Stable near-to-ideal performance of a solution-grown single-crystal perovskite X-ray detector

detect every single incoming fundamentally lowest limit by the photon statistics. near-to-ideal X-ray detection characteristics demonstrated few semiconductor materials Si 1 and CdTe 2 their industrial deployment medical diagnostics still elaborate and costly fabrication processes. Hybrid metal halide perovskites – newcomer semiconductors - – for a viable alternative 3,4,5 to their scalable, inexpensive, robust, and versatile solution growth and recent demonstrations of single gamma-photon counting under high applied bias voltages 6,7 . The major hurdle with perovskites as mixed electronic-ionic conductors, however, arises from the rapid material's degradation under high electric field 8,9,10,11 , thus far used in perovskite X-ray detectors 12 , 13 . Here we show that both near-to-ideal and long-term stable performance of perovskite X-ray detectors can be attained in the photovoltaic mode of operation at zero-voltage bias, employing thick and uniform methylammonium lead iodide (MAPbI 3 ) single crystal (SC) films (up to 300 µm), solution-grown directly on hole-transporting electrodes. The operational device stability is equivalent to the intrinsic chemical shelf lifetime of MAPbI 3 , being at least one year in the studied case. Detection efficiency of 88% and noise equivalent dose of 90 pGy air (lower than the dose of a single incident photon) are obtained with 18 keV X-rays, allowing for single-photon counting, as well as low-dose and energy-resolved X-ray imaging. These findings benchmark hybrid perovskites as practically suited materials for developing low-cost commercial detector arrays for X-ray imaging technologies. of flight (ToF) used for the measurement of the drift velocity of photo-excited charge carriers under an applied electric field. The ToF experiment was performed in the differential mode, where the total number of photo-excited charge carriers is kept 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. The photo-excitation is applied through the ITO glass substrate with a diode laser from Becker & Hickl (model BDL-488-SMN 488 nm, pulse duration about 40 ps,). To prevent a field-induced polarization ( i.e. accumulation the bias is applied as a pulse train of alternating polarity from ±20 to ±150V with a frequency of 150 Hz from HP 8116A function generator via FS WMA-300 high voltage amplifier. The drift-time τ is inversely proportional to the drift mobility µ and is given by µ=d 2 /(τ V). Where d is the drift distance, τ is the drift-time and V is the applied bias.

For a semiconductor to serve as an X-ray detector with characteristics approaching ideal performance, 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, high carrier mobility-lifetime (µτ) product for the efficient collection of photon-generated carriers, and absorption of (nearly) all X-ray photons-the latter scales with the thickness and the average atomic number (Z) of constituting elements. Very few high-Z semiconductors were proposed to fulfill these requirements at room temperature 6,14,15,16,17 and thus far, only costly, ultrapure CdTe and CdZnTe single crystals, usually grown from a melt by high-pressure Bridgman or by Czochralski methods, have been commercially deployed 18,19 . Lead halide perovskite semiconductors (general formula APbX3, 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 3,4,5,6,7,12,13,20,21,22,23,24,25,26,27,28 . Excellent electronic characteristics are commonplace with both inexpensive solution-growth techniques (for all A-cations) 6,7,28 and with the melt-growth (CsPbBr3 or CsPbCl3) 26,29 , often using conventional purity of precursors. Calculated X-ray absorption coefficients are even a few-fold higher compared to 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 characteristics of such devices.
Even for such high-Z and high-µτ materials as CdTe and APbI3 perovskites, the required collection of photocarriers requires high voltages of hundreds-to-thousands volts applied across mm-to-cm materials thicknesses (depending upon the detected photons energies, which range from tens to hundreds of keV). The longterm operational stability is limited mainly 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 8,9,10,11 .
We consider the problem of 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, wherein 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 MAPbI3 (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 one volt, 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 a 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 µm.
Utilization of polycrystalline thick perovskite layers is unacceptable owing to orders-of-magnitude lower µτvalues due to carrier scattering at the grain boundaries and defects 31,32 , which proportionally compromises the CCE values and necessitates higher applied bias.
Such an order-of-magnitude thicker SC layer was grown directly on a conductive substrate by a low-temperature solution method. While operating in the XPV mode (e.g. zero applied bias), the devices exhibit near-to-ideal performance, which includes noise-equivalent dose below one X-ray photon and detection efficiency close to unity. These characteristics are retained for at least a year. X-ray imaging at extremely low doses at the tens of nGyair level is obtained as well. Furthermore, energy-resolved X-ray imaging could be demonstrated, discriminating between materials of different compositions, which are otherwise indistinguishable in contrastonly X-ray transmission imaging.

MAPbI3 SC XPV devices.
For obtaining a few hundred micrometers thick MAPbI3 SC films, a space-confined inverse temperature crystallization method was adopted and adjusted from Ref 33,36 . 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 C60/bathocuproine (BCP) layers 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 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) 37 . The issue was satisfactorily mitigated with the extensive post-drying of crystals at room temperature in a nitrogen-filled drybox. Supplementary Fig. 1 illustrates the improvement of the 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 decrease of shunt conductivity and the rise of the X-ray photocurrent. SNR value reaches a saturated value typically in ca. one month. The scale bar is 50 µm. c, Energy band alignment and operation principle in XPV mode. d, X-ray sensitivity dependence on the electric field for different materials. e, SNR degradation with the applied external electric field for a MAPbI3 SC detector under constant X-ray irradiation. f, Decrease of DL and increase of SNR at longer integration times come at the cost of a high dose, for a MAPbI3 SC XPV detector under X-ray irradiation. g, h, X-ray imaging of stencil mask ( Supplementary Fig. 2) at doses of 8 nGyair (d) and 32 nGyair (e). Insets show imaging with the GOS scintillator detector. i, DQE dependencies on the dose. The solid black line and points represent, respectively, model and experimental data (calculated from g and h) for a MAPbI3 SC. Red points are experimental data for the GOS scintillator. Green points are amorphous Se data from Ref. 21 . Black open squares show calculated DQE for doses, at which X-ray imaging was previously demonstrated with MAPbI3 detectors 25,13 .

Figures-of-merit and ideality of perovskite X-ray detectors.
Performance characteristics that are most relevant practically and can objectively compare perovskite detectors across the laboratories need to be discussed first. Xray 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 and hence at the cost of excessive noise and dramatic degradation of the signal-to-noise ratio (Fig. 1d, e). Unlike conventional semiconductors such as CdTe, lead halide perovskites are mixed electronicionic conductors 38 , 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 39 . The latter, however, accordingly also increases the noise levels, response time and device instability. This approach is of somewhat limited utility for the materials with poor charge transport characteristics (i.e. a-Se, QDs, etc.) and, in the case of perovskites, would require imparting imbalanced charge transport by, for instance, intentional deterioration of the material by introducing charge traps.
Another characteristic, commonly used for perovskite detectors is the detection limit (DL) of the dose rate 24,20,40 , which remains a highly ambiguous parameter as it scales with the integration time (Fig. 1f). As the resulting DL is lower for a higher accumulated dose, the utility of reported DL values is higher when the integration times are specified (see details in Supplementary Notes 1-3). An overarching objective, foremost in medical imaging, is to attain the desired imaging performance at the lowest acquired radiation dose. In this regard, MAPbI3 SC detector operated in XPV-mode (0V-bias) compares favorably with the state-of-the-art commercial scintillator gadolinium oxysulfide (GOS) detectors in terms of image contrast and image noise, especially when decreasing the dose to as low as 8 nGyair (Fig. 1g, h). Quantitatively, the image quality is determined by the SNR, which for the ideal detector has the fundamental limit given by Poisson statistics -the photon shot noise. Denoting nph as the mean number of X-ray photons incident to the detector, the limit for SNR is SNR ideal = √ n ph 41 .
Consequently (1) where NED is the Noise Equivalent Dose 43 Fig. 2). For the simplest case, that is a single kind of charge carriers originating from the absorption of photons by the device surface, CCE can be expressed with the Hecht equation 46 :   (Fig. 2a), which was additionally confirmed with the photocurrent dependence on the bias voltage under X-ray irradiation (Extended Data Fig. 3a). Estimation of μτ values are, however, somewhat ambiguous. Their lower limit (µeτmin= 6·10 -4 cm 2 V -1 and µhτmin= 2·10 -4 cm 2 V -1 ) was estimated by separately measuring the mobility of each carrier type using the time-of-flight technique 48 (Fig. 2b-d) and multiplying these values by their mean lifetime estimated from the transient photocurrent response (τ≥6 µs; Supplementary Fig. 3). The upper µτ limit for the majority carrier (µeτmax= 3·10 -3 cm 2 V -1 ) was directly obtained as a fitting parameter (in the Hecht equation) of photocurrent vs. bias voltage dependence (Extended Data Fig. 3b). For devices illuminated from the side of the hole-collecting electrode, µeτ values set the CCE dependency on the detector thickness, being in good agreement with the experiment (Fig. 2e).
Then the thickness-dependent DE is calculated for both limits, combining photon-energy-dependent AE and CCE, and accounting for ambipolar charge transport. For µhτmax we take a value of 30% of the µeτmax, considering µe/µhratio measured by time-of-flight. Calculated DE values are in good agreement with experimental data (Fig. 2f).
In particular, the DE of the 110 µm-thick device is mostly limited by AE, and reaches 88% for 18 keV X-ray radiation, while at the thicknesses larger than 200 µm, the DE becomes limited by CCE. NED is the comprehensive descriptor for the noise of the detector. To estimate NED, the X-ray dose-ratedependent total noise (NT) of MAPbI3 SC detector was obtained as the noise current spectral density (Fig. 3a, Extended Data Fig. 4). NT 2 is also expressed in photon-equivalents units, where a single photon-equivalent is the root-mean-square (RMS) of the noise-charge equal to the charge generated by one photon in the time window t (equal to 500 μs, given by the amplifier bandwidth 1 kHz; see the additional Y-axis on the right of Fig. 3a). In Fig. 3a the dose rate is recalculated to an equivalent photon quantity within t. The dependence of NT 2 vs. nph is a linear function with a slope of DE and an offset of DN 2 (details in Supplement Note 2):

Fig. 3 | X-and γ-ray detection performance for
The red line on for X-ray imaging at low doses and which is limited mostly by the photon shot noise (Fig. 1g, h). In this energy range, the DQE reaches 90% upon absorption of just a dozen of photons by the device (within t, Extended Data Fig. 6). Low-noise and high charge collection characteristics allow single-photon counting from a 241 Am source (60 keV) with an energy resolution of ca. 50% (Fig. 3c).
Owing to zero-bias operation, these XPV devices retain their characteristics for at least one year (in air, without encapsulation), with the projected device half-life (defined as 50% drop of normalized SNR) of several years, whereas complete degradation occurs within a few hours at high applied electric fields (Fig. 3d). The operational stability of XPV devices thus reaches the typical chemical shelf-life of MAPbI3 SC, despite the relatively high dose accumulated during these tests (equivalent to ca. 500 conventional X-ray medical scans; see Supplementary Fig. 5).

Fig. 4 | X-ray energy-resolved imaging. a,
Imaged object is a rectangle comprising two complementary patterns -5 mm thick ETH letters made of NdO2 powder surrounded by the 2 mm thick steel frame. b, Attenuation coefficients vs. X-ray photon energy for Fe (black curve) and NdO2 (green curve) shown on top of an example of 50 kVp energy spectrum transmitted through the Nd part of the object recorded by MAPbI3 SC detector. Spectrum was binned into low (blue) and high (red) channels, with a border that corresponds characteristic K-line of Nd. c, Energy resolved X-ray imaging of the object from (a) under 50 kVp X-ray with MAPbI3 SC detector, where the colors decode transmittance for corresponding 2 energy channels from (b). d, Transmittance of low (blue) and high (red) channels along white dashed line on (c).
X-ray energy-resolved imaging. While the obtained energy resolution is not suitable for applications in highresolution γ-spectroscopy, it fully suffices for energy-discriminated X-ray spectral imaging, so-called "X-ray multicolor imaging" 50 . As a showcase, we used a several-mm-thick rectangular object consisting of two complementary "ETH" patterns made of two different materials with different X-ray attenuation vs. X-ray energy dependencies (Fe and NdO2, Fig. 4a). Specifically, compared to Fe, the X-ray attenuation coefficient of Nd is much lower below 43 keV and much higher above this value (due to its K-atomic shell, Fig. 4b). 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. 6). One can readily distinguish between two materials and obtain a high-contrast image when recording the images using low-energy channel (more attenuated by Fe) or high-energy channel (more suppressed by Nd), seen as red and blue regions, respectively (Fig. 4c-d).
In conclusion, MAPbI3 SC X-ray detectors operated in the photovoltaic mode are shown to exhibit longterm stable and near-to-ideal performance in the soft X-ray range (18-25 keV), with DQE~87% at a low dose of
Preparation of substrates for SC growth. ITO substrates with the area of 5×5 cm 2 (8-15 Ω, Delta Technologies LTD,) were cleaned by sonication in soap, deionized water, acetone, and isopropanol sequentially, followed by UV-ozone surface treatment for 10 minutes. Next, the PTAA solution (2.5 mg/ml in toluene) was spin-coated for 30 s at 4000 rpm, and subsequently annealed at 100 °C for 10 min.
Growth of MAPbI3 SC. The crystal growth is modified from the previous reports 33,34  with a lead chopper wheel, the signal was restored on lock-in amplifier SR860 from Stanford Research. SNR, detection limit, noise, and stability measurements (Fig. 1e,f, Fig. 3a,d) were obtained with samples connected via the low-noise current amplifier Femto DLPCA-200 to the spectral network analyzer SR770 from Stanford Research with irradiation by modulated 20 kVp X-ray irradiation, attenuated by a 3 mm glass filter. The noise current spectral density dependence on the dose rate (Fig. 3a)  X-ray imaging. All images were acquired in a single-photon counting mode while an object was 2D-scanned in a lateral direction towards the detector. The image at Fig. 4c was obtained under 50kVp X-ray filtered by 500 µm thick steel plate to cut lower energy part (the corresponding spectrum is presented in the Supplementary Fig. 7a), the accumulated dose per pixel is about 10 µGy. Images at Fig. 1g, h were made with 20kVp X-ray irradiation filtered by 3 mm glass to get quasi-monoenergetic spectrum with mean 18 keV energy ( Supplementary Fig. 7b).
The detector was calibrated to get the highest contrast on reference points of the imaged object, indicating that the threshold in the energy spectrum is set near 43 keV as it is shown in Fig. 4b.

Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.