Achieving ideal transistor characteristics in conjugated polymer semiconductors

Organic thin-film transistors (OTFTs) with ideal behavior are highly desired, because nonideal devices may overestimate the intrinsic property and yield inferior performance in applications. In reality, most polymer OTFTs reported in the literature do not exhibit ideal characteristics. Supported by a structure-property relationship study of several low-disorder conjugated polymers, here, we present an empirical selection rule for polymer candidates for textbook-like OTFTs with high reliability factors (100% for ideal transistors). The successful candidates should have low energetic disorder along their backbones and form thin films with spatially uniform energetic landscapes. We demonstrate that these requirements are satisfied in the semicrystalline polymer PffBT4T-2DT, which exhibits a reliability factor (~100%) that is exceptionally high for polymer devices, rendering it an ideal candidate for OTFT applications. Our findings broaden the selection of polymer semiconductors with textbook-like OTFT characteristics and would shed light upon the molecular design criteria for next-generation polymer semiconductors.


Supplementary Materials Section 1. Additional information of polymers investigated
c Thin films were spin-coated on glass substrates, λ is the peak of the first low energy absorption band of the polymer d Estimated optical gap was calculated using onset of the thin-film absorption spectra (Eopt = 1240/λonset)

Section 2. Optical characterization of PffBT4T-2DT films UV-Vis measurement
In Fig. S2, the absorption spectrum of PffBT4T-2DT thin film is presented. A strong, structured vibronic progression of the internal charge-transfer (ICT) state near the energy-gap edge at at 700 nm, and the -* transition at 440 nm each agree well with previous experimental results for the same polymer (39). The strong transition electric dipole moment for the 0-0 vibronic peak suggests J-aggregate behaviour (59) which is well-reported for other polymers of this class with planar chains (60), low energetic disorder and weak intermolecular coupling (39) (59). (A) Normalized PL spectrum of bulk films. (B) Normalized PL spectrum of the first pixel within each sample (pixel on the topleft corner). (C) Local PL centre-of-mass maps of polymers. Pixels that cannot be Gaussian fitted are in white and excluded from the statistical analysis, scalebars are 10 µm. (D) Distribution of local PL centre-of-mass (10,000 pixels in total, size of each: 660 x 660 nm 2 ) for all the four materials within the region of interest.

Section 3. Torsional disorder calculations
The torsion potentials between various comonomer units of cationic and neutral PffBT4T-2DT was computed at DFT/B3LYP/def2-TZVP level of theory. All the long alkyl chains were replaced by methyl groups to reduce the computational cost.  According to our previous procedure(61)(62), polymer crystal structure of PffBT4T was constructed with optimized monomer structure, interdigitated alkyl side chains, and lattice parameters from GIWAXS experiments. The crystal structure was then fully optimized with periodic-boundary-condition (PBC). A 368 supercell was built with 3 lamellar layers of 6 π-stacked chains with 8 repeating units. The supercell was subjected to a 50-ps molecular dynamics simulation under NPT ensemble (P = 110 5 Pa, T = 500 K) to induce polymer packing disorders, following a 1-ns molecular dynamics at room temperature under NPT ensemble (P = 110 5 Pa, T = 298 K). The equilibrium state was then extracted and visualized. Molecular dynamics calculations were performed with Materials Studio package using the Dreiding force field(63), Gasteiger charges(64), velocity scale thermostat, Berendsen pressure coupling, and time step of 2 fs. Tz-T stands for the angle between the benzothiadiazole unit and the thiophene unit which shows a wider distribution, and T-T stands for the angle between tow thiophene units.

Fig. S6. Comparison between the theoretical and the measured voltage difference between the two voltage probes (ΔV) in a gated four probe transistor measurement.
For the gated four probe transistor measurement (Fig. S6), the applied drain voltage is -5 V, and the channel length L and the distance between 2 voltage sensing probes ΔL are 420 µm and 140 µm respectively. Assuming that the potential drops linearly between the source and the drain, the theoretically predicted ΔV should be -1.67 V. The measured value, however, is -1.77 V, the magnitude of which is even slightly larger than the theoretical value. If the measured value is used to calculate the contact resistance, we would get a small but negative contact resistance for this device, which is obviously not reasonable. One possible explanation of the negative apparent contact resistance is that the gradual channel approximation is not 100% valid (i.e., the potential drop across the channel is slightly non-linear). The observation of the negative apparent contact resistance suggests that the true contact resistance should be negligible compared with the channel resistance, because the existence of any noticeable contact resistance would lead to a smaller magnitude of ΔV than the theoretically predicted value.  Data for IDT-BT and N2200 are reproduced from Ref (16) and (28) respectively.

Section 7. More details of Seebeck measurements
The schematic and optical image of the measured Seebeck device is shown in Fig. S11. A microfabricated heater and two temperature sensors (sensors at the hot and the cold end of the device, respectively) are positioned along the OTFT channel, while the two sensors also work as the source and drain electrodes of the OTFT device. The linear and saturation mobility of the measured device at room temperature is shown in Fig. S12. The mobility measured from the Seebeck device shows a lower value compared with the one measured from normal OTFTs. This is likely due to the photolithographic patterning process, which was used to pattern the polymer film to realize this architecture (65) and which negatively affects the performance of the PffBT4T-2DT layer. The Seebeck coefficient is determined by measuring the electromotive force EMF (ΔV) across the material when a temperature differential ΔT is generated by the heater along the same direction, and is given by the equation below: In this experiment, the temperature gradient is created by resistive heating (applying a voltage to the on-chip heater). The temperature difference between the hot side and the cold side is calculated by first measuring the temperature coefficient of resistance ( , Fig. S13A) of the metal temperature sensors, and then obtaining the heating power (P) dependence of sensor resistance ( , Fig. S13B).
The thermal voltage is also measured under the same heating power ( , Fig. S13C). Consequently, the final expression of S is: A narrow-band model is used to interpret the Seebeck coefficient based on the following equation (66): The first contribution is related to the change of the entropy of mixing associated with adding a carrier into the density of thermally accessible transport states, with N denoting the total number of available states and nc the mobile carrier concentration. The second term is the entropy change due to spin degeneracy, while the third term is the entropy change arising from the molecular vibration (67). Within the equation, only the first term is carrier concentration-dependent, and since in the case of an OTFT nc ≪ N, the plot of versus the logarithm of nc would give a straight line with the slope of (kB/e)ln(10) = 198 μV K −1 decade −1 . In reality, most polymer systems exhibit slope larger than 198 μV K −1 decade −1 . This discrepancy could be reconciled by taking into account the proportion f of trap states within all the thermally accessible sites, which gives nc = n(1-f). Then the slope of the S-log(n) plot is modified to be −(kB/e)ln(10)/(1-f).

Section 8. Ring oscillator simulation
We evaluated the critical impacts of reliability factor on circuit performance by simulating the oscillation frequency of seven-stage ring oscillators using Technology Computer-Aided Design (TCAD)(68) (69). The schematic of seven-stage ring oscillator in simulation is shown in Fig. S14A, constructed by cascading seven inverters with p-type OTFTs acting as both the driver and the load. Six seven-stage ring oscillators were simulated based on six types of p-type OTFTs with identical drain current at -50 V but increasing non-linearity (reliability factors ranging from 101% to 20% (Fig. S14B)).
OTFTs with reliability factor of 100% are considered as ideal transistors with gate independent mobility, while 101% ones resembling the OTFTs based on PffBT4T-2DT of this work and 80% being the maximum value of most polymer-based OTFTs exhibiting certain levels of non-linearity reported in literature. The driver and load OTFTs have the same channel length but different channel width, denoted as Wdriver and Wload respectively. However, the ratio between Wdriver and Wload has minimum effects on the relative frequency of oscillators based on OTFTs with different reliability factors compared with that based on ideal OTFTs (Fig. S14C). The output waveforms of oscillators based on OTFTs with different reliability factors are shown in Fig. S14D at supply voltage of 50V, with the frequency of the oscillator of 101% reliability factor reaching 49.434 kHz and that of 20% reliability factor close to 0. Voltage dependent frequencies of oscillators are shown in Fig. S14E, showing clear positive correlation between oscillation frequency and supply voltage as well as positive correlation between oscillation frequency and reliability factor. To compare the performance of ring oscillators with different reliability factors, their oscillation frequencies are normalized by the frequency of the oscillator with 100% reliability factor (f/fRF=100%) and summarized in Fig. S14F. The oscillation frequency decreases as the OTFTs become more and more non-ideal, due to smaller carrier mobility values of non-ideal OTFTs around operating point thus larger propagation delay time (70) The oscillator based on OTFTs with 101% reliability factor has almost identical frequency to that of ideal OTFTs at all supply voltages, while the difference between non-ideal OFTFs and ideal OTFTs enlarges as the supply voltage decreases; for instance, fRF=80%/fRF=100% equals to 82.5% at 50V and decreases to 45.2% at 15V. Notably, the oscillator based on OTFTs with 20% reliability factor has oscillation frequency two orders of magnitude smaller than ideal OTFTs at 50V and shows negligible frequency and amplitude when the supply voltage decreases below 30V. These results indicate that low reliability factor not only degrades circuit performance but also blocks its normal operation completely under certain conditions, creating obstacles in designing functional circuits and predicting their performance in real applications. (F) Voltage dependent oscillation frequency of seven-stage ring oscillators relative to the frequency at 100% reliability factor versus the reliability factor of the constructing OTFTs.