Measurement of the diffusivity of fullerenes in polymers using bilayer organic field effect transistors

Bilayer poly(3-hexylthiophene):[6,6]-phenyl C${}_{61}$-butyric acid methyl ester (PC${}_{61}$BM) [P3HT:PC${}_{61}$BM] organic field-effect transistors (OFETs) have been fabricated using a bottom-contact, bottom-gate (BCBG) architecture. By annealing these devices and monitoring the magnitude of the electron field-effect mobility, information about the diffusion properties of PC${}_{61}$BM in P3HT can be obtained. Using a solution to the one-dimensional diffusion equation and an application of percolation theory, a relationship between electron field-effect mobility, diffusion coefficient, and annealing time has been obtained. By applying this model to time-dependent mobility measurements, a rough approximation of 5 nm${}^2$s${}^{-1}$ has been made for the diffusion coefficient of PC${}_{61}$BM in P3HT at a temperature of 130 °C.

Figure 1

(a) Normalized optical-absorption spectra of spin-cast PC${}_{61}$BM, vacuum-deposited PC${}_{61}$BM, and vacuum-deposited C${}_{60}$. Transfer characteristics of (b) spin-cast PC${}_{61}$BM and (c) vacuum-deposited PC${}_{61}$BM TCBG OFETs fabricated on BCB-coated SiO${}_2$ with aluminium source and drain electrodes. The devices were characterized under ambient pressure in N${}_2$ without being annealed. In both cases the transistors had channel lengths and widths of 40 μm and 1000 μm, respectively. Inset to (c): schematic diagram of TCBG transistor structure employed.

Figure 2

(a) Schematic diagram of BCBG bilayer OFET structure used in this study and molecular structures of PC${}_{61}$BM (top) and P3HT (bottom). Output characteristics of example bilayer P3HT:PC${}_{61}$BM BCBG transistors measured under ambient-pressure N${}_2$ before annealing with applied gate voltages of (b) $V_{\mathrm{G}}$ = 0 V to $V_{\mathrm{G}}$ = −40 V and (c) $V_{\mathrm{G}}$ = 0 V to $V_{\mathrm{G}}$ = 40 V. This device had a channel length and width of 7.5 μm and 10 000 μm, respectively, and P3HT and PC${}_{61}$BM thicknesses of 8 nm and 31 nm, respectively.

Figure 3

(a) Average saturation-regime field-effect mobility of holes and electrons in five bilayer P3HT:PC${}_{61}$BM OFETs measured at room temperature under ambient-pressure N${}_2$ after being annealed at various temperatures for 30 minutes. The error bars represent the standard deviation in the measured field-effect mobility. When the electron mobility was not detectable it was plotted as 10${}^{-9}$ cm${}^2$V${}^{-1}$s${}^{-1}$. The thicknesses of the P3HT and PC${}_{61}$BM layers were 8 nm and 40 nm, respectively. (b) Average saturation-regime field-effect mobility of holes and electrons in five bilayer P3HT:PC${}_{61}$BM transistors measured under ambient-pressure N${}_2$ after being annealed at 130 °C, plotted as a function of time. The thicknesses of the P3HT and PC${}_{61}$BM layers were in this case 25 nm and 31 nm, respectively.

Figure 4

(a) Initial 2D concentration profile (C/$C_0$) of PC${}_{61}$BM in bilayer P3HT:PC${}_{61}$BM organic FET with P3HT and PC${}_{61}$BM thicknesses of 25 nm and 31 nm, respectively [Eq. (3)] and PC${}_{61}$BM concentration profile calculated using Eq. (6), evaluated at various times. The parameters used in this calculation were: $x_p$ = 25 nm, $x_c$ = 55 nm, and D = 5 nm${}^2$s${}^{-1}$. (b) Points: average PC${}_{61}$BM concentration calculated using Eq. (11) and saturation-regime field-effect mobility of electrons measured using two sets of bilayer P3HT:PC${}_{61}$BM transistors measured under ambient-pressure N${}_2$ after being annealed at 130 °C, plotted as a function of time. The PC${}_{61}$BM thickness was 31 nm in both devices. The curves represent a best-fit to the experimental data using Eq. (7). The extracted diffusion coefficient in this case was found to be D = 5 nm${}^2$s${}^{-1}$.

Figure 5

Graphic illustrating how the electron field-effect mobility is computed for α = 0.1, ${\mu }_0$ = 1, and C/$C_0$ = 0.3 using Eq. (11). The $x$ axis shows the desired bond-occupation probability. On the $y$ axis is mobility. As $p$ is increased, the lattice constant necessary to obtain that particular $p$ is also increased. Inset (a) shows a 100 × 100-random lattice with $c$ = 0.3 and $a$ = 1. This corresponds to a bond-occupation probability of 0.09 and hence a mobility of zero. Inset (b) shows the same lattice rescaled with $a$ = 2. The lattice is now much better connected and the mobility is nonzero. Note the conductance is severely limited by the increase in lattice constant.