Enhancement of the internal quantum efficiency in strongly coupled P3HT-C60 organic photovoltaic cells using Fabry–Perot cavities with varied cavity confinement

Abstract The short exciton diffusion length in organic semiconductors results in a strong dependence of the conversion efficiency of organic photovoltaic (OPV) cells on the morphology of the donor-acceptor bulk-heterojunction blend. Strong light–matter coupling provides a way to circumvent this dependence by combining the favorable properties of light and matter via the formation of hybrid exciton–polaritons. By strongly coupling excitons in P3HT-C60 OPV cells to Fabry–Perot optical cavity modes, exciton-polaritons are formed with increased propagation lengths. We exploit these exciton–polaritons to enhance the internal quantum efficiency of the cells, determined from the external quantum efficiency and the absorptance. Additionally, we find a consistent decrease in the Urbach energy for the strongly coupled cells, which indicates the reduction of energetic disorder due to the delocalization of exciton–polaritons in the optical cavity.


S1. Optical constants of P3HT
In Fig. S1(a), the real and imaginary refractive index spectra of P3HT films can be found for different P3HT concentration.These spectra were obtained via ellipsometry measurements.
In Fig. S1(b) the corresponding absorption coefficient of P3HT is given and can be compared to the absorption coefficient of C 60 .

S2. Additional dispersion measurements of the absorptance of the OPV cells
In Fig. S2, the measured and calculated absorptance of the reference cells, the Fabry-Perot cells with 10 nm mirrors and the Fabry-Perot cells with 30 nm mirrors can be found for different angles of incidence in a range between -40 and 40 degrees.For the calculated absorptance, the transfer matrix method (TMM) is used.
Part of the discrepancy between measurements and calculations is caused by the difference in substrate.In the case of the calculation, the glass substrate has an infinite thickness with the light source located inside the substrate, while for the measurement the light source is located in air, thus outside the substrate.(c) Fabry-perot cell t A g = 10 nm t P 3HT = 60 nm.(d) Fabry-perot cell t A g = 10 nm t P 3HT = 80 nm.(e) Fabry-perot cell t A g = 30 nm t P 3HT = 60 nm.(f) Fabry-perot cell t A g = 30 nm t P 3HT = 60 nm.The FP cells show the formation of polariton bands, whose wavelengths decreases with increasing angle.
Additionally, small variations in the refractive index used for the calculations and the refractive index of the deposited material can exist.For the P3HT layer, the refractive index used in the calculations was determined via ellipsometry of spin-coated P3HT layers (See section S1).This means the refractive index values are expected to be the same for measurement and calculation.However, the anisotropy of the P3HT layer and the difference between in-plane and out-of-plane refractive indices was not taken into account in the calculation.
For the thin silver film of the Fabry-Perot cells, the ellipsometry data of a uniform 100 nm thick silver film was used.The values obtained for this thicker film are only an estimation of the refractive index values of the silver films used in the measurement due to the non-uniform evaporated thin layers (see section S4).The difference is the largest for the 10 nm silver films, which explains the large discrepancy between calculation and measurement for these cells.

S3. JV-curves
Figure S3 shows all the JV-curve measurements of the four substrates, each containing four contacted cells.

S4. Scanning electron microscope images of thin film Ag (10 nm)
A scanning electron microscope (SEM) image is taken for the Ag film with 10 nm to check the deposited film quality.The SEM image (Fig. S4) shows a poor-quality film that forms islands instead of planar film.This film quality explains the poor results for the Fabry-Perot OPV cells with 10 nm Ag mirrors.

S5. Electric field distributions
We compare the fields ins the different layers of the solar cell for the reference cell and the Fabry-Perot cavity cell using the transfer matrix method (TMM).For the FP cavity solar cell (20 nm Ag), we observe a large enhancement of the electric fields around the lower polariton wavelength and a slight enhancement of the fields at the UPB wavelength, while the field is reduced for other wavelengths compared to the reference.

S6. Low energy absorption tails
The low energy absorption tail of the EQE measurement of the P3HT-C 60 solar cells with 60 nm P3HT thickness was shown in the main text.For reference, we include the low energy tail for cells with 70 nm P3HT thickness and 80 nm P3HT thickness in Fig. S6.In the case of a P3HT thickness of 80 nm, the lower polariton peak has an energy in the absorption tail, making an accurate analysis of the Urbach energy difficult.However, for the 70 nm P3HT layer cells similar results are found as for the 60 nm P3HT cells.The reduced Urbrach energies found for cells with 70 nm P3HT are presented in Fig. S7, together with the Urbach energies of the cells with 60 nm P3HT.The uncertainty in the Urbach energy is given by the uncertainty of the exponential decay fit. Figure S7: The Urbach energy, equal to the decay constant retrieved from the exponential decay fits (eq.(??)), plotted as a function of Ag film thickness for PV cells with a P3HT layer of 60 ad 70 nm.

S7. Bare Fabry-Perot resonances and uncoupled excitons
The energy of the Fabry-Perot resonance (E F P ) for different angles of incidence has been determined by fitting the bare cavity structure calculated using the TMM (see methods).
This fit was done in Matlab using the peak finding function.The result is shown in Fig. S8 for t P 3HT = 80 nm and t Ag = 20 nm for s-polarization.In this figure, the fit is depicted by the green-dotted curve.The cavity loss, γ F P , has been determined from the full width at half maximum of the FP resonance at normal incidence.For a P3HT layer of 80 nm and an Ag film thickness of 20 nm, it is equal to γ F P = 0.08 eV.This value is used in the coupled oscillator model (see Methods), as it can not be directly retrieved from the measurements due to the P3HT exciton absorption.

Figure
Figure S1: (a) Real and imaginary refractive index spectrum of P3HT.Measured via ellipsometry for a P3HT layer spin-coated using a solution with a concentration of 15 and 22 mg/ml.(b) Absorption coefficient of P3HT and C 60 , calculated from the corresponding refractive index spectra.

Figure S2 :
Figure S2: Measurements and TMM calculations of the angular absorption dispersion of P3HT-C 60 -BCP solar cells.(a) reference cell t P 3HT = 60 nm.(b) reference cell t P 3HT = 80 nm.(c) Fabry-perot cell t A g = 10 nm t P 3HT = 60 nm.(d) Fabry-perot cell t A g = 10 nm t P 3HT = 80 nm.(e) Fabry-perot cell t A g = 30 nm t P 3HT = 60 nm.(f) Fabry-perot cell t A g = 30 nm t P 3HT = 60 nm.The FP cells show the formation of polariton bands, whose wavelengths decreases with increasing angle.

Figure S3 :
Figure S3: Additional JV measurements of the cells in the four different substrates.
Figure S4: SEM image of a Ag film with a thickness of 10 nm evaporated onto an ITO/glass substrate.
Figure S5: a. Wavelength-dependent field distribution and simulated absorption in a reference solar cell, and b. in a FP cavity solar cell with a 20 nm thick silver mirror.

Figure
Figure S6: (a) Low energy tail of the measured EQE spectra of PV cells with a P3HT thickness of 70 nm, fitted using an exponential decay fit.The graphs show a steepening of the absorption edge in the case of strongly coupled Fabry-Perot cells.(b) Lower energy tail of the measured EQE spectra of PV cells with a P3HT thickness of 80 nm.The lower polariton peak is located in the absorption tail, making it difficult to determine the Urbach energy.

Figure S8 :
Figure S8: Fabry-Perot resonance fitted for a cavity thickness of 80 nm filled with a dielectric with the same real component of the refractive index as P3HT but without absorption, and an Ag film thickness of 20 nm.The fit is shown by the green dotted line.

Figure S9 :
Figure S9: Fitted Exciton peaks of a full solar cell structure without top contact for a P3HT layer thickness of 80 nm.