(368g) Asymptotic Analysis of Double-Carrier, Space-Charge-Limited Transport in Organic Light-Emitting Diodes
In organic light-emitting diodes (OLEDs), an applied voltage drives the injection and transport of charge carriers, electrons and holes, across an organic semiconducting thin film; the carriers then recombine to generate light emission. We analyze electron and hole transport in 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 nonuniform. 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 are 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 J scales as J ~ εμ V2/L2λ, where V is the applied voltage, ε is the permittivity, and μ is the electric mobility, in contrast to the familiar diffusion-free scaling J ~ εμ V2/L3. Thus, diffusion is seen to lead to a large O(L/λ) 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 timescale than diffusion and drift.