Supplementary Materials for
Deep-ultraviolet transparent conducting SrSnO
3
via heterostructure design
Fengdeng Liu
et al.
Corresponding author: Bharat Jalan, bjalan@umn.edu; Fengdeng Liu, liu00492@umn.edu;
Zhifei Yang, yang7001@umn.edu
Sci. Adv.
10
, eadq7892 (2024)
DOI: 10.1126/sciadv.adq7892
This PDF file includes:
Sections S1 to S10
Figs. S1 to S9
References
I. HAADF-STEM of a ~4 nm SrSnO
3
/~19 nm La-doped SrSnO
3
film
Fig. S1.
HAADF
-STEM of
SrSnO
3
film
.
Low magnification HAADF-STEM image of
a
representative
~4 nm
SrSnO
3
/~19 nm
La-doped
SrSnO
3
film. Scale bar
is
100 nm. Magnified
region boxed in orange
is a high resolution HAADF-STEM image,
showing
the structure of the
film. Scale bar is 10 nm.
II. Characterization of superlattice samples
Fig. S2.
Characterization of superlattices.
High-resolution X-
ray diffraction scan of superlattice
samples with thickness of the SrSnO
3
layers
x
= 0, 0.6 1.1, 2.1 nm.
A schematic of the sam
ple
structure is illustrated in the inset.
III. Temperature-dependent transport measurement
Fig. S3. Electrical transport of
4 nm SrSnO
3
/19 nm La-doped SrSnO
3
thin films.
(a)
Temperature-dependent Hall sheet carrier density for samples grown with 1080 °C ≤
T
La
≤ 1240
°C.
(b)
Measured Hall mobility as a function of temperature for these samples.
Due to charge transfer at the SSO/La:SSO interface and electron doping in the SSO layer,
both SSO and La:SSO layers will contribute to the measured transport properties. Therefore, here
we choose to use sheet carrier density from the Hall measurement
n
H
2D
as
푛
!
"#
=
퐼
퐵
푉
!
푒
where
I
is the excitation current,
B
is the applied magnetic field,
V
H
is the measured Hall voltage
and
e
is the electron charge, since this quantity does not exclusively depend on the film thickness.
Similarly, Hall mobility
μ
H
can be calculated by
휇
!
=
1
푅
%
푛
!
"#
푒
where
R
s
is the measured sheet resistance.
IV. Extracted bulk-layer properties from the two-channel conduction model
Fig. S4. Extracted bulk-layer properties from the two-channel conduction model.
Extracted
bulk-layer (19 nm La-doped SrSnO
3
) mobilities as a function of the bulk carrier density with the
fraction value
f
= ±2% at
(a)
300 K and
(b)
200 K.
V. Reversibility and leakage current in ion-gel gated SSO/La:SSO thin films
Fig. S5.
Switching
and leakage
current
with electrolyte gating.
(a)
Sheet resistance vs. time for
gate voltage
V
g
= 0 V
→ +4 V → 0 V→
-4 V→ 0 V
cycle at 250 K.
Corresponding
leakage current
between gate and drain
I
GD
as a function of time during the
V
g
switching at
(b)
positive gate
voltages and
(c)
negative gate voltages
Sheet resistance
R
s
of the sample described in the manuscript is recorded while
V
g
is
gradually increased from 0 V to +4 V at a +1 V interval. Then the gate voltage is removed. Another
cycle with negative
V
g
increasing to
-4 V at a
-2 V interval is also carried out. Note here that at
each gate voltage switching, there is a rapid change of sheet resistance. After removing the gate
voltage after
V
g
= ±4 V,
R
s
returns quickly to near the initial value shown as the dashed line in Fig.
S5(a), indicating an excellent reversibility at 250 K. At 250 K, after waiting for some time after
applying the gate voltages |
V
g
| ≤ 4 V, the leakage current between gate and drain
I
GD
falls below
100 nA as illustrated in Fig. S5(b) and (c), much smaller than the excitation current 10
μA used for
transport measurements. Therefore, the accuracy of our transport measurements at 250 K is not
affected.
VI. Sheet resistance of the sample before and after ion gel gating
Fig. S6.
Reversibility of ion-gel gating.
Measured sheet resistance
R
s
as a function of temperature
for the sample before and after ion-gel gating with 2 trials.
Fig. S6 shows the measured sheet resistance of the sample as a function of temperature before
and after ion-gel gating experiments. The relatively small change (~8%) from the sheet
resistance of the pristine sample (black squares in Fig. S6) to the sheet r
esistance of the sample
after multiple cycles of ion-gel gating (purple diamonds in Fig. S6) demonstrates the electrostatic
nature of the gating process on SrSnO
3
.
VII. Calculation of accumulation-layer carrier density and mobility due to electrostatic
modulation and error analysis
The depth dependent potential
φ
(
z
) and electron density distribution
n
3D
(
z
) due to
electrostatic modulation by ion gels at different
V
g
can be obtained by solving the Poisson’s
equation (
29, 30
):
훻
"
휑
=
−
휌
휀
푑
"
휑
푑
푧
"
=
−
(
−
푒
)
(
푛
&#
−
푛
'
&#
)
휅
휀
(
at the SSO/La:SSO interface.
κ
=15 is the dielectric constant in SSO
(
18
). Potential
φ
can be related
to electron distribution
n
3D
by Thomas-Fermi approximation,
푒휑
=
ℏ
"
푘
)
"
2
푚
*
∗
=
ℏ
"
2
푚
,
∗
(
3
휋
"
푛
&#
)
"
/
&
where
m
e
*
= 0.4
m
e
is the effective electron mass in SSO
(
19
) and
m
e
is the electron mass.
The second-order differential equation needs appropriate boundary conditions to solve.
One boundary condition is at the La:SSO/GSO substrate (
z
= 0) where we assume the modulation
effect by ion gels is negligible and the potential corresponds to the initial doping level in the La
-
doped SSO layer,
휑
(
0
)
=
ℏ
"
2
푚
,
∗
푒
(
3
휋
"
푛
.
&
/
(
0
)
)
"
/
&
The second boundary condition is that at the ion gel/SSO interface (
z
=
d
= 23 nm), there is an
electric field due to the induced charges by ion gels,
푑휑
푑푧
|
0
1
2
=
푒
∫
>
푛
&#
−
푛
'
&#
?
푑푧
2
(
휅
휀
(
푛
'
&#
is the electron density profile at
V
g
= 0 and is used as the initial conduction for solving the
differential equation at different positive gate voltages
V
g
.
푛
'
&#
is obtained with the similar
calculation shown in the main text Fig. 1(b) which accounts for the charge transfer at the
SSO/La:SSO interface (
21
).
The value of accumulation
-layer thicknesses
d
A
can be obtained from the
n
3D
profiles and
it is defined as the thickness which 90% of electrostatically induced electrons are confined within
(
29, 30
)
in the main text. We have also performed error analysis assuming different confinement
depths for the induced electrons.
d
A
can be assumed to be the thickness over which 90% ± 5% of
the electrostatically induced electrons are confined. This gives us
d
A
= 3.14 nm (85%) to 3.73 nm
(95%) at
V
g
= 0 and
d
A
= 2.90 nm (85%) to 3.71 nm (95%) at
V
g
= +4 V. The extracted
accumulation-layer mobility
μ
A
= 152 cm
2
V
-1
s
-1
(85%) to 131 cm
2
V
-1
s
-1
(95%) at
V
g
= 0 and
μ
A
=
126 cm
2
V
-1
s
-1
(85%) to 114 cm
2
V
-1
s
-1
(95%) at
V
g
= +4 V.
VIII. Comparison between extracted accumulation-layer mobility due to ion-gel gating and
calculated phonon-limited mobility
n
A
3
D
(10
19
cm
-
3
)
μ
A
(cm
2
V
-
1
s
-
1
)
V
g
(V)
1
2
3 4
Calculated phonon
-
limited mobility
Extracted accumulation
-
layer mobility
250 K
Fig. S7. Extracted accumulation-layer properties with electrolyte gating.
Extracted
accumulation-layer mobility
μ
A
as a function of electron density
n
A
3D
at 250 K at different gate
voltages. The gray solid line is the calculated phonon
-
limited mobility over the similar electron
density range.