Distribution of Localized States from Fine Analysis of Electron Spin Resonance Spectra in Organic Transistors

We developed a novel method for obtaining the distribution of trapped carriers over their degree of localization in organic transistors, based on the fine analysis of electron spin resonance spectra at low enough temperatures where all carriers are localized. To apply the method to pentacene thin-film transistors, we proved through continuous wave saturation experiments that all carriers are localized at below 50 K. We analyzed the spectra at 20 K and found that the major groups of traps comprise localized states having wave functions spanning around 1.5 and 5 molecules and a continuous distribution of states with spatial extent in the range between 6 and 20 molecules.

Figure 1

Continuous wave saturation of (a) ESR intensity and (b) linewidth of pentacene TFTs at gate voltage of $-200\mathrm{V}$ are plotted as a function of $(P/P_s{)}^{1/2}$, where $P$ is the incident microwave power and $P_s$ is the saturation microwave power. Curves $A$ and $B$ in (b) present the ideal lines for homogeneous and inhomogeneous cases. Inset shows the temperature dependence of $P_S$ and the corresponding magnetic field $B_S$.

Figure 2

Temperature dependence (Arrhenius plot) of ESR linewidths $\Delta B_{1/2}$ for pentacene TFTs at four different gate voltages. Reported values of linewidth for pentacene cation solution [12] and for low-mobility TFT [7] are also shown. $\Delta B_{1/2}{}^{MN}$ (open circles) and $\Delta B_{1/2}{}^{SL}$ (crosses) indicate the contribution of motional narrowing and spin-lattice relaxation effects, respectively, as obtained by cw saturation analysis of spin-lattice relaxation time $T_1$ [$T_1=(2T_2{\gamma }^{2}B_S{}^2{)}^{-1}$; $T_2$ is the spin-spin relaxation time related to the observed linewidth].

Figure 3

(a) High-precision FESR spectrum of pentacene TFT measured at 20 K and at gate voltage of $-200\mathrm{V}$. Also shown is a simulated curve reproduced by multiple-Gaussian fitting, with three components indicated by dashed lines. (b) Residuals for the stochastic optimization analysis (red line) using the final distribution function $D(N)$ shown in Fig. 4. Residual for a simple Lorentzian fitting is also shown (blue line).

Figure 4

(a) Distribution of trap states in pentacene TFTs are plotted against the spatial extent $N$ of the wave function, as obtained by stochastic optimization analysis of FESR spectrum at 20 K and at gate voltage of $-200\mathrm{V}$. Inset shows the distribution of trap states as a function of binding energy $E_B$ in the low-energy region, where the distribution as a function of $N$ is converted by approximation-free diagrammatic Monte Carlo method.