of 46
Reviewers' comments:
Reviewer #1 (Remarks to the Author):
The authors report on an experimental work on dynamic modulation of spontaneous emission from
quantum emitters in a plasmonic heterostructure. The general idea is to introduce quantum dots in a
gated metal
-
insulator
-
semiconductor device whose epsilon
-
near
-
zero (ENZ) dispersion regime can be
tuned through the injection or removal of free carriers. By electrostatically gating the device, the local
density of optical states (LDOS)felt by the emitters in the cavity is modified, hence dynamically
modulating the
emission into the far
-
field. The overall idea is interesting and original. This naturally
follows on from the authors previous works on gate tunable ITO [Nano letters 10, 2111 (2010), and
ref. 9 in the manuscript]. However, as shown in Fig. 4a
--
which is
the main direct result of the paper
--
the reported modulation amplitude is somewhat weak. Indeed, the maximum modulation depth is
less than 15% when the applied voltage is varied from
-
1V to +1V. It is hard to envision how such a
low modulation amplitude
could be used in applications such as the one mentionned by the authors
(displays). Furthermore, there are no indications on a potential improvement of this modulation
amplitude. For this reason, I have doubts on the future impact of such a work.
In addit
ion, I have a number of comments concerning the manuscript:
i) The Fig. 4a shows a modulation of the PL intensity as detected in the far field, which is the main
direct result of the study. This change in PL intensity is not an evidence per se of a “Purc
ell
modulation”, as this result could arise from multiple other factors such as a change in the non
-
radiative decay rate, a modification in the absorption or even a change in the pump efficiency. For
example, one could alternatively explain the increase (d
ecrease) in PL intensity when Vg>0 (Vg<0) to
be produced by a decrease (increase) in the absorbance of the device (displayed in Fig. S9). However,
the authors measured the quantum yield of the emitters and its variation as a function of the applied
voltage
. From that they were able to extract the variation of the radiative rate (even though it is not
explicitly said in the paper, I assume they used the measured total lifetime to estimate the radiative
rate following the relation Γrad=QY* Γtot). The correspo
nding variation of radiative rates with the
applied voltage is therefore a proof on the enhancement of the LDOS. This also indicates that all of the
claims in the paper rely on an accurate measurement of the quantum yield. However, even though
there is a s
ubstantial description on how the quantum yield experiment was performed, there is only
one graph on the related results of quantum yield measurements, corresponding to Vg=0 (Fig. S8).
The authors should display all of their data related to quantum yield m
easurement as a function of Vg
in the supplementary. For the same reasons, they should display the error bars in both the quantum
yield measurements (Fig. 5)and the lifetime measurements (Fig. 4c). (they have done so for the PL
measurements so they should
stay consistent throughout the paper).
ii) The LDOS enhancement, as calculated and displayed in Fig. 4d is only valid for a z
-
oriented dipole.
It is mentionned in the supplementary that a qualitatively similar result would be obtained in a more
realistic
case where dipoles are isotropically oriented. I believe it would be worth showing the
corresponding LDOS enhancement for isotropic emitters as a function of wavelength, so that one will
be able to compare this result to the values obtained experimentally
in the paper. In other words,
does the simulation indicates that we should effectively see a twofold enhancement in the radiative
rate upon modulating the bias from
-
1V to +1V? Or is there any other competing effects at play?
iii) The evolution of the i
maginary part of permittivity against the carrier concentration, shown in Fig.
2 is rather strange. Indeed, the Im(Eps) constantly increases with the concentration of free carriers
but suddenly decreases between N=1.8*10^22 and 4.1*10^22 cm
-
3. In addition
, for this latter
sample, the evolution of Im(Eps) as a function of wavelength is not monotonic, what is also surprising
if we compare to other studies. And finally, the fitting model for this sample is different: the authors
used 3 Lorentz oscillators in
that particular sample while they used 2 Lorentz oscillators for all other
cases. This does not necessarily mean that the fit is wrong, but it is a strong indication that this
particular sample is different than the others (probably due to structural diffe
rences between
samples). Therefore, I strongly doubt a TiN thin film, initially prepared as ENZ
-
TiN, will effectively see
its optical dispersion behaves similarly as in Fig. 2 upon injection of carriers through electrode gating.
This is corroborated by res
ults shown in Fig. S2: if the accumulation (depletion) of carriers in ENZ
-
TiN
was qualitatively similar to changing the TiN from optically plasmonic to optically dielectric, the
reflectance value of ENZ
-
TiN should oscillate between the respective ones of p
lasmonic and dielectric
TiN (80% for optically plasmonic, 95% for optically dielectric, as displayed in Fig. S2). This is
obviously not the case here, as the reflectance of ENZ
-
TiN under applied bias changes from ~67% to
~82%, what indicates that the effec
tive changes in the optical dispersion of ENZ
-
TiN are different than
the optical dispersions shown in Fig.2. Therefore, I believe a better way of presenting things would be
to show the optical modulation against the gate voltage as measured by ellispometry
(similarly to
what was done by the authors in Nano letters 10 2111 (2010)).
iv) There are 4 TiN samples displayed in Fig. 2 and the corresponding material properties values of all
4 are shown in table S1, but in the Drude
-
Lorentz fitting parameters tabl
e S2, only 3 of them are
shown. Why? This is especially surprising given that the missing sample is the most important one,
i.e. the ENZ
-
TiN that is used for all of the modulation devices. This data needs to be included in the
supplementary.
v) The dynam
ic modulation is convincingly shown in Fig. S3 but there are no indications on the
modulation amplitude. It should be explicitly mentionned in the paper. Also, why is the applied bias
±5V in that case while it is ± 1V throughout the manuscript? What happen
s in the device containing
QDs when the voltage is increased to voltages higher than 1V. The authors should explain that in the
manuscript as it could be a limitation to potential applications.
In conclusion, this manuscript starts on an interesting conc
ept and shows some first proof
-
of
-
principle
but I believe the different points I raised should be addressed before considering this paper for
publication in Nature C ommunications. Especially, the authors should give details on how the
modulation amplitude
of their device could be improved.
Reviewer #2 (Remarks to the Author):
In this manuscript, the authors experimentally demonstrated dynamic control of the visible
spontaneous emission of colloidal quantum dots by electrically tuning the local optical
environment.
Specifically, by carefully changing the doping level of TiN, its permittivity can reach near zero (ENZ) at
the visible wavelength regime. Using external voltage to build up a charge depletion or accumulation
layer in TiN, its refractive index
will be greatly tuned near ENZ wavelength, thus leading to the LDOS
change of QDs and resulting in the modulation of spontaneous emission.
This manuscript is well written and the results are technologically sound. Electrically active control of
the visi
ble light emission have great potential applications. The layered structure in this work can be
easily fabricated and the dynamic modulation through LDOS could reach ultrafast speed. I believe it is
a good contribution to the field of optoelectronics. Thus
, I recommend it to be considered for
publication in Nature C ommunications after addressing the following concerns.
1. While discussing the photoluminescence (PL) intensity modulation (i.e., lines 88
-
99 of page 4), the
authors attributed the modulation t
o LDOS change caused by varied external voltages (Fig. 4a).
However, although the external optical pump power was constant for varied voltages, the actual pump
field intensity at the emitter locations might still vary for different voltages, thus leading t
o modulation
of PL intensity as well. Although the lifetime results (based on LDOS) in Fig. 4c can partially explain
the modulated PL intensity, the pump effect may also contribute to such modulation. As shown in Fig.
3a, the reflectance varies (in wide sp
ectral range ~450 to 800nm) for different external voltages. The
authors should comment on this pump effect of 375nm excitation wavelength in the main text.
2. In the section “Active control of quantum yield of QDs” (lines 109
-
123), the authors only brie
fly
summarized the results of radiative/non
-
radiative rate and quantum yields. A little more discussion
about the observed results may be helpful for the readers. In addition, although the experimental
details for this section are covered in the Supplement
ary Materials, it may be better to add some
descriptions in either the main text or the Methods section.
Reviewer #3 (Remarks to the Author):
The manuscript presented by Lu et al reports the demonstration of an interesting and long
-
sought
-
after mecha
nism to control the spontaneous emission yield of InP / ZnS core
-
shell nanostructures by
dynamically controlling the local density of photonic modes they experience using an electrically
tunable nano
-
plasmonic device. The use of the TiN layer as a tunable
plasmonic material, having a
plasma frequency in the visible range, is an interesting result that will certainly be of interest to the
community of researchers working in photonics and plasmonics. However, the observed effect is weak,
consisting of a ±7% c
hange in the radiative luminescence efficiency as the voltage applied to the field
-
effect capacitor is tuned from
-
1V to +1V. Moreover, whilst an impressive array of supplementary
material is presented that certainly helps to support the conclusions that t
he spontaneous emission
rate, and hence the quantum efficiency, of the colloidal QDs is indeed varied by tuning the electric
field, but I have some questions for the authors that should be addressed before publication is further
considered. I feel that the
topic of the paper is of sufficient interest and timeliness to warrant
publication in nature communications, providing that the technical concerns raised below are fully
addressed.
• The predictions of fig 4d would indicate that one might expect a tunab
le enhancement of the LDOS
over the spectral range between ca 550
-
750nm, with a maximum response occurring around
~600nm, but active over the whole of this spectral range. In the PL spectra presented in the inset of
fig 4a, the field induced emission enhan
cement seems to be only present in a much narrower spectral
range 600
-
660nm. How do the authors account for this discrepancy?
• There does seem to be a shift of the peak position of the PL data presented in the inset of fig 4a
upon modifying the applied
voltage. Large static electric fields can impact on the average charge
status of the quantum dots and such effects can give rise to both spectral shifts and a change in the
radiative efficiency. How can the authors discount the possibility that the charge
status of the dots are
tuned by the electric field, giving rise to the observed change in radiative efficiency? Here, perhaps it
would help to present the raw PL data more prominently (larger panel, logarithmic scale, differential
spectra recorded with a g
ate voltage V, relative to the spectra obtained at V=0...). This is to my mind
a crucial point, since the spectral dependence of the LDOS modulation / enhancement for ENZ TiN and
Optically Plasmonic TiN is likely to be of significant interest to readers and
the result should be
unambiguous.
• The use of either two or three Lorentz oscillators to fit the ellipsometry data and produce the carrier
density dependent dielectric function (fig 2) seems to be somewhat arbitrary? C ould the authors
please relate the
frequencies of the Lorentz oscillators to the expected bandstructure of the n
-
doped
TiN and explain the rationale behind the choice of using either 2 or 3 Lorentz oscillators to fit the
dielectric function as the free carrier density N varies?
• The met
hod used to record the time resolved data involves integrating over the 500
-
650nm spectral
range. This approach is reasonable, but assumes that the form of the emission spectrum is
independent of the excitation level. Did the authors check that the form of
the emission spectrum was
not time dependent ?
2
Detailed Response to Reviewer #1’s Comments:
The authors report on an experimental work on dynamic modulation of spontaneous emission from
quantum emitters in a plasmonic heterostructure. The general idea is to introduce quantum dots in a
gated metal
-
insulator
-
semiconductor device whose epsilon
-
near
-
zero (ENZ) dispersion regime can be
tuned through the injection or removal of free carriers. By electrostatically gating the device, the local
density of optical states (LDOS) felt by the emitters in the cavity is modified, hence dynamically
modulatin
g the emission into the far
-
field. The overall idea is interesting and original. This naturally
follows on from the authors previous works on gate tunable ITO [Nano letters 10, 2111 (2010), and ref. 9
in the manuscript]. However, as shown in Fig. 4a
--
whi
ch is the main direct result of the paper
--
the
reported modulation amplitude is somewhat weak. Indeed, the maximum modulation depth is less than
15% when the applied voltage is varied from
-
1V to +1V. It is hard to envision how such a low
modulation ampl
itude could be used in applications such as the one mentioned by the authors (displays).
Furthermore, there are no indications on a potential improvement of this modulation amplitude. For this
reason, I have doubts on the future impact of such a work. In a
ddition, I have a number of comments
concerning the manuscript:
In conclusion, this manuscript starts on an interesting concept and shows some first proof
-
of
-
principle
but I believe the different points I raised should be addressed before considering this
paper for
publication in Nature Communications. Especially, the authors should give details on how the modulation
amplitude of their device could be improved.
We thank the reviewer for her or his insightful comments.
First, we would like to mention th
at
besides
the
proposed display applications, our findings could be used for visible light communication
systems such as Li
-
Fi, a counterpart
to
Wi
-
Fi that utilizes the visible range of the spectrum
[1, 2]
. In
future visible light communication networks, LED lights are likely candidates for
access points
that will
transmit information via subtle intensity variations en
coded in the emitted light. It is notable that
cadmium
-
free QDs are currently used for improving
the quality of
light
from
LED light bulbs. In
such
lighting devices
, the
QDs absorb
blue
LED light
,
down
-
convert it
,
and re
-
emit
it
with the desired color
characteristics. In principle, instead of modulating
the
intensity of
the
LED pump, one could modulate
the
emission properties of QDs via LDOS modulation. The proposed approach would enable more flexible
visible light communication s
ystems. For example, by separately modulating
the
emission intensity of
QDs with different emission wavelengths, one c
ould
obtain
an
actively tunable wavelength multiplexing
device. Notably, within the context of visible light communication systems, one do
es not need to have
large modulation
depth
of the emitted light
[1, 2]
.
3
When considering display applications,
indeed, having large modulation
depth
is very important. We
have some suggestions how we could increase modulation amplitude of our device:
a.
Using gate dielectrics with larger
DC
permittivity
In our design we use SiO
2
as a gate dielectric since it is known to have very low leakage current.
However
, the DC
permittivity of SiO
2
is also relatively low
(
ɛ
dc
=4.5
)
. One straightforward
improvement could be
to
replac
e
the
SiO
2
with a
dielectric
having
higher
DC
permittivity
,
such as
HfO
2
(
ɛ
dc
=25)
[3]
. This would enable larger variation of the carrier concentration in
the
TiN and,
hence, larger LDOS and PL intensity modulation.
b.
Using resonant structure
s
We suggest using
a
plasmonic cavi
ty (Fig. S9a) that can be formed by placing an appropriately
designed patch antenna on top of
the
Ag/SiO
2
/TiN heterostructure (akin to structure shown in
Refs.
[4, 5]
). It has been shown that the lifetime of a quantum emitter embedded in the dielectric
gap of the patch antenna reson
ator is very sensitive to
the
gap thickness
[5]
. If the resonant
wavelength of the cavity is aligned with the emission wavelength of the emitter, this
configuration will yield large modulation of
the
PL intensity und
er applied bias. Figure S9b
shows
the
distribution of the electric field excited by the point dipole embedded in
a
5 nm
-
thick
gap of the proposed patch antenna structure (Fig. S9a). The assumed dielectric permittivity of
the
7 nm
-
thick TiN film is identica
l to that of
the
ENZ
-
TiN film used in the present work (
i.e.,
the
film with carrier concentration
N= 1.8
×
10
22
cm
-
3
from
Fig. 2). In case of positive bias, we assume
that
a
1 nm
-
thick accumulation layer is formed in
the
TiN, at the
SiO
2
interface. The dielec
tric
permittivity of the accumulation layer is assumed to be identical to that of the metallic TiN
described in the present work (
i.e.,
the film with carrier concentration
N= 4.1
×
10
22
cm
-
3
from
Fig.
2). Figure S9c shows
the
LDOS enhancement for two different biases. As one can see,
the
suggested structure enables significant LDOS modulation under applied bias. Even though
the
dielectric permittivity of the accumulation layer of TiN is likely to differ from that of metallic
T
iN
as assumed in the
present work, the simulation shown in Fig. S9 aims to demonstrate the
sensitivity of the lifetime of the emitter with respect to variation of the refractive index of the
material in the gap. Finally, we would like to note that using pa
tch antenna resonator
s
can
increase the emission intensity from the device by orders of magnitude
[4]
.
4
Figure S9 | (a)
Schematic of the proposed patch antenna with a quantum emitter embedded in a
5 nm
-
thick SiO
2
layer
.
(b)
Calculated electric field distribution in the patch antenna structure. The depicted
electric field is excited by the point dipole oriented normally to the planar layers of Ag, SiO
2
, and TiN.
(c)
Calculated z
-
projection of the LDOS enhancement with respect
to bulk InP LDOS, as a function of
the emission wavelength, for zero bias and positive bias.
Finally, we would like to mention that
the
energy
efficiency of the proposed device can be
considerably improved by using higher quality QDs:
c.
Using quantum
dots with higher quantum yield
The quantum yield of our InP/ZnS QDs suspended in the solution is
17%
,
while
the measured
quantum yield of QDs embedded in
a
9 nm
-
thick SiO
2
layer is 15%. This modest value of quantum
yield implies that only 15% of
the
photo
ns absorbed by
the
QD
s
will be reradiated into the far field.
Hence, using QDs with higher quantum yield would enhance emission intensity from the structure,
and hence
improve the
absolute (but not relative) modulation of PL intensity under applied bias.
d.
Using a quantum dot ensemble with narrower spectral width of PL intensity.
Note that
the
experimentally observed PL intensity spectrum is formed by emission of multiple
colloidal QDs with different sizes and, consequently, different emission wavelengths. T
he size
distribution of QDs gives rise to a broad PL intensity spectrum observed in our experiment (see Fig.
3).
The observed PL intensity spectrum is centered at 630 nm and its full width at half maximum
5
(FWHM) is
around 90 nm. Since the LDOS in the SiO
2
spacer of the planar heterostructure has no
resonant features (Fig. 4d),
we would expect a fairly broadband modulation of PL intensity. Thus, in
principle, PL intensity is equally modulated for each individual QD coupled to the plasmonic
heterostructure. H
owever, due to larger number of QDs emitting in the wavelength range from 600
nm to 650 nm, absolute value of the PL intensity modulation (but not relative PL intensity change) is
larger for the central emission wavelength. If, for an identical QD density,
the considered QD
ensemble had a narrower PL intensity spectrum, then the absolute,
but not relative, modulation at the
central emission wavelength would be stronger due to the large number of QDs emitting at a single
wavelength. Note that some commercial
ly available QDs have 30
-
40 nm FWHM over whole visible
spectrum
[6]
. Thus, using these QDs in our device would significantly enhance absolute value of the
PL intensity modulation
at a given intensity of pump field.
We added the following paragraphs to the main text of the manuscript:
When considering display applications, it is crucial to have large relative modulation of PL intensity.
An
obvious improvement would be replacing
SiO
2
by a gate dielectric with higher
DC
permittivity such as
Al
2
O
3
or
HfO
2
.
The relative modulation strength of our device can further be improved by incorporating
a
TiN layer into a plasmonic cavity that can be formed, e.g.,
by placing
an
appropriately d
esigned patch
antenna on top of
the
Ag/SiO
2
/TiN heterostructure
[4, 5]
.
It has been shown that the lifetime of a quantum
emitter embe
dded in the dielectric gap of the patch antenna resonator is very sensitive to gap thickness
[5]
.
If the resonant wavelength of the cavity is aligned with the emission wavelength of the emitter, this
configuration wi
ll yield
a
large modulation of PL intensity under
an
applied bias (see SI).
Moreover,
using
a
patch antenna resonator can increase emission intensity by orders of magnitude
[4]
thus making
the whole device more energy efficient.
The e
nergy efficiency of our device can further be improved by
using QDs with
a
higher quantum yield, and by using a QD ensemble with narrower spectral width of PL
intensity (for a m
ore detailed discussion see SI).
Our findings can readily be used for visible light communic
ation systems such as Li
-
Fi, a
counterpart of Wi
-
Fi that utilizes
the
visible
spectral
range
[1, 2]
.
In future visible light communication
networks, LED light bulbs
are likely candidates for devices that will transmit information encoded via
subtle intensity v
ariations of the emitted light.
C
admium
-
free
QDs are
currently
used for improving
quality of light of LED light bulbs
by
making the emitted light more pleasant for the human eye. In many
lighting devices QDs absorb blue LED light,
and then
down
-
convert and re
-
emit
it
with the desired color
characteristics.
It is currently suggested that light intensity modulations can be ach
ieved by
varying the
intensity of the blue LED pump. Instead of varying intensity of LED pump, we propose to dynamically
6
control emission properties of QDs via LDOS modulation. The proposed approach would enable realizing
more flexi
ble visible light commun
ication systems
. For example,
an
actively tunable wavelength
multiplexing device
can be obtained by separately modulating the emission intensity of QDs with
different emission wavelengths
.
W
e would like emphasize that within the context of visible light
co
mmunication systems,
a
large amplitude modulation of the emitted light
is not
necessary
[1, 2]
.
We also added the following part to the
Supplementary Information (
SI
)
:
“To enhance the amount of observed LDOS modulation, we suggest using
a
plasmonic cavity (Fig. S9a)
that can be formed by placing an appropriately designed patch antenna on top of
an
Ag/SiO
2
/TiN
heterostructure (akin to previously demonstrated reflectarray antennas
[4, 5]
). It has been shown that the
lifetime of a quantum emitter embedded in the dielectric gap of the patch antenna resonator is very
sensitive to gap thickness
[5]
. If the resonant wavelength of the cavity is aligned
with the emission
wavelength of the emitter, this configuration will yield
a
large modulation of
the
PL intensity under
an
applied bias. Figure S9b shows
the
distribution of the electric field excited by the point dipole embedded
in
the
5 nm thick gap of
the proposed patch antenna structure (Fig. S9a). The assumed dielectric
permittivity of 7 nm thick TiN film is identical to that of ENZ
-
TiN film used in the present work (the film
with carrier concentration N= 1.8
×
10
22
cm
-
3
from Fig. 2). In
the
case of
a
positive bias, we assume that
a
1 nm thick accumulation layer is formed in TiN at the TiN
/
SiO
2
interface.
The dielectric permittivity of
the accumulation layer is assumed to be identical to that of the metallic TiN described in the present work
(the film
with carrier concentration N= 4.1
×
10
22
cm
-
3
from Fig. 2).
The
LDOS enhancement for two
different biases
is shown in Figure S9c, where it can be seen that the
suggested structure enables
significant LDOS modulation under
an
applied bias.
T
he simulation s
hown in Fig. S9 aims to demonstrate
the sensitivity of the lifetime of the emitter with respect to variation of the refractive index of the material
in the gap
, despite the difference in dielectric permittivity between the value assumed for the TiN
accumul
ation layer and that of metallic TiN derived in the present work (N= 4.1
×
10
22
cm
-
3
)
. Finally, we
would like to note that using patch antenna resonator can increase the emission intensity from the device
by two orders of magnitude
[4]
.
7
Figure S9 | (a)
Schematic of the proposed patch antenna with a quantum emitter embedded in
5 nm
thick SiO
2
layer
.
(b)
Calculated electric field distribution in the patch antenna structure.
The d
epicted
electric field is excited by the point dipole oriented normal to the p
lanar layers of Ag, SiO
2
, and TiN.
(c)
Calculated z
-
projection of the LDOS enhancement with respect to LDOS in the bulk InP as a
function of the emission wavelength for
both
zero bias and positive bias.”
R1
-
1.
The Fig. 4a shows a modulation of the PL intensity as detected in the far field, which is the main
direct result of the study. This change in PL intensity is not an evidence per se of a “Purcell modulation”,
as this result could arise from multiple other f
actors such as a change in the non
-
radiative decay rate, a
modification in the absorption or even a change in the pump efficiency. For example, one could
alternatively explain the increase (decrease) in PL intensity when Vg>0 (Vg<0) to be produced by a
dec
rease (increase) in the absorbance of the device (displayed in Fig. S9). However, the authors
measured the quantum yield of the emitters and its variation as a function of the applied voltage. From
that they were able to extract the variation of the radiat
ive rate (even though it is not explicitly said in the
paper, I assume they used the measured total lifetime to estimate the radiative rate following the relation
Γ
rad=QY*
Γ
tot). The corresponding variation of radiative rates with the applied voltage is th
erefore a
proof on the enhancement of the LDOS. This also indicates that all of the claims in the paper rely on an
accurate measurement of the quantum yield. However, even though there is a substantial description on
how the quantum yield experiment was pe
rformed, there is only one graph on the related results of
quantum yield measurements, corresponding to Vg=0 (Fig. S8). The authors should display all of their
data related to quantum yield measurement as a function of Vg in the supplementary. For the same
8
reasons, they should display the error bars in both the quantum yield measurements (Fig. 5)and the
lifetime measurements (Fig. 4c). (they have done so for the PL measurements so they should stay
consistent throughout the paper).
We agree with
the
rev
iewer’s observation that
a
change in PL intensity is not
direct evidence of
LDOS modulation o
r
“Purcell modulation”.
However, modulation of the emitter lifetime (or, equivalently
,
total decay rate
Γ
tot
) is direct evidence of LDOS modulation since
Γ
tot
is proportional to LDOS
[7]
.
I
ncreas
ing
both non
-
radiative and radiative decay rates,
Γ
nr
and
Γ
rad
, respectively, may con
tribute to
LDOS enhancement since
(
Γ
tot
=
Γ
rad
+
Γ
nr
).
Thus, in principle, LDOS enhancement can also be
accompanied by
a
decrease in PL intensity
[8, 9]
.
Hence, to prove that
LDOS enhancement contributes to
the
observed
increase in
PL intensity
,
we
study
the
variation of
both t
otal decay rate
Γ
tot
and radiative
emission decay rate
Γ
rad
u
nder
an
applied bias
.
From this we can deduce variation of
quantum yield of
our QDs
under
an
applied bias
. As Reviewer 1 mentioned, in our work we define
quantum yield of an
emitter
η
as a ratio of radiative and total decay rates
η
=
Γ
rad
/
Γ
tot
.
Following
the
reviewer’s suggestion, we critically analyzed our approach to calculate the radiative
emissio
n rate and quantum yield of QDs.
Below
is the summary of the approach
we used
that
has
also
been
added to the Methods section of the manuscript.
When calculating
the
radiative emission decay rate,
we take into account that our InP QDs are embedded in
the
SiO
2
layer of
the
TiN/SiO
2
/Ag heterostructure.
As a result, a portion of the laser e
xcitation (
λ
=375 nm) is going to be absorbed in the top TiN layer
,
which
will affect
the
excitation intensity of
the
QDs. To estimate the effect of
the
possible variation of
the
excitation intensity, we measure
the
absorbance of
the
ENZ
-
TiN/SiO
2
/Ag plasmon
ic heterostructure at
an
excitation wavelength of
λ
=375 nm under
an
applied bias (Figs. S13 and S14). As
can be
see
n
,
the
absorbance stays almost constant for negative biases and shows
a
slight decrease for positive biases. Since
absorption primarily occur
s in
the
TiN layer,
a
high absorbance results in
a
reduced excitation intensity of
the
QDs. Taking this into account,
the
bias dependent radiative emission decay rate (
Γ
rad
)
can be
given by
the following formula
[5, 10]
:
Γ
rad
(V)/
Γ
rad
0
= (
I
PL
(V)/I
PL
0
)[(1
A
laser
(V))/(1
A
laser
0
)].
(1)
Here
Γ
rad
0
is the
radiative emission decay rate under zero bias, I
PL
0
is the peak PL intensity under zero bias
,
I
PL
(V) is the bias
-
dependent PL intensity
,
A
laser
0
is the
absorbance in TiN/SiO
2
/Ag heterostructure at
excitation wavelength of
λ
=375 nm at zero bias, and A
laser
(V) is the bias dependent absorbance at
λ
=375
nm. We would like to emphasize that absorbance in TiN/SiO
2
/Ag heterostructure primarily occurs in TiN
layer. To calculate
the
bia
s
-
dependent quantum yield of our QDs embedded in TiN/SiO
2
/Ag
9
heterostructure, we use Eq. (1) and take into account that quantum yield of the emitter
η
is defined as a
ratio of radiative and total decay rates
η
=
Γ
rad
/
Γ
tot
.
To address
the
reviewer’s
concerns
regarding
the relationship between
LDOS and measured PL intensity,
we added the following two paragraphs to the main text of the manuscript.
Thus, in our experiment we observe simultaneous increase (decrease) of PL int
ensity and total decay rate
of
emission
Γ
tot
. However, it still needs to be proven that the measured LDOS modulation contributes to
the observed PL intensity modulation. For example, variation of excitation field intensity under applied
bias could also result in modulation of PL intensi
ty. To investigate this option, we measure
the
absorbance spectrum of
the
ENZ
-
TiN/SiO
2
/Ag plasmonic heterostructure
at the laser excitation
wavelength of
λ
=375 nm (Fig. S13a) as a function of applied voltage. We observe a slight
decrease
in
absorbance at p
ositive voltages
, which
implies
an
increased excitation intensity
, and consequently,
an
increased PL intensity
.
The o
bserved PL intensity modulation can also be attributed to
the
reduction or
increase of absorbance of
the
ENZ
-
TiN/SiO
2
/Ag plasmonic heterost
ructure at
the
QD emission
wavelengths (Fig. S13b). However, we would like to point out that absorbance modulation at
the
QD
emission wavelength and modulat
ion of the total decay rate of a
QD are interrelated since QDs are placed
in the immediate vicinity of TiN layer (see Fig. 1). In what follows we further investigate how LDOS
modulation contributes to the observed PL modulation.
and
Our measurements show that under positive bias, t
he radiative emission decay rate (
Γ
rad
) increases by
15% while under negative bias
Γ
rad
decreases by 11% (Fig. 5a). This amounts to
the
relative modulation
of
Γ
rad
of 26% when applied gate voltage ranges between
1 V and +1
V (see Methods for further detai
ls).
The measured voltage
-
dependent total emission decay rate (see Fig. 4c) and radiative decay rate can be
used to determine variation of quantum yield of
the
QDs
η
=
Γ
rad
/
Γ
tot
under
an
applied bias. We observe
a
35% relative increase
in
quantum yield at
an
applied bias of +1
V and
a
21% relative decrease
in
quantum
yield at
an
applied bias of
1 V. This
in situ
control of quantum yield is a unique consequence of the bias
-
induced modulation of LDOS.
Finally, we would like to emphasize that LDOS, radiative em
ission decay
rate
,
and quantum yield do not depend on absorbance at
the
excitation
wavelength of
λ
=375 nm.
To summarize, we observe that at
a
positive bias increase in PL intensity is always accompanied by
an
increase of both total and radiative emission d
ecay rates,
Γ
tot
and
Γ
rad
(see Figs. 4 and 5). This implies
that
in addition to a
reduced absorption of
the
ENZ
-
TiN/SiO
2
/Ag plasmonic heterostructure at
the
QD
10
emission wavelength
λ
=630 nm and
a
slightly increased
excitation
intensity at
λ
=375 nm
, LDOS
modulation also contributes to
an
increase of PL intensity
an
under applied bias (even though, as it has
been mentioned above,
LODS modulation and absorbance modulation at QD emission wavelengths
cannot be fully decoupled
). This contrasts
with the
p
reviously reported case of
a
bias
-
induced LDOS
modulation, where
an
increase of LDOS has always been accompanied by
a
decrease in PL intensity
,
implying that primarily non
-
radiative emission decay rate has been modulated
[8, 9]
.
We
previously
clarified
an
approach
used
to calculate the quantum yield
. The updated methodology to
extract
the
radiative emission decay rate and quantum yield of QDs is described now in the Methods
section.
When calculating radiative emission decay rate, we take into account that our
InP QDs are embedded in
the
SiO
2
layer of
the
ENZ
-
TiN/SiO
2
/Ag heterostructure.
As a result, a portion of the laser excitation
(
λ
=375 nm) is going to be absorbed in the top TiN layer
, which
will affect
the
excitation intensity of
the
QDs. To estimate the effect of
the
possible variation of
the
excitation intensity, we measure
the
absorbance of
the
ENZ
-
TiN/SiO
2
/Ag plasmonic heterostructure at
an
excitation wavelength of
λ
=375 nm
under
an
applied bias (Figs. S13 and S14).
As one can see,
the
absorbance stays almost constant for
negative biases and shows
a
slight decrease for positive
biases. Since absorption primarily occurs in
the
TiN layer, high absorbance results in
the
reduced excitation intensity of
the
QDs. Taking this into account,
the
bias dependent radiative emission decay rate (
Γ
rad
)
can be
given by the following formula
[5, 10]
:
Γ
rad
(V)/
Γ
rad
0
= (
I
PL
(V)/I
PL
0
)[(1
A
laser
(V))/(1
A
laser
0
)].
(1)
Here
Γ
rad
0
is the
radiative emission decay rate under zero bias, I
PL
0
is the peak PL intensity under zero
bia
s,
I
PL
(V) is the bias
-
dependent PL intensity
,
A
laser
0
is the
absorbance in
the
ENZ
-
TiN/SiO
2
/Ag
heterostructure
at
an
excitation wavelength of
λ
=375 nm
at zero bias, and
A
laser
(V)
is the bias dependent
absorbance at
λ
=375 nm
. We would like to emphasize that absorbance in
the
TiN/SiO
2
/Ag heterostructure
primarily occurs in TiN layer (see Figs. S13 and S14). To calculate
the
bias
-
dependent
quantum yield of
our QDs embedded in
TiN/SiO
2
/Ag
heterostructure, we use Eq. (1) and take into account that quantum
yield of the
emitter
η
is defined as a ratio of radiative and total decay rates
η
=
Γ
rad
/
Γ
tot
.
11
By using the described
approach,
we have generated revised Fig. 5
and added error bars to all
subfigures
of Figure 5.
Figure 5
|
Active control of quantum yield of QDs embedded in a gated plasmonic heterostructure.
(
a
) Radiative decay rate (
Γ
rad
) of InP QDs
(normalized to radiative decay rate at zero bias)
embedded in
the
TiN/SiO
2
/Ag plasmonic heterostructure as a function of gate voltage.
Under positive bias
Γ
rad
shows
a
relative increase
of
15% while under negative bias
Γ
rad
shows
a
relative decrease of
11%.
(
b
) Dynamically
tunable quantum yield of QDs
(normalized to quantum yield at zero bias)
. When gate voltage V
G
is
increased from 0 V to +1
V, we observe
a
35% relative increase of quantum yield. As gate voltage V
G
varies from 0 V to
1
V, we observe
a
relative quantum yield decrease
of
21%.
12
The erro
r bars shown in Fig
s
.
4 and
5
have been derived
by using consideration
s
described in
the caption
of
Fig. R1.1.
Figure R1.1|
PL intensity spectrum measured at the same excitation spot of the sample (curves 1, 2, 3, 4).
The
PL intensity
measurement error
is ~2%.
Since Figure 5 has been derived by calculati
ng
the ratio of
PL spectra with and without
an
applied bias
, the total measurement error bar in Fig
s. 4 and 5
is
estimated
to be ~ 5%.
13
We added an additional figure to SI that
that was used when calcul
ating bias
-
dependent quantum yield of
QDs
.
Figure
S1
4
|
Lifetime at zero bias and a
bsorbance at excitation and emission wavelength
s
. (a)
By
using time
-
resolved PL measurements, we
identify the total decay of InP QDs at zero bias
Γ
tot
=2.56
×
10
9
s
1
.
(b)
Absorbance at the excitation wavelength (
λ
=
375 nm) in
the
ENZ
-
TiN/SiO
2
/Ag heterostructure
.
(c)
Absorbance at
the
emission wavelength (
λ
=
630 nm) in
the
ENZ
-
TiN/SiO
2
/Ag heterostructure
.
Absorbance primarily occurs in the top TiN layer.
14
R1
-
2
The LDOS enhancement, as calculated and displayed in Fig. 4d is only valid for a z
-
oriented
dipole. It is mentionned in the supplementary that a qualitatively similar result would be obtained in a
more realistic case where dipoles are isotropically orien
ted. I believe it would be worth showing the
corresponding LDOS enhancement for isotropic emitters as a function of wavelength, so that one will be
able to compare this result to the values obtained experimentally in the paper. In other words, does the
sim
ulation indicates that we should effectively see a twofold enhancement in the radiative rate upon
modulating the bias from
-
1V to +1V? Or is there any other competing effects at play?
We thank the reviewer for
this
comment
.
We replaced previously plott
ed z
-
projection of the LDOS
z
by an averaged out LDOS: LDOS=(LDOS
x
+ LDOS
y
+ LDOS
z
)/3.
The revi
sed Fig. 4d plots averaged out
L
DOS enhancement.
The observed
lifetime
as well
as
the
PL intensity and reflectance modulation reported in our work
cannot be fully explained by
changing carrier concentration
in
the Drude term of the Drude
-
Lorenz model
that describes
the dielectric permittivity of TiN
.
At
high carrier concentrations
(N= 1.8
×
10
22
cm
-
3
)
,
a
number of
different effects may contribute to
the
observed
optical modulation
,
such as
the
dependence of
the
electron effective mass on
the
applied voltage due to
the
nonparabolicity of
the
conduction band and
the
dependence of
the
electron mobility on
the
applied bias.
I
n Fig. 4d we assume that the dielectric
permittivity of
the
1 nm thick accumulation layer in
the
TiN is
given by the measured dielectric
permittivity of
the
TiN film with carrier concentration of N= 4.1
×
10
22
cm
-
3
(
see Fig. 2). Strictly speaking,
this assumption is not accurate; however, it allows us to estimate the sensitivity of the calculated LDOS
with respect to
the
variation of
the
refractive index of
the
1 nm thick accumulation layer (Fig. 4d).
To
summarize, we
do not expect to have a quantitative match between our simulations and experimental data.
15
To address reviewer’s concern we modify Fig. 4d.
Figure 4
|
Gate
-
tunable spontaneous emission of QDs via modulation of the LDOS.
(
a
)
. (
b
(
c
) (
d
)
Calculated LDOS e
nhancement
spectra at the position of a QD
(averaged over QD dipole orientation
s
)
for
different carrier densities in a 1 nm thick modulated TiN layer. The black curve corresponds a
homogeneous TiN film which is in the ENZ region (N= 1.8
×
10
22
cm
-
3
). The
red curve corresponds to a
TiN film with a 1 nm thick modulated TiN layer that is plasmonic but far from the ENZ region. T
he t
op
panels show the simulated spatial distribution of the optical frequency electric field |E| radiated by a QD
(
λ
=630 nm). Both th
e calculated LDOS and optical field intensity |E| in the SiO
2
gap increase with gate
voltage.
We have also added the following paragraph to the main text of the manuscript:
“The observed lifetime as well as
the
PL intensity and reflectance modulation reported in our work cannot
be fully explained by changing
the
carrier concentration in the Drude term of the Drude
-
Lorenz model
that describes the dielectric permittivity of TiN. At high carrier concentrations (N=
1.8
×
10
22
cm
-
3
for
ENZ
-
TiN),
a
number of different effects may contribute to observed optical modulation
,
such as
the
dependence of
the
electron effective mass on
the
applied voltage due to
the
nonparabolicity of
the
conduction band and
the
dependence of
the
electron mobility on
the
applied bias. In Fig. 4d we assume
that the dielectric permittivity of
the
1 nm thick accumulation layer
of
TiN is given by the measured
16
dielectric permittivity of
the
TiN film with carrier concentration of N= 4.1
×
10
22
cm
-
3
(
see Fig. 2).
Strictly speaking, this assumption is not accurate; however, it allows us to estimate the sensitivity of the
calculated LDOS with respect to variation of refractive index of
the
1 nm thick accumulation layer (Fig.
4d).”
R1
-
3
The evolution
of the imaginary part of permittivity against the carrier concentration, shown in
Fig. 2 is rather strange. Indeed, the Im(Eps) constantly increases with the concentration of free carriers
but suddenly decreases between N=1.8*10^22 and 4.
1*10^22 cm
-
3. In
addition
, for this latter sample, the
evolution of Im(Eps) as a function of wavelength is not monotonic, what is also surprising if we compare
to other studies. And finally, the fitting model for this sample is different: the authors used 3 Lorentz
oscilla
tors in that particular sample while they used 2 Lorentz oscillators for all other cases. This does
not necessarily mean that the fit is wrong, but it is a strong indication that this particular sample is
different than the others (probably due to structur
al differences between samples). Therefore, I strongly
doubt a TiN thin film, initially prepared as ENZ
-
TiN, will effectively see its optical dispersion behaves
similarly as in Fig. 2 upon injection of carriers through electrode gating. This is corroborate
d by results
shown in Fig. S2: if the accumulation (depletion) of carriers in ENZ
-
TiN was qualitatively similar to
changing the TiN from optically plasmonic to optically dielectric, the reflectance value of ENZ
-
TiN
should oscillate between the respective o
nes of plasmonic and dielectric TiN (80% for optically
plasmonic, 95% for optically dielectric, as displayed in Fig. S2). This is obviously not the case here, as
the reflectance of ENZ
-
TiN under applied bias changes from ~67% to ~82%, what indicates that t
he
effective changes in the optical dispersion of ENZ
-
TiN are different than the optical dispersions shown in
Fig.2. Therefore, I believe a better way of presenting things would be to show the optical modulation
against the gate voltage as measured by elli
spometry (similarly to what was done by the authors in Nano
letters 10 2111 (2010)).
Indeed, the imaginary part of ellipsometrically measured dielectric permittivity monotonically
increases with the carrier concentration for carrier concentrations
le
ss than
or equal to 1.8
×
10
22
cm
-
3
, and
shows abrupt decrease for the sample with carrier concentration
4
.
1
×
10
22
cm
-
3
. However, we would
like to point out that this kind of behavior has been previously reported in the literature (see Fig
.
1b of Ref.
[11]
).
In one case shown in
Fig
.
1b of Ref.
[11]
, Im(
ɛ
) of “intermediately doped” TiN is higher than Im(
ɛ
)
of “dielectric” TiN. On the other hand, over a broad wavelength range, Im(
ɛ
) of metallic TiN is smaller
than Im(
ɛ
) of “intermediately doped” or “dielectric”
TiN (see Fig 1b of Ref.
[11]
). In Ref.
[11]
it is argued
that when oxygen impurity concentration in TiN is lowered
,
the crystallinity of TiN film
s
is improved
and
17
R(
ɛ
) becomes more negative and Im(
ɛ
) decreases.
We agree with the reviewer’s observation that when
sp
uttering TiN films under different deposition conditions, the resulting TiN films will likely have
compositional and structural differences. For example, the observed non
-
monotonic dependence of Im(
ɛ
)
on the carrier concentration of the
sputtered films
gives an indirect evidence of compositional and
structural differences between the films.
Moreover, w
e performed compositional analysis of
135 nm thick
TiN films deposited on Si substrate via
DC
sputtering
. The sputtering conditions have been chosen to be
identical to those used to deposit TiN in the tunable
ENZ
-
TiN/SiO
2
/Ag heterostructure
. We found that
the
stoichiometry of our film is given as TiN
0.8
O
0.2
, where oxygen has been introduced into our film
unintentionally. This result is consistent with previo
us reports
[11, 12]
.
We thank the reviewer
for asking about
non
-
monotonic behavior of Im(
ɛ
) of TiN as a function of
wavelength. We would like to address the question
of
how this compares with other studies. In the visible
wavelength range, n
on
-
monotonic behavior of Im(
ɛ
) as a function of wavelength is commonly observed
(see Fig. 1b of Ref.
[11]
, Fig. 1c of Ref.
[13]
, Fig. 1b of Ref.
[14]
). In our work we also observe non
-
monotonic behavior of Im(
ɛ
) as a function of wavelength only i
n the visible wavelength range. On the
other hand, as we observe in our work, Im(
ɛ
) typically monotonically grows as a function of wavelength
in the near
-
infrared wavelength range
[11, 13, 14]
.
As we have mentioned when responding
Q
uestion 2 of Reviewer
1
, our calculations have shown that
observed reflectance modulation cannot be fully explained by simply changing the carrier concentration
in the Drude term of the Drude
-
Lorentz model that defines the dielectric permittivity of TiN. The carrier
concentratio
n of our ENZ
-
TiN
film (1.8
×
10
22
cm
-
3
) is
at least 2 orders of magnitude
greater than
carrier
concentrations that one typically deals with in ITO
-
based gate
-
tunable devices
[15]
(3
×
10
20
cm
-
3
).
Hence,
a
number of different effects may contribute to
the
observed optical modulation such as
dependence of electron effective mass on applied voltage due to nonparabolicity of conduction band and
dependence of electron mobility on applied bias, etc. In Fig.
S6
we assume that the dielectric permittivity
of 1 nm t
hick accumulation layer in TiN is given by the measured dielectric permittivity of TiN film with
carrier concentration of N= 4.1
×
10
22
cm
-
3
(see Fig. 2). As Reviewer 1 has pointed out, this assumption is,
strictly speaking, not correct; however, it allows us to estimate the sensitivity of the calculated reflectance
with respect to variation of
the
refractive index of 1 nm thick TiN layer whic
h is located at the interface of
TiN and SiO
2
(Fig.
S6
). To summarize, due to
the
high carrier concentration of TiN films,
modifying
the
carrier concentration in the Drude term of the Drude
-
Lorentz model cannot reproduce experimentally
observed reflectance
modulation.
18
We would also like to address reviewer’s comment regarding performing ellipsometry under applied
bias.
As Reviewer 1 has requested, we have performed ellipsometry of our
ENZ
-
TiN/SiO
2
/Ag
heterostructure
under applied bias. However, obtained data is not amenable to unambiguous interpretation
due to reasons described below.
The area of our gate
-
tunable
E
NZ
-
TiN/
SiO
2
/Ag
heterostructure is only
1
mm
2
.
T
he reason why we cho
o
se such small device area is that the
thickness of
SiO
2
gate dielectric is
only
9 nm.
Larger area
gate
-
tunable
ENZ
-
TiN/SiO
2
/Ag
heterostructures would typically exhibit high leakage
current upon biasing
,
due to defects
in the
gate dielectric.
When performing ellipsometry it is important
that incoming light is reflected
only
form the
working area of the device
. Hence, during ellipsometry
measurements we had to use
a
focused light beam. However, the beam spot was still larger than the
working are
a of the device, especially for larger incidence angles.
By using this approach we have been
able to obtain
Ψ
and
Δ
for different incidence angles
.
However, we haven’t been able to obtain a reliable
ellipsometry fit
to extract
the
dielectric permittivity of TiN. Nevertheless, we have
acquired
Ψ
and
Δ
for a
given incidence angle (60°)
and
different applied biases.
We observe optical modulation around 430 nm
where
Ψ
and
Δ
exhibit maximum and minimum,
respectively
.
Finally, we would l
ike to note that
since
ellipsometry has been performed several months after fabricating the sample, the observed optical
modulation is modest as compared to the result shown in Fig. 3 of the manuscript.
We combined the response to the current co
mment with
the response to the C
omment 3 of Reviewer 3,
and added the following paragraph to our SI:
When analyzing ellipsometry data, we use
d
two or three Lorentz oscillators to fit the data obtained from
the fabricated films. The key issue here is that optical properties of TiN films strongly depend on the film
stoichiometry (N/Ti ratio), impurities (residual oxygen, post growth oxidation), gr
ain size (which affects
the mean free path of the conduction electrons) and density/porosity (which affect the conduction electron
density)
[13]
. All these
factors likely differ from one film to another resulting in different values of fitting
parameters of
a
Drude
-
Loren
t
z model, such as electron mobility and frequencies o
f Lorentz oscillators. In
particular, it has been previously shown that the spectral position of
the
zero crossing (ENZ point) is an
indicator of film stoichiometry. It has been shown that for stoichiometric TiN films this crossing occurs at
2.65 eV (468 n
m)
[16]
.
As one can see from Fig. 2a, none of our films has
an
ENZ crossing at 468 nm.
Hence, all films reported in this work are non
-
stoichiometric. Moreover, it has been recently shown that
amount of residual oxygen in the
sputtering chamber can dramatically affect optical properties of TiN
films
[11, 12, 14]
. Based on these reports, we expect that each fabricated film has different chemical and
structural composition. The review article
[13]
discusses
the
relation between
the
band structure of TiN
obtained via density functional theory (DFT) calculations and
the
spectral
positions of Lorentz oscillators
in an ellipsometry fit. As one can see from Table 2 of the mentioned review article
[13]
, the
spectral
19
positions of Lorentz oscillators show significant variation. Moreover,
the
reported spectra
l position values
do
not always agree with DFT calculations. The reason for this is that the DFT calculations are performed
for
stoichiometric TiN while the films shown in our work as well as a number of films shown in the
review article
[13]
are non
-
stoichiometric. Moreover, we performed
compositional analyses on
135 nm
-
t
hick TiN films deposited on
Si substrate
s
via
DC
sputtering. The sputtering conditions
were
chosen to be
identical to those used to deposit TiN in the tunable ENZ
-
TiN/SiO
2
/Ag heterostructure. We found that the
stoichiometry of our film is given as TiN
0.8
O
0.2
, where oxygen has been introduced into our film
unintentionally. This result is consistent with previous
reports
[11, 12]
. Hence,
most likely, 7
nm
-
thi
ck
TiN films incorporated in our TiN/SiO
2
/Ag films also include
a
significant amount of oxygen impurities.
Based on this, it is not straightforward to relate position
s
of Lorentz oscillators to the band
structure of
our
TiN, due to limited knowledge of the
band
structure of the actual film. To summarize, the choice of
the model that we use to fit
the
ellipsometry data
two
vs.
three
Lorentz oscillators, etc.) is
largely
dictated
by the composition and structure of the films, which varies
. Due to
a
limited
knowledge of the
dependence of the TiN band structure on the material stoichiometry and the amount of incorporated
oxygen im
purities, we are not able to perform
a
direct comparison between
the
position
s
of Lorentz
oscillators and
the
material band structur
e.
One can obtain indirect evidence of compositional and structural differences
in
sputtered TiN
films when analyzing the dependence of the imaginary part of the measured dielectric permittivity Im(
ɛ
)
on the carrier concentration of the films. Indeed, Im
(
ɛ
) monotonically increases with the carrier
concentration for carrier concentrations
less than
or equal to 1.8
×
10
22
cm
-
3
a
nd
abruptly decreases
for the
sample with carrier concentration 1.8
×
10
22
cm
-
3
. This kind of behavior has been previously reported
in
literature
[11]
. In the
mentioned paper
,
Im(
ɛ
) of “intermediately doped” TiN is
greater
than Im(
ɛ
) of
“dielectric”
TiN
[11]
. On the other
hand, over a broad wavelength range, Im(
ɛ
) of
metallic
TiN is
smaller than Im(
ɛ
) of “intermediately doped” or “di
electric”
TiN
[11]
. It is
argued that when
the
oxygen
impurity concentration in TiN is
lessened
, the crystallinity of TiN films is improved, R
e
(
ɛ
) becomes more
negative
,
and Im(
ɛ
) decreases.
Interestingly, in the visible wavelength range we observe a non
-
mon
otonic behavior of Im(
ɛ
) as a
function of wavelength (Fig. 2b) that is consistent with previously reported functional dependences of
Im(
ɛ
) on wavelength
[11, 13, 14]
. On the other hand, as we observe in our work, Im(
ɛ
) typically grows
monotonically
as a function of wavelength in the near
-
infrared wavelength range
[11, 13, 14]
.
We
added
the following paragraph and Figure S2 into SI:
20
We have also performed ellipsometry of our
ENZ
-
TiN/SiO
2
/Ag
heterostructure
under applied
bias. However, obtained data is not amenable to unambiguous interpretation due to reasons described
below. The area of our gate
-
tunable
ENZ
-
TiN/SiO
2
/Ag
heterostructure is only 1
mm
2
. The reason why we
choose such small device area is that the
thickness of
SiO
2
gate dielectric used in our study is only 9 nm.
Larger area
gate
-
tunable
ENZ
-
TiN/SiO
2
/Ag
heterostructures would typically exhibit high leakage current
upon biasing due to defects of gate dielectric. When performing ellipsometry it is imp
ortant that incoming
light is reflected form the working area of the device only. Hence, during ellipsometry measurements we
had to use focused light beam. However, the beam spot was still larger than the working area of the
device, especially for larger i
ncidence angles. By using this approach we have been able to obtain
Ψ
and
Δ
for different incidence angles. However, we haven’t been able to obtain a reliable ellipsometry fit to
extract dielectric permittivity of TiN. Nevertheless, we have acquired
Ψ
and
Δ
for a given incidence angle
(60°) and different applied biases. We observe optical modulation around 430 nm where
Ψ
and
Δ
exhibit
maximum and minimum,
respectively
.
Finally, we would like to note that since ellipsometry has been
performed several months after fabricating the sample, the observed optical modulation is modest as
compared to the result shown in Fig. 3 of the manuscript.
Figure S2 | Reflectance mod
ulation measured via focused beam spectroscopic ellipsometry.
Δ
and
Ψ
for the ENZ
-
TiN/SiO
2
/Ag heterostructure as a function of wavelength at different voltages.
In this
measurement, t
he incidence angle is 60°. We observe modulation of
Ψ
and
Δ
under applied
electrical bias.
When electrical bias increases from
1
V to +1
V, we observe a monotonic increase of
Ψ
and monotonic
decrease of
Δ
.
Inset shows the SEM image of the device and the normal incident beam size of
focused
beam
spectroscopic ellipsometry
.