4.4 Trapping Characteristics

Fig 4.9 and 4.10 illustrate the temperature dependence of the carrier conductivity for different trap concentrations. The parameters are $N_t=10^{22}$ cm$^{-3}$, $E_d=-0.67$eV, $T_0=800$K, $T_1=400$K, $\alpha^{-1}=2$$\AA$ and $\sigma_0=1\times 10^ 4$ S/cm. Despite the effect of the traps, we can see an almost perfect Arrhenius-type temperature dependence in Fig 4.9, with the slope affected by the trap concentration. Increasing the latter, the activation energy decreases. In Fig 4.10, $\log\sigma$ versus $T^{-2}$ is plotted . The deviation from a straight line occurs at higher temperature, where nearly all carriers occupy the intrinsic states, and the filled extrinsic trap states do not change the trap-free hopping relation $\log\sigma\propto T^{-2}$ [98]. However, at lower temperature, the carrier distribution will be pinned near the peak of trap DOS [68].

In Fig 4.11 we compare the analytical model with experimental data reported in [99]. Parameters are the relative trap concentration $c_t=N_d/N_t=1\times 10^{-2}$, $T_0=1200$K, $T_1=400$K, $E_d=-0.15$eV, $\alpha^{-1}=1.6$$\AA$ and $\sigma_0=4.2784\times 10^8$ S/m. The data are for TTA with doping DAT.

The relation between conductivity and $T_1$ is shown in Fig 4.12. Parameters are $N_t=1\times 22$ cm$^{-3}$, $N_d=1\times 19$ cm$^{-3}$, $T_0=1200$ K,

Figure 4.9: Conductivity of an organic semiconductor versus $T^{-1}$ for different trap concentrations.

Figure 4.10: Conductivity of an organic semiconductor versus $T^{-2}$ for different trap concentrations.

Figure 4.11: Temperature dependence of the zero-field mobility for TTA doped with DAT. Symbols represent experimental data from [99].

Figure 4.12: Conductivity of an organic semiconductor versus the width of the trap distribution, $T_1$.

Figure 4.13: The dependence of the conductivity on the trap concentration.

Figure 4.14: The dependence of the conductivity on the Coulombic trap energy.

$T=150$ K, $E_d=-0.5$ eV, $\alpha^{-1}=3$Åand $\sigma_0=100$ S/m. For the exponential DOS function of the traps, the parameter $T_1$ is a characteristicstic temperature, where $k_BT_1$ represents the activation energy [100] and defines the width of the distribution [101]. Fig 4.12 confirms that the conductivity decreases with $T_1$ almost linearly.

The relation between conductivity and trap concentration is shown in Fig 4.13. The parameters are $N_t=10^{22}$ cm$^{-3}$, $\alpha^{-1}=1.6$Å, $T_0=1000$K, $T_1=500$K, $E_d=-0.2$ eV, the temperature is $T=400$K and $\sigma_0=1\times 10^ 4$ S/m.

At a critical trap concentration the conductivity has a minimum. This has been verified by experiments [102] and Monte Carlo simulation [103]. The minimum is due to the onset of inter-trap transfer that alleviates thermal detrapping of carriers, which is a necessary step for charge transport [103]. We can also see that a small trap concentration has virtually no effect on the conductivity. At higher trap concentration, however, the activation energy for the conductivity decreases. The traps themselves can serve as an effective hopping transport band, so the effect of traps on the charge conductivity is qualitatively similar to that caused by a high carrier concentration. It is interesting that such transition has also been observed in thermally stimulated luminescence (TSL) measurements [104].

The relation between the conductivity and the trap energy $E_t$ is shown in Fig 4.14. Parameters are $T_0=600$K, $T_1=300$K, $N_t=1\times 10^{22}$ cm$^{-3}$, $N_d=1\times 10^{19}$ cm$^{-3}$, $\alpha^{-1}=2.5$Å, $T=200$K and $\sigma_0=1\times 10^ 4$ S/m. From Fig 4.14 we can conclude that the conductivity increases approximately exponentially for $\mid E_d\mid$ below a certain critical value and saturates for larger $\mid E_d\mid$.