Effect of electronic state for in-materio physical reservoir computing performance with a porphyrin-polyoxometalate/single-walled carbon nanotube network Open Access

Recent advances in computer systems with physical miniaturization have significantly improved their performance, enabling the execution of complex computational processing tasks. Although von Neumann computing system is a traditional method for information processing, alternative computing approaches should be explored because of the rapid increase in the demand for computing with huge power consumption.

One such approach is the development of non-von Neumann computing system, in which arithmetic and memory units can be integrated. Artificial neural networks (ANNs) represent a type of non-von Neumann computing that mimics the computing methods of the human brain and is anticipated to exhibit unconventional computing capabilities. ANNs are separated as feed-forward neural networks, where information processing occurs in only one direction, or recurrent neural networks (RNNs), which feature feedback loops in the connection paths of nodes.¹ Reservoir computing (RC)² is a special type of RNN that updates weights at the readout region between intermediate and output layers, requiring less calculation than other ANNs. This advantage facilitates efficient optimization calculations from the perspective of the learning algorithm, resulting in significant reductions in power consumption and computational requirements during learning. Recently, reservoir layers in RCs have been implemented using high-dimensional nonlinear dynamical physical systems,³ such as optical systems,^4,5 soft bodies,^6,7 spintronics,⁸ ionic liquids,^9,10 and nanomaterial networks^11–16 to establish information processing hardware.

Single-walled carbon nanotube (SWNT)/polyoxometalate (POM) networks have emerged as excellent candidates for achieving high RC performances by nanomaterial.^17–19 POM molecules were adsorbed onto the side walls of the SWNTs, which exhibited rich nonlinear electrical properties, including negative differential resistances (NDR) to noise owing to the multiple redox states of POM.^20,21 In this study, we present two tetraphenyl porphyrin (TPP)-sandwiched POMs, namely, bis(5,10,14,20-tetralphenylporphyrin-21,23-diium) (μ-sulfato)-tetracosakis(μ-oxido)-dodecaoxo-deca-tungsten-di-vanadium ([H₄TPP]₂[SV₂W₁₀O₄₀], H₄TPP-POM), and bis(5,10,15,20-tetrakis(4-t-butylphenyl)porphyrin-21,23-diium) (μ-sulfato)-tetracosakis(μ-oxido)-dodecaoxo-deca-tungsten-di-vanadium acetonitrile ([H₄^tBuTPP]₂[SV₂W₁₀O₄₀], ^tBu H₄TPP-POM), as illustrated in Fig. 1.²² These molecules exhibited localization of two TPP molecules on one POM molecule. Porphyrin and POM were diverged by dissolving solution and formed amorphous structure. However, porphyrin and POM were still interacted with each other and partly crystallographic structure. Relatively high electrical conductivity of ^tBu H₄TPP-POM has been reported with the generation of NDR²² owing to the high electron-transfer characteristics between porphyrin and POM compared with porphyrin or POM only.^23,24 The difference between the two por-POMs is whether a ^tBu group is bonded to TPP, which influence the RC performance due to the different interaction between porphyrin and POM. Here, SWNT/por-POM random networks were fabricated using ^tBu H₄TPP-POM and H₄TPP-POM to experimentally compare their RC performances. Benchmark tasks for the RC performances, waveform generation tasks, and function approximation tasks were performed, for which the SWNT/H₄TPP-POM network achieved better results than the ^tBu H₄TPP-POM network, indicating that H₄TPP-POM had richer chemical dynamics and exhibited improved RC performance.

The semiconducting SWNTs with (5,6) chirality (10 mg, Aldrich, 773735-1G) were purified to remove amorphous carbon and impurity metal particles by heating them in an electric furnace at 200 °C for 20 h. After heat treatment, concentrated hydrochloric acid (10 ml) was added to the SWNTs, and the mixture was stirred at 109 °C and 280 rpm for 1 h. Next, the suspension was filtered through a cellulose filter. The products were washed with de-ionized water (1 L) to be neutral.

Sixteen maze-like electrode patterns¹⁹ were fabricated using lithography. A positive resist [GL2000 (Gluon lab LLC: anisole = 1:1)] was deposited by spin coating (5000 rpm, 60 s) on a Si/SiO₂ substrate. Subsequently, heat treatment was conducted at 180 °C for 2 min. An electron beam lithography system [ELS-7500 (ELIONIX)] was used to draw the electrode patterns. Subsequently, the film was developed in a methyl isobutyl ketone solution for 5 min, and a 60-nm thick Al electrode was deposited by sputtering. The Al electrode was obtained by immersing the substrate in a dimethyl sulfoxide solution at 80 °C for 20 min and lifting off the resist.

The SWNT/POM random network devices were fabricated using the following process: purified SWNTs (0.1 mg) were mixed with 1,2-dichloroethane (10 ml) and sonicated for 1 h. The suspension was filtered through a cellulose filter paper to obtain the network structures. Then, the filter paper was adhered to the substrate with the electrode patterns, dissolved, removed with acetone vapor, and transferred to the electrodes. Graded porphyrin-sandwiched POMs ([H₄^tBuTPP]₂[SV₂W₁₀O₄₀] or [H₄TPP]₂[SV₂W₁₀O₄₀]) (0.2 mg) were mixed with 1,2-dichloroethene (10 ml) and sonicated for 1 h. The transferred SWNT device was placed on a hot plate, and the POM solution was dropped onto the substrate to fabricate the SWNT/POM network device.

A semiconductor parameter analyzer (HEWLETT PACKARD, 4156 B) and probe station (Pascal, PP4-LWR) were used for I–V measurements. For the V–t and I–t measurements, a DC or AC bias, respectively, was applied to the device by a function generator (Hewlett Packard, model33120A), and the outputs were sequentially recorded by the data acquisition module (DAQ, National Instruments model9234). The remaining electrodes were open during measurement. All measurements were performed under ambient conditions.

In the waveform generation task, sinusoidal waves were used as input signals (amplitude: ±1 V and frequency: 11, 41, and 71 Hz). One electrode was used as the input, and 15 electrodes were used as the output. The output voltage signals from the device were split into training (80%) and testing (20%) data. Then, linear regression was performed to approach target waveforms (triangle, sawtooth, square, and sin2ωt waves).

In Eq. (2), W, X, and Y are the weight matrix, matrix of outputs, and target matrix, respectively. In Eq. (3), s, k, W_i, and x_i represent the optimized output summation, total number of outputs, output weights, and output signal at the electrode, respectively. After optimizing the weights, testing was carried out to calculate the task error rate between s(n) and target functions.

Figure 2(a) shows the I–V characteristics of the SWNT/H₄TPP-POM network with a bias voltage sweep of approximately 10 V, in which the arrows indicate sweep directions. The I–V curve shows nonlinear and hysteresis behaviors with an NDR, indicating that the device has highly electrically nonlinear memory properties. The SWNT/^tBu H₄TPP-POM network also exhibited these properties [Fig. S1(a)], whereas only the SWNT [Fig. S2(a)] network exhibited linear behavior, indicating that nonlinearity and memory properties were generated from the por-POM. The V–t characteristics show a phase shift between the input and output, as shown in Fig. 2(b). This is because the device includes a capacitive component originating from carrier transport.¹⁹ In addition to I–V characteristics, only the SWNT network did not show a phase shift, indicating that the capacitive component originated from the por-POM. From the V–t characteristics, a fast Fourier transform of the output was performed, as shown in Figs. 2(c), S1(c), and S2(c). Higher harmonics [integer multiples of the input sinusoidal wave frequency (11 Hz)] were generated due to output distortion in the SWNT/por-POM networks. From these results, it was concluded that the SWNT/por-POM networks have a nonlinear electrical property and experience phase shifts and higher harmonics, which are expected to result in high RC performances.

Figure S3 shows the Lissajous plots of the SWNT/H₄TPP-POM network device with a sinusoidal input of 11 Hz and 2V_pp. Elliptical shapes with different phase shifts were obtained at each electrode, indicating that the network could be used as a reservoir because the input signal could be transformed into various outputs through the rich chemical dynamics. Figures 2(d) and 2(e) show the phase shift with different frequencies (11 and 71 Hz, respectively). The phase shift increased with a decrease in the frequency. This is because the relaxation process of the charge mobilities in the H₄TPP-POM was in the range of 0.1–10 s owing to chemical dynamics, including ion movement,²² which generates abundant chemical dynamics at relatively low frequencies.

The current–time (I–t) characteristics were measured in the SWNT/por-POM networks to investigate the difference in the charge transfer mechanism in the SWNT/^tBu H₄TPP-POM and SWNT/H₄TPP-POM networks. Figure 3 shows the I–t characteristics of (a) the SWNT/^tBu H₄TPP-POM and (b) SWNT/H₄TPP-POM networks obtained by applying a positive DC bias voltage. The SWNT/^tBu H₄TPP-POM network generated positive current pulses, whereas the SWNT/H₄TPP-POM network generated negative current pulses. Current pulse generation was also detected on the SWNT/POM network in our previous work,¹⁷ suggesting that the current pulse was generated from charge accumulation and release involved in the multivalent electric state of the POM molecule. Inter-spike intervals (ISIs) of the current pulses were measured to quantify the self-similarity in the pulse generation process. Figure S4 shows the Poincaré plots of SWNT/por-POM networks against the applied positive constant bias voltages. Schematic sequences of ISIs are shown in the inset of Fig. S4(a), where t_n represents the nth ISI. Each Poincaré plot was created by a dot at (t_n, t_n+1). Poincaré plot shows 10¹–10²s ISI distributions in SWNT/por-POM networks. SWNT/POM network generated shorter ISI distributions (10⁻²–10¹ s) than SWNT/por-POM networks, indicating that charge accumulation becomes more extended by porphyrin. These longer ISIs might have occurred from the multivalent electric structure of POM stabilized by the interaction with porphyrin. SWNT/H₄TPP-POM increases the ISI distributions compared with SWNT/^tBu H₄TPP-POM, suggesting that H₄TPP has a more stabilized structure with POM than H₄TPP.

Although porphyrin and POM were diverged in solution, they formed the unit complexes again in the solid state. Therefore, the opposite pulse direction behavior between SWNT/H₄TPP-POM and SWNT/tBu H₄TPP-POM could be originated from the difference of electronic state in these molecules. The conduction and valence bands of “SWNT with (5,6) chirality” were approximately 3.9 and 5.0 eV, respectively.²⁸ UV-visible (UV-Vis) absorbance spectrum and cyclic voltammetry (CV) results of ^tBu H₄TPP-POM are shown to highlight the molecular orbitals (Fig. S5). The oxidation and reduction peaks in the CV for ^tBu H₄TPP-POM were assigned to ^tBu H₄TPP and POM, respectively, based on the literature on H₄TPP and POM.²⁹ The lowest unoccupied molecular orbit (LUMO) levels of H₄TPP and POM were reported to be −3.46 and −4.32 eV from experimental results of UV-Vis spectrum and CV.²⁹ Using the same calculation method, the LUMO levels of ^tBu H₄TPP and POM were estimated to be −3.13 eV with a 1.83 eV highest occupied molecular orbit (HOMO)-LUMO gap and −5.12 eV, respectively. Figure S6 shows an energy diagram of electron transfer between SWNTs and por-POMs. As written above, current pulse generation was attributed from the charge accumulation and release of POM; therefore, carrier transfer was focused on between SWNT and POM. From the energy diagram, LUMO of POM with ^tBu H₄TPP was almost the same with the conduction band of SWNT. In this case, electron is transferred from SWNT to POM with ^tBu H₄TPP. When a positive bias is applied, the conduction band of the SWNT shifts to lower energy levels, thereby reducing the energy gap between the SWNT and the molecule with the lower HOMO, facilitating electron transfer from POM to SWNT. As a result, it was found that ^tBu H₄TPP-POM and H₄TPP-POM exhibit electron transfer in opposite directions. This finding also suggests that the direction of the current pulses may reverse, either directly due to the electron transfer or due to the structural stabilization of the SWNT/por-POM network accompanying that transfer.

Benchmark tasks were used to evaluate the RC performance of the SWNT/por-POM network device. The waveform generation task is a representative benchmark for evaluating the nonlinearity and high dimensionality of the RC. A sinusoidal input was applied to the SWNT/por-POM network device, and 15 outputs were combined and approached to the target waves, namely, triangle, sawtooth, square, and second-harmonic sinusoidal (sin 2ωt) waves, as shown in Fig. 4(a). The normalized mean squared error (Δ) of the output waveforms to the target wave was used as an index of the RC performance. Figures 4(b)–4(e) show the results of the waveform generation task for the four target waves in the SWNT/H₄TPP-POM network device. From this result, triangular and square waves were relatively easy to generate because their $Δ$ values were below 0.2, whereas those of the sawtooth and sin2ωt waves were relatively difficult to follow. The Fourier series of the waveforms shows that the triangular and square waves contain harmonic components with only odd orders, while the sawtooth and sin2ωt waves contain harmonic components of a certain frequency or both odd and even order, which is difficult to extract. These results are almost the same as or better than those of a previously reported SWNT/^tBu H₄TPP-POM network device.¹⁹ In addition, $Δ$ reduced as the input frequency decreased, as shown in Figs. 4(f)–4(i). As described in the Lissajous curve analysis, the input frequency decreases, and the chemical dynamics of the H₄TPP-POM become richer by charge accumulation in POM interacted with porphyrin. Consequently, higher accuracies were obtained in waveform generation tasks in low-frequency regions.

A function approximation task was conducted to compare the RC performances of the SWNT/por-POM networks. The larger the value of parameter ν in Eq. (2), the more the nonlinear function needs to be approximated. The larger the value of τ, the more past information must be retained. Figures 5(a) and 5(b) show the accuracy of the nonlinear memory task with different amounts of dropped por-POM solution. The blue and orange lines represent the results of the SWNT/H₄TPP-POM and SWNT/^tBu H₄TPP-POM networks, respectively. Figure 5(a) shows that $Δ$ tends to increase as the amount of por-POM increases. In contrast, Fig. 5(b) shows Δ decreased along with the amount of POM dropped solution. These results indicate that the trade-off relationship between the nonlinearity and short-term memory, similar to the literature,^30,31 was confirmed by the SWNT/por-POM network. Under every condition, the SWNT/H₄TPP-POM network performed better than the SWNT/^tBu H₄TPP-POM network. From the I–t properties, it is considered that a SWNT/H₄TPP-POM generates richer chemical dynamics based on charge accumulation in stabilized multivalent POM structure interacted with porphyrin and an improved RC performance.

In summary, SWNT/porphyrin-coordinated POM random networks were fabricated using ^tBu H₄TPP-POM and H₄TPP-POM to compare the RC performances. The SWNT/por-POM network showed better results in the benchmark tasks for the RC performance, waveform generation tasks, and function approximation tasks than the SWNT/^tBu H₄TPP-POM network, indicating that the ^tBu H₄TPP-POM generated richer chemical dynamics and had an improved RC performance. These results could be originated from the stabilized multivalent structure of POM interacted with porphyrin with different energy levels. This implies that we can explore the optimal material and structure for in-materio physical RC devices by controlling the molecular interaction with electronic state in a network, which becomes the basis for developing material-based AI electronics.

See the supplementary material for the details of electrical properties of the only SWNT network (Fig. S1), SWNT/^tBu H₄TPP-POM network (Fig. S2), Lissajous plots of the SWNT/H₄TPP-POM network (Fig. S3), Poincaré plots against the applied positive constant bias voltages (Fig. S4), UV-Vis absorbance and cyclic voltammetry spectra of ^tBu H₄TPP-POM (Fig. S5), and schematics of energy diagram of SWNT/por-POM device (Fig. S6).

The authors thank Dr. K. Yamashita at the University of Osaka for providing por-POMs. The authors thank Professor T. Matsumoto, Dr. H. Ohoyama, and Dr. T. Misaka at the University of Osaka for fruitful discussion of charge transfer. This study was technologically supported by the Yamaguchi University and Kitakyushu Semiconductor Center under the “Advanced Research Infrastructure for Materials and Nanotechnology in Japan (ARIM Japan)” of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. This study was financially supported by KAKENHI (Grant Nos. 19H02559, 19K22114, 20K21819, 21K14527, 22H01900, 23K17864, and 23K18495), JST CREST (Grant No. JPMJCR21B5), ACT-X (Grant No. JPMJAX22K4), ALCA-Next (Grant No. JPMJAN23F3), and JSPS Core-to-Core Project (Grant No. JPJSCCA20220006). Y.U. thanks Asahi Kohsan Co. Ltd. for their financial support through the Kitakyushu Foundation for the Advancement of Industry, Science, and Technology of Japan.

The authors have no conflicts to disclose.

Yuki Usami: Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Shuho Murazoe: Investigation (lead); Methodology (lead); Software (supporting); Writing – original draft (supporting). Deep Banerjee: Methodology (supporting); Supervision (supporting); Validation (supporting); Writing – review & editing (supporting). Takumi Kotooka: Methodology (supporting); Software (lead); Supervision (supporting); Validation (supporting). Hirofumi Tanaka: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.