Differential perovskite hemispherical photodetector for intelligent imaging and location tracking

Advanced photodetectors with intelligent functions are expected to take an important role in future technology. However, completing complex detection tasks within a limited number of pixels is still challenging. Here, we report a differential perovskite hemispherical photodetector serving as a smart locator for intelligent imaging and location tracking. The high external quantum efficiency (~1000%) and low noise (10−13 A Hz−0.5) of perovskite hemispherical photodetector enable stable and large variations in signal response. Analysing the differential light response of only 8 pixels with the computer algorithm can realize the capability of colorful imaging and a computational spectral resolution of 4.7 nm in a low-cost and lensless device geometry. Through machine learning to mimic the differential current signal under different applied biases, one more dimensional detection information can be recorded, for dynamically tracking the running trajectory of an object in a three-dimensional space or two-dimensional plane with a color classification function.

nm laser.XRD data were collected using a PANalytical B.V.-Empyream Diffractometer with Cu Kα radiation.The SEM cross-section images were acquired by Hitachi Cold Field Emission SEM with Bruker X-ray. 1 H NMR and 13 C NMR spectra were obtained on Bruker AVANCE III 500 MHz.Chemical shifts were reported in ppm relative to the residual solvent peak (MeOD: 1 H, 3.34; 13 C, 49.03; ACN: 1 H, 1.96).High-resolution mass spectrometry data was obtained using Agilent 1290 -Bruker micrOTOF QII.

Computational spectral reconstruction.
Xenon light was monochrome by a monochromator, the exit slit is controlled to 1 mm, and the current-voltage curve of the device is scanned by Keithley 2400 source meter under different irradiance and wavelength.The irradiance of light at each monochromatic wavelength is measured using a standard silicon photodetector.The response matrix of the responsivity of the device under different irradiance with voltage and wavelength is calculated and used as the reference standard data.The responsivity is calculated by following Eq.( 1): where Res is responsivity, and Jlight is the current density under light.Jdark is the current density under dark.I0 is the power density of the light.The EQE of the photodetector can be calculated by the following Eq.( 2): where EQE is external quantum efficiency.h is Planck constant (h = 6.626×10 -34 J s). υ is the frequency of the light.q is the absolute value of electron charge (q = 1.602×10 -19 C).
The current density and voltage curve of the photodetector under the unknown light is measured.The corresponding spectral curve was calculated by the algorithm reported by Yoon and Sun et al 2 .The difference is that we used reverse bias tunable response as the source in the learning process.
Supplementary Fig. 1 |  The morphology of the NGAI and NGAI-PbI2 complex in the polar solvent was investigated using TEM.Samples are prepared in the following way.The NGAI (3.1 mg) was dissolved in a mixed solvent of ACN: DMF: 2-Me = 3: 1: 1 (v/v, 1.5 mL), with or without PbI2 (4.6 mg), to obtain the solutions of NGAI and NGAI-PbI2.The solution was deposited onto Holey Carbon Grids (HCG) and subsequently air-dried.The TEM images of the NGAI-PbI2 complex are depicted in Supplementary Fig. 3a and Supplementary Fig. 3b, showcasing its nanoparticle morphology.
The crystallinity of NGAI-PbI2 complex can be enhanced by appropriately reducing the amount of DMF in the mixed solvent.The amplified TEM image revealed the presence of the (102) plane in PbI2 (Supplementary Fig. 3b).Supplementary Fig. 3c shows the (102) plane of the PbI2 crystal.
The average diameter of nanoparticles is ~4.7 nm.The radius of nanoparticles approaches the reported Bohr radius of perovskites 3 .Therefore, it is reasonable to propose that the NGAI-PbI2 complex assumes the structure of the quantum dot.Subsequently, we fabricated films comprising NGAI, NGAI-PbI2, and PbI2 to obtain XRD spectra and absorbance spectra.The NGAI, NGAI (w 1 equiv.PbI2), and PbI2 were dissolved in the mixed solvent of ACN: DMF: 2-Me = 3: to obtain the precursor of 0.2 M (PbI2 can not be dissolved in the mixed solvent in this step.Thus, the PbI2 precursor was saturated solution in this condition.).Each kind of precursor was spraycoated onto the substrate to obtain the film.The XRD spectra are shown in Supplementary Fig. 3d (The peak of ~10 degrees is the system noise of the instrument.).The diffraction peak identification of NGAI is referred to as the single crystal data.Peaks of NGAI-PbI2 mainly come from (200) and (112) of NGAI.No peaks corresponding to PbI2 in the NGAI-PbI2 complex sample were observed, and the peaks of NGAI-PbI2 exhibit distinct difference compared to those of NGAI.Therefore, it is plausible that the interaction between NGAI and PbI2 in the NGAI-PbI2 film could induce a reorientation of NGAI molecules.The crystallinity of PbI2 is simultaneously diminished by NGAI.
Supplementary Fig. 3e shows the (100) plane of the NGAI crystal.The Supplementary Fig. 3f presents the absorbance spectra of NGAI, NGAI-PbI2, and PbI2.It is observed that the absorbance spectrum of NGAI-PbI2 exhibits a blue shift compared to that of PbI2, which can potentially be attributed to the quantum size effect.

The characterization of perovskite (with 1-(naphthalen-2-yl)guanidinium iodide) film
The FAPbI3 films were fabricated by spray coating with varying amounts of NGAI in order to investigate the impact of NGAI dosage.The absorbance spectra of FAPbI3 films, fabricated by spray-coating with varying amounts of NGAI, are presented in Supplementary Fig. 4a.The increase in NGAI amounts resulted in a rise of the peak at ~380 nm.This peak may originate from the NGAI-PbI2 complex, supported by its similar absorbance spectra but with a blue shift.The TEM image of FAPbI3 (w 50%mol NGAI) is shown in Supplementary Fig. 4b.The TEM sample was prepared in the following process.The precursor solution (~1 mg mL -1 FAPbI3 with 50%mol NGAI and 30%mol MACl) was deposited onto HCG for TEM analysis.The solvent used was a mixture of ACN, DMF, and 2-Me in a ratio of 3: 1: 1 (v/v).Subsequently, the HCG sample underwent annealing at 120℃ for a duration of 15 minutes.The morphology of FAPbI3 (with 50%mol NGAI) also exhibits a nanoparticle structure.The average diameter of the nanoparticles is ~3.9 nm, which is smaller compared to the nanoparticles formed by the NGAI-PbI2 complex (Supplementary Fig. 3a).These differences should come from the interaction between FA + /MA + and [PbI6] 4-.The transient absorption spectra are shown in Supplementary Fig. 4c and Supplementary Fig. 4d.No discernible peak corresponding to low dimensional perovskite was observed in the spray-coated film of FAPbI3 perovskite (w30%mol NGAI).The negative peak at ~500 nm was attributed to PbI2.The presence of NGAI induced a transformation in the crystallization process of the FAPbI3 film through the formation of the NGAI-PbI2 complex.
Because of the highly ordered molecular arrangement of NGAI with rigid structures, the crystallization process is also templated by NGAI.The addition of NGAI promotes the preferential formation of crystalline grains exposed to the (111) lattice plane, as observed in Fig. 1h,  To study the interaction between the NGAI and PbI2 in the solution state, 1 H NMR spectra of NGAI, NGAI (w 1 equiv.PbI2), and NGAI (w 1 equiv.FAPbI3) were obtained (Supplementary Fig. 5a).The concentration of NGAI is 0.02M.The solvent is ACN (CD3CN-d3) with adding 1% 2-Me.In the case of NGAI (w 1 equiv.FAPbI3), 0.3 equiv.MACl was added to better simulate the precursor.After adding PbI2, chemical shifts of NGAI exhibit a down-field shift.The biggest change is the peak of H (1, 7) and H (2, 3).These changes reflect the electron cloud differences caused by the interaction between PbI2 and guanidinium because H (1, 7) and H (2, 3) are close to the guanidinium in space.After adding FAI, chemical shifts (H (1) and H (2, 3)) of NGAI exhibit a slightly up field shift, which is possibly influent by the interaction between FAI and PbI2.Supplementary Fig. 5 | The interaction in the solution state.a, The 1 HNMR spectra of NGAI, NGAI-PbI2 complex and NGAI-FAPbI3 complex.NGAI exhibits lower solubility (0.032 mg mL -1 ) in water, which is lower than other hydrophobic ammonium salt widely used (Supplementary Fig. 6a).The NGAI augments the perovskite's chemical inertness.NGAI are distributed in the grain boundary inhibiting the invasion of water and oxygen.Additionally, facet engineering can also enhance the stability of perovskite films 4 .The stability of FAPbI3 (w 10%mol NGAI) film was monitored by absorbance spectra.The film was aged for 30 days without any decomposing at R.H. 40% ~ 85% (Supplementary Fig. 6b).

Supplementary
The device structure of the perovskite photodetector fabricated by spray-coating is Cr/PTAA/FAPbI3(w 10%mol NGAI)/C60/BCP/Cr/Au.The Au side serves as the incident side for light illumination.The top metal electrode (Cr and Au) is designed to have a thin thickness in order to maintain high transmittance 5 .Supplementary Fig. 7a shows the dark current density and the light current density of the photodetector.The dark current density of the photodetector is 2.20 × 10 -8 A cm -2 at -1.0 V bias.Lower dark current density benefits from the improved density of the film by adding NGAI.The light current density of the photodetector at 532 nm, 10 µW cm -2 , and -1.0 V bias is 5.1 × 10 -5 A cm -2 .The responsivity of the photodetector is 5.1 A W -1 and calculated by Eq. ( 1).The EQE of the photodetector is 1180%.The EQE higher than 100% results from the external injection of carriers by the power source.Supplementary Fig. 7b shows the trap density of state (tDos) of the photodetectors fabricated by spray-coating (FAPbI3 w 10%mol NGAI) and spin-coating (FAPbI3 w/o NGAI).The tDos ( ~10 -15 ~ 10 -17 eV cm -3 ) of photodetectors fabricated by spray-coating (FAPbI3 w 10%NGAI) is higher than that (~10 -11 -10 -15 eV cm -3 ) of photodetectors fabricated by spin-coating (FAPbI3 w/o NGAI).The tDos was evaluated by measuring the frequency and capacitance of the device.The demarcation energy (Eω) with the applied frequency by the following Eq.(3) 6 .
where ω is the applied angular frequency.The ω0 we used is the published data 7 .kB is the Boltzmann constant, and T is the absolute temperature.The distribution of the tDos can be calculated by Eq. ( 4).

𝑡𝐷𝑜𝑠(𝐸
where Vbi is the built-in potential.W is the width of the depletion region, and the thickness of the active layer is employed as W. q is the elementary charge.Meanwhile, the fabrication of photodetectors by spray-coating (FAPbI3 without NGAI) poses significant challenges.The resulting photodetector exhibits substantial leakage current and fails to function effectively.
Voltages of the trap filling limit (VTFL) of Device 1 and Device 2 are 1.19 V and 2.59 V.The average thickness of films is ~2.00 × 10 -4 cm measured by the step profiler.The dielectric constant (ε0ε) is 1.63 × 10 -11 F cm -1 .The trap density (Nt) of films can be calculated in the following Eq.( 5) where L is the thickness of the film.The hole Nt of the FAPbI3 (w 10%mol NGAI) film is 6.03 × 10 15 and the electron Nt of the FAPbI3 (w 10%mol NGAI) film is 1.30 × 10 16 .The mobility of FAPbI3 (w 10%mol NGAI) film can also be analyzed by Mott-Gurney law (Eq.( 6)).
According to the carrier transport behavior and the trap density states of the FAPbI3 (w 10%mol NGAI) film, the gain of the photodetector is induced by the traps of electrons at the surface of perovskite after adding NGAI, which leads to the hole injection (Supplementary Fig. 7d).The photodetector also performs the noise current of ~10 -13 A Hz -0.5 and shown in the Supplementary Fig. 7e.The detectivity (D * ) of photodetector is ~10 13 Jones (Supplementary Fig. 7f) at -1.0 bias, which is calculated by the following Eq.(7).
where A is the effective area of the photodetector.B is the bandwidth.Reconstructing the spectra of two adjacent wavelengths ranging from 590 nm to 610 nm allowed us to evaluate the resolution of the computational spectrometer.The photodetector exhibits the ability to discriminate between wavelengths of 597.5 nm and 602.3 nm, with a resolution of ~4.7 nm (Supplementary Fig. 8a).During the learning process, each step of wavelength is 2 nm.The FWHM of the incident light is ~2 nm, which is calculated by the reciprocal linear dispersion of the instrument.The reference spectra of monochromatic light are also calculated by reciprocal linear dispersion in the following Eq.(8).The responsivity of the photodetector is changed by the irradiance of the incident light 2 .The variation in incident light depth is attributed to the differences in irradiance levels.Therefore, the reconstruction of spectra from arbitrary combinations of light intensity and wavelength can be achieved by establishing a model that relates the light intensity to the voltage-wavelengthresponsivity matrix.The responsivities of photodetectors at different voltages and wavelengths are presented in Supplementary Fig. 8c -8e, where the incident light irradiance is ~10 1 and ~10 -1 µW cm -2 , as referenced in Supplementary Fig. 8b.imaging.Nevertheless, this approach presents a promising avenue for research.In subsequent investigations, refinement in color imaging is anticipated through algorithmic optimization and enhanced information capture.The range of integration was classified for discussion and shown in Supplementary Fig. 12d.In the condition of long pixel, the range of integration can be divided into two segments (0 to α, 0 to  2 − ) where α is the angle between the line through the light source and the bottom center of the hemisphere and the line through the foot point of the light source and the bottom center of the hemisphere.In the condition of the short pixel, the range of integration needs to be classified for discussion.If  <  4

Supplementary
, the range of integration can be divided into two segments (0 to α, 0 to  The substrate was covered by a mask (Supplementary Fig. 13a) and deposited Cr by vacuum evaporation.The substrate with 8 pixels was obtained (Supplementary Fig. 13b).The hemispherical photodetector for the location was fabricated by depositing the active material onto the substrate step by step.Supplementary Fig. 13c shows the circuit diagram of the read-out system of the hemispherical photodetector for location.Supplementary Fig. 13d shows the printed circuit board (PCB) of the read-out system.Pixels were parallel connected while each pixel was connected

Fig. 3 |
The interaction between NGAI and PbI2.a, The TEM image of the NGAI-PbI2 complex, scale bar: 200 nm.b, The high-resolution transmission electron microscopy image of the NGAI-PbI2 complex.Inset is the FFT image of the NGAI-PbI2 complex, scale bar: 5 nm.c, The lattice plane (102) of the PbI2 crystal.d, The XRD spectra of films (NGAI, NGAI-PbI2, PbI2) fabricated by the spray-coating method.e, The lattice plane (100) of the NGAI crystal.f, The absorbance spectra of films fabricated by spray-coating.
in the polycrystalline films.The SEM images of FAPbI3 films with varying concentrations (0%mol ~ 30%mol) fabricated through spray-coating are presented in Supplementary Fig. 4e.With the amount of NGAI increased grain boundary of the FAPbI3 film broadened.The films tend to form bigger grains with the addition of a small amount of NGAI.Excess amounts of NGAI inhibit the growth of FAPbI3.We considered that the NGAI mainly exists in the grain boundary.Supplementary Fig. 4 | The interaction between NGAI and FAPbI3.a, The absorbance spectra of FAPbI3 (w 5%mol ~ 30%mol NGAI) films fabricated by spray-coating.b, The TEM image of FAPbI3 (w 50%mol NGAI), scale bar: 20 nm.c, d, The transient absorption spectrum of the FAPbI3 NGAI) film.e, The SEM images of FAPbI3 (0%mol ~ 30%mol NGAI) films fabricated by spray-coating method, scale bar: 2 μm.

7 |
photodetectors fabricated by spray-coating (FAPbI3 w 10%mol NGAI) and spin-coating (FAPbI3 linear dispersion.dg, ψ and F are the spacing of grating grooves, diffraction angle, and effective focal length of the system, respectively, and n is the diffraction order.

Fig. 8 | 1 )
The performance of the computational spectrometer.a, The spectra to evaluate the resolution of the computational spectrometer.Solid lines are the spectra after b, The 2D patterns generated by projector when m = 47, 48, 49, 50, 51, 52, 53, 54.c, The original imaging of the Rubik's cube by the single pixel imaging under different biases obtained from the single pixel hemispherical photodetector.d, Photograph of the Rubik's cube.Supplementary Fig. 10a is the confusion matrix generated from the training process.Each sample has 9 elements from V1 to V9 as the eigenvector.The main algorithm of the color classification is the K-nearest neighbor (KNN).The confusion matrix plot is to understand how the currently selected classifier performed in each class.For each color, we select 121 pixels (11 × 11) as the training group.The size of the image after cutting the background is 146 × 151.The accuracy of the prediction in the select group of the machine learning model is 100%.The ROC curve shows the true positive rate (TPR) versus the false positive rate (FPR) for different thresholds of classification scores, computed by the currently selected classifier.Supplementary Fig.10bshows the ROC curve of the "Red" class.

𝜋 4 − 4 ,
), similar to the long pixel.If  ≥  the range of integration is from  −  4 to α.The total effective incident flux of the arcs with the parameters (h and d) changing is normalized into the same scale and shown in Supplementary Fig. 12e and Supplementary Fig. 12f.The variation tendency of the long pixel and the short pixel is different.Thus, the design of different shapes of pixels can improve the accuracy of location tracking in theory.Supplementary Fig. 12 | The analysis of effective incident flux intensity of different pixels.a, The schematic diagram to analyze the effective incident flux distribution (vertical incident light).b, The schematic diagram to analyze the effective incident flux distribution (arbitrary position incident light).c, The schematic diagram to analyze the effective incident flux distribution (on the planar surface).d, The schematic diagram to analyze the effective incident flux intensity in different conditions.e, The total effective incident flux (φ) of 1/4 circle with different horizontal distance (d) and height (h).f, The total effective incident flux (φ) of 1/8 circle with different horizontal distance (d) and height (h).

Ф
(arb.units) with a resistance of 1 MΩ in series.The signals collected by the computer are the voltages of the resistance and are read out by NI9205.The optical photograph of the hemispherical photodetector and the read-out system are shown in Supplementary Fig. 13e.The bottom electrodes (x1, x2, …, x8) were connected positive pole of the system by simple welding.The top electrode was lead out with a copper wire and connected to the negative electrode of the system.