Articles
https://doi.org/10.1038/s41928-018-0058-4
© 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
Field-effect transistors made from solution-grown
two-dimensional tellurene
Yixiu Wang
1,9
, Gang Qiu
2,3,9
, Ruoxing Wang
1,9
, Shouyuan Huang
4
, Qingxiao Wang
5
, Yuanyue Liu
6,7,8
,
Yuchen Du
2,3
, William A. Goddard III
6
, Moon J. Kim
4
, Xianfan Xu
3,4
, Peide D. Ye
2,3
* and
Wenzhuo Wu
1,3
*
1
School of Industrial Engineering, Purdue University, West Lafayette, IN, USA.
2
School of Electrical and Computer Engineering, Purdue University, West
Lafayette, IN, USA.
3
Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA.
4
School of Mechanical Engineering, Purdue University, West
Lafayette, IN, USA.
5
Department of Materials Science and Engineering, University of Texas at Dallas, Richardson, TX, USA.
6
The Resnick Sustainability
Institute, California Institute of Technology, Pasadena, CA, USA.
7
Materials and Process Simulation Center, California Institute of Technology, Pasadena,
CA, USA.
8
Texas Materials Institute, Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX, USA.
9
These authors
contributed equally: Yixiu Wang, Gang Qiu and Ruoxing Wang *e-mail: yep@purdue.edu; wenzhuowu@purdue.edu
SUPPLEMENTARY INFORMATION
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tuRe eLectR
oNIcS
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1
1.
Supplementary Note
s
Supplementary Note
1:
Discussion on the temperature effect
The
tellurene
synthesis
is
also influenced by
the reaction temperature
. The reaction was
carried out through the reduction of Na
2
TeO
3
by hydrazine in alkaline solution. The reaction
equat
ion can
be written
as follow
9
:
푇푒푂
3
2
−
+
3
퐻
2
푂
+
4
푒
−
→
푇푒
+
6
푂퐻
−
휑
휃
=
−
0
.
57
푉
푁
2
퐻
4
+
4
푂퐻
−
→
푁
2
↑
+
4
퐻
2
푂
+
4
푒
−
휑
휃
=
−
1
.
16
푉
where
휑
휃
is the standard electrode potential. They are measured at 298 K and under standard
pressure (
푝
휃
=
100
푘푃푎
). According to Nernst equation,
∆
퐺
=
−
푧퐸퐹
, where z is the number of
transferred electrons, E is the electromotive force, and F is the Faraday con
stant, which is 96500
C∙mol
-
1
, the overall reaction is spontaneous change because of the negative change of Gibbs free
energy, which seems not to be related to the temperature. However, the half reaction of
hydrazine oxidation is endothermic reactions, dri
ven by the increase of entropy.
The higher
temperature promotes
the forward reaction rate in this half reaction, leading to higher
productivity of 2D Te. It can be seen in
Supplementary Fig.
8
that the productivity dramatically
increased from 160
°C
to 180
°C
. But there is no significant difference between 180
°C
and 200
°C
, possibly due to the breaking of the weak van der Waals bonds between Te chains and the
damaging the 2D Te nanostructures by the high temperature with extra energy of Te atoms.
There may be
a balance between the improvement of the degree of reaction and the excessive
energy
decomposing the nanostructure. These results
warrant further in
-
depth investigations.
Thickness
-
mobility dependence fitting
The field
-
effect mobility displays a non
-
monot
onic dependence on Te film thickness. Thomas
-
Fermi screening effect
10
has been successfully applied to model the total conductance in a biased
2D material film with
a
ce
rtain
thickness, such as graphene,
MoS
2
,
and black phosphorus
11
-
13
. Here
we adopted the same method to fit the mobility
-
thickness relati
onship. Due to charge screening,
the mobility
μ
and carrier density
n
in thin films
are
no longer uniform but a function of the depth
from the interface
z
.
C
onsidering a slab with infinitesimal thickness
dz
at depth
z
, the total
conductance σ(z+dz) will be the conductance of this thin slab plus the total conductance of σ(z)
in series with two interlayer resistance
R
int
to form a resistor network as shown in
Fig. S
1
5
,
which
gives recursion equation
11
:
σ
(
z
+
dz
)
=
qn
(
z
)
μ
(
z
)
dz
+
σ
(
z
)
1
2
푅
푖푛푡
σ
(
z
)
+
1
2
푅
푖푛푡
(
1
)
By replacing
R
int
with
the
resistance
of unit length
r
multiplied by
dz
, we can reform the eq.
(1) into a differential equation:
2
푑
σ
푑푧
=
qn
(
z
)
μ
(
z
)
−
σ
(
z
)
2
r
(
2
)
The Thomas
-
Fermi screening effect goes that the carrier density and mobility decays as depth
increases with
a characteristic
screening length
λ
. T
herefore
we can express n(z) and μ(z) as
12
:
n
(
z
)
=
n
(
0
)
exp
(
−
푧
λ
)
(
3
)
μ
(
z
)
=
μ
푖푛푓
−
(
μ
푖푛푓
−
μ
0
)
exp
(
−
푧
−
푧
0
λ
)
(
4
)
w
here
μ
inf
and
μ
0
are the mobility at infinity and the interface respectively.
By substituting eq.3 and eq.4 back to eq.2, we can derive an expression for total conductance
σ(z).
Finally
,
we convert the total conductance into
effective
mobility with
the
simple
relation:
휇
퐹퐸
(
z
)
=
휎
(
푧
)
푄
푡표푡
(
5
)
w
here Q
tot
is the total gate
-
induced charge in the entire channel which can be estimated by
multiplying gate voltage by C
ox
.
This model fits well with our experiment
data
,
and the calculated Thomas
-
Fermi screen length
is 4.8
nm which is a reasonable value compared to other material systems such as MoS
2
and black
pho
sphorus.
Thickness
-
dependent on/off ratio in 2D Te FETs
Most of the
2D
FETs
are operated
in accumulation
-
mode or depletion
-
mode junction
-
less
type field
-
effect transistors with oxide as the
dielectric
. Their device operation is very similar to
III
-
V MESFETs or HEMTs and thin film transistors such as Indium
–
gall
ium
–
zinc oxide (IGZO) ones.
They are very different from the conventional Si MOSFETs which
are operated
in inversion
-
mode
and independent on film thickness. A simplified model to demonstrate the degradation of on/off
ratio with thickness is presented follo
wing. At on
-
state, the carrier transport
is mainly
contributed
by gate induced accumulated carriers located within a few nanometers from the
interface and the doped channel. Therefore, the on
-
state current varies several times for a wide
range of thickness
as confirmed by the
experimental
data. We define the off
-
state to be the
scenario where the Fermi energy is at charge neutral point at the interface, as shown in Figure 1
(for simplicity, we ignore Schottky contact impact and electron and hole mobility di
fference in
off
-
state). The surface potential or band bending at off
-
state is deduced to be around 0.15 V,
which is a reasonable estimation considering the 0.35 eV bandgap of
Te and
the fact that the
Fermi level of bulk Te is closer to its valence band. Un
der depletion approximation, we can then
derive the surface potential at
certain
depth x (distance to the interface) by solving Poisson’s
equation:
3
휑
푠
(
푥
)
=
푞
푁
퐴
2
휀
푠
휀
0
(
푥
−
푥
푑
)
2
,
where
휀
푠
is the permittivity of Te,
휀
0
is the vacuum permittivity,
푁
퐴
is the intrinsic doping level
and
푥
푑
is the maximum depletion width which is calculated to be
푥
푑
=
√
2
휀
푠
휀
0
휑
푠
(
0
)
푞
푁
퐴
⁄
≈
22
푛푚
,
cl
ose t
o experimentally observed thickness range where the on/off ratio starts to saturate. The
hole density at
푥
then ca
n be expressed by:
푝
(
푥
)
=
푝
0
exp
(
−
푞휑
푠
(
푥
)
푘푇
⁄
)
.
We plotted the surface potential and carrier distribution as a function of distance
푥
in Figure 2.
By integrating carrier density
푝
(
푥
)
with
푥
, the off
-
state sheet carrier density can be numerically
calculated
as a function of flake thickness t:
푛
2
퐷
_
표푓푓
(
푡
)
=
∫
푝
(
푥
)
푑푥
푡
0
,
as shown in Figure 3.
We can see that the off
-
state carrier sheet density increases by more than
4
orders as the thickness increases from monolayer to over 22 nm. Since
퐼
표푛
/
퐼
표푓푓
≈
1
/
퐼
표푓푓
∝
1
/
푛
2
퐷
_
표푓푓
(
푡
)
,
w
e
expect the on/off ratio degrades as carrier density increases in thicker flakes. If the film
thickness is larger than the maximum depletion width, the device cannot be turned off,
and
the
situation becomes trivial and obvious.
Noted that the above discussion is barely a simplified illustration why on/off ratio has such a
thickness
-
dependent trend whereas in real devices the situation can be much more complicated.
Figure 1.
Band diagram at along MOS stack direction. We define the off
-
state to be the scenario where the Fermi
level at the interface
is located
at the charge neutral level.
4
0
5
10
15
20
25
30
0.00
0.05
0.10
0.15
0
5
10
15
20
25
30
0.0
0.2
0.4
0.6
0.8
1.0
Potential |
F
|/V
Maximum depletion width
Carrier Concentration (10
18
cm
-3
)
distance (nm)
Figure 2.
The potential (upper) and carrier concentration (lower) distribution at off
-
state as a function of distance
from the
semiconductor
-
oxide
interface. The maximum depletion width is around 22.3 nm.
0
5
10
15
20
25
30
10
8
10
9
10
10
10
11
10
12
Off-state Sheet density (cm
-2
)
Thickness (nm)
Figure 3.
The 2D sheet density at
off
-
states for flakes with different thickness.
5
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Blöchl, P. E. Projector augmented
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Supplementary
Figures
Supplementary
Figure 1
Thickness
-
dependent bandgap for tellurene, calculated by HSE
functional.
T
he bandgap shows a linear dependence on the
inverse
number of layers, following
E
g
= 0.38 + 1.8/n (eV). As n goes to
infinit
y
, this relation gives a band gap of 0.38 eV for the bulk
Te, in good agreement with the experimental data. Given the interlayer distance ~ 3.91
Å
, this
relation can be rewritten as E
g
= 0.38 + 1.8*3.91/t (eV), where t is the thickness (
Å
).
7
Supplementary
Figure 2
Large
-
scale transfer and assembly of 2D tellurene into
(a)
networked
thin film through ink
-
jet printing and
(b)
monolayer thin film through LB method.
8
Supplementary
Figure
3
Optical and AFM images of tellurene flakes with various edge lengths
and thicknesses.
The
scale bar
is
20
m
.
9
Supplementary
Figure
4
Structural, composition, and quality
characterization
of tellurene.
a
,
Low
-
resolution TEM image of a tellurene flake. The contour contrast is due to bending of the
flake.
b
,
Simulated diffraction pattern.
c
,
XRD result of
2D Te crystals
show high crystallization
without impurity peaks in the material, in good agreement with
JCPDF card number:36
-
1452
for
tellurium
.
d
,
EDS spectra confirming
the
chemical composition of Te.
The Cu peak
s
in EDS spectra
come
from Cu TEM grid.