Understanding the Thickness and Light-Intensity Dependent Performance of Green-Solvent Processed Organic Solar Cells

For indoor light harvesting, the adjustable band gap of molecular semiconductors is a significant advantage relative to many inorganic photovoltaic technologies. However, several challenges have to be overcome that include processability in nonhalogenated solvents, sufficiently high thicknesses (>250 nm) and high efficiencies at illuminances typically found in indoor environments. Here, we report on the development and application of new methods to quantify and identify performance losses based on thickness- and intensity-dependent current density–voltage measurements. Furthermore, we report on the fabrication of solar cells based on the blend PBDB-T:F-M processed in the nonhalogenated solvent o-xylene. In the low-intensity regime, insufficiently high shunt resistances limit the photovoltaic performance and by analyzing current density voltage–curves for solar cells with various shunt resistances we find that ∼100 kΩ cm2 are required at 200 lux. We provide a unified description of fill factor losses introducing the concept of light-intensity-dependent apparent shunts that originate from incomplete and voltage-dependent charge collection. In experiment and simulation, we show that good fill factors are associated with a photo-shunt inversely scaling with intensity. Intensity regions with photo-shunt resistances close to the dark-shunt resistance are accompanied by severe extraction losses. To better analyze recombination, we perform a careful analysis of the light intensity and thickness dependence of the open-circuit voltage and prove that trap-assisted recombination dominates the recombination losses at low light intensities.

Best efficiencies are reached for LEDs with a 2700 K spectrum due to the maximized overlap of the device's external quantum efficiency  e,PV and the spectral irradiance  e,λ of the LED.Note, that compared to the measured/interpolated  sc s (Figure 7, ~30 µA/cm² at 200 lux), strongly reduced  sc s are found in this calculation.As we measured our data close to 200 lux with an OD 2 Filter, LED spectra are strongly red-shifted and the input-power density is ~140 µW/cm².Hence, the measured data shows increased  sc s.This example illustrates again, that device performance can only be evaluated correctly if corresponding LED spectra and accurately measured input-power densities are shown.Usually, organic solar cells are measured in a sealed sample box to be protected from degradation.Cui et al. pointed out that the use of aperture masks with a reflecting surface like stainless-steel can lead to higher  sc by absorption of scattered light. 2 Here we demonstrate, the impact of silver lids on the measured irradiances.We performed absolute spectral irradiance measurements of our used LED without a lid and with a windowed stainless-steel lid at the exact position of the solar cell.In order to compare both measurements, the irradiance without a lid is corrected by -8 %, as the light entering the sample box is refracted at the glass window two times.In Figure S3 the irradiances are plotted against the illuminances.The irradiance (and therefore also the illuminance) measured with the silver lid (squares) are ~23 ± 0.8 % higher compared to the corrected irradiance without a lid (triangles) for the whole intensity range.We assume that a black lid is not refracting any light.Hence, for samples measured in boxes with black lids we use the irradiances/illuminances without lid corrected by the -8 % refractions losses.Consequently, if comparing samples measured with a silver lid and a black lid, silver lid measurements will be shifted towards higher illuminances/irradiance.The exact values of the whole measuring range are depicted in Table S1.
Table S1.Input-power densities and illuminances of all LED currents and filters measured with an integrating sphere at the exact position of the solar cell with and without a silver lid.
with lid w/o lid x 0.92 Table S2.Device performance of OPV devices (A = 0.16 cm² and A = 0.06 cm²) fabricated for this work under illumination with the 2 OD filter @45 mA (resulting in ~200 lux)  Table S3.Parameters for the simulation of a generic organic solar cell in ASA using the effective-medium model 3,4 .For simplicity, the generation rate G was kept constant over the entire volume.It was defined in such a way that the generation-current density is independent of the active-layer thickness as G = Jgen/(qd).(c) .Exemplary JV characteristics (circles) and corresponding fit (solid lines).For devices with non-linear shunts, the JV dependence is not reproduced accurately (blue).In some cases, fitting the (, Φ) −  sc data leads to underestimated  s as the diode region is less pronounced (red).

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In general, with the simple equivalent-circuit a good fit is achieved, but in some cases, where the shunt is non-linear, the small-voltage region is not reproduced accurately.
Nevertheless, as the  p,dark is by the magnitude of data, and not by the exact JV dependence, the fitting procedure is sufficient to determine the  p,dark .For the fitting procedure of the (, ) −  sc () data the  s is not reproduced well for high intensities, as the region dominated by the diode is less pronounced.maintained.The extraction of charge carriers is lower under a certain voltage than in the short-circuit condition.The term Δ ph (, ) < 0 (dashed lines in Figure S10c)) and thus, the shifted JV curves (, ) +  sc () =  dark () − Δ ph (, ) increase with increasing intensities.For lower intensities in some cases, we see | ph (, )| > | sc ()| and the term Δ ph (, ) > 0 (solid lines in Figure S10c)).Here, the shifted JV curves fall below the dark JV curve.Usually, one would expect the photocurrent under a certain voltage to be lower than the current in the short-circuit condition, so this behavior is still under debate, but can be discussed by considering the spatial generation and recombination rates.The photocurrent and short-circuit current density can be expressed as the difference between charge  Figure S13.a)  oc plotted against / ln () for the simulated cases of direct, mixed and SRH recombination at an active-layer thickness of ~100 nm.The slope indicates the ideality factor  id,l .For SRH recombination the  oc is increasing faster with increasing light intensity compared to the case of direct recombination as the ideality factor is higher.b) Different terms of Equation 8 are compared for direct and SRH recombination and for different intensities at a constant thickness of ~100 nm on a double-logarithmic axis.The generated current  gen (green triangles) is increasing linearly with the intensity (slope of 1 on doublelogarithmic axis).The exponential term in Equation 8 exp (− oc /) (spheres) is displayed for direct (purple) and SRH (blue) recombination.If we plug in  oc =  id / ln () into the exponential term of Equation 8, we get to exp (− oc /) =  − id .Consequently, the slope on the double-logarithmic axis  ln(exp (− oc /))/ ln() = − id .This means that for direct recombination where  id = 1, the exponential term is decreasing as fast as the  gen is increasing, so that the  0,oc is constant with the intensity.On the other hand, for SRH recombination, the  oc is increasing faster with increasing intensity (with a slope of ~1.7).Hence, the exponential term is decreasing faster compared to  gen resulting in a decreasing  0,oc .This discussion shows that for increasing  id the  0,oc is decreasing.

Note 6: Derivation of 𝑱 𝟎,𝑽𝐨𝐜 (𝒅)
For the open-circuit condition and for sufficient negative biases, where  gen ≈  sc , the measured  0,oc is described by Note, that in the case of direct recombination of free charges, the recombination rate is given by  dir = ( −   2 ).Additionally, we assume  ≫  i 2 and  =  i 2 exp (/).As the voltage dependence cancels out,  0,oc simplifies to  0,oc =  i , which is not a function of the light intensity and constantly increases with thickness with a slope  = 1.

Figure S1 .
Figure S1.Performance parameters of the devices with different active-layer thicknesses with A = 0.16 cm² for different LED spectra and an illumination of 200 lux according to the analysis presented in Ref 1. Best efficiencies are reached for LEDs with a 2700 K spectrum due to the maximized overlap of the device's external quantum efficiency  e,PV and the spectral irradiance  e,λ of the LED.Note, that compared to the measured/interpolated  sc s (Figure7, ~30 µA/cm² at 200 lux), strongly reduced  sc s are found in this calculation.As we measured our data close to 200 lux with an OD 2 Filter, LED spectra are strongly red-shifted and the input-power density is ~140 µW/cm².Hence, the measured data shows increased  sc s.This example illustrates again, that device performance can only be evaluated correctly if corresponding LED spectra and accurately measured input-power densities are shown.

Figure S2 .Note 1 :Figure S3 :
Figure S2.Absolute spectral irradiances of a 2700 K LED for different LED currents  LED and normalized spectral irradiances for the used OD 2 (blue), OD 1 (red) filter and without filter (green, OD 0).Note, that the normalized spectral irradiances are plotted for all  LED , showing that the spectra are constant within the used LED current range.

A
Figure S4.Thickness-dependent performance parameters of PBDB-T:F-M organic solar cells at 1 sun conditions for cell areas of A = 0.16 cm² (full circles) and A = 0.06 cm² half circles.

FigureNote 2 :
Figure S5.a) Short-circuit current density  sc , b) output-power density  out and c) inputpower density  in of the PBDB-T:F-M solar cells with A = 0.06 cm on a double-logarithmic scale.

FigureNote 3 :)
Figure S7.a) Simulated  curves at 1 sun.b) s of the simulated  curves plotted against the intensity.Simulation shifted curves for devices with an active-layer thickness of a) 250 nm b)150 nm and c) 85 nm for direct (solid lines) and SRH (dashed lines) recombination.No mayor differences between direct and SRH recombination can be seen.

V
Figure S9.Photo-shunt resistances of the measured shifted JV characteristics versus the irradiance for a wide variety of samples.Dark blue points correspond to high a)  and b)  oc and light blue points correspond to low a)  and b)  oc .

FigureNote 5 Figure
Figure S11.a) Short-circuit current density  sc , b) the open-circuit voltage  oc and c) fill factor  plotted against the photo-shunt resistance  p,photo on a double-logarithmic scale for the devices with different thicknesses and A = 0.06 cm².The dashed lines indicate the dark-shunt resistance  p,dark .
hand, the recombination-current density can be described as the integral over the spatially recombination rates  rec = ∫ ()  with  SRH = / eff () for traps in the middle of the band gap.Here,  is the concentration of free electrons and  eff is the effective lifetime, assuming  =  and equal lifetimes for electrons and holes.Hence, for SRH recombination the recombination-current density is  rec = / eff () .Alternatively, we can describe the dependence of  eff on  by defining a constant lifetime and express the dependency on  with a voltage-dependent term  SRH  i is the intrinsic charge-carrier density and  id is the ideality factor.Then, the recombinationcurrent density is  rec ( oc ) =  sc = S4 into Equation S3 leads us to  0,oc ( oc ) =  i / 0 exp ( In the case of Shockley-Read-Hall recombination, we assumed a distribution of acceptor-like trap states around the center of the bandgap.The recombination mechanisms stated below are the only recombination pathways allowed in the simulations.If not mentioned otherwise, no external resistances are included.