Optical conductivity and optical effective mass in a high-mobility organic semiconductor: Implications for the nature of charge transport

We present a multiscale modeling of the infrared optical properties of the rubrene crystal. The results are in very good agreement with the experimental data that point to nonmonotonic features in the optical conductivity spectrum and small optical effective masses. We find that, in the static-disorder approximation, the nonlocal electron-phonon interactions stemming from low-frequency lattice vibrations can decrease the optical effective masses and lead to lighter quasiparticles. On the other hand, the charge-transport and infrared optical properties of the rubrene crystal at room temperature are demonstrated to be governed by localized carriers driven by inherent thermal disorders. Our findings underline that the presence of apparently light carriers in high-mobility organic semiconductors does not necessarily imply bandlike transport.

Figure 1

Optical conductivity spectra along the $b$ (stacking) direction of the rubrene crystal calculated at different temperatures. The inset shows the chemical and crystal structures of rubrene. Here, ${\sigma }_0=\pi e^{2}b/\hslash N$.

Figure 2

(a) Optical effective mass at different temperatures and (b) carrier mean free path (circles and left axis) and optical conductivity peak energy (squares and right axis) at 300 K as a function of e-ph coupling strength. The inset in (a) presents the optical effective mass with and without considering the impact of CTE as a function of temperature.

Figure 3

Optical effective mass obtained from Eq. (8) as a function of temperature for different strengths of e-ph coupling.

Figure 4

(a) Optical conductivity spectra as a function of the e-ph coupling symmetry parameter $c$ (in intervals of 0.25); (b) and (c) energy-resolved $\Xi \left(E_{\mathrm{ini}},E_{\mathrm{fin}}\right)$ (left part) and optical absorptions of the optical conductivity peaks projected onto the DOS (right part) for: (b) symmetric coupling $\left(c=1\right)$ and (c) antisymmetric coupling $\left(c=0\right)$. Here, $T=300\mathrm{K}$; ${\sigma }_0=\pi e^{2}b/\hslash N$; the white lines in (b) and (c) denote the paths of the integral in Eq. (9) for the optical conductivity peaks.

Figure 5

Fermi-level dependence of (a) optical conductivity peak energy as a function of the e-ph coupling symmetry parameter $c$ (in intervals of 0.25) and (b) mean energy of the initial and final states associated with the absorption of the optical conductivity peak in the rubrene crystal; (c) schematic diagram of the optical absorption near the band tail. Here, $T=300\mathrm{K}$; in (a) and (b), the dashed lines indicate the band edge in the absence of e-ph coupling; in (c), the filled region represents the occupation of carriers and $E_{\mathrm{edge}}$ denotes the energy of the band edge.

Figure 6

Temperature dependence of the optical conductivity peak energy (squares and left axis) and the band-tail width (triangles and right axis) in the rubrene crystal in the limit of low carrier concentration. The inset illustrates the linear relationship between the optical conductivity peak energy and the band-tail width.