Machine learning-assisted prediction: unveiling α-MoO3
Our machine learning model development process included data aggregation, feature engineering, model evaluation, and application (see flow chart in Supplementary Fig. 1). Building upon the dataset reported by A. Tash et al.24, we developed an expanded version comprising over 1927 samples and 23 features, and a target variable responsivity with the values ranging from \(1.9\times {10}^{-4}\) to 239.43 A/W. It includes material properties such as valence electrons, atomic number, density, mobility, and the band gaps. Out of the 23 features used for modeling, 7 correspond to device configurations such as PIN, NIP, PN, Ohmic, Schottky, NN, and FET. Data were collected from 29 experimental studies on photodetector testing under visible and ultraviolet (UV) range, with a small portion also covering the EUV region, detailing active layer and substrate properties, including bandgaps, thickness, and responsivity under varying conditions (e.g., wavelength, intensity, and applied bias). Additional features were sourced from experimental and theoretical studies, the Materials Project API, and the NIST database17,25. Comprehensive details are meticulously outlined in Supplementary Table 1. Feature engineering involved identifying key features using Pearson correlation analysis (Supplementary Figs. 1 and 2). Only one feature from pairs with an absolute correlation coefficient of 0.9 or higher was retained to reduce redundancy. The refined dataset, containing 13 distinct features as shown in Supplementary Fig. 3, improved regression model performance slightly compared to the unrefined dataset (Supplementary Fig. 2), enhancing predictive accuracy. Device architecture features (PIN, NIP, FET, SBD, NN, Ohmic, and PN) were excluded from the correlation-based feature elimination step to preserve model generalizability and prevent misclassification across mutually exclusive device types (for further details, see Supplementary Note 3).
Due to the limited dataset in EUV range, a series of regression algorithms were applied for cross-spectral response prediction, with the dataset split 70:30 for training and testing. Seven algorithms demonstrated strong predictive power, capturing over 99% of the variance in responsivity and confirming their accuracy with minimal error. Model performance was assessed using metrics such as mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2), as defined in Eqs. (1−4). RMSE, which is sensitive to outliers and shares units with the target variable (responsivity), was selected as the primary metric. A detailed comparison of the performance of the seven models is presented in Supplementary Figs. 4 and 5, as well as in Supplementary Table 2.
$${MSE}=\frac{1}{n}{\sum }_{i=1}^{n}{\left({y}_{i}-{\hat{y}}_{i}\right)}^{2}$$
(1)
$${RMSE}=\sqrt{\,\frac{1}{n}{\sum }_{i=1}^{n}{\left({y}_{i}-{\hat{y}}_{i}\right)}^{2}\,}$$
(2)
$${MAE}=\,\frac{1}{n}\mathop{\sum }_{i=1}^{n}|{y}_{i}-{\hat{y}}_{i}|$$
(3)
$${R}^{2}=1-\,\frac{\mathop{\sum }_{i=1}^{n}{\left({y}_{i}-{\hat{y}}_{i}\right)}^{2}}{\mathop{\sum }_{i=1}^{n}{\left({y}_{i}-{\bar{y}}_{i}\right)}^{2}}$$
(4)
where \({y}_{i}\) denotes the actual experimental values, \({\hat{y}}_{i}\) represents the predicted values, \({\bar{y}}_{i}\) is the mean of the actual experimental values, and \(n\) is the total number of observations.
The Extra Trees Regressor (ETR) outperformed other models, achieving an RMSE of 0.27 and an R2 value of 0.99995 on an unseen test set of ~578 samples, as shown in Fig. 1a. The model’s performance relies on all input features, each contributing significantly to responsivity predictions, as illustrated in Fig. 1b. With a responsivity range of ~240 A/W in Fig. 1a, the minimal deviation between predicted and experimental values, reflected in the RMSE, highlights the model’s robustness and readiness for accurate predictions on unseen materials.
a Performance of the optimal model, Extra Trees Regressor (ETR), on the unseen test dataset, illustrating predicted responsivity values in strong concordance with experimental (actual) values. The inset displays the model performance metrics, including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and R2 values, underscoring the model’s precision and reliability. b Influence of various input parameters, including active layer characteristics, device configuration, and experimental conditions, on ETR model predictions (see Supplementary Table 1 for the definition of the parameters). c Predictions in the extreme ultraviolet (EUV) region for an ohmic device at photon energy = \(13.5\,{nm}\) and bias = \(1\,{mV}\), for the \(168\,{nm}\) thick α-MoO3 active layer. α-MoO3 emerges as a top-performing material for responsivity, based on the responsivity plotted as a function of active layer density and atomic number. d Based on the active layer band gap, α-MoO3 is identified as the most responsive material under the same condition as (c), with an optimal active layer thickness of \(150-320\,{nm}\).
In pursuit of an optimal active layer material, responsivity predictions were conducted by varying two primary attributes, total atomic number, and density of the active layer to identify promising candidates from a vast materials pool. The optimal predicted values for the total atomic number and density were approximately 66 and 4.6 \(g/{{\mathrm{cm}}}^{3}\), respectively, pointing to α-MoO3 as illustrated in Fig. 1c. After selecting the material, we optimized the α-MoO3 device thickness by examining the relationship between thickness and the band gap of the active layer. The analysis revealed that the maximum predicted responsivity of \(57.4\,{A}/W\pm 2.2\%\) was achieved at a band gap of \(3.2\,{eV}\), within optimal thickness range of \(150\,{nm}\) \({to}\) \(320\,{nm}\) (see Fig. 1d). Further 1D simulation confirmed that a thickness of \(150\,{nm}\) maximizes responsivity, reaching \(57.4\,A/W\) (Supplementary Fig. 6).
The analysis also identified additional promising candidates with similar material parameters, such as MoS2, SnO2, and ReS2 etc. Examination of these materials by varying four key parameters of the active layer; experimental band gap, atomic number, density, and mobility, assuming deposition on a Si/SiO2 substrate under an EUV wavelength of \(13.5\,{nm}\) (or \(91.8\,{eV}\)) at \(1\,{mV}\) bias and a thickness of \(\sim < 200\,{nm}\), α-MoO3 achieved the highest responsivity in the EUV region followed by materials such as PbI2, MoS2, and SnO2, as displayed in the five-dimensional plot in Fig. 2a, a remarkable performance compared to silicon-based EUV detectors.
a Machine learning ETR model predictions in the EUV region at photon energy = \(13.5\,{nm}\) and bias = \(\,1\,{mV}\), for the ohmic active layers grown on Si/SiO2 substrate. A five-dimensional plot visualizes predicted responsivity across various materials, with α-MoO3 achieving the highest value; marker shape and color correspond to active layer mobility and band gap, respectively, enriching the multidimensional analysis. The Monte Carlo simulations depict electron generation in b α-MoO3 and c Si within the EUV region. Electron generation is presented as a function of EUV photon energy (or wavelength) and the thickness of the active layer. The results demonstrate that the α-MoO3 active layer exhibits nearly uniform electron generation efficiency across the majority of the EUV region, whereas Si shows significant electron generation only in a narrow range of higher EUV energies (i.e., >110 eV). The dashed lines indicate a photon energy of 91.85 eV (13.5 nm) and a thickness of 168 nm, with the red cross marking their intersection, corresponding to the experimental condition used in this study.
To further strengthen our results, we also conducted Monte Carlo simulations to evaluate the number of electrons generated by α-MoO3 and Si in the EUV region as a function of thickness, as illustrated in Fig. 2b, c respectively. The simulations were performed by irradiating the active layers with 1 million EUV photons while varying their thickness. The results confirm that α-MoO3 generates significantly higher and, more importantly, nearly uniform electrons across the EUV region compared to Si, even when the Si layer is twice as thick as the α-MoO3 layer, as illustrated in Fig. 2b, 2c. As shown in Fig. 2c, Si exhibits high efficiency only within two very narrow energy ranges (Energy \( < \,15\,{eV}\) and Energy \( > \,110\,{eV}\)) in the EUV region. Furthermore, α-MoO3 demonstrates nearly an order of magnitude higher electron generation at the key wavelength of interest, \(13.5\,{nm}\), which is critical for advanced lithography applications. α-MoO3’s potential for advanced EUV radiation sensing is attributed to its high attenuation coefficient, nearly an order of magnitude higher than that of silicon in the EUV region. This is further supported by the atomic number of molybdenum (Z = 42) and its high density (4.69 \(g/c{m}^{3}\)), which significantly enhances its ability to attenuate EUV-range radiation (see Supplementary Note 8). These attributes enable α-MoO3-based devices to utilize photoelectric conversion, directly generating charge carriers from EUV radiation for enhanced detection26. The promising predictions from machine learning and Monte Carlo simulations motivated the fabrication of a α-MoO3-based device and its subsequent experimental evaluation under EUV conditions.
Experimental performance of α-MoO3-based EUV sensor
The current-time \(({IT})\) data provides a rapid and effective method for evaluating the performance of any radiation detector. In these measurements, when the sensor device is illuminated by EUV radiation, the current generated by the EUV photons adds to the dark current (Supplementary Note 9). This photocurrent, \(\Delta I\) (Fig. 3a) illustrates signal strength at different photon energies and bias voltages. Under EUV illumination, measurements were conducted at \(1\,{mV},\,1.5\,V,\,3\,V,{and}\) \(5\,V\) to observe the device’s responses to different photon energies. The device shows photon energy-dependent differentiable photocurrent responses at different biases. For instance, ∆I is approximately 5 \({nA}\) at 90 \({eV}\) and increases to \(14\,{nA}\) at \(150\,{eV}\) under a bias of \(1\,{mV}\). It is important to note that increasing the bias voltage can further elevate photocurrent values to a certain extent. However, while the dark current also increases with bias voltage, the high energy consumption at elevated bias levels poses risks to external readout electronics27,28.
a Current-time (I−T) curves were measured at different photon energies and bias voltages, with EUV radiation being turned OFF and ON in cycles. Time was normalized to display all figures in the same panel. With increasing bias, the signal increases, but there is also an increase in dark current. b. Signal-to-noise ratio (SNR) in decibels (\({dB}\)) as a function of photon energy shows a strong signal strength of ~ 15 dB at a low bias of \(1\,{mV}\). The signal strength is decreased at higher bias voltages due to increased dark current values at a given higher bias voltage. The green shaded area highlights the SNR values corresponding to a wavelength of 13.5 nm. c The EUV induced current response to sequentially increase in photon flux at a given photon energy, indicating no saturation or degradation in detecting very high fluxes of ~ \({10}^{12}\) \({Photons}/s\), showing device stability. d Density plot of recorded currents as a function of bias voltages (\(-5{V}\) to \(5V\)) for 100 consecutive repeated measurements under very high flux (~\({10}^{12}{Photons}/s\)) was analyzed to test the device’s radiation hardness. The output current remained consistent across repeated exposures, demonstrating the device’s stability under intense radiation conditions.
The signal-to-noise ratio (SNR) was also calculated to quantify the detector’s signal strength. Data from Fig. 3a was used to calculate SNR values, which increased with photon energy and flux (Fig. 3b), with peak signals of \(\sim 15\,{dB}\) calculated at a bias of \(1\,{mV}\). The device’s high responses at \(1\,{mV}\) are due to very low dark currents of the order of pico amperes at this bias. Additionally, signal strength rises with photon energy due to an increase in carrier generation under high photon energy and flux. SNR values ranging from \(1\) to \(10\, {dB}\) at \({V}_{{ds}}=1.5\) to \(5\,V\) were obtained, which are 1 to 2-fold lower than those at \(1\,{mV}\). With increased bias, relatively high dark currents play a crucial role in suppressing the signal strength. High \({dB}\) values at a few millivolts can substantially reduce power consumption in large-scale detection and sensing applications. This demonstrates the detector’s performance when strong signal strength is recorded instantly (with detector speed on the order of milliseconds, see Supplementary Note 10) under relatively low EUV exposures.
Another important factor in detector performance is the efficient detection of specific radiation flux at fixed photon energy. A specialized experiment, controlled the photon flux by adjusting beamline slit sizes. At a bias of \(1\,{mV}\), the device was exposed to continuous EUV radiation with flux increased from 0 to ~1.98 × 1012 ph/s in four steps and then reversed. The current response showed a near-linear relationship with flux, consistently increasing or decreasing as flux values changed, demonstrating stable and dynamic performance. For instance, at a photon energy of \(90\,{eV}\) and a bias of \(1\,{mV}\), currents of approximately \(0\,{nA},\,1.1\,{nA},\,1.98\,{nA},\,3.5\,{nA},\) and \(5.1\,{nA}\) were recorded at \(0\,{ph}/s,\,3.62\times {10}^{11}\,{ph}/s,\,7.02\times {10}^{11}\,{ph}/s,\,1.39\times {10}^{12}\,{ph}/s,\) and \(1.98\times {10}^{12}\,{ph}/s\), respectively. Similar performance was also observed at other photon energies and \(1\,{mV}\) (Supplementary Fig. 12a). This also reflects the radiation hardness of the detector, as it demonstrated successful detection of specific photon flux at fixed photon energy with differentiable current responses and no signs of saturation at high flux exposures on the order of \({10}^{12}\,{ph}/s\).
EUV radiation can degrade detector performance under prolonged exposure, making stability and degradation resistance essential for commercial applications. To evaluate the α-MoO3-based detector’s stability, a specialized experiment recorded EUV-induced photocurrent responses across 100 repeated bias voltage cycles (−5 V to 5 V). This dataset was collected using \(150\,{eV}\) EUV radiation at a flux of \(1.2\times {10}^{12}\,{ph}/s\), illuminating a device for continuous exposures to obtain 100 measurements. Current increased symmetrically with bias voltage around 0 V, as shown in Fig. 3d, indicating nearly ohmic contact between α-MoO3 and gold. The consistent I−V behavior within the range of −2 V to 2 V confirmed stable conductivity over repeated exposures. At higher voltages (>+2 V), minor current variations (~10−20%) occurred due to semiconductor heating but remained negligible. The detector’s high breakdown voltage enables reliable performance under elevated voltages, while its stability under repeated exposures ensures suitability for commercial applications requiring low bias voltages.
Figures of merit for α-MoO3 based EUV Ddetector
Building upon these promising device characteristics, we then experimentally validated the responsivity of an α-MoO3-based detector. Its current response and responsivity in response to EUV photon energies at bias voltages of \(1\,{mV}\) and \(5\,V\) are plotted in Fig. 4. \(\Delta I\) as a function of photon energies at specific bias voltages demonstrates an almost linear relationship, indicating a linear increase in photogeneration of electron-hole pairs with increasing EUV photon energies and efficient extraction of charge carriers under external electric fields. Linear current responses are advantageous in commercial applications, minimizing errors in output signals. Simple linear fits to these data points yield the slope for the increase in photocurrent values. The slope of \(0.1\) for \(\Delta I\) at \(1\,{mV}\) increases to \(0.4\) at a bias of \(5\,V\) (Supplementary Fig. 13), indicating strong signal sensitivity even to minor changes in photon energies. A steeper slope in the linear relationships indicates a higher photocurrent at elevated bias voltages and photon energies, leading to the device’s high responsivity.
a, b Current response to various photon energies in the EUV range at bias voltages of 1 mV (\(\varDelta I\) = 5.27 nA at photon energy ~ 92 eV) and 5 V (\(\varDelta I\) = 6 nA at photon energy ~ 92 eV). The EUV-induced current increases almost linearly with photon energy, with indicators highlighting values corresponding to EUV radiation at a wavelength of approximately 13.5 nm. c, d At bias voltages of 1 mV and 5 V, the device demonstrates high responsivity of ~60 to 160 A/W, depending on the photon energy and bias voltage. The peak responsivity is approximately 80 A/W at 1 mV bias and ~160 A/W at 5 V bias. For EUV radiation at a wavelength of 13.5 nm, the responsivity ranges from ~60 to ~70 A/W at both bias voltages.
A responsivity ‘\(R\)’ of the device is calculated using formula i.e., \({{\rm{R}}}=\,\Delta I/P\times S\) (where \(\varDelta I\) is the change in current under EUV exposure, \(P\) is the power density of photon energies, and \(S\) is the area of the material exposed to EUV radiation)29. At a synchrotron beam energy of ~\(92\,{eV}\) and a power density of \(7.86\,W/{m}^{2}\), the responsivity of the α-MoO3-based detector at biases of \(1\,{mV}\) and \(5\,V\) is calculated as ~\(60\,A/W\) and \(70\,A/W\), respectively, as shown in Fig. 4−c,d. Depending on bias voltage and other EUV photon energies, these values range from ~50 to \(160\,A/W\), demonstrating the high responsivity of the EUV detector, which, to our knowledge, surpasses that of any other device in the EUV range (Supplementary Table 4). The α-MoO3-based EUV detector exhibits a responsivity that is 800 times greater than that of conventional Si-based EUV detectors, a factor that directly contributes to its superior detectivity.
This performance is further validated through detectivity calculations (see Supplementary Note 11), highlighting the detector’s ability to distinguish weak EUV signals from noise with remarkable precision. For the device operating at biases of \(1\,{mV}\) and \(5\,{V}\), the detector demonstrates detectivity values ranging from \(6-8(\!\times \!{10}^{12}{Jones})\) and \(0.15-4\,(\!\times \!{10}^{12}{Jones})\), respectively, in the EUV range. This demonstrates the device’s strong capability to detect weak signals and convert them into measurable values. Additionally, External Quantum Efficiencies (EQE) are also calculated (Supplementary Fig. 14c, d). At \(92\,{eV}\) (or \(13.5\,{nm}\)), the calculated EQE values exceed \({10}^{5}\%\), indicating a high conversion rate from absorbed EUV photons to generated carriers via the photoelectric effect. These values gradually increase by an order of magnitude, with peak values exceeding \(2\times {10}^{6}\%\) at \(150\,{eV}\) when the device operates at \(5\,{V}\). A brief comparison of EUV detectors from the literature, alongside the performance of our device, is presented in Supplementary Table 4. These high performance metrics including, responsivity, detectivity, and EQE underscore the transformative potential of α-MoO3-based EUV detector, making it a promising candidate for applications requiring unparalleled sensitivity, precision, and efficiency in the EUV range. To further strengthen machine learning predictions, we also demonstrated the experimental responsivity of another material, ReS2 (~20 \(A/W\) under 1 \({mV}\) and 91.8 \({eV}\)), also aligned well with the prediction of ~18 \(A/W\) (see Supplementary Notes 12 and 13 for details). This further highlights the potential of utilizing machine learning to identify other suitable materials for sensing across different spectral ranges.
In summary, we demonstrated a cross-spectral response prediction framework based on Extremely Randomized Trees to bridge the gap between visible/UV and EUV detection domains. Feature importance analysis revealed wavelength as the dominant feature for predictions (~18%), followed by bandgap, bias voltage, and device configuration. This data-driven approach identified materials achieving high EUV responsivities including α-MoO3 and ReS2, spanning from 20 to \(60\,{A}/W\), surpassing conventional silicon photodiodes by a factor of 800. Monte Carlo simulations confirmed the enhanced electron generation rates in these materials compared to silicon. Experimental characterization subsequently validated the predicted results, with measured values ranging from ~50 to 160 A/W, depending on the bias voltage and EUV photon energies. Notably, these measured values exceeded the predicted range, highlighting the high responsivities of the EUV detectors. The demonstrated success of this predictive framework establishes a robust methodology for accelerating the discovery of high-performance materials across diverse spectral ranges, particularly in domains with limited experimental datasets.
