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Supporting Information for:
New method for lateral mapping of bimolecular recombination in thin
film organic solar cells
Jonas Bergqvist, Wolfgang Tress, Armantas Melianas, Zheng Tang, David Haviland and Olle
Inganäs
Figure S1 Simulated current-voltage curves for Fig. 2a.
Figure S2 Global 1 sun current-voltage response of the TQ1:PC71BM solar cell in Fig. 5 and
8.
1. Frequency dependence of photocurrent
We observe a frequency dependence for both the reverse and the forward bias of the solar cell
(S 3a). To investigate the cause we replace the solar cell with a resistor and drive it with a
modulated voltage from the lock-in. The current response is measured with the pre-amplifier
and lock-in amplifier. We plot the normalized frequency response at different solar cell bias
(S 3b). We conclude that the main frequency dependence is in the measurement apparatus,
while a slight drop in the photo-current occurs at higher frequencies for a bias close to opencircuit. The influence is small enough not to interfere with the measurements.
Figure S3 Frequency response of the solar cell including the frequency dependence of all
components in the setup at different applied bias (a). (b) Shows the normalized data of (a) and
the frequency dependence of a 2 MΩ resistor in series before the preamplifier input with a
modulated voltageto achieve a similar signal strength as in (a). The frequency dependance
below 10 kHz is mainly governed by the frequency dependence of the intermodulation
amplifier.
2. Potential sources of non-linear response
We have demonstrated that well operating organic solar cells do generate 2nd order
intermodulation (IMP) signals, which do not originate from artefacts in the measurement
setup. However, theoretical considerations indicate that there might still be some other causes
(besides those discussed in the main text) for the 2nd order IMP signals.
A non-linearity in current-voltage does generate 2nd order responses and could contribute to
the signal. This would occur if the amplitude of the modulated current is high enough to bias
the voltage along the IV-curve. The more charge that recombines, the stronger would be the
generated signal, as this enhances the non-linearities of the IV-curve.
A high series resistance of the solar cell (especially of the transparent electrode) could cause a
voltage drop strong enough to modulate the point of operation, not only in light intensity, but
also along the IV-curve. To investigate this we connect external resistances (RS_EXT) of 0.2
and 2 kΩ in series with the solar cell. Adding 0.2 kΩ RS_EXT to the circuit with a modulated
current of ~1 μA generates a voltage modulation of 200 μV. This small voltage modulation
does not influence the 2nd order response (S4a). However, the addition of 2 kΩ causes 2 mV
additional voltage modulation and is enough to slightly affect the 2nd order response close to
open-circuit.
The sheet resistances of the transparent electrodes in this study are 10-20 Ω/□ for ITO and
~100 Ω/□ for PEDOT:PSS. As an external 2 kΩ resistor did not affect the IMP signal (except
marginally around VOC) we conclude that we are in the ‘safe zone’, i.e. the series resistance
does not interfere with the measurement. However, this may cause problems for full device
measurements, where the area is usually ~4 mm2 (compared to the ~0.04 mm2 area of the
laser spots) generating 100 times higher currents.
An increasing RS_EXT increases the voltage where the photocurrent changes sign, VS (S4a).
This is due to a series resistance induced potential drop, VS = VF – JRS, where VF is the
voltage with equipotential (zero sheet resistance) electrodes. At VS > VOC the solar cell is at
forward bias and generates a significant dark current (S4b) leading to a higher J and thereby a
larger voltage drop. The dark current at VS is ~60 μA. Defining ΔVS = J*RS_EXT results in a
maximal ΔVS of 12 and 120 mV for RS_EXT = 0.2 and 2 kΩ. The corresponding measured ΔVS
is ~0-5 (low measurement resolution) and ~60 mV (S4c). The effect of the series resistance is
the most pronounced at forward bias, where the response of the 1st drops significantly with an
increasing RS_EXT. The signal is lost when the pre-amplifier input is saturated, which occurs at
0.5 mA. The influence of the series resistance is also evident in the characteristic plot (S4d).
The effect does however not change the characteristic parabola-like behaviour of the 2nd order
response for RS_EXT < 2 kΩ. This confirms that the series resistance must be taken into
account, but that the effect on the 2nd order response is not causing a problem as long as the
series resistance is kept to ‘normal’ levels (such as the resistances used in this study) for
organic solar cells.
Figure S4 Current-voltage response with external series resistances connected to the circuit
(a) and the corresponding global dark IV-curve (b). Zoom in on the voltage where the photo
current changes sign (c) to determine ΔVS and the corresponding characteristic plots for
varying external series resistances (d). ΔVS below 60 mV is confirmed to not affect the 2nd
order response.
To make sure that we are not measuring a non-linearity in the current-voltage relation, we
compare the derivative of the 1st order signal with respect to voltage
derivative multiplied with 1st , i.e.
𝑑1𝑠𝑡
𝑑𝑉
𝑑1𝑠𝑡
𝑑𝑉
and also the
∗ 1𝑠𝑡 , to the measured 2nd order response (S 5a). The
measured 2nd response clearly behaves differently, i.e. with a signal at lower voltages, while
the mathematical products start generating a signal closer to open-circuit. Also in the
characteristic plot the response rise of the derivatives at higher reverse voltages is clear and
can be ruled out (S 5b).
Figure S5 Current-voltage response of the mathematical derivatives
𝑑1𝑠𝑡
𝑑𝑉
∗ 1𝑠𝑡 and
𝑑1𝑠𝑡
𝑑𝑉
and
nd
the experimental 2 response (a) and the corresponding characteristic plots (b). The
difference in shape excludes a 2nd order response signal contribution due to non-linearities in
voltage.
To investigate amplification induced non-linearities in the pre-amplifier we have measured
the 1st and 2nd order responses at two amplifications, 5 and 20 µA/V (S 6). From the perfect
overlap after normalizing to the same amplification we conclude that the amplification level
do not introduce additional 2nd order non-linarities.
Figure S6 Current-voltage response of 1st and 2nd with 20 μA/V (black, signal *4) and 5
μA/V (color) amplification on the preamplifier. As all curves overlap we conclude that the
amplification does not introduce contributions to the 2nd order response signal.
3. Bimolecular recombination in TQ1:PC71BM and P3TI:PC71BM
Figure S7 Photo-generated carrier density decay in TQ1:PC71BM and P3TI:PC71BM. Photoinduced absorption (empty circles) and time-delayed charge extraction (photo-CELIV, filled
circles) experiments indicate that recombination in both blend systems is bimolecular, as
confirmed by the relatively good fit (dashed line) to a bimolecular decay dn/dt = -𝛽n2. The
photo-induced absorption traces were recorded at a similar pump-fluence for both blend
systems, i.e. 2×1012 photon/cm2/pulse for P3TI:PC71BM and 2.5×1012 photon/cm2/pulse for
TQ1:PC71BM.
4. Mapping DC light dependence
We use the characteristic plots to validate that the recombination in the IMLBIC mapped
device in Fig. 9 is bimolecular. Both high and low current rendering areas display the
parabola-like shape characteristic of bimolecular recombination. However, at the lower
current density area a slightly distorted shape is observed. To fully validate that the
recombination is bimolecular we also vary the dc background illumination IDC. The current
was measured under two 𝐼1 = 𝐼2 = 𝐼𝐷𝐶 + 𝐼0 conditions; 0.18 suns + 0.7 suns and 0.1 suns +
0.3 suns. The 2nd order IMP signal normalized to 𝐼02 for the high (S 8a) and low (S 8b) current
regimes shows a clear reverse dependence on 𝐼𝐷𝐶 with reduced 2nd order response with
increasing 𝐼𝐷𝐶 . When normalized to 𝐼𝐷𝐶 the two 2nd curves from the high current part (S 8c)
overlap very well, as expected from simulation. Also both curves from the low current part
overlap well (S 8d), however with a small difference around the 2nd maxima. From this we
conclude that the recombination mechanism in both the high and low photocurrent density
generating areas is mainly bimolecular. However, the distorted parabola and the lower
amplitude in the low current area could be an indication of monomolecular recombination.
Given a homogenous device thickness, the lower saturation current in the low photocurrent
density is evidence of a monomolecular recombination likely caused by non-dissociated
excitons.
Figure S8 Characteristic plots normalized to I02 for (a) high current area and (b) low current
area. Normalization to IDC gives a good overlap in the high current area (c) and in the low
current area.
5. Lateral potential drops
The high photocurrent generating area has ~60 mV higher VS compared to the lower current
generating area (Fig 8f). This we assign to the series resistance in the top PEDOT:PSS
electrode causing a voltage drop over the surface. The effect is most pronounced for V > VOC,
when the contribution from the dark current enhances the voltage drop. However ΔVS = 60
mV is confirmed not to affect the shape of the characteristic plot (S 4d).
6. Laser spot size determination
Figure S9 Photocurrent cross section scan for laser L1 (black) and L2 (blue) and the DC laser
(red). L1 and L2 overlap well and the overlapping curves confirm very similar spot sizes,
while the DC laser spot is larger. From the current onset and saturation the illumination spot
size is quantified.