of 19
Gate
-Variable Mid
-Infrared Optical Transit
ions in a
(Bi
1-x
Sb
x
)
2
Te
3
Topological Insulator
1
William S. Whitney,
2,3
Victor W. Brar,
4
Yunbo Ou,
5,6
Yinming Shao,
2
Artur R. Davoyan,
5,6
D.
N. Basov,
7
Ke He,
7
Qi-Kun Xue and
2
Harry A. Atwater
1
Department of Physics, California Institute of Technology
, Pasadena, California 91125, USA
2
Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena,
California 91125, USA
3
Kavli Nanoscience Institute, California Institute of Technolo
gy, Pasadena, California 91125,
USA
4
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, The Chinese
Academy of Sciences, Beijing 100190, China
5
Department
of Physics
, University of California
-San Diego, La Jolla, California 92093, USA
6
Department of Physics, Columbia University, New York, NY
7
State Key Laboratory of Low
-Dimensional Quantum Physics, Department of Physics, Tsinghua
University, Beijing 100084, China
*Corresponding author: Harry A. Atwater (
haa@caltech.edu
)
Abstract:
We report mid
-infrared spectroscopy measurement
s of an electrostatically gated topological
insulator, in which we observe several percent modulation of transmittance and reflectance of
(Bi
1-x
Sb
x
)
2
Te
3
films as gating shifts the Fermi level.
Infrared transmittance measurements of
gated (Bi
1-x
Sb
x
)
2
Te
3
films were enabled by use of an epitaxial lift
-off meth
od for large
-area
transfer of topological insulator
films from infrared
-absorbing SrTiO
3
growth substrates to
thermal oxidized silicon substrates. We combine these optical experiments with transport
measurements and
angle
-resolved photoemission spectroscopy to identify the observed spectral
modulation as a gate-
driven transfer of spectral wei
ght between both bulk and topological
surface channels and i
nterband and intraband channels. We develop a model for the complex
permittivity of gated (Bi
1-x
Sb
x
)
2
Te
3
, and find a good match to our experimental data. These
results open the path for layered topological insulator materials as a new candidate for tunable
infrared optics and highlight
the possibility of switching
topological optoelectronic phenomena
between bulk and spin-
polarized surface regimes.
1
Topological insulators –
narrow band-
gap semiconductors that exhibit both an insulating
bulk and metallic Dirac surface states – have been found experimentally in the past several years
to display a remarkable range of new electronic phenomena.
1-4
In addition, these Dirac surface
states have been predicted to host unique and technologically compelling optical and
optoel
ectronic behavior
. Some of these effects have been experimentally demonstrated –
giant
magneto
-optical effects, helicity
-dependent photocurrents
and more
– but many others, including
gapless infrared photodetection, gate
-tunable, long-
lived Dirac plasmons
and hybrid spin-
plasmon modes, remain elusive
.
5-16
One of the most fascinating features of topological insulator systems is the coexistence
and interplay of massless Dirac electrons and massive bulk carriers.
While systems like the
bismuth telluride family of materials are strong topological insulators, they are also structurally
two
-dimensional, layered Van der Waals semiconductors.
17
,18
For technologies like tunable
optics, for which the graphene Dirac system is promising, excitations of both Dirac electrons and
these low effective mass bulk carriers are equally compelling
.
19
-22
The low density of states of
both of these classes of
carriers and availability of thin, gate
-tun
able films by Van der Waals
epitaxy indicate the possi
bility of highly tunable infrared absorption.
23
,24
Furthermore
, by tuning
the Fermi level of these materials it may
be possible to switch dynamically
between
optoelectronic
regime
s dominated by spin-
polarized topological surface physics and by bulk
semiconductor physics.
In this paper
, we report a measurement of
the
infrared reflectance and transmittance of
(Bi
1-x
Sb
x
)
2
Te
3
topological insulator (TI) films while applying a gate voltage to modulate the
Fermi level. To allow gated transmittance measurements, we developed an
epitaxial lift-
off
method for large
-area transfer of TI
films from
the
infrared
-absorbing SrTiO
3
growth substrates
to thermal oxidized silicon
substrates
.
25
,26
We combine these optical experiments with gated
transport measurements and angle
-resolved photoemission spectroscopy to identify the
mechanism o
f the observed spectral modulation. T
his behavior consists of a gate
-driven transfer
of spectral weight between both bulk and topological surface channels and i
nterband and
intraband channels. We propose that the physical bases for these phenomena are Pa
uli
-blocking
of bulk interband transitions for higher photon energies and modulation of intraband transitions
with carrier density for lower photon energies. We develop a model for the complex permittivity
of gated (Bi
1-x
Sb
x
)
2
Te
3
, and find a good match to
our experimental data.
2
Results
:
Device Structure
.
Our experimental optical setup and device structure are shown in Fig. 1. The
topological insulator film sits atop
a thermal
ly oxidiz
ed silicon
substrate
, allowing control
of its
Fermi level by applying a voltage between electrodes on the film and the doped silicon
to
accumulate or deplete carriers by the field effect
.
27
As depicted in Fig. 1, the topological surface
state
is thought to occupy a 1 – 2 nm
region
at the
top and bottom interfaces of the (Bi
1-
x
Sb
x
)
2
Te
3
film.
28
An optical microscope image and AFM cross
-cut are shown for a
(Bi
1-
x
Sb
x
)
2
Te
3
film transferred from its growth substrate to thermally oxidized silicon and patterned
into an electrically isolated device.
Gated Mid
-Infrared Spectroscopy.
The primary result of this work is the observation of gate
-
control of inter and
intra
-band optical transitions in transmittance and reflectance (Fig. 2a,b).
Infrared transmittance and reflectance are probed using an infrared microscope coupled to an
FTIR spectrometer, while the gate bias is varied.
Modulation of transmittance and reflectance of
several percent is observed, with respect to the
ir values at zero
-bias
applied to the silicon gate
.
In transmittance, two major
features are seen. At lower photon energies, transmittance is
increased
as the
Fermi level is increased
. At higher photon energies, transmittance is decreased
as the Fermi level
is increased
. Between these
features
– l
abelled A
and B, respectively, in Fig.
2b – is an iso
sbestic point
that sees no modulation, suggesting
a cross
-over
between two
competing effects
.
Transport
and Angle
-Resolved Photoemission Spectroscopy
.
To locate the Fermi level in our
films
, we measured the sheet
-resistance
as functions of gate voltage and
temp
erature
(Fig
. 3a
-c).
With negative gate bias,
sheet resistance is seen to increase as p-
type carriers
are depleted by the
field effect and the Fermi level of our film
is increased.
Likewise, with positive bias, sheet
resistance is seen to decrease as p
-type carriers
are accumulated and the Fermi level is decreased.
In measurements of sheet resistance versus temperature, a transition from metallic to insulating
character is seen
as the gate bias passes
-40 V – indicating that the Fermi level has crossed the
bulk valence band edge.
29
Angle
-resolved photoemission spectroscopy (Fig. 3c) is used to map
3
the band structure of (Bi
1-x
Sb
x
)
2
Te
3
in this region. The total carrier density in the film at zero
bias, n
2D
= 2.5∙10
13
cm
-2
, is obtained from Hall measurements.
Discussion
:
From transport measurements, we conclude that unbiased (Bi
1-x
Sb
x
)
2
Te
3
films are hole
-
doped, with a Fermi level position slightly below the bulk valence band edge. Th
e modulation of
sheet resistance seen with gating
indicates
that the Fermi level of the entire film is modified by
the gate, though some band bending is expect
ed, as is discussed in Fig 4.
8,23
It further suggests
that electrostatic gating is forcing the film between regimes where topological surface carriers
and bulk c
arriers are expected to
dominate the conductivity, respectively. At 4.2 K, gate
-biasing
allows the Fermi level to be pushed from below the bulk valence band edge to near the Dirac
point. T
he R
sh
on-
off ratio is much lower than that seen in films of other
layered materials with
a similar thickness and band gap, such as black phosphorus, consistent with the presence of a
conductive topological surface state that shorts the insulating ‘off’ state of the field effect
device.
30
Given
the
identified Fermi level position of the film, we sugges
t that feature A
in the
optical response at higher photon energies
is driven by gate
-modulat
ion of
interband transitions
via population of bulk valence band states with holes
. As shown in Fig. 2c, a doped
semiconductor has a characteristic effective bandg
ap defined –
for hole
-doped samples – by the
distance from the Fermi level to the conduction band.
In the (Bi
1-x
Sb
x
)
2
Te
3
system investigated
here, this Fermi level shifts with V
g
, altering the allowed and forbidden optical transitions and
hence its band edge optical constants. Similar behavior is seen for electrostatic doping in
graphene, and
for
chemical doping in narrow
-band
-gap semiconductor materials
, in which it is
known as the Burstein-
Moss effect
.
24
,31 -33
This behavior is seen only in thin films of materials
with a low density of states, and indicates possible technological applications
for narrow
-gap TI
materials
as optoelectronic modulators
. The observed modulation persists at room temperature,
albeit with a lower strength. At a temperature of
10 K, as discussed in the Supplementary
Information
, the band
-edge modulation is stronger and sharper – indicative of a narrower Fermi
distribution – and an additional feature appears.
The resulting change in the optical band gap can
be approximated as follows, where H(E
BVB
- E
F
, T) is a Heaviside step
-function with a
temperature-
dependent broadening
that accounts for the width of the Fermi
-Dirac distribution
.
34
4
∆퐸퐸
퐺퐺
=
2
(
퐸퐸
퐵퐵퐵퐵퐵퐵
−퐸퐸
퐹퐹
)
퐻퐻�퐸퐸
퐵퐵퐵퐵퐵퐵
−퐸퐸
퐹퐹
,
푇푇�
(
1)
We propose that feature
B in the optical response
at lower photon energies
is
characterized by a
change in the intraband absorption associated with both topological surface
state
s and bulk states
. While depressing the Fermi level into the bulk valenc
e band
will decrease
the band-
edge interband transition rate – increasing transmittance
near the band edge
– it
simultaneously transfers
spectral weight to intraband channels
, increasing absorption and
decreasing transmittance at lower energies.
We suggest that the physical mechanism of this
change in intraband absorption is the modulation of carrier density
in the film – by as much as 27
percent – via electrostatics
. This behavior indicates the possibility of extending the tunable, mid-
infrared Dirac plasmons seen in graphene to spin-
polarized topological insulator materials.
10
,35 ,36
This conjecture is supported by our transport data,
which
indicat
es that the Fermi level is shifting
back and forth ac
ross the bulk valence band edge,
but transmittance can also be modeled directly
using measured values
and one free fitting parameter. A simple picture of the modulated bulk
interband absorption is provided by experimental
measurements of the band edge dielectric
function, which was determined from infrared ellipsometry measurements of an as
-grown (Bi
1-
x
Sb
x
)
2
Te
3
film on sapphire. The change in
the band edge dielectric function energy
as a function
of gate voltage
, is modeled by shifting the zero
-bias dielectric function by an energy
ΔE
S
,
proportional to the corresponding voltage, suc
h that the dielectric function as a function of gate
voltage can be described by a single free parameter.
To model the optical response at small negative Fermi level positions
, the topological
surface state and bulk carrier densities are first parameteriz
ed as a function of
gate voltage.
From our fit of the absorption-
edge energy
shift
s, a gate voltage of V
g
= +/
-45V corresponds to a
shift of the Fermi level of approx
imately 28 meV. The observed metal
-insulator
transition
occurs at V
g
40V, so the Fermi level at zero bias must be at approximately
(28 meV
40 V
/
45V
) = 25 meV below the bulk valence band edge. The bulk valence band
is observed to be 150
meV below the Dirac point in angle
-resolved photoemission measurements, indicating a
Fermi
level of
E
F
= -
175 meV relative to the Dirac point.
17
The
topological surface state
carrier density
can be calculated from this Fermi level by assuming the electronic structure is characterized by
the well
-known topological surface state dispersion relation
.
17
,37
We find that
n
TSS
=
k
F
2
=
4∙10
12
cm
-2
for each surface, where
푘푘
퐹퐹
=
퐸퐸
퐹퐹
ℏ푣푣
퐹퐹
. Including both surfaces, our
topological
surface state density
/ bulk carrier
density
ratio is found to be
n
2D,TSS
/
n
2D
= 30%. As our films
5
are deeply subwavelength
in thickness
, we approximate the (Bi
1-x
Sb
x
)
2
Te
3
film as having a
single effective dielectric function that includes contributions from both of these types of
carriers, as well as interband absorption, as discussed above
. The intraband
dielectric functions
for the topological surface state and bulk free carriers were treated using
Kubo and Drude
models, respectively.
38
,39
휀휀
(
휔휔
)
=
휀휀
interband
(
휔휔
,
퐸퐸
퐹퐹
,
푇푇
)
+
휀휀
intraband
,
TSS
�휔휔
,
푛푛
2D
,
TSS
+
휀휀
intraband
,
bulk
�휔휔
,
푛푛
2D
,
bulk
=
휀휀
interband
(
휔휔
,
퐸퐸
퐹퐹
,
푇푇
)
푒푒
2
푣푣
퐹퐹
푑푑ℏ 휔휔�휔휔
+
푖푖
휏휏
푛푛
2D
,
TSS
2
휋휋
1
2
푒푒
2
푛푛
2D
,
bulk
푑푑푑푑휔휔�휔휔
+
푖푖
휏휏
(2)
This dielectric function model is combined with a simple capacitor model that defines the
change in carrier concentration
with gate voltage
– up to 27 percent at 90 V
. The charge on each
plate is given by Q = V
g
C, where the capacitance
C is calculated to be 12 nF/cm
2
for the 285 nm
SiO
2
using a standard parallel plate
geometry
.
40
Combining these elements
, we use the transfer
matrix method to calculate transmittance (Fig. 2d) through the (Bi
1-x
Sb
x
)
2
Te
3
film and substrate
stack.
41
The modeled values
for
ΔT/T
– based on experimental parameters
and a single fitting
parameter
yield a close match to our experimental
results.
We note that band bending, as described in Fig. 4, adds an additional degree of
complexity to this system.
8,23 ,42
While our transport data indicate
that gating modifies the Fermi
level of the entire film, the persistence of feature A in 10 K measurem
ents
suggests t
hat gating is
less efficient further
from the silicon oxide interface.
We further note two smaller features seen
in FTIR spectra. In Fig. 2a,b a small dip in transmittance and reflectance modulation is seen near
8 microns, which we attribute to absorption in the silicon oxide due to the presence of a phonon
line. In Fig. 2b, a small peak in transmittance modulation is seen near 3.8 microns. We
speculate that this peak may be due to a defect state or subband, and add that it persists in room
temperature measurements and is thus unlikely to be excitonic in nature.
12
,43 -45
In conclusion, we have experimentally investigated the
mid
-infrared optical response of
(Bi
1-x
Sb
x
)
2
Te
3
films
as the Fermi level position is varied by electrostatic gating
. This response
is characterized by a gate
-driven transfer of spectral weight between both bulk and topological
surface channels and i
nterband and intraband channels. We associate t
he higher photon energ
y
behavior
with
Pauli
-blocking of bulk interband optical transitions
, and the lower energy behavior
with topological surface and bulk intraband transition rates that vary with their respective carrier
concentrations
. These results present
layered topological insulator materials as
a new candidate
6
material
for tunable infrared photonics
and
illustrate the possibilities for
switching topological
optoelectronic phenomena – tunable, mid-
infrared Dirac
plasmons
, hybrid spin-
plasmons and
more
– between bulk and spin-
polarized surface regimes
.
Methods:
Sample Preparation.
The 20 nm (Bi
1-x
Sb
x
)
2
Te
3
films are grown by molecular beam epitaxy on
heat
-
treated 500 μm
-thick SrTiO
3
(111) substrates, as previously reported.
17
A mixing ratio of
x=0.94 is used for this work. Epitaxial lift
-off was used to transfer these films to thermal
oxidized silicon substrates, as described in the Supplementary Information
. Electron
-beam
lithography (EBPG 5000+) and reactive ion etching (
SF
6
) are used to pattern the film into
electrically isolated squares, and
Cr/Au contacts (5 nm / 150 nm) are deposited via thermal
evaporation to allow gating and Van der Pauw transport measurements.
Infrared Spectroscopy.
Infrared spectroscopy measurements are performed with a Nicolet iS50
FTIR coupled to a Continuum mi
croscope with a 50 μm spot size. Samples are wire
-bonded and
mounted in a
Linkam vacuum
stage for temperature control
at 78 K and 300 K
. The band-
edge
optical constants of the (Bi
1-x
Sb
x
)
2
Te
3
are extracted with a J.A. Woollam IR
-VASE infrared
ellipsometry system.
Transport
.
Sheet resistance i
s measured using the Van der Pauw method and a Janis ST
-400
liquid helium
cryostat
for temperature control from 4.2 to 300 K
. Carrier densities are measured
in an MMR Te
chnologies Hall system.
Acknowledgements:
The authors gratefully acknowledge support from the Department of Energy, Office of Science
under Grant DE
-FG02
-07ER46405 and for facilities of the DOE
“Light
-Material Interactions in
Energ
y Conversion” Energy Frontier Research Center (DE
-SC0001293). W.S.W. also
acknowledges support from an NDSEG Graduate Research Fellowship. A.R.D acknowledges
fellowship support from the Resnick Institute and the Kavli Nanoscience Institute at Caltech. The
authors are grateful to Prof. George Rossman for helpful discussions and use of his FTIR
facilities.
7
Author Contributions
:
W.S.W., V.W.B
and H.A.A. conceived the ideas.
Y.O. grew the films and W
.S .W.
fabricated
the devices
. W
.S.W, Y.S. and Y.O. perf
ormed measurements
. W.S.W and A.R.D
calculated the
optical model. All authors contributed to writing the paper.
D.N.B, K.H., Q.K.X., and H.A.A.
supervised the project.
8
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Figure 1
: Schematic of experiment.
(a)
Schematic of setup. The sample structure consists of a
10 nm a
-Te layer atop a 20 nm (Bi
1-x
Sb
x
)
2
Te
3
(BST) film on 285 nm thermal oxide on silicon.
The metallic topological surface states in the BST penetrate 1
-2 nm into the insulating bulk. The
transmittance and reflectance of this stack are probed by an FTIR spectrometer coupled to an
infrared microscope as the gate voltage is modulated. Inset: AFM cross
-cut of transferred film,
showing 30 nm total height of a
-Te and BST.
(b)
Schematic of observed behavior. The optical
response of the BST consists of contributions from bulk and topological surface carriers.
46
With
changing gate voltage, spectral weight is trans
ferred between both bulk (blue)
and topological
surface (green)
channels and between interband (unshaded region) and intraband (shaded region)
channels, as indicated by the arrow. Inset: Schematic band structure of BST, with bulk valence
and conduction ba
nds, topological surface states and 0.3 eV band gap indicated.
12
Figure 2
: Gate
-variable FTIR reflectance and transmittance.
(a)
Change in reflectance with
electrostatic
gate bias at T = 78 K, normalized to the zero
-bias case.
(b)
Change in transmittance
with gate bias at T = 78 K, nor
malized to the zero
-bias case. Similar behavior is observed at
room T, but with lower
modulation strength.
(
c)
Schematic of the Burstein
-Moss effect. As E
F
decreases into the BVB, lower energy bulk interband transitions are forbidden. The bulk band
gap energy is approx. 300 meV / 4.1
μ
m.
( d)
Modelled
transmittance based on
a combined model
of gate-
variable Pauli
-blocking / Burstein
-Moss shifting of bulk interband transitions at higher
energies and m
odulation of topological surface and bulk spectral weights at lower energies
. As a
simple model of the Burstein
-Moss shift, band edge optical constants are shifted in energy
-space.
Varying surface and bulk free carrier contributions to the dielectric fun
ction are modelled by the
Kubo and Drude models, respectively, and a simple capacitor model of carrier density
modulation. From Hall, transport and ARPES results, the zero-
bias carrier density is calculated
to be 30% topological surface carriers
and 70% b
ulk carriers.
13
Figure 3
: Electrical characterization and gate
-driven metal
-insulator transition.
(a)
Sheet
resistance (R
sh
) of film versus bias applied over SiO
2
gate dielectric at T = 4.2 K. R
sh
increases
with decreasing
V
g
/ increasing
E
F
, indicating initial hole doping. The R
sh
value approaches a
maximum at
the Dirac point, which we posit to be
near
- 150 V. Further electrostatic doping
results in electrical breakdown.
(b)
R
sh
versus T at three V
g
levels indicates a transition from
meta
llic behavior, where R increases with T, to insulating behavior, where R decreases with T.
At this transition voltage, approximately
- 40 V
, the Fermi level crosses the bulk valence band
edge.
(c)
Schematic illustrating E
F
crossing the bulk valence band (
BVB) edge at the metal
-
insulator transition voltage
, overlaid on ARPES results for a similar (Bi
1-x
Sb
x
)
2
Te
3
film,
including the main features of the band structure.
Inside the bulk gap are the two spin-
polarized
Dirac bands.
14
Figure 4
: Schematic of energy bands
across sample structure. Energy bands are shown for the
silicon oxide, BST surfaces (green and red, at interfaces), BST bulk, and air. For negative bias,
additional holes are accumulated in the BST layer. For positive bias, holes are deplet
ed. The
screening length is of order the width of the BST layer. As a result, the two topological surfaces
likely experience di
fferent doping. Due to the much lower doping in the a
-Te
, band bending at
the BST / a
-Te interface occurs mostly in the a-
Te
a nd so is not shown here
.
15
Supplementary Information
for: “
Gate
-Variable Mid
-Infrared Optical Transitions in a
(Bi
1-x
Sb
x
)
2
Te
3
Topological Insulator
1
William S. Whitney,
2,3
Victor W. Brar,
4
Yunbo Ou,
5,6
Yinming Shao,
2
Artur R. Davoyan,
5,6
D.
N. Basov,
7
Ke He,
7
Qi-Kun Xue and
2
Harry A. Atwater
1
Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
2
Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena,
California 91125, USA
3
Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125,
USA
4
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, The Chinese
Academy of Sciences, Beijing 100190, China
5
Department
of Physics
, University of California
-San Diego, La Jolla, California 92093, USA
6
Department of Physics, Columbia University, New York, NY
7
State Key Laboratory of Low
-Dimensional Quantum Physics, Department of Physics, Tsinghua
University, Beijing 100084, China
*Cor
responding author: Harry A. Atwater (
haa@caltech.edu
)
Epitaxial lift
-off methodology:
After spin
-coating PMMA (950 A8) onto the surface of the films and baking them on a hot
-plate
at 170 C for 2 minutes, the chips a
re placed into a bath of buffered hydrofluoric acid. The film
begins peeling off the substrate after 2
-3 hours, at which point the chip is placed into a series of
DI water baths. The chip is held at the surface of the water, and surface tension is used t
o
complete peeling of the film. The film floats on the surface of the water, and is lifted out with a
thermal oxide on silicon chip. This chip is dried overnight, and the PMMA is removed with
acetone. This process and a transferred film are shown in Supplementary Fig. 1.
16