Self-defined dual charge percolation networks for solution-processed multithreshold transistors

Introduction

Multivalued transistors (MVTs), which can attain multiple electrical states beyond simple on/off-based 0 and 1 binary states, offer a new paradigm in logic design that could yield dramatic improvements in information-processing efficiency and circuit compactness^1,2,3,4,5,6. Realizing MVTs requires a channel material that can exhibit stable intermediate electrical states between on and off binary states with ensured noise tolerance. This necessitates delicate exploitation of the electronic states of the channel material, which can become increasingly complicated when the number of conductive states that contribute to MVT characteristics increases³. For example, crystalline zinc oxide (ZnO) nanoparticles embedded in an amorphous matrix of themselves were exploited to energetically isolate the localized conductive states from the mobility edge, which resulted in multiple saturable conduction states⁴. To increase the number of states in such an approach, the organic barrier layers and semiconducting layers must be sequentially deposited to shift the threshold voltages of each state to different degrees. Various chemical approaches, including the excitation of different oxidative states or morphological phases by external electrical stimuli, have also been used to emulate multiple conductive states in a single material^3,6,7,8,9. Although these approaches have been successfully demonstrated, they have been unable to meet the critical figures of merit (FOMs) for MVTs—the equiprobable, distinctive, and stable manifestation of all logic states—owing to challenges in harnessing higher-order states and narrow controllable windows for the intermediate states. To this end, the incorporation of multiple semiconducting materials with different threshold voltages, either in stacked or staggered geometry, has been proposed, as it enables the selective engineering of their threshold voltages, i.e., multithreshold engineering, to be mechanistically implemented^10,11,12. Nevertheless, it has been difficult to separately control or even emulate their different threshold voltages in a single device because of the equilibrium charge transfer between the semiconducting domains. Therefore, different transport or turn-on mechanisms for separate channels, or even the geometrical separation of the charge-transport channels, have inevitably been employed thus far^10,11. Such approaches offer distinct advantages in controlling the FOMs for intermediate states, but they still require complicated fabrication processes and lack harnessing methods for higher-order logic states.

In this regard, tetrapod-shaped semiconductor nanocrystals (TpNCs) can be a compelling candidate for addressing the intricate requirements of FOMs for MVT channels. TpNCs have a structure consisting of a core and four arms that extend in a tetrahedral geometry, and they exhibit intriguing characteristics due to their unique shape^13,14. The four arms bound to a single core are extended isotropically in three dimensions, and each arm has a high aspect ratio. Therefore, unlike those made of other materials with high aspect ratios, the thin films of TpNCs facilitate the formation of percolation networks at relatively low thresholds without the need for meticulous alignment. The resulting network, characterized by abundant voids, provides an ideal scaffold for incorporating other electronic materials, such as polymer semiconductors. This synergy enables the creation of an interpenetrating percolated structure, offering dual independent charge-transport pathways. The two independent pathways can be exploited to create transistors with two separate turn-on voltages, leading to MVTs with multiple electrical states. Moreover, such an architecture with separate charge-transport pathways can be formed through a simple solution process using a mixture solution of the components, thereby simplifying the manufacturing process.

In this research, electrochemical MVTs capable of implementing broad multithreshold engineering windows were fabricated by employing a heterojunction comprising solution-processed interpenetrating percolated networks of n-type CdSe TpNCs and an n-type polymeric organic semiconductor (OSC), namely, poly(5,6-dicyano-2,1,3-benzothiadiazole-alt-indacenodithiophene) (DCNBT-IDT)^15,16. The geometry of the isotropic four-long-armed structure in TpNCs enables a broad concentration window of charge percolations in the blend, where the equilibrium charge transfer between the two domains selectively determines their threshold voltages for the current onsets in its transistor characteristics. Specifically, charge percolation studies based on the model polymer (OSC or insulator)/TpNC systems revealed that the charge-transport channels for both materials are separately secured to emulate multithreshold voltages. When the CdSe TpNC networks have a low density, the low charge percolation threshold concentration of DCNBT-IDT can be easily secured, resulting in a stable intermediate state (“1/2” logic state). In such a case, the current flowing through the on state (“1” logic state) from the CdSe TpNCs is governed by the formation of CdSe TpNC percolating networks. In contrast, when the CdSe TpNC network is sufficiently high to form a fully percolated structure, the current flowing through the intermediate state is mostly determined by the interference of the crystallographic formation of DCNBT-IDT domains, while that for the on state is insignificantly affected. A cryogenic (78 K) photoluminescence (PL) investigation further revealed that a preferential charge redistribution commences from the CdSe TpNC to DCNBT-IDT domains, effectively shifting the threshold voltages of the polymer networks. These features, along with the broad percolation window of the separate channels and selective threshold voltage management, allow for effective multithreshold engineering of the heterojunction transistors. Consequently, when the relative concentration of the CdSe TpNC domain increases, the threshold voltage of the DCNBT-IDT channel gradually shifts from 1 V to −1 V, while that of the CdSe TpNCs remains above 1.5 V, providing stable and distinctive ternary logic states, i.e., off (“0”), intermediate (“1/2”), and on (“1”) states. The operation of various ternary logic gates based on the optimized heterojunction MVTs, such as T-NOT, T-NAND, and T-NOR, is described herein. Our findings are expected to foster the development of efficient MVTs with adjustable operation ranges, potentially offering new avenues in high-performance printed plastic electronics.

Results

Figure 1A presents the schematic of a crossbar array of electrochemical MVTs based on the interpenetrating percolated network of CdSe TpNCs and DCNBT-IDT. The CdSe TpNCs were prepared using the continuous precursor injection method described previously^13,17. The long arms of the TpNCs were in a Wurtzite structure (length: 90 nm and diameter: 5 nm) and were grown on the surface of a zinc blende NC core (see the transmission electron microscopy (TEM) image in Fig. 1a inset). A dispersion of the CdSe TpNCs was spin-coated onto a substrate with prepatterned Cr/Au electrodes (serving as the source electrode of MVT), and then a short ligand treatment (immersing the film in a 0.08 M sodium hydroxide solution in methanol for 20 min) was performed to form the n-type percolated network that constitutes the structural framework of the vertical channel (see the scanning electron microscopy (SEM) image in Fig. 1a inset). The voids in the TpNC network were infiltrated with DCNBT-IDT by spin-coating the polymer solution onto the network, which resulted in an additional n-type transport pathway within the vertical channel. The pre-defined percolated networks of TpNCs with non-diffusive heterogeneous interfaces with polymers allowed forming self-defined, separated charge transport channels with separate threshold voltages. Note that hydrophilic oligoethylene glycol side chains are commonly incorporated to enhance ion transport and accommodate more ionic species from the electrolyte, thereby increasing the transconductance of the transistor^18,19. In this study, we instead employed DCNBT-IDT with hydrophobic alkyl side chains to achieve an intermediate state in a multi-threshold transistor rather than maximizing transconductance. After depositing Au electrodes (in the direction orthogonal to the underlying Cr/Au electrodes) onto the vertical channel, ion gel containing an ionic liquid with bulky ions, namely, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIM⁺][TFSI⁻]), was applied to serve as the gate dielectric^20,21,22,23. Finally, Au electrodes were deposited on top of the ion gel layer to serve as the gate electrode of the MVTs^24,25. Figure 1b shows a photograph of the crossbar array of electrochemical MVTs based on the CdSe TpNC–DCNBT-IDT heterojunction.

Self-defined dual charge percolation networks for solution-processed multithreshold transistors — **Fig. 1: Constructions and Electrical Characteristics of MVTs.**

The black curve in Fig. 1c shows the semilogarithmic transfer characteristic (drain current (I_D) to gate voltage (V_G) relation of the electrochemical MVT obtained at a constant drain voltage (V_D = 0.1 V). As V_G increased positively (above the first threshold of the device (V_T,1)), I_D initially increased gradually, similar to the behavior observed in a typical n-type electrochemical transistor, and then reached a V_G regime where the current level saturates over a specific range of V_G (V_G,inter; the channel current was about 4.7 μA for V_Gs from 1.1 to 1.98 V, i.e., 1.10 V < V_G,inter < 1.98 V), which can serve as the intermediate electrical state of the MVT. The mild hysteresis behavior was observed as shown in Supplementary Fig. 1. Figure 1d shows the magnified plot of the transfer characteristics at this V_G regime. As V_G increased further, I_D eventually increased again, indicating that the secondary n-channel is activated at such high V_Gs. We refer to the threshold for this secondary n-channel as V_{T, 2}. 16 different MTV devices were examined, and their average intermediate voltage window was 0.49 ± 0.32 V (Supplementary Fig. 2 and Supplementary Fig. 3). Consequently, the MVTs produced three distinct electrical states with a current ratio of 1 (off state):10^{3.3 ± 0.2} (intermediate state):10^{5.4 ± 0.4} (fully on state) within a small V_G window spanning from −1 to 5 V (Fig. 1E and Supplementary Fig. 4). These three states serve as the basis for the ternary logic in this work. The output characteristic is shown in Supplementary Fig. 5. Supplementary Fig. 6 shows the transient response of the device, indicating that the rise and fall time constants (τ) for turning on the CdSe TpNC channel were 2.89 ms and 1.97 ms, respectively. The cyclic stability of the device was also investigated as shown in Supplementary Fig. 7. The CdSe TpNC channel remained stable for 1000 cycles, whereas the DCNBT-IDT channel degraded after 600 cycles.

Since the channel contained two different n-type materials, we originally hypothesized that the transfer characteristics could be simply attributed to the independent onset of the two percolated channels having two different thresholds. To verify this hypothesis, we fabricated vertical electrochemical transistors using either CdSe TpNC or DCNBT-IDT films. Note that the deposition of the top drain electrode inevitably leads to an electrical short because CdSe TpNC films are porous. Thus, the voids in the films were filled with poly(methyl methacrylate) (PMMA), which is insulating but permits good penetration of [EMIM]⁺. The dotted red and blue curves in Fig. 1c represent the transfer characteristics of a vertical electrochemical transistor based on CdSe TpNC channels and DCNBT-IDT channels, respectively. The DCNBT-IDT channel could be turned on at ~1 V and yielded a maximum current below 10⁻⁵ A, whereas the CdSe TpNC channel could be turned on at ~3 V and reached a maximum current above 10⁻⁴ A. If the two n-channels within the CdSe TpNC–DCNBT-IDT heterojunction film fully operate independently, the transfer characteristic of the vertical transistors based on the heterojunction film (the black curve) should be equal to the simple sum of that of each component, which is represented as the gray curve in Fig. 1c. Even if the current levels of the off, intermediate, and fully on states for the gray curve match well with those of the black curve obtained experimentally, the first and second conduction regimes turned on at significantly low V_Gs. Based on the maximum current levels, we conjecture that the first conduction at V_T,1 < V_G < V_G,inter occurs through the DCNBT-IDT channel, while the second conduction at V_G > V_G,inter occurs through the CdSe TpNCs (Fig. 1f). However, we conjecture that the two materials interact to lower the onset of both conduction regimes, but this requires an in-depth analysis of the electrical characteristics of the heterojunction channel, beyond the hypothesis based on a simple sum of the two independent transport channels.

Accordingly, we systematically investigated the electrical transport characteristics of the heterojunction channels that were formed with different CdSe TpNC and polymer (DCNBT-IDT or PMMA) compositions^26,27. Fig. 2a, b shows the transfer curves of vertical electrochemical transistors based on the heterojunctions with different compositions. For the heterojunction shown in Fig. 2a, the CdSe TpNC concentration used to form the heterojunction film was varied (5–20 mg mL⁻¹), while the polymer concentration was fixed at a low level (5 mg mL⁻¹). Due to the unique spiky shape of TpNCs, they do not form a film that has definitive surfaces when spin-coated, and the nominal thickness remained around 40–50 nm within the range of concentration variations. Instead, the lateral density of the TpNC network increased as the concentration of the solution increased. This resulted in a set of heterojunctions with varied interconnectivities of CdSe TpNC networks infiltrated with a fixed polymer quantity. Conversely, for the heterojunction shown in Fig. 2b, the polymer concentration was varied (5–20 mg mL⁻¹), while the CdSe TpNC concentration was fixed at a high level (20 mg mL⁻¹). The resulting set of heterojunctions exhibited a constant and fully percolated CdSe TpNC network density infiltrated with different polymer concentrations. Figure 2c illustrates the network density of CdSe TpNCs fabricated with varied solution concentrations (top row) and their changes upon infiltration of polymers with different ratios (middle and bottom rows). Evidently, even at low CdSe TpNC concentrations, the geometrical structure of the crystals caused percolating network structures to form in the film, where an increase in the concentration enhanced the network density. The infiltration of low polymer concentrations into the low-density CdSe TpNCs resulted in a fully interpenetrated, smooth film. In contrast, the introduction of polymers in the high-density CdSe TpNC films caused the polymers to gradually infiltrate the network structure and increase the overall thickness to 70–75 nm. Once fully infiltrated, the remaining polymers stacked up on the polymer/TpNC hybrid films to reach a thickness of 100 nm. Considering that the electrode configuration of the devices is in the vertical direction (source and drain electrodes), the thickness of the films will define the channel length in the vertical direction where its increment is expected to degrade the current flow. Although the thickness of TpNC remained almost unvaried, the change of the polymer thickness (50–100 nm) is expected to decrease the current level of the intermediate state by half. On the other hand, the surface area of the CdSe TpNC network in contact with the electrodes would also decrease with increasing the amount of infiltrated polymers, gradually hindering the formation of fully percolated charge-transport channels between two electrodes. Therefore, along with the changes in the network density, such a percolation effect will result in the additional modulation of charge transport through the CdSe TpNC domains.

**Fig. 2: Electrical and Morphological Characterizations of the Heterostructures.**

Based on the abovementioned results, we conducted further studies on the charge percolation behavior of the DCNBT-IDT–CdSe TpNC hybrid films. To distinguish the charge transfer between the homointerface and heterointerface, a model system comprising the insulating PMMA and TpNC was studied and compared with the DCNBT-IDT–CdSe TpNC hybrid films. Figure 2a shows that increasing the TpNC network density caused the fully on-state current to gradually increase around V_G = 5 V. Such a trend was consistently observed for both cases where n-type DCNBT-IDT (solid lines) and insulating PMMA (dotted lines) were used to infiltrate the TpNC network. These results indicate that the transport at the fully on state is mainly determined by the transport through the percolated TpNC network, which is dependent on its density. A previous report on transistor devices with different CdSe TpNC network densities demonstrated that the conductivity of the network is linearly proportional to the concentration of casting solutions¹³. Therefore, it is reasonable to expect that an increase in CdSe TpNC concentration will result in proportional changes in current levels. However, we noticed that the current level of the on state increased by 1.5 orders of magnitude (blue line vs. gray line) even though the amount of CdSe TpNCs used was increased by four times. The severe drop in the current levels at a low CdSe TpNC density indicates that the impact of DCNBT-IDT infiltration intensifies as the network density decreases. The same trend was also observed when insulating PMMA was introduced in place of DCNBT-IDT. The morphological images (Fig. 2c) also agree with such electrical behavior, where even low polymer concentrations can provide full coverage over low-density CdSe TpNC networks. Therefore, in addition to the changes in the CdSe TpNC concentration, the observed superlinear dependency of on-state currents on CdSe concentrations can be attributed to (1) the interference of charge transport through CdSe TpNC network by polymers and (2) the noticeable alterations of TpNC percolation networks upon its concentration changes. Such inference is also corroborated by the fact that the DCNBT-IDT-based transistors exhibited lower current levels than the CdSe TpNC-based transistors.

Meanwhile, the current level of the intermediate state remained nearly invariant, even when the density of the CdSe TpNC network varied. The marginal impact on the intermediate-state current also indicates that the percolation of the DCNBT-IDT domains is weakly interfered with by the presence of CdSe TpNC domains, which could be due to (1) the well-infused polymers in the TpNC network voids forming low percolation thresholds and/or (2) the facile transfer of charges from DCNBT-IDT to the CdSe TpNC, followed by their transport through the CdSe TpNC channels. However, since the CdSe channels are not in the on state within the voltage range of interest (<1.5 V), it is unlikely that the charges induced in the intermediate state would seamlessly transfer between the DCNBT-IDT and TpNC domains. Therefore, it is highly reasonable to assume that the DCNBT-IDT channels can be secured by facilely infiltrating the CdSe networks, leading to a low threshold concentration for charge percolation.

To further understand the percolation network formation of DCNBT-IDT in the heterostructure, the polymer concentration applied onto the preformed well-percolated TpNc network was varied (5–20 mg mL⁻¹) (Fig. 2b). From the thickness variations, it could easily be expected that the current would decrease as the concentration increases. However, the current levels of the intermediate state increased by 1.5 orders of magnitude. Moreover, opposite trends were observed for the current levels of both the intermediate and on states compared to Fig. 2a. When the polymer concentration was increased fourfold, the current at the on state remained invariant, while that at the intermediate state varied by an order of magnitude. The gradual increase in intermediate-state current levels as the polymer concentration increases indicates an enhancement in either (1) the degree of percolation of transport networks, (2) the surface coverage, i.e., the amount of DCNBT-IDT in contact with the electrodes, or (3) the quality of domain interconnection (the degree of orbital overlap among adjacent molecules; transfer integral). The third parameter, that is, the quality of domain interconnection, should be specifically considered because of the low threshold concentration for the percolation in the DCNBT-IDT channels inferred from Fig. 2a, as well as the superlinear changes in intermediate-state current levels upon concentration increments. Variations in such a parameter could stem from different morphological evolutions (amorphous/crystalline) of the DCNBT-IDT domains at different concentrations (discussed in detail later in this section). Conversely, the invariance of the on-state current levels as the polymer concentration increases indicates that the transport of electrons through the preformed dense CdSe TpNC domains is unperturbed by the presence of DCNBT-IDT but largely dependent on the percolation of the TpNC network. By comparing this finding with the results obtained for the PMMA/TpNC hybrid films, where an increase in polymer concentrations severely decreased the on-state current levels, it can be inferred that charge transfer from the TpNC to DCNBT-IDT domains is not hindered. The previous observation that DCNBT-IDT forms an overlayer for fully infiltrated polymer/TpNC hybrid films (Fig. 2c) further corroborates the facile charge transfer from the CdSe TpNCs to DCNBT-IDT during the on-state operation of the CdSe TpNC channels. These observations imply that the mutual percolation network critically influences the charge-transport behavior of both the intermediate and on states of the proposed heterojunction transistors. Prior to the formation of fully percolated networks of CdSe TpNC channels (low density), the inclusion of polymers in the heterojunction could strongly affect the degree of percolation of TpNC networks and thus alter the on-state current levels. However, once fully percolated, unperturbed charge transport between two electrodes could be secured owing to the probable charge transfer among the heterojunctions. Apart from the CdSe TpNC channels, another fully percolated channel for DCNBT-IDT could be easily acquired even at low threshold concentrations. This behavior is promoted by the infiltration of polymers through the CdSe TpNC voids. The current flowing through such domains substantially depends on the coherence (or crystallinity) of the infiltrated DCNBT-IDT molecules.

A more detailed analysis of the transport regimes of the mutual percolation networks was conducted based on the model analysis of the composition-dependent electrical characteristics (Fig. 2d). The portion of polymer (x-axis) was estimated by the concentration ratio of polymer and TpNC solutions employed to form the network films. It is well known that blending (or diluting) the semiconductor with another molecularly miscible material causes deterioration of charge transport through the following mechanisms: 1) the expansion of a lattice that governs the hopping distance and orbital overlap among adjacent molecules and 2) the incomplete formation of percolation networks due to domain isolation. First, under the assumption of 3D incoherent charge transport within the diluted domains, the relative concentration (c)-dependent mobility (μ) of the blend can be described using Bässler’s transport model. The model can be expressed using a combination of the mean displacement per hop (ac^−2/3) and the orbital overlap factor (−2γa), where a denotes the average distance between the nearest molecules^28,29,30:

$$mu ={mu }_{0}{c}^{-2/3}exp (-2gamma a{c}^{-1/3}).$$

(1)

Second, as the concentration of the desired semiconductor decreases further, the percolation of the domains manifests as the dominant factor governing the mobility. Therefore,

$$mu sim {(c-{c}_{{rm{TH}}})}^{k},$$

(2)

where C_TH denotes the threshold concentration for percolation. The power k is determined by the crystallographic structure, and in this analysis, we assumed k = 1.5 in consideration of a simple cubic lattice. The estimated characteristic behavior of the abovementioned mechanisms, intermolecular hopping, and interdomain percolation is illustrated in Supplementary Fig. 8 and Supplementary Fig. 9, respectively. When the CdSe TpNC concentration was varied with low polymer concentrations, the reduction in charge transport through the CdSe TpNCs (on the state) followed the percolation model, with a threshold composition ratio C_TH of 0.56. Since the intercalation of polymers directly into the preformed inorganic crystal lattice is improbable unless there is a supply of sufficient external energy to expand the lattice spacing, the high threshold concentration further confirms that the current flow through the CdSe TpNC domains from the source to drain electrodes at low concentrations could be hampered by the abovementioned multiple origins, namely, the formation of 3D percolation networks among different CdSe TpNCs. Conversely, the slow change in intermediate-state current cannot be sufficiently explained by the percolation model; rather, it follows the lattice expansion model with low orbital overlap factors. The short crystallographic coherence length caused by low DCNBT-IDT concentrations can be attributed to such behavior, which can be forcefully interfered with as the TpNC network densifies, meaning that less space is secured for DCNBT-IDT to form highly coherent crystals. Contrarily, for the fully formed CdSe TpNC percolation networks, the change in on-current levels upon changes in polymer concentration was insignificant to fall into the percolation or lattice expansion regime. However, the intermediate state was well within either the lattice expansion model of the crystalline domains or the percolation model, with extremely low threshold composition ratios. Considering that such behavior was only observed in the case of high-density CdSe TpNCs and that the relative changes in the CdSe TpNC ratio did not significantly alter the intermediate-state levels, it is unlikely that the perforation of DCNBT-IDT into the CdSe TpNC network and the corresponding formation of their percolation network would have a large impact on charge transport through the DCNBT-IDT domains. This trend is corroborated by the cross-sectional SEM images of the heterostructures (Fig. 2c), where DCNBT-IDT conformally adheres to the CdSe TpNCs rather than completely filling up the voids in the CdSe TpNC network from the bottom. Thereafter, the percolated domains would no longer interfere with the increment in DCNBT-IDT. In summary, the percolation and lattice expansion models further corroborate the conclusion derived from Fig. 2a, b, indicating that the formation of a self-percolating network plays the most critical role for the CdSe TpNC domains, while the quality, i.e., the crystallographic coherence, of the DCNBT-IDT networks determine charge transport rather than charge percolation. Finally, in addition to the apparent changes in charge transport, significant shifts in the threshold voltages were observed (Fig. 2e). For estimating the threshold voltages of CdSe TpNC channels in the hybrid devices, the relative shifts of the on-state portion in the transfer curves were calculated with respect to CdSe TpNC:PMMA devices. The presence of either PMMA or DCNBT-IDT did not significantly impact the threshold voltages for the on state. Contrastingly, the increase in the DCNBT-IDT ratio increased the threshold voltages for the intermediate state, regardless of the absolute concentration of base TpNC networks. Based on the observation of possible charge transfer from the CdSe TpNC to DCNBT-IDT domains (Fig. 2b), such behavior can be explained by the framework of the equilibrium distribution of charges between DCNBT-IDT and the TpNCs resulting from their different energy levels (conduction band and Fermi levels). To further understand this behavior, a photophysical analysis of the equilibrium electronic states should be conducted.

Figure 3a–c shows the optical characteristics of the single components and heterojunctions. The CdSe TpNCs exhibited a band edge around 650 nm with marginal reorganization energies, along with a characteristic broad absorption feature around 920 nm that coincides with intragap trap state emissions. DCNBT-IDT exhibited a narrow band edge around 800 nm, along with a noticeable reorganization of 240 meV due to the softness of the polymer chains. The dependence of the PL intensities of DCNBT-IDT on excitation wavelengths is indicated by the distribution of absorbance in its absorption spectra, where the excitation at 410 nm naturally led to a significant quenching of the intensity (Supplementary Fig. 10). When the two semiconducting materials were mixed, PL was observed from both materials, with the emission intensity from DCNBT-IDT remaining almost invariant even after selective excitation at 750 nm (Fig. 3d). The result simply indicates that the transfer of electrons from DNCBT-IDT to the CdSe TpNCs is not preferable since energy transfer could not occur with such low photon energy. However, the CdSe TpNC emission from the heterostructure excited at 410 nm exhibited a significant 50% quenching, while the emission from the CdSe TpNC trap states increased almost twofold (Fig. 3e). Since the polymer emission that overlapped with the trap emission of the CdSe TpNCs amounted to <1% of the intensity of the trap emission, the increment in the emission around 860 nm indicates that energy transfer occurred from DCNBT-IDT to the CdSe TpNCs or that excited-electron recombination was facilitated, as depicted in Fig. 3f. However, due to the low quantum yield of DCNBT-IDT emission, it is unlikely that such a strong enhancement in trap emission was caused by energy transfer. Therefore, it can be inferred that remnant holes from the preferential transfer of electrons from the CdSe TpNCs to DCNBT-IDT result in increased non-geminate recombination of trapped electrons, leading to increased PL intensity.

**Fig. 3: Optical Characterizations of the Heterostructures.**

To investigate the transfer, we analyzed the temperature-dependent emission spectra of the films from cryogenic (78 K) to room temperature. Figure 3j shows the intensity evolution of emissions from DCNBT-IDT and the CdSe TpNCs in both the single component and heterostructure films. Generally, the characteristic time for the exciton dissociation depends on the temperature, where increased geminate recombination results in elevated PL intensity (({I}_{{PL}})) at low temperatures, as described by Eq. (3)^31,32,33,34:

$${I}_{rm{PL}}left(Tright)={int }_{0}^{{{infty }}}frac{n(t)}{tau }{dt}={n}_{0}left(frac{1}{1+Aexp left(-frac{{E}_{b}}{{k}_{B}T}right)}right),$$

(3)

where (n,,{n}_{0},,tau), and ({E}_{b}) are the total density, initial density, lifetime, and the binding energy of excitons, respectively. (A,,{k}_{B}), and (T) are the pre-exponential factor of the dissociation rate constant, the Boltzmann constant, and temperature, respectively. Evidently, DCNBT-IDT exhibited almost the same temperature dependence both as a single component and in the heterostructures, indicating that the exciton binding energy and its dissociation probability remain the same. Conversely, the CdSe TpNCs exhibited different temperature dependencies as a single component and in the heterostructure films. The CdSe TpNCs exhibited strong temperature dependence as a single component, indicating a weak exciton binding energy, possibly due to the tetrapod structure having a large confinement space (~100 nm). However, the CdSe TpNCs exhibited weak temperature dependence in the heterostructure, indicating that either the exciton binding energy changed or a separate decay route other than thermal dissociation governed the exciton decay. The charge transfer at the heterojunctions, which mostly depends on the exciton diffusion length, is one of the most prominent exciton decay pathways that can strongly quench the emission even at low temperatures. Depending on the energy-level distribution, the diffusion coefficient of excitons can be expressed as Eq. (4)³⁵:

$${D}_{{ex}} sim exp left(-frac{{sigma }_{0}^{2}}{2{left({k}_{B}Tright)}^{2}}right),$$

(4)

where ({D}_{{ex}}) is the exciton diffusion coefficient, and ({sigma }_{0}) is the width of static disorders. At low temperatures, exciton diffusion is hindered because of the limited hoping among chromophores. Such behavior results in an enhancement in ({I}_{{PL}}) due to the slightly reduced charge-transfer probability at the interface, as observed for the CdSe TpNC in the heterostructure.

The impact of the disorder is prominent on the position and broadening of the emission peaks. Generally, a reduction in phonon dispersion leads to a blueshift in the peak position ((E(T))) at low temperatures. However, in the presence of strong exciton localization, lowering the temperature results in a redshift in emission due to a decrease in the population of band tails, following the modified Varshni equation below^36,37:

$$Eleft(Tright)=Eleft(0right)-frac{alpha {T}^{2}}{T+beta }-frac{{sigma }_{0}^{2}}{{k}_{B}T},$$

(5)

where (alpha) and (beta) are Varshni constants. As shown in Fig. 2k, both the DCNBT-IDT and CdSe TpNCs exhibited red shifts as the temperature decreased, indicating that the excitonic transition processes depend on the presence of shallow subgap disorders. The dependence is weaker for the CdSe TpNCs in the heterostructure than for the single-component CdSe TpNCs, corroborating the limited charge-transfer excitonic emission previously mentioned. The blueshift in the entire spectra of the CdSe TpNCs in the heterostructure is attributable to the absorption of the red-side edges of the CdSe TpNC emission caused by the region overlapping with the DCNBT-IDT absorption spectra. Conversely, the broadening of the peaks indicates the presence of localizations for both shallow and deep traps. The broadening can be characterized by the full-width-half-maximum (FWHM) of the peaks. Figure 3l shows the FWHM of the emission peaks. Generally, the phonon scattering of the excited state, including acoustic, longitudinal optical, and impurity scattering, leads to peak broadening, which decreases as the temperature decreases. Consequently, sharp vibronic progressions can be observed at low temperatures. DCNBT-IDT exhibited the expected trends, where the FWHM of the peak narrowed from 200 to 100 meV as the temperature decreased to 78 K. However, the CdSe TpNCs exhibited bowing behavior, where temperature reduction had an insignificant impact and only slightly increased the peak broadening. Such behavior has been reported for cases involving facilitated carrier redistribution among the shallow and deep traps, which are activated by temperature. The CdSe TpNCs in the heterostructure also exhibited the same bowing behavior, but their temperature dependence was observed to be weaker. This result, along with the weak temperature dependence of the peak intensity and position, indicates that electrons are predominantly transferred from the TpNCs to DCNBT-IDT rather than directly redistributed between the trap states. Thus, the remnant population of trapped charges preferably recombines with the remnant and transferred holes, resulting in enhanced PL. Besides the trends in composition-dependent threshold voltage changes stemming from the directional charge transfers, the facile transfer of charges from TpNC to DCNBT-IDT would also be related to the charge transport in percolated networks. At a high density of TpNC networks (Fig. 2b), the presence of DCNBT-IDT with different concentrations did not exert a significant impact on the on-state current levels, while the one with PMMA showed super-linear dependency on the polymer concentration as expected from their interference of charge transport percolations in TpNC. Such behavior could only happen if charge transfer from TpNC to DCNBT-IDT is facilitated when both channels are in on-state.

Finally, we successfully fabricated and characterized various logic gates, including ternary NOT (TNOT), ternary NAND (TNAND), and ternary NOR (TNOR) gates, based on electrochemical ternary transistors that operate in the n-type accumulation mode^10,11. Figure 4a shows the schematic circuit diagrams of the logic gates. The TNOT gate was constructed by serially connecting a single transistor with a resistor. The TNAND and TNOR gates were fabricated by connecting two transistors in series and parallel, respectively (Fig. 4a). The voltage-transfer characteristics of the TNOT gate (Fig. 4b) exhibited ternary logic states, namely, low (“0”), intermediate (“1”), and high (“2”) states. The voltage gains, which are calculated as the absolute value of the differential output voltage relative to the input voltage (|∂V_OUT/∂V_IN|), were determined to be 0.28 and 0.19 for V_DD = +0.5 V. The gain value was close to zero between two peaks, indicating that the intermediate state is rationally flat. Figure 4c presents the dynamic switching property of the TNOT gate, which indicates its stable ternary operation. The intermediate state, which corresponds to the turn-on of the OSC, exhibits a slower response than the “0” state, which corresponds to the turn-on of the TpNC. The time constants for each transition were calculated, as illustrated in Supplementary Fig. 11. Figure 4d shows the dynamic switching properties of the TNAND and TNOR gates under nine possible input signals of (0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), and (2,2). The input voltages (V_A and V_B) were switched from −2 to +4 V, with a V_DD of +0.5 V. The TNAND gate produced a “0” state for the (2,2) input combination, a “1” state for the combinations of (1,1), (1,2), and (2,1), and a “2” state for the other input scenarios. Conversely, the TNOR gate produced a “2” state for the (0,0) input combination, a “1” state for (0,1), (1,0), and (1,1), and a “0” state for the other input combinations. While the present demonstration of logic gates was performed using an n-type vertical transistor coupled with a resistor, constructing complementary circuits with both n– and p-type transistors or even coupling with ambipolar/antiambipolar transistors³⁸ is expected to further diversify the possible logic configurations.

**Fig. 4: Application of the MVT to the logic gates.**

Discussion

Our study offers novel insights into the multithreshold engineering of solution-processible MVTs made from interpenetrating percolation networks of TpNCs and polymer OSC heterojunctions. The FOMs for the MVTs, which include an equiprobable manifestation of distinctive multiple logic states, were controlled by adjusting the ratio of domains in the heterostructure and the density of TpNC networks. A systematic charge percolation study and a morphological investigation revealed that the formation of mutual percolation networks significantly determines the charge transport through both the intermediate and on states. Specifically, the percolation of CdSe TpNCs was largely affected by the interference of polymer infiltration. However, once full percolation was achieved, the charge transport through the CdSe TpNC channel was no longer perturbed, securing a distinctive on-state (“1”). Conversely, the infiltration of polymers into the TpNC voids could easily provide a low threshold concentration for charge percolation, securing a stable manifestation of the intermediate-state current (“1/2”). The modulation of the composition and density also provided a broad controllable window for each logic state. The polymer OSC, i.e., DCNBT-IDT, exhibited an early turn-on at lower voltages than expected in the standalone devices. This turn-on is amplified at low polymer concentrations. Such behavior was elucidated by conducting cryogenic PL investigations on the heterostructures, which revealed that the equilibrium charge redistribution from the CdSe TpNC to DCNBT-IDT channels selectively and gradually alters the threshold voltage of the DCNBT-IDT channels. Our findings underscore the importance of polymer concentration in influencing the operational characteristics of MVTs and suggest the possibility of developing highly efficient MVTs with adjustable operational ranges. These insights offer new avenues for enhancing the functionality and performance of nanoelectronic devices, contributing to a broad understanding of the operation and design of solution-processible MVTs.

Methods

Material synthesis

The n-type polymer, DCNBT-IDT (number-average molecular weight (M_n) = 62.9 kg mol⁻¹ and dispersity (Đ) = 3.3), was synthesized using previously reported procedures^16,39. Supplementary Figure 12 depicts the ¹H NMR spectrum of DCNBT-IDT.

Device fabrication

A Cr/Au layer with thicknesses of 5 nm and 50 nm, respectively, was deposited on a cleaned glass substrate to fabricate the bottom source electrode of the device. We prepared solutions of different CdSe TpNC concentrations of 5, 10, and 20 mg mL⁻¹ in chloroform. To construct the structural framework, these solutions were spin-coated onto the substrate with source patterns at 2000 rpm for 60 s and subsequently annealed on a hot plate at 120 °C for 1 h. The surface was subjected to ligand substitution through treatment with a 0.08 M sodium hydroxide solution in methanol for 20 min. Thereafter, it was annealed at 120 °C for 1 h. Separately, we prepared chloroform solutions containing P(IDTC₈-DCNBT) at concentrations of 5, 10, and 20 mg mL⁻¹. These solutions were then spin-coated at 1000 rpm for 60 s to fill the voids within the TpNC framework. Au drain electrodes (thickness: 100 nm) were patterned via thermal evaporation to create a crossbar array. The ion gel, which comprised [EMIM⁺][TFSI⁻] ionic liquid, a poly(ethylene glycol) diacrylate matrix, and a 2-hydroxy-2-methylpropiophenone photoinitiator in a weight ratio of 88:8:4, was flat-cast and cross-linked under UV light (365 nm, 100 mW cm⁻²). Finally, a 40 nm-thick Au gate electrode was patterned through thermal evaporation.

Characterization

The electrical properties of the vertical transistors and logic gates were measured with a 6-arm probe station (MS Tech. Co.) using a Keithley 4200 semiconductor characterization system. The SEM images were obtained using a Jeol-7800F instrument from Jeol Ltd. Energy-dispersive X-ray (EDX) mapping was conducted to visually demonstrate the formation of intermixed domains of DCNBT-IDT and CdSe TpNCs (Supplementary Fig. 13). The cryogenic PL measurements were conducted using a spectrofluorometer (FS-5, Edinburgh, Ltd.) coupled with a liquid nitrogen cryostat (OptistatDN, Oxford Instrument, Ltd.). The ¹H NMR spectra were acquired in a CDCl₃ solution using a Bruker Avance III HD 500 spectrometer. The M_n and Đ of DCNBT-IDT were determined using an Agilent gel-permeation chromatography (GPC) 1200 series, with o-dichlorobenzene serving as the eluent and referenced to polystyrene standards.