The characteristics of tunnel junctions formed between n- and p-doped graphene are investigated theoretically. The single-particle tunnel current that flows between the two-dimensional electronic states of the graphene (2D–2D tunneling) is evaluated. At a voltage bias such that the Dirac points of the two electrodes are aligned, a large resonant current peak is produced. The magnitude and width of this peak are computed, and its use for devices is discussed. The influences of both rotational alignment of the graphene electrodes and structural perfection of the graphene are also discussed.

1.
T.
Ando
,
A. B.
Fowler
, and
F.
Stern
,
Rev. Mod. Phys.
54
,
437
(
1982
).
2.
J. P.
Eisenstein
,
L. N.
Pfeiffer
, and
K. W.
West
,
Appl. Phys. Lett.
58
,
1497
(
1991
).
3.
J. P.
Eisenstein
,
T. J.
Gramila
,
L. N.
Pfeiffer
, and
K. W.
West
,
Phys. Rev. B
44
,
6511
(
1991
).
4.
K. M.
Brown
,
E. H.
Linfield
,
D. A.
Ritchie
,
G. A. C.
Jones
,
M. P.
Grinshaw
, and
M.
Pepper
,
Appl. Phys. Lett.
64
,
1827
(
1994
).
5.
T.
Kawamura
,
H. A.
Fertig
, and
J. P.
Leburton
,
Phys. Rev. B
49
,
5105
(
1994
).
6.
E.
Tutuc
,
S.
Melinte
,
E. P.
De Poortere
,
R.
Pillarisetty
, and
M.
Shayegan
,
Phys. Rev. Lett.
91
,
076802
(
2003
).
8.
J. P.
Eisenstein
and
A. H.
MacDonald
,
Nature
(London)
432
,
691
(
2004
).
9.
S. K.
Banerjee
,
L. F.
Register
,
E.
Tutuc
,
D.
Reddy
, and
A. H.
MacDonald
,
IEEE Electron Device Lett.
30
,
158
(
2009
).
10.
D.
Basu
,
L. F.
Register
,
D.
Reddy
,
A. H.
MacDonald
, and
S. K.
Banerjee
,
Phys. Rev. B
82
,
075409
(
2010
).
11.
S.
Luryi
,
Appl. Phys. Lett.
52
,
501
(
1988
).
12.
J.
Bardeen
,
Phys. Rev. Lett.
6
,
57
(
1961
).
13.
J.
Tersoff
and
D. R.
Hamann
,
Phys. Rev. B
31
,
805
(
1985
).
14.
The κ term in tunneling has a typical form of [(2mφ/2)+k||2]1/2, where φ is a barrier height and k|| is the parallel momentum. For graphene, the latter is essentially equal to the momentum at the K or K’ point (i.e., 4π/3a).
15.
R. M.
Feenstra
,
J. A.
Stroscio
, and
A. P.
Fein
,
Surf. Sci.
181
,
295
(
1987
).
16.
N. H.
Shon
and
T.
Ando
,
J. Phys. Soc. Jpn.
67
,
2421
(
1998
);
Y.
Zheng
and
T.
Ando
,
Phys. Rev. B
65
,
245420
(
2002
).
17.
Actually, the situation of zero doping is unphysical for all voltages except V=0, due to the charging effects in the graphene electrodes described in Sec. II E. Nevertheless, it is perfectly fine to consider the zero doping case in the limit of zero geometrical capacitance for the purpose of introducing the computation method for the tunnel current, recognizing that for any realistic computation the doping will be nonzero.
18.
The voltage V is applied to some location in each electrode that is removed from the vicinity of the junction. Within each graphene electrode, the charge density and electrostatic potential both vary as a function of position from those contact points to the junction itself.
19.
The formulas of Secs. II A–II D are applicable for the case ΔE>0. If ΔE<0 is found from Eq. (30), then this situation can be handled using the formulas of Secs. II A–II D simply by interchanging the roles of the two electrodes (so that ΔE and V both change signs).
20.
I.
Gierz
,
C.
Riedl
,
U.
Starke
,
C. R.
Ast
, and
K.
Kern
,
Nano Lett.
8
,
4603
(
2008
).
21.
K.
Brenner
and
R.
Murali
,
Appl. Phys. Lett.
96
,
063104
(
2010
).
22.
C.
Coletti
,
C.
Riedl
,
D. S.
Lee
,
B.
Krauss
,
L.
Patthey
,
K.
von Klitzing
,
J. H.
Smet
, and
U.
Starke
,
Phys. Rev. B
81
,
235401
(
2010
).
23.
S.
Lara-Avila
,
K.
Moth-Poulsen
,
R.
Yakimova
,
T.
Bjørnholm
,
V.
Fal’ko
,
A.
Tzalenchuk
, and
S.
Kubatkin
,
Adv. Mater.
23
,
878
(
2011
).
24.
K. S.
Novoselov
,
A. K.
Geim
,
S. V.
Morozov
,
D.
Jiang
,
Y.
Zhang
,
S. V.
Dubonos
,
I. V.
Grigorieva
, and
A. A.
Firsov
,
Science
306
,
666
(
2004
).
25.
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.
Home
,
Nature Nanotech.
5
,
722
(
2010
).
26.
A.
Nagashima
,
N.
Tejima
,
Y.
Gamou
,
T.
Kawai
, and
C.
Oshima
,
Phys. Rev. B
51
,
4606
(
1995
).
27.
A.
Reina
,
X.
Jia
,
J.
Ho
,
D.
Nezich
,
H.
Son
,
V.
Bulovic
,
M. S.
Dresselhaus
, and
J.
Kong
,
Nano Lett.
9
,
30
(
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
,
Nature
(London)
457
,
706
(
2009
).
29.
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
,
Science
324
,
1312
(
2009
).
30.
J.
Hass
,
J. E.
Millán-Otoya
,
P. N.
First
, and
E. H.
Conrad
,
Phys. Rev. B
78
,
205424
(
2008
).
31.
F.
Varchon
,
P.
Mallet
,
L.
Magaud
, and
J.-Y.
Veuillen
,
Phys. Rev. B
77
,
165415
(
2008
).
You do not currently have access to this content.