Self-Heating, Bistability, and Thermal Switching in Organic Semiconductors

We demonstrate electric bistability induced by the positive feedback of self-heating onto the thermally activated conductivity in a two-terminal device based on the organic semiconductor ${\mathrm{C}}_{60}$. The central undoped layer with a thickness of 300 nm is embedded between thinner $n$-doped layers adjacent to the contacts, minimizing injection barriers. The observed current-voltage characteristics follow the general theory for thermistors described by an Arrhenius-like conductivity law. Our findings include hysteresis phenomena and are of general relevance for the entire material class since most organic semiconductors can be described by a thermally activated conductivity.

Figure 1

Self-consistent current-voltage characteristics including self-heating according to Eqs. (4, 5) (red), revealing that thermal switching can only occur above the critical value of the activation energy $E_{\mathrm{act}}>4k_B{T}_a$. Unstable NDR regions are indicated by dashed lines. Thermal resistance ${\Theta }_{\mathrm{th}}=1000\mathrm{K}/\mathrm{W}$. Blue line: isothermal current-voltage relation (1) with $\alpha =1$ at ambient temperature $T_a=T_0=293\mathrm{K}$.

Figure 2

Calculated current-voltage characteristics of an electrical circuit consisting of a device including self-heating together with a load resistance $R_{\mathrm{L}}$ in series (red), for $E_{\mathrm{act}}=8k_B{T}_a$, a thermal resistance ${\Theta }_{\mathrm{th}}=1000\mathrm{K}/\mathrm{W}$, and different values of the load. The dashed parts indicate the NDR region of the intrinsic device as shown in Fig. 1. Blue line: isothermal current-voltage relation (1) with $\alpha =1$ at constant temperature $T_a$. Black dotted lines indicate load resistance only.

Figure 3

Measurement of the current at $U=1.0\mathrm{V}$ over temperature, revealing an activation energy of $E_{\mathrm{act}}=8.2k_B{T}_0$. The possible influence of self-heating can be excluded by reducing the time per measurement point to 2 ms (see Supplemental Material [22]).

Figure 4

Thermal switching measured during a voltage sweep upwards and downwards. For comparison, an isothermal current voltage characteristic is measured by applying short voltage pulses. The sample is cooled to $T_a=-52°\mathrm{C}$ (221 K).

Figure 5

Current-voltage characteristic of the organic $S$-NDR element recovered by $U=U_{\mathrm{tot}}-R_{\mathrm{L}}I$ with load resistance $R_{\mathrm{L}}=11.2\Omega$ from the measured data ($U_{\mathrm{tot}}$, $I$) plotted in Fig. 4 showing the switching along the load line. The dashed line is a guide to the eye for the load line. The highest temperature achieved is about $178°\mathrm{C}$, or 230 K above the ambient temperature in the Peltier cooler.