Variability effects in graphene: Challenges and opportunities for device engineering and applications

Proceedings of the IEEE

Volumn 101, Issue 7, 2013, Pages 1670-1688

  Xu, Guangyu ^a,b   Zhang, Yuegang ^c,d   Duan, Xiangfeng ^a   Balandin, Alexander A ^e   Wang, Kang L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b HARVARD UNIVERSITY   (United States)

^c LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^d SUZHOU INSTITUTE OF NANO TECH AND NANO BIONICS   (China)

^e UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Device engineering; device scalability; edge disorder; graphene; interface traps; low frequency noise; metrology; sensing applications; variability effects

Indexed keywords

GRAPHENE DEVICES; YARN;

CRITICAL ISSUES; DEVICE APPLICATION; DEVICE ENGINEERING; DEVICE SCALABILITY; EDGE DISORDER; INTERFACE TRAPS; LOW-FREQUENCY NOISE; SENSING APPLICATIONS; SURROUNDING ENVIRONMENT; VARIABILITY EFFECT;

GRAPHENE;

EID: 84879889686     PISSN: 00189219     EISSN: None     Source Type: Journal    
DOI: 10.1109/JPROC.2013.2247971     Document Type: Article

References (174)

1. A. K. Geim, ''Graphene: Status and prospects,'' Science, vol. 324, pp. 1530-1534, 2009.
2. S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, ''Giant intrinsic carrier mobilities in graphene and its bilayer,'' Phys. Rev. Lett., vol. 100, 2008, 016602.
3. C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, ''Boron nitride substrates for high-quality graphene electronics,'' Nature Nanotechnol., vol. 5, pp. 722-726, 2010.
4. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, ''Electric field effect in atomically thin carbon films,'' Science, vol. 306, pp. 666-669, 2004. (Pubitemid 39440910)
5. A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, ''The electronic properties of graphene,'' Rev. Mod. Phys., vol. 81, pp. 109-162, 2009.
6. C. Lee, X. Wei, J. W. Kysar, and J. Hone, ''Measurement of the elastic properties and intrinsic strength of monolayer graphene,'' Science, vol. 321, pp. 385-388, 2008. (Pubitemid 352029970)
7. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, ''Superior thermal conductivity of single-layer graphene,'' Nano Lett., vol. 8, pp. 902-907, 2008.
8. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, ''Large-area synthesis of high-quality and uniform graphene films on copper foils,'' Science, vol. 324, pp. 1312-1314, 2009.
9. A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, ''Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,'' Nano Lett., vol. 9, pp. 30-35, 2009.
10. M. Choucair, P. Thordarson, and J. A. Stride, ''Gram-scale production of graphene based on solvothermal synthesis and sonication,'' Nature Nanotechnol., vol. 4, pp. 30-33, 2009.
11. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, ''Graphene photonics and optoelectronics,'' Nature Photon., vol. 4, pp. 611-622, 2010.
12. X. Jia, M. Hofmann, V. Meunier, B. G. Sumpter, J. Campos-Delgado, J. M. Romo-Herrera, H. Son, Y. Hsieh, A. Reina, J. Kong, M. Terrones, and M. S. Dresselhaus, ''Controlled formation of sharp zigzag and armchair edges in graphitic nanoribbons,'' Science, vol. 323, pp. 1701-1705, 2009.
13. M. Sprinkle, M. Ruan, Y. Hu, J. Hankinson, M. Rubio-Roy, B. Zhang, X. Wu, C. Berger, and W. A. de Heer, ''Scalable templated growth of graphene nanoribbons on SiC,'' Nature Nanotechnol., vol. 5, pp. 727-731, 2010.
14. X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, ''Chemically derived, ultrasmooth graphene nanoribbon semiconductors,'' Science, vol. 319, pp. 1229-1232, 2008. (Pubitemid 351323015)
15. X. Wang, Y. Ouyang, L. Jiao, H. Wang, L. Xie, J. Wu, J. Guo, and H. Dai, ''Graphene nanoribbons with smooth edges behave as quantum wires,'' Nature Nanotechnol., vol. 6, pp. 563-567, 2011.
16. Y. Lin, A. Valdes-Garcia, S. Han, D. B. Farmer, I. Meric, Y. Sun, Y. Wu, C. Dimitrakopoulos, A. Grill, P. Avouris, and K. A. Jenkins, ''Wafer-scale graphene integrated circuit,'' Science, vol. 332, pp. 1294-1297, 2011.
17. Y. Wu, Y. Lin, A. A. Bol, K. A. Jenkins, F. Xia, D. B. Farmer, Y. Zhu, and P. Avouris, ''High-frequency, scaled graphene transistors on diamond-like carbon,'' Nature, vol. 472, pp. 74-78, 2011.
18. L. Liao, Y. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, ''High-speed graphene transistors with a self-aligned nanowire gate,'' Nature, vol. 467, pp. 305-308, 2010.
19. S. Han, K. A. Jenkins, A. Valdes Garcia, A. D. Franklin, A. A. Bol, and W. Haensch, ''High-frequency graphene voltage amplifier,'' Nano Lett., vol. 11, pp. 3690-3693, 2011.
20. X. Yang, G. Liu, M. Rostami, A. A. Balandin, and K. Mohanram, ''Graphene ambipolar multiplier phase detector,'' IEEE Electron Device Lett., vol. 32, no. 10, pp. 1328-1330, Oct. 2011.
21. J. S. Moon, D. Curtis, D. Zehnder, S. Kim, D. K. Gaskill, G. G. Jernigan, R. L. Myers-Ward, C. R. Eddy, P. M. Campbell, K.-M. Lee, and P. Asbeck, ''Low-phase-noise graphene FETs in ambipolar RF applications,'' IEEE Electron Device Lett., vol. 32, no. 3, pp. 270-272, Mar. 2011.
22. H. Wang, A. Hsu, J. Wu, J. Kong, and T. Palacios, ''Graphene-based ambipolar RF mixers,'' IEEE Electron Device Lett., vol. 31, no. 9, pp. 906-908, Sep. 2010.
23. J. Bai, L. Liao, H. Zhou, R. Cheng, L. Liu, Y. Huang, and X. Duan, ''Top-gated chemical vapor deposition grown graphene transistors with current saturation,'' Nano Lett., vol. 11, pp. 2555-2559, 2011.
24. F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, ''Ultrafast graphene photodetector,'' Nature Nanotechnol., vol. 4, pp. 839-843, 2009.
25. Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, ''Plasmon resonance enhanced multicolour photodetection by graphene,'' Nature Commun., vol. 2, 2011, article 579.
26. T. Mueller, F. Xia, and P. Avouris, ''Graphene photodetectors for high-speed optical communications,'' Nature Photon., vol. 4, pp. 297-301, 2010.
27. R. Murali, K. Brenner, Y. Yang, T. Beck, and J. D. Meindl, ''Resistivity of graphene nanoribbon interconnects,'' IEEE Electron Device Lett., vol. 30, no. 6, pp. 611-613, Jun. 2009.
28. Q. Shao, G. Liu, D. Teweldebrhan, and A. A. Balandin, ''High-temperature quenching of electrical resistance in graphene interconnects,'' Appl. Phys. Lett., vol. 92, 2008, 202108.
29. J. Yu, G. Liu, A. V. Sumant, V. Goyal, and A. A. Balandin, ''Graphene-on-diamond devices with increased current-carrying capacity: Carbon sp2-on-sp3 technology,'' Nano Lett., vol. 12, pp. 1603-1608, 2012.
30. S. Subrina, D. Kotchetkov, and A. A. Balandin, ''Heat removal in silicon-on-insulator integrated circuits with graphene lateral heat spreaders,'' IEEE Electron Device Lett., vol. 30, no. 12, pp. 1281-1283, Dec. 2009.
31. K. M. F. Shahil and A. A. Balandin, ''Graphene-multilayer graphene nanocomposites as highly efficient thermal interface materials,'' Nano Lett., vol. 12, pp. 861-867, 2012.
32. M. Bae, Z. Ong, D. Estrada, and E. Pop, ''Imaging, simulation, electrostatic control of power dissipation in graphene devices,'' Nano Lett., vol. 10, pp. 4787-4793, 2010.
33. A. D. Liao, J. Z. Wu, X. Wang, K. Tahy, D. Jena, H. Dai, and E. Pop, ''Thermally limited current carrying ability of graphene nanoribbons,'' Phys. Rev. Lett., vol. 106, 2011, 256801.
34. C. A. Merchant, K. Healy, M. Wanunu, V. Ray, N. Peterman, J. Bartel, M. D. Fischbein, K. Venta, Z. Luo, A. T. C. Johnson, and M. Drndic, ''DNA translocation through graphene nanopores,'' Nano Lett., vol. 10, pp. 2915-2921, 2010.
35. G. F. Schneider, S. W. Kowalczyk, V. E. Calado, G. Pandraud, H. W. Zandbergen, L. M. K. Vandersypen, and C. Dekker, ''DNA translocation through graphene nanopores,'' Nano Lett., vol. 10, pp. 3163-3167, 2010.
36. S. Garaj, W. Hubbard, A. Reina, J. Kong, D. Branton, and J. A. Golovchenko, ''Graphene as a subnanometre trans-electrode membrane,'' Nature, vol. 467, pp. 190-193, 2010.
37. S. K. Banerjee, L. F. Register, E. Tutuc, D. Basu, S. Kim, D. Reddy, and A. H. MacDonald, ''Graphene for CMOS and beyond CMOS applications,'' Proc. IEEE, vol. 98, no. 12, pp. 2032-2046, Dec. 2010.
38. L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, ''Field-effect tunneling transistor based on vertical graphene heterostructures,'' Science, vol. 335, pp. 947-950, 2012.
39. E. B. Song, B. Lian, S. M. Kim, S. Lee, T. Chung, M. Wang, C. Zeng, G. Xu, K. Wong, Y. Zhou, H. I. Rasool, D. H. Seo, H. Chung, J. Heo, S. Seo, and K. L. Wang, ''Robust bi-stable memory operation in single-layer graphene ferroelectric memory,'' Appl. Phys. Lett., vol. 99, 2011, 042109.
40. K. Kim, J. Choi, T. Kim, S. Cho, and H. Chung, ''A role for graphene in silicon-based semiconductor devices,'' Nature, vol. 479, pp. 338-344, 2011.
41. D. S. Boning, K. Balakrishnan, H. Cai, N. Drego, A. Farahanchi, K. M. Gettings, L. Daihyun, A. Somani, H. Taylor, D. Truque, and X. Xiaolin, ''Variation,'' IEEE Trans. Semicond. Manuf., vol. 21, no. 1, pp. 63-71, Feb. 2008.
42. K. J. Kuhn, M. D. Giles, D. Becher, P. Kolar, A. Kornfeld, R. Kotlyar, S. T. Ma, A. Maheshwari, and S. Mudanai, ''Process technology variation,'' IEEE Trans. Electron Devices, vol. 58, no. 8, pp. 2197-2208, Aug. 2011.
43. B. Nikolic, J.-H. Park, J. Kwak, B. Giraud, Z. Guo, L.-T. Pang, S. O. Toh, R. Jevtic, K. Qian, and C. Spanos, ''Technology variability from a design perspective,'' IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 58, no. 9, pp. 1996-2009, Sep. 2011.
44. A. Asenov, ''Simulation of statistical variability in nano MOSFETs,'' in Proc. IEEE Symp. Very Large Scale Integr. Technol., 2007, pp. 86-87.
45. C. Shin, X. Sun, and T.-J. K. Liu, ''Study of random-dopant-fluctuation (RDF) effects for the trigate bulk MOSFET,'' IEEE Trans. Electron Devices, vol. 56, no. 7, pp. 1538-1542, Jul. 2009.
46. S. Nassif, K. Bernstein, D. J. Frank, A. Gattiker, W. Haensch, B. L. Ji, E. Nowak, D. Pearson, and N. J. Rohrer, ''High performance CMOS variability in the 65 nm regime and beyond,'' in Proc. IEEE Int. Electron Devices Meeting, 2007, pp. 569-571.
47. N. Drego, A. Chandrakasan, and D. Boning, ''Lack of spatial correlation in MOSFET threshold voltage variation and implications for voltage scaling,'' IEEE Trans. Semicond. Manuf., vol. 22, no. 2, pp. 245-255, May 2009.
48. L. Pang, K. Qian, C. J. Spanos, and B. Nikolic, ''Measurement and analysis of variability in 45 nm strained-Si CMOS technology,'' IEEE J. Solid-State Circuits, vol. 44, no. 8, pp. 2233-2243, Aug. 2009.
49. Z. Guo, A. Carlson, L. Pang, K. T. Duong, T.-J. K. Liu, and B. Nikolic, ''Large-scale SRAM variability characterization in 45 nm CMOS,'' IEEE J. Solid-State Circuits, vol. 44, no. 11, pp. 3174-3192, Nov. 2009.
50. B. Cheng, S. Roy, A. R. Brown, C.Millar, and A. Asenov, ''Evaluation of intrinsic parameter fluctuations on 45, 32 and 22 nm technology node LP N-MOSFETs,'' in Proc. 38th Eur. Solid-State Device Res. Conf., 2008, pp. 47-50.
51. M. Choudhury, Y. Yoon, J. Guo, and K. Mohanram, ''Graphene nanoribbon FETs: Technology exploration for performance and reliability,'' IEEE Trans. Nanotechnol., vol. 10, no. 4, pp. 727-736, Jul. 2009.
52. Y. Taur, D. A. Buchanan, W. Chen, D. J. Frank, K. E. Ismail, S.-H. Lo, G. A. Sai-Halasz, R. G. Viswanathan, H.-J. C. Wann, S. J. Wind, and H.-S. Wong, ''CMOS scaling into the nanometer regime,'' Proc. IEEE, vol. 85, no. 4, pp. 486-504, Apr. 1997.
53. K. Patel, T.-J. K. Liu, and C. J. Spanos, ''Gate line edge roughness model for estimation of FinFET performance variability,'' IEEE Trans. Electron Devices, vol. 56, no. 12, pp. 3055-3063, Dec. 2009.
54. T. Yu, R. Wang, R. Huang, J. Chen, J. Zhuge, and Y. Wang, ''Investigation of Nanowire line-edge roughness in gate-all-around silicon nanowire MOSFETs,'' IEEE Trans. Electron Devices, vol. 57, no. 11, pp. 2864-2871, Nov. 2010.
55. X. Sun and T.-J. K. Liu, ''Spacer gate lithography for reduced variability due to line edge roughness,'' IEEE Trans. Semicond. Manuf., vol. 23, no. 2, pp. 311-315, May 2010.
56. C. Fenouillet-Beranger, T. Skotnicki, S. Monfray, N. Carriere, and F. Boeuf, ''Requirements for ultra-thin-film devices and new materials on CMOS roadmap,'' in Proc. IEEE Int. SOI Conf., 2003, pp. 145-146.
57. C. G. Kang, S. K. Lee, Y. G. Lee, H. J. Hwang, C. H. Cho, J. S. Heo, H. J. Chung, H. J. Yang, S. E. Seo, and B. H. Lee, ''Variability and feasibility of CVD graphene interconnect,'' in Proc. Int. Symp. Very Large Scale Integr. Technol. Syst. Appl., 2011, DOI: 10.1109/ VTSA.2011.5872224.
58. G. Xu, C. M. Torres, Jr., J. Tang, J. Bai, E. B. Song, Y. Huang, X. Duan, Y. Zhang, and K. L. Wang, ''Edge effect on resistance scaling rules in graphene nanostructures,'' Nano Lett., vol. 11, pp. 1082-1086, 2011.
59. G. Xu, C. M. Torres, Jr., J. Bai, J. Tang, T. Yu, Y. Huang, X. Duan, Y. Zhang, and K. L. Wang, ''Linewidth roughness in nanowire-mask-based graphene nanoribbons,'' Appl. Phys. Lett., vol. 98, 2011, 243118.
60. G. Xu, J. Bai, C. M. Torres, Jr., E. B. Song, J. Tang, Y. Zhou, X. Duan, Y. Zhang, and K. L. Wang, ''Low-noise submicron channel graphene nanoribbons,'' Appl. Phys. Lett., vol. 97, 2010, 073107.
61. Y. Lin and P. Avouris, ''Strong suppression of electrical noise in bilayer graphene nanodevices,'' Nano Lett., vol. 8, pp. 2119-2125, 2008.
62. S. Rumyantsev, G. Liu, W. Stillman,M. Shur, and A. A. Balandin, ''Electrical and noise characteristics of graphene field-effect transistors: Ambient effects, noise sources and physical mechanisms,'' J. Phys., Condensed Matter, vol. 22, 2010, 395302.
63. G. Liu, W. Stillman, S. Rumyantsev, Q. Shao, M. Shur, and A. A. Balandin, ''Low-frequency electronic noise in the double-gate single-layer graphene transistors,'' Appl. Phys. Lett., vol. 95, 2009, 033103.
64. G. Liu, S. Rumyantsev, M. Shur, and A. A. Balandin, ''Graphene thickness-graded transistors with reduced electronic noise,'' Appl. Phys. Lett., vol. 100, 2012, 033103.
65. G. Xu, C. M. Torres, Jr., Y. Zhang, F. Liu, E. B. Song, M. Wang, Y. Zhou, C. Zeng, and K. L. Wang, ''Effect of spatial charge inhomogeneity on 1/f noise behavior in graphene,'' Nano Lett., vol. 10, pp. 3312-3317, 2010.
66. Y. Sui, T. Low, M. Lundstrom, and J. Appenzeller, ''Signatures of disorder in the minimum conductivity of graphene,'' Nano Lett., vol. 11, pp. 1319-1322, 2011.
67. E. J. H. Lee, K. Balasubramanian, R. T. Weitz, M. Burghard, and K. Kern, ''Contact and edge effects in graphene devices,'' Nature Nanotechnol., vol. 3, pp. 486-490, 2008.
68. K. A. Ritter and J. W. Lyding, ''The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,'' Nature Mater., vol. 8, pp. 235-242, 2009.
69. K. Kim, H. J. Park, B. Woo, K. J. Kim, G. T. Kim, and W. S. Yun, ''Electric property evolution of structurally defected multilayer graphene,'' Nano Lett., vol. 8, pp. 3092-3096, 2008.
70. A. N. Pal and A. Ghosh, ''Ultralow noise field-effect transistor from multilayer graphene,'' Appl. Phys. Lett., vol. 95, 2009, 082105.
71. G. Xu, C. M. Torres, Jr., E. B. Song, J. Tang, J. Bai, X. Duan, Y. Zhang, and K. L. Wang, ''Enhanced conductance fluctuation by quantum confinement effect in graphene nanoribbons,'' Nano Lett., vol. 10, pp. 4590-4594, 2010.
72. I. Calizo, W. Bao, F. Miao, C. N. Lau, and A. A. Balandin, ''The effect of substrates on the Raman spectrum of graphene: Graphene-on-sapphire and graphene-on-glass,'' Appl. Phys. Lett., vol. 91, 2007, 201904.
73. G. Liu, D. Teweldebrhan, and A. A. Balandin, ''Tuning of graphene properties via controlled exposure to electron beams,'' IEEE Trans. Nanotechnol., vol. 10, no. 4, pp. 865-870, Jul. 2011.
74. S. L. Rumyantsev, G. Liu, M. S. Shur, and A. A. Balandin, ''Observation of the memory steps in graphene at elevated temperatures,'' Appl. Phys. Lett., vol. 98, 2011, 222107.
75. S. Rumyantsev, G. Liu, M. S. Shur, R. A. Potyrailo, and A. A. Balandin, ''Selective gas sensing with a single pristine graphene transistor,'' Nano Lett., vol. 12, no. 5, pp. 2294-2298, 2012.
76. M. G. Sung, H. Lee, K. Heo, K. Byun, T. Kim, D. H. Seo, S. Seo, and S. Hong, ''Scanning noise microscopy on graphene devices,'' ACS Nano, vol. 5, pp. 8620-8628, 2011.
77. A. N. Pal, S. Ghatak, V. Kochat, E. S. Sneha, A. Sampathkumar, S. Raghavan, and A. Ghosh, ''Microscopic mechanism of 1/f noise in graphene: Role of energy band dispersion,'' ACS Nano, vol. 5, pp. 2075-2081, 2011.
78. M. D. McDonnell, ''Is electrical noise useful?'' Proc. IEEE, vol. 99, no. 2, pp. 242-246, Feb. 2011.
79. C. Dekker, A. J. Scholten, F. Liefrink, R. Eppenga, H. van Houten, and C. T. Foxon, ''Spontaneous resistance switching and low-frequency noise in quantum point contacts,'' Phys. Rev. Lett., vol. 66, pp. 2148-2151, 1991.
80. Y. T. Yang, C. Callegari, X. L. Feng, and M. L. Roukes, ''Surface adsorbate fluctuations and noise in nanoelectromechanical systems,'' Nano Lett., vol. 11, pp. 1753-1759, 2011.
81. C. Gomez-Navarro, P. J. D. Pablo, J. Gomez-Herrero, B. Biel, F. Garcia-Vidal, A. Rubio, and F. Flores, ''Tuning the conductance of single-walled carbon nanotubes by ion irradiation in the Anderson localization regime,'' Nature Mater., vol. 4, pp. 534-539, 2005. (Pubitemid 40952748)
82. G. Zheng, X. P. A. Gao, and C. M. Lieber, ''Frequency domain detection of biomolecules using silicon nanowire biosensors,'' Nano Lett., vol. 10, pp. 3179-3183, 2010.
83. A. van der Ziel, ''Thermal noise in field-effect transistors,'' Proc. IRE, vol. 50, no. 8, pp. 1808-1812, Aug. 1962.
84. J. Tworzydao, B. Trauzettel, M. Titov, A. Rycerz, and C. W. J. Beenakker, ''Sub-poissonian shot noise in graphene,'' Phys. Rev. Lett., vol. 96, 2006, 246802.
85. S. Ghosh, W. Bao, D. L. Nika, S. Subrina, E. P. Pokatilov, C. N. Lau, and A. A. Balandin, ''Dimensional crossover of thermal transport in few-layer graphene,'' Nature Mater., vol. 9, pp. 555-558, 2010.
86. E. G. Mishchenko, ''Effect of electron-electron interactions on the conductivity of clean graphene,'' Phys. Rev. Lett., vol. 98, 2007, 216801.
87. J. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, ''Charged-impurity scattering in graphene,'' Nature Phys., vol. 4, pp. 377-381, 2008.
88. E. H. Hwang, S. Adam, and S. Das Sarma, ''Carrier transport in two-dimensional graphene layers,'' Phys. Rev. Lett., vol. 98, 2007, 186806.
89. F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, ''Detection of individual gas molecules adsorbed on graphene,'' Nature Mater., vol. 6, pp. 652-655, 2007. (Pubitemid 47359547)
90. Z. H. Ni, L. A. Ponomarenko, R. R. Nair, R. Yang, S. Anissimova, I. V. Grigorieva, F. Schedin, P. Blake, Z. X. Shen, E. H. Hill, K. S. Novoselov, and A. K. Geim, ''On resonant scatterers as a factor limiting carrier mobility in graphene,'' Nano Lett., vol. 10, pp. 3868-3872, 2010.
91. X. Jia, J. Campos-Delgado, M. Terrones, V. Meunier, and M. S. Dresselhaus, ''Graphene edges: A review of their fabrication and characterization,'' Nanoscale, vol. 3, pp. 86-95, 2011.
92. A. Hashimoto, K. Suenaga, A. Gloter, K. Urita, and S. Iijima, ''Direct evidence for atomic defects in graphene layers,'' Nature, vol. 430, pp. 870-873, 2004. (Pubitemid 39119210)
93. W. Bao, F. Miao, Z. Chen, H. Zhang, W. Jang, C. Dames, and C. N. Lau, ''Controlled ripple texturing of suspended graphene and ultrathin graphite membranes,'' Nature Nanotechnol., vol. 4, pp. 562-566, 2009.
94. 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, pp. 60-63, 2007. (Pubitemid 46348040)
95. D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim, and K. S. Novoselov, ''Control of graphene's properties by reversible hydrogenation: Evidence for graphane,'' Science, vol. 323, pp. 610-613, 2009.
96. D. Sylvester, K. Agarwal, and S. Shah, ''Variability in nanometer CMOS: Impact, analysis, minimization,'' VLSI J. Integr., vol. 41, pp. 319-339, 2008, 5. (Pubitemid 351637611)
97. S. R. Nassif, ''Design for variability in DSM technologies [deep submicron technologies],'' in Proc. IEEE 1st Int. Symp. Quality Electron. Design, 2000, pp. 451-454.
98. K. J. Kuhn, ''Reducing variation in advanced logic technologies: Approaches to process and design for manufacturability of nanoscale CMOS,'' in Proc. IEEE Int. Electron Devices Meeting, 2007, pp. 471-474.
99. L.-T. Pang and B. Nikolic, ''Measurements and analysis of process variability in 90 nm CMOS,'' IEEE J. Solid-State Circuits, vol. 44, no. 5, pp. 1655-1663, May 2009.
100. A. Asenov, S. Kaya, and A. R. Brown, ''Intrinsic parameter fluctuations in decananometer MOSFETs introduced by gate line edge roughness,'' IEEE Trans. Electron Devices, vol. 50, no. 5, pp. 1254-1260, May 2003.
101. Y. Ye, F. Liu, M. Chen, S. Nassif, and Y. Cao, ''Statistical modeling and simulation of threshold variation under random dopant fluctuations and line-edge roughness,'' IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 19, no. 6, pp. 987-996, Jun. 2011.
102. I. Heller, S. Chatoor, J. Mannik, M. A. G. Zevenbergen, J. B. Oostinga, A. F. Morpurgo, C. Dekker, and S. G. Lemay, ''Charge noise in graphene transistors,'' Nano Lett., vol. 10, pp. 1563-1567, 2010.
103. M. J. Uren, D. J. Day, and M. J. Kirton, ''1/f and random telegraph noise in silicon metal-oxide-semiconductor field-effect transistors,'' Appl. Phys. Lett., vol. 47, pp. 1195-1197, 1985.
104. Y. Yuzhelevski, M. Yuzhelevski, and G. Jung, ''Random telegraph noise analysis in time domain,'' Rev. Sci. Instrum., vol. 71, pp. 1681-1688, 2000.
105. K. K. Hung, P. K. Ko, C. Hu, and Y. C. Cheng, ''Random telegraph noise of deep-submicrometer MOSFETs,'' IEEE Electron Device Lett., vol. 11, no. 2, pp. 90-92, Feb. 1990. (Pubitemid 20666219)
106. A. P. van der Wel, E. A. M. Klumperink, L. K. J. Vandamme, and B. Nauta, ''Modeling random telegraph noise under switched bias conditions using cyclostationary RTS noise,'' IEEE Trans. Electron Devices, vol. 50, no. 5, pp. 1378-1384, May 2003.
107. Z. Shi, J.-P. Mieville, and M. Dutoit, ''Random telegraph signals in deep submicron n-MOSFET's,'' IEEE Trans. Electron Devices, vol. 41, no. 7, pp. 1161-1168, Jul. 1994.
108. C. Monzio Compagnoni, R. Gusmeroli, A. S. Spinelli, A. L. Lacaita, M. Bonanomi, and A. Visconti, ''Statistical model for random telegraph noise in flash memories,'' IEEE Trans. Electron Devices, vol. 55, no. 1, pp. 388-395, Jan. 2008.
109. A. van der Ziel, ''Unified presentation of 1/f noise in electron devices: Fundamental 1/f noise sources,'' Proc. IEEE, vol. 76, no. 3, pp. 233-258, Mar. 1988.
110. F. Liu, M. Bao, H. Kim, K. L. Wang, C. Li, X. Liu, and C. Zhou, ''Giant random telegraph signals in the carbon nanotubes as a single defect probe,'' Appl. Phys. Lett., vol. 86, 2005, 163102.
111. F. Liu, K. L. Wang, C. Li, and C. Zhou, ''Study of random telegraph signals in single-walled carbon nanotube field effect transistors,'' IEEE Trans. Nanotechnol., vol. 5, no. 5, pp. 441-445, Sep. 2006. (Pubitemid 44444382)
112. F. Liu, M. Bao, K. L. Wang, D. Zhang, and C. Zhou, ''Coulomb attractive random telegraph signal in a single-walled carbon nanotube,'' Phys. Rev. B, vol. 74, 2006, 035438.
113. K. K. Hung, P. K. Ko, C. Hu, and Y. C. Cheng, ''A unified model for the flicker noise in metal-oxide-semiconductor field-effect transistors,'' IEEE Trans. Electron Devices, vol. 37, no. 3, pt. 1, pp. 654-665, Mar. 1990. (Pubitemid 20699942)
114. B. Min, S. P. Devireddy, Z. Celik-Butler, F. Wang, A. Zlotnicka, H. Tseng, and P. J. Tobin, ''Low-frequency noise in submicrometer MOSFETs with HfO2, HfO2/Al2O3 and HfAlOx gate stacks,'' IEEE Trans. Electron Devices, vol. 51, no. 8, pp. 1315-1322, Aug. 2004.
115. Y. Lin, J. Appenzeller, J. Knoch, Z. Chen, and P. Avouris, ''Low-frequency current fluctuations in individual semiconducting single-wall carbon nanotubes,'' Nano Lett., vol. 6, pp. 930-936, 2006. (Pubitemid 43836606)
116. A. Balandin, K. L. Wang, A. Svizhenko, and S. Bandyopadhyay, ''The fundamental 1/f noise and the Hooge parameter in semiconductor quantum wires,'' IEEE Trans. Electron Devices, vol. 46, no. 6, pp. 1240-1244, Jun. 1999.
117. F. N. Hooge, ''1/f noise sources,'' IEEE Trans. Electron Devices, vol. 41, no. 11, pp. 1926-1935, Nov. 1994.
118. Z. Cheng, Q. Li, Z. Li, Q. Zhou, and Y. Fang, ''Suspended graphene sensors with improved signal and reduced noise,'' Nano Lett., vol. 10, pp. 1864-1868, 2010.
119. Y. Zhang, E. E. Mendez, and X. Du, ''Mobility-dependent low-frequency noise in graphene field-effect transistors,'' ACS Nano, vol. 5, pp. 8124-8130, 2011.
120. P. Dutta and P. M. Horn, ''Low-frequency fluctuations in solids: 1/f noise,'' Rev. Mod. Phys., vol. 53, pp. 497-516, 1981.
121. F. N. Hooge, ''1=f noise sources,'' in Advanced Experimental Methods For Noise Research in Nanoscale Electronic Devices, vol. 151. Amsterdam, The Netherlands: Springer-Verlag, 2005, ch. I, pp. 3-10, ser. NATO Science Series.
122. A. Hajimiri and T. H. Lee, ''A general theory of phase noise in electrical oscillators,'' IEEE J. Solid-State Circuits, vol. 33, no. 2, pp. 179-194, Feb. 1998. (Pubitemid 128576193)
123. Q. Shao, G. Liu, D. Teweldebrhan, A. A. Balandin, S. Rumyantsev, M. S. Shur, and D. Yan, ''Flicker noise in bilayer graphene transistors,'' IEEE Electron Device Lett., vol. 30, no. 3, pp. 288-290, Mar. 2009.
124. G. Xu, F. Liu, S. Han, K. Ryu, A. Badmaev, B. Lei, C. Zhou, and K. L. Wang, ''Low-frequency noise in top-gated ambipolar carbon nanotube field effect transistors,'' Appl. Phys. Lett., vol. 92, 2008, 223114.
125. K. H. Duh and A. van der Ziel, ''Hooge parameters for various FET structures,'' IEEE Trans. Electron Devices, vol. ED-32, no. 3, pp. 662-666, Mar. 1985.
126. A. van der Ziel, P. H. Handel, X. Zhu, and K. H. Duh, ''A theory of the Hooge parameters of solid-state devices,'' IEEE Trans. Electron Devices, vol. ED-32, no. 4, pp. 667-671, Apr. 1985. (Pubitemid 15492509)
127. A. N. Pal, A. A. Bol, and A. Ghosh, ''Large low-frequency resistance noise in chemical vapor deposited graphene,'' Appl. Phys. Lett., vol. 97, 2010, 133504.
128. A. N. Pal and A. Ghosh, ''Resistance noise in electrically biased bilayer graphene,'' Phys. Rev. Lett., vol. 102, 2009, 126805.
129. Y. Lin, V. Perebeinos, Z. Chen, and P. Avouris, ''Electrical observation of subband formation in graphene nanoribbons,'' Phys. Rev. B, vol. 78, 2008, 161409.
130. M. Y. Han, J. C. Brant, and P. Kim, ''Electron transport in disordered graphene nanoribbons,'' Phys. Rev. Lett., vol. 104, Feb. 1, 2010, 056801.
131. Y. Dan, Y. Lu, N. J. Kybert, Z. Luo, and A. T. C. Johnson, ''Intrinsic response of graphene vapor sensors,'' Nano Lett., vol. 9, pp. 1472-1475, 2009.
132. D. L. Nika, E. P. Pokatilov, A. S. Askerov, and A. A. Balandin, ''Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering,'' Phys. Rev. B, vol. 79, 2009, 155413.
133. S. Ghosh, D. L. Nika, E. P. Pokatilov, and A. A. Balandin, ''Heat conduction in graphene: Experimental study and theoretical interpretation,'' New J. Phys., vol. 11, 2009, 095012.
134. A. A. Balandin, S. Ghosh, D. L. Nika, and E. P. Pokatilov, ''Thermal conduction in suspended graphene layers,'' Fullerenes, Nanotubes Carbon Nanostruct., vol. 18, pp. 474-486, 2010.
135. A. A. Balandin, ''Thermal properties of graphene and nanostructured carbon materials,'' Nature Mater., vol. 10, pp. 569-581, 2011.
136. Y. Ouyang, Y. Yoon, and J. Guo, ''Edge chemistry engineering of graphene nanoribbon transistors: A computational study,'' in Proc. IEEE Int. Electron Devices Meeting, 2008, DOI: 10.1109/IEDM.2008. 4796739.
137. Y. Kobayashi, K. Fukui, T. Enoki, K. Kusakabe, and Y. Kaburagi, ''Observation of zigzag and armchair edges of graphite using scanning tunneling microscopy and spectroscopy,'' Phys. Rev. B, vol. 71, 2005, 193406.
138. P. Koskinen, S. Malola, and H. Ha?kkinen, ''Evidence for graphene edges beyond zigzag and armchair,'' Phys. Rev. B, vol. 80, 2009, 073401.
139. M. Y. Han, B. Ozyilmaz, Y. Zhang, and P. Kim, ''Energy band-gap engineering of graphene nanoribbons,'' Phys. Rev. Lett., vol. 98, 2007, 206805.
140. F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, ''Structural defects in graphene,'' ACS Nano, vol. 5, pp. 26-41, 2011.
141. K. Kim, Z. Lee, B. D. Malone, K. T. Chan, B. Alema'n, W. Regan, W. Gannett, M. F. Crommie, M. L. Cohen, and A. Zettl, ''Multiply folded graphene,'' Phys. Rev. B, vol. 83, 2011, 245433.
142. Z. Liu, K. Suenaga, P. J. F. Harris, and S. Iijima, ''Open and closed edges of graphene layers,'' Phys. Rev. Lett., vol. 102, 2009, 015501.
143. J. Zhang, J. Xiao, X. Meng, C. Monroe, Y. Huang, and J. Zuo, ''Free folding of suspended graphene sheets by random mechanical stimulation,'' Phys. Rev. Lett., vol. 104, 2010, 166805.
144. M. Evaldsson, I. V. Zozoulenko, H. Xu, and T. Heinzel, ''Edge-disorder-induced Anderson localization and conduction gap in graphene nanoribbons,'' Phys. Rev. B, vol. 78, 2008, 161407.
145. F. Sols, F. Guinea, and A. H. C. Neto, ''Coulomb blockade in graphene nanoribbons,'' Phys. Rev. Lett., vol. 99, 2007, 166803.
146. J. Poumirol, A. Cresti, S. Roche, W. Escoffier, M. Goiran, X. Wang, X. Li, H. Dai, and B. Raquet, ''Edge magnetotransport fingerprints in disordered graphene nanoribbons,'' Phys. Rev. B, vol. 82, 2010, 041413.
147. P. Gallagher, K. Todd, and D. Goldhaber-Gordon, ''Disorder-induced gap behavior in graphene nanoribbons,'' Phys. Rev. B, vol. 81, 2010, 115409.
148. C. Lian, K. Tahy, T. Fang, G. Li, H. G. Xing, and D. Jena, ''Quantum transport in graphene nanoribbons patterned by metal masks,'' Appl. Phys. Lett., vol. 96, 2010, 103109.
149. J. Bai, X. Duan, and Y. Huang, ''Rational fabrication of graphene nanoribbons using a nanowire etch mask,'' Nano Lett., vol. 9, pp. 2083-2087, 2009.
150. Y. Yang and R. Murali, ''Impact of size effect on graphene nanoribbon transport,'' IEEE Electron Device Lett., vol. 31, no. 3, pp. 237-239, Mar. 2010.
151. Z. Chen, Y. Lin, M. J. Rooks, and P. Avouris, ''Graphene nano-ribbon electronics,'' Phys. E, Low-Dimensional Syst. Nanostruct., vol. 40, pp. 228-232, 2007. (Pubitemid 350102338)
152. L. Jiao, X. Wang, G. Diankov, H. Wang, and H. Dai, ''Facile synthesis of high-quality graphene nanoribbons,'' Nature Nanotechnol., vol. 5, pp. 321-325, 2010.
153. L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, ''Narrow graphene nanoribbons from carbon nanotubes,'' Nature, vol. 458, pp. 877-880, 2009.
154. R. Yang, L. Zhang, Y. Wang, Z. Shi, D. Shi, H. Gao, E. Wang, and G. Zhang, ''An anisotropic etching effect in the graphene basal plane,'' Adv. Mater., vol. 22, pp. 4014-4019, 2010.
155. X. Wang and H. Dai, ''Etching and narrowing of graphene from the edges,'' Nature Chem., vol. 2, pp. 661-665, 2010.
156. 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, pp. 872-876, 2009.
157. J. B. Oostinga, B. Sacepe, M. F. Craciun, and A. F. Morpurgo, ''Magnetotransport through graphene nanoribbons,'' Phys. Rev. B, vol. 81, 2010, 193408.
158. J. H. Bardarson, J. Tworzydao, P. W. Brouwer, and C. W. J. Beenakker, ''One-parameter scaling at the Dirac point in graphene,'' Phys. Rev. Lett, vol. 99, 2007, 106801.
159. M. S. Purewal, B. H. Hong, A. Ravi, B. Chandra, J. Hone, and P. Kim, ''Scaling of resistance and electron mean free path of single-walled carbon nanotubes,'' Phys. Rev. Lett., vol. 98, 2007, 186808.
160. M. Wang, E. B. Song, S. Lee, J. Tang, M. Lang, C. Zeng, G. Xu, Y. Zhou, and K. L. Wang, ''Quantum dot behavior in bilayer graphene nanoribbons,'' ACS Nano, vol. 5, pp. 8769-8773, 2011.
161. Y. Yoon and J. Guo, ''Effect of edge roughness in graphene nanoribbon transistors,'' Appl. Phys. Lett., vol. 91, 2007, 073103.
162. D. Basu, M. J. Gilbert, L. F. Register, S. K. Banerjee, and A. H. MacDonald, ''Effect of edge roughness on electronic transport in graphene nanoribbon channel metal-oxide-semiconductor field-effect transistors,'' Appl. Phys. Lett., vol. 92, 2008, 042114.
163. M. Luisier and G. Klimeck, ''Performance analysis of statistical samples of graphene nanoribbon tunneling transistors with line edge roughness,'' Appl. Phys. Lett., vol. 94, 2009, 223505.
164. J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, M. Muoth, A. P. Seitsonen, M. Saleh, X. Feng, K. Mullen, and R. Fasel, ''Atomically precise bottom-up fabrication of grapheme nanoribbons,'' Nature, vol. 466, pp. 470-473, 2010.
165. D. Kingrey, O. Khatib, and P. G. Collins, ''Electronic fluctuations in nanotube circuits and their sensitivity to gases and liquids,'' Nano Lett., vol. 6, pp. 1564-1568, 2006. (Pubitemid 44195349)
166. P. Wei, W. Bao, Y. Pu, C. N. Lau, and J. Shi, ''Anomalous thermoelectric transport of Dirac particles in graphene,'' Phys. Rev. Lett., vol. 102, 2009, 166808.
167. H. B. Heersche, P. Jarillo-Herrero, J. B. Oostinga, L. M. K. Vandersypen, and A. F. Morpurgo, ''Bipolar supercurrent in graphene,'' Nature, vol. 446, pp. 56-59, 2007. (Pubitemid 46350681)
168. M. Xiao, I. Martin, E. Yablonovitch, and H. W. Jiang, ''Electrical detection of the spin resonance of a single electron in a silicon field-effect transistor,'' Nature, vol. 430, pp. 435-439, 2004. (Pubitemid 38987900)
169. J. Hwang, C. Kuo, L. Chen, and K. Chen, ''Correlating defect density with carrier mobility in large-scaled graphene films: Raman spectral signatures for the estimation of defect density,'' Nanotechnology, vol. 21, 2010, 465705.
170. Y. Zhou, Z. Liao, Y. Wang, G. S. Duesberg, J. Xu, Q. Fu, X. Wu, and D. Yu, ''Ion irradiation induced structural and electrical transition in graphene,'' J. Chem. Phys., vol. 133, 2010, 234703.
171. I. Childres, L. A. Jauregui, J. Tian, and Y. P. Chen, ''Effect of oxygen plasma etching on graphene studied using Raman spectroscopy and electronic transport measurements,'' New J. Phys., vol. 13, 2011, 025008.
172. N. Petrone, C. R. Dean, I. Meric, A. M. van der Zande, P. Y. Huang, L. Wang, D. Muller, K. L. Shepard, and J. Hone, ''Chemical vapor deposition-derived graphene with electrical performance of exfoliated graphene,'' Nano Lett., vol. 12, pp. 2751-2756, 2012.
173. N. Levy, S. A. Burke, K. L. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A. H. C. Neto, and M. F. Crommie, ''Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nanobubbles,'' Science, vol. 329, pp. 544-547, 2010.
174. I. Meric, C. R. Dean, A. F. Young, N. Baklitskaya, N. J. Tremblay, C. Nuckolls, P. Kim, and K. L. Shepard, ''Channel length scaling in graphene field-effect transistors studied with pulsed current-voltage measurements,'' Nano Lett., vol. 11, pp. 1093-1097, 2011.