Unusual Thermoelectric Behavior Indicating a Hopping to Bandlike Transport Transition in Pentacene

An unusual increase in the Seebeck coefficient with increasing charge carrier density is observed in pentacene thin film transistors. This behavior is interpreted as being due to a transition from hopping transport in static localized states to bandlike transport, occurring at temperatures below $\sim 250\mathrm{K}$. Such a transition can be expected for organic materials in which both static energetic disorder and dynamic positional disorder are important. While clearly visible in the temperature and density dependent Seebeck coefficient, the transition hardly shows up in the charge carrier mobility.

Figure 1

The density of states used in (a) the ME model, (b) the VRH model, and (c) the hybrid model, including the relevant energy levels. The gray area below $E_{\mathrm{C}}$ represents the density of occupied localized states.

Figure 2

Measurements (symbols) and calculations (lines) of the Seebeck coefficient vs gate bias in a pentacene thin film transistor. The gate bias $V_g$ is corrected for the threshold voltage $V_{\mathrm{th}}$ of the TFT.

Figure 3

(a) The measured (symbols) and calculated (lines) linear mobility vs gate bias with intervals of $T=20\mathrm{K}$. The deviations at small gate voltage are attributed to leakage currents and the breakdown of the assumption that $|V_g-V_{\mathrm{th}}|\gg V_{\mathrm{sd}}$ ($V_{\mathrm{sd}}=\mathrm{\text{source}}\mathrm{\text{−}}\mathrm{\text{drain voltage}}$). The inset shows ${\mu }_{\mathrm{free}}·n_{\mathrm{free}}(\sim {\sigma }_{\mathrm{ME}}$) vs $T$ for $V_g-V_{\mathrm{th}}=-30\mathrm{V}$. (b) Activation plot of the measured (symbols) and calculated (lines) mobility for different gate bias, with intervals of 2 V

Figure 4

(a) Measured (symbols) and calculated (lines) Seebeck coefficients at $T=200\mathrm{K}$. $S_{\mathrm{hyb}}$ is the conductivity-weighted average of $S_{\mathrm{VRH}}$ and $S_{\mathrm{ME}}$. (b) The ratio of the VRH and the ME contributions to the conductivity vs gate bias for different temperatures. The inset shows the temperature dependent band mobility ${\mu }_{\mathrm{free}}$ assuming $n_0={10}^{27}{\mathrm{m}}^{-3}$ for the DOS above $E_{\mathrm{C}}$.