Reply to: Triplet-triplet annihilation in rubrene/C60 OLEDs with electroluminescence turn-on breaking the thermodynamic limit

In ref. 1 , we reported a detailed analysis of the electroluminescence (EL) characteristics for a series of rubrene/C 60 organic light emitting diodes (OLEDs) that exhibit low voltage threshold for detectable emission. Based on extensive kinetic models, we conclude that nonlinear processes are not necessary to describe the emission of the baseline device but can be significant under certain interlayer modifications. In ref. 2 , Qiao and Ma question our recent analysis of these devices by pointing out that the rate of photon emission exceeds the limit set by the generalized Planck (GP) equation reproduced for reference below: $${\mathrm{d}}N = \frac{{2a\left( \lambda \right)c}}{{\lambda ^4}}\frac{1}{{\exp \left( {\frac{{\frac{{hc}}{\lambda } \,-\, eV}}{{k_{\mathrm{{B}}}T}}} \right) - 1}}{\mathrm{d}}\lambda,$$ (1) with a being the absorptivity of the material, h the Planck constant, λ the wavelength, k B the Boltzmann constant, c the speed of light, and T the temperature of the lattice. Eq. ( 1 ) is known to hold for the EL of crystalline and amorphous inorganic semiconductors 3 , 4 , where it quantitatively predicts both the form and magnitude of the EL spectrum. This is not the case for the analysis in ref. 2 , where imposing a sharp bandgap cutoff at ~2.2 eV for rubrene formally precludes any emission below this energy according to Eq. ( 1 ), in sharp contrast to the observed rubrene EL spectrum in Fig. 1 . This large spectral discrepancy in applying Eq. ( 1 ) naturally questions the validity of its use in predicting the associated EL intensity. Fig. 1 EL spectrum for a rubrene/C 60 heterojunction as reported in the original manuscript for an applied voltage of 1.15 V. The emission at this level is 3 cd m −2 . Also shown is the absorbance of a 40-nm-thick film of rubrene Full size image

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