Modeling of transient electroluminescence overshoot in bilayer organic light-emitting diodes using rate equations

When a voltage pulse is applied under forward biased condition to a spin-coated bilayer organic light-emitting diode (OLED), then initially the electroluminescence (EL) intensity appearing after a delay time, increases with time and later on it attains a saturation value. At the end of the voltage pulse, the EL intensity decreases with time, attains a minimum intensity and then it again increases with time, attains a peak value and later on it decreases with time. For the OLEDs, in which the lifetime of trapped carriers is less than the decay time of the EL occurring prior to the onset of overshoot, the EL overshoot begins just after the end of voltage pulse. The overshoot in spin-coated bilayer OLEDs is caused by the presence of an interfacial layer of finite thickness between hole and electron transporting layers in which both transport molecules coexist, whereby the interfacial energy barrier impedes both hole and electron passage. When a voltage pulse is applied to a bilayer OLED, positive and negative space charges are established at the opposite faces of the interfacial layer. Subsequently, the charge recombination occurs with the incoming flux of injected carriers of opposite polarity. When the voltage is turned off, the interfacial charges recombine under the action of their mutual electric field. Thus, after switching off the external voltage the electrons stored in the interface next to the anode cell compartment experience an electric field directed from cathode to anode, and therefore, the electrons move towards the cathode, that is, towards the positive space charge, whereby electron–hole recombination gives rise to luminescence. The EL prior to onset of overshoot is caused by the movement of electrons in the electron transporting states, however, the EL in the overshoot region is caused by the movement of detrapped electrons. On the basis of the rate equations for the detrapping and recombination of charge carriers accumulated at the interface expressions are derived for the transient EL intensity I, time t_m and intensity I_m corresponding to the peak of EL overshoot, total EL intensity I_t and decay of the intensity of EL overshoot. In fact, the decay prior to the onset of EL overshoot is the decay of number of electrons moving in the electron transporting states. The ratio I_m/I_s decreases with increasing value of the applied pulse voltage because I_m increases linearly with the amplitude of applied voltage pulse and I_s increases nonlinearly and rapidly with the increasing amplitude of applied voltage pulse. The lifetime τ_t of electrons at the interface decreases with increasing temperature whereby the dependence of τ_t on temperature follows Arrhenius plot. This fact indicates that the detrapping involves thermally-assisted tunneling of electrons. Using the EL overshoot in bilayer OLEDs, the lifetime of the charge carriers at the interface, recombination time of charge carriers, decay time of the EL prior to onset of overshoot, and the time delay between the voltage pulse and onset time of the EL overshoot can be determined. The intense EL overshoot of nanosecond or shorter time duration may be useful in digital communication, and moreover, the EL overshoot gives important information about the processes involving injection, transport and recombination of charge carriers. The criteria for appearance of EL overshoot in bilayer OLEDs are explored. A good agreement is found between the theoretical and experimental results.