## 3 Results and Discussion
These equations lead to the equation  
\[R_{2}\frac{1}{R_{1}+R_{2}}(V-R_{1}i_{c})=\frac{1}{C}\int i_{c}dt. \tag{1}\]  
Because \(i_{c}\) can be denoted as \(i_{c}=dQ_{c}/dt\) using the quantity of electric charge (\(Q_{c}\)), Equation (1) can be expressed as  
\[R_{2}\frac{1}{R_{1}+R_{2}}\bigg{(}V-R_{1}\frac{dQ_{c}}{dt}\bigg{)}=\frac{1}{C} Q_{c}, \tag{2}\]  
which can be transformed into  
\[\frac{dQ_{c}}{dt}+\frac{R_{1}+R_{2}}{R_{1}R_{2}C}Q_{c}=\frac{V}{R_{1}}. \tag{3}\]  
Considering an initial condition of \(Q_{c}\) = 0, Equation (3) can be solved as  
\[Q_{c}=\frac{R_{2}}{R_{1}+R_{2}}CV\bigg{\{}1-\exp\bigg{(}-\frac{R_{1}+R_{2}}{R_{ 1}R_{2}C}t\bigg{)}\bigg{\}}, \tag{4}\]  
and supposing the emission intensity change induced by the accumulated charges (\(\Delta I_{a}\)) is proportional to \(Q_{c}\), we obtain  
Figure 3:0  
by introducing proportionality constant \(A\). Here, because \(\Delta I_{a}\) is the change in emission intensity during \(t\), \(\Delta I\) for an exposure time of 10 s can be denoted as  
Figure 3:1  
This equation adequately reproduces the observed proportional dependence of the emission intensity change on the reverse-bias voltage. With the parameter sets \(R_{1}\) = 50 \(\Omega\), \(R_{2}\) = 5.0 \(\times\) 10\({}^{6}\)\(\Omega\), and \(C\) = 10 \(\times\) 10\({}^{-9}\) F, where \(R_{1}\) and \(R_{2}\) are the estimated resistances of the ITO electrode and OLED, respectively, and \(C\) is a typical value [14], Equation (6) produces the solid line shown in Figure 3 with a variable parameter of \(A\) = 2.88 \(\times\) 10\({}^{6}\) and 6.35 \(\times\) 10\({}^{5}\) count C\({}^{-1}\) for the ITO/TPD/Alq\({}_{3}\)/Al and ITO/CoPc/Alq\({}_{3}\)/Al devices, respectively. Equations (5) and (6) clearly indicate that \(\Delta I\) also dependson the time of the reverse-bias application \(t\). Figure 5 depicts the \(t^{-1}\) (i.e., \(2f\)) dependence of \(\Delta I\) derived from Figure 2 together with the values calculated using the parameter sets in Figure 3:2 Clearly, they are not consistent. This might be because \(A\) is not a common constant for \(t\) but a function of \(t\). At this time, we cannot evaluate \(A(t)\). To understand the mechanism of the reverse-bias emission enhancement, we consider the vacuum level shift (\(\Delta\)) at the organic/metal interface. When a reverse bias is applied to an OLED and it acts as a capacitor, the interfacial dipole at the organic/ITO interface with negative (positive) \(\Delta\) decreases (increases), while that at the organic/Al interface with negative (positive) \(\Delta\) increases (decreases), because of the accumulation of negative and positive charges at the organic/ITO and organic/Al interfaces, respectively. In any case, whether \(\Delta\) at the organic/metal interfaces is negative or positive, this situation causes \(\Delta\) at the organic/ITO interface to shift positively and \(\Delta\) at the organic/Al interface to shift negatively. Therefore, the vacuum level shifts at the organic/metal interfaces were modulated to shift both the HOMO of a hole injection material and the LUMO of an electron injection material close to the Fermi levels of the ITO and Al electrodes, respectively, leading to a decrease in both the hole injection barrier at the organic/ITO interface and the electron injection barrier at the organic/Al interface. Consequently, we believe that both the hole and electron injections occur easily under forward bias after reverse bias has been applied, resulting in an increase of the number of carriers that can arrive at the organic/organic interface compared to ordinary DC or alternating zero-forward bias. Based on this model, we can interpret the tendency of \(\Delta I\) to depend on \(t\) by dividing Figure 5 into five regions, I, II, III, IV and V, according to \(t\). Figure 3:3 Equivalent circuit based on a model in which the OLED acts as a capacitor during the reverse bias.