Download 1 Supporting information for Ultrafast dynamics of carrier mobility in

Supporting information for
Ultrafast dynamics of carrier mobility in a conjugated polymer probed at
molecular and microscopic length
A. DEVIŽIS1, A. SERBENTA1, K. MEERHOLZ2, D. HERTEL2 and V. GULBINAS1
1
Institute of Physics, Savanoriu 231, Vilnius, Lithuania
2
Department of Chemistry, Physical Chemistry, University of Cologne,
Luxemburgerstr. 116, 50939 Cologne, Germany
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Sample preparation
The devices were fabricated on indium-tin oxide (ITO) covered glass by spin coating
from toluene solution. The aluminum counter electrode was deposited by thermal
evaporation. Where appropriate, the devices were encapsulated with a thin glass slide.
Devices for conventional TOF were prepared by drop casting onto ITO substrates and
evaporation of aluminum electrodes. After preliminary measurements the samples were
annealed at 150°C for 12 h or at 280°C for 30 min. This procedure yields improved
transport characteristics.
Experimental setup
The experimental setup for TREFISH investigations is based on an amplified
femtosecond Ti-sapphire laser generating 130 fs pulses (810nm) at 1 kHz repetition rate
(supporting info). The polymer film was excited with 460 nm pulses obtained by Raman
shifting of the second harmonic (405 nm) of the fundamental laser radiation (810 nm) in
ethanol. The excitation intensity was about 7 µJ/cm2. Pulses of the fundamental laser
radiation at 810 nm were used to probe the sample with variable time delay with respect
to the excitation (460 nm). Excitation and probe beams were directed to the polymer film
at 45o angle to the film surface through the ITO coated glass. The second harmonics of
the probe pulse (810 nm) generated in a polymer film was reflected by the top aluminum
and measured with a PMT. Voltage pulses of 10 µs duration were applied to the sample
synchronously with optical excitation. To avoid charge carrier injection from the
aluminum electrode it was positively biased.
Integral TOF investigations were performed simultaneously by measuring the voltage on
the integrating capacitance (1 nF) connected in series to the sample with an oscilloscope
in parallel. The capacitor discharging time was set by a resistor Rint to be several times
shorter than the interval between laser pulses.
The TREFISH setup is sketched in Fig. S1 together with the ISHG as a function of the
square of applied bias. The fitted line allows to extract the built in field (0.6 V).
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Figure S1. Upper part: The experimental setup used to measure TREFISH and integral
TOF. Lower part: The field dependence of the ISHG intensity of PSF-BT
without excitation pulse.
Contributions to the electric field kinetics
For comparison the TREFISH signal and the PL decay of PSF-BT from Fig 1 (2 V
applied bias) are shown in Fig. S2. The similarity of the kinetics is striking. This is
completely different at higher applied electric fields (Fig. 1).
We now address the question what other processes, besides carrier motion and exciton
generation might contribute to the electric field change and why we consider them as
negligible.
1) Relaxation of excitons in the DOS
The relaxation of excitons within the density of states (DOS) has no effect on the electric
field since the exciton correlation length (electron-hole distance) is constant. Otherwise
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the exciton has to undergo dissociation (charge transfer) before both carriers can drift
separately.
2) Charge transfer states
In principle the charge carrier contribution ∆ECC(t) includes coulombically bound charge
pairs (CT states), if they are present. The small number of charge pairs created by exciton
splitting on impurities or structural defects without assistance of electric field does not
contribute directly to the field kinetics, because the charge separation direction is not
aligned with electric field. They contribute only indirectly by changing the polarizability
of the ionized polymer segment. Assuming polarizability change being comparable to
that due to polymer segment excitation, which is 2006 Å3 in the related polymer MeLPPP
[15], we obtain the charge displacement being less than 1 Å.
The decay of CT states (and thus the decay of polarization) is far beyond the time scale
probed by TREFISH. As mentioned above the number of CT states generated without
electric field is two orders of magnitude smaller compared with the field assisted
dissociation [16]. The contribution of the field assisted exciton dissociation is taken into
1.01
1.00
1.00
0.99
0.99
0.98
0.98
0.97
0.97
/I0
SHG
I
0.96
PL intensity (a.u.)
1.01
SHG
(a.u.)
account by the time dependent carrier generation function.
0.96
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Time (ns)
Figure S2.
Left axis, symbols: TREFISH signal at 2 V from PSF-BT (from fig. 1)
Right axis, line: Fluorescence decay of PSF-BT at 2 V measured by
TCSPC. The decay of fluorescence is inverted a scaled for comparison.
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Calculation of the carrier density
The carrier density changes due to the time-dependent carrier generation and their
extraction from the sample. To obtain the carrier generation function we use the
fluorescence quenching method. It was demonstrated that the carrier generation rate is
proportional to the fluorescence quenching rate. Figure S3 shows the fluorescence decay
kinetics at different applied voltages.
1.0
0.8
0.6
g(t)
Fluorescence Intensity (a. u.)
10-1
0.4
0.2
10-2
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Time (ns)
0.5
1.0
Time (ns)
Figure S3. Fluorescence kinetics obtained after deconvolution of the fluorimeter
response function. The kinetics from top to bottom correspond to the
following voltages 0V black line, 6V magenta line, 9V blue line, 12V green
line and 15V red line. The inset shows the carrier generation function.
The carrier generation function (inset Fig. S3) is:
t
g (t ) =
1
γ (t ' )nexc (t ' )dt '
q ∫
nexc
0
(E1)
q
is total quenched exciton density, γ (t ) is the
Here nexc (t ) is the exciton density, nexc
fluorescence quenching rate. The g(t) function expresses the carrier density during their
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generation time normalized to the total generated carrier density n0. The total generated
carrier density is obtained from the integral TOF measurement. The fluorescence
quenching rate γ (t ) was obtained from the fluorescence intensity F (Fig. S3) under
applied field F(t)E and at zero field F(t)E=0 as:
γ (t ) =
1 dF (t ) 0
1 dF (t ) E
,
−
2 F (t ) 0 dt
2 F (t ) E dt
(E2)
In case of homogeneous sample excitation the carrier extraction kinetics can be
expressed by the average carrier drift distance l as: next=n0l(t)/d. The number of extracted
carriers is next. Since carrier generation is much faster than their extraction we can express
the carrier density as: n(t ) = n0 g (t )(1 − l (t ) / d ) . Now the photocurrent density is:
I (t ) = n0 eg (t )[1 − l (t ) / d ](dl (t ) / dt ) ) .
(E3)
Here e is the electron charge. We solve equation E3 numerically, by using the iteration
method to obtain the carrier density and the average drift distance l(t.)
Time-of-flight (TOF) mobility in thick samples
Transient photocurrents were recorded with the time of flight (TOF) technique. The
currents, amplified with by low noise current amplifier with a time resolution of 50 ns,
were detected with an oscilloscope. The charge carriers were generated by illumination
through the ITO anode with pulses of the third harmonic (355 nm) of a Nd/YAG laser or
a dye laser operated at 440 nm. To avoid space-charge accumulation in the sample the
excitation density was chosen to limit the emitted charge to <0.05 CV, where C is the
sample capacitance and V the applied voltage. All measurements were done in a
temperature controlled cryostat under vacuum.
The mobility as measured by conventional TOF is plotted in Figure S4. The mobility was
calculated from :
µ= d2/Vttr
V is the applied voltage. The sample thickness d is 3.6 µm. For the determination of the
transit time ttr either linear plots of the transient photocurrent vs. time or double log plots
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were used, depending on the degree of dispersion. Photocurrents were averaged over
typically 100 excitation pulses. The transit times were taken from the intersection of
tangents on the photocurrent plateau and trailing edge. Although the material PSF-BT has
been selected because it is completely amorphous and no ordered phases have been found
annealing has some influence on transport. The degree of dispersion depends on the sign
of the carrier only little on sample annealing. For electron transport the dispersion is
relatively high, while hole transport is non-dispersive. The tail of the photocurrent
transients is slightly less extended for annealed samples.
10-2
Mobility (cm2/Vs)
10-3
10-4
10-5
10-6
300 400 500 600 700 800 900 1000 1100 1200
(Electric Field)1/2 (V/cm)1/2
Figure S4 TOF mobility of holes (squares) and electrons (circle) in a 3.6 µm thick
PSF-BT sample. The data correspond to measurements before (solid
symbols) and after (open symbols) annealing. Error bars represent
uncertainties due to transit time determination and variations due to repeated
measurements.
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The data displayed in Fig S4 are obtained before and after annealing at 280°C on the
same sample. Although annealing increases the electron mobility (due to reduced
dispersion) almost no influence on the hole mobility can be detected within experimental
error. The mobility increases with the electric field although with slightly different slope
for electrons and holes. At high field saturation of the drift velocity of both carriers is
visible. Saturation for electrons sets in at lower fields.
For thick samples the hole mobility varies by a factor of two with thickness. However,
the thickness range that can be studied is small (2.6 to 3.6 µm). Since the mobility in
disordered materials depends inherently on morphology, the sample to sample variation
of the mobility is a factor of two as well. Therefore the carriers are not range limited. For
the TREFISH mobility there is currently no indication on a thickness dependence of the
mobility.
Further studies on this issue are conducted with TREFISH on thin and conventional TOF
in thick devices. The details will be described in a future publication.
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