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Theoretical modeling of electron emission from graphene

Published online by Cambridge University Press:  10 July 2017

Y.S. Ang ,
Shi-Jun Liang  and
L.K. Ang
Y.S. Ang
Affiliation:
Singapore University of Technology and Design, Singapore; [email protected]
Shi-Jun Liang
Affiliation:
Singapore University of Technology and Design, Singapore; [email protected]
L.K. Ang
Affiliation:
Singapore University of Technology and Design, Singapore; [email protected]
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Abstract

The theories of thermionic emission and field emission (also known as the Richardson–Dushman [RD] and Fowler–Nordheim [FN] Laws, respectively) were formulated more than 80 years ago for bulk materials. In single-layer graphene, electrons mimic massless Dirac fermions and follow relativistic carrier dynamics. Thus, their behavior deviates significantly from the nonrelativistic electrons that reside in traditional bulk materials with a parabolic energy-momentum dispersion relation. In this article, we assert that due to linear energy dispersion, the traditional thermionic emission and field emission models are no longer valid for graphene and two-dimensional Dirac-like materials. We have proposed models that show better agreement with experimental data and also show a smooth transition to the traditional RD and FN Laws.

Keywords

thermionic emissionfield emissionnanostructure
Type
Research Article
Information
MRS Bulletin , Volume 42 , Issue 7: Electron-Emission Materials , July 2017 , pp. 505 - 510
Copyright
Copyright © Materials Research Society 2017 

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References

Richardson, O.W., Proc. Cambridge Philos. Soc. 11, 286 (1901).Google Scholar
Dushman, S., Rev. Mod. Phys. 2, 381 (1930).Google Scholar
Fowler, R.H., Nordheim, L., Proc. R. Soc. Lond. A 199, 173 (1928).Google Scholar
Nordheim, L.W., Proc. R. Soc. Lond. A 121, 626 (1928).Google Scholar
Einstein, A., Ann. Phys. 17, 132 (1905).Google Scholar
Fowler, R.H., Phys. Rev. 38, 45 (1931).Google Scholar
DuBridge, L.A., Phys. Rev. 39, 108 (1932).Google Scholar
Jensen, K.L., J. Appl. Phys. 102, 24911 (2007).Google Scholar
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, V., Firsov, A.A., Nature 306, 666 (2004).Google Scholar
Geim, A.K., Novoselov, K.S., Nat. Mater. 6, 183 (2007).Google Scholar
Falkovsky, L.A., J. Phys. Conf. Ser. 129, 012004 (2008).CrossRefGoogle Scholar
Bonaccorso, F., Sun, Z., Hasan, T., Ferrari, A.C., Nat. Photonics 4, 611 (2010).CrossRefGoogle Scholar
Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K., Rev. Mod. Phys. 81, 109 (2009).Google Scholar
Balandin, A.A., Nat. Mater. 10, 569 (2011).Google Scholar
Pop, E., Varshney, V., Roy, A.K., MRS Bull. 37, 1273 (2012).Google Scholar
Wallace, P.R., Phys. Rev. 71, 622 (1947).CrossRefGoogle Scholar
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., Firsov, A.A., Nature 438, 197 (2005).Google Scholar
Xiao, D., Chang, M.-C., Niu, Q., Rev. Mod. Phys. 82, 1959 (2010).Google Scholar
Zhang, Y., Tan, Y.-W., Stormer, H.L., Kim, P., Nature 438, 201 (2005).Google Scholar
Novoselov, K.S., McCann, E., Morozov, S.V., Fal’ko, V.I., Katsnelson, M.I., Zeitler, U., Jiang, D., Schedin, F., Geim, A.K., Nat. Phys. 2, 177 (2006).Google Scholar
Katsnelson, M.I., Novoselov, K.S., Geim, A.K., Nat. Phys. 2, 620 (2006).Google Scholar
Beenakker, C.W.J., Phys. Rev. Lett. 97, 067007 (2006).Google Scholar
Beenakker, C.W.J., Rev. Mod. Phys. 80, 1337 (2008).Google Scholar
Cheianov, V.V., Fal’ko, V., Altshuler, B.L., Science 315, 1252 (2007).CrossRefGoogle Scholar
Lee, G.-H., Park, G.-H., Lee, H.-J., Nat. Phys. 11, 925 (2015).Google Scholar
Lemme, M.C., Li, L.-J., Palacios, T., Schwierz, F., MRS Bull. 39, 711 (2014).Google Scholar
Geim, A.K., Grigorieva, I.V., Nature 499, 419 (2013).Google Scholar
Jariwala, D., Marks, T.J., Hersam, M.C., Nat. Mater. 16, 170 (2017).CrossRefGoogle Scholar
Allain, A., Kang, J., Banerjee, K., Kis, A., Nat. Mater. 14, 1195 (2015).Google Scholar
Xu, Y., Cheng, C., Du, S., Yang, J., Yu, B., Luo, J., Yin, W., Dong, E.LS., Dan, R.E.X., ACS Nano 10, 4895 (2016).CrossRefGoogle Scholar
Liang, S.-J., Ang, L.K., Phys. Rev. Appl. 3, 014002 (2015).CrossRefGoogle Scholar
Ang, Y.S., Ang, L.K., Phys. Rev. Appl. 6, 034013 (2016).Google Scholar
Liang, S.-J., Hu, W., Di Bartolomeo, A., Adam, S., Ang, L.K., “A Modified Schottky Model for Graphene-Semiconductor (3D/2D) Contact: A Combined Theoretical and Experimental Study,” presented at the IEEE International Electron Device Meeting (IEDM), San Francisco, 2016.CrossRefGoogle Scholar
Malesevic, A., Kemps, R., Vanhulsel, A., Chowdhury, M.P., Volodin, A., van Haesendonck, C., J. Appl. Phys. 104, 084301 (2008).Google Scholar
Watcharotone, S., Ruoff, R.S., Read, F.H., Phys. Procedia 1, 71 (2008).CrossRefGoogle Scholar
Eda, G., Unalan, H.E., Rupesinghe, N., Amaratunga, G.A.J., Chhowalla, M., Appl. Phys. Lett. 93, 233502 (2008).Google Scholar
Qian, M., Feng, T., Ding, H., Lin, L., Li, H., Chen, Y., Sun, Z., Nanotechnology 20, 425702 (2009).Google Scholar
Wu, Z.-S., Pei, S., Ren, W., Tang, D., Gao, L., Liu, B., Li, F., Liu, C., Cheng, H.-M., Adv. Mater. 21, 1756 (2009).Google Scholar
Huang, C.-K., Ou, Y., Bie, Y., Zhao, Q., Yu, D., Appl. Phys. Lett. 98, 263104 (2011).CrossRefGoogle Scholar
Yamaguchi, H., Murakami, K., Eda, G., Fujita, T., Guan, P., Wang, W., Gong, C., Bisse, J., Miller, S., Acik, M., Cho, K., Chabal, Y.J., Chen, M., Wakaya, F., Takai, M., Chhowalla, M., ACS Nano 5, 4945 (2011).Google Scholar
Kumar, S., Duesberg, G.S., Pratap, R., Raghavan, S., Appl. Phys. Lett. 105, 103107 (2014).CrossRefGoogle Scholar
Palnitka, U.A., Kashid, R.V., More, M.A., Joag, D.S., Panchakarla, L.S., Rao, C.N.R., Appl. Phys. Lett. 97, 063102 (2010).Google Scholar
Xu, J., Wang, Q., Tao, Z., Qi, Z., Zhai, Y., Wu, S., Zhang, X., Lei, W., ACS Appl. Mater. Interfaces 8, 3259 (2016).Google Scholar
Soin, N., Roy, S.S., Roy, S., Hazra, K.S., Misra, D.S., Lim, T.H., Hetherington, C.J., McLaughlin, J.A., J. Phys. Chem. C 115, 5366 (2011).Google Scholar
Kleshch, V.I., Bandurin, D.A., Orekhov, A.S., Purcell, S.T., Obraztsov, A.N., Appl. Surf. Sci. 357, 1967 (2015).Google Scholar
Lau, Y.Y., Chernin, D., Colombant, D.G., Ho, P.-T., Phys. Rev. Lett. 66, 1446 (1991).Google Scholar
Ang, L.K., Kwan, T.J.T., Lau, Y.Y., Phys. Rev. Lett. 91, 208303 (2003).Google Scholar
Srisonphan, S., Kim, M., Kim, H.K., Sci. Rep. 4, 3764 (2014).CrossRefGoogle Scholar
Qin, X.-Z., Wang, W.-L., Xu, N.-S., Li, Z.-B., Forbes, R.G., Proc. R. Soc. Lond. A 467, 1029 (2011).Google Scholar
Xiao, Z., She, J., Deng, S., Tang, Z., Li, Z., Lu, J., Xu, N., ACS Nano 4, 6332 (2010).Google Scholar
Ye, D., Moussa, S., Ferguson, J.D., Baski, A.A., El-Shall, M.S., Nano Lett. 12, 1265 (2012).Google Scholar
Late, D.J., Shaikh, P.A., Khare, R., Kashid, R.V., Chaudhary, M., More, M.A., Ogale, S.B., ACS Appl. Mater. Interfaces 6, 15881 (2014).Google Scholar
Starodub, E., McCarty, K.F., Appl. Phys. Lett. 100, 181604 (2012).Google Scholar
Zhu, F., Lin, X., Fan, S., Nano Res. 7, 553 (2014).Google Scholar
Tongay, S., Lemaitre, M., Miao, X., Gila, B., Appleton, B.R., Hebard, A.F., Phys. Rev. X 2, 011002 (2012).Google Scholar
Yang, H., Heo, J., Park, S., Song, H.J., Seo, D.H., Byun, K.-E., Kim, P., Yoo, I., Chung, H.-J., Kim, K., Science 336, 1140 (2012).CrossRefGoogle Scholar
Sinha, D., Lee, J.U., Nano Lett. 14, 4660 (2014).Google Scholar
Liang, S.-D., Quantum Tunneling and Field Electron Emission Theories (World Scientific, Singapore, 2014).Google Scholar
Xu, K., Zeng, C., Zhang, Q., Ru, R.S., Ye, P., Wang, K., Seabaugh, A., Xing, H., Suehle, J.S., Richter, C.A., Gundlach, D.J., Ngen, N.V., Nano Lett. 13, 131 (2012).Google Scholar
Christodoulou, C., Giannakopoulos, A., Nardi, M.V., Ligorio, G., Oehzelt, M., Chen, L., Pasquali, L., Timpel, M., Giglia, A., Nannarone, S., Norman, P., Linares, M., Parvez, K., Mullen, K., Beljonne, D., Koch, N., J. Phys. Chem. C 118, 4784 (2014).Google Scholar
Sata, Y., Moriya, R., Morikawa, S., Yabuk, N., Masubuchi, S., Machida, T., Appl. Phys. Lett. 107, 023109 (2015).CrossRefGoogle Scholar
Tomer, D., Rajput, S., Hudy, L.J., Li, C.H., Li, L., Nanotechnology 26, 215702 (2015).Google Scholar
Tomer, D., Rajput, S., Hudy, L.J., Li, C.H., Li, L., Appl. Phys. Lett. 105, 021607 (2014).Google Scholar
Martin, J., Akerman, N., Ulbricht, G., Lohmann, T., Smet, J.H., von Klitzing, K., Yacoby, A., Nat. Phys. 4, 144 (2008).Google Scholar
Adam, S., Hwang, E.H. Galitski, V.M., Das Sarma, S., Proc. Natl. Acad. Sci. U.S.A. 104, 18392 (2007).CrossRefGoogle Scholar
Tan, Y.-W., Zhang, Y., Bolotin, K., Zhao, Y., Adam, S., Hwang, E.H., Das Sarma, S., Stormer, H.L., Kim, P., Phys. Rev. Lett. 99, 246803 (2007).Google Scholar
Kim, S., Seo, T.H., Kim, M.J., Song, K.M., Suh, E.-K., Kim, H., Nano Res. 8, 1327 (2015).Google Scholar
Luo, L.-B., Chen, J.-J., Wang, M.-Z., Hu, H., Wu, C.-Y., Li, Q., Wang, L., Huang, J.-A., Liang, F.-X., Adv. Funct. Mater. 24, 2794 (2014).Google Scholar
Kumar, A., Kashid, R., Ghosh, A., Kumar, V., Singh, R., ACS Appl. Mater. Interfaces 8, 8213 (2016).Google Scholar
Rajput, S., Chen, M.X., Liu, Y., Li, Y.Y., Weinert, M., Li, L., Nat. Commun. 4, 2752 (2013).Google Scholar
Liu, Y., Stadins, P., Wei, S.-H., Sci. Adv. 2, e1600069 (2016).Google Scholar
Mak, K.F., Shan, J., Heinz, T.F., Phys. Rev. Lett. 104, 176404 (2010).Google Scholar
Kane, E.O., J. Phys. Chem. Solids 1, 249 (1957).Google Scholar
Jozwiak, C., Park, C.-H., Gotlieb, K., Hwang, C., Lee, D.-H., Louie, S.G., Denlinger, J.D., Rotund, C.R., Brgenea, R.J., Hssan, Z., Lanzara, A., Nat. Phys. 9, 293 (2013).Google Scholar