Diffusion of triplet excitons in an operational organic light-emitting diode

Measurements of the diffusion length $L$ for triplet excitons in small molecular-weight organic semiconductors are commonly carried out using a technique in which a phosphorescent-doped probe layer is set in the vicinity of a supposed exciton generation zone. However, analyses commonly used to retrieve $L$ ignore microcavity effects that may induce a strong modulation of the emitted light as the position of the exciton probe is shifted. The present paper investigates in detail how this technique may be improved to obtain more accurate results for $L$. The example of $4,4^{\prime }$-bis(carbazol-9-yl)$1,1^{\prime }$-biphenyl (CBP) is taken, for which a triplet diffusion length of $L=16\pm 4\text{nm}$ (at $3\text{mA}/{\text{cm}}^2$) is inferred from experiments. The influence of triplet-triplet annihilation, responsible for an apparent decrease in $L$ at high current densities, is theoretically investigated, as well as the “invasiveness” of the thin probe layer on the exciton distribution. The interplay of microcavity effects and direct recombinations is demonstrated experimentally with the archetypal trilayer structure [$\text{N},{\text{N}}^{\prime }$-bis(naphthalen-1-yl)-$\text{N},{\text{N}}^{\prime }$-bis(phenyl)]-$4,4^{\prime }$-diaminobiphenyl (NPB)/CBP/ 2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline (named bathocuproine, BCP). It is shown that in this device holes do cross the NPB/CBP junction, without the assistance of electrons and despite the high energetic barrier imposed by the shift between the HOMO levels. The use of the variable-thickness doped layer technique in this case is then discussed. Finally, some guidelines are given for improving the measurement of the diffusion length of triplet excitons in operational OLEDs, applicable to virtually any small molecular-weight material.

Figure 1

Structure of the diode used in Sec. 2. The layer thicknesses are indicated on the bottom in nanometers. The HOMO and LUMO energy levels are taken from literature (Refs. 25, 26) and specified for each compound (negative values). The profile of the optical field is plotted in the CBP layer (see Sec. 4A for details).

Figure 2

(Color online) Photoluminescent spectra of some of the compounds used in this paper with their chemical structure. The electroluminescent spectrum of DCM is plotted in dotted line.

Figure 3

(Color online) Current density versus voltage curves for diodes with different $d$ positions of the probe layer. Inset: external quantum efficiency (EQE) versus current density for a diode with $d=7.5\text{nm}$.

Figure 4

Electroluminescent spectrum for a diode described in Fig. 1 with $d=12.5\text{nm}$ at a current density of $3.3\text{mA}/{\text{cm}}^2$.

Figure 5

(Color online) The circles correspond to the red intensity (around 650 nm) corrected by the optical field versus the $d$ position of the probe layer at $J=3.3\text{mA}/{\text{cm}}^2$. The fit by Eq. (1) is plotted in continuous line. Inset: fits from Eq. (1) of experimental data for different current densities.

Figure 6

(Color online) Effective diffusion length $L$ of triplet exciton versus the current density, defined from Eq. (1) and inferred from the fits shown in the inset of Fig. 5.

Figure 7

The calculated dependence of the emitted signal in the presence of triplet-triplet quenching and noninvasive probe inferred from Eq. (8). The inset gives the semilogarithmic view of the same set of data.

Figure 8

The influence of the probe on the distribution of excitons in space $n\left(x\right)/n\left(0\right)$ for various levels of invasiveness ${\beta }_I$. The sensing layer of thickness $\delta =0.05L_0$ is placed as $d=1.5L_0.$

Figure 9

The dependence of the signal intensity $I\left(d\right)/I\left(0\right)$ on the position $d$ of the probe, for various levels of its invasiveness ${\beta }_I$. The formulas are indicated on the graph for the limits of noninvasive and strongly invasive probe.

Figure 10

Structure of the diode used in Sec. 4A. The layer thicknesses are indicated on the bottom in nanometers. The HOMO and LUMO are taken from literature (Refs. 25, 26) and specified for each compound (negative values). The profile of the optical field is plotted in the CBP layer.

Figure 11

(Color online) Electroluminescent spectra of diodes described in Fig. 10 for different $d$ positions at $J=3.3\text{mA}/{\text{cm}}^2$.

Figure 12

(Color online) The circles correspond to the red detected intensity normalized to its blue part versus the $d$ position of the probe layer at $J=3.3\text{mA}/{\text{cm}}^2$. The profile of the optical field calculated over the spectral range of $\text{Ir}{\left(\text{btp}\right)}_2$ emission is plotted in continuous line.

Figure 13

(Color online) Current density versus voltage curves for hole-only diodes with different thicknesses of the CBP layer. Inset: structure of the hole-only diodes.

Figure 14

(Color online) Electroluminescent spectra of diodes NPB/CBP/${\text{Alq}}_3$ (continuous line) and NPB/CBP/BCP/${\text{Alq}}_3$ (dotted line) at $J=1.7\text{mA}/{\text{cm}}^2$.

Figure 15

The dependence of the strength of the signal $I\left(d\right)/I\left(0\right)$ on the position $d$ of the probe for various strengths $g$ of the triplet source (or triplet-triplet quenching rate). The inset shows the graphs un-normalized by the strength $I\left(0\right)$ of the signal.