Asymptotic analysis of double-carrier, space-charge-limited transport in organic light-emitting diodes

Abstract

We analyse electron and hole transport in organic light-emitting diodes (OLEDs) via the drift–diffusion equations. We focus on space-charge-limited transport, in which rapid variations in charge carrier density occur near the injecting electrodes, and in which the electric field is highly non-uniform. This motivates our application of singular asymptotic analysis to the drift–diffusion equations. In the absence of electron–hole recombination, our analysis reveals three regions within the OLED: (i) ‘space-charge layers’ near each electrode whose width is much smaller than the device width , wherein carrier densities decay rapidly and the electric field is intense; (ii) a ‘bulk’ region whose width is on the scale of , where carrier densities are small; and (iii) intermediate regions bridging (i) and (ii). Our analysis shows that the current scales as , where is the applied voltage, is the permittivity and is the electric mobility, in contrast to the familiar diffusion-free scaling . Thus, diffusion is seen to lead to a large increase in current. Finally, we derive an asymptotic recombination–voltage relation for a kinetically limited OLED, in which charge recombination occurs on a much longer time scale than diffusion and drift.