Speedup of Doping Fronts in Organic Semiconductors through Plasma Instability

The dynamics of doping transformation fronts in organic semiconductor plasma is studied for application in light-emitting electrochemical cells. We show that new fundamental effects of the plasma dynamics can significantly improve the device performance. We obtain an electrodynamic instability, which distorts the doping fronts and increases the transformation rate considerably. We explain the physical mechanism of the instability, develop theory, provide experimental evidence, perform numerical simulations, and demonstrate how the instability strength may be amplified technologically. The electrodynamic plasma instability obtained also shows interesting similarity to the hydrodynamic Darrieus-Landau instability in combustion, laser ablation, and astrophysics.

Figure 1

(a) Schematic of the $p$- and $n$-doping fronts in an organic semiconductor film; (b) internal structure of the planar fronts at 90 s.

Figure 2

Experimental photos of the doping fronts demonstrate development of the instability: (a) at the initial stage, $t=46\mathrm{s}$; (b) at the developed stage, $t=80\mathrm{s}$; (c) at the dynamic $p\mathrm{\text{−}}n$ junction, $t>170\mathrm{s}$. The bright line in (c), taken in a dark room, is the light-emitting $p\mathrm{\text{−}}n$ junction, while the remaining part of the sample appears dark. (d) compares the $p$-front shapes obtained in the simulations (white curve) and experiments (shading) at 70 s. (e) and (f) show the relative increase in the electric field in the undoped region obtained numerically for (e) the whole front squeezed along the $Y$ axis and (f) the selected part with equal scales.

Figure 3

Mean front position for $p$ and $n$ fronts versus time obtained experimentally, predicted theoretically for the planar fronts, and calculated numerically for the wrinkled fronts (see the legend). The error bars of the experimental data indicate the difference in the positions of the fastest and slowest parts of the corrugated front brush.

Figure 4

Experimental photographs showing the time evolution of the $p$-type doping front in an LEC device with the initial corrugations of the anode. The corresponding time instances are indicated on the photographs. The inset shows a characteristic shape of a strongly curved hump obtained in the theory.