Subsections

• 7.3.1 Theory
• 7.3.2 Results and Discussion

7.3 Device Model for Unbipolar OLEDs

In this section we present a unified device model for unbipolar OLEDs which includes charge injection, transport, and space charge effects in the organic material.

7.3.1 Theory

In order to analyze the interplay between charge injection and bulk conductivity one must use specific models for both injection and charge transport in bulk. Here we treat the charge injection as diffusion controlled and the transport within multiple trapping theory as presented in Chapter 5. By multiplying $\exp\left(-\frac{e\varphi\left(x\right)}{k_BT}\right)$ in both sides of (5.2) and integrating $x$ from 0 to $x_d$, we obtain

$$\frac{-J}{qD_n}\int_0^{x_d}\exp\left(-\frac{q\varphi\left(x\right)}{k_BT}\right)dx=f\left(x_d\right)-f\left(0\right),$$ (7.18)

where $D_n$ is the diffusion coefficient and

$$f\left(x\right)=n_e\left(x\right)\exp\left(-\frac{q\varphi\left(x\right)}{k_BT}\right).$$

In the transport regime of the device, the potential expression (5.1) does not hold true anymore, instead, the potential must be calculated from the Poisson equation

$$\frac{d^2q\varphi}{dx^2}=-\frac{dF}{dx}=-\frac{q}{\epsilon_0\epsilon}p\left(x\right).$$ (7.19)

In the bulk regime, (5.2) is rewritten as

$$p_e\left(x\right)=\left[p_e\left(x_d\right)-\frac{J}{qD_n}\int_0^... ...T}\right)\right] \times\exp\left(-\frac{p\varphi\left(x\right)}{k_BT}\right).$$ (7.20)

In order to calculate the $J/V$ characteristics of OLEDs, one must solve (7.19) together with (5.4) and (7.20) self-consistently. The injection boundary conditions are $\varphi\left(0\right)=\varphi\left(x_d\right)$, $J=J_{inj}\left(F_0\right)$ and $F\left(0\right)=F_0$.

7.3.2 Results and Discussion

With the device model presented above we calculate the device characteristics of one carrier type at different barrier height $\Delta$, as shown in Fig 7.9. The input parameters are $T=300K$, $\sigma_0=0.08$eV, $N_t=1\times 10^{16}$cm$^{-3}$, $\nu_0=10^{11}$s$^{-1}$, $\tau_0=10^{-11}$s, $\mu=1\times 10^{-4}$cm$^2$/Vs and the device length is 100$nm$. The comparison between our work and experimental data of hole only ITO/NPB/Al [135] is plotted in Fig 7.10 with $\Delta=0.1$eV, $\mu=2.9\times 10^{-1}$cm$^2$/Vs and device length 65$nm$. The other parameters are the same as in Fig 7.9. The current is neither the pure injected limited current nor SCLC [135].

A single carrier OLED model including charge injection and transport is presented here. This model is based on a Gaussian DOS and multiple trapping theory. It can explain barrier height dependence of current/voltage characteristics and agrees with experimental data [135].

Figure 7.9: Barrier height dependence of current/voltage characteristics for unbipolar OLED.

Figure 7.10: Comparison between the model and experimental data for unbipolar OLED.