Full Electrothermal OLED Model Including Nonlinear Self-heating Effects

Organic light-emitting diodes (OLEDs) are widely studied semiconductor devices for which a simple description by a diode equation typically fails. In particular, a full description of the current-voltage relation, including temperature effects, has to take the low electrical conductivity of organic semiconductors into account. Here, we present a temperature-dependent resistive network, incorporating recombination as well as electron and hole conduction to describe the current-voltage characteristics of an OLED over the entire operation range. The approach also reproduces the measured nonlinear electrothermal feedback upon Joule self-heating in a self-consistent way. Our model further enables us to learn more about internal voltage losses caused by the charge transport from the contacts to the emission layer which is characterized by a strong temperature-activated electrical conductivity, finally determining the strength of the electrothermal feedback. In general, our results provide a comprehensive picture to understand the electrothermal operation of an OLED which will be essential to ensure and predict especially long-term stability and reliability in superbright OLED applications.

Figure 1

Experimental current-voltage curve of an OLED in steady state shows a regime of negative differential resistance after the voltage turnover (7.6 V) takes place at a current density of about $360\mathrm{mA}/{\mathrm{cm}}^2$. Our electrothermal model takes this into account by allowing for a positive feedback between the temperature, the voltage-dependent characteristic $j=j(V,T)$, and the power-dependent temperature increase. For comparison, a pulsed measurement shows no electrothermal feedback but fully agrees with the steady-state curve in the range from 1 to $10\mathrm{mA}/{\mathrm{cm}}^2$. Reducing the thermal resistance to 0 K/W, the modeled curve also agrees with the pulsed measurement. The model allows determination of a maximum temperature increase of 83.6 K, yielding a temperature of $103.5{}^{\circ }\mathrm{C}$ at the point shortly before abrupt degradation occurs, starting from about $1000\mathrm{mA}/{\mathrm{cm}}^2$.

Figure 2

Three different devices are investigated: devices of (a) $p$-doped–intrinsic–$p$-doped layers or (c) $n$-doped–intrinsic–$n$-doped layers mimic the hole transporting $p$ system, and the electron transporting $n$ system, respectively, as used in the full OLED stack, see (b). Simplified energy diagrams are shown in (d)–(f) corresponding to (a)–(c). (e) Recombination is simplified, described by assuming a homogeneous recombination within a certain region, e.g., the emission layer (EML, gray). The energetic distances and barriers of the energy diagram have no direct relation to the investigated experimental structure but simply represent the ideal case that the intrinsic charge blocking layers restrict recombination to the EML. In that case, the quasi-Fermi-levels for electrons $E_{Fe}$ and for holes $E_{Fh}$ are splitted by the applied voltage $V$. The conduction level for electrons $E_e$ and the valence level for holes $E_h$ are denoted as well. The OLED stack in (b) is modeled by connecting the elements in (g) $p$ system, (h) recombination, and (i) $n$ system in series.

Figure 3

Experimental current-voltage curves from 223 to 353 K superimposed with a fit by our global model for (a) the $p$ system and (b) the $n$ system. The activation energies resulting from the model are shown in (c) and (d), respectively. Generally, the activation energy decreases when the device operation goes from the linear to the nonlinear voltage range.

Figure 4

(a) Fitting of the experimental current-voltage curves from 223 to 353 K by the model approach shown in Fig. 2. Leakage currents mainly below 1.5 V are not considered. Blue indicates recombination-related aspects. (b) Modeled activation energies resulting from the fit in (a) show a linear decrease at voltages below 2 V (recombination) and a saturation around 0.3 eV for larger voltages, related to the $p$ and the $n$ system of the OLED.

Figure 5

Modeled curves corresponding to the fit in Fig. 1 including electrothermal feedback. (a) Cumulative voltage drop for the sequence recombination, the $n$ system ($+n$) and the $p$ system ($+p$). The $n$ system consumes most of the applied potential at high current densities, whereas at low current densities the OLED is fully determined by recombination in the exponential current-voltage regime. (b) The individual voltage drops for each system. The dashed horizontal line represents the voltage turnover of the complete OLED. It can be seen that the voltage turnover of the $n$ system happens at lower current densities whereas the $p$ system has a voltage turnover at higher current densities. Thus, electrothermal feedback in OLEDs can internally affect the layers differently.

Figure 6

Experimental current-voltage curves of p-i-p (left) and n-i-n (right) devices. The upper two graphs show samples without an intrinsic layer and a variation of the total doped layer thickness. The lower two graphs show samples with a 30-nm-doped layer below and above the intrinsic layer. While the $p$ system is less affected by inserting an intrinsic layer, the $n$ system shows a strong reduction of conductivity upon introducing even just 10 nm of intrinsic material.