1
Supporting Information for: “Gate-Variable Mid-Infr
ared 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 Tech
nology, Pasadena, California 91125, USA
2
Thomas J. Watson Laboratory of Applied Physics, Cal
ifornia Institute of Technology, Pasadena,
California 91125, USA
3
Kavli Nanoscience Institute, California Institute o
f Technology, Pasadena, California 91125,
USA
4
Beijing National Laboratory for Condensed Matter Ph
ysics, 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 Yor
k, NY
7
State Key Laboratory of Low)Dimensional Quantum Phy
sics, Department of Physics, Tsinghua
University, Beijing 100084, China
*Corresponding author: Harry A. Atwater (
haa@caltech.edu
)
Epitaxial lift-off methodology:
After spin)coating PMMA (950 A8) onto the surface o
f the films and baking them on a hot)plate
at 170 C for 2 minutes, the chips are placed into a
bath of buffered hydrofluoric acid. The film
begins peeling off the substrate after 2)3 hours, a
t 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 to
complete peeling of the film. The film floats on t
he 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 s
hown in Fig. S1.
2
Figure S1
: Transfer method and result.
(a)
Outline of transfer process. PMMA is spin)coated
onto (Bi
1)x
Sb
x
)
2
Te
3
film on its STO growth substrate. The sample is t
hen submerged into
buffered HF until the PMMA / Te / (Bi
1)x
Sb
x
)
2
Te
3
stack peels from the STO. The stack is
scooped out of water with a SiO
2
/ Si chip, dried, and treated with acetone to remo
ve the PMMA.
(a)
Optical microscope image of devices fabricated on
a film transferred to SiO
2
/ Si.
Low temperature transmittance:
Gate)variable FTIR transmittance is also measured a
t 5 K, in order to understand the low
temperature infrared response of the (Bi
1)x
Sb
x
)
2
Te
3
film and look for TSS to TSS interband
transitions. These measurements are performed in a
modified Oxford cryostat using a Bruker
Lumos infrared microscope and spectrometer, in the
Basov Lab facilities at UCSD. The
behavior seen – shown in Fig. S2 – is consistent wi
th that seen at 78 K, with a smaller Fermi)
Dirac distribution width. An additional kink featu
re is seen near six microns, but no clear
evidence of TSS to TSS interband transitions – whic
h should show a universal optical
conductivity of πe
2
/8h above 2E
F
– is seen.
1
The persistence of bulk)related modulation at hig
h
gate voltage and low temperature indicates that som
e band bending is likely present. The
presence of accumulating ice dampens the modulation
around a narrow feature at three microns.
2
3
Figure S2
: Gate)variable FTIR transmittance at T = 5 K. Tra
nsmittance is shown normalized to
zero bias case, as the Fermi level is pushed into t
he bulk band gap and towards the Dirac point.
Similar behavior is seen as in T = 78 K, with two m
ain differences. The band)edge Pauli)
blocking effect is sharper and more pronounced, lik
ely due to narrowing of the Fermi)Dirac
distribution of carrier energies. There also appea
rs a kink feature in transmittance near 6
microns. This feature may be related, but no clear
evidence of TSS to TSS interband transitions
is observed.
Room temperature transmittance and reflectance:
Gate)variable FTIR transmittance and reflectance ar
e also measured at 300 K, in order to
understand how the infrared response of the (Bi
1)x
Sb
x
)
2
Te
3
film varies with temperature and
demonstrate the possibility of room temperature opt
ical modulation. These measurements are
performed in the same configuration as the 78 K mea
surements. The behavior seen, shown in
Fig. S3 – is consistent with that seen in the 78 K
measurements, but show less modulation.
4
Figure S3:
Room temperature FTIR spectra.
(a)
Gate)variable FTIR transmittance, shown
normalized to the zero bias case.
(b)
Gate)variable FTIR reflectance, shown normalized to
the
zero bias case. Similar behavior is seen as with 7
8 K measurements, but with a smaller
modulation depth.
Thomas-Fermi model of screening:
The screening of the gate)induced potential in the
(Bi
1)x
Sb
x
)
2
Te
3
film is complex, due to the
interaction of charges in the two conductive surfac
es and bulk. For a simple estimate of the
characteristic screening length, we use a Thomas)Fe
rmi model of screening in the bulk that has
been applied to other layered semiconductors.
3, 4
The voltage drop across a film of thickness D
is modelled by Castellanos)Gomez, et al
3
, as follows.
∆ 2
2
1
1
Here
2
||
and
4
⁄
are constants,
/0
, and
,
and
are the gate)induced areal charge, interlayer spaci
ng and out)of)plane dielectric constant,
respectively. Using an in)plane effective mass
||
0.054
5
, out of plane dielectric constant
168
6
and the areal charge due to a +/) 90 V applied bia
s, we find that the voltage drop falls
by a factor of e over a screening length of 10 nm.
References:
5
1. Li, Z.; Carbotte, J. P.
Phys. Rev. B
2013,
87, (15), 155416.
2. Lynch, D.
The Infrared Spectral Signature of Water Ice in the
Vacuum Cryogenic AI&T
Environment
; DTIC Document: 2005.
3. Castellanos)Gomez, A.; Cappelluti, E.; Roldán, R
.; Agraït, N.; Guinea, F.; Rubio)
Bollinger, G.
Adv. Mater.
2013,
25, (6), 899)903.
4. Low, T.; Roldán, R.; Wang, H.; Xia, F.; Avouris,
P.; Moreno, L. M.; Guinea, F.
Phys.
Rev. Lett.
2014,
113, (10), 106802.
5. Yavorsky, B. Y.; Hinsche, N. F.; Mertig, I.; Zah
n, P.
Phys. Rev. B
2011,
84, (16),
165208.
6. Antimony telluride (Sb2Te3) dielectric constants
. In
Non-Tetrahedrally Bonded Elements
and Binary Compounds I
, Madelung, O.; Rössler, U.; Schulz, M., Eds. Sprin
ger Berlin
Heidelberg: Berlin, Heidelberg, 1998; pp 1)4.