As an interesting optoelectronic technology, photonic memories have attracted increasing attention in the last few years. Such devices have great potentials to overcome the von Neumann bottleneck. Moreover, integrated systems consisted of arrayed photonic memories have attracted increasing interests for adoption as building blocks in the biospired vision system.^[71]

ZnO is a typical wide band gap semiconductor material with a band gap of ∼ 3.37 eV. It has high exciton binding energy and excellent selective absorption of ultraviolet (UV) light. Thus, it has broad application prospects in ultraviolet detectors due to the significant photoelectric performances. As typical functional materials in microelectronic field, ZnO has also been proposed as RS layer in memristor. Recently, ZnO nanorods have been proposed for optically modulated artificial synapse applications.^[44] The high resistance state (HRS) of the device is non-volatile, while the low resistance state (LRS) is volatile. This volatile characteristic is beneficial for simulating the short-term synaptic plasticity behavior. The HRS and LRS overlap immediately when exposing to UV illumination, as shown in the yellow part in Fig. 1(a). Since the decay kinetics in the light-excited LRS is similar to that in the electric-excited LRS, it is hardly to tell whether the device was in LRS or HRS before illumination. Such light-induced shielding of HRS and LRS is called optical shielding (OS). When a series of electric pulses are applied, the overlapped LRS and HRS show different responses and become discernible again, as shown in the blue part of Fig. 1(a). This process is called electrical shielding (ED). Such OS and ED functions can be used to encrypt and decrypt data, respectively, making it possible to process massive data for ANN applications. In such a device, oxygen vacancies are distributed along the surfaces of the vertically aligned nanorods, which helps the unique electrical characteristics.

Fig. 1.

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Fig. 1. Optoelectric neuromorphic memristors for neuromorphic applications. (a) Optical shielding (OS) and electrical deshielding (ED) of the memristor based on a vertically arranged ZnO nanorod structure. The blue arrows indicate the time scale of the ED process. (b) Photonic EPSC behavior under different light pulse power density. The read voltage is 0.1 V. (c) Photonic PPF behavior. (d) Cumulative probability plot of resistance measured for 150 times on 15 different samples under NIR and dark conditions. (e) Photonic potentiation and electric habituation in the W/MoS2/p-Si memristive synapse. (f) System integration of the RRAM array with light signal. (g) The light signals are stored in the 13 × 13 RRAM array. (a) Reprinted with permission from Ref. [44], Copyright 2018, AIP Publishing. (b) and (c) Reprinted with permission from Ref. [39], Copyright 2018, American Chemical Society. (d), (f), and (g) Reprinted with permission from Ref. [43], Copyright 2018, Wiley-VCH. (e) Reprinted with permission from Ref. [45], Copyright 2018, Wiley-VCH.

Furthermore, ZnO_{1 – x}/AlO_y heterojunction based photoelectric memristor has also been proposed with ITO/ZnO_{1 – x}/AlO_y/Al stacks.^[39] Here, the AlO_y layer is naturally formed on Al. The device shows typical current–voltage (I–V) sweeping curves in the dark and under UV-light illumination, displaying LRS and HRS. The operation mechanism is related to the electron trapping/detrapping at the trapping sites in the AlO_y layer. Under negative bias, an electron depletion layer is formed in the AlO_y layer, realizing a reset process from the LRS to the HRS. Under positive bias, the depletion layer will get narrow, which causes LRS. While the UV-light illumination modulates the resistive behaviors due to photogenerated holes and persistent photoconductivity effects. Thus, the device can demonstrate photoelectric plasticity by setting light pulse stimulation at different pulse width, pulse intensity, pulse number, and pulse frequency. Figure 1(b) shows the conversion from short-term plasticity to long-term plasticity by changing the optical power density of the light pulse. As a typical form of short-term plasticity, paired pulse facilitate (PPF) plays an important role in processing temporal auditory or visual information.^[72] Figure 1(c) shows the PPF behavior simulated on the memristor under light stimuli. Moreover, neuromorphic facilitation, depression and long-term plasticity have been mimicked on the device.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) are considered as promising candidates for the next generation optoelectronics and photodetection due to their unique electrical, mechanical, and optical properties.^[45,73] Especially, they have also been proposed for photonic memristor applications with light illumination at near-infrared region (NIR) due to the small band gap, showing great potentials in memristive synapses. Due to the combination of photonic and electric neuromorphic functions, they would have prospectives in synthetic retinas and optoelectronic interfaces. Zhai et al.^[43] used a heterostructure formed with upconversion nanoparticles (UCNPs) and molybdenum disulfide (MoS₂) to achieve optically tunable memory performance under NIR illumination. The upconversion material has excellent light response performances in the NIR due to its photon conversion characteristics.^[74,75] With the increased light intensity, both the SET voltage and the RESET voltage gradually decrease. While the ON current and OFF current increase correspondingly. Figure 1(d) shows the cumulative probability plot of resistance measured for 150 times on 15 different samples under NIR and dark conditions. Such NIR light tunable behavior lays the foundation for the application of multifunctional memory devices. Furthermore, memory functions of photon write-electric erase can also be implemented based on photonic potentiation and electric habituation characteristics.^[45] For W/MoS₂/p-Si memristive synapse, the increase of the conductance corresponding to EPSC can be used to mimic the potentiation of the synaptic strength, while the decrease of the conductance corresponding to IPSC can be used to mimic the habituation of the synaptic strength. A continuous optical pulse sequence (power intensity: 0.11 mW/cm², width: 1 s) gradually increases the conductances due to the photogenerated electrons and holes, as shown in Fig. 1(e). This behavior simulates the potentiation of the synaptic strength. While a continuous negative voltage pulse sequence (amplitude: –8 V, width: 5 ms) gradually decreases the conductances, thus mimicking the habituation of the synaptic strength. In addition, synaptic potentiation and habituation behaviors can be modulated by changing the amplitude or width of light and electrical pulse stimuli.

In human visual system, eyes can receive image information from retina. And the optic nerve can transfer visual signals to the visual center to form visual memory. Figure 2(a) schematically shows the whole process. Such visual perception system can be simulated by integrating memory devices and image sensors. Shen et al.^[40] proposed a memristor system to imitate human visual memory by integrate UV resistive image sensors and resistive switching memory devices. Figure 2(b) schematically shows the bioinspired visual memory unit. The In₂O₃ micrometer-sized wires array is used to detect the UV signals. Ni/Al₂O₃/Au memristor is fabricated to connect the photosensor and to store the detected optical signals. The flexible visual memory arrays fabricated on PI substrate are composed of 10 × 10 pixels. When UV light is applied, the memristor will be programmed. When the light is removed, the memristor has been programmed to a non-volatile state. In another word, the stored information of light distribution on the pixel shows long-term retention performances due to the nonvolatile characteristic of the resistance switching memristor. Especially, the light image can be maintained for at least one week. When a UV image with a special pattern, for example a butterfly, has been received by the visual memory arrays, the pattern will be memorized, as shown in Fig. 2(c). When applying negative voltage on the memrsistor, the visual memory arrays can be programmed again, i.e., the resistance state is switched from LRS to HRS. In another word, the stored light information can be erased. Thus, the visual memory arrays can be re-used for a new image. Visual memory function can also be mimicked directly on optoelectronic memory device arrays. As discussed in the previous part that the heterostructure of UCNPs/MoS₂ can achieve optically tunable memory performance under NIR illumination.^[43] Thus, the sensor and the visual memory can be realized on the single optoelectronic memristor. Figure 1(f) schematically shows 13 × 13 optomemory arrays. Pattern characters “FMEG” can be written into the arrays under the assistance of NIR illumination. Whereafter, the resistance states of the memory arrays can be read out electrically at a read voltage of 0.5 V, as shown in Fig. 1(g). Moreover, Mennel et al.^[76] proposed an ANN vision sensor for ultra-fast recognition and encoding of optical images. It provides various training possibilities for ultra-fast machine vision applications.

Fig. 2.

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	Fig. 2. Artificial visual memory. Schematic illustration of (a) human visual memory system and (b) artificial visual memory device. (c) Information storage and reprogrammable capability of the visual memory device arrays. (a)–(c) Reprinted with permission from Ref. [40], Copyright 2018, Wiley-VCH.

These optical-assistance storage systems can reapear the stored image information, and provide a novel approach to imitate human echoic memory and haptic memory. Moreover, the flexible visual memory device will have potentials in wearable electronics, electronic eyes, etc.

The transmission of information between neurons depends on the delivery of neurotransmitters between synaptic clefts. The release of neurotransmitters leads to different kinds of synaptic functions, including synaptic potentiation and depression, excitatory post-synaptic current, paired pulse facilitation, synaptic filtering, short-term plasticity, long-term plasticity, etc. Thus, one of the main tasks for phototransistors in neuromorphic engineering applications would be the realization of these basic synaptic functions. In phototransistors, light stimuli are regarded as pre-synaptic spikes to trigger the synaptic responses. With smart designs and strategies, basic synaptic response and unique neural functions have been mimicked on these kinds of neuromorphic transistors.

Recently, layered 2D materials have been paid attention for neuromorphic system applications.^[80,82,83] Kim et al.^[80] designed MoS₂ phototransistors for optical synaptic device applications, as schematically shown in Fig. 3(a). P-type Ge acts as the back gate. When Ge absorbs light in the region from visible to infrared (λ = 520–1550 nm), band bending happens in Ge, which changes the modulation behaviors of the Ge back gate. It exhibited a fast rising time of 0.1 ms and a decay time of 45 ms for infrared light. The process could simulate the visual information identifications in retina. Both potentiation and depression behaviors have been demonstrated under different light illumination, including visible (λ = 520 nm), dark, and infrared (λ = 1550 nm), as shown in Fig. 3(b). The results indicate potentials in both optical-sensing and synaptic operations in one device. Recently, black phosphorus (BP) is also emerged as an exciting 2D material. The strong light–matter coupling brings great potentials in broadband photodetection (UV to infrared), demonstrating exotic electronic and optoelectronic properties. With distinctive photoresponse characteristics and strong light–matter coupling, BP has also been selected for applications in artificial synaptic devices, demonstrating both excitatory and inhibitory synaptic plasticity.^[53,54] TAhmed et al.^[54] reported an optically stimulated artificial synapse based on layered BP. The device can imitate both inhibitory and excitatory action potentials by applying optical stimulation. No additional alternating-polarity electrical stimuli are needed. Inhibitory post-synaptic current (IPSC) is also an important synaptic response in biological nerve system.^[84] Thus, realization of inhibitory synaptic responses on hardware devices would be interesting for neuromorphic platforms.^[85] The BP synaptic device demonstrates several kinds of neural functions, including spike-duration dependent plasticity (SDDP), short-term and long-term memory transitions, IPSC, EPSC, PPF, spatiotemporally correlated synaptic response, classical Pavlov’s learning, and STDP. As shown in Figs. 3(c) and 3(d), both EPSC and IPSC behaviors have been demonstrated at different wavelengths of 280 nm and 365 nm, respectively. In the nerve system, it is observed that stimuli duration may affect the modulation of the synaptic response.^[86] The present device also demonstrates SDDP on both light induced EPSC and IPSC. Similarly, PPF behaviors have been mimicked by applying paired light stimuli. Ebbinghaus’ forgetting curve, an important brain-like learning mechanism,^[87] has also been mimicked on the device. By connecting two separate BP synaptic devices together, symmetric STDP responses have been mimicked by applying optical pulses on the two synaptic devices with certain pulse intervals. The energy consumption is estimated to be ∼ 3.5 pJ per synaptic activity. Interestingly, the device would prone to unintentional optical exposures during multi-wavelength synaptic operations.

Fig. 3.

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Fig. 3. Short-term plasticity on optoelectronic synapse transistors. (a) Schematic diagram of MoS2 phototransistors based optical synaptic device. (b) Potentiation and depression behaviors obtained under different light conditions: visible (λ = 520 nm), dark, and infrared (λ = 1550 nm). (c) 280 nm optical stimulus-emulating EPSC. (d) 365 nm optical stimulus-emulating IPSC. (e) EPSC triggered by a light pulse. (f) EPSCs triggered by a pair of light pulses (500 nm, 0.1 mW/cm2, ΔT = 2 s). (g) Schematic diagram demonstrating light programming operation and electrical erasing operation for photonic flash memory based on all-inorganic CsPbBr3 perovskite quantum dots (QDs). (a) and (b) Reprinted with permission from Ref. [80], Copyright 2019, American Chemical Society. (c)(f) Reprinted with permission from Refs. [54,81], Copyright 2019, Wiley-VCH. (g) Reprinted with permission from Ref. [37], Copyright 2018, Wiley-VCH.

As discussed in the previous part, quantum dots (QDs) have been proved to be good choices in functional optoelectronic device applications. Photoresponse behaviors could be modulated by the sizes and the compositions of the QDs. The strategies have also great potentials in artificial light-sensitive synaptic devices. Recently, Huang et al.^[81] reported a light-stimulated synaptic transistors (LSSTs) by blending inorganic halide perovskite quantum dots (IHP QDs) and organic semiconductors (OSCs) together. The device demonstrates improved charge separation efficiency of the photoexcited charges. Moreover, the IHP QDs/OSCs hybrid film demonstrates delayed decay in photocurrent, which is important for achieving synaptic performances. A light pulse (500 nm, 0.1 mW/cm², pulse width 500 ms) induces a typical EPSC response with peak EPSC value of ∼ 1.3 nA, as shown in Fig. 3(e). When the pulse ends, the EPSC gradually decays back to rest state due to the slow recombination of the trapped electrons and holes. With the increased light pulse width, the EPSC increases correspondingly due to the increased photogenerated charges. When paired light pulses are introduced, the typical biological PPF function is also simulated on the LSSTs, as shown in Fig. 3(f). Photonic flash memory based on all-inorganic CsPbBr₃ perovskite QDs was also demonstrated.^[37] The CsPbBr₃ QDs and semiconductor layer form a heterostructure to serve as a optically programmable and electrically erasable unit in the photonic flash memory. Figure 3(g) schematically shows the energy diagram under light programming operation and electrical erasing operation. During light illumination, large numbers of charge carriers are generated within the QDs layer. The photogenerated holes will escape to pentacene due to the energy band bending. Thus, photoinduced electrons will remain in the conduction band of the CsPbBr₃ QDs. Such trapped electrons can trigger an additional internal electric field to accelerate holes to be swept into the pentacene channel. When light illumination stops, such trapped electrons will be retained by the potential well with a long lifetime. Thus, such CsPbBr₃-based flash memory could be used to emulate information transmission in neuromorphic architectures. It is observed that the PPF index ratio decays with the increased optical pulse interval time. Moreover, it increases with the increased light intensity from 0.041 mW/cm², 0.069 mW/cm², 0.129 mW/cm² to 0.153 mW/cm². The observation is related to the fact that the increased light intensity promotes the generation of photoelectrons inside the CsPbBr₃ QDs and prolongs the decay time of the post-synaptic current (PSC). Furthermore, the device also demonstrates wavelength dependent synaptic plasticities.

It is interesting to note here that ionic-liquid or ionic-gel based electrolyte gated transistors (EGTs) can operate at low-voltage due to the unique interfacial ionic gating effects.^[17,88–90] Interestingly, ion gating behaviors in EGTs are quite similar to those in biological synapse, which means that unique ion modulation behavior in EGTs could establish bridges between iontronic devices and neuromorphic platforms. Thus, there are several reports on ion-gated EGTs for neuromorphic device applications.^[18–20,91] For example, starch-based bio-polysaccharide electrolyte gated indium–gallium–zinc oxide (IGZO) photoelectric synergic coupled neuromorphic transistors have been reported, demonstrating potentials in visual perception–learning system applications.^[92] Figure 4(a) shows the schematic diagram of the device. The IGZO neuromorphic transistor demonstrates photon response activities. The photosensitivity (S) reaches a maximum value of ∼ 1.6 × 10⁷% with V_gs at –0.45 V. When receiving light stimulus, the device demonstrates photo-electrical synergic synaptic responses. Figure 4(b) illustrates a typical PSC with absolute PSC amplitude of ∼ 63 nA. When paired light pulses are applied, PPF behaviors are also demonstrated, as shown in Fig. 4(c). Interestingly, in the nervous system, synaptic response can be trigged by multiple pre-synaptic stimuli.^[93] When different types of stimuli arrive in a temporal and spatial manner, a spatiotemporal integration phenomenon will happen in the neuron. The photoelectric synergic coupled neuromorphic transistors can also mimic synergic stimuli responses by applying photo-stimuli and electric stimuli in a temporal and spatial manner, as shown in Figs. 4(d) and 4(e). Thus, such photo-electrical synergic neuromorphic transistor will have potentials in bionic visual intelligent perception–learning system.

Fig. 4.

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Fig. 4. Starch gated IGZO photoelectric neuromorphic transistors. (a) Schematic diagram of the device. (b) A typical post-synaptic current. (c) Typical PSC triggered with paired light pulses. (d) Schematic diagram of synergic effect in neurons activated by electric and light stimuli. (e) Absolute EPSC amplitude at zero time (t = 0) as a function of ΔTPre2-Pre1. Reprinted with permission from Ref. [92], Copyright 2020, Royal Society of Chemistry.

In nervous system, synaptic plasticity is closely related to human brain learning and memory functions. In 1968, Atkinson and Shiffrin proposed a multistore model to explain the memory behavior.^[94] The model describes three kinds of memories, including sensory memory (SM), short-term memory (STM), and long-term memory (LTM), as schematically shown in Fig. 5(a). With frequent maintenance rehearsals, the memory level will be enhanced. In another word, SM can be transferred to STM and STM can be transferred to LTM with rehearsals. The phenomena of synaptic plasticity and transformation from STM to LTM have been mimicked on pn-junction-decorated IGZO phototransistors.^[48] Figure 5(b) shows a transition from STP to LTP with the increased input light pulse intensity. The behavior is quite similar to the transition between STM and LTM with the increased electric spike amplitude observed on solid-state electrolyte gated oxide synaptic transistor.^[95] Furthermore, a fading memory behavior is observed from the volatile part and nonvolatile part as shown in Fig. 5(c). STM-to-LTM transition has also been demonstrated on ITO/Nb:SrTiO₃ heterojunction artificial optoelectronic synapse by increasing the spike numbers or frequencies.^[69] The current decay time and the steady current after decay also increase with the intensity, number, and frequency of the light pulse. In addition, both light pulse width and light pulse wavelength can also affect the transition characteristics between STM and LTM.^[37,81]

Fig. 5.

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	Fig. 5. Short-term memory (STM) and long-term memory (LTM). (a) Schematical diagram for the multistore model. (b) Continuous increase in PSC changes with the increased pulse intensity. (c) A fading memory behavior. (d) LTP/LTD characteristics of the CuPc/p-6P optoelectronic synapse for neuromorphic computing. (b) and (d) Reprinted with permission from Refs. [48,97], Copyright 2019, Elsevier.

Besides, there are two kinds of long-term synaptic plasticity includes long-term potentiation (LTP) and long-term depression (LTD).^[96] The short-term synaptic plasticity provides temporary selection for neuron circuits, while LTP/LTD in synapses is the biological basis for continuous learning and memory. Thus, it is essential to mimic LTP and LTD to achieve cognitive complexity in artificial synapses. Qian et al.^[97] achieved optical LTP and electrical LTD characteristics in optoelectronic synaptic device fabricated on a heterojunction consisted of copper-phthalocyanine (CuPc) and para-sexiphenyl (p-6P) layers. Figure 5(f) shows that the PSC increases linearly in the LTP area after applying 85 light pulses (width of 0.5 s and wavelength of 365 nm). Subsequently, the PSC in the LTD region drops non-linearly to the initial value after applying 85 electrical pulses (magnitude of –10 V, width of 0.1 s). The LTD behavior selectively leads to the decline of learning and memory. The LTP/LTD characteristic curves depend greatly on the light pulse conditions. The transition between LTP and LTD could be also realized by obeying spike-timing dependent plasticity (STDP) learning rules.

STDP plays a critical role in cognitive activities and determines the sign and magnitude of LTP or LTD. It refers to the change in synaptic weight with the interval time (Δt_pre–post) between pre-synaptic and post-synaptic spikes and is considered to be a key feature of synaptic plasticity in biological nervous system.^[98,99] STDP is a complement to Hebbian synaptic plasticity and is considered to be the basis for learning and memory by competitively strengthening and weakening of synapses in the neural network.^[100] In canonical STDP, the strength of neuron connections will increase if pre-synaptic spike arrives before post-synaptic spike within a short interval time. Conversely, the strength of neuron connections will decrease if pre-synaptic spike arrives after post-synaptic spike within a short interval time. Thus, mimicking STDP is also highly important for neuromorphic system. By modifying the spike conditions, including spike duration and amplitude, spike shapes, different kinds of STDP behaviors have been mimicked on neuromorphic devices.^{[24,101–103]} The coexistences of multiple types of synaptic plasticity enable the design of advanced neural structures. Yin et al.^[55] reported several types of STDP behaviors on silicon nanocrystals (Si NCs) phototransistors through combinations of light and electrical stimuli. As shown in Fig. 6(a), a symmetric Hebbian characteristic is observed when both the pre-synaptic and post-synaptic stimuli are positive V_gs (E⁺). A symmetrical anti-Hebbian learning rule is obtained when both the pre-synaptic and post-synaptic stimuli are light stimuli (L), as shown in Fig. 6(b). Figure 6(c) shows the asymmetric Hebbian learning rule when the pre-synaptic and post-synaptic pulses are L and E⁺, respectively. Finally, the device achieves asymmetric anti-Hebbian when the pre-synaptic and post-synaptic pulses are L and E⁻, respectively (Fig. 6(d)).

Fig. 6.

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	Fig. 6. Four kinds of STDP learning behaviors. (a) Symmetric Hebbian STDP rule. (b) Symmetric anti-Hebbian STDP rule. (c) Asymmetric Hebbian STDP rule. (d) Asymmetric anti-Hebbian STDP rule. Reprinted with permission from Ref. [55], Copyright 2019 Elsevier.

In addition, STDP learning rules have been demonstrated with the synergistic effect of light and electrical stimuli on photoelectric synaptic devices based on 2D materials (MoS₂,^[18,82] black phosphorus,^[53,54]), one-dimensional nanomaterials,^[59] and metal–oxide–semiconductor materials.^[61] Diverse learning rules can help artificial neural networks to deal with more complex situations and improve the learning efficiency.

In physiology, classic conditioning is a typical form of associative learning in nervous system.^[104] Figure 7(a) schematically shows classic Pavlovian associative learning. Initially, bell-ringing, considered as neutral stimulus (NS), can not trigger salivation. While feeding-food, considered as unconditioned stimulus (US), will activate salivation (unconditioned response, UR). During training, both US and NS are provided simultaneously, causing salivation. Thus, an association between NS and US is established. After training, NS only can cause salivation. Now, NS and UR convert to conditional stimulus (CS) and conditioned response (CR), respectively. Several groups have reported electrical stimuli triggered associative learning.^{[12,105–107]} Moreover, Yu et al. have also established the relation between STDP and classic conditioning.^[103] John et al.^[82] simulated Pavlovian classic conditional reflection on a synergistic gating of electro-iono-photoactive 2D chalcogenide neuristors. The storage level of light pulses on the device is much better than that of electrical pulses. Thus, the electrical pulses were deemed as bell-ringing (Fig. 7(b)), while the light pulses were deemed as feeding-food (Fig. 7(c)). Initially, the PSC obtained by electrical pulse stimulation (NS) is less than salivation threshold of 500 nA (phase a in Fig. 7(d)). While the PSC obtained by light pulse stimulation (US) is higher than the salivation threshold (UR, phase b in Fig. 7(d)). After training for 40 cycles by applying light pulse stimulation (US) and electrical pulse stimuli (CS) together, CS only will trigger “salivation”, indicating the establishment of an effective association between light pulse stimuli (feeding-food) and electrical pulse stimuli (bell-ringing). Moreover, extinction behaviors have been observed on the 2D chalcogenide neuristors. Pavlovian classical condition was also mimicked on electrolyte gated photoelectric synergic coupled oxide neuromorphic transistor with simple device configurations.^[92] Light spikes are deemed as feeding food (US), while gate voltage spikes are deemed as bell ringing (NS). Moreover, Pavlovian classical condition experiments can also be simulated on synaptic devices under all-light stimulation.^[54,65] These multi-input optical signal synapse devices do not need to add additional electrodes, and have a faster response speed with lower energy consumption, indicating great potentials in neuromorphic engineering.

Fig. 7.

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	Fig. 7. Pavlovian associative learning. (a) Schematic diagram of Pavlov’s dog experiment. (b) Electrical pulses as conditioned stimulus (CS) with EPSC < 500 nA (no salivation). (c) Optical pulses as unconditioned stimulus (US) with EPSC > 500 nA (salivation). (d) Imitation of Pavlovian conditioning. Reprinted with permission from Ref. [82], Copyright 2018 Wiley-VCH.