Unified Mobility Model for Diffusion-Limited Current in Organic Diodes Based on Fermi-Dirac Statistics

The Fermi-Dirac statistics is adopted to consider degenerate effects in organic diodes. The degenerate drift-diffusion equation is analytically solved under the uniform-electrical-field approximation. The analytical expressions for the current-voltage relationship and carrier density are derived. The mobility model of Pasveer [Pasveer et al., Phys. Rev. Lett. 94, 206601 (2005)] is improved to consider correct characteristic length scales and combined with the analytical solution to analyze the properties of six organic diodes. The theoretical results are in good agreement with experimental data. Six model parameters are extracted for six devices, namely, the parameters $N_0$ and σ for the density of states; the parameters ${\mu }_0$ and a for the mobility model; and the potential barriers $W_{\mathrm{an}}$ and $W_{\mathrm{cat}}$ at the anode and cathode, respectively. The degenerate parameter $\overline{\eta }$ at 300 K is deduced. It is shown that two materials, MEH-PPV and F8BT, are degenerate. Although four other materials can be treated as nondegenerate, the degenerate effects are not negligible near the anode region.

Figure 1

Comparison of fitting curves from Eq. (22a) (solid lines) with simulated data [19] (symbols) for two coefficients, c₁ and c₂, versus $a{N}_0^{1/3}$.

Figure 2

Comparison of theoretical curves (solid lines) with experimental data (symbols) for devices made from the materials PFO [4] (a) and MEH-PPV [5] (b).

Figure 3

Comparison of theoretical curves (solid lines) with experimental data (symbols) for devices made the materials F8BT [20] (a) and 2-TNATA [21] (b).

Figure 4

Comparison of theoretical curves (solid lines) with experimental data (symbols) for devices made from materials Spiro-TAD [21] (a) and TCTA [21] (b).

Figure 5

Theoretical curves at three temperatures, 220, 260, and 300 K, for devices made from PFO [4], with all parameters taking values given in Table 1, except for other one parameter: (a) with W_an= 0.5 eV (dashed lines) and W_cat= 0.9 eV (dotted-dashed lines), and (b) with σ = 0.05 eV (dashed lines) and a = 0.5 nm (dotted-dashed lines).

Figure 6

Theoretical curves, p(x), for devices made from PFO at 0.5 V [4] (a) and MEH-PPV at 2 V [10] (b), at 220, 260, and 300 K.

Figure 7

Theoretical curves, η(x), for devices made from PFO at 0.5 V [4] (a) and MEH-PPV at 2 V [5] (b) at 220, 260, and 300 K.