# Metal-organic framework single crystal for in-memory neuromorphic computing with a light control

Semyon V Bachinin, Alexandr Marunchenko, Ivan Matchenya, Nikolai Zhestkij, Vladimir Shirobokov, Ekaterina Gunina, Alexander Novikov, Maria Timofeeva, Svyatoslav A Povarov, Fengting Li, et al.

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Semyon V Bachinin, Alexandr Marunchenko, Ivan Matchenya, Nikolai Zhestkij, Vladimir Shirobokov, et al.. Metal-organic framework single crystal for in-memory neuromorphic computing with a light control. Communications Materials, 2024, 5 (1), pp.128. 10.1038/s43246-024-00573-6. hal-04974306

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# Metal-organic framework single crystal for in-memory neuromorphic computing with a light control

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Semyon V. Bachinin<sup>1,2</sup>✉, Alexandr Marunchenko<sup>1</sup>, Ivan Matchenya<sup>1</sup>, Nikolai Zhestkij<sup>1</sup>, Vladimir Shirobokov<sup>1</sup>, Ekaterina Gunina<sup>1</sup>, Alexander Novikov<sup>2,3</sup>, Maria Timofeeva<sup>1</sup>, Svyatoslav A. Povarov<sup>1</sup>, Fengting Li<sup>4</sup>✉ & Valentin A. Milichko<sup>1,5</sup>✉

Neuromorphic architectures, expanding the limits of computing from conventional data processing and storage to advanced cognition, learning, and in-memory computing, impose restrictions on materials that should operate fast, energy efficiently, and highly endurant. Here we report on in-memory computing architecture based on metal-organic framework (MOF) single crystal with a light control. We demonstrate that the MOF with inherent memristive behavior (for data storage) changes nonlinearly its electric response when irradiated by light. This leads to three and more electronic states (spikes) with 81 ms duration and 1 s refractory time, allowing to implement 40 bits s<sup>-1</sup> optoelectronic data processing. Next, the architecture is switched to the neuromorphic state upon the action of a set of laser pulses, providing the text recognition over 50 times with app. 100% accuracy. Thereby, simultaneous data storage, processing, and neuromorphic computing on MOF, driven by light, pave the way for multifunctional in-memory computing architectures.

The transition from conventional von Neumann architecture with physically separated computing and memory units into an alternative neuromorphic<sup>1,2</sup> provides a fundamental jump to fast and energy-efficient in-memory computing<sup>3,4</sup>. Inspired by highly connected and energy-efficient (up to atto Joule per operation)<sup>5</sup> neural network of a human brain<sup>2</sup>, the neuromorphic architecture expands the limits of computing from conventional data processing and storage to advanced cognition, inference, in-memory computing, and even learning<sup>6-8</sup>. Leaving aside complex optical fiber neuromorphic architectures<sup>9-11</sup>, a key element for in-memory (including neuromorphic) computing is an active material, providing multilevel states (up to several hundred)<sup>12,13</sup> and history-dependent behavior. Tracing the evolution of such materials over the last decade, from conventional metal oxides and hybrid nanocomposites to atomically thin inorganic two-dimensional materials<sup>14-25</sup>, one can notice a significant miniaturization of the neuromorphic architectures with decreased energy consumption<sup>5</sup>. However, the simultaneous transition to recyclable green electronics<sup>26-30</sup>, reduction in learning time (up to milliseconds, corresponding to human brain axon connection) and energy consumption, as well as increase in the endurance of in-memory (neuromorphic) computing architectures with the above materials, are still challenging.

To address this, a combination of abundant elements linked together by diverse chemical interactions is desired<sup>30</sup>. Indeed, the hybridization of organic and inorganic building blocks into the structure through a series of weak (hydrogen, van der Waals) and strong (coordination, covalent) chemical bonding paves the way for energy-efficient, relatively fast, and reversible transformation of the structure between multiple states<sup>31,32</sup>. Thus, such hybrid materials (like metal-organic frameworks, MOFs) can demonstrate stimuli-controlled<sup>33-46</sup> changes in their electronic/optical properties for data processing and storage<sup>47-52</sup>. Currently, MOFs are considered sustainable alternatives to conventional semiconductors for microelectronics with a special focus on in-memory (and neuromorphic) computing<sup>23-60</sup>.

Here we report on in-memory neuromorphic computing elements based on stimuli-responsive MOF single crystals with a light control. This concept is implemented on the memristive MOF, whose electronic states can be additionally modulated by laser irradiation, leading to the formation of spikes with 81 ms duration and 1 s refractory time. Through the electronic control of the amplitude and polarity of the spikes, we demonstrate 40 bits s<sup>-1</sup> binary data processing. Next, the element can be switched to the

<footnote n="1">¹School of Physics and Engineering, ITMO University, Saint Petersburg, 197101, Russia. ²Saint Petersburg State University, Saint Petersburg, 199034, Russia.</footnote>

<footnote n="3">³Peoples' Friendship University of Russia, Moscow, 117198, Russia. ⁴Key Laboratory of Climate change and adaptation, China Administration of Meteorology; Shanghai Institute of Pollution Control and Ecological Security; College of Environmental Science and Engineering, Tongji University, 201804 Shanghai, China.</footnote>

<footnote n="5">⁵Institut Jean Lamour, Universit de Lorraine, UMR CNRS 7198, 54011 Nancy, France. ✉e-mail: semen.bachinin@metalab.ifmo.ru; fengting@tongji.edu.cn;</footnote>

<footnote>v.milichko@metalab.ifmo.ru</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 1** | MOF-based in-memory neuromorphic computing element. a Scheme of three-channel logic elements with corresponding optical images (b, c). d The concept of in-memory neuromorphic computing. Scale bars, 100 µm (b, c).</figcaption></figure>

neuromorphic state upon the action of a set of laser pulses, allowing recognition of the handwritten text over 50 times with app. 100% accuracy. Thereby, simultaneous demonstration of data storage (over $10^4$ s retention time), optoelectronic processing, and neuromorphic computing on a MOF single crystal paves the way for multifunctional in-memory computing architectures.

# Results and discussion

## MOF selection

To select the desired MOF for simultaneous data storage, processing, and in-memory neuromorphic computing, we considered representative HKUST-1 ([Cu₃(BTC)₂(H₂O)₃]n (BTC, benzene-1,3,5-tricarboxylate))⁶¹ with inherent memristive feature⁴⁷,⁵⁷. Important is that this framework exhibits a dehydration process⁶² similar to the appearance of action potentials in human brain neurons (Supplementary Fig. S1)⁶³. Indeed, the dehydration of HKUST-1 manifests as a reversible shrinking of [Cu₂C₄O₈] structure-forming cages upon the action of different stimuli (including light) and underlies the basis for electronic/optical data processing on HKUST-1⁶⁴⁻⁶⁹. Thus, as in the case of change in the membrane potential of neurons with the corresponding movement of Na⁺ and K⁺ ions through the cell membrane under an external chemical stimulus (neurotransmitter, see Supplementary Fig. S1), we thought that the light-induced release of H₂O molecules from HKUST-1 should result in its neuromorphic behavior⁶⁵.

## MOF-based logic element

As mentioned, we focused on commercially available HKUST-1 (see Methods). Considering its stimuli-controlled electronic and optical properties⁶⁴⁻⁶⁹, we designed a three-channel logic element based on a single crystal of HKUST-1 as an active material (Fig. 1a). The electrical input channel allows one to apply voltage pulses of various shapes and repetition rates, which is required to record and read the information through HKUST-1 memristive behavior; as well as to control the amplitude and polarity of spikes (see below). The optical input channel can be considered as an input for a sequence of laser pulses to initiate the water desorption process and, hence, to result in spiking activity. Then, the output channel is to analyze the electronic response (measured in Volts) of the element (Fig. 1d).

To fabricate the logic element from Fig. 1a, we deposited 100 nm thick Au film on a glass substrate by thermal evaporation of Au in a vacuum. The film was then cut by a laser beam to form electrical contacts with a 1–50 µm gap, as shown in Fig. 1b, c. Then, commercially available HKUST-1 single crystals (50–200 µm in size, analyzed in advance by powder X-ray diffraction and Raman spectroscopy, Supplementary Figs. S2 and S3) were manually placed onto the Au contact gap. Before optical and electronic measurements under ambient conditions (see Methods), we prove the physical contact between single MOF crystal and Au contacts via cross-section scanning electron microscopy coupled with elemental analysis (Supplementary Fig. S4).
<figure><img src="image_6.png" /><figcaption>**Fig. 2 | MOF-based logic element performance.** a Output signal (measured in Volts) vs electrical input of the element with (red curve) and without (blue curve) laser irradiation (1050 nm, 14 mW integral power). b, c Three electronically distinguished states of the element (detected in the output): b the time evolution of spike amplitudes from the element's output channel for electrical input voltages of 0.5 V (red curve), 0.7 V (blue curve), and 0.8 V (black curve), under a constant integral laser power of 14 mW; c the time evolution of spike amplitudes (measured in volts) from the element's output channel at a fixed electrical input voltage of 5 V, while</figcaption></figure>

varying the laser power (10 mW, red dotted curve; 12.5 mW, blue dotted curve; and 15 mW green dotted curve). d Dependence of spike amplitude of the element upon the laser irradiation of varied integral power (10 mW, red dotted curve; 12.5 mW, blue dotted curve; and 15 mW, green dotted curve). e Time resolution of the spike of the element, appeared due to laser irradiation (1050 nm, 14 mW integral power) at 5 V in the electrical input channel.

## Logic element performance

To test the resulting logic element, we performed electronic measurements for 6 independent elements in the dark (Fig. 2a, and Supplementary Fig. S5), which demonstrated a stepwise 10–10³ change in HKUST-1 resistivity (ON/ OFF ratio, Table 1) at $V_{set}$ = 15 V in the electrical input channel (corresponding to 8 kV cm⁻¹ electric field strength, and varying from 4 to 15 kV cm⁻¹ depending on the crystal, Supplementary Fig. S5). We also analyzed the set/reset speed and endurance of the logic elements in the memristor state, demonstrating 0.227/0.06 s and 16 cycles on average (Supplementary Figs. S6–S8). However, the detected retention time of electronically recorded information was 40 min with a potential of 200 days (Supplementary Fig. S9), being a competitive value for memristors based on different materials (Supplementary Table S2)⁴⁷,⁵⁷⁻⁵⁹. It should also be noted that the obtained performance correlates well with previously reported MOF-based memristors (operating at 0.1–300 kV cm⁻¹ of the field strength, Supplementary Table S2)⁴⁰,⁴⁷. Herein, an applied electric field strength in our case turned out to be 1 order less than that for conventional inorganic and hybrid neuromorphic architectures (operating generally at 100–1000 kV cm⁻¹, see statistical analysis in Supplementary Table S2)⁵,¹⁹,²³,²⁴.

Next, the irradiation of the element via the optical input channel at the optical absorption wavelength for HKUST-1 (1050 nm, 14 mW integral power)⁶² revealed the following: (i) At zero voltage in electrical input channel, the element demonstrates spike behavior with –0.022 V amplitude in the output channel (Fig. 2a); (ii) while an applied voltage in electrical input channel up to 5 V (corresponding to 10 kV cm⁻¹ electric field strength) leads the output signal to cross the value of 0 and reaches 0.5 V (Fig. 2a), being 3 orders of magnitude greater than the dark signal (Fig. 2a, inset). We also found that exposure to laser light led to stepwise change in HKUST-1 resistivity at 0.5 V (1 kV cm⁻¹), which is 8 times lower than that in the dark (Fig. 2a, inset). Herein, an increase of the laser power from 10 to 15 mW also resulted in an 8-fold increase in the slope of the output signal (Fig. 2d). In addition, as in the case of the memristive behavior of HKUST-1 (Supplementary Fig. S5), a hysteresis loop was observed for the element upon the laser irradiation (Supplementary Fig. S11).

Data in Fig. 2a allowed us to highlight three specific points corresponding to the transition from the negative amplitude of spike to a positive one through a near-zero value upon the action of laser light. Figure 2b, c represents these points as a time evolution of the amplitude of spikes
<table><caption>Table 1 | MOF-based in-memory neuromorphic element performance</caption><thead><tr><th rowspan="2">Memristor</th><th colspan="2">In-memory computing</th><th colspan="2">Neuromorphic</th><th colspan="2">Data processing</th><th rowspan="2">ON/OFF ratio</th></tr><tr><th>E<sub>set</sub>/E<sub>read</sub> (kV cm<sup>-1</sup>)</th><th>Endurance (cycles)</th><th>ON/OFF ratio</th><th>Retention time (s)</th><th>Set/reset speed (s)</th><th>Bits s<sup>-1</sup></th><th>Spike duration (ms)</th><th>Refractory time (s)</th></tr></thead><tbody><tr><td>Data storage</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>8/2.1</td><td>16</td><td>10<sup>-1</sup>-10<sup>4</sup></td><td>2.4*10<sup>-3</sup>-2*10<sup>7</sup></td><td>0.227/0.06</td><td>40</td><td>81</td><td>1</td><td>55</td><td>10</td><td>200<sup>a</sup></td></tr></tbody><tfoot><tr><td colspan="13"><sup>a</sup>Measured at 14 mW laser irradiation (via optical input) and 5 V of applied voltage (via electrical input, Fig. 2e). Values E<sub>set</sub>, E<sub>read</sub> corresponds to electric field strength (applied voltage divided by the width of Au contact gap).</td></tr></tfoot></table>

(in Volts in the output channel) of the element at 0.5, 0.7, and 0.8 V in the electrical input channel. This indicates that the laser irradiation at a fixed integral power of 14 mW (through the optical input channel) with an applied electric field strength from 1 to 1.6 kV cm⁻¹ (in the electrical input channel) leads to at least three electronically distinguished states of the element in the output, which can be used to process the binary information (see below). Alternatively, the variation of the integral laser power at a fixed electrical input (5 V, corresponding to 10 kV cm⁻¹) also made it possible to detect at least three states (spikes), which were different in amplitude (Fig. 2c).

To analyze the time evolution of the observed spikes, we performed time-resolved measurements of their amplitude at 5 V (10 kV cm⁻¹) in the electrical input channel. As one can see in Fig. 2e, the element responded electronically to the laser irradiation with a 10 ms delay; then, the rise of the amplitude of the spike to its maximum (ON/OFF ratio is 200, see Table 1) took 41 ms. During 15 ms, the amplitude of the spike was constant, followed by the relaxation to the initial state (zero electric signal in the output channel) at 25 ms. On the one hand, the detected 81 ms spike duration is quite short (see Supplementary Table S2), with some exceptions⁴⁵, compared to the electronic response of MOF-based photodetectors to light³³,³⁸,³⁹,⁴⁴. On the other hand, it correlates well with the time needed for the sorption/desorption process of H₂O molecules during the laser-induced heating of HKUST-1 (app. 50 ms)⁶², as we predicted.

Since the orientation of MOF crystals affects their optical and electronic responses⁷⁰, we analyzed the spike behavior for a single HKUST-1 crystal at different orientations. As can be seen in Supplementary Fig. S13, the same crystal placed manually on different edges revealed similar spike behavior (with a 30% difference in duration), the amplitude of which depended linearly on the area of the MOF crystal between Au contacts.

In addition, to check the effect of the laser light on the efficiency of HKUST-1 electronic response (spike), we analyzed its wavelength and power dependencies. As one can see in Fig. 3a, the spikes were detected in the output channel (at 5 V in the electrical input channel) when the element was irradiated with wavelengths from 600 to 1200 nm at fixed laser power (14 mW). The observed behavior correlates well with the absorption spectrum of HKUST-1 (Fig. 3a, dotted curve), which speaks in favor of an efficient absorption of light for charge generation. Intriguing is that the low-amplitude spike with the reverse polarity was detected in the output channel at 0 V in the electrical input channel (Fig. 3a). We attributed the latter to the light-induced generation of initial charges inside HKUST-1. Also, the analysis of the dependence of the amplitude of spikes on the laser power (at a fixed laser wavelength of 1050 nm) revealed their threshold behavior at 10 mW at any value in the electrical input channel (0 and 5 V, Fig. 3b). However, an increase in the laser power below 20 mW resulted in the decrease of the amplitude of spike in the output channel, which can be attributed to the light-induced blue shift of the absorption spectrum of HKUST-1⁶².

## Mechanism

Summing up the results on the effect of the laser irradiation on the electronic response of the element (Fig. 2a), its spike behavior (Fig. 2e), and spectral dependencies for HKUST-1 (Fig. 3), we assumed that sorption/desorption of H₂O molecules can be responsible for the generation of the additional charges (even at zero input voltage). Therefore, the molecular mechanics simulation has been implemented to reveal the behavior of 24 H₂O molecules encapsulated inside the pores (Supplementary Fig. S19). For this, we modulated the desorption of H₂O molecules under the laser irradiation of HKUST-1. As a result, at the first stage we observed the molecule disordering and evenly distribution throughout the pore. The distances between the inner wall of the pore and the nearest encapsulated H₂O molecules were very large (3 Å or more), resulting in negligible electrostatic interactions between the molecules and the pore. However, in such a case, H₂O molecules created a non-zero polarization inside the pore with a total dipole moment of 7.72 Debye, while the dipole moment for an isolated molecule at the selected level of theory was 2.18 Debye. In the second stage,
<figure><img src="image_7.png" /><figcaption>**Fig. 3** | **Light control parameters.** a Laser wavelength dependence of spike amplitude of the element, measured at 0 V (blue dots) and 5 V (red dots) in the electrical input channel and a constant laser power (14 mW). b Laser power dependence of spike amplitude of the element, measured at 0 V (blue dots) and 5 V (red dots) in the electrical input channel and a constant laser wavelength of 1050 nm.</figcaption></figure>

the relaxation of the encapsulated H₂O molecules led to their ordering inside the pore due to the hydrogen bonding. Therefore, it minimized the total energy and decreased the total polarization to 2.82 Debye. This case is similar to the moment when all available H₂O molecules were desorbed, and the laser irradiation could no longer create new charges, which then relaxed and reduced the electronic response of the element (25 ms relaxation of spike in Fig. 2e).

To prove this experimentally, we analyzed the capacitance of the element (Supplementary Fig. S14): The results showed that the laser irradiation led to a stepwise change in the capacitance of HKUST-1 in air from 4 to 7 pF, followed by a rapid relaxation to the initial state. We attribute this change to removing H₂O molecules from HKUST-1, which can increase the resulting capacitance⁷¹. Then, the effect of humidity was analyzed. For this, we controlled the humidity level during the spike measurements in a chamber and revealed the growth of the spike amplitude with increasing humidity (Supplementary Fig. S15). In addition, we controlled the humidity by heating of the element in air: a single HKUST-1 crystal with a pronounced spike behavior lost the spike response to laser irradiation in 1 min of heating at 80 °C. After 20 min of exposure to the air without heating, spike behavior on laser irradiation was restored due to the physical absorption of H₂O molecules from the air (Supplementary Fig. S16).

Taking into account the laser-induced modulation of the electronic response of HKUST-1, we hypothesized the following mechanism: (i) In the dark, HKUST-1 exhibits memristive behavior between 2 resistive states when the voltage is applied⁴⁷; (ii) Upon the laser irradiation (and zero voltage in the electrical input channel), HKUST-1 demonstrates the spiking behavior due to initiated sorption/desorption processes of H₂O molecules. The amplitude of the spike is determined by the concentration of H₂O molecules, the area of the laser irradiation of the MOF crystal, and the laser wavelength. (iii) However, when the electrical and optical input channels are turned on, the combination/competition between the defect formation in MOFs (for memristive behavior)⁷²,⁷³ and low-energy processes of water sorption/desorption (for spike formation) can contribute to the complex electronic response of the element in the output signal. The latter is expressed as at least three electronically distinguished states controlled by laser light and applied voltage over time (Fig. 2b, c).

## In-memory neuromorphic computing

Next to the electronic data recording and storage on MOF single crystal through its conventional memristive behavior (Fig. 2a, Supplementary Fig. S5), we switched the element to the data processing regime (Fig. 4a). For this, we analyzed in advance the reaction of the element on a square

waveform electronic signal (with 10 Hz, 1 kHz, and 10 kHz frequency, and 5 V amplitude) passing through the MOF, irradiated by laser light of a fixed wavelength (1050 nm) and power (14 mW). As one can see in Supplementary Fig. S17, 10 Hz and 1 kHz electronic signal (applied to the input channel) can be read in the output as an asymmetrically damped set of peaks, oscillating at 10 Hz and 1 kHz frequency (during the spike duration) from negative to positive values of the voltage. However, when the oscillation frequency of the applied electronic signal (10 kHz) is higher than the electronic response of the element (81 ms spike duration, Fig. 2e), we detected unreadable modulation of the electronic signal in the output channel (Supplementary Fig. S17c). Thus, taking into account the discernible 1 kHz modulation, one can assume that the application of a control voltage in the electrical input channel will provide the modulation of the electronic signal at the output during the 81 ms spike. Figure 4b reflects this concept and allows us to estimate the speed of optoelectronic binary data processing at a minimal level of 40 bits s⁻¹.

Then, we switched to the neuromorphic application, for which the active materials should satisfy the following specific conditions: The threshold response (spike) to an external stimuli; its history-dependent behavior, and the presence of refractory time during which the element is inactive. To confirm the latter, we performed the analysis of the sequence of the electronic response (in Volts in the output channel) on repeated laser irradiation with different periods (Fig. 5a, Supplementary Fig. S18): (i) When the time interval between the laser irradiation is less than 1 s, the element remains electronically inactive, demonstrating thereby the competitive value of the refractory time for existing MOF-based neuromorphic architectures (Supplementary Table S2). (ii) When the time interval between the laser irradiation is equal to 1 s, the spike intensity decreases (depression mode, Fig. 5a, blue area). (iii) However, when the time interval between the laser irradiation reaches 2 s, the amplitude of the electronic response starts to restore to its original value (potentiation, Fig. 5a, red area). Therefore, the history-dependent (Fig. 5a) and threshold electronic response (spike) of the element to the laser light (Fig. 3b) occurs for 81 ms followed by 1 s refractory time (Fig. 2e), which brings it to the list of neuromorphic architectures. Using this conclusion, we simulated the performance of a neural network based on experimentally measured neuromorphic behavior of the element (Fig. 5a). An open-access IBM Analog Hardware Acceleration Kit (aihwkit) was utilized⁷⁴. As one can see in Fig. 5b-d, the element appears to overcome the values of accuracy for efficient neuromorphic materials⁷⁵, operating at the same parameters (see also Methods). Moreover, we revealed that the handwritten digits classification accuracy of the model, based on the element, is even larger than an
<figure><img src="image_8.png" /><figcaption>**Fig. 4** | From data storage to processing. a Scheme of the occurrence of spikes in the logic element upon the laser irradiation, as well as control of their amplitude via laser intensity and applied voltage in the electrical input channel. b Demonstration of (at</figcaption></figure>

least 40 bits s⁻¹) optoelectronic binary («0» and «1») data processing during the spike duration (81 ms) through the applied electrical input of a varied voltage (from 0.5 to 0.8 V).

ideal numeric (Fig. 5c) and is able to overcome more than 50 cycles of operation (Fig. 5d).

## Conclusion

We report on in-memory neuromorphic computing elements based on stimuli-responsive MOF single crystals with light control. This concept is implemented on the memristive HKUST-1 single crystal, whose electronic states can be additionally modulated by laser irradiation, leading to the formation of spikes with 81 ms duration and 1 s refractory time. Through the electronic control (at 1 kV cm⁻¹ of applied electric field strength) of the amplitude and polarity of the spikes, we demonstrate 40 bits s⁻¹ binary data processing. Next, the element can show the neuromorphic behavior upon the action of a set of laser pulses, allowing recognition of the handwritten text over 50 times with app. 100% accuracy. Thereby, the simultaneous demonstration of data storage (over 10⁴ s retention time), optoelectronic processing, and neuromorphic computing on a MOF single crystal paves the way for multifunctional in-memory computing architectures.

## Methods

### MOF

Commercial HKUST-1 (Copper benzene-1,3,5-tricarboxylate, Cu-BTC MOF, C₁₈H₆Cu₃O₁₂, Basolite® C 300) has been purchased from Sigma Aldrich, MDL number MFCD10567003.

### Electronic measurements

Spike measurements: To study the electronic behavior of the element, we connected a Keysight DSOX6004A oscilloscope (10 nA resolution) with an internal shunt resistor of 1 MΩ and voltage source Keysight 33600a in series with the Au contacts, which allowed us to track the time behavior with 0.16 ms accuracy (Supplementary Figs. S6, S9, S15–S18). The electronic response from the element was recorded by an oscilloscope at the moment the light was turned on by a mechanical shutter at 50 µs.

Memristor: A Keithley 2700 multimeter (sensitivity 10 nA) and an Element 305 dB power supply were used to analyze the memristor behavior of the element. Automation was achieved through the controller, allowing us to adjust the power source voltage, polarity, and data retrieval from the multimeter to the PC.

Time analysis: To study the switching speed and retention time (Supplementary Figs. S6, S9, S13), a DSOX6004A oscilloscope, Keysight

33600a voltage source, and Keysight 33502 A amplification were used to achieve the detected time of the forming of conduction channel and time of it retention.

Effect of humidity: To study the effect of humidity, we assembled an experimental setup (Supplementary Figs. S15 and S16) that allowed us to control the level of humidity near the crystal under study. The setup consisted of a tube that communicated with a vessel with distilled water, which was heated on a hotplate above the boiling point to create a directed flow of water vapor onto the crystal. The humidity meter sensor was located closer to the MOF surface (Supplementary Fig. S15b).

### Optical instruments

To activate the element, the MOF single crystal has been irradiated with laser pulses at a wavelength of 1050 nm (150 fs pulse duration, 80 MHz repetition rate, and 25 mW integral power) through a 10×/0.26NA NIR objective. For the study of the wavelength dependence (Fig. 3a), a Pharos PH1-SP-20 W laser source (central wavelength of 1030 nm, 220 fs pulse duration, 1 MHz repetition rate) coupled with an Orpheus HP Optical parametric amplifier with the possibility of changing the operating wavelength (from 400 to 2000 nm), was utilized.

### Capacitance measurements

To measure the capacitance in situ of HKUST-1 single crystal, we have used a Mastech MS5308 LCR (RLC) meter at frequencies of 100 Hz, 120 Hz, 10 kHz, and 100 kHz, allowing one to detect the capacitance twice per second with sub pF resolution (Supplementary Fig. S14).

### Neural network

The simulation of our neural network has been used to analyze the MNIST dataset (a large image version (28 × 28 pixels) of handwritten digits)⁷⁶. A model has been created as a simple, fully connected, four-layer network with two hidden layers. The neural network model consisted of 784 input neurons (the resolution of the digits image is 28 × 28 pixels), 2 hidden layers with 256 and 128 neurons (Fig. 5b), respectively, and 10 output neurons (the label was set from 0 to 9). Sigmoid activation function has been used inside the hidden layers, while LogSoftmax function—for output layer. In one batch, the neural network has been trained through the input of 60.000 images. Then the accuracy of the trained network was tested with 10.000 testing images.
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 5 | Neuromorphic application.** a Experimental spike behavior and b simulated performance of the neural network based on experimentally measured neuromorphic behavior of the element with c corresponding accuracy. d Number of cycles</figcaption></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

of the electronic response (spikes) of the element (laser irradiation: 1050 nm, 14 mW integral power; 5 V in the electrical input channel).

## Modeling

Molecular mechanics simulation was performed for 24 encapsulated water molecules inside the pore of HKUST-1 (Avogadro program package for molecular mechanics simulation, UFF force field, 500 steps for geometry optimization procedure, steepest descent algorithm for geometry optimization, and convergence criterion was 10⁻⁷). The dipole moments were calculated at the ωB97XD/6-311++G** level of theory with the help of the Gaussian-09 program package).

## Data availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Received: 16 October 2023; Accepted: 12 July 2024;

Published online: 20 July 2024

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## Acknowledgements

V.A.M. acknowledges the Priority 2030 Federal Academic Leadership Program and the financial support from the Russian Science Foundation (Grant No. 22-72-10027). A.N. is grateful to the RUDN University Scientific

Projects Grant System, project № 021342-2-000, for support of molecular mechanics simulation and DFT calculations. The Authors thank A. Lyubimova and A. Bachinina for supporting with I-V measurements and the Figures design, respectively.

## Author contributions

S.V.B. and V.A.M. designed the concept. S.V.B. performed general optical and electric measurements. A.M. and I.M. supported electrical measurements. N.Z., E.G., and S.A.P. assisted with the fabrication of logic elements. V.S. performed neuromorphic modeling. A.N. performed modeling. F.L. assisted with MOF selection. M.T. performed SEM and EDX analysis. S.V.B. and V.A.M. wrote the paper with corrections coming from all authors.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s43246-024-00573-6.

**Correspondence** and requests for materials should be addressed to Semyon V. Bachinin, Fengting Li or Valentin A. Milichko.

**Peer review information** *Communications Materials* thanks Yang Li and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Aldo Isidori. A peer review file is available.

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