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

摘要

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 λ?_s is much smaller than the device width L?, wherein carrier densities decay rapidly and the electric field is intense; (ii) a 'bulk' region whose width is on the scale of L?, where carrier densities are small; and (iii) intermediate regions bridging (i) and (ii). Our analysis shows that the current ? scales as ?∞ ε? μ ?V?~2/L?~2 λ?_s, where V? is the applied voltage, ε? is the permittivity and μ? is the electric mobility, in contrast to the familiar diffusionfree scaling ?∞ ε? μ?V? ~2/L?~3. Thus, diffusion is seen to lead to a large O(L?/λ?_s) 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.