Impact of doping on the density of states and the mobility in organic semiconductors

We experimentally investigated conductivity and mobility of poly(3-hexylthiophene) (P3HT) doped with tetrafluorotetracyanoquinodimethane $\left({\mathrm{F}}_4\mathrm{TCNQ}\right)$ for various relative doping concentrations ranging from ultralow $\left({10}^{-5}\right)$ to high $\left({10}^{-1}\right)$ and various active layer thicknesses. Although the measured conductivity monotonously increases with increasing doping concentration, the mobilities decrease, in agreement with previously published work. Additionally, we developed a simple yet quantitative model to rationalize the results on basis of a modification of the density of states (DOS) by the Coulomb potentials of ionized dopants. The DOS was integrated in a three-dimensional (3D) hopping formalism in which parameters such as energetic disorder, intersite distance, energy level difference, and temperature were varied. We compared predictions of our model as well as those of a previously developed model to kinetic Monte Carlo (MC) modeling and found that only the former model accurately reproduces the mobility of MC modeling in a large part of the parameter space. Importantly, both our model and MC simulations are in good agreement with experiments; the crucial ingredient to both is the formation of a deep trap tail in the Gaussian DOS with increasing doping concentration.

Figure 1

Hole mobility from model I (solid lines) and MC (dots) using the standard parameter set. Energetic disorder is ${\sigma }_{\mathrm{DOS}}=0.05\mathrm{eV}$ (black), 0.075 eV (red), and 0.1 eV (blue).

Figure 2

Dependence of hole mobility on doping concentration from model II (solid lines) and MC (dots) for different parameters: (a) energetic disorder: ${\sigma }_{\mathrm{DOS}}=0.05\mathrm{eV}$ (black), 0.075 eV (red), and 0.1 eV (blue); (b) energy level difference: $\mathrm{\Delta }E=-0.2\mathrm{eV}$ (black), 0 eV (red), and 0.3 eV (blue); (c) intersite distance $a_{\mathrm{NN}}=1.0\mathrm{nm}$ (black), 1.8 nm (red), and 3.0 nm (blue); (d) temperature: $T=200\mathrm{K}$, 225 K, 250 K, 275 K, 300 K, 320 K, and 340 K.

Figure 3

Fraction of carrier charges at various positions: at dopant ions (solid lines), at CT position (dashed lines) and free (dots) vs doping concentration from MC for the same parameters as Fig. 2. (a) Energetic disorder: ${\sigma }_{\mathrm{DOS}}=0.05\mathrm{eV}$ (black), 0.075 eV (red), and 0.1 eV (blue); (b) energy level difference: $\mathrm{\Delta }E=-0.2\mathrm{eV}$ (black), 0 eV (red), and 0.3 eV (blue); (c) intersite distance: $a_{\mathrm{NN}}=1.0\mathrm{nm}$ (black), 1.8 nm (red), and 3.0 nm (blue); (d) temperature: $T=200\mathrm{K}$, 225 K, 250 K, 275 K, 300 K, 320 K, and 340 K.

Figure 4

DOS for different doping concentrations from (a) model I [Eq. (4), solid lines]; (b) model II [Eq. (6), solid lines], and MC (dashed lines) with the standard parameter set. The insets show the full energy scale.

Figure 5

Hole conductivity of P3HT vs ${\mathrm{F}}_4\mathrm{TCNQ}$ concentration for different film thicknesses (symbols, solid lines connect the data points, thicknesses: 50 nm, 150 nm, 265 nm, 360 nm, and 2.5 µm). The dotted line is a manual spline through the data.

Figure 6

Ohmic mobility dependence on ${\mathrm{F}}_4\mathrm{TCNQ}$ concentration from experiments (black dots) and calculated from model II (solid lines) with different energy level differences ($\mathrm{\Delta }E=0$, 0.1, 0.2, 0.3, 0.4, and 0.5 eV). For P3HT:${\mathrm{F}}_4\mathrm{TCNQ}\mathrm{\Delta }E\approx 0.24\mathrm{eV}$.