臺灣博碩士論文加值系統

弱局域效應(weak localization)為無序(disorder)系統中電子散射(electron scattering)而產生量子干擾傳輸(quantum interference transport)的結果。
在這篇論文裡，我們製作了由堆疊(stacked)氮化硼(h-BN)與硒化銦(InSe)而成的凡得瓦異質結構(van der Waals heterostructure )的堆疊石墨烯元件並與無堆疊石墨烯元件(graphene device)比較，發現堆疊石墨烯與無堆疊石墨烯(pure graphene device)比起來有較強的弱局域效應(weak localization)，並分別以麥肯(McCann)模型與HLM模型擬和(fitting)，在我們樣品中兩者的結果會非常相近，表示可以省略麥肯模型中谷內散射長度(intravalley scattering length)項的貢獻，另外堆疊會造成相干長度(Coherence length)變短與谷間散射(intervalley scattering length)長度變長，可能是來自非彈性散射(inelastic scattering)增加與原子層級的位能變化(atomically sharp scatters)被抑制。由溫度對相干長度(Coherence length)的對數座標斜率得知，電子電子交互作用(electron-electron interaction)在兩個樣品中皆有不同程度的貢獻，但是由於不夠強的溫度依賴性推測應該有其他的機制參與。

Weak localization is a result of electron scattering produced quantum interference transport in a disordered system. In this thesis, we compare a stacking graphene device, which is a van der Waals heterostructure stacked with h-BN and InSe, with a pure graphene device. Upon comparison, we find that the pure graphene device has a stronger weak localization effect. We then fitted our data with two different models, the McCann model and the HLN model, which showed similar results implying that the intravalley scattering length in the McCann model may be neglected. On a side note, the heterostructure may cause the coherence length to be lowered and the intervalley scattering length to be extended. The two effects mentioned above may be caused by increase of inelastic scattering and suppression of atomically sharp scattering events, respectively. From the logarithmic scale graph of temperature versus coherence length, we find that electron-electron interactions of the two devices have different amounts of significance. However, according to the lack of strong temperature dependence, we suggest that there could be some other mechanisms involved.

口試委員會審定書 #
誌謝 1
中文摘要 3
Abstract 4
CONTENTS 5
LIST OF FIGURE 8
Chapter 1 Introduction 1
Bibliography 2
Chapter 2 Theory and Background 4
2.1 Graphene 4
2.1.1 Electrical Properties of Graphene 4
2.1.2 Band Structure and Heterostructure of Graphene 5
2.1.3 Pseudo-Spin 8
2.1.4 Different Fabrication Method of Graphene 10
2.2 Indium Selenide ( InSe ) 15
2.2.1 Properties of InSe 15
2.3 Hexagonal Boron Nitride ( hBN ) 17
2.3.1 Properties of hBN 17
2.4 Basic concepts 19
2.4.1 Drude Model 19
2.4.2 Density of States 20
2.5 Length scales 21
2.5.1 Inelastic Scattering Length 21
2.5.2 Elastic Scattering Length 21
2.6 Landau Quantization 23
2.6.1 Landau Levels 23
2.6.2 Shubnikov-de Hass oscillations 24
2.6.3 Integer Quantum Hall Effect 25
2.7 Variable Range Hopping 27
2.8 Weak Localization and Universal Conductor Fluctuations 29
2.9 Bibliography 31
Chapter 3 Device Fabrication and Experimental Techniques 35
3.1 Graphene Hall Bar Device 35
3.2 Confocal Laser Scanning Microscopy 37
3.3 Atomic Force Microscopy 39
3.4 Raman Spectroscopy 40
3.5 Hall Bar Fabrication 43
3.6 Prepare and Transfer of 2D Materials 46
3.7 Measurement Circuits and Proteox Dilution Refrigerator 49
3.8 Bibliography 51
Chapter 4 Variation of Magnetoresistance and Weak Localization in Graphene and hBN/InSe/Graphene coupling System 53
4.1 Introduction 53
4.2 The Device Structure and Experiment Set Up 53
4.3 Result and Discussion 54
4.3.1 The magnetoresistance at high magnetic fields 54
4.3.2 Weak localization 58
4.4 Bibliography 71
Chapter 5 Conclusion 73

Chapter 1
[1] Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, Nat.Nanotechnol. 7, 699 (2012).
[2] D. A. Bandurin, A. V. Tyurnina, C. L. Yu, A. Mishchenko, V. Zólyomi, S. V. Morozov, R. K. Kumar, R. V. Gorbachev, Z. R. Kudrynskyi, S. Pezzini, Z. D. Kovalyuk, U. Zeitler, K. S. Novoselov, A. Patanè, L. Eaves, I. V. Grigorieva, V. I. Fal’ko, A. K. Geim, and Y. Cao, Nat. Nanotechnol. 12, 223 (2017).
[3] M. Brotons-Gisbert, D. Andres-Penares, J. Suh, F. Hidalgo, R. Abargues, P. J. Rodríguez-Cantó, A. Segura, A. Cros, G. Tobias, E. Canadell, P. Ordejón, J. Wu, J. P. Martínez-Pastor, and J. F. Sánchez-Royo, Nano Lett. 16, 3221 (2016).
[4] G. W. Mudd, M. R. Molas, X. Chen, V. Zólyomi, K. Nogajewski, Z. R. Kudrynski, Z. D. Kovalyuk, G. Yusa, O. Makarovsky, L. Eaves, M. Potemski, V. I. Fal’ko, and A. Patanè, Sci. Rep. 6, 39619 (2016).
[5] W. Feng, W. Zheng, W. Cao, and P. A. Hu, Adv. Mater. 26, 6587 (2014).
[6] R. T. Srinivasa, Y.-Y. Lu, U. Rajesh Kumar, R. Sankar, C.-D. Liao, B. Karukanara Moorthy, C.-H. Cheng, F. C. Chou, and Y.-T. Chen, Nano Lett. 14, 2800 (2014).
[7] G. W. Mudd, S. A. Svatek, L. Hague, O. Makarovsky, Z. R. Kudrynskyi, C. J. Mellor, P. H. Beton, L. Eaves, K. S. Novoselov, Z. D. Kovalyuk, E. E. Vdovin, A. J. Marsden, N. R. Wilson, and A. Patanè, Adv. Mater. 27, 3760 (2015).
[8] N.-F. Shen, X.-D. Yang, X.-X. Wang, G.-H. Wang, and J.-G. Wan, Chem. Phys. Lett. 749, 137430 (2020).
[9] Y.-T. Huang, Y.-H. Chen, Y.-J. Ho, S.-W. Huang, Y.-R. Chang, K. Watanabe, T.Taniguchi, H.-C. Chiu, C.-T. Liang, R. Sankar, F.-C. Chou, C.-W. Chen, and W.-H. Wang, ACS Appl. Mater. Interfaces 10, 33450 (2018).
[10] Z. R. Kudrynskyi, M. A. Bhuiyan, O. Makarovsky, J. D. G. Greener, E. E. Vdovin, Z. D. Kovalyuk, Y. Cao, A. Mishchenko, K. S. Novoselov, P. H. Beton, L. Eaves, and A. Patanè, Phys. Rev. Lett. 119, 157701 (2017).
[11] M. A. Bhuiyan, Z. R. Kudrynskyi, D. Mazumder, J. D. G. Greener, O. Makarovsky, C. J. Mellor, E. E. Vdovin, B. A. Piot, I. I. Lobanova, Z. D. Kovalyuk, M. Nazarova, A. Mishchenko, K. S. Novoselov, Y. Cao, L. Eaves, G. Yusa, and A. Patanè, Adv. Funct. Mater. 29, 1805491 (2019).
[12] J. Zeng, S.-J. Liang, A. Gao, Y. Wang, C. Pan, C. Wu, E. Liu, L. Zhang, T. Cao, X. Liu, Y. Fu, Y. Wang, K. Watanabe, T. Taniguchi, H. Lu, and F. Miao, Phys. Rev. B 98, 125414 (2018).
Chapter 2
[ 1 ] N. T. T. Tran, Y. Lin, C. Y. Lin and M. F. LinS, CRC Press ISBN 9781138556522 (2018).
[ 2 ] V. I. Fal’koKechedzhi, E. McCann, B. L. Altshuler, H. Suzuura, and T. AndoK, Solid State Commun. 144, 33 (2007).
[ 3 ] X.-Z. Yan, and C. S. Ting, Phys. Rev. Lett. 101, 126801 (2008).
[ 4 ] P. E. Allain, and J. N. Fuchs, Eur. Phys. J. B 83, 301 (2011).
[ 5 ] K. I. Bolotin, F. Ghahari, M. D. Shulman, H. L. Stormer, and P. Kim, Nature 462, 196 (2009).
[ 6 ] V. P. Gusynin, and S. G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005).
[ 7 ] Antonio Maffucci, and Giovanni Miano, Appl. Sci. 4, 305 (2014)
[ 8 ] A. K. Geim, and K. S. Novoselov, Nat. Mater. 6, 183 (2007).
[ 9 ] A. K. Geim, and K. S. Novoselov, Science 306, 666 (2004).
[ 10 ] H.Tan, Deguo Wang, and Yanbao Guo, Coatings 8(1), 40 (2018).
[ 11 ] Min Yi, and Zhigang Shen, J. Mater. Chem. A 3, 11700 (2015).
[ 12 ] D.V. Badami, Nature 193, 569 (1962).
[ 13 ] T. Ohta, Report. Sandia National Lab (USA) (2011).
[ 14 ] X. Chen, L. Zhang, and S. Chen, Synthetic Met. 210, 95 (2015).
[ 15 ] Y. Zhirko, V. Trachevsky, and Z.Kovalyuk, In Hydrogen Storage, InTech: Rijeka Croatia (2012).
[ 16 ] B. Gürbulak, M. Şata, S. Dogan, S. Duman, A.Ashkhasi, and E.F. Keskenler, Physica E 64, 106 (2014).
[ 17 ] C.M. Julien, and M. Balkanski, Mater. Sci. Eng. B 100, 263 (2003).
[ 18 ] G. W. Mudd, M. R. Molas, X. Chen, V. Zólyomi, K. Nogajewski, Z. R. Kudrynskyi, Z. D. Kovalyuk, G. Yusa, O. Makarovsky, L. Eaves, M. Potemski, V. I. Fal'ko, and A. Patanèa, Sci. Rep. 6, 39619 (2016).
[ 19 ] A.Politano, G.Chiarello, R. Samnakay, G. Liu, B. Gurbulak, S.Duman, A.A. Balandin, and D.W. Boukhvalov, Nanoscale 8, 8474 (2016).
[ 20 ] H. Fang, S.L. Bai, and C.P. Wong, Compos Commun. 2, 19 (2016).
[ 21 ] S. Tang, H. Wang, Y. Zhang, A. Li, H. Xie, X. Liu, L. Liu, T. Li, F. Huang, X. Xie, and M. Jiang, Sci. Rep. 3, 2666 (2013).
[ 22 ] A. Falin, Q. Cai, E. J. G. Santos, D. Scullion, D. Qian, R. Zhang, Z. Yang, S. Huang, K. Watanabe, T. Taniguchi, M. R. Barnett, Y. Chen, R. S. Ruoff, and L. H. Li, Nat. Commun. 8, 15815 (2017).
[ 23 ] M. Topsakal , E. Aktürk, and S. Ciraci , Phys. Rev. B: Condens. Matter Mater. Phys. 79 , 11544201 (2009).
[ 24 ] A. V. Kretinin, Y. Cao, J. S. Tu, G. L. Yu, R. Jalil, K. S. Novoselov, S. J. Haigh, A. Gholinia, A. Mishchenko, M. Lozada, T. Georgiou, C. R. Woods, F. Withers, P. Blake, G. Eda, A. Wirsig, C. Hucho, K. Watanabe, T. Taniguchi, A. K. Geim, and R. V. Gorbachev, Nano Lett. 14, 3270 (2014).
[ 25 ] P. Drude, Ann.Phys. (Leopzig) 306, 566 (1900).
[ 26 ] P. Drude, Ann.Phys. (Leopzig) 308, 369 (1900).
[ 27 ] David J. Griffiths, Prentice-Hall. (1999).
[ 28 ] K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
[ 29 ] H. W. Jiang, C. E. Johnson, and K. L. Wang, Phys. Rev. B 46, 12830 (1992).
[ 30 ] W. Y. Yang, The impact of width-induced inhomogeneity on the carrier transport in graphene system, Master thesis NTU. (2015).
[ 31 ] N. F. Mott, and J. Non-Cryst, Solids. 1, 1 (1968).
[ 32 ] A. L. Efros, and B. I. Shklovskii, J. Phys. C: Solid State Phys. 8, L49 (1975).
[ 33 ] Paola Lecca, and Angela Re, CRC Press. 17 (2019).
[ 34 ] F. V. Tikhonenko, A. A. Kozikov, A. K. Savchenko, and R. V. Gorbachev, Phys. Rev. Lett. 103, 226801 (2009).
[ 35 ] D-K Ki, D. Jeong, J-H Choi, H-J Lee, and K-S Park, Phys. Rev. B 78, 125409 (2008).
[ 36 ] H. Suzuura, and T. Ando, Phys. Rev. Lett. 89, 266603 (2002).
[ 37 ] T. Ando, J. Phys. Soc. Jpn. 73, 1273 (2004).
[ 38 ] A. F. Morpurgo, and F.Guinea, Phys. Rev. Lett. 97, 196804 (2006).
[ 39 ] E. McCann, K. Kechedzhi, V. I. Fal’ko, H. Suzuura, T. Ando, and B. L. Altshuler, Phys. Rev. Lett. 97, 146805 (2006)
[ 40 ] V. I.Fal’ko, K. Kechedzhi, E. McCann, B. L. Altshuler, H. Suzuura,
and T. Ando, Solid State Commun. 143, 33 (2007).
[ 41 ] A. Drabińska, A. Wołoś, M. Kamińska, W. Strupinski, and J. M. Baranowski, Phys. Rev. B 86, 045421 (2012).
Chapter 3
[ 1 ] Y. Yang, G. Cheng, P. Mende, I. G. Calizo, R. M. Feenstra, C. Chuang, C.-W. Liu, C.-I. Liu, G. R. Jones, A. R. Hight Walker, and R. E. Elmquist, Carbon 115, 229 (2017).
[ 2 ] M. A. Real, E. A. Lass, F.‐H. Liu, T. Shen, G. R. Jones, J. A. Soons, D. B. Newell, A. V. Davydov, and R. E. Elmquist, IEEE Trans. Instrum. Meas. 62, 1454 (2013).
[ 3 ] M. Kruskopf, D.M. Pakdehi, K. Pierz, S. Wundrack, R. Stosch, Th. Dziomba, M. Götz, J. Baringhaus, J. Aprojanz, C. Tegenkamp, J. Lidzba, Th. Seyller, F. Hohls, F.J. Ahlers, and H.W. Schumacher, 2D Mater. 3, 041002 (2016)
[ 4 ] K.D. Kihm, Near-Field Characterization of Micro/Nano-Scaled Fluid Flows Springer 55 (2011).
[ 5 ] M. Ghafoor, Synthesis of high refractive index materials for manufacturing
apochromatic lens by 3D printing, Master thesis UEF. (2017).
[ 6 ] T. Schumann, K. J. Friedland, M. H. Oliveira, A. Tahraoui, J. M. J. Lopes, and H. Riechert, Phys. Rev. B 85, 235402 (2012).
[ 7 ] M. K. Yakes, D. Gunlycke, J. L. Tedesco, P. M. Campbell, R. L. Myers-Ward, C. R. Eddy Jr., D. K. Gaskill, P. Sheehan, and A. R. Laracuente, Nano Lett. 10, 1559 (2010).
[ 8 ] D. Momeni Pakdehi, J. Aprojanz, A. Sinterhauf, K. Pierz, M. Kruskopf, P. Willke, J. Baringhaus, J.P. Stöckmann, G.A. Traeger, F. Hohls, C. Tegenkamp, M. Wenderoth, F.J. Ahlers, and H.W. Schumacher, ACS Appl. Mater. Interfaces 10 (6), 6039, (2018).
[ 9 ] Bi Yi Wu, Electronic Transport Properties of Monolayer Graphene and Graphene Ribbons, Doctoral thesis NTU. (2019)
[ 10 ] T. Taniguchi, and K. Watanabe, J. Cryst, Growth 303, 525 (2007)
[ 11 ] L. J. van der Pauw, Philips Res. Rep. 13, 1 (1958).
[ 12 ] Graham Walker, Cryocoolers, Springer 265 (1983).
[ 13 ] Triton 200/400 cryofreeze dilution refrigerator Operator's Handbook (Oxford
Instrument) (2012).
Chapter 4
[ 1 ] M. Amado, E. Diez, F. Rossella, V. Bellani, D. Lopez- Romero, and D. K. Maude, J. Phys. Condens. Matter 24, 305302 (2012).
[ 2 ] F. H. Liu, C. S. Hsu, C. Chuang, T. P. Woo, L. I. Huang, S. T. Lo, Y. Fukuyama, Y. Yang, R. Elmquist, and C.T. Liang, Nanoscale Res. Lett. 8, 360 (2013).
[ 3 ] S. Kivelson, D.H. Lee, and S. C. Zhang, Phys. Rev. B 46, 2223 (1992).
[ 4 ] H. W. Jiang, C. E. Johnson, K. L. Wang, and S. T. Hannahs, Phys. Rev. Lett. 71, 1439 (1993).
[ 5 ] R. J. F. Hughes, J. T. Nicholls, J. E. F. Frost, E. H. Linfield, M. Pepper, C. J. B. Ford, D. A. Ritchie, G. A. C. Jones, E. Kogan, and M. Kaveh, J. Phys. Condens. Matter 6 4763 (1994).
[ 6 ] T. Wang, K. P. Clark, G. F. Spencer, A. M. Mack, and W. P. Kirk, Phys. Rev. Lett. 72, 709 (1994).
[ 7 ] S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, L. A. Ponomarenko, D. Jiang, and A. K. Geim, Phys. Rev. Lett. 97, 036802 (2006).
[ 8 ] F. V. Tikhonenko, D. W. Horsell, R. V. Gorbachev, and A. K. Savchenko, Phys. Rev. Lett. 100, 056802 (2008).
[ 9 ] W. Pan, I. A. J. Ross, S. W. Howell, T. Ohta, T. A. Friedmann, and C. T. Liang, New J. Phys. 13, 113005 (2011).
[ 10 ] B. Jouault, B Jabakhanji, N. Camara, W. Desrat, C. Consejo, and Camassel, J,Phys. Rev. B 83 195417 (2011).
[ 11 ] J. Jobst, D. Waldmann, I. V. Gornyi, A. D. Mirlin, and H. B. Weber, Phys. Rev. Lett. 108, 106601 (2012).
[ 12 ] X. Wu, X. Li, Z. Song, C. Berger and W. A. de Heer ,Phys. Rev. Lett. 98, 136801 (2007).
[ 13 ] S. Hikami, A. I. Larkin, and Y. Nagaoka, Prog. Theor. Phys. 63, 707 (1980).
[ 14 ] E. McCann, K. Kechedzhi, V. I. Falko, H. Suzuura, T. Ando, and B. L. Altshuler, Phys. Rev. Lett. 97, 146805 (2006).
[ 15 ] A. Drabińska, A. Wołoś, M. Kamińska, W. Strupinski, and J. M. Baranowski, Phys. Rev. B 86, 045421 (2012).
[ 16 ] S. T. Lo, H. E. Lin, S.W. Wang, H. D. Lin, Y. C. Chin, H. H. Lin, J. C. Lin and C. T. Liang, Nanoscale Res. Lett. 7, 640 (2012).
[ 17 ] S. Engels, B. Terrés, A. Epping, T. Khodkov, K. Watanabe, T. Taniguchi, B. Beschoten, and C. Stampfer, Phys. Rev. Lett. 113, 126801 (2014).
[ 18 ] E. Tiras, S. Ardali, T. Tiras, E. Arslan, S. Cakmakyapan, O. Kazar, J. Hassan, E. Janzn, and E. Ozbay, J. Appl. Phys. (Melville, NY, US) 113, 043708 (2013).
[ 19 ] J. Lin and J. P. Bird, J. Phys. Condens. Matter 14, R501 (2002).