Higher order effects in organic LEDs with sub-bandgap turn-on

Spin-dependent nonlinear processes in organic materials such as singlet-fission and triplet-triplet annihilation could increase the performance for photovoltaics, detectors, and light emitting diodes. Rubrene/C60 light emitting diodes exhibit a distinct low voltage (half-bandgap) threshold for emission. Two origins for the low voltage turn-on have been proposed: (i) Auger assisted energy up-conversion, and (ii) triplet-triplet annihilation. We test these proposals by systematically altering the rubrene/C60 interface kinetics by introducing thin interlayers. Quantitative analysis of the unmodified rubrene/C60 device suggests that higher order processes can be ruled out as the origin of the sub-bandgap turn-on. Rather, band-to-band recombination is the most likely radiative recombination process. However, insertion of a bathocuproine layer yields a 3-fold increase in luminance compared to the unmodified device. This indicates that suppression of parasitic interface processes by judicious modification of the interface allows a triplet-triplet annihilation channel to be observed.


Supplementary Figures
Supplementary Figure 1  In addition to the electrical characterization, we investigated the magneto-electroluminescence (MEL) of the devices with BCP interlayer. It has been discussed often that an Auger assisted up conversion process significantly differs from a TTA mechanism in its MEL-characteristics. TTA shows an increase in luminescence with small applied magnetic fields, before a steady decrease in the luminescence can be observed for large fields. 1-4 An Auger process should have a somewhat inverted dependence as singlet fission becomes dominant and increased fields lead to increased MEL. 5,6 The measured MEL-characteristics for our devices, shown in Supplementary   Figure 3, agree well with those reported for other materials exhibiting a triplet-triplet annihilation mechanism, 1-4 luminescence increase for small fields (here <25 mT) and steady decrease (here 25 mT < B < 100 mT) thereafter. However, the relative change in MEL response is very small, between +1 % and -4 %, such that this result is not conclusive and might be due to small changes in recombination dynamics of free charges independent of TTA.
In all Rate equations, it was assumed that product of the charge carrier densities, np , is large compared to intrinsic charge carrier density np >>n i 2 , with the intrinsic charge carrier density and the non-equilibrium charge carrier densities approximated by: 6 Supplementary Note 3: Built-in Potential Shown in Supplementary Figure 4 are the schematics of an intrinsic homojunction with charge carrier injection directly into the transport levels, this corresponds to the common point of view for organic electronics, a pn-homojunction and a pn-heterojunction.

Supplementary Figure 4 -Flatband band structure
Band structure under flatband conditions: a) intrinsic homojunction with charge carrier injection into the transport levels; b) pn-homojunction, c) pn-heterojunction (different bandgaps, but smaller bandgap material lies not within the bigger bandgap material).
In the field of organic electronics, the built-in potential (built-in voltage V bi ) is often viewed as difference between the transport levels and as such approximately the bandgap of the semiconductor. This leads to the believe that the turn-on voltage in OLEDs, which is roughly the built-in voltage, must be equivalent to the bandgap of the material. However, from the point of view of a classical homojunction and its adaption to organic materials the built-in potential is smaller than the band gap as does the turn-on of the device. The built-in potential is the difference of the quasi-fermi energy levels of electrons E F,n and holes E F,p which for Boltzmann statistics and complete ionization yields: which for complete ionization of dopants leads to , ln , , ,  recombination. However, we believe that charge transport via hopping from tail states plays a significant role in organic electronics. To effectively simulate transport via these states, we replaced the HOMO / LUMO energies of rubrene and C 60 with an effective energy representing the tail states. It is reasonable to assume that disorder will lead to 10 15 cm -3 to 10 16 cm -3 trap states that might reach up to (50 to 150) meV further into the gap. This leads us to an effective gap of 2 eV in case of the rubrene and 1.85 eV in case of C 60 . Below is a detailed summary of all simulation parameters in the GPVDM notation.   n,p

Short Circuit Current dependence
The dependence of the short circuit current on interlayer thickness was modeled using the following set of rate equations. These correspond to Eqn. (2 -5) of the main manuscript but include a generation term of singlets on rubrene due to light absorption. Further, it was assumed that free charge carriers are extracted with yield 1. , 0, , , , , ,