries in Grown Graphene,” ACS Nano, vol. 9, no. 6, pp. 5792–5798, 2015.
[60] X. Zhang, Z. Xu, Q. Yuan, J. Xin, and F. Ding, “The favourable large misorientation angle grain boundaries in graphene,” vol. 7, pp. 20082–20088, 2015.
[61] L. Sun et al., “Hetero-site nucleation for growing twisted bilayer graphene with a wide range of twist angles,” Nat. Commun., vol. 12, no. 1, p. 2391, 2021.