Temperature and field dependence of hole mobility in poly(9,9-dioctylfluorene)

Detailed studies of hole mobility in the electroluminescent conjugated polymer poly($9,9^{\prime }$-dioctylfluorene) by the time-of-flight technique are reported. The hole mobility is studied in a number of samples over a wide range of temperatures and electric field strengths. Significant sample-to-sample variations are observed in both hole mobility and the character of hole transport in as-spun films of different thicknesses. Hole mobility is found to improve irreversibly as a result of thermal annealing at elevated temperatures. Analysis of the experimental results is carried out within the Gaussian disorder model (GDM), the polaronic correlated disorder model (PCDM), and the geometry fluctuation model based on torsional interactions (known here as the Los Alamos model). The PCDM is found to be more successful than the GDM in explaining the experimental data. Moreover, the Los Alamos model succeeds in explaining the data when modified to include polaron hopping. Analysis with both PCDM and Los Alamos models leads to the conclusion that the improvement in hole mobility upon annealing is consistent with reduced energetic disorder and reduced polaron binding energy, both of which may result from crystallization of the material. Spectroscopic ellipsometry is used to confirm that crystallization occurs upon annealing.

Figure 1

The chemical structure of poly $9,9^{\prime }$-dioctylfluorene (PFO).

Figure 2

Typical arrangement of the time-of-flight setup. A typical nondispersive transient is illustrated schematically on the right.

Figure 3

Typical time-of-flight transients measured in two different samples with thicknesses $1.9\mu \mathrm{m}$ (a), (c) and $1\mu \mathrm{m}$ (b), (d) and plotted on a double logarithmic scale. (a) and (b) show transients measured in the nonannealed samples, (c) and (d) present the transients measured in the same samples, annealed at $120°\mathrm{C}$ for $16\mathrm{h}$ (c) or $9\mathrm{h}$ (d). Insets in each graph show the same data plotted on a linear scale.

Figure 4

(a) Room-temperature TOF hole mobilities in nonannealed PFO samples of different thicknesses (indicated in legend). Data for an aligned PFO sample from Ref. 17 is shown for comparison. (b) Room-temperature TOF hole mobility in a single sample #3 $(d=2.5\mu \mathrm{m})$ before annealing and after annealing for at least $15\mathrm{h}$ at $100°\mathrm{C}$, $120°\mathrm{C}$, and $140°\mathrm{C}$. Room temperature TOF hole mobility after annealing in another sample, #6 $(d\sim 1\mu \mathrm{m})$, is shown for comparison.

Figure 5

Typical TOF hole transients measured in a $4\mu \mathrm{m}$ thick nonannealed sample (#1) at different temperatures (as indicated) and at an electric field of $5\times {10}^5\mathrm{V}∕\mathrm{cm}$.

Figure 6

TOF hole mobility as a function of electric field and temperature for a $4\mu \mathrm{m}$ thick nonannealed sample (#1).

Figure 7

TOF hole mobility as a function of electric field and temperature for a $2.5\mu \mathrm{m}$ thick sample (#3), after annealing at $120°\mathrm{C}$ for $15\mathrm{h}$.

Figure 8

Comparison of room-temperature TOF hole mobilities in a nonannealed sample, #2 $(d=4\mu \mathrm{m})$ calculated using $t_0$ (squares) and using $t_{1∕2}$ (triangles) as the transit times. The inset shows the corresponding dispersion parameter $W=(t_{1∕2}-t_0)∕t_{1∕2}$ as a function of electric field.

Figure 9

GDM fitting of experimental data from Figs. 6, 7 for nonannealed (solid symbols) and annealed (open symbols) samples. (a) Non-Arrhenius temperature dependence of mobility yielding parameters ${\mu }_0$ and $\sigma$. (b) Temperature dependence of the field-dependence gradient $\alpha =\partial \left(\ln \mu \right)∕\partial \left(E^{1∕2}\right)$ yielding parameters $\Sigma$ and $C_0$.

Figure 10

Arrhenius plot of zero-field mobility for the nonannealed (#1) and annealed (#3) samples.

Figure 11

Fitting according to the polaronic CDM. The experimental data are for the samples #1 (annealed, shown by solid symbols) and #3 (nonannealed, shown by open symbols). (a) The slopes of the electric field dependence, plotted against ${(e∕k_{B}T)}^{3∕2}$, which yield the given values of the energetic disorder $\sigma$ and the parameter $\Gamma$. (b) Plots of the temperature dependence of the zero-field mobility, which yield the mobility pre-factor ${\mu }_0$ and the polaron activation energy $E_a$.

Figure 12

Fit of the polaronic LA model to the data at selected temperatures for (a) the nonannealed sample #1 and (b) the annealed sample #3. The parameters used were (a) $\Delta =0.38\mathrm{eV}$, $K=0.1\mathrm{eV}{\mathrm{nm}}^{-1}$, $\nu =0.4\mathrm{eV}{\mathrm{rad}}^{-1}$; (b) $\Delta =0.17\mathrm{eV}$, $K=0.1\mathrm{eV}{\mathrm{nm}}^{-1}$, $\nu =0.28\mathrm{eV}{\mathrm{rad}}^{-1}$. Full lines show the model results using temperature independent energetic disorder in both cases, while the model results assuming temperature dependent disorder are also shown (dashed lines) in (a). A different hopping rate prefactor ${\omega }_0$ was used to fit the magnitude of mobility in (a) and (b).

Figure 13

Wavelength dependence of the refractive index $n$ (diamonds) and extinction coefficient $k$ (squares) for a film of thickness approximately $1\mu \mathrm{m}$, before (open symbols) and after (filled symbols) annealing.