Threshold Voltage and Space Charge in Organic Transistors

We investigate rubrene single-crystal field-effect transistors, whose stability and reproducibility are sufficient to measure systematically the shift in threshold voltage as a function of channel length and source-drain voltage. The shift is due to space charge transferred from the contacts and can be modeled quantitatively without free fitting parameters, using Poisson’s equation, and by assuming that the density of states in rubrene is that of a conventional inorganic semiconductor. Our results demonstrate the consistency, at the quantitative level, of a variety of recent experiments on rubrene crystals and show how the use of field-effect transistor measurements can enable the determination of microscopic parameters (e.g., the effective mass of charge carriers).

Figure 1

Panels (a) and (b) show optical microscope images of devices used in this work. Panel (c) shows the transfer characteristics of FETs with different channel lengths, measured at $V_{DS}=60\mathrm{mV}$ (the curves are offset vertically for clarity). The sublinear $V_G$ dependence is characteristic of contact dominated devices [10]. The vertical arrows point to the position of the threshold voltage in different devices. The two arrows with a continuous line indicate that for each data set the gate voltage is swept up and down.

Figure 2

Transfer characteristics of a rubrene single-crystal FET with channel length $L=600\mathrm{nm}$, measured for different values of the source-drain voltage $V_{DS}$. The arrows indicate that in all measurements the gate voltage has been swept up and down. The inset illustrates how the threshold voltage is extracted from the data.

Figure 3

The dots represent $V_T$ values of short-channel single-crystal devices as a function of $V_{DS}$ measured on devices with different channel length $L$ (the dotted lines are guides for the eye).

Figure 4

Panel (a) shows schematics of the region between the source and drain contacts of a FET device. The arrows indicate charge transfer from the contacts into the semiconductor; the transferred charge is represented by the shaded region. Panel (b) shows the potential energy band diagram near one metal-rubrene interface. Panel (c) shows the comparison between the measured $\delta V_T(L)$ and the values calculated using Poisson’s equation. The blue dotted line and the red line represent the values calculated with ${\Phi }_0=0.13$ and 0.15 eV, respectively (corresponding to the known range of measured values for the ${\mathrm{CuO}}_x/\mathrm{\text{rubrene}}$ interface). The inset shows that $d[\delta V_T(V_{DS})]/d{V}_{DS}$ scales linearly with $L^{-2}$.