1
Field
-
effect transistors made from solution
-
grown two
-
dimensional tellurene
Yixiu Wang
1*
,
Gang Qiu
2
,
3
*
,
Ruoxing Wang
1
*
,
Shouyuan Huang
4
,
Qingxiao Wang
5
,
Yuanyue Liu
6
,
7
,
8, 9
,
Yuchen
Du
2, 3
,
William A. Goddard
III
6
,
Moon J. Kim
4
,
Xianfan Xu
3, 4
,
Peide
D.
Ye
2, 3
,
Wenzhuo Wu
1
, 3
1
School of
Industrial
Engineering,
Purdue University
,
West Lafayette
,
Indiana 47907
, USA
2
School of Electrical and Computer Engineering, Purdue University,
West Lafayette, Indiana
47907, USA
3
Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
4
School of
Mechanical
Engineering, Purdue University, West Lafayette, Indiana 47907, USA
5
Department of
Materials Science and
E
ngineering,
University
of Texas at Dallas, Richardson,
Texas
75080, USA
6
The Resnick Sustainability Institute, California Institute of Technology, Pasadena, California
91125, United States
7
Materials and Process Simulation Center
, California Institute of
Technology, Pasadena,
California 91125, United States
8
Department of Mechanical Engineering, The University of Texas at Austin, Texas 78712
, United
States
9
Texas Materials Institute, and Department of Mechanical Engineering, The University of Texas
at Aust
in, Texas 78712
, United States
e
-
mail:
Correspondence and requests for materials should be addres
sed to W
.
Z
. W
(
w
enzhuowu@purdue.edu
)
or
P
.
D
.
Y.
(
yep@purdue.edu
)
*
These authors contributed
equally to this work.
2
Abstract
The reliable production of two
-
dimensional crystals is essential for the development of
new technologies based on 2D materials. However, current synthesis methods suffer from a
variety of drawbacks, including limitations in
crystal size and stability. Here, we report the
fabrication of large
-
area, high
-
quality 2D tellurium (tellurene) using a substrate
-
free solution
process. Our approach can create crystals with a process
-
tunable
thickness, from monolayer
to tens of
nanomet
r
e
s
, and with lateral sizes of up to 100 μm. The chiral
-
chain van der Waals
structure of tellurene gives rise to strong in
-
plane anisotropic properties and large thickness
-
dependent shifts in Raman vibrational modes, which is not observed in other 2D layered
materials. We also fabricate tellurene field
-
effect transistors, which exhibit air
-
stable
performance at room temperature for over two months, on/off ratios on the order of 10
6
and
field
-
effect mobilities of around 700 cm
2
/Vs. Furthermore, by scaling
down
the channel
length and integrating with high
-
k dielectrics, transistors with a significant on
-
state current
density of 1 A/mm are demonstrated
.
Main
The continuing development of two
-
dimensional materials, be it the exploration of new
science
1
-
3
or the implementation of new technologies
4
-
8
, requires reliable methods of
synthesising 2D crystals. Whether current approaches can be
scaled up though remains
uncertain
9,10
and are restricted
by factors such as growth substrates and conditions
11
-
13
, small
crys
tal sizes
14
and the instability of the synthesized material
s
11,15,16
.
3
Group VI
t
ellurium
(Te)
has
a
unique chiral
-
chain
crystal lattice
where
individual
helical
chain
s
of Te atoms
are stacked together by van der Waals
(vdW)
type
bonds
and
spiral around
axes parallel to the
[
0001
]
direction
at the
centre
and corners of the hexagonal elementary
cell
17
(Fig. 1a).
Ea
ch
tellurium atom
is covalently bonded
with
its
two near
est
neighbours
on the
same chain
.
Earlier studies
revealed
bulk Te has
small effective mass
es
and
high
hole
mobi
lit
ies
due to
spin
-
orbit
coupling
18
.
The lone
-
pair and anti
-
bonding orbitals give rise to a
slightly
indirect bandgap in the infrared r
egime (~0.35 eV) in bulk Te
19
,
which has a
conduction band
minimum (CBM)
located at the H
-
point
of the Brillouin zone
,
and a
valence band maximum
(VBM)
that
is slightly shifted from the H
-
point along the chain
direction, giv
ing rise to hole
pockets near H
-
point
20
.
When
the
thickness
is reduced
, the
indirect
feature becomes more
prominent, as shown by our first
-
principles calculatio
ns (see Methods for computation details).
For example, the VBM of 4
-
layer Te is further shifted to (0.43, 0.34) (in the unit of
the
surface
reciprocal
cell), while CBM remains at (1/2, 1/3) (Fig. 1b
inset
). Accompanied by the shift of
VBM, the band gap
also increases (Methods, Supplementary Fig. 1), due to the quantum
confinement effect, and eventually reaches ~ 1 eV for monolayer Te
21
.
T
e
has
other
appealing
properties,
e.g.
,
p
hotoconductivity
22
,
t
hermoelectric
ity
20
,
and
piezoelectricity
23
,
for
ap
plications
in
sensors
,
optoelectronics
,
and energy devices.
A wealth of
synthetic
methods
ha
s
been
developed to
derive
Te
nanostructures
24
-
26
,
which
favour
the
1D form due to the
inherent
structural
anisotropy
in
Te.
Much
less
is
known
about the
2D form
of Te and
related
properties.
Synthesis
and Structural Characterization
of 2D Tellurene
In this article,
we
report
a substrate
-
free solution process
for synthesizing
large
-
area, high
-
quality 2D
Te
crystal
s
(termed tellurene) with
a
thickness
of
a monolayer to tens of
nanometres
4
and a
unique chiral
-
chain vdW structure
which is
fundamentally different from the layered vdW
materials.
We use the term
X
-
ene
to describe
2D
form
s
of elemental materials without
considering the specific bo
nding
21,27
.
The
samples are grown
through the reduction of sodium
tellurite (Na
2
TeO
3
)
by hydrazine hydrate (N
2
H
4
)
in an
alkaline
solution
at temperatures from
160
-
200
o
C
,
with the presence of
crystal
-
face
-
blocking ligand
polyvinylpyrrolidone
(PVP) (see
Methods).
Fig.
1c
inset
shows the optical image of a typical tellurene solution dispersion after
reactions at 180
o
C for 20 hours when
the
Na
2
TeO
3
:
PVP
mole ratio is
52.4:
1 (Methods).
The 2D
Te flakes can be transferred and assembled at large scale into a single layer continuous
thin film
through a Langmuir
-
Blodgett
(LB)
process
28
or a networked continuous thin film
8,29,30
through
ink
-
jet printing (Methods), onto various substrates (
Supplementary
Fig. 2) for future
characterization and device integration.
It should
be noted
that the current LB approaches still
lack the sort of desired capabilities
in terms o
f
the film continuity and uniformity, compared to
other methods such as ink
-
jet printing
8,29,30
, for assembling
solution
-
derived 2D materials into
high
-
performance
device. These preliminary results (Supplementary Fig. 2) show potential and
warrant more systematic work for future large
-
scale assembly and applications of solution
-
derived 2D function
al materials.
Individual 2D flakes have edge lengths ranging from 50 to 100
m, and thicknesses from
10
to
100 nm (
Fig
s
. 1
d
and
Supplementary
Fig. 3
).
The structure, composition, and quality of these
tellurene crystals have been analyzed by high angle
annular dark field
scanning
transmission
electron microscopy (HAADF
-
STEM),
high
-
resolution transmission electron microscopy
(HRTEM),
energy dispersive X
-
ray spectroscopy (EDS), and X
-
ray diffraction (XRD)
(
Fig. 1
e
,
f
, and
Supplementary
Fig. 4
)
.
Fig. 1e
shows
a typical
atomically
-
resolved
HAADF
-
STEM image
of
5
tellurene
flake
(see Methods).
The helical
chains
and
a
threefold screw symmetry along <0001>
are visible
(
Fig. 1
e
)
.
The interplanar spacings are 2.2
Å
and 6.0 Å , corresponding to Te (1
2
1
0)
and (0001
) planes
31
, respectively.
Fig. 1
f
shows
the
selective area electron diffraction (SAED)
pattern along the [10
1
0] zone axis, which is perpendicular to the top surface of the flake. No
point defects or dislocations were observed over a large area within single crystals
(
Supplementary
Fig. 4).
EDS
result confirmed the chemical composition of Te (
Supplementary
Fig. 4). Similar characterizations and analyses of dozens of
2D Te
flakes with different sizes
indicate that all samples grow laterally along the <0001> and <1
2
1
0> directions, with
the
vertical stacking along the <10
1
0> directions (Fig. 1
g
).
Synthesis Mechanism
and
Geometric
Control
for 2D Tellurene
The
con
trolled
PVP
concentration
is the key
for
obtaining
2D
telluren
e
. Fig. 2a shows the
productivity (see
Methods
) of tellurene grown at 180
o
C
with time for a
broad
range of
Na
2
TeO
3
/PVP mole ratios.
When a smaller amount of PVP
is
used
, the first
2D structures
occur
after a shorter reaction time (
Fig. 2a,
Supplementary
Fig
.
5
).
A closer
examination
of
reactions
with different PVP concentrations
reveals
an
intriguing
morphology evolution
in growth
products
with time
.
For each PVP concentration, the
initial
growth products a
re dominantly 1D
nanostructures
(
Fig. 2b,
Supplementary
Fig.
5
)
, similar to
previous reports
24
-
26
.
After a
certain
period
of reaction
,
structures
possessing
both 1D and 2D
characteristics start to emerge (Fig.
2b,
Supplementary
Fig.
5
).
TEM characterizations indicate that
the long axes
(showing 1D
characteristics) of these
flakes
are
<0001>
oriented
,
and
the
lateral protruding
regions (showing
2D characteristics) grow along the <1
2
1
0
> directions,
with the {10
1
0} facets as the top/bottom
surfaces (
Supplementary
Fig. 6).
The
2D
regions
are enclosed
by
edges
with atomic level step
6
roughness
(
Supplementary
Fig. 6
)
.
These high energy edges are not specific to certain planes
during the intermediate states.
These structures also have
more uneven surfaces
compared to
2D tellurene (
Supplementary
Fig. 6
)
, further
manifesting
their
intermediate
nature.
Finally,
the
ratio of
2D tellurene flakes which have a straight {1
2
1
0}
edge
increases
with
a reduction
in
1D
and
intermediate
structures (
Supplementary
Fig.
5
)
and reaches a plateau after an extended
growth,
e.g.
~30 hours (Fig. 2a,
Supplementary
Fig. 5
).
The
growth
with a lower level of PVP has
a smaller
final productivity (Fig. 2a,
Supplementary
Fig. 5
)
.
The observed
morphology evolution
suggests that
the balance between the kinetic and thermodynamic growth
dictates the
transformation from 1D structures to 2D forms
(Fig. 2b)
.
In the initial growth, PVP
is
preferentially adsorbed
on the {10
1
0} surfaces of the
nucleated
seeds
26
, which
promotes
the
kinetic
-
driven 1D
gro
wth
(
Supplementary
Fig. 5
)
.
When the
reaction continues
,
{10
1
0} surfaces
of the formed structures
would
become partially covered due to the
insufficient PVP capping
.
Since {10
1
0}
surfaces have the lowest free energy
in tellurium
32
,
the
growth
of
{10
1
0}
surfaces
along the <1
2
1
0
> direction
significantly increases
through the
thermodynamic
-
driven
assembly,
giving rise to the
observed intermediate structures.
The enhanced growth along the <1
2
1
0
>
directions
together with the continued
<0001>
growth
(
Supplementary
Fig. 6)
lead
s
to the
formation of 2D tellurene
(Supplementary
Fig. 5
, Fig. 2b
)
.
The
sizes and thicknesses of tellurene can
also
be
effectively
modulated
by
controlling
the
ratio between
sodium tellurite
and PVP
(Fig. 2c
,
Supplementary
Fig. 7
)
.
The width of tellurene
monotonically decreases with the
reduction
of PVP level
;
the thickness
is
minimized
when
a
medium level of PVP
is used
(
e.g.
,
Na
2
TeO
3
/PVP ratio
~
52.4/1
, Group #12
in Fig. 2c
and
Supplementary
Fig. 7
)
, and increases with both the increase and decrease of PVP
(Fig. 2c
).
With
7
a small amount of PVP,
the solution
is supersaturated
with Te
source
,
and
homogeneous
nucleation
of Te
can occur
in large scale, consuming
re
source
for
subsequent
growth
. As a
result, the
Ostwald
ripening of
Te
nuclei
is shortened
, and the final
tellurene crystals
have
smaller
size
s
compared to samples grown
at
high
er
PVP
c
oncentration
s
.
The low PVP level
also
leads to more significant growth along
thickness
directions.
On the other hand,
when the PVP
level is high,
the fewer nucleation events allow the
sufficient supply of Te source for
subsequent growth, leading to
the increased width and thickness.
Also
, the productivity of
tellurene
increases with the reaction temperature from 160
o
C to 180
o
C (
Supplementary
Fig.
8
).
This
is likely
because
higher temp
erature promotes the forward reaction rate in the
half
reaction of endothermic hydrazine oxidation (see Supplementary Notes). However, when
temperature increases from 180
°C
to 200
°C
, the
possible
breaking of the van der Waals bonds
between Te chains by the excessive energy
could lead to the
saturated
productivity.
T
ellurene crystals with
a
thickness
smaller
than 10 nm
to ultimately monolayer
structure
can
be
further
derived
through a
solvent
-
assisted post
-
growth thinning process
(see Methods
).
The thickness of tellurene decreases with time after acetone
is introduced
into the growth
solution
(
Supplementary
Fig.
9
).
After 6
hour
s
, the average thickness of tellurene is reduced to ~
10 nm
, with the
thinnest flake down to
4 nm
thick
(~
10
layers) (
Supplementary
Fig. 9
).
Due to
the
poor solubility in acetone, PVP molecules
tend
to desorb from the
tellurene
and
undergo
aggregation
33
, giving
rise to
the sediment of
tellurene
over the time
in acetone
(
Supplementary
Fig. 9
).
Lacking the protection of PVP
, the
tellurene
surfaces
get
exposed
and react with
the
alkaline
growth solution
(
pH ~
11.5
)
34
,
leading to the reduced thickness.
We have also
performed control experiments
using
other types of solvents
in the growth solution
8
(
Supplementary
Fig.
10
)
, the results of which
suggest that
PVP solubility i
n the solvent
significantly affects the
above
process.
L
arge
-
area (
up
to 100
-
m
in
lateral
dimensions
)
tellurene crystals with monolayer, bi
-
layer, tri
-
layer
and few
-
layer
thicknesses
can be
further
obtained
(Fig. 2d,
Supplementary
Fig. 11
)
,
by controlling
the pH value
s
of the tellurene
dispersion solution in the above post
-
growth thinning process
(see Methods, Fig. 2d,
Supplementary
Fig. 12)
.
Thickness
-
and Angle
-
dependent Raman Spectra
These high
-
quality ultrathin tellurene crystals with
controlled
thicknesses provide an ideal
system to explore their intrinsic properties in the 2D limit.
We first characterized the optical
properties of as
-
synthesized tellurene
with a wide range of thickness
(
from
a
monolayer
to
37.4 nm
)
by angle
-
resolved
polarized
Ra
man spectroscopy at
room temperature (see
Methods). The incident light comes in along the [
10
1
0
] direction and
is polarized
into the
[0001] helical chain direction of the tellurene.
The Raman spectra
of
tellurene samples with
different thickness
(Fig. 3a)
exhibits
three main Raman
-
active modes,
with
one
A
-
mode
and two
E
-
modes
which correspond
to
the
chain expansion in basal plane, bond
-
bending around [
1
2
10
]
direction and asymmetric stretching mainly along [0001] helical chain
35
, respectively
(
Supplementary
Fig. 1
3
).
For the 2D Te samples
thicker
than
20.5 nm,
t
hree Raman
-
active
modes locating at 92 cm
-
1
(E
1
transverse (TO) phonon
mode), 121 cm
-
1
(
A
1
-
mode) and
143
cm
-
1
(E
2
-
mode) were identified (Fig.
3a
), which agrees
well with previous observations in bulk
and
nanostructured
tellurium
36
-
38
,
indicating that although
these thicker crystals possess
2D
morphology
, the
ir
symmetric properties
can still be characterized as
bulk.
The
appreciable
effective dynamic charge
induced for
the
E
1
mode
in tellurium
leads to
a
split of E
1
doublets at
9
92
cm
-
1
and
105
cm
-
1
for transverse (TO) or longitudinal (LO) phonons
, respectively
37
.
The
absence of E
1
(
L
O
)
mode
in
our observed results for
2D Te thicker than
20.5 nm
, similar to
previous
reports
on
bulk and nanostructured tellurium
36
-
38
,
may be attributed to
the
different
signs in the deformation potential and electro
-
optic contribution to the Raman scattering
tensor,
which gives rise
to
the
cancellation if both contributions have the same magnitude
39
.
As
the thickness
decreases
from 20.5 nm to 9.1 nm (Fig.
3a
), the deformation potential
in tellurene
lattice
increase
s
while the electro
-
optic effect weaken
s
40
, leading to the appearance of
E
1
(LO)
mode
in
the
Raman spectra
for
2D Te
crystals
with
intermediate
thickness
.
When
the 2D Te’s
thickness
further
reduces
(smaller than 9.1 nm i
n Fig. 3a)
, the degeneracy in
the
E
1
TO and LO
modes
occurs with peak broadening, possibly due to the intra
-
chain atomic displacement, the
electronic band structure
changes
and the symmetry assignments for each band
41
, all of which
are affected by the sample thickness
.
When
tellurene’s
thickness
decreases
, there are
significant
blue
-
shift
s
for both A
1
(shift
to
136
cm
-
1
for monolayer)
and E
2
modes
(shift to
149
cm
-
1
for monolayer)
(Fig. 3a)
. The
hardened
in
-
plane
E
2
vibration
mode
in
thinner
tellurene
, similar to
reported observations for
black
phosphorus
42
and MoS
2
43
,
,
may be
attributed to the
enhanced
interlayer long
-
range Coulombic
interactions
when thinned down
.
The
observed
blue
-
shift for
the
A
1
mode
in
2D Te
,
in
strong
contrast to 2D layered
vdW
materials
which
usually witness red
-
shift for the
out
-
of
-
plane
vibration mode when thinned down
15,42,43
,
is thought to be closely related to
the
unique
chiral
-
chain
vdW
structure of
tellurene
.
When thinned down, t
he lattice deformation
within the 2D
plane
g
ave
rise to the
attenuated inter
-
chain vdW interaction
s
and
en
hanced intra
-
chain
covalent
interactions
in
the
individual
tellurene layer
, leading
to
more effective
restoring forces
10
on
tellurium
atoms
and hence hardened out
-
of
-
plane A
1
vibration mode
(
Supplementary
Fig.
13)
.
Such unique
structure
of
tellurene
also
results in
the
giant
thickness
-
dependent
shift
in
Raman vibrational modes,
which is unseen in
2D
layered
vdW materials
42
-
44
.
The
interaction
betwe
en
the
substrate
(SiO
2
/Si)
and 2D Te flakes
could
also contribute to the
hardened
A
1
and
E
2
modes
36
.
The
stiffening
of vibrational
modes in monolayer tellurene (Fig. 3a) is consistent
with
its
structure
reconstruction
where
extra
bonds
are
formed
between
neighbouring
chains
in
the single layer tellurium
21,27,45
.
Reduced in
-
plane symmetry in the
chiral
-
chain
vdW
structure of tellurene indicates a
strong
in
-
plane anisotropy for
its
material properties
.
We further
characterized the anisotropic
optical properties of as
-
synthesized tellurene with three
different
thickness
es
(
28.5 nm, 13.5
nm
,
and 9.7 nm
)
by angle
-
resolved
polarized
Raman spectroscopy at
room temperature (see
Methods).
By rotating the tellurene flake
s
in steps of
15
o
, we observed the changes in the
angle
-
resolved Raman peak intensities (Fig.
3b
,
Supplementary
Fig
s
. 14a, 15a
). We extracted
the peak intensities of different
modes
by fitting with
Lorentz
function and plotted them into
the corresponding polar figures (Figs.
3c
-
f
,
Supplementary
Figs. 14b
-
e
, 15b
-
d
) (see Methods).
While all the modes change in intensity with the polarization angle, we find that the peak
for
the
A
1
mode
in all samples exhibits the largest sensitivity
to the relative orientation between
the [0001] direction and the polarization of the excitation laser (middle panel
s
of
Fig. 3b,
Supplementary
Figs. 14a, 15a
).
It is worth to note that the direction
of
maximum intensity in
A
1
polar plot changes
with the sample
thickness. More specifically,
A
1
polar plots for
the 13.5
nm and 28.5 nm sample
s
show
the maximum intensity at 90
°
and 270
° along
the
[1
2
1
0
]
direction
(
Fig. 3e,
Supplementary
Fig.
15c
)
. However, when the thickness decreases to 9.7 nm,
11
the
maximum intensity
direction
switches to 0
°
and
180
° along
the
[0001] direction
(
Supplementary
Figs. 14d
)
.
A s
imilar
phenomenon
also occurs
for E
1
-
L
O mode
s in
the 13.5 nm
and 9.7 nm samples (
Fig. 3d,
Supplementary
Figs. 14c
)
.
Such
thickness
-
dependent
anisotropic
Raman scattering could
be attributed
to the different absorption spectral range in [0001]
and
[1
2
1
0
]
directions
46
and anisotropic interference effect
41
.
The angle
-
resolved Raman
results
also
confirm that the helical Te atom chains in the as
-
synthesized tellurene are oriented
along the growth direction of the tellurene flake, which matches the TEM results (Fig. 1e).
Device Implementation of
Tellurene Field
-
effect Transistors
Finally, w
e
explor
ed
the electrical performance of
tellurene
field
-
effect
transistors
(FETs)
to
demonstrate its
great
potential for logic electronics application
.
Back
-
gate devices were
fabricated on high
-
k dielectric
substrates
and s
ource
/
drain regions were patterned by
electron beam lithography
with the channel parallel to the
[0001]
direction of tellurene
(details
see Methods)
.
We chose Pd/Au (50/50 nm) as metal contacts since Pd has
relatively high work
function that can
reduce the contact resistance in
p
-
type transist
ors
47
-
49
.
L
ong channel devices
were first
examined
(channel length 3
m) where the
contact
resistance
is negl
igible, and
the
transistor behavior
is dominated by
intrinsic electrical properties of channel material.
Fig.
4a
show
s
the
transfer
curve of a typical 7.5
-
nm
-
thick
2D
Te
FET
measured at room temperature.
The device exhibits
p
-
type characteristics with
slight
ambipolar transport behavior due to its
narrow bandgap na
ture, with large drain current over
300
mA/mm
(see Supplementary
Fig.
23)
and high on/off ratio
on the order of
~10
5
.
The
p
-
type behavior originates from the high level of
Te
valance band edge, as shown by our first
-
principles calculations (
Supplementary
Fig. 16).
Meanwhile, the process
-
tunable thickness of tellurene allows the modulation of electrical
12
performance in tellurene transistors.
Overall,
important
metrics of tellure
ne
-
based transistors
such as on/off ratio, mobility, and on
-
state current
level
are superior or comparable to
transistors based on other 2D materials
11,15,16,50
.
We further
investigate
d
the thickness
dependence of two key metrics of
device
performance,
namely
on/off ratios and field
-
effect
mobilities
,
for more than 50 2D Te long channel devices with flake thicknesses ranging from
over 35 nm down to
a
monolayer
(~0.5 nm
)
, to elucidate the transport mechanism of
2D Te
FETs
(Fig. 4b)
. The linear behavior of the output curves in the low V
ds
region
(Supplem
entary
Fig.
23)
suggests that the contact resistance is low
(see Supplementary Notes and
Supplementary Fig. 19 for the extracted contact resistance)
which
ensures the sound
ness
of
the
field
-
effect mobility
extraction
from the slope of the linear region of
the transfer curves (see
Methods).
The f
ield
-
effect mobilities
of 2D Te transistors peak
with ~700 cm
2
/Vs at room
temperature at around 16 nm thickness and decreases gradually with the further increase of
the thickness.
The transfer curves of devices with
thin
thickness of 2.8 nm (~ 6 layers), 1.7 nm (~
4 layers), 1.0 nm (bi
-
layer) and 0.5 nm (monolayer)
are included
in
Supplementary Fig. 24.
A
benchmark comparison with black phosphorus, which is also a narrow bandgap p
-
type 2D
material, shows that solution
-
synthesized 2D Te has ~ 2
-
3 times higher mobility than black
phosphorus when the same device structure, geometry, and mobility extraction method are
adopted
15
(Supplementary Fig. 21).
This
thickness
-
dependence
is similar to
other
layered
materials that experie
nce screening and interlayer coupling
15,16
(Supplementary Notes and
Supplementary Fig. 20). The field
-
effect mobility is also affected by the contribution
of the
carriers
from layers
near the semiconductor
-
oxide
interface
. Thinner samples are more
susceptible to the charge impuritie
s at the interface and surface scattering, which explains the