石墨烯，一個單原子層碳原子二維蜂窩狀結構，由於其獨特的物理特性，成為相對論凝聚態物理學中的一個新興模型。基於其獨特優良的光學與電學特性，石墨烯很有機會成為下一代電子產品應用的主流。 2010年 Geim 和 Novoselov 由於成功的分離出單層石墨烯獲得了諾貝爾物理學獎。 石墨烯是最薄的天然二維材料，只有一個原子厚度。目前，石墨烯可藉由在晶片級上的過渡金屬表面利用化學氣相沉積達到30英寸。對於相關流程石墨烯電子器件的製造，目前還有幾個障礙需要克服。本研究中，我們嘗試將半導體工藝與石墨烯結合，以促進石墨烯商業化與工業化的應用。第一章將介紹石墨烯的基本性質的概述。第二章將介紹如何製造石墨烯電子元件，但對於石墨烯電子產品成為主流，仍有一些生產流程上的困難需要克服。我們嘗試將石墨烯的電子工藝與半導體產業相結合，其中的第一步是改善石墨烯備製方式。因此，第三章將透過遠端銅蒸氣催化提供高效率和高成本效益的石墨烯化學氣象沉積系統，以改善目前的石墨烯製備方案。在第四章中，我們將展示雷射雕刻石墨烯技術，可精準控制到一個原子層的解析度，此技術也可以用來圖形化石墨烯。雷射雕刻石墨烯的技術，將大幅改善過去的石墨烯圖形化技術，且有助於石墨烯電子元件的電性改善。第五章，我們建立了石墨烯雷射雕刻技術的相關理論模組與分析。前五章，我們提出了有關石墨烯的電子產品製造過程中的兩個重要的技術突破，第六章中我們試圖通過使用這些新的石墨烯製造工藝製作石墨烯光電探測器，並得到相當有趣的成果。

Graphene, an isolated mono-atomic carbon layer conformed into two-dimensional honeycomb lattice building blocks, has triggered off numerous novel research possibilities, due to its intriguing physics and as an emerging paradigm for relativistic condensed matter physics as well as showing great promise for its application in next generation electronics. In 2010 the Nobel Prize in physics was awarded to A. Geim and K. S. Novoselov for their pioneer work in solating single-atomic-layer of graphite sheet on silicon dioxide. Graphene is the thinnest natural 2D material consisting of hexagonal carbon network in only one atom thick. Now a days, graphene can be synthesized by chemical vapor deposition on transition metal surface in wafer scale and even up to the 30 inches. For the relevant processes for graphene electronic devices fabrication, there are currently several hurdles to be overcome before widespread industrial production of graphene-based devices becomes a reality. In the course of this dissertation, we try to link semiconductor processes and adapt them to work with gaphene. Chapter 1 will introduce an overview of the fundamental properties of graphene. Graphene has many outstanding properties, of special importance for graphene electronics is the electrical properties. How to fabricate graphene electronics is described in chapter 2, but for graphene electronics production to reach mainstream status, there are still a few difficulties to be overcome. Furthermore, we try to combine the graphene electronics process with the semiconductor industry. The first step for the process is graphene film fabrication. Chapter 3 will introduce an efficient and cost-effective CVD process by remote catalyzation in the form of copper vapor. In chapter 4, we will show the laser engraving can be used in layered materials such as graphene with enough precision to ablate one atomic-layer each time through the precise control of the surface reaction. Photochemical elimination of an individual layer becomes possible, while leaving the next exposed layer intact after processing. This tech-nology also can be used to pattern the graphene. We also discuss the theoretical framework for layer-resolved thinning technology in chapter 5. So far, we provide two important technological breakthroughs about graphene electronics fabrication process. In chapter 6, we try to fabricate a graphene photodetector by making use of these new graphene fabrication process. In short, graphene has followed a relatively fast paced track (around 10 years) from its discovery down to being actively considered as the key material in technologies close to industrial production and availability to the wider public. It is clear that this direction will lead to exciting new possibilities and has certainly opened the door for the active study of other 2D layered materials, such as transition metal di chalcogenides.

Absrtact I
Publication List III
Acknowledgements V
目錄 IX
1 Graphene properties 1
1.1 Carbon family 1
1.2 Band structure of graphene 3
1.3 Optical properties of graphene 5
1.3.1 Raman bands in graphene 5
1.3.2 Optical transmittance 8
1.4 Electrical properties of graphene 12

2 Fundamental processes for graphene electronics 15
2.1 Graphene synthesis 15
2.1.1 CVD on Copper 16
2.1.2 ECR CVD 20
2.2 Graphene transfer 22
2.3 Graphene patterning 24
2.4 Device fabrication 26

3 Direct synthesis of graphene on nonmetallic substrate 29
3.1 Introduction 29
3.2 Remote catalyzation in the form of copper vapor 30
3.3 Lateral epitaxial graphene growth from exfoliated graphene seeds 40
3.4 Mechanisms of graphene growth on nonmetallic substrates 40
3.4.1 Nucleation mechanism 40
3.4.2 Structural stability 44

4 Layer-resolved thinning and patterning of graphene 49
4.1 Motivation 49
4.2 Instrumental setup 50
4.3 Layer-by-layer thinning of graphene 50
4.4 Quality of graphene layers 53
4.5 Patterning 58

5 Theoretical framework for layer-resolved thinning technology 61
5.1 Thermal analysis of laser heating 61
5.2 Analysis of reaction rare 66
5.2.1 Ozone physisorption and chemisorption 66
5.2.2 Oxidation level 68
5.2.3 Reaction steps 70
5.3 Reaction mechanisms 72
5.3.1 Oxidation at high temperatures in the static mode 72
5.3.2 Oxidation at low temperatures in the static mode 72
5.4 Calculation of reaction rate 74
5.4.1 Activation energy for single-crystal graphene 74
5.4.2 Activation energy for polycrystalline graphene 76

6 Graphene-based photodetectors 77
6.1 Introduction 77
6.1.1 Si-based photodetector 78
6.2 Hybrid Si/graphene photodetector 82
6.2.1 Photodetection mechanism 82
6.2.2 Fabrication of Si/graphene photodetectors 84
6.3 Analog to Digital converter 86
6.3.1 Design and simulation 86
6.3.2 Breadboard test 90
6.4 Device manufacturing 93
6.4.1 Process and device Simulation 93
6.4.2 Manufacturing process 96
6.5 Measurements of photoresponse 102

7 Summary and outlook 107

[1] H. Dai, “Carbon nanotubes: Synthesis, Structure, Properties and Application,” Top. Appl. Phys., 2001.

[2] H. Dai, “Carbon nanotubes: synthesis, integration, and properties,” Acc. Chem. Res., vol. 35, no. 12, pp. 1035–1044, 2002.

[3] A. G. Nasibulin, A. S. Anisimov, P. V. Pikhitsa, H. Jiang, D. P. Brown, M. Choi, and E. I. Kauppinen, “Investigations of nanobud formation,” Chem. Phys. Lett., vol. 446, no. 1, pp. 109–114, 2007.

[4] C. Frondel and U. B. Marvin, “Lonsdaleite, a hexagonal polymorph of diamond,” 1967.

[5] P. Harris, “Fullerene-related structure of commercial glassy carbons,” Philos. Mag., vol. 84, no. 29, pp. 3159–3167, 2004.

[6] A. V. Rode, S. Hyde, E. Gamaly, R. Elliman, D. McKenzie, and S. Bulcock, “Structural analysis of a carbon foam formed by high pulse-rate laser ablation,” Appl. Phys. A, vol. 69, no. 1, pp. S755–S758, 1999.

[7] R. Heimann, S. E. Evsyukov, and L. Kavan, Carbyne and carbynoid structures, vol. 21. Springer Science & Business Media, 1999.

[8] A. Ferrari, J. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. Novoselov, S. Roth, et al., “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett., vol. 97, no. 18, p. 187401, 2006.

[9] A. C. Ferrari, “Raman spectroscopy of graphene and graphite: disorder, electron–phonon coupling, doping and nonadiabatic effects,” Solid State Commun., vol. 143,
no. 1, pp. 47–57, 2007.

[10] J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, “Electric field effect tuning of electronphonon coupling in graphene,” Phys. Rev. Lett., vol. 98, no. 16, p. 166802, 2007.

[11] A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. Saha, U. Waghmare, K. Novoselov, H. Krishnamurthy, A. Geim, A. Ferrari, et al., “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat.
Nanotechnol., vol. 3, no. 4, pp. 210–215, 2008.

[12] M. Pimenta, G. Dresselhaus, M. S. Dresselhaus, L. Cancado, A. Jorio, and R. Saito, “Studying disorder in graphite-based systems by Raman spectroscopy,” Phys. Chem. Chem. Phys., vol. 9, no. 11, pp. 1276–1290, 2007.

[13] N. Ferralis, R. Maboudian, and C. Carraro, “Evidence of structural strain in epitaxial graphene layers on 6H-SiC (0001),” Phys. Rev. Lett., vol. 101, no. 15, p. 156801,
2008.

[14] L. Malard, M. Pimenta, G. Dresselhaus, and M. Dresselhaus, “Raman spectroscopy in graphene,” Phys. Rep., vol. 473, no. 5, pp. 51–87, 2009.

[15] L. G. Cançado, A. Jorio, E. M. Ferreira, F. Stavale, C. Achete, R. Capaz, M. Moutinho, A. Lombardo, T. Kulmala, and A. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett.,
vol. 11, no. 8, pp. 3190–3196, 2011.

[16] S. Piscanec, M. Lazzeri, F. Mauri, A. Ferrari, and J. Robertson, “Kohn anomalies and electron-phonon interactions in graphite,” Phys. Rev. Lett., vol. 93, no. 18, p. 185503, 2004.

[17] V. Carozo, C. M. Almeida, E. H. Ferreira, L. G. Cancado, C. A. Achete, and A. Jorio, “Raman signature of graphene superlattices,” Nano Lett., vol. 11, no. 11, pp. 4527–4534, 2011.

[18] R. Nair, P. Blake, A. Grigorenko, K. Novoselov, T. Booth, T. Stauber, N. Peres, and A. Geim, “Fine structure constant defines visual transparency of graphene,” Science, vol. 320, no. 5881, pp. 1308–1308, 2008.

[19] A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater., vol. 6, no. 3, pp. 183–191, 2007.
[20] H. A. Macleod, Thin-film optical filters. CRC Press, 2010.

[21] P. Blake, E. Hill, A. C. Neto, K. Novoselov, D. Jiang, R. Yang, T. Booth, and A. Geim, “Making graphene visible,” Appl. Phys. Lett., vol. 91, no. 6, p. 063124, 2007.

[22] J. Martin, N. Akerman, G. Ulbricht, T. Lohmann, J. Smet, K. Von Klitzing, and A. Yacoby, “Observation of electron–hole puddles in graphene using a scanning single-electron transistor,” Nat. Phys., vol. 4, no. 2, pp. 144–148, 2008.

[23] Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature, vol. 438, no. 7065,
pp. 201–204, 2005.

[24] Y. Wang, Y. Li, L. Tang, J. Lu, and J. Li, “Application of graphene-modified electrode for selective detection of dopamine,” Electrochem. Commun., vol. 11, no. 4, pp. 889–892, 2009.

[25] K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, ,I. Grigorieva, and A. Firsov, “Electric field effect in atomically thin carbon films,” Science, vol. 306, no. 5696, pp. 666–669, 2004.

[26] K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, et al., “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater., vol. 8, no. 3, pp. 203–207, 2009.

[27] P. Sutter, “Epitaxial graphene: How silicon leaves the scene,” Nat. Mater., vol. 8, no. 3, pp. 171–172, 2009.

[28] K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for
stretchable transparent electrodes,” Nature, vol. 457, no. 7230, pp. 706–710, 2009.

[29] Q. Yu, J. Lian, S. Siriponglert, H. Li, Y. P. Chen, and S.-S. Pei, “Graphene segregated on Ni surfaces and transferred to insulators,” Appl. Phys. Lett., vol. 93,
no. 11, p. 113103, 2008.

[30] X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, et al., “Large-area synthesis of high-quality and uniform graphene films
on copper foils,” Science, vol. 324, no. 5932, pp. 1312–1314, 2009.

[31] S. Bhaviripudi, X. Jia, M. S. Dresselhaus, and J. Kong, “Role of kinetic factors in chemical vapor deposition synthesis of uniform large area graphene using copper
catalyst,” Nano Lett., vol. 10, no. 10, pp. 4128–4133, 2010.

[32] I. Vlassiouk, M. Regmi, P. Fulvio, S. Dai, P. Datskos, G. Eres, and S. Smirnov, “Role of hydrogen in chemical vapor deposition growth of large single-crystal graphene,” ACS nano, vol. 5, no. 7, pp. 6069–6076, 2011.

[33] H. Medina, Y.-C. Lin, D. Obergfell, and P.-W. Chiu, “Tuning of charge densities in graphene by molecule doping,” Adv. Funct. Mater., vol. 21, no. 14, pp. 2687–
2692, 2011.

[34] X. Li, Y. Zhu, W. Cai, M. Borysiak, B. Han, D. Chen, R. D. Piner, L. Colombo, and R. S. Ruoff, “Transfer of large-area graphene films for high-performance transparent
conductive electrodes,” Nano Lett., vol. 9, no. 12, pp. 4359–4363, 2009.

[35] L. Gao, W. Ren, H. Xu, L. Jin, Z. Wang, T. Ma, L.-P. Ma, Z. Zhang, Q. Fu, L.-M. Peng, et al., “Repeated growth and bubbling transfer of graphene with millimetresize single-crystal grains using platinum,” Nat. Commun., vol. 3, p. 699, 2012.

[36] Y. Zhou and K. P. Loh, “Making patterns on graphene,” Adv. Mater., vol. 22, no. 32, pp. 3615–3620, 2010.

[37] Y.-C. Lin, C. Jin, J.-C. Lee, S.-F. Jen, K. Suenaga, and P.-W. Chiu, “Clean transfer of graphene for isolation and suspension,” ACS nano, vol. 5, no. 3, pp. 2362–2368,
2011.

[38] R. Sahin, E. Simsek, and S. Akturk, “Nanoscale patterning of graphene through femtosecond laser ablation,” Appl. Phys. Lett., vol. 104, no. 5, p. 053118, 2014.

[39] G. Kalita, L. Qi, Y. Namba, K. Wakita, and M. Umeno, “Femtosecond laser induced micropatterning of graphene film,” Mater. Lett., vol. 65, no. 11, pp. 1569–1572, 2011.

[40] J.-H. Yoo, J. B. Park, S. Ahn, and C. P. Grigoropoulos, “Laser-Induced Direct Graphene Patterning and Simultaneous Transferring Method for Graphene Sensor
Platform,” Small, vol. 9, no. 24, pp. 4269–4275, 2013.

[41] D. C. Bell, M. C. Lemme, L. A. Stern, J. R. Williams, and C. M. Marcus, “Precision cutting and patterning of graphene with helium ions,” Nanotechnology, vol. 20,
no. 45, p. 455301, 2009.

[42] I.-S. Byun, D. Yoon, J. S. Choi, I. Hwang, D. H. Lee, M. J. Lee, T. Kawai, Y.-W. Son, Q. Jia, H. Cheong, et al., “Nanoscale lithography on monolayer graphene using hydrogenation and oxidation,” ACS nano, vol. 5, no. 8, pp. 6417–6424, 2011.

[43] H. Kim, I. Song, C. Park, M. Son, M. Hong, Y. Kim, J. S. Kim, H.-J. Shin, J. Baik, and H. C. Choi, “Copper-vapor-assisted chemical vapor deposition for high-quality and metal-free single-layer graphene on amorphous SiO2 substrate,” ACS nano, vol. 7, no. 8, pp. 6575–6582, 2013.

[44] A. Moisala, A. G. Nasibulin, D. P. Brown, H. Jiang, L. Khriachtchev, and E. I. Kauppinen, “Single-walled carbon nanotube synthesis using ferrocene and iron pentacarbonyl in a laminar flow reactor,” Chem. Eng. Sci., vol. 61, no. 13, pp. 4393–4402, 2006.

[45] F. Geiger, C. Busse, and R. Loehrke, “The vapor pressure of indium, silver, gallium, copper, tin, and gold between 0.1 and 3.0 bar,” Int. J. Thermophys., vol. 8, no. 4, pp. 425–436, 1987.

[46] C. Zhang and P. Hu, “Methane transformation to carbon and hydrogen on Pd (100): Pathways and energetics from density functional theory calculations,” J. Chem. Phys., vol. 116, no. 1, pp. 322–327, 2002.

[47] I. Ciobica, F. Frechard, R. Van Santen, A. Kleyn, and J. Hafner, “A DFT study of transition states for CH activation on the Ru (0001) surface,” J. Phys. Chem. B,
vol. 104, no. 14, pp. 3364–3369, 2000.

[48] W. Zhang, P. Wu, Z. Li, and J. Yang, “First-principles thermodynamics of graphene growth on Cu surfaces,” J. Phys. Chem. C, vol. 115, no. 36, pp. 17782–17787, 2011.

[49] S. Reich and C. Thomsen, “Raman spectroscopy of graphite,” Philos. Trans. R. Soc. London, Ser. A, vol. 362, no. 1824, pp. 2271–2288, 2004.

[50] Y. Wang, Z. Ni, Z. Shen, H. Wang, and Y. Wu, “Interference enhancement of raman signal of graphene,” Appl. Phys. Lett., 2008.

[51] A. Ismach, C. Druzgalski, S. Penwell, A. Schwartzberg, M. Zheng, A. Javey, J. Bokor, and Y. Zhang, “Direct chemical vapor deposition of graphene on dielectric
surfaces,” Nano Lett., vol. 10, no. 5, pp. 1542–1548, 2010.

[52] B. Krauss, T. Lohmann, D.-H. Chae, M. Haluska, K. von Klitzing, and J. H. Smet, “Laser-induced disassembly of a graphene single crystal into a nanocrystalline network,”
Phys. Rev. B, vol. 79, no. 16, p. 165428, 2009.

[53] M. H. Rummeli, A. Bachmatiuk, A. Scott, F. Borrnert, J. H. Warner, V. Hoffman, J.-H. Lin, G. Cuniberti, and B. Buchner, “Direct low-temperature nanographene CVD synthesis over a dielectric insulator,” ACS nano, vol. 4, no. 7, pp. 4206–4210, 2010.

[54] M. Lafkioti, B. Krauss, T. Lohmann, U. Zschieschang, H. Klauk, K. v. Klitzing, and J. H. Smet, “Graphene on a hydrophobic substrate: doping reduction and hysteresis suppression under ambient conditions,” Nano Lett., vol. 10, no. 4, pp. 1149–1153, 2010.

[55] P. Y. Huang, C. S. Ruiz-Vargas, A. M. van der Zande, W. S. Whitney, M. P. Levendorf, J. W. Kevek, S. Garg, J. S. Alden, C. J. Hustedt, Y. Zhu, et al., “Grains and grain boundaries in single-layer graphene atomic patchwork quilts,” Nature, vol. 469, no. 7330, pp. 389–392, 2011.

[56] Q. Yu, L. A. Jauregui, W. Wu, R. Colby, J. Tian, Z. Su, H. Cao, Z. Liu, D. Pandey, D. Wei, et al., “Control and characterization of individual grains and grain boundaries in graphene grown by chemical vapour deposition,” Nat. Mater., vol. 10, no. 6, pp. 443–449, 2011.

[57] A. Rao, E. Richter, S. Bandow, B. Chase, P. Eklund, K. Williams, S. Fang, K. Subbaswamy, M. Menon, A. Thess, et al., “Diameter-selective Raman scattering from vibrational modes in carbon nanotubes,” Science, vol. 275, no. 5297, pp. 187–191, 1997.

[58] M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, “Raman spectroscopy of carbon nanotubes,” Phys. Rep., vol. 409, no. 2, pp. 47–99, 2005.

[59] R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics, vol. 2, no. 4, pp. 219–225, 2008.

[60] C.-C. Lu, Y.-C. Lin, Z. Liu, C.-H. Yeh, K. Suenaga, and P.-W. Chiu, “Twisting bilayer graphene superlattices,” ACS nano, vol. 7, no. 3, pp. 2587–2594, 2013.

[61] H. Zhao, Y.-C. Lin, C.-H. Yeh, H. Tian, Y.-C. Chen, D. Xie, Y. Yang, K. Suenaga, T.-L. Ren, and P.-W. Chiu, “Growth and Raman spectra of single-crystal trilayer graphene with different stacking orientations,” ACS nano, vol. 8, no. 10, pp. 10766–10773, 2014.

[62] L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, “Narrow graphene nanoribbons from carbon nanotubes,” Nature, vol. 458, no. 7240, pp. 877–880, 2009.

[63] D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature, vol. 458, no. 7240, pp. 872–876, 2009.

[64] S. Huh, J. Park, Y. S. Kim, K. S. Kim, B. H. Hong, and J.-M. Nam, “UV/ozone-oxidized large-scale graphene platform with large chemical enhancement in surface-enhanced Raman scattering,” ACS nano, vol. 5, no. 12, pp. 9799–9806, 2011.

[65] C.-A. Palma, K. Diller, R. Berger, A. Welle, J. Bjork, J. L. Cabellos, D. J. Mowbray, A. C. Papageorgiou, N. P. Ivleva, S. Matich, et al., “Photoinduced C–C Reactions on Insulators toward Photolithography of Graphene Nanoarchitectures,” J. Am. Chem. Soc., vol. 136, no. 12, pp. 4651–4658, 2014.

[66] J.-L. Li, K. N. Kudin, M. J. McAllister, R. K. Prud¡¯homme, I. A. Aksay, and R. Car, “Oxygen-driven unzipping of graphitic materials,” Phys. Rev. Lett., vol. 96, no. 17, p. 176101, 2006.

[67] S. Jandhyala, G. Mordi, B. Lee, G. Lee, C. Floresca, P.-R. Cha, J. Ahn, R. M. Wallace, Y. J. Chabal, M. J. Kim, et al., “Atomic layer deposition of dielectrics on graphene using reversibly physisorbed ozone,” ACS nano, vol. 6, no. 3, pp. 2722–2730, 2012.

[68] N. Leconte, J. Moser, P. Ordejon, H. Tao, A. Lherbier, A. Bachtold, F. Alsina, C. M. Sotomayor Torres, J.-C. Charlier, and S. Roche, “Damaging graphene with ozone treatment: a chemically tunable metal- insulator transition,” ACS nano, vol. 4, no. 7, pp. 4033–4038, 2010.

[69] W. Li, Y. Liang, D. Yu, L. Peng, K. P. Pernstich, T. Shen, A. H. Walker, G. Cheng, C. A. Hacker, C. A. Richter, et al., “Ultraviolet/ozone treatment to reduce metalgraphene
contact resistance,” Appl. Phys. Lett., vol. 102, no. 18, p. 183110, 2013.

[70] E. Snitzer, “Cylindrical dielectric waveguide modes,” JOSA, vol. 51, no. 5, pp. 491–498, 1961.

[71] G. Römer, A. Huis, et al., “Matlab laser toolbox,” Physics Procedia, vol. 5, pp. 413–419, 2010.

[72] A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys., vol. 4, 1905.

[73] G. Lee, B. Lee, J. Kim, and K. Cho, “Ozone adsorption on graphene: ab initio study and experimental validation,” J. Phys. Chem. C, vol. 113, no. 32, pp. 14225–14229, 2009.

[74] R. Larciprete, P. Lacovig, S. Gardonio, A. Baraldi, and S. Lizzit, “Atomic oxygen on graphite: chemical characterization and thermal reduction,” J. Phys. Chem. C,
vol. 116, no. 18, pp. 9900–9908, 2012.

[75] S. L. Stephens, J. W. Birks, and J. G. Calvert, “Ozone as a sink for atmospheric carbon aerosols today and following nuclear war,” Aerosol Sci. Technol., vol. 10,
no. 2, pp. 326–331, 1989.

[76] R. S. Quimby, Photonics and lasers: an introduction. John Wiley & Sons, 2006.

[77] X. An, F. Liu, Y. J. Jung, and S. Kar, “Tunable graphene–silicon heterojunctions for ultrasensitive photodetection,” Nano Lett., vol. 13, no. 3, pp. 909–916, 2013.