Resonant tunneling diode based on graphene/h-BN heterostructure

0.51 MB·English

by  Nguyen Viet Hung

1
Resonant tunneling diode based on graphene/h-BN
heterostructure
V. Hung Nguyen, F. Mazzamuto, A. Bournel, and P. Dollfus
2 Abstract—In this letter, we propose the resonant tunneling
1 diode (RTD) based on a double-barrier graphene/boron nitride Air
0 (BN) heterostructure as device suitable to take advantage of
2 the elaboration of atomic sheets containing different domains graphene D
of BN and C phases within a hexagonal lattice. The device
n operation and performance are investigated by means of a self-
a consistent model within the non-equilibrium Green’s function BN substrate 10 nm
J
formalism on a tight-binding Hamiltonian. This RTD exhibits

3 a negative differential conductance effect which involves the
2 resonant tunneling through both the electron and hole bound
Fig. 1. Simulated device wherein the graphene sheets are deposited on a
states of the graphene quantum well. It is shown that the peak- h-BN substrate and two barriers are thus formed by the BN layers between
] to-valley ratio can reach the value of 4 at room temperature for thegraphenezones.
l
l gapless graphene and the value of 13 for a bandgap of 50 meV.
a
h Index Terms—Graphene, Boron nitride substrate, Resonant
- tunneling diode. In the field of quantum devices, graphene resonant tun-
s
e nelling diodes (RTDs) have been proposed and investi-
m gated previously [12], [13]. However, while the operation of
I. INTRODUCTION graphene nanoribbon (GNR) RTDs is strongly dependent on
.
t
a THE benefits of the extraordinary intrinsic transport prop- the device shape [12], the 2D graphene structure studied in
m [13] assumes that a bandgap opens in graphene epitaxially
ertiesofgraphene[1]areusuallyhinderedbythedefects
- of the supporting insulating substrate. Indeed, graphene on grown on SiC, which is a debated question, in addition to
d the substrate-induced mobility reduction. In this work, we
n various substrates such as SiO2 [2], SiC [3] or other high- thus propose a new graphene RTD based on graphene/h-BN
o κ insulators [4] shows a reduced carrier mobility, which is
heterostructures, where the two barriers are assumed to be
c usually attributed to surface roughness, charge surface states
[ formed by large bandgap h-BN zones, as schematized in Fig.
or surface optical phonons. Recently, it has been shown that
1. Though it may be useful and possible in case of Bernal
2 graphene reported on hexagonal boron nitride (h-BN) has
stackingon BNsubstrate [14],thebandgap ingraphene isnot
v higher mobility than on any other substrate [5], [6], [7]. A
8 necessary for this device to operate correctly.
mobility of 275 000 cm2/Vs at low temperature and 125 000
5 To investigate the electrical characteristics of this RTD, we
cm2/Vs at room temperature, i.e. as high as for suspended
2
have developed a self-consistent simulation code based on the
4 graphene, has even been reported [8]. It is due to the fact that
Green’s function formalism [15] to solve the tight-binding
. the surface of h-BN is flat, with a low density of charged
1 Hamiltonian suggested in [16].
0 impurities, does not have dangling bonds and is relatively
2 inert [5]. Hence, with the same atomic structure as graphene
1 and a 1.8% higher lattice constant [9] h-BN is becoming a II. PHYSICALMODELANDRESULTS
:
v very promising candidate as high bandgap insulating material In the structure schematized in Fig. 1, the BN barriers
i to make possible reaching the ballistic transport regime in
X are inserted in a monolayer graphene sheet reported on a
graphenedevicesevenatroomtemperatureandexploitingthe
h-BN substrate of thickness 10 nm and dielectric constant
r
peculiarities of graphene properties inherent in the massless
a (cid:15) = 3.5 [5]. We assume the transverse width along OY
r
and chiral character of charge carriers. Additionally, it has
direction to be much larger than the typical device length
been shown that it is possible to obtain atomic sheets con-
along the transport direction, i.e. a few tens of nanometers,
taining different domains of h-BN and C phases with various
so that the extension along the transverse direction can be
compositions [10], which offers the perspective of designing
considered through Bloch periodic boundary conditions [17].
new heterostructures and devices [11].
The length of the heavily doped regions at both device ends
andtheBNbarrierthicknessareassumedtobe17nmand1.3
V.HungNguyeniswiththeInstitutd’ElectroniqueFondamentale,CNRS,
nm, respectively. Our approach is based on the self-consistent
Universite´ Paris-Sud, UMR8622, 91405 Orsay, France and also with the
CenterforComputationalPhysics,InstituteofPhysics,VAST,P.O.Box429 solution of the 2D Poisson and Schro¨dinger equations. The
BoHo,Hanoi10000,Vietnam(e-mail:[email protected]). nearest-neighbor tight-binding Hamiltonian with parameters
F. Mazzamuto, A. Bournel and P. Dollfus are with the Institut
determinedin[16]issolvedusingtheGreen’sfunctionmethod
d’ElectroniqueFondamentale,CNRS,Universite´Paris-Sud,UMR8622,91405
Orsay,France. [15] in the ballistic approximation. In this simulation, the null
2
(a)
(a)
(b)
(b)
Fig. 2. (a) Self consistent data of potential energy and (b) corresponding Fig. 4. I-V characteristics (a) for different doped concentrations in two
electron density at different applied biases. The doped concentration in two contactsand(b)fordifferentwellwidthsD.D=4.3nmin(a)andND =
device ends ND = 5×1016m−2. The vertical-dashed lines indicate the 5×1016 m−2 in(b).
h-BNregions.
a strong negative different conductance (NDC) in both cases
Neumannconditionsareappliedatthe2D-domainboundaries of gapless and gapped graphene. In principle, the valley
(dashed line in Fig. 1). In the case of Bernal stacking, current in semiconductor RTDs occurs at a finite bias when
graphene reported on a h-BN substrate was shown to exhibit there is no available state in the emitter region for tunneling
a finite bandgap, but this bandgap vanishes when graphene via the confined states in the quantum well. This feature
is misaligned with respect to h-BN lattice [14]. Therefore, is essentially due to the finite bandgap of the emitter. The
unless otherwise stated, the zero bandgap of graphene was results obtained here are thus explained as follows. Though
assumedinourstudy.Allsimulationswereperformedatroom the energy bandgap of graphene may be actually zero for the
temperature. transverse momentum mode corresponding to the Dirac (or
√
In Fig. 2, the self-consistent solutions of potential and K) point (i.e., k ≡ K = 2π/3 3a ), a finite energy gap
y y √ c
electron density are plotted for different biases applied to the Eˆg(ky) = 2tCC(cid:12)(cid:12)1−2cos(cid:0)acky 3/2(cid:1)(cid:12)(cid:12) still appears for the
device with well width D = 4.3 nm and doping concentration other modes (see in ref. [19]), where t =2.5 eV [16] and
CC
in access regions N =5×1016 m−2. The low doping in the a isthecarbon-carbondistance.Forinstance,Eˆ (k )≈0.11
D c √ g y
central zone generates a potential barrier which controls the eV for k = K +0.008π/a 3 as seen in the diagram of
y y c
threshold voltage of the device. Differently from the conven- Fig. 3(a). Therefore, since the total current results from the
tionalRTDs[18],Fig.2(b)showsthatthelocalchargedensity contribution of many transverse momentum modes, the valley
is not symmetrical even at zero bias. This feature can be current occurs even in gapless graphene devices as seen in
understoodasaconsequenceofthedeviceasymmetrybetween Fig. 3(b) when the tunneling corresponding to finite values
the left graphene section coupled to nitrogen atoms and the of |k −K | is suppressed at high bias. Moreover, because
y y
right section bounded to boron atoms of the h-BN lattice. of the zero (or small) bandgap of graphene, it also shows
Besides, it is shown that the electron density accumulated in that the current valley in this device is much narrower than
the quantum well increases when increasing the bias voltage that in conventional RTDs [18]. Besides, when introducing
from0Vto0.4Vanddecreaseswhenfurtherraisingthebias a finite bandgap [12], [14] in graphene, both the valley and
from 0.4 V to 0.6 V. This feature is nothing but an effect of peakcurrentsarereducedwhilethepeak-to-valleycurrentratio
resonant tunneling [18] as described below. (PVR)increases.Thelatterreaches4and13forzerobandgap
We now go to explore the electrical behavior of the device. and Eg = 50 meV, respectively.
In Fig. 3, we display the I-V characteristics together with Especially, from Fig. 3, we find an interesting feature:
a diagram showing the LDOS and the corresponding trans- differentlyfromotherRTDs[12],[18]whereonlytheelectron
mission coefficient at V = 0.4 V. Indeed, the diagram in states in the quantum well (QW) are resonant, in this device,
bias
Fig. 3(a) shows that the large bandgap (≈ 3.9 eV [16]) in both electron and hole states can contribute to the current,
the h-BN barriers generates the quantization of carrier states as a consequence of the chirality of carriers in graphene. This
in the graphene quantum well, which gives rise to resonant pointhasbeenalsodiscussedin[20]andwasshowntoreduce
tunnelingeffects.Asaconsequence,theI-Vcurvescanexhibit the NDC effect in single potential barrier graphene structures.
3
E
FL
E
FR
(a) (b)
Fig.3. (a)DiagramshowingtheLDOSandthetransmissioncoefficientasafunctionofenergyatVbias=0.4Vand(b)I-Vcharacteristicsofthesimulated
device(forbothcasesofzeroandfinitebandgaps).Thefiguresin(a)areplottedforatransversalmomentumky (cid:54)=Ky (momentumattheDiracpoint).The
correspondingelectron/holepotentialprofilesaresuperimposedontheLDOS(solidlines).ThedopedconcentrationND =5×1016m−2.
Practically, as we can understand from Fig. 3(a), the confined the self-consistent solution of the 2D Poisson and Schrdinger
hole state in the QW makes the tunneling from hole states equations within the tight-binding. It was shown that the
in the emitter to electron states in the collector possible. This resonant tunneling and the resulting NDC behavior may in-
band-to-band (BTB) process contributes to the rapid increase volve both the electron and hole bound states of the graphene
of current beyond V = 0.25 V, in addition to the normal quantum well. The sensitivity of the electrical characteristics
bias
resonant tunneling of electrons via the electron state in the tothedeviceparametersasthedopingdensityofaccesszones,
QW. The vanishing of the latter process is responsible for theQWthicknessandthebarrierthicknesshasbeenanalyzed.
the valley regime in the I-V characteristics. When further Though the chiral band-to-band tunneling tends to reduce the
increasing V , the BTB tunneling through the first electron width of the valley region in the I-V characteristics and to
bias
level in the QW occurs, which leads to the rapid re-increase induce a rapid re-increase of current, the PVR of NDC effect
of current and a narrow current valley seen in Fig. 3(b). can reach the value of 4 at room temperature for gapless
To evaluate the role of device parameters on the RTD oper- graphene and the value of 13 for a small bandgap of 50
ation, we display in Figs. 4(a) and (b) the I-V characteristics meV which may result from Bernal stacking of graphene on
obtained for different doping concentrations N in the access h-BN. This work suggests that the engineering of graphene/h-
D
regions and for different well widths D, respectively. In fact, BN structures is opening a new route for high-performance
when increasing N , the energy spacing between the Fermi graphene devices.
D
level (zero-energy point) and the flat potential energy in the
device ends at zero bias increases. This results in shifting ACKNOWLEDGMENT
the valley region to high bias. Besides, the enhancement of
This work was partially supported by the French ANR
BTB resonant tunneling at high bias makes both the peak
through the projects NANOSIM-GRAPHENE (ANR-09-
and valley currents higher when increasing N . It finally
D NANO-016) and MIGRAQUEL (ANR-10-BLAN-0304).
reduces the PVR which reaches ∼ 3.9, 3.8, 2.2 and 1.8
for N = 2.5 × 1016, 5.0 × 1016, 7.5 × 1016, and 1017
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