Negative transconductance in multi-layer organic thin-film transistors

The multi-terminal devices based on NTC behavior have been heavily studied due to their potential applications in future electronic circuits, such as high-speed switching devices, high-frequency oscillators and memories [1–5]. Most of the reported NTC devices so far were inorganic semiconductor materials, including III–V semiconductors, Si-based materials and two-dimensional atomic crystals [6–10]. However, the counterparts of organic semiconductors were rarely reported due to the poor film quality and low charge carrier mobility. Recently, various organic film growth technologies that can precisely control the thin film thickness and morphology have been developed, such as self-assembly guided strategy [11, 12], alignment of crystalline domains [13, 14] and vapor van der Waals epitaxy [15–17]. The ultra-thin single crystal organic film can be extended to millimeter scale [14, 15, 18]. Coupling with device optimizations, the resulting few-layer molecular crystals have shown outstanding electrical and photo-responsive properties [19–23], and have gained more and more attentions. For instance, several kinds of organic single crystals, such as C8-BTBT, rubrene and 2,6-diphenyl anthracene (DPA), have exhibited the band-like transport behavior with mobility over 30 cm²V⁻¹s⁻¹ [24–26] and photo-responsibility up to 10⁵ A W⁻¹ [20]. Nevertheless, most of studies on organic thin-film transistors (OTFTs) were focused on the electron lateral intralayer transport and how to optimize the contact. The vertical interlayer transport inside organic single crystals has rarely been reported, in which it will afford us a lot of opportunities to explore the new physics in OTFTs.

Here, we studied the interlayer and intralayer charge transport properties of high-quality multi-layer DPA OTFTs grown on h-BN. Antibipolar and NTC behavior were repeatedly observed due to the gate-induced vertical potential barrier change between the charge accumulation region near the substrate and the neutral bulk region inside the DPA thin film under the contact metal, different from the conventional quantum mechanical tunneling and mobility degradation. We systematically investigated the origin of the antibipolar and NTC through variable temperature and bias voltage measurements. Based on the observed NTC phenomenon, we fabricated a frequency doubler on a single OTFT. Our work simplified the structure of the logic device and expanded the application scope of OTFTs.

2.1. Growth of DPA single crystal film

2.2. Characterization

2.3. Device fabrication and measurement

We first focus on the van der Waals epitaxial growth of single crystal DPA films on exfoliated h-BN substrate, where the atomical flatness and free dangling bonds on the h-BN surface are crucial to deposit the high-quality single crystal thin film (figure 1(b)). Many molecular clusters were found on the surface of h-BN during the first step growth, which would be served as the seed layer for growing the multi-layer single crystal during the second step (figure 1(c); figure S1 is available online at stacks.iop.org/NANO/30/02LT01/mmedia; see experiment section for detailed information about the two-step growth). From figure 1(c), we found that the DPA crystal film preferentially grew on h-BN, in a layer-by-layer growth fashion with atomic smoothness. The average thickness of each molecular layer is 1.89 nm, which is close to the length of DPA (1.777 nm; figure 1(a)), indicating a perpendicular packing on the substrate, which is consistent with previously reported results [27]. Cross-polarized optical micrographs showed that the brightness of the DPA film changed uniformly with a twofold symmetry, as expected for high-quality single crystal (figures 1(d)–(f)).

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Next, we focus on the electrical transport properties of multi-layer DPA transistors, including four-terminal and two-terminal structures (figure S2). Because of the mismatch between the highest occupied molecular orbital (HOMO) energy level of DPA (5.6 eV) and the work function of gold (5.1 eV), a relatively large contact resistance is expected at low bias voltage. To eliminate the influence of the contact resistance and investigate the intrinsic transport properties of DPA single crystal, a four-terminal structure (inset of figure 1(g)) is used in our measurement. The channel conductance $\left({\sigma }_{4{\rm{P}}}=\tfrac{{I}_{{\rm{ds}}}}{{\rm{\Delta }}V}\right),$ the intrinsic mobility ${\mu }_{4{\rm{P}}}=\left(\tfrac{D}{W{C}_{{\rm{i}}}{\rm{\Delta }}V}\right)\left(\tfrac{d{I}_{{\rm{ds}}}}{d{V}_{{\rm{bg}}}}\right)$ and the contact resistance $\left({R}_{C}=\tfrac{{V}_{{\rm{ds}}}}{{I}_{{\rm{ds}}}}-\left(\tfrac{L}{D}\right)\left(\tfrac{{\rm{\Delta }}V}{{I}_{{\rm{ds}}}}\right)\right)$ could be extracted [28], where ${I}_{{\rm{ds}}}$ is the current passing through the channel, ${\rm{\Delta }}V$ is the voltage drop between the two probes in the middle separated by D, L is the channel length, W is the channel width, ${C}_{{\rm{i}}}$ is gate capacitance and ${V}_{{\rm{bg}}}$ is the back gate voltage applied in the devices. Figure 1(g) shows the temperature-dependent channel conductance as a function of the gate voltage of a four-terminal DPA transistor. The DPA single crystal exhibits clear band-like transport until ∼120 K, shown by the increase of ${\sigma }_{4{\rm{P}}}$ and mobility with the cooling. The mobility at V_bg = −50 V increases almost monotonically from ∼1.6 to 4.3 cm²V⁻¹s⁻¹ with temperature decreasing from 300 to 120 K (figure 1(h)). Figure S3 shows the temperature-dependent electrical transport results of another four-terminal DPA transistor with the same qualitative behavior.

Figure 2(a) displays the typical I_ds-V_bg transfer characteristics at various temperatures for a two-terminal device with DPA thickness of 18.6 nm (∼10 layers). At room temperature, the device exhibits a standard p-type transport character (figure 2(a), red solid line), consistent with the previous work [26, 27]. Notably, with the temperature decreasing, I_ds tends to saturate at large V_bg (e.g., at 170 K), and changes to non-monotonic behavior as a function of V_bg (T < 150 K), showing an interesting antibipolar transfer characteristic and NTC behavior. Such behavior has been reported in multi-layer MoS₂ transistors [10], but has never been observed in organic systems to the best of our knowledge. Figure 2(b) shows the I_ds-V_ds output characteristic at 90 K, where the NTC behavior could be clearly observed at low V_ds and persist up to −1.2 V. To further demonstrate the effect of V_ds, we plot the I_ds-V_bg curves under various V_ds from −0.5 V to −1.5 V at 90 K (figure 2(c)). With increasing V_ds, the NTC behavior weakens and eventually disappears, and the device restores to a normal p-type OTFT. We note that NTC was observed in all of multi-layer devices and showed significant thickness-dependence as its thickness was over 8.5 nm, but in the thinner DPA devices, typical p-type transistor behavior is observed without NTC (figures S4–S6).

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To further explore the origin of the NTC in multi-layer DPA devices, we have quantitatively analyzed the effective potential barrier of the device based on the variable temperature data. The current across a Schottky contact into a 2D channel can be described by 2D thermionic emission [29, 30], ${I}_{{\rm{ds}}}\propto {T}^{3/2}\exp \left(-\tfrac{q{\rm{\Phi }}}{{k}_{{\rm{B}}}T}\right),$ where the q is the electronic charge, ${\rm{\Phi }}$ is the effective potential barrier height, ${k}_{{\rm{B}}}$ is the Boltzmann constant and $T$ is the temperature. We extracted the effective potential barrier by linear fitting of the Arrhenius plot at different V_bg (figure 3(a)). The barrier height as a function of V_bg was plotted as shown in figure 3(b). The barrier first decreases and then slowly increases as the V_bg sweeps from −30 V to −60 V, and the position of the minimum ${\rm{\Phi }}$(V_peak) corresponds to peak conductance in transfer characteristics. Counterintuitively, we did not observe this variation trend of barrier and NTC in thinner DPA OTFTs. Therefore, we speculated that the change of potential barrier is the main factor leading to the NTC phenomenon. In order to explain the NTC mechanisms, we draw the band diagram under various gate voltage conditions in thicker DPA, as shown in figure 3(d). Here, the barrier includes (I) the Schottky barrier at contact interface and (II) the vertical potential barrier between the charge accumulation region near the substrate and the neutral bulk region under the contacts inside the DPA organic thin film. These two barriers can be effectively tuned by the gate electrostatic coupling effect and source-drain bias. Under the gate voltage being smaller than the threshold voltage, the device is in the off-state. When increasing the gate voltage at the range of V_th ∼ V_peak, the Schottky barrier dominated the electrons injection and the drain current monotonically increased. With continually increasing gate voltage, the Fermi level of the charge accumulation layer of DPA film near the substrate further shifts down the HOMO and that of the neutral bulk region remaining unchanged owing to the screening effect. Then, the vertical potential barrier height (${\rm{\Delta }}{E}_{b}$) was enlarged. This larger vertical barrier reduced the electron transport from charge accumulation layer to neutral bulk region, thus resulting in an n-type behavior. So, the n-type vertical interlayer transport in series with p-type intralayer transport is the main reason for the observed NTC, as shown in figures 2(a) and (c). Meanwhile, due to the drain-induced barrier lowing effect, we did not observe the NTC behavior at large source-drain bias. Furthermore, we carried out four-terminal measurements in the NTC regime. Figure 3(c) shows the total, channel and contact resistance as a function of V_bg. We observe that R_contact is one order of magnitude larger than R_channel and presents a non-monotonic change (figure 3(c) inset), while the R_channel always decreases with increasing gate voltage, consistent with the expected p-type behavior, indicating that the vertical potential barrier dominates the electron transport.

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Due to the unique NTC behavior, the sign of the transconductance could be switched from positive to negative, which provides new opportunities in the field of analog circuits applications. We fabricate a frequency doubler using a single multi-layer DPA OTFT. As displayed in figure 4(a), the DC offset voltage carrying a sinusoidal AC signal is applied as the input signal, with a 50 MΩ resistor connected to the source electrode in the circuit. From the transfer characteristic of the device in the circuit shown in figure 4(b), we could get that the peak-to-valley ratio is about 5.1, which is defined by the ratio of maximum peak current (I_peak) versus the valley current at the largest gate voltage (I_valley at V_bg = −70 V,), and V_peak = −50 V. When V_in < V_peak, the transconductance is positive and the output voltage increases with increasing of the input AC signal; when V_in > V_peak, the transconductance is negative and the output voltage decreases as the input AC signal increases. Therefore, a maximum and a minimum value appear simultaneously on one side of V_peak when V_offset is set to V_peak, implementing a frequency doubler. We set the V_offset = −50 V and use the sinusoidal AC signal with a frequency of 40 mHz as the input single, shown in the upper panel of figure 4(c), then an 80 mHz AC signal (bottom panel of figure 4(c)) will output from the circuit.

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In conclusion, high-quality multi-layer DPA single crystal films have been grown on h-BN substrate, and the OTFTs exhibited obvious band-like transport characteristics down to 120 K. Further, we observed a unique antibipolar and obvious NTC behavior in the multi-layer organic semiconductor transistors, due to a competition for charge carrier transport between lateral and vertical directions. The vertical potential barrier between the charge accumulation region near the substrate and the charge neutral bulk region inside DPA organic thin film under the contact metal, effectively modulated by the applied extrinsic electric field, is the fundamental origin, which was further testified from the temperature and source-drain bias dependence measurement. Based on the NTC and antibipolar phenomena, a frequency doubler had been fabricated using a single organic transistor.

The authors acknowledge support from the National Natural Science Foundation of China (Grant Nos. 61734003, 61704073, 61521001, 51725304, 51633006), National Key Basic Research Program of China (Grant Nos. 2013CBA01604 and 2015CB921600) and the Ministry of Science and Technology of China (2017YFA0204503).