Stable perovskite single-crystal X-ray imaging detectors with single-photon sensitivity

A major thrust of medical X-ray imaging is to minimize the X-ray dose acquired by the patient, down to single-photon sensitivity. Such characteristics have been demonstrated with only a few direct-detection semiconductor materials such as CdTe and Si; nonetheless, their industrial deployment in medical diagnostics is still impeded by elaborate and costly fabrication processes. Hybrid lead halide perovskites can be a viable alternative owing to their facile solution growth. However, hybrid perovskites are unstable under high-field biasing in X-ray detectors, owing to structural lability and mixed electronic–ionic conductivity. Here we show that both single-photon-counting and long-term stable performance of perovskite X-ray detectors are attained in the photovoltaic mode of operation at zero-voltage bias, employing thick and uniform methylammonium lead iodide single-crystal films (up to 300 µm) and solution directly grown on hole-transporting electrodes. The operational device stability exceeded one year. Detection efficiency of 88% and noise-equivalent dose of 90 pGyair are obtained with 18 keV X-rays, allowing single-photon-sensitive, low-dose and energy-resolved X-ray imaging. Array detectors demonstrate high spatial resolution up to 11 lp mm−1. These findings pave the path for the implementation of hybrid perovskites in low-cost, low-dose commercial detector arrays for X-ray imaging. We show perovskite X-ray detection at zero-voltage bias with operational device stability exceeding one year. Detection efficiency of 88% and noise-equivalent dose of 90 pGyair are obtained with 18 keV X-rays, allowing single-photon-sensitive, low-dose and energy-resolved X-ray imaging.

A major thrust of medical X-ray imaging is to minimize the X-ray dose acquired by the patient, down to single-photon sensitivity. Such characteristics have been demonstrated with only a few direct-detection semiconductor materials such as CdTe and Si; nonetheless, their industrial deployment in medical diagnostics is still impeded by elaborate and costly fabrication processes. Hybrid lead halide perovskites can be a viable alternative owing to their facile solution growth. However, hybrid perovskites are unstable under high-field biasing in X-ray detectors, owing to structural lability and mixed electronic-ionic conductivity.
Here we show that both single-photon-counting and long-term stable performance of perovskite X-ray detectors are attained in the photovoltaic mode of operation at zero-voltage bias, employing thick and uniform methylammonium lead iodide single-crystal films (up to 300 µm) and solution directly grown on hole-transporting electrodes. The operational device stability exceeded one year. Detection efficiency of 88% and noise-equivalent dose of 90 pGy air are obtained with 18 keV X-rays, allowing single-photon-sensitive, low-dose and energy-resolved X-ray imaging. Array detectors demonstrate high spatial resolution up to 11 lp mm −1 . These findings pave the path for the implementation of hybrid perovskites in low-cost, low-dose commercial detector arrays for X-ray imaging.
For a semiconductor to serve as a direct X-ray detector capable of single-photon counting, several requirements must be fulfilled: high resistivity (≤10 10 |Ω| cm) and hence sufficiently low noise levels for resolving charges generated by a single photon, a high carrier mobilitylifetime (µτ) product for the efficient collection of photon-generated carriers and the absorption of (nearly) all X-ray photons-the latter scales with the thickness and average atomic number (Z) of the constituent elements. Very few high-Z semiconductors were proposed to fulfil these requirements at room temperature [1][2][3][4][5][6][7] and thus far, only costly, ultrapure CdTe and CdZnTe single crystals, usually grown from Article https://doi.org/10.1038/s41566-023-01207-y

MAPbI 3 SC XPV devices
For obtaining a few-hundred-micrometre-thick MAPbI 3 SC film, a space-confined inverse-temperature crystallization method was adopted and adjusted from other work 33,37 . The perovskite films were grown on indium tin oxide (ITO) substrates coated with poly(triaryl) amine (PTAA) as a hole-transporting layer, followed by the thermal evaporation of fullerene (C 60 )/bathocuproine (BCP) layer as the electron-transporting layer and Cu electrode, completing the XPV device ( Fig. 1a-c). Contacts with asymmetric work-function potentials for establishing an internal electrical field and good charge selectivity of the transport layers are paramount for the desired XPV operation mode. Nevertheless, the as-obtained thick XPV devices had poor detector performance, which we attribute to the effect of persistent, residual solvates that may form with the specific solvent used (γ-butyrolactone) (ref. 38), trapped in the interfaces between the SC and PTAA layer ( Supplementary Fig. 1a). The issue was satisfactorily mitigated with the extensive post-drying of crystals at room temperature in a nitrogen-filled drybox ( Supplementary Fig. 1b). Supplementary  Fig. 1c illustrates the improvement in X-ray detection performance (expressed in normalized signal-to-noise ratio (SNR) under the same dose rate) with post-conditioning time, which is correlated with the increase in shunt resistance and rise in X-ray photocurrent. The SNR value reaches a saturated value typically in around one month.

Figures of merit of perovskite X-ray detectors
The performance characteristics that are most relevant, practical and can objectively compare perovskite detectors across laboratories need to be discussed first. X-ray sensitivity is by far the most commonplace reported figure of merit in the rapidly growing area of perovskite X-ray detectors, owing to the simplicity of its measurement. Higher sensitivities are achieved by device biasing at higher electrical fields (Extended Data Fig. 2a) and hence at the cost of excessive noise and dramatic degradation in SNR ( Supplementary Fig. 2). Unlike conventional semiconductors such as CdTe, lead halide perovskites are mixed electronic-ionic conductors 39 , further magnifying the electronic and electrochemical instabilities at high bias. Furthermore, emphasizing sensitivity may erroneously motivate research efforts towards photoconductors, as in the latter, the sensitivity can be amplified via photoconductive gain 40 . The latter, however, also increases the noise levels, response time and device instability. This approach is of somewhat limited utility for materials with poor charge transport characteristics (namely, amorphous Se, quantum dots and so on) and, in the case of perovskites, would require imparting imbalanced charge transport by, for instance, the intentional deterioration of material by introducing charge traps. Another characteristic, commonly used for perovskite detectors, is the detection limit of the dose rate 14,19,41 , which remains a highly ambiguous parameter as it scales with the integration time (Extended Data Fig. 2b). As the resulting detection limit is lower for a higher accumulated dose, the utility of the reported detection limit values is higher when the integration times are specified ( Supplementary Notes 1-3).
An overarching objective, foremost in medical imaging, is to attain the desired imaging quality and minimizing the acquired radiation dose. In this regard, the MAPbI 3 SC detector operated in the XPV mode (0 V bias) favourably compares with the state-of-the-art commercial gadolinium oxysulfide (GOS) scintillator detectors in terms of image contrast and image noise, especially when decreasing the dose to as low as 8 nGy air (Fig. 1d and Supplementary Figs. 3 and 4). Quantitatively, the image quality is determined by the SNR, which-for the ideal detector-has the fundamental limit given by Poissonian statistics, that is, the photon shot noise. Denoting n ph as the mean number of X-ray photons incident on the detector, the limit for SNR is SNR ideal = √ n ph (ref. 42). Consequently, a well-thought figure of merit is the detective quantum efficiency (DQE) defined via the SNR analysis as a melt by high-pressure Bridgman or Czochralski methods, have been commercially deployed 8,9 . Lead halide perovskite semiconductors (general formula of APbX 3 , where A is a cation, either organic methylammonium (MA + ) or formamidinium, or inorganic Cs + ; and X is an anion of I, Br or Cl halogen) are the most intensely studied class of contender high-Z materials for high-energy photon detection 4,10-24 . Excellent electronic characteristics are commonplace with both inexpensive solution growth techniques (for all A cations) 4,17,24 and melt growth techniques (CsPbBr 3 or CsPbCl 3 ) 21,25 , often using the conventional purity of precursors. Calculated X-ray absorption coefficients are even a few-fold higher compared with CdTe for soft X-rays (Extended Data Fig. 1).
We find that the major question, pertaining to the eventual utility of perovskites as commercial X-ray detectors, is the demonstration of simultaneously stable operation and near-ideal detection efficiency (DE) of such devices. Even for high-Z and high-µτ materials such as CdTe and APbI 3 perovskites, the required collection of photocarriers requires high voltages of hundreds to thousands of volts applied across material thicknesses ranging from millimetres to centimetres (depending on the detected photon energies, which range from tens to hundreds of kiloelectronvolts). The long-term operational stability is mainly limited by the stability of the semiconductor and interfaces under such high electric bias. The issue is especially acute for perovskites, as they are mixed electronic-ionic conductors, in which high dark currents and unstable performance often arise from the ion migration or electromigration of the contact materials, as well as electrochemical damage to the active material [26][27][28][29] . In recent years, progress has been achieved in improving the stability of all-inorganic perovskites 26 . Yet, the instability issue is perpetrating for hybrid perovskites, which are particularly attractive for their versatile and facile solution synthesis and device integration.
We consider the problem of the high-bias stability of perovskites as inherently insurmountable, necessitating the research into low-voltage device concepts. In this work, we focus on using a photovoltaic device, where the only electric field is the one originating from the work-function asymmetry of the used electrical contacts. This notion is supported by the recent advancements in the long-term operational stability of perovskite solar cells 30 . Considering the high calculated value of the soft X-ray linear absorption coefficient of MAPbI 3 (Extended Data Fig. 1), taking the highest reported µτ values for this material (up to 10 −2 cm 2 V −1 ), and a typical build-in potential of 1 V, we estimate that the requirement of simultaneously high charge-collection efficiency (CCE) close to unity along with near-complete X-ray absorption (10-30 keV) can be met by an active layer having a thickness in the range of 50-500 µm. The practical embodiment of such an X-ray photovoltaic (XPV) device is essentially a highly efficient perovskite solar cell with a single-crystalline (SC) absorption layer of several hundred micrometres. The utilization of polycrystalline thick perovskite layers is unacceptable owing to the orders of magnitude lower µτ values due to carrier scattering at the grain boundaries and defects 31,32 , which proportionally compromises the CCE and necessitates higher applied bias.
Motivated by the recent advances in the solution growth of highly efficient SC perovskite solar cells (∼20 µm (refs. 33-36)), we sought to examine several-hundred-micrometre-thick perovskite MAPbI 3 SC XPV devices (Fig. 1a,b). Such an order of magnitude thicker SC layer was directly grown on a conductive substrate by a low-temperature solution method as a single-pixel device and as a two-dimensional (2D) panel and one-dimensional (linear) arrays with high spatial resolution. Although operating in the XPV mode (that is, zero applied bias), the devices exhibit a noise-equivalent dose below one X-ray photon and DE close to unity. Poissonian-photon-statistics-limited X-ray imaging was thus demonstrated, down to extremely low doses of tens of nanogray in air (nGy air ). These characteristics are retained for at least a year. Furthermore, energy-resolved X-ray imaging could be demonstrated, discriminating between materials of different compositions, which are otherwise indistinguishable in contrast-only X-ray transmission imaging.
ideal as a function of incident dose D (ref. 43). The DQE is commonly used for benchmarking commercial X-ray imagers, regardless of the detector technology (that is, scintillating or direct detection). To represent the DQE as a function of D (∝n ph ), we propose the following model for a single-pixel device (spatial frequency, ν = 0): where NED is the noise-equivalent dose 44 and DE is the detection efficiency (Supplementary Note 1 provides the derivation of equation (1)). DE is the fraction of detected photons versus total incoming photons, which is given by an integral for a product of the X-ray attenuation efficiency and CCE over the detector thickness. The NED is such a dose D(n ph ) for which the photon shot noise is equal to the intrinsic electric detector noise, the latter comprising thermal noise, charge-carrier shot noise and so on. In the ideal case, a detector should have a DE value of unity and NED much less than the dose of a single photon and hence a dose-independent DQE value approaching unity. Thus, an X-ray dose would be minimized to the theoretical value required to reach the desired SNR, as the latter is only limited by Poissonian photon statistics. Figure 1e compares the DQE versus D values for a commercial direct conversion detector (amorphous Se (ref. 15)) and scintillator (GOS, obtained via SNR analysis of the images), and MAPbI 3 SC operated in the XPV mode (calculated according to equation (1), using the measured values of NED = 90 pGy air and DE = 88%). The DQE values for MAPbI 3 SC were further confirmed by an SNR analysis of the X-ray images at doses of 8 and 32 nGy air (Fig. 1d, Supplementary Fig. 4 and Methods). Noteworthily, a dose of 8 nGy air is around three orders of magnitude lower than the one received by a patient during typical X-ray imaging 45 or those typically used for X-ray imaging with perovskites 13,20 . With NED being smaller than one photon, the noise levels need not be further improved for minimizing the accumulated dose for achieving the same X-ray imaging quality.
Owing to the zero-bias operation, these XPV devices retain their characteristics for at least one and a half year (in air, without encapsulation), with the projected device half-life (time that corresponds to a 50% drop in the normalized SNR) of several years. On the contrary, complete degradation occurs within a few hours at high applied electric fields (Fig. 1f). The operational stability of XPV devices, thus, reaches the typical chemical shelf-life of MAPbI 3 SC, despite the relatively high dose accumulated during these tests (6 mGy, equivalent to ~500 conventional X-ray medical scans). Additionally, the radiation hardness was tested as an X-ray photocurrent stability under the dose rate of 1 Gy air min -1 for 14 h, resulting in an accumulated high dose of 850 Gy air (equivalent to 80,000 computed tomography scans of the chest), without any notable deterioration in the photocurrent (Supplementary Fig. 5).
Using the advantages of solution-grown synthesis, MAPbI 3 SC XPV was directly fabricated on conductive substrates patterned in the form of linear and 2D panel array detectors ( Fig. 1g-i, Supplementary Fig. 6 and Extended Data Fig. 3). To estimate the spatial resolution, modulation transfer function (MTF) dependence on the spatial resolution was evaluated and compared with previously reported polycrystalline MAPbI 3 device and commercial detectors (Fig. 1g). The MTF reaches 20% for the spatial frequency of 11 lp mm −1 for the linear detector array with a 40 µm pixel pitch, which is superior to the state-of-the-art commercial detector materials, and is so far the highest spatial resolution for perovskite X-ray direct detectors, to the best of our knowledge. This is confirmed with the X-ray intensity profile of 100 µm slits with a spatial frequency of 5 lp mm −1 , where the profile obtained with MAPbI 3 is evidently sharper than that obtained with the GOS scintillator (Fig. 1h). Additionally, the high-resolution X-ray image is obtained, where features with a size down to 100 µm are effectively resolvable ( Supplementary Fig. 7). MTF dependencies on a spatial frequency normalized on the pixel pitch (in units of Nyquist frequency fraction) are shown in Extended Data Fig. 4, where a notable divergence from the theoretical prediction is evident for the 40-µm-pitch MAPbI 3 XPV device. This indicates that the spatial resolution is approaching the limit given by the size of the X-ray-generated charge cloud, which is evaluated in the next section. Based on the estimated MTF values and as per another work 46 , DQE as a function of spatial frequency is evaluated (Extended Data Fig. 5), emphasizing that the DQE values are higher than 50% for spatial frequencies up to 5 lp mm −1 .
In the following, we further detail the rationale and experimental path to attain such high X-ray detection characteristics of the MAPbI 3 SC detector.

DE and charge transport properties
The highest DE values are expected in the SC thickness range of 50-220 µm, where the experimentally obtained CCE and X-ray attenuation efficiency, computed from the database values 47 , are high (Extended Data Fig. 6). High efficiency of photovoltaic devices with a thickness of up to 220 µm is additionally verified with the J-V characteristic under one-sun illumination ( Supplementary Fig. 8), showing only a minor change in the short-circuit current and open-circuit voltage. Comparing the simulated 48 and measured J-V characteristics (Supplementary Fig. 8), the surface trap density of the fabricated XPV MAPbI 3 SC devices is evaluated to be in the range of 10 16 -10 17 cm −3 . We also note that a further decrease in the surface defect density does not evidently increase the short-circuit current and thus the CCE, but moderately affects the open-circuit voltage and hence is more relevant for solar cells 34 . For the simplest case, namely, a single kind of charge carrier originating from the absorption of photons by the device surface, CCE can be expressed with the Hecht equation 49 as where d is the drift distance (equal to the device thickness) of a charge to the corresponding electrode, L d = µτE is the charge-carrier drift length, E is the electrical field (E = U/d and U is the electrical potential). Another work 50 developed a model for the CCE (and DE) under X-ray exposure, where the Hecht equation is modified to account for the penetration depth of X-rays and hence a volumetric distribution of generated charges, as well as the asymmetry of transport properties for electrons and holes. We first use this model to assess the expected performances of XPV devices with the given charge transport properties and in relation to the SC thickness and then compare with the experimental CCE and DE values. In the XPV mode, the electrical-field strength E is fully defined by the build-in potential U, that is, the open-circuit voltage V oc = 1.1 V under one-sun illumination conditions (Fig. 2a), which was additionally confirmed with the photocurrent dependence on the bias voltage under X-ray irradiation (Extended Data Fig. 7a). The estimation of µτ values is, however, somewhat ambiguous. Their lower limit (µ e τ min = 6 × 10 −4 cm 2 V −1 and µ h τ min = 2 × 10 −4 cm 2 V −1 ) was estimated by separately measuring the mobility of each carrier type using the time-of-flight (ToF) technique 51 (Fig. 2b,c and Supplementary Fig. 9) and multiplying these values by their mean lifetime estimated from the transient photocurrent response (τ ≥ 6 µs; Supplementary Fig. 10). The measured charge carriers' mobility (91 cm 2 V −1 s −1 for electrons and 31 cm 2 V −1 s −1 for holes) is an order of magnitude higher than the typical values reported in polycrystalline perovskite thin films 12 , owing to the lower trap density. The upper µτ limit for the majority carrier (µ e τ max = 3 × 10 −3 cm 2 V −1 ) was directly obtained as a fitting parameter (in the Hecht equation) of photocurrent versus bias voltage dependence (Extended Data Fig. 7b). For the devices illuminated from the side of the hole-collecting electrode, µ e τ values set the CCE dependence on the detector thickness, being in good agreement with the experiment Article https://doi.org/10.1038/s41566-023-01207-y ( Supplementary Fig. 11a,b). Then, the thickness-dependent DE is calculated for both limits, combining photon-energy-dependent X-ray attenuation efficiency and the CCE, as well as accounting for ambipolar charge transport. For µ h τ max , we take a value of 30% of µ e τ max , considering the µ e /µ h ratio measured using the ToF. The calculated DE values are in good agreement with the experimental data (Fig. 2d). In particular, the DE of the 220-µm-thick device is mostly limited by X-ray attenuation efficiency, and reaches 80% for 22 keV X-ray radiation, whereas at thicknesses larger than 220 µm, the DE becomes limited by the CCE. The charge drift length (L d = µτV oc d −1 ) remains very high even for 200-µm-thick crystals ( Supplementary Fig. 11a), allowing to simultaneously reach a CCE value of ~100% and high X-ray absorption (80% at 40 keV). The theoretical limit of the spatial resolution is mainly defined by the diffusive spreading of the X-ray-generated charge cloud in devices with a moderate electric field (XPV mode). The latter is evaluated as the charge-carrier diffusion length L dif = √μτkTe −1 , where k is the Boltzmann constant, T is the temperature and e is the elementary charge. For electrons, the diffusion length is equal to ~40 µm, agreeing well with the dependence of spatial resolution on pixel density (Supplementary Fig. 12a), which becomes nonlinear at a density greater than 10 pixels per mm (that is, a pixel pitch of 100 µm). Consequently, MTF growth becomes slower than expected with a further decrease in pitch size (Supplementary Fig. 12b).

Assessing noise and DQE
Although DE is sufficient to describe the detector signal, NED is the comprehensive descriptor for the noise of a detector. To estimate the NED, the X-ray dose-rate-dependent total noise (N T ) of the MAPbI 3 SC detector was obtained as the noise-current spectral density ( Fig. 2e and Extended Data Fig. 8). Also, N T 2 is expressed in photon-equivalent units, where a single-photon equivalent is the root mean square (r.m.s.) of the noise charge equal to the charge generated by one photon in time window t (equal to 500 µs, given by the amplifier bandwidth of 1 kHz; Fig. 2e, right). In Fig. 2e, the dose rate is recalculated to an equivalent photon quantity within t. The dependence of N T 2 versus n ph is a linear The red line in Fig. 2e shows the theoretical limit for the sum of photon shot noise and thermal noise. A fit of the experimental data with equation (3) gives DE = 0.93, in good agreement with the DE estimated from the CCE and X-ray attenuation efficiency (Fig. 2d). The experimental detector noise exceeds the fundamental lowest limit by only 30%, which is given by the thermal noise 52 , calculated based on the device resistance. Such a low detector noise emphasizes the absence of dark-current-induced electron shot noise and the negligible effects of ionic diffusivity in the XPV mode. NED was then calculated as the offset/slope ratio in equation (3) (ref. 44) and amounted to ~0.4 photon equivalents at 18 keV, which corresponds to a dose of ~90 pGy air for a 0.8 mm 2 detector area.
NED versus X-ray energy plot allows the estimation of the energy onset for the photon-counting regime (for instance, ~7 keV for 110-and 220-µm-thick devices; Fig. 2f). At lower photon energies (with higher flux), the charge-integration mode is used instead and DQE begins to decline with a further increase in photon energies as the X-ray attenuation efficiency drops (Fig. 2f, 220-µm-thick device; Supplementary Fig. 13, 110-µm-thick device; Supplementary Note 4 provides details of the calculation of NED and DQE dependence on energy), defining the ranges of ~10-25 keV (110-µm-thick device) and ~10-50 keV (220-µm-thick device) as optimal for X-ray imaging at low doses and mostly limited by the photon shot noise (Fig. 1d and Supplementary  Fig. 4). In this energy range, the DQE reaches 60%-90% on absorption of just a dozen photons by the device (within the integration time window; Supplementary Fig. 14a, 110-µm-thick device; Supplementary Fig. 14b, 220-µm-thick device)

X-ray energy-resolved imaging
Single-photon detection capability directly stems from the NED being below one photon equivalent; examples of the obtained single-photon signal traces with different types of preamplifier are provided in Fig. 3a and Supplementary Fig. 15. The maximum counting rate reaches 10 7 photons s −1 mm −2 at 100 µm pitch size ( Supplementary  Fig. 16), which is suitable for application in mammography. A further decrease in pitch size below the X-ray photon-generated charge cloud size (~100 µm for our case) will hinder the photon-counting efficiency and X-ray energy resolution due to charge sharing between the neighbouring pixels. Low-noise and high-charge-collection characteristics allow single-photon counting from 241 Am source (60 keV)   Fig. 3 | X-ray energy-resolved imaging. a, γ-ray single-photon counting. An event from 241 Am radiation source (E γ = 60 keV) was recorded with a MAPbI 3 SC (thickness, 110 µm; 0 V bias). The black curve is a trace from the chargeintegrating preamplifier, and the red curve is the corresponding trace from the shaping amplifier. b, Energy-resolved spectrum of 60 keV photons from a radioactive 241 Am source. c, The imaged object is a rectangle comprising two complementary patterns: 5-mm-thick ETH letters made of Nd 2 O 3 powder surrounded by a 2-mm-thick steel frame. d, Attenuation coefficients versus X-ray photon energy for Fe (black curve) and Nd 2 O 3 (green curve) shown on top of an example of 50 kV p energy spectrum transmitted through the Nd part of the object recorded by the MAPbI 3 SC detector. The spectrum was binned into low-energy (blue) and high-energy (red) channels, with a border that corresponds to the characteristic K line of Nd. e, Energy-resolved X-ray imaging of the object from c under 50 kV p X-ray irradiation with the MAPbI 3 SC detector, where the colours denote the transmittance for the corresponding two energy channels from d. f, Transmittance of low-energy (blue) and high-energy (red) channels along the white dashed line in e.
Article https://doi.org/10.1038/s41566-023-01207-y with an energy resolution of ~34% (Fig. 3b). Although the obtained energy resolution is not suitable for applications in high-resolution γ-spectroscopy, it is feasible for energy-discriminated X-ray spectral imaging, the so-called X-ray dual-colour imaging 53 at moderate count rates, reaching limits required by digital mammography. As a showcase, we used a several-millimetre-thick rectangular object consisting of two complementary 'ETH' patterns made of two different materials with different X-ray attenuation versus X-ray energy dependencies (Fe and Nd 2 O 3 ; Fig. 3c). Specifically, compared with Fe, the X-ray attenuation coefficient of Nd is much lower than 43 keV and much higher above this value (due to its K atomic shell; Fig. 3d). The thicknesses of each pattern were adjusted for attaining minimal overall X-ray transmission contrast; the letters are then somewhat readable only due to X-ray shadowing when imaging at a non-orthogonal angle to the X-ray tube ( Supplementary Fig. 17). One can readily distinguish between the two materials and obtain a high-contrast image when recording the images using a low-energy channel (more attenuated by Fe) or high-energy channel (more suppressed by Nd), as indicated by the red and blue regions, respectively (Fig. 3e,f).

Discussion
In conclusion, MAPbI 3 SC X-ray detectors operated in the photovoltaic mode are shown to exhibit long-term stable and high X-ray detection performance in the soft X-ray range (20-50 keV), with DQE of ~87% at a low dose of 8 nGy air , NED of ~90 pGy air and DE of up to 88% at a spatial resolution of 11 lp mm −1 (corresponding to MTF = 20%). The compelling aspects of the hybrid perovskite SC XPV technology are summarized in Extended Data Table 1. A comparison with existing radiation detection materials in terms of basic materials properties and state-of-the-art device characteristics is shown in Supplementary Table 1. Our findings attest to the suitability of hybrid lead halide perovskites-when operated in the photovoltaic mode-as a practical low-cost detector technology for medical X-ray imaging such as mammography and radiography, where high SNR at a low dose is crucial and hence motivate future work on the commercial implementation of perovskite-based XPV array detectors.

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Growth of MAPbI 3 SC
The crystal growth is modified from the previous reports 33,34 . Briefly, 1.55 M of methylammonium iodide and lead (ii) iodide were dissolved in γ-butyrolactone at 60 °C by stirring overnight. Then, 50-750 µl of the solution was placed on a prepared substrate with a spacer (thickness, 20-300 µm) preheated to the solution temperature and enclosed by another PTAA-coated substrate. To induce nucleation and to promote growth, the hotplate was gradually heated to 130 °C at a rate of 2 °C h -1 . After the crystallization was finished, the substrates were separated and the remnant solution was quickly cleaned with Kimwipes. The substrates were allowed to slowly cool to room temperature on the hotplate to ensure good electrical and mechanical contact between the substrate and thin SCs. All the procedures other than substrate cleaning were carried out in a nitrogen atmosphere.

MAPbI 3 SC growth on patterned conductive substrates
Substrates, patterned in the form of linear or 2D pixel arrays, were fabricated by photolithography from a fully covered ITO substrate. The ITO substrates (Zhuhai Kaivo Optoelectronic Technology) were sequentially cleaned with anisole, isopropanol and oxygen plasma for 3, 3 and 2 min, respectively. Then, photoresist AZ1518 was spin coated on a substrate at 500 rpm for 5 s and 5,000 rpm for 60 s, followed by baking at 115 °C for 2 min on a hotplate. Next, patterns were written into the samples by exposure to 375 nm ultraviolet light using direct laser writing (Heidelberg Instruments, DWL66+) and development in AZ400K:H 2 O (1:4) for 2 min. The samples were baked at 120 °C for another 4 min before being ashed by O 2 plasma for 1 min. Finally, the patterns were etched onto the ITO film (100 nm thick) by wet etching with HCl (37%) for 6 min. For MAPbI 3 SC growth on patterned substrates, two patterned substrates were analogously prepared to continuous ITO substrates. Briefly, the patterned substrates were coated with PTAA and the perovskite solution was enclosed by two PTAA-coated patterned substrates. A 100 µm spacer was used for crystal growth on the patterned substrates. To induce nucleation and to promote growth, the hotplate was gradually heated to 130 °C at a rate of 2 °C h -1 . Only the crystals grown on the pixelated area were selected for further electrode deposition and characterization. Three types of device were fabricated (Fig. 1g (inset), Fig. 1i and Extended Data Fig. 3) at different pixel pitch sizes (40, 120 and 500 µm) and contact configuration (one and two dimensions). A total of 14 array devices were fabricated. Common electrode contact deposition was done similar to the single-pixel device, as described below.

Device fabrication
C 60 (20 nm) and BCP (3 nm) were thermally evaporated without an evaporation mask at a rate of 0.1 Å s -1 on top of the crystals. Then, Kapton tapes were used to form an evaporation mask for Cu electrode (thickness, 80 nm) on the edge of the SCs to avoid short-circuiting. When not specifically mentioned, all further described measurements were conducted with MAPbI 3 SC XPV devices with the electrode structure shown in Fig. 1c.

Device fabrication for ToF measurement
First, the ITO substrates were treated with an OTS-based self-assembled monolayer and ensured that the surface was insulating and hydrophobic. Then, 1 mM OTS solution bath in isopropanol was prepared and the ITO substrates were dipped inside for 10 min. Later, the substrates were washed with fresh isopropanol to remove the excess absorbed OTS.
The perovskite single crystals were grown on the self-assembledmonolayer-treated substrates using the same crystallization technique to fabricate the XPV devices. After crystal growth, the devices are completed with Cu evaporation.
CCE was estimated to be equivalent to the internal quantum efficiency (considering the corresponding travel distance of charge carriers), measured using a QEX10 spectral response measurement system (PV Measurements), calibrated against a reference silicon photodiode.
Scanning electron microscopy images were obtained using a Teneo VS instrument (Thermo Fisher Scientific). The thicknesses of the crystals were measured by using a profilometer (KLA-Tencor P-7 Stylus).
The ToF method was used for the measurement of the drift velocity of photoexcited charge carriers under an applied electric field. The ToF experiment was performed in the differential mode, where the total number of photoexcited charge carriers is maintained sufficiently below the total charge on the electrodes of SC and the RC time constant of the ToF apparatus is below the transit time of the charge carriers. Photoexcitation is applied through the ITO glass substrate with a diode laser from Becker & Hickl (model BDL-488-SMN; wavelength, 488 nm; pulse duration, about 40 ps). To prevent field-induced polarization (that is, accumulation of ions at the electrodes), the bias is applied as a pulse train of alternating polarity from ±20 to ±150 V at a frequency of 150 Hz from an HP 8116A function generator via Falco Systems WMA-300 high-voltage amplifier. Drift time τ is inversely proportional to drift mobility µ and is given by µ = d 2 /(τV), where d is the drift distance, τ is the drift time and V is the applied bias.

Photoresponse
For evaluating the mobility-lifetime product µτ, a current versus voltage measurement was obtained with the symmetrical (both contacts are Cu) laterally contacted MAPbI 3 SC under modulated light from a light-emitting diode with a wavelength of 450 nm. The sample was biased by a Keithley 236 source-measure unit, whereas the photoinduced current was restored by a lock-in amplifier (SR830, Stanford Research).

Lifetime measurements with transient photocurrent
The transient photocurrent lifetime measurements were performed with the symmetrical (both contacts are Cu) laterally contacted MAPbI 3 SC under pulsed (20-100 µs long; wavelength, 450 nm) light-emitting diode illumination. The lifetime was extracted from the exponential fit of the signal decay 55 .

X-ray characterization
X-ray attenuation is calculated based on the NIST open database 47 . All the X-ray irradiation experiments (except the radiation hardness test) were performed using the X-ray tube from Amptek (model Mini-X, with a Ag target). The radiation dose rate measurements are performed with a PM1621A dosimeter from Polimaster. Sensitivity measurements (Extended Data Fig. 2a) for MAPbI 3 and CdZnTe SCs are carried out with a Keithley 236 source-measure unit under X-ray irradiation at 40 kV p (peak kilovoltage or the maximum high voltage applied across an X-ray tube). For a.c. bias measurements, the symmetrical laterally contacted MAPbI 3 SC with Cu was used. The function generator HP 8116A with an a.c. voltage amplifier (Falco Systems WMA-300) was utilized for biasing, 40 kV p X-ray irradiation was modulated with a lead chopper wheel and the signal was restored on a lock-in amplifier (SR860, Stanford Article https://doi.org/10.1038/s41566-023-01207-y Research). SNR, detection limit, noise and stability measurements ( Supplementary Fig. 2, Extended Data Fig. 2b and Figs. 2e and 1f) were obtained with the samples connected via a low-noise current amplifier (Femto DLPCA-200) to a spectral network analyser (SR770, Stanford Research) under modulated 20 kV p X-ray irradiation, attenuated by a 3 mm glass filter. The noise-current spectral density dependence on the dose rate (Fig. 2e) was measured at a frequency of 960 Hz with the 110-µm-thick device with an area of 0.8 mm 2 and resistance of 6 MΩ. The experimental DQE values (Fig. 1e) were calculated according to where SNR detector was calculated as the ratio of the average count number at certain X-ray photon flux to the corresponding r.m.s. counts, whereas SNR ideal was taken as √ n ph , where photon number n ph was evaluated based on the count rate of a reference CdZnTe SC detector. The sensitivity values for DE evaluation (Fig. 2d) were estimated with modulated X-ray irradiation; the sample was connected via the low-noise current amplifier (Femto DLPCA-200) and the signal was restored by the lock-in amplifier (SR860). For the photon energies of 60 keV, we obtained DE as a ratio of the measured counting rate to the expected calculated value, taking into account the activity of the 241 Am source. The energy-resolved spectrum for the Am 241 source (activity, 0.4 MBq) was measured with a charge-sensitive preamplifier (A250CF CoolFET, Amptek) and digital-shaper amplifier based on Picoscope 2208B (for energy resolution measurements). For the maximal count rate estimation, a signal after a charge-sensitive preamplifier was treated with an analogue-shaper amplifier (Model 572, ORTEC). The shaping time was adjusted to 10 µs for the energy-resolved spectra measurements and 2 µs for the maximal counting rate experiments. After being processed with the shaper, the signal was fed to a digital multichannel analyser (MCA-8000D, Amptek). For the radiation hardness test ( Supplementary Fig. 5), the 220-µm-thick device was irradiated by an X-ray tube from General Electrics. The X-ray tube current and acceleration voltage were set to 43 mA and 40 kV p , respectively, resulting in a dose rate of 1 Gy air min -1 . The device X-ray photocurrent stability was monitored for 14 h of continuous irradiation.

X-ray imaging
The images shown in Figs. 1d and 3e and Supplementary Fig. 4 were acquired in the single-photon-counting mode, whereas an object was 2D scanned in the lateral direction towards the single-pixel detector. The detector was connected to a charge-sensitive preamplifier (A250CF CoolFET, Amptek) and analogue-shaper amplifier (Model 572, ORTEC). The shaping time was adjusted to 10 µs. After being processed with a shaper, the signal was fed to a digital multichannel analyser (MCA-8000D, Amptek). For multicolour imaging, two amplitude thresholds were set on the MCA to obtain two energy channels. Events with amplitude below the lowest threshold were discarded (attributed to noise), whereas when an amplitude falls into the region between the first and second threshold, such event was counted as low-energy photons. Events with amplitude higher than the second threshold were counted as high-energy photons. Threshold values were adjusted to obtain the highest contrast on the reference points of the imaged object, indicating that the threshold separating the high-and low-energy channels was set near 43 keV (Fig. 3d). The image shown in Fig. 3e was obtained under a 50 kV p X-ray irradiation filtered by a 500-µm-thick steel plate to cut the lower-energy part (the corresponding spectrum is presented in Supplementary Fig. 18a), the accumulated dose per pixel is about 10 µGy. The images shown in Fig. 1d and Supplementary Fig. 4 were obtained with 20 kV p X-ray irradiation filtered by 3 mm glass to get a quasi-monoenergetic spectrum with a mean energy of 18 keV (Supplementary Fig. 18b). The imaging experiments with pixelated array detectors ( Fig. 1h and Supplementary Fig. 7, linear; Supplementary Fig. 6, 2D pixels) were performed in the charge-integration mode, whereas the device was connected to a 64-channel application-specific integrated circuit, where each channel consists of a charge-integration amplifier connected to an analogue-digital converter. For the linear array, an object was 2D scanned in the lateral direction towards the detector: along the X axis, the line pitch of the step was 40 µm, whereas along the Y axis, it was 80 µm. The X-ray beam was collimated with a rectangular steel aperture (vertical width, 200 µm), having a profile shown as the dashed line in Fig. 1g, inset. The vertical spatial resolution of the MAPbI 3 X-ray image ( Supplementary Fig. 7, inset) is limited by the aperture size, whereas the horizontal spatial resolution is given by the intrinsic linear array properties. A commercial GOS scintillation detector, Remote RadEye HR, with a 20 µm pixel pitch was used in the imaging experiments as the reference. Images in the insets of Supplementary Fig. 7 were taken under 50 kV p X-ray irradiation under identical geometrical conditions with an accumulated dose of 193 µGy.

MTF
The MTF curve is calculated with a linear detector array of 40 µm pitch using the slanted-edge method. The edge spread function (ESF(x)) was derived from the slanted-edge profile, obtained from the one-dimensional X-ray image of a thin steel slice under 20 kV p X-ray irradiation. Afterwards, the MTF is calculated as where ν is the spatial frequency and x is the position of the lines. Similar to this formula, the line spread function (LSF(x)) is the derivative of ESF(x) and MTF(ν) is the Fourier transform (F) of LSF(x).

DQE
The DQE dependence on spatial frequency is calculated according to the following formula 46 : where DQE(ν = 0, D = 5 µGyair) = 87% is obtained according to the derived model, and NTF(ν) is the noise transfer function, which, for the photon-counting detector, is assumed 46 to be independent of spatial frequency and equal to 1.

Data availability
All relevant data supporting the findings of this study are available within the article and its Supplementary Information. Source data are provided with this paper.