Figure 1

Transfer characteristics of PQT-12 at different temperatures showing the increase in the threshold voltage. The data are measured with a pulsed gate voltage to reduce bias-stress effects and with a drain voltage of $1\mathrm{V}$. The data are scaled by the factors indicated.Reuse & Permissions

Figure 2

TFT mobility vs inverse temperature for two samples of PQT-12, showing the change of activation energy near $250\mathrm{K}$ in the higher-mobility material, but not in the lower-mobility material. The high-mobility sample is deposited on an octadecyltrichlorosilane (OTS) self-assembled monolayer and the lower-mobility sample is the same material deposited on the untreated silicon oxide dielectric.Reuse & Permissions

Figure 3

Effective mobility (as defined in the text) vs inverse temperature for high-mobility PQT-12, measured at different gate voltages. The dashed line corresponds to an activation energy of $0.22\mathrm{eV}$ and a mobility prefactor of $500{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$. The change of slope at the highest temperature, also seen in Fig. 2, is due to thermal changes in the sample.Reuse & Permissions

Figure 4

Illustration of the structure of PQT-12 showing the ordering of the adjacent chains and the location of the alkyl chains, $R$. In PQT-12, $R={\mathrm{C}}_{12}{\mathrm{H}}_{25}$, while in the model structure employed in the electronic structure calculation, $R$ is represented by a single H atom. The registration between the chains is such as to minimize the interaction between the alkyl side chains with neighboring chains.Reuse & Permissions

Figure 5

Illustration of polythiophene lamella showing long-range order within the lamella, small local fluctuations in chain position, and disordered chain ends (adapted from Ref. 10). The alkyl chains are omitted.Reuse & Permissions

Figure 6

Schematic illustration of possible grain boundary structure for small-angle (upper figure) and large-angle boundaries (lower figure), illustrating that the large-angle boundary has more disorder.Reuse & Permissions

Figure 7

Illustration of eight rings of an infinite two-dimensional sheet of polythiophene, as used for the electronic structure calculations. The smallest unit cell is described by the lattice vectors $\mathbf{a}$ and $\mathbf{b}$, and the lengths of these vectors are determined by energy minimization. The lattice points $\mathbf{R}=\mathrm{n}\mathbf{a}+\mathrm{m}\mathbf{b}$ span a two-dimensional plane and the polythiophene material therefore forms a two-dimensional sheet. The calculations take place in a supercell with a third lattice vector $\mathbf{c}$ (length $14.8\mathrm{\AA }$) that is orthogonal to both $\mathbf{a}$ and $\mathbf{b}$.Reuse & Permissions

Figure 8

The energy position, relative to the vacuum level, and the widths of the electron and hole bands, calculated as a function of the spacing between the chains. The energies $v_1$ and $v_2$ ($c_2$ and $c_1$) are the energies of the top and bottom of the hole (electron) band corresponding to transport perpendicular to the polymer chains.Reuse & Permissions

Figure 9

Band structure for the two-dimensional sheet of PQT-12 for the lattice constants, $a=14.6\text{bohr}$ and $b=7.2\text{bohr}$. The dispersion from $\Gamma$ to $\mathrm{J}=(\pi ∕a,0)$ and from $\Gamma$ to ${\mathrm{J}}^{\prime }=(0,\pi ∕b)$ is shown. The topmost hole band $H1$ has a dispersion of $1.72\mathrm{eV}$ along $\Gamma \text{−}\mathrm{J}$ and a dispersion of $0.60\mathrm{eV}$ along $\Gamma \text{−}{\mathrm{J}}^{\prime }$. The zero of energy is at the valence-band maximum.Reuse & Permissions

Figure 10

Illustration of how the valence bands of ordered lamella and disordered intergranular regions of the valence band line up to give a barrier to holes transferring between lamella.Reuse & Permissions

Figure 11

Proposed density-of-states distribution combining ordered and disordered material and showing the sharp band edge and constant 2D DOS in the ordered layer and the shifted band edge, with a wider band tail for the disordered intergranular material.Reuse & Permissions

Figure 12

Schematic illustration of the proposed transport path along preferential directions with low-angle grain boundaries, forming a high-mobility percolation path.Reuse & Permissions

Figure 13

Numerical calculation of the effective mobility in the high-temperature regime for two gate voltages, based on the model described in the text. The assumed DOS above the band edge is $2\times {10}^{14}{\mathrm{cm}}^{-2}{\mathrm{eV}}^{-1}$ (open points) and $5\times {10}^{14}{\mathrm{cm}}^{-2}{\mathrm{eV}}^{-1}$ (closed points), the band mobility is 30 and $10{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$ respectively, and the other parameters are given in the text.Reuse & Permissions

Figure 14

Numerical calculation of the effective mobility, with the same parameters as for Fig. 13, but including a nonzero band- tail mobility.Reuse & Permissions

Figure 15

Numerical calculation of the TFT mobility (lines) obtained by calculating the linear transfer characteristics, compared to the measured data (points). The model includes a nonzero band-tail mobility. The DOS is $5\times {10}^{14}{\mathrm{cm}}^{-2}{\mathrm{eV}}^{-1}$ for model 1 and $2\times {10}^{14}{\mathrm{cm}}^{-2}{\mathrm{eV}}^{-1}$ for model 2, with the other parameters chosen to give the best fit.Reuse & Permissions

Figure 16

Schematic diagram showing the increase in the temperature dependence of the mobility when percolation is taken into account.Reuse & Permissions