Over the past decade, there has been a surging computational demand for deep learning applications, particularly in the training of large foundational models. This has prompted a growing interest in developing new computing paradigms to overcome the limitations of existing digital hardware in executing deep-learning-specific computations with enhanced speed and energy efficiency. These emerging paradigms include photonic computing [1–5], neuromorphic computing [3–7], and analog-based systems [8,9].

Among these approaches, optical neural networks (ONNs) have attracted significant attention due to their potential for becoming a high-speed, highly parallel, energy-efficient, and thus more sustainable computing platform. Using light as an information carrier rather than electrons, mathematical computations can be performed via light interference and scattering with minimal energy consumption. This allows for forward propagation through ONNs at the speed of light, making ONN runtime essentially independent of their sizes. There have been many studies proposing architectures akin to the multilayer perceptron and convolutional neural networks using optical matrix-vector multiplication [10,11], diffraction [12,13], and phase modulation [14]. Based on these fundamental components, more advanced architectures such as all-optical backpropagation [15], optical encoders [16], efficient ONNs with low photon number [17], and optical graph neural networks [18] have also been developed. Apart from these, another popular research direction within the ONN community is reservoir computing [19,20], including the photonic extreme learning machine (PELM) [21] and the time-Floquet extreme learning machine [22]. These approaches use light to process information within a scattering medium, enabling applications such as chaotic system predictions [23] and single-shot light polarimetry [24].

Currently, typical PELM system designs rely on sophisticated high-speed CCD cameras as photodetectors to capture ONN outputs. In this configuration, the nonlinearity of the architecture, necessary for the neural networks to learn complicated functions, is achieved by driving CCD pixels close to saturation, out of their linear operating regions.

Here, we propose an alternative approach by replacing the CCD cameras with perovskite solar cells in an open circuit configuration to capture the ONN outputs. This method leverages the fact that the open circuit voltage of a solar cell varies logarithmically with the incident light intensity, and thus offers an embedded highly nonlinear activation function at the point of acquisition. Additionally, the features of perovskite solar cells, including their efficiency, ease of processing, and potential for semitransparency, offer unique opportunities for ONN applications, for example, to measure light at different planes, over an extended volume [25–28]. To demonstrate the suitability of perovskite solar cells for ONN applications, we have built a simple ONN setup, as depicted in Fig. 1, using a six-pixel solar-cell unit, and compared it to the same setup but with a CCD camera of the same resolution. Both ONN setups were evaluated on MNIST classification tasks, and our results show that the solar-cell setup has been able to achieve a binary classification accuracy of 91% on the reduced test set, which consistently outperforms its equivalent six-pixel CCD counterpart.

The perovskite solar cells used in the ONN setup follow an “n-i-p” configuration. Their design consists of an indium tin oxide (ITO) transparent contact, with a tin oxide (SnOx) electron transport layer, a triple cation perovskite (CsMAFA) absorber layer, a hole transport layer (HTL) made from 2,2’,7,7’-Tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9’-spirobifluorene (Spiro-OMeTAD), and a gold top electrode. Figure 2 shows a sketch of the device. The perovskite solar cells were fabricated following the procedure developed by Cheng et al. [29]. The SnOx layer was deposited via spin coating and annealing on a patterned ITO substrate. The sample was then transferred to a nitrogen-filled glovebox, where the perovskite absorber layer was deposited from a precursor solution via spin coating and annealing.

The Spiro-OMeTAD layer was deposited via spin coating in the nitrogen glovebox, without annealing. Following spin coating, the spiro-coated cells were left in a dry air desiccator overnight for oxygen doping, and finally 80 nm of gold was deposited as the top electrode via thermal evaporation. Each active region had dimensions $4\mathrm{mm}\times 3\mathrm{mm}$, and the six solar-cell pixels covered a total area of $1\mathrm{cm}\times 1\mathrm{cm}$. After fabrication, the solar cells were encapsulated by gluing a piece of glass over the active area with UV epoxy.

The fabricated solar-cell samples were characterized by measuring their voltage response against the incident light power. For this experiment, we used a continuous wave laser beam with a wavelength $\lambda =532\mathrm{nm}$ and known optical power, collimated and expanded to a diameter of 2 cm, thus overfilling the area occupied by the active regions. The photovoltage generated by the cells was then measured using a voltmeter as a function of input light power, which was varied from 1 mW to 100 mW. As shown in Fig. 3, the average voltage response against the incident power closely follows a logarithmic relationship, which is in agreement with the theoretical performance first calculated by Schockley and Queisser [30]. The fit deviates significantly at very low light intensities where background light and leakage current start to play a significant role.

Figure 4 shows the ONN setup, which uses a $512\times 512$ pixels liquid crystal spatial light modulator (SLM) to encode the input image into a collimated laser beam through phase modulation. The desired Fourier components of the encoded beam are then selected using an iris to remove the unwanted background and improve the contrast of encoded images. An optically thick layer of alumina particles with an average size of 1 μm was placed in front of the photodetector, acting as randomized and fixed linear weights. Each solar-cell pixel independently generates a nonlinear voltage signal against the incident light, and a collection of these pixels is used to capture the ONN output states. The physical propagation process shown in Fig. 4 can be formulated as $$h^{(i)}=(A\circ F)(x^{(i)})=(A\circ M\circ S_{\mathrm{iris}}\circ e)(x^{(i)}),$$(1)where $x^{(i)}$ and $h^{(i)}$ are the $i$th input image and its corresponding output state, $e$ denotes the image encoding process of the SLM, $S_{\mathrm{iris}}$ is a sparse selection mask implemented by the iris, $M$ is a randomized and fixed linear mapping carried out by the scattering medium, $A$ is a nonlinear acquisition operator representing the conversion of the captured light power into analogue voltage signal via the solar-cell pixels, and $F=M\circ S_{\mathrm{iris}}\circ e$ represents the entire computing reservoir formed by the optical components. The operator $A$ may be further decomposed into ${\sigma }_{\log }\circ q\circ S_{\mathrm{sc}}$. $S_{\mathrm{sc}}$ is a sparse selection mask representing the capillary distribution of the solar-cell pixels, $q(p_j)$ is a function taking the element-wise magnitude of the incident light, and ${\sigma }_{\log }$ is a logarithmic-like element-wise activation function representing the conversion of the incident light power to analogue signals. For simplicity, the above formulation neglects the complex field transfer matrix of the free space between each optical component. The ONN output $h^{(i)}$ can be trained for various downstream tasks. Here we consider the classification setting, where a single layer of linear weights ${\theta }^{*}$ is digitally trained to solve the regression problem $$\underset{\theta }{\min }||\widehat{Y}(\theta )-Y{||}_2^2+c||\theta {||}_2^2,$$(2)where $Y$ is the target label, $\widehat{Y}(\theta )=\theta H$ is the model classification result, $H=[h^{(1)},h^{(2)},\dots ,h^{(n)}]$, and $c$ is a regularization parameter. For low-dimensional $H$, the output weights ${\theta }^{*}$ can be easily computed using [31] $${\theta }^{*}={(H^{T}H+cI)}^{-1}{H}^{T}Y.$$(3)

We evaluated the above ONN setup for solving MNIST classification tasks, where $x^{(i)}$ is the $i$th pre-processed MNIST image. In this experiment, the pre-processing only involves resizing the input images from $28\times 28$ pixels to $512\times 512$ pixels, the same resolution as the SLM screen. The SLM displays the pre-processed images one by one in rapid succession, with an interval of approximately 11 ms per image. This interval represents the sum of the interfacing time between the computer with the SLM, and the computer with the solar-cell voltage reader, and the response time of the SLM. After training, this ONN system can reach an average classification accuracy of 91% on the two-class MNIST datasets and 54% for the full 10-class classification. It is worth noting that this performance is competitive with just six output channels, where the number of output channels is less than the number of classes. The performance of the network can be improved by simply increasing the number of solar-cell pixels.

Our further investigation also demonstrated the competitiveness of our solar-cell-based ONN setup, where we evaluated the same ONN setup but with a CCD camera instead of solar cells. The CCD camera has a linear response against the incident light power until saturation, at which point the pixel readout will be capped at its maximum value. This saturation process can be expressed by a simple element-wise top hat activation function ${\sigma }_{\mathrm{sat}}(p_j)=\min \{p_j,255\}$, with 255 being the maximum readout of pixel $p_j$. The physical propagation process can thus be reformulated as $$h^{(i)}=(A^{\prime }\circ F)(x^{(i)})=(A^{\prime }\circ M\circ S_{\mathrm{iris}}\circ e)(x^{(i)}),$$(4)where $A^{\prime }={\sigma }_{\mathrm{sat}}\circ q$ is a weakly nonlinear acquisition operator. Note that $A^{\prime }$ does not contain a selection mask term, as we assume the tightly packed pixels of a CCD camera are capable of capturing the full image field. Furthermore, to simulate the large pixels as well as the pixel layout of the solar cells, the captured $1024\times 1024$ CCD images were resized by binning and averaging the image pixels to a shape of $3\times 2$. This setup has achieved accuracy of 88% and 49% on two- and ten-class MNIST classification, consistently underperforming compared to its solar-cell equivalent, and sometimes by a sizable margin. The full comparison is shown in Fig. 5.

This study shows that utilizing a set of just six distinct solar-cell elements is sufficient for completing classification tasks and that for an equivalent number of pixels solar-cell-based ONNs can perform better than CCD-based ONNs. The complexity of the task tackled by the ONN scales with the density of the pixels used [32]. There exist multiple techniques that enable the patterning of large-area perovskite devices into multicolor sub-pixels with micrometer-scale resolution [33–35]. Together with their low cost and scalable fabrication [36], this means there is potential to fabricate highly complex ONNs. High-density detectors are particularly relevant in the context of indoor photovoltaic applications, where perovskite-based technology excels. An alternative framework for scaled-up photovoltaic ONNs utilizes the existing solar infrastructure at solar farms or residential areas with rooftop solar panel installations. In this case, each solar panel can be treated as an independent pixel, and a collection of these distributed pixels can provide information for detecting and analyzing geological and meteorological events.

A key consideration in the use of solar cells for ONN application is the stability of their photovoltage. Perovskite solar cells are known to undergo photodegradation if exposed to high light powers for extended periods [37], and this could be detrimental to their usefulness in ONNs. It should be noted that the solar cells used in this work were optimized for efficiency rather than stability, and only a very basic encapsulation method was used. Despite these very non-optimal conditions, we still found that the stability was sufficient to train and use the network successfully at the used powers.

Although the stability of perovskite solar cells is still an area of active research [38,39], recent studies have shown that perovskite solar cells can achieve more than 2000 h of stability under accelerated aging conditions if the right processing and encapsulation methods are used [40], which shows that perovskite-based ONNs could easily be stable enough for most applications. Finally, it should be noted that our results are not expected to be different for conventional silicon-based solar cells [38,41]. These are generally more stable, but they have a weaker voltage response and do not offer the advantages of light weight, semitransparency, and ease of fabrication that perovskite solar cells can offer [42].

Importantly, unlike CCD cameras that require external power sources to operate, solar cells can self-generate electricity while simultaneously capturing incoming information. The generated electricity can then be harnessed to power the subsequent digital or analog systems to analyze the signals. To our best knowledge, no other photodetectors possess similar dual power-signal-generating capability, making this a truly unique characteristic that can be leveraged for developing self-powered, battery-free, and thus more portable novel edge-computing systems. Furthermore, the captured information by solar cells in the form of analog signal is immediately accessible at the point of acquisition, with a refresh rate up to 100 kHz [43], allowing the data to be processed by the subsequent electronic computing systems without any additional need for amplification.

Additionally, the type of information collected by the large-sized solar-cell pixels can also be very different from that of smaller CCD pixels. Not only can the low-resolution nature of the solar-cell pixels be desirable for reducing the privacy and safety concerns to individuals and institutions, but their large acquisition area can also bring other advantages, such as providing a larger dynamic range, better signal-to-noise ratio, and better depth-of-field [44,45]. Finally, when deployed at scale, ONNs based on solar cells are excellent candidates for environmental monitoring tasks.

We have successfully demonstrated the possibility of integrating perovskite solar cells for ONN applications through a simple proof-of-concept setup. Their advantages of being inexpensive, easily accessible, and having an intrinsic nonlinear activation make it an ideal choice over CCD cameras for large-scale deployment. The utilization of solar cells as both a photodetector and an energy source nevertheless presents intriguing prospects and opens the door to the development of novel self-powered edge-computing systems.

Acknowledgment. KZ acknowledges support from the Carnegie Trust for the Universities of Scotland. CC acknowledges PRIN 2022597MBS PHERMIAC. ADF was supported by the European Research Council (ERC) under the European Union Horizon 2020 Research and Innovation Program (Grant Agreement No. 819346).