By considering the effect of Klein tunneling for low energy electrons with linear energy dispersion, a model has been constructed to calculate the amount of emitted line current density from a single-layer graphene sheet, which is vertically aligned inside a dc gap. It is found that the current-voltage scaling obtained from the constructed Klein tunneling model is very different from the traditional field emission model based on the Fowler-Nordheim (FN) law. Under the same geometrical field enhancement factor, our model predicts a much higher emitted current as compared to the FN law at low voltages.
REFERENCES
1.
K. S.
Novoselov
, A. K.
Geim
, S. V.
Morozov
, D.
Jiang
, Y.
Zhang
, S. V.
Dubonos
, I. V.
Gregorieva
, and A. A.
Firsov
, Science
306
, 666
(2004
).2.
A. H. C.
Neto
, F.
Guinea
, N. M. R.
Peres
, K. S.
Novoselov
, and A. K.
Geim
, Rev. Mod. Phys.
81
, 109
(2009
).3.
U. A.
Palnitkar
, R. V.
Kashid
, M. A.
More
, D. S.
Joag
, L. S.
Panchakalar
, and C. N. R.
Rao
, Appl. Phys. Lett.
97
, 063102
(2010
).4.
A.
Malesevic
, R.
Kemps
, A.
Vanhulsel
, M. P.
Chowdhury
, A.
Volodin
, and C. V.
Haesendonck
, J. Appl. Phys.
104
, 084301
(2008
).5.
S.
Wang
, J.
Wang
, P.
Miraldo
, M.
Zqhu
, R.
Outlaw
, K.
Hou
, X.
Zhou
, B. C.
Holloway
, D.
Manos
, T.
Tyler
, et al, Appl. Phys. Lett.
97
, 183103
(2006
).6.
Z. S.
Wu
, S. F.
Pei
, W. C.
Ren
, D. M.
Tang
, L. B.
Gao
, B. L.
Liu
, F.
Li
, C.
Liu
, and H. M.
Cheng
, Adv. Mater.
21
, 1756
(2009
).7.
K.
Uppireddi
, C. V.
Rao
, Y.
Ishikawa
, B. R.
Weiner
, and G.
Morell
, Appl. Phys. Lett.
97
, 062106
(2010
).8.
G.
Eda
, H. E.
Unalan
, N.
Rupesinghe
, G. A. J.
Amaratunga
, and M.
Chhowalla
, Appl. Phys. Lett.
93
, 233502
(2008
).9.
H. M.
Wang
, Z.
Zheng
, Y. Y.
Wang
, J. J.
Qiu
, Z. B.
Guo
, Z. X.
Shen
, and T.
Yu
, Appl. Phys. Lett.
96
, 023106
(2010
).10.
11.
O.
Klein
, Z. Phys.
53
, 157
(1929
).12.
M. I.
Katsnelson
, K. S.
Novoselov
, and A. K.
Geim
, Nat. Phys.
2
, 620
(2006
).13.
R.
Miller
, Y. Y.
Lau
, and J. H.
Booske
, Appl. Phys. Lett.
91
, 074105
(2007
).14.
F.
Guo
, A.
Mukhopadhyay
, B. W.
Sheldon
, and R. H.
Hurt
, Adv. Mater.
23
, 508
(2011
).15.
K. L.
Jensen
, J. Vac. Sci. Technol. B
13
(2
), 516
(1995
).16.
O. K.
Reity
, V. Y.
Lazur
, and S. I.
Myhalyna
, Proc. Inst. Math. NAS Ukraine
50
, 1429
(2004
).17.
V. Y.
Lazur
, O. K.
Reity
, and V. V.
Rubish
, Theor. Math. Phys.
143
, 559
(2005
).18.
L.
Wu
and L. K.
Ang
, Appl. Phys. Lett.
89
, 133503
(2006
).19.
Y. Y.
Lau
, Phys. Rev. Lett.
87
, 278301
(2001
).20.
R. J.
Umstattd
and J. W.
Luginsland
, Phys. Rev. Lett.
87
, 145002
(2001
).21.
L. K.
Ang
, T. J. T.
Kwan
, and Y. Y.
Lau
, Phys. Rev. Lett.
91
, 208303
(2003
).22.
L. K.
Ang
and P.
Zhang
, Phys. Rev. Lett.
98
, 164802
(2007
).© 2011 American Institute of Physics.
2011
American Institute of Physics
You do not currently have access to this content.
