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C: Energy Conversion and Storage; Energy and Charge Transport
Substrate-Dependent Photoconductivity Dynamics in a High-Efficiency Hybrid Perovskite Alloy Ali Moeed Tirmzi, Jeffrey A. Christians, Ryan Patrick Dwyer, David T. Moore, and John A. Marohn J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11783 • Publication Date (Web): 17 Jan 2019 Downloaded from http://pubs.acs.org on January 17, 2019
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The Journal of Physical Chemistry
Substrate-Dependent Photoconductivity Dynamics in a High-E ciency Hybrid Perovskite Alloy Ali Moeed Tirmzi,† Jerey A. Christians,‡ Ryan P. Dwyer,† David T. Moore,‡ and John A. Marohn∗ † ,
†Dept. of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA ‡National Renewable Energy Laboratory, Golden, CO 80401, USA E-mail:
[email protected] Abstract
in a lead-halide perovskite crystal depends on the concentration (i.e., the chemical potential) of the relevant
Films
of
(FA0.79 MA0.16 Cs0.05 )0.97 Pb(I0.84 Br0.16 )2.97
chemical species present in the solution or vapor from
conductivity was interrogated by measuring the in-
13,5,9 Nonequi10 librium growth of the perovskite in the thin- lm form
phase
were grown over TiO2 , SnO2 , ITO, and NiO. and
out-of-phase
forces
acting
which the perovskite was precipitated.
the
should generate additional point- and grain-boundary
We followed the
defects. The concentration of defects in the crystal also
lms' conductivity vs. time, frequency, light intensity,
depends on the electron and hole chemical potential
and
con-
which if the perovskite's background carrier concen-
ductivity was high and light-independent over ITO
tration is su ciently low could be strongly aected
and NiO.
by the substrate.
lm and a charged microcantilever. temperature
(233
to
312 K).
between
Film
Perovskite
Over TiO2 and SnO2 ,
the conductivity
Evidence that the substrate aects
was low in the dark, increased with light intensity,
band alignment and induces p- or n-type conductivity
and persisted for 10's of seconds after the light was
can be seen in XPS,
removed.
ments of lead-halide perovskite lms, in one example in
At elevated temperature over TiO2 ,
the
rate of conductivity recovery in the dark showed an activated temperature dependence (Ea
a lm as thick as
= 0.58 eV).
11 UPS, 12,13 and IPES 12 measure-
400 nm. 12
How the substrate changes
the near-surface and bulk conductivity of the perovskite
13 eects include the for-
Surprisingly, the light-induced conductivity over TiO2
is a topic of current research;
and SnO2 relaxed essentially instantaneously at low temperature. We use a transmission-line model for
mation of an interface dipole, the creation of a chem-
mixed ionic-electronic conductors to show that the
changes in perovskite lm morphology.
ically distinct passivation layer, and substrate-induced
measurements presented are sensitive to the sum of electronic and ionic conductivities.
Defects in halide perovskites are challenging to study
We rationalize
for a number of reasons.
Many of these defects are
the seemingly incongruous observations using the idea
mobile under the application of electric eld and/or
that
light, with iodine species and vacancies considered to
holes,
introduced
either
by
equilibration
with
1422 Moreover, recent reports
the substrate or via optical irradiation, create iodide
be most mobile species.
vacancies.
by Maier and coworkers show that the concentration of mobile iodine vacancies depends on illumination inten-
1
19 This eect, which is expected from defect-energy 1,3,9 needs to be considered in addition to calculations,
Introduction
sity.
the established eects of light on charge motion and
The extraordinary performance of solar cells made from
polarization when trying to understand light-related
solution-processed lead-halide perovskite semiconduc-
hysteresis phenomena.
tors is attributed to the material's remarkably high defect tolerance and low exciton binding energy.
15 The
Here rial
theoretically predicted ionic defect formation energy is
we with
15,20,2329
study
a
precursor
high-performing solution
relatively low and consequently the equilibrium defect
(FA0.79 MA0.16 Cs0.05 )0.97 Pb(I0.84 Br0.16 )2.97
solar cells to reach their Shockley-Queisser limit, it is
substrates TiO2 , SnO2 , ITO, and NiO.
2,6 For perovskite concentration should be quite high.
(here-
after referred to as FAMACs) grown over four dierent tians and coworkers reported
necessary to understand how these defects form and
1000
hours
3032 Chris-
operational
stability for FAMACs devices prepared with an SnO2
identify which ones contribute to non-radiative recombination, loss of photovoltage, and device hysteresis.
mate-
stoichiometry
7,8
electron acceptor layer. based
At equilibrium, the concentration of a speci c defect
stable.
devices,
SnO2
devices
were
much
more
While degradation of TiO2 devices has previ-
ACS Paragon Plus Environment 1
the
30 When compared to TiO 2
The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
ously solely been attributed to ultraviolet light induced degradation,
Page 2 of 20
dependent.
33,34 they revealed, using ToF-SIMS mea-
As in Ref. 35, here we follow conductivity dynamics
surements, dierent ionic distributions in TiO2 - and
using a charged microcantilever.
SnO2 -based devices after several hours of operation.
primarily used in scanning-probe microscope experi-
This observation demonstrates a clear dierence in the
ments to create images. However, they have also proven
light and/or electric eld induced ion/vacancy motion
useful in non-scanning experiments because of their
in SnO2 - and TiO2 -based devices. Motivated by these ndings, here we measure the
tremendous sensitivity as force sensors.
AC conductivity of the FAMACs lms in the kHz to
perovskite solar-cell materials have used Kelvin probe
MHz regime and study this conductivity as a func-
force microscopy to observe the dependence of the sur-
tion of light intensity, time, and temperature.
We
face potential and surface photovoltage on time, elec-
show that the light-on conductivity returns to its ini-
tric eld, and light intensity in order to draw con-
100
clusions about the spatial distribution of charges and
tial light-o value on two distinct timescales (sub ms and
10's
Microcantilevers are
Prior scan-
ning probe microscopy (SPM) studies of lead-halide
of seconds) in the material grown on the
ions.
5162 In studies of organic solar cell materials,
electron accepting substrates TiO2 and SnO2 . In con-
frequency-shift measurements have been used to follow
trast, material grown on the hole acceptor (NiO) and
the time evolution of photo-induced capacitance and
ITO substrates shows frequency-independent conduc-
correlate the photocapacitance risetime with device
tivity. We tentatively assign these distinct behaviors to
performance.
dierences in the perovskites' background carrier type
used
and concentration.
icon
monitor
local
dopant
concentration
in
sil-
44 and GaAs; 36 probing quantizied energy levels 38 examine photo-induced damage in in quantum dots; 41,42 quantify local dielectric organic solar cell materials;
We nd that the SnO2 -substrate
lms show higher dark conductivity and slower relaxation than the TiO2 -substrate lms.
to
6367 Sample-induced dissipation has been
We show that
43,4649,68 and probe
at room temperature and above, the relaxation of the
uctuations in insulating polymers;
conductivity is activated over TiO2 (and possibly over
dielectric uctuations and intra-carrier interactions in
SnO2 also).
semiconducting small molecules.
Surprisingly, the relaxation of conduc-
39 Here we make use of
tivity becomes considerably faster when the sample is
the tremendous sensitivity of a charged microcantilever
cooled to a low temperature of 233 K.
to passively observe the time evolution of a thin- lm
The simplest
35 through changes in cantilever
explanation we can devise for these diverse observa-
sample's conductivity
tions is that the measured conductivity changes arise
dissipation induced by conductivity-related electric- eld
from light-dependent electronic uctuations; at room
uctuations in the sample.
69
temperature, these electronic uctuations are coupled to slow, light-induced ionic/vacancy uctuations that are frozen out at low temperature.
2
Our observation
that the timescale of the conductivity recovery in the
2.1 Materials
SnO2 -substrate sample is much slower than in the TiO2 substrate sample supports the Christians
et al.
hypoth-
Methylammonium bromide (CH3 NH3 Br, MABr), and
esis of slower ionic motion in the SnO2 -substrate sample
formamidinium iodide (CH(NH2 )2 ,
30
compared to TiO2 -substrate sample. These experiments were motivated by our previ-
FAI),
were pur-
chased from Dyesol and used as received.
Lead (II)
iodide (99.9985% metals basis) and the SnO2 colloid
ously reported scanning probe microscopy study of
precursor (Tin(IV) oxide,
light- and time-dependent conductivity in a thin lm
35
Experimental Section
15%
in H2 O colloidal disper-
sion) were purchased from Alfa Aesar. All other chem-
3649
of CsPbBr3 . We used sample-induced dissipation 50 and broadband local dielectric spectroscopy (BLDS)
icals were purchased from Sigma-Aldrich and used as received.
to demonstrate for CsPbBr3 that conductivity shows o, with an activation energy and time-scale consis-
2.2 Oxide Layer Deposition
tent with ion motion.
a slow activated recovery when the light was switched We concluded that the sample
Indium tin oxide (ITO) glass was cleaned by soni-
conductivity dynamics were controlled by the coupled
cation in acetone and isopropanol, followed by UV-
motion of slow and fast charges. While CsPbBr3 served
ozone cleaning for
as a sample robust to temperature- and light-induced
additional thin oxide layer was deposited on the ITO
degradation, it has a relatively high band gap and is
glass (if necessary).
thus poorly suited for use in high e ciency solar cells.
a previously reported low temperature TiO2 process.
Many high e ciency devices reported to date rely on a
15 min.
Following cleaning,
an
TiO2 layers were deposited using
mixed cation/anion perovskite absorber layer (such as
Brie y, TiO2 nanoparticles were synthesized as reported 70 and a 1.18 wt. previously by Wojciechowski et al.
FAMACs) to reach the desired bandgap and enhanced
%
stability needed for photovoltaic applications. The goal
nium diisopropoxide bis(acetylacetonate), was spin-cast
of the present study is to ascertain whether the con-
onto the ITO substrates with the following procedure:
ductivity dynamics observed for CsPbBr3 are evident
700
in FAMACs lms and to see whether they are substrate
Tin oxide electron transport layers were deposited on
ethanolic suspension,
rpm,
10 sec;
ACS Paragon Plus Environment 2
along with
1000 rpm,
10 sec;
20 mol %
2000 rpm,
tita-
30 sec.
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The Journal of Physical Chemistry 71 The aqueous SnO colloid 2
charge is modulated by physically oscillating the can-
solution, obtained from Alfa Aesar, was diluted in water
tilever, by applying a time-dependent voltage to the
cleaned ITO substrates. with a ratio of
1 : 6.5
and spin-cast at 3000 rpm for
cantilever tip, or by doing both simultaneously. A sum-
30 sec. Both the TiO2 and SnO2 lms were then dried ◦ at 150 C for 30 min and cleaned for 15 min by UV-ozone
mary of the distinct measurements carried out below is given in Figure 1.
immediately before use. NiO lms were deposited from
Changes in the cantilever frequency and amplitude
H
a solution of nickel nitrate hexahydrate and ethylenedi-
may be expressed in terms of a transfer function
amine in ethylene glycol following a previously reported
which relates the voltage
procedure.
tip (the sample substrate is grounded) to the voltage
72
Vts
applied to the cantilever
Vt
dropped between the cantilever tip and the sample sur-
2.3 FAMACs Perovskite Film Deposition
operating in parallel with a capacitor
Deposition of the FAMACs perovskite layers was car-
The resulting transfer function is given in the frequency
ried out in a nitrogen glovebox following the method
domain by
face. The cantilever is modeled electrically as a capacitor
reported in Ref. 31. The precursor solution was made
172 mg
while the sample is modeled as resistor
FAI,
1000
for
20 sec.
10 sec,
rpm for
While the substrate was spinning,
1 + j g −1 ωτfast ˆ . H(ω) = 1 + j ωτfast
6000 rpm
0.1 mL
of
chlorobenzene was rapidly dripped onto the lm with approximately
6 sec
where
remaining in the spin-coating pro-
cedure, forming a transparent orange lm.
1
were then annealed for
hr at
◦
100 C
Z.
The lms
to form highly
(5
× 10=6 mbar)
were in
a
performed
custom-built
(Rs−1 + jωCs )−1
(2)
de nes the sample impedance
The transfer function
H
can be viewed as a lag
are given by, respectively,
τfast = Rs (Cs + Ctip ) = Rs Ctot
2.4 Scanning probe microscopy experiments
(1)
compensator whose time constant and gain parameter
specular FAMACs perovskite lms.
All
Rs
(Figure S2).
which simpli es to
deposited by spin coating this precursor solution with the following procedure:
Cs
(jωCtip )−1 Vˆt (ω) ˆ = H(ω) = −1 (Rs + jωCs )−1 + (jωCtip )−1 Vˆts (ω)
507 mg PbI2 , 22.4 mg MABr, and 73.4 mg PbBr2 (1 : 1.1 : 0.2 : 0.2 mole ratio) and 40 µL of CsI stock solution (1.5 M in DMSO) in 627 mg DMF and 183 mg DMSO (4 : 1 v/v). The lms were by dissolving
Ctip
and
g = Ctot /Cs .
(3)
We give the time constant the subscript fast because
under scanning
vacuum
of the time constant's similarity to τfast measured
Kelvin
probe microscope described in detail elsewhere.
in impedance spectroscopy.
67,73
below that
Ctip Cs ;
35 We show experimentally
consequently,
τfast ≈ Rs Ctip .
The cantilever used was a MikroMasch HQ:NSC18/Pt
This simpli cation allows us to associate photo-induced
conductive probe. The resonance frequency and quality
changes in cantilever frequency and amplitude to photo-
factor were obtained from ringdown measurements and
induced changes in sample resistance or, equivalently,
found to be
ωc /2π = fc = 70.350 kHz
and
Q = 24 000
sample conductivity.
respectively at room temperature. The manufacturer's
The complex-valued transfer function in Eq. 2 has
speci ed resonance frequency and spring constant were
a real part which determines the in-phase forces and
fc = 60
to
75 kHz
and
k = 3.5 N m−1 .
Cantilever
an imaginary part which determines the out-of-phase
motion was detected using a ber interferometer operating at
1490 nm
forces acting on the cantilever.
(Corning model SMF-28 ber). More
We show the equiv-
alent circuit and plot the shape of transfer function in
experimental details regarding the implementation of
Figure S2. The frequency shift measurements presented
broadband local dielectric spectroscopy and other mea-
in Figure 4b probe the real part of the transfer function,
surements can be found in the Supporting Information.
3
fc δF 0 2k A 2 fc 00 ˆ c) =− Cq + ∆C 00 Re H(ω V −φ 4k
∆f = −
Results
3.1 Theoretical background
where
Let us begin by summarizing the equations we will use
fc = ωc /2π
is the resonance frequency,
spring constant, and
to connect scanning-probe data to sample properties.
of the cantilever;
Interested readers are directed to Ref. 35 and Ref. 69
F0
A
k
(4)
is the
is the amplitude, respectively,
is the in-phase force;
Ct
is the
cantilever capacitance computed at rest with the can-
for a detailed derivation of the following equations. In
tilever at its equilibrium position;
our measurements we modulate the charge on the can-
∆C 00 ≡ 2(Ct0 )2 /Ct ,
with primes indicating derivatives with respect the tip-
tilever tip and the sample and observe the resulting
∆Cq00 ≡ Ct00 − ∆C 00 ; V is the voltage applied to the cantilever tip; and φ is the surface potensample distance;
change in the cantilever frequency or amplitude. This
ACS Paragon Plus Environment 3
The Journal of Physical Chemistry (a)
Broadband local dielectric spectroscopy Figs. 3, 7, 10 Parameters controlled: Vt = VAC Parameters probed: frequency shift ∆f BLDS(ωm) alpha α (ωm) Re (Ĥ (ωm))
(b)
(c)
Ring-down dissipation measurement Figs. 5, 6, 8, 9 Parameters controlled: drive Parameters probed: amplitude vs time
Frequency shift vs Voltage/ Amplitude vs Voltage Fig. 4 Parameters controlled: Vt = VDC Parameters probed: frequency shift ∆f (ωc) Re (Ĥ (ωc)) alpha α (ωc) normalized dissipation Υs amplitude change ∆A
quality factor Q
sample-induced dissipation Γs
Im (Ĥ (ωc))
Driving Force ON Amplitude [nm]
Im (Ĥ (ωc))
fam = ωam/2π = 45 Hz
{
VAC
FAMACs
FAMACs
FAMACs
VDC = Vt (-4 V to 4 V)
ITO
SnO2 or TiO2 or NiO
Driving Force OFF
Time [ms]
{
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 20
VDC = Vt (-4 V)
fm= ωm/2π = 200 Hz to 1.5 MHz
ITO
SnO2 or TiO2 or NiO
ITO
SnO2 or TiO2 or NiO
Figure 1: Schematic of the three scanning probe measurements used in this manuscript, highlighting the parameters that are controlled and probed. The measurements probe the complex frequency dependent tip-sample transfer function Hˆ (Eq. 2 and Figure S2). (a) In a broadband local dielectric spectroscopy measurement, the tip voltage Vt = VAC (ωm , ωam ) is amplitudemodulated at a xed frequency of fam = ωam /(2π) = 45 Hz and sinuodially modulated at a frequency fm = ωm /(2π) that is varied from 200 Hz to 1.5 MHz. At each fm the component of the cantilever frequency shift ∆fBLDS (ωm ) at frequency fam is measured using a frequency demodulator and lock-in ampli er and α(ωm ) is calculated using Eq. 8. The quantity α(ωm ) primarily ˆ m )) (Eq. 7). (b) In a frequency shift ∆f vs. Vt measurement or an amplitude A vs. Vt measurement, the tip measures Re(H(ω voltage Vt = VDC is slowly varied from −4 V to 4 V while the cantilever frequency shift ∆f and the cantilever amplitude A are recorded. From ∆f a voltage-normalized frequency shift α(ω0 ) is calculated using Eq. S4; the quantity α(ω0 ) primarily measures ˆ c )). From A a voltage-normalized sample-induced dissipation γs is calculated using Eq. S9; the quantity γs primarily Re(H(ω ˆ c )) (Eqs. 6 and S8). (c) In a ring-down dissipation measurement, the cantilever drive is periodically switched measures Im(H(ω o, the cantilever amplitude is measured as a function of time, and the cantilever's mechanical quality factor Q is calculated from this ring-down transient. The observed change in Q is converted to an equivalent change in sample-induced dissipation Γs using ˆ c )) (Eq. 6). Eq. S10. The parameter Γs primarily measures Im(H(ω tial. The variable
α0
plotted in Figure 4a is a voltage-
have assumed the amplitude modulation frequency
∆f vs. ∆f = α0 (V − φ)2 and
ωm
normalized frequency shift, the curvature of the
is much smaller than
V
Supporting Information).
data de ned by the equation
given by
transfer function
α0 = −
1/τfast
fc 00 ˆ c) . Cq + ∆C 00 Re H(ω 4k
From Eq. 5 we can see that
α0
BLDS spectra obtained at low light intensity over SnO2 and TiO2 , Figure 3, where the majority of the response
ωc , with addi-
rolls o at
tional contributions from in-phase forces present at low frequency (ω/2π
< 0.1 Hz).
The sample-induced dissi-
where
F 00
is
the
out-of-phase
force
acting
on
We conclude that the BLDS
the modulation frequency. The voltage-normalized frequency shift
to the out-of-phase part of the transfer function,
1 δF 00 ∆C 00 ˆ c) V − φ 2, = Im H(ω ωc A ωc
ωm ωc .
measurement primarily measures the in-phase forces at
pation plotted in Figures 4a, 5, 6, 8, and 9 is sensitive
Γs = −
The term in Eq. 7 containing the factors
ˆ c −ωm ) and H(ω ˆ c +ωm ) is small as indicated by the H(ω
is sensitive to the real
part of the transfer function at frequency
The imaginary part of the
is signi cant only at the frequency
where the real part of the transfer function starts
to roll-o.
(5)
ˆ H
∆fBLDS
α
plotted in Figures 3, 7, 10 is related to
by
α=
(6)
∆fBLDS (ωm ) . Vm2
measured quantity in each of the three dierent scan-
The voltage-normalized dissipation γs ∝ ˆ c )) plotted in Figure 4b is related to Γs through Im(H(ω 2 the equation Γs = γs (V −φ) . The BLDS measurements
ning probe measurements employed in this manuscript.
3.2 Experimental ndings
of Figures 3, 7, and 10 are frequency-shift measurements that probe the response of the sample to an oscillating
We now present data acquired on the FAMACs sam-
applied voltage,
ples prepared on a range of substrates. All of the substrates (TiO2 , SnO2 , NiO, ITO) are planar structures. The FAMACs thickness was ∼700 nm; the thickness of
fc Vm2 h 00 ˆ m + ωc ) Cq + ∆C 00 Re H(ω ∆fBLDS (ωm ) = − 16k i ˆ m − ωc ) |H(ω ˆ m )|2 (7) + H(ω
ETL/HTL layer was of
∼10 nm,
∼40 nm
and
Vm
illuminated from the top.
are the frequency and amplitude,
with average roughness
and the thickness of the ITO was
with an average roughness of
ωm
(8)
Figure 1 summarizes the experimental set-up and the
the
cantilever.
where
ωam
(see Experimental Section in
∼2 nm.
∼100 nm
The samples were
The high absorption coef-
cient of the perovskite lm means that electron and
respectively, of the oscillating applied voltage and we
ACS Paragon Plus Environment 4
Page 5 of 20
other words, a decrease in the time constant
a)
τfast
light. In Figure 3 we clearly see a roll-o of the
ωm
Ag
with
α
vs.
curves that depends on the light intensity in the
case of electron-acceptor substrates (TiO2 and SnO2 ),
spiro-OMeTAD
whereas in the case of the NiO-(hole acceptor) and ITO-
FAMACs Perovskite
substrate samples,
α
is independent of both
ωm
and
light intensity.
TiO2
For the rest of this section of the manuscript, we compare the light and frequency dependence of the conductivity in the TiO2 and SnO2 -substrate samples.
ITO
b)
glass
response. However some signi cant dierences can also be seen: 1. In the dark, the SnO2 -substrate sample is more conductive than the TiO2 -substrate sample as seen by their dark BLDS response curves.
20
-2
)
20 15
Power Density (mW cm
)
-2
Both
samples show a light-dependent roll-o of the dielectric
25
Current Density (mA cm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
10 5
18.7 mW/cm2
15
2. The conductivity of the SnO2 -substrate sample is more strongly aected by light than that of
10
the TiO2 -substrate sample; the roll-o moves to
5 0
higher frequencies for the same light intensity 0
400
Time (s)
800
for the SnO2 -substrate sample compared to the TiO2 -substrate sample.
1200
0 0.0
0.2
0.4
0.6 0.8 Potential (V)
1.0
These light-dependent conductivity eects can be
1.2
con rmed through quasi-steady-state measurements of the cantilever frequency shift (∆f ) vs. applied tip voltage (Vts ) and cantilever amplitude (A) vs. applied
Figure 2: (a) Control perovskite solar cells were fabricated with the TiO2 /FAMACs/spiro-OMeTAD/Ag architecture depicted in the schematic. (b) A reverse scan (scan taken from opencircuit voltage, VOC , to short-circuit current, JSC ) current density-voltage (J − V ) curve taken for a device with the architecture depicted in (a). From the reverse J − V scan, the VOC , JSC , ll factor, and power conversion e ciency were measured to be 1.141 V, 22.49 mA/cm2 , 0.744, and 19.1%. The inset shows the power density of the device monitored at a constant bias of 0.94 V over the course of 1200 s which was found to stabilize at 18.7% e ciency.
tip voltage (Figure 1b).
In these measurements the
cantilever is driven using constant-amplitude resonant excitation and the cantilever amplitude and frequency shift are recorded at each applied
Vts .
By tting the
measured frequency shift and amplitude data to Eq. S4 and Eq. S9 respectively see Figure S3 for representative curves and Sec. S3 for calculation details we can calculate the curvature (α0 ) change and a voltagenormalized sample-induced dissipation constant (γs ). These values are not aected by the tip voltage sweep width; the large wait time (500 ms) employed at each
hole generation was con ned to the top
∼200 nm
applied tip voltage ensure that the measured response
of
is a steady-state response.
the sample, a distance signi cantly smaller than the
700 nm
Figure 4a shows the sample-induced dissipation mea-
thickness of the FAMACs layer. Figure 2 shows
sured
device-performance data for a representative FAMACs lm prepared on a TiO2 substrate; this data demon-
a maximum and then decreases with light intensity can be explained by the existence of a time constant
τfast
α at large voltage-modulation
indicates qualitatively that not all of the
conductivity state. When
τfast
is less than
ωc−1 = 2 µs,
most of the sample charge responds instantaneously to
In our impedance model of the tip-sample interaction,
RC
that increased monotonically with light intensity.
At high light intensities, the sample reaches its high-
sample charge is able to follow the modulated tip charge. Figure S2, this decrease is attributed to the
In
sity. A non-linear increase in dissipation which reaches
50 Figure 1a) acquired of lms
the Experimental Section in Supporting Information).
ωm
method.
Figure S4 illustrates the predicted dependence of the
prepared on TiO2 , SnO2 , ITO, and NiO substrates (see
frequency
amplitude-voltage
curvature and sample-induced dissipation on light inten-
Figure 3 shows Broadband Local Dielectric Spec-
In Figure 3, a decrease in
the
response of the sample at the cantilever frequency.
strates the high quality of the lms used in this study.
troscopy data (BLDS,
through
this measurement we are sensitive to the out-of-phase
changes in the tip position, leading to a decrease in
roll-o
the out-of-phase force acting on the cantilever and a
of the tip-sample circuit. A light-dependent change in
reduction in sample-induced dissipation.
the roll-o frequency is consistent with sample conduc-
We see for
both the TiO2 -substrate sample and the SnO2 -substrate
tivity increasing with increasing light intensity or, in
sample that dissipation reached a maximum before
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a)
b)
c)
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d)
540 mW/cm2
1 mW/cm2
Figure 3: Distinct Broadband Local Dielectric Spectroscopy (BLDS) curves seen in FAMACs thin lms grown on (a) TiO2 , (b) SnO2 , (c) ITO, and (d) NiO. Curves are colored according to the applied light intensity (See right hand legend)and vertically opset by 0.05 for clarity. For reference, BLDS curve in the dark is shown in open black circles. Experimental parameters: modulation voltage Vm = 6 V, λ = 639 nm, tip-sample separation h = 200 nm except for the TiO2 -substrate sample where h = 150 nm. a)
a)
hν 0
b)
b)
Figure 5: Dissipation recovery in the dark is substrate dependent. Dissipation vs. time for FAMACs lm on (a) TiO2 (b) SnO2 -substrate. The indicated illumination intensity was turned o at t = 0 sec. Experimental parameters: Vts = −4 V, T = 292 K, (a) λ = 535 nm, h = 175 nm, (b) λ = 639 nm, h = 200 nm. applied tip voltage parabola (α0 ). The data of Figure 4,
which primarily measures
sample response at a single frequency (ωc ), corroborates the data of Figure 3 which shows the sample response at multiple frequencies. The solid lines in Figure 4 are a t to a one-time-constant impedance model described
Figure 4: Normalized (a) out-of-phase (dissipation) (b) inphase (curvature) force for FAMACs lms on dierent substrates. Shaded points indicate values in the dark. Solid lines show a t to the impedance model described in Ref 35. Experimental parameters: λ = 639 nm, h = 200 nm, A0 = 45 nm, Vts = −4 V to 4 V (bipolar sweeps).
in Ref. 35 and summarized in Sec. 3.1.
qualitatively
The model
explains the seemingly-anomalous peak in
sample-induced dissipation vs. light intensity data over both TiO2 and SnO2 . The one-time-constant model only qualitatively describes the charge dynamics in the SnO2 -substrate sample; adding further electrical components to the sample-impedance model, justi ed by the double roll-o seen in the Figure 3b data, would
decreasing when the light intensity was increased monotonically.
improve the SnO2 -substrate ts in Figure 4.
Figure 4b shows that, concomitant with a
We observed the dynamics of
dissipation peak, there is a non-linear change in the in-
two dierent methods.
phase response at the cantilever frequency, observed as
τfast in real time through
In Figure 5a, we show how
the dissipation changes for the TiO2 -substrate sample
a changes in the curvature of the frequency shift vs.
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The Journal of Physical Chemistry a)
for dierent light intensities. Here we inferred sample-
b)
induced dissipation by measuring changes in the quality factor of the cantilever through a ring-down measurement (Figure 1c and Sec. S4).
The recovery of dis-
sipation clearly had two distinct timescales a fast component and a slow component.
In Figures 5a
and b, when the light was switched on, there was a large and prompt (≤
100 ms)
increase in dissipa-
tion followed by a small and much slower increase that lasted for
10 s
or longer.
The presence of the
slow component was especially clear when the light intensity was greater than the light intensity giving the maximum dissipation.
Figure 6: Dissipation recovery over the TiO2 -substrate sample is temperature dependent. (a) Dissipation recovery transients in the dark after a period of continuous illumination. (b) Time constant for dissipation recovery Γs recovery vs. temperature with error bars calculated from the ts in (a). Error bars are small on the y-axis scale. The shaded region represents 2 standard deviations for a weighted least squares t to an exponential model τΓ (T ) = A−1 exp(Ea /kB T ). The best t parameters with two standard deviation error bars were Ea = 0.58±0.07 eV and A = 4.9±1.0 × 102 s−1 . Experimental parameters: Vts = −4 V, Ihν = 292 mW/cm2 , tsoak = 27 s, h = 150 nm, λ = 639 nm.
Whether the dissipation
increased or decreased when the light was switched o depended on the value that
τfast
(i.e. sample conduc-
tivity) reached during the light-on period. At low light
−2
15.6 mW cm−2 for the −2 TiO2 -substrate sample, Figure 5a, and 13 mW cm for intensities (2.06 mW cm
and
the SnO2 -substrate sample, Figure 5b), the dissipation
Γs
decreased when the light was switched o, indicating
that
τfast
was
tial rise in
Γs
≥ 2 µs.
On the other hand, the ini-
when the light was switched o for the
331 mW cm−2 dataset in Figure 5a and the 72 mW cm−2 dataset in Figure 5b is consistent with a light-on τfast being ≤ 2 µs. In such a case, when the light was switched o, the Γs promptly increased in ≤ 200 ms as τfast approached the value of 2 µs. Subsequently, Γs gradually decreased over 10's of seconds as τfast became ≥ 2 µs. In
Figure
induced
5b,
we
dissipation
show
a
time-resolved
measurement
dielectric response at a xed modulation frequency (ωm ). The response at each
light-
ωm
corresponds to the in-
phase force at that modulation frequency.
By doing
the measurement at dierent modulation frequencies,
substrate sample. The slow part of the recovery of dis-
we can visualize the time evolution of the full dielectric
500 sec)
the
we illuminate the sample and measure the time-resolved
SnO2 -
sipation was extremely slow (>
for
response for the TiO2 -substrate sample (Figure 7). Here
at room tem-
response curve in the dark after the light was turned
perature. This slow recovery indicates that the SnO2 -
o.
substrate sample retained its conductive state for a
curves for time just before switching o the light (open
much a longer time than did the TiO2 -substrate sample.
circles) and
Interestingly, the slow time constant for dissipation
circles) shows a fast (
