Relative importance of polaron activation and disorder on charge transport in high-mobility conjugated polymer field-effect transistors

The charge transport properties of conjugated polymer semiconductors are governed by strong electron phonon coupling, leading to polaron formation as well as the presence of structural and electronic disorder. However, the relative contribution which polaronic relaxation and disorder broadening make to the temperature activation of the mobility of these materials is not well understood. Here we present a combined study of the temperature and concentration dependences of the field-effect mobility and the optically induced electron-transfer transitions of a series of poly(3-hexylthiohene) field-effect transistors of different molecular weight. We apply a vibronic coupling model to extract the reorganization energy and the strength of electronic coupling from the optical spectra. We observe a transition from a localized to a delocalized transport regime as a function of molecular weight and crystalline quality. Polaron activation is comparable to disorder-induced activation in the low-mobility regime $[\sim {10}^{-3}{\mathrm{cm}}^2∕\left(\mathrm{V}\mathrm{s}\right)]$ and needs to be taken into account when interpreting the field-effect mobility, while disorder becomes the dominant mechanism to limit charge transport in the high-mobility regime with mobilities $>{10}^{-2}–{10}^{-1}{\mathrm{cm}}^2∕\left(\mathrm{V}\mathrm{s}\right)$.

Figure 1

Transfer characteristics $(V_{ds}=-5\mathrm{V})$ of TCB spin-cast transistors with MW of (a) $270\mathrm{kD}$ and (b) $15\mathrm{kD}$ at different temperatures on a ${\text{semilog}}_{10}$ scale.

Figure 2

(a) Field-effect mobility vs inverse temperature extracted from the linear transfer characteristics $(V_{ds}=-5\mathrm{V})$ of P3HT FETs at $V_g=-80\mathrm{V}$ for $270\text{−}\mathrm{kD}$, $37\text{−}\mathrm{kD}$, and $15\text{−}\mathrm{kD}$ MW polymers. Open and solid symbols denote the TCB and chloroform spin-cast devices, respectively. (b) Activation energy of the field-effect mobility vs $V_g$ for devices with different MW and solvents.

Figure 3

(Color) Experimental FTIR CMS spectra (colored lines) and calculated absorption profiles from Piepho’s model (solid lines) and the PKS model (dotted lines).

Figure 4

Adiabatic potential surfaces in the off-diagonal coupling calculated for $15\text{−}\mathrm{kD}$ (solid lines) and $270\text{−}\mathrm{kD}$ (dashed lines) polymers. Note that we transfer the antisymmetric coordinate $Q_{-}$ into a dimensionless variable $q_{-}=\sqrt{2l_{-}^2∕\lambda \hslash {\omega }_{-}}{Q}_{-}$ to exclude the unknown parameters, e.g., $k_{-}$ and $l_{-}$, in Eq. (4). Charge transport in $15\text{−}\mathrm{kD}$ polymer is in the localized regime $(\lambda >\Delta )$ and requires activation energy $E_a$ for polaron hopping. Charge transport in $270\text{−}\mathrm{kD}$ polymer is in the delocalized regime $(\Delta >\lambda )$.

Figure 5

DOS of polymer for the ME model and carrier density at $400\mathrm{K}$ and $100\mathrm{K}$ extracted from fitting the $270\text{−}\mathrm{kD}$ P3HT transistor.

Figure 6

Experimental data (open symbols) and ME model fit (solid lines) of gate voltage dependent mobility at different temperatures for (a) $270\text{−}\mathrm{kD}$ TCB and (b) $15\text{−}\mathrm{kD}$ TCB transistors. The dotted lines in (a) show the fitting result if the deep trap states are not included in the ME model.

Figure 7

Vissenberg-Matters hopping model fits (solid lines) to the experimental data (open symbols) of the gate voltage dependent mobility at different temperatures for $270\text{−}\mathrm{kD}$ TCB devices.