Differential perovskite hemispherical photodetector for intelligent imaging and location tracking

The study addresses the challenge of achieving advanced, multi-functional, and compact photodetection and imaging with minimal pixel counts. Conventional imaging pipelines rely on bulky optics and large sensor arrays that contain redundant information and increase cost and complexity. Single-pixel imaging using Fourier transforms demonstrates that scene information can be captured without an array sensor, but integrating multiple functions (wide-angle, color, spectral analysis, localization) within limited hardware remains difficult. Machine learning and computational spectrometers have enabled lensless color imaging and fine spectral reconstruction, yet a key limitation is the small differential response among pixels under varying conditions, which constrains intelligent processing. Hemispherical detector geometries, inspired by compound eyes, inherently provide wide-angle detection and strong spatial variations in responsivity due to curvature and varying incidence distances. This work proposes and demonstrates a differential perovskite hemispherical photodetector with 8 differential pixels that, together with Fourier-transform single-pixel imaging and machine-learning (including neural network fitting), delivers lensless color imaging, high-resolution computational spectroscopy, and intelligent 2D/3D location tracking with color classification.

The paper situates its contribution within advances in intelligent photodetection, including wide-angle vision, color classification, and object localization. Prior work in Fourier-transform single-pixel imaging showed that 2D images can be reconstructed from a single detector by capturing photocurrent variations under structured illumination and applying inverse Fourier algorithms. Computational spectrometers have been miniaturized using algorithmic reconstruction from devices with wavelength-dependent responsivities, including approaches using van der Waals junctions, nanowires, and quantum dots. Hemispherical or curved sensor arrays emulate compound eyes for wide field-of-view imaging and differ from planar sensors by providing position-dependent incidence and responsivity. However, prior implementations often produce limited or monotonous signal variations and lack integrated intelligent functions. Machine learning has enabled processing of large signal datasets for robust classification and reconstruction, but small inter-pixel differentials limit performance. The present work leverages perovskite film engineering and hemispherical geometry to amplify differential signals, enabling intelligent functions (spectral reconstruction, color imaging without filters, and localization).

Materials and device fabrication: An amphiphilic supramolecular additive, naphthoguanidinium iodide (NGAI), was synthesized and characterized (monoclinic P2₁/c; π–π stacked naphthalene layers; guanidinium–iodide chelation). In solution, NGAI forms nanosheets; with PbI₂ present, it forms ~4.7 nm nanoparticles, indicating interaction with lead halide species. FAPbI₃ precursor solutions with varying NGAI content (0–30 mol% relative to Pb²⁺) were prepared in DMF:2-Me:ACN (1:1:3 v/v) with FAI, PbI₂, MACl, and L-ascorbic acid. Films were spray-coated on heated substrates (~100–130 °C) with nitrogen-assisted crystallization and annealed (120–130 °C, 15 min). NGAI slows crystallization by wrapping [PbI₄]²⁻ intermediates, yielding larger grains and promoting (111) orientation (XRD). Device stack: Cr/PTAA/perovskite/C60 (25 nm)/BCP (8 nm)/Cr (5 nm)/Au (5 nm) on hemispherical glass substrates. Bottom Cr electrodes were patterned (polyimide masking) into 8 differential pixels (45° segments) and also used to define 0.1 cm² effective areas. PTAA was spray-coated (0.5 mg mL⁻¹ in toluene; ~25 µL cm⁻²), followed by air-plasma treatment and perovskite spray deposition. Characterization and signal modeling: EQE spectra were measured versus reverse bias, irradiance, and wavelength (350–850 nm). Bias-dependent carrier collection was modeled: at low bias, drift length < film thickness produces CCN narrowband response; at high bias, full collection increases EQE across the spectrum. Noise current density was measured to derive detectivity. Effective incident flux distributions for planar vs hemispherical geometries were calculated using spherical symmetry, cosine-law projection, and geometric relations between light source position (horizontal distance d, height h) and surface coordinates. Computational spectrometer: A reconstruction algorithm exploited bias-dependent EQE/responsivity maps to infer input spectra. Monochromatic and polychromatic test spectra were reconstructed; resolution was estimated from reciprocal linear dispersion and verified using simulated steps of 5 nm and a 520 nm laser (FWHM ~5.8 nm). Responsivity maps vs bias and irradiance were used to generalize reconstruction for arbitrary conditions. Fourier single-pixel imaging and color classification: Two-dimensional Fourier phase-shift patterns were projected onto objects (e.g., smooth Rubik’s cube) while measuring device photocurrent (Keithley 2400). m=10,000 patterns were used. Images were reconstructed via Fourier transform of photocurrent at multiple reverse biases, then optimized (background subtraction, noise reduction, smoothing, linear weighting). For color classification, the gray value of each pixel across 9 biases (−0.1 to −0.9 V) formed a 9D feature vector; K-Nearest Neighbor (Fine KNN, MATLAB) was trained using 121 pixels per color region over five classes (R, G, B, Y, black), achieving classification on reconstructed images. Intelligent localization and tracking: A hemispherical detector with two electrode designs (short and long) enhanced angular sensitivity. An LED source mounted on an X–Y motorized stage scanned a 6×6 cm² area in 3 mm steps (20×20 grid). For each position, signals from 8 pixels formed an input feature (400×8 matrix) to train a Neural Network Fitting (NNF, MATLAB) model (Bayesian Regularization; 10 hidden neurons) mapping to 2D coordinates (400×2 output). Trajectories were reconstructed by feeding time-series signals into the trained model. Color-distinguishable tracking used three LEDs (450, 520, 660 nm) and three biases (−0.30, −0.35, −0.40 V), expanding inputs to 400×24 and outputs to 400×3 (X, Y, color). 3D tracking used two biases (−0.30, −0.35 V) and multiple heights (9.5, 9.8, 10.1, 10.4 cm), mapping inputs (400×16) to outputs (400×3: X, Y, Z).

• Hemispherical perovskite photodetectors with NGAI additive exhibit large device gain and differential responsivity: EQE up to ~1000% (e.g., responsivity 5.1 A W⁻¹ at −1 V, 10 µW cm⁻² corresponds to EQE ~1180%).
• Low noise current of ~10⁻¹³ A Hz⁻⁰·⁵ enables high specific detectivity D* ≈ 2×10¹³ Jones; spectral response spans 350–850 nm.
• Computational spectrometer: Bias-dependent EQE enables reconstruction of monochromatic lines with step size 5 nm and computational spectral resolution better than 4.7 nm; reconstruction of a 520 nm laser (FWHM ~5.8 nm) and polychromatic LED (white) spectra matches references.
• Lensless color imaging: Fourier single-pixel imaging combined with bias-dependent differential response enables color classification without filters. KNN classifier using 9-bias feature vectors achieved 100% accuracy on the training set (sample size 121×5), with confusion matrix indicating perfect class separation in training.
• Intelligent localization/tracking: An 8-pixel hemispherical differential detector learned spatial mappings over a 20×20 grid (3 mm steps) and reconstructed predefined 2D motion trajectories. Neural network fitting achieved high correlation coefficients: training 0.99976, test 0.99967, all 0.99976.
• Color-distinguishable tracking: Using three biases (−0.30, −0.35, −0.40 V) enabled simultaneous trajectory reconstruction and color classification for red, green, and blue light sources.
• 3D tracking: By varying bias and source height, the system reconstructed 3D trajectories in a 20×20×3 array, consistent with designed paths.
• Materials/physics insights: NGAI supramolecular aggregates slow perovskite crystallization, improve grain size and (111) orientation, and in the presence of PbI₂ form nanoparticles that facilitate charge injection and device gain; bias-dependent drift-length modulation explains transition from narrowband CCN response at low bias to broadband high-EQE at high bias. Hemispherical geometry yields strongly position-dependent effective incident flux, enhancing differential signals for localization.

The findings demonstrate that coupling a hemispherical perovskite photodetector with engineered differential pixels and machine-learning algorithms converts modest hardware into a multifunctional intelligent sensing platform. High EQE, low noise, and hemispherical geometry enlarge differential signal space, enabling fine spectral reconstruction (sub-5 nm resolution), lensless color imaging without filters, and accurate 2D/3D localization with color identification. The bias degree of freedom serves as an additional channel for encoding spectral and spatial information, overcoming the common limitation of small inter-pixel variance in conventional arrays. The results validate that algorithm–device co-design (Fourier single-pixel imaging, KNN classification, Bayesian-regularized NNF regression) can extract rich information from only eight differential pixels. This approach reduces optical complexity and sensor count while achieving functions typically requiring larger arrays and lenses, thereby advancing compact, cost-effective intelligent photodetectors. Remaining challenges include managing computational load and robustness under varying scenes and irradiances; however, the measured responsivity maps versus bias and irradiance suggest feasible generalization after calibration.

This work introduces a differential perovskite hemispherical photodetector that integrates multiple intelligent functions—computational spectroscopy, lensless color imaging, and 2D/3D location tracking with color classification—using only eight differential pixels. Materials engineering with NGAI produces nanoparticle-induced gain and controlled crystallization, yielding high EQE (~1000%), low noise (~10⁻¹³ A Hz⁻⁰·⁵), and high detectivity (~2×10¹³ Jones). Bias-dependent responsivity variations are harnessed by Fourier-transform imaging and machine learning (KNN, Bayesian-regularized NNF) to reconstruct spectra and trajectories with high accuracy and sub-5 nm spectral resolution. The compact, lensless design reduces system complexity and cost, pointing toward miniaturized, intelligent photodetectors for future AI-enabled applications. Future work should focus on algorithm/model optimization for reduced latency and improved robustness, expanded bias/geometry encoding for finer color and depth resolution, and integration of larger hemispherical arrays for scalable, real-time intelligent sensing.

• Computational burden: Data acquisition and machine-learning-based analysis require robust computing power, which may delay output (latency) or impair accuracy in resource-limited settings.
• Potential interference in color classification from spatial variations in reflected intensity; mitigated by algorithmic optimization but still a consideration in unconstrained scenes.
• General challenge in intelligent photodetection: small differential variations among pixels under different conditions; hemispherical geometry alleviates this, but calibration across irradiance and bias conditions remains necessary.
• Demonstrations are controlled (set distances, biases, LEDs); performance in complex, dynamic real-world illumination and backgrounds will require further validation and model adaptation.