Influence of energetic disorder on electroluminescence emission in polymer:fullerene solar cells

Electroluminescence (EL) spectroscopy and imaging can be useful techniques to analyze various loss mechanisms in solar cells, but the interpretation of the results is not trivial in solar cells made from disordered materials such as organic semiconductors. In this case the interpretation of EL measurements may be affected by the presence of a tail of localized states. Here, we study several polymer:fullerene systems and show that, despite the presence of tail states, the shape of the EL spectrum is insensitive to the applied voltage. This indicates that the emission originates mainly from mobile charges in higher lying states recombining at the polymer:fullerene interface and that most charges in deeper tail states do not contribute to the EL spectrum. The consequence of our finding is that simple models of EL emission in ideal semiconductors can be applied to polymer:fullerene solar cells and can therefore be used to evaluate the potential of different material systems in terms of recombination losses and to study resistive losses using luminescence imaging.

Figure 1

Band diagrams of a (a) pn-junction solar cell (here the example of a Cu(In,Ga)Se${}_2$/CdS solar cell) and a (b) thin organic solar cell. In case of the pn-junction solar cell, the internal voltage can be defined as the quasi-Fermi-level splitting in the space charge region, which is roughly constant. Only in the quasineutral region, the quasi-Fermi level of electrons drops drastically. In case of the organic solar cell, both quasi-Fermi levels are a function of position, and there is no region where to define a constant quasi-Fermi level. We therefore use the average quasi-Fermi-level splitting instead.

Figure 2

Semilogarithmic plot of experimental external quantum efficiency (EQE) (open circles), normalized electroluminescence (EL) spectrum (open triangles), and calculated EQE from EL (solid lines) as a function of energy for P3HT:PCBM (black) and MDMO-PPV:PCBM (red/dark gray) blends. The EL spectra were measured at 1250 mA/cm${}^2$ injection current density for P3HT:PCBM and at 200 mA/cm${}^2$ for MDMO-PPV:PCBM. The slope of the Urbach absorption tail for the two blends is also shown (blue/medium gray dashed lines).

Figure 3

Comparison of (a) simulated carrier population in crystalline and (c) disordered materials and (b) simulated emission spectra in crystalline and (d) disordered materials for increasing applied voltage ($V$).

Figure 4

Schematic showing the relation between the exponential density of states $N$($E$), the occupation probability [Fermi-Dirac function $f$($E$)], and the total carrier concentration $n$($E$). In addition, the scheme shows a hypothetical function μ($E$) describing the energy-dependent mobility, which will decrease for smaller energies because of decrease in states and the increase in distance between states. From the energy-dependent carrier concentration and the energy-dependent mobility we can determine the free carrier concentration (proportional to the energy-dependent conductivity), which is above the quasi-Fermi level $E_{\mathrm{fn}}$ and which therefore scales with exp($E_{\mathrm{fn}}$/$kT$).

Figure 5

Normalized electroluminescence (EL) spectra of P3HT:PCBM and MDMO-PPV:PCBM measured at different injection current densities $J$. In both cases the EL shifts slightly to higher energy with increasing injection current.

Figure 6

Comparison of the EL peak center shifts of different Polymer:PCBM blends. The peak center is defined as the energy about which the integral over the EL spectrum is divided into two equal halves. In both cases the peak energy shifts to higher energies with higher injection currents but with a slope that is smaller than the dashed line expected for $n_{\mathrm{id}}$ $=$ 1, electron and hole state tails with $E_{\mathrm{ch}}$ > $kT$, and constant transition matrix elements.