Investigation of the dimensionality of charge transport in organic field effect transistors

Ever since the first experimental investigations of organic field effect transistors (OFETs) the dimensionality of charge transport has alternately been described as two dimensional (2D) and three dimensional (3D). More recently, researchers have turned to an analytical analysis of the temperature-dependent transfer characteristics to classify the dimensionality as either 2D or 3D as well as to determine the disorder of the system, thereby greatly simplifying dimensionality investigations. We applied said analytical analysis to the experimental results of our OFETs comprising molecularly well-defined polymeric layers as the active material as well as to results obtained from kinetic Monte Carlo simulations and found that it was not able to correctly distinguish between 2D and 3D transports or give meaningful values for the disorder and should only be used for quasiquantitative and comparative analysis. We conclude to show that the dimensionality of charge transport in OFETs is a function of the interplay between transistor physics and morphology of the organic material.

Figure 1

(a) Linear mobility of monolayer OFETs plotted as a function of gate voltage. The inset shows the gate field dependence of the current from which the mobility has been calculated. (b) Schematic of the top-gate OFETs used in this paper.

Figure 2

(a) Transfer characteristics of a two-ML P(NDI2OD-T2) OFET at different temperatures on a double-logarithmic scale. The symbols are experimentally obtained data points, and the solid lines are power-law fits to the high gate voltage range of these data. (b) γ values obtained from the inclination of the power-law fits to the transfer characteristics (symbols) vs inverse temperature. The lines are linear fits extrapolated to the γ axis. The intersections should indicate the dimensionality of the system. The inset shows said intersections as a function of the number of MLs.

Figure 3

(a) The solid lines are the calculated mobilities as a function of gate field for simulated devices with a rectangular lattice and thicknesses ranging from one to five MLs, which are compared to experimental curves of P(NDI2OD-T2) OFETs from Fig. 1 (full symbols). (b) Comparison of the mobilities calculated for a rectangular lattice with exponential energetic disorder for various numbers of MLs as indicated by the color of the lines and disorders of 30, 50, 80, and 100 meV.

Figure 4

(a) Simulated transfer characteristics at different temperatures of OFETs with two MLs using a rectangular lattice for hopping (dots). The solid lines are guides to the eye. (b)–(d) γ values plotted against inverse temperature (open circles) and linear fits extrapolated to the γ axis (solid lines) for (b) a rectangular lattice at high fields, (c) a rectangular lattice at low fields, and (d) a cubic lattice for the whole field range. The insets in (b)–(d) show the intercept with the γ axis as a function of the number of MLs. The dashed lines indicate intercepts for 2D and 3D according to eVM.

Figure 5

(a) Intercepts with the γ axis for all cases discussed above as a function of the number of MLs. The dashed line corresponds to 2D and 3D behaviors according to the eVM model. (b) Extracted width $T_0$ of the exponential DOS. The dashed line indicates the input $T_0$ of the MC simulations.

Figure 6

Percentage of carriers in the first ML as a function of gate voltage and total number of MLs in the device for (a) a rectangular lattice and (b) a cubic lattice.