Fano Noise Research Articles

Unraveling Fano noise and the partial-charge-collection effect in x-ray spectra below 1 keV

Unraveling Fano noise and the partial-charge-collection effect in x-ray spectra below 1 keV

The response of thick (10 μm) AlInP x-ray and γ-ray detectors at up to 88 keV

The development of new x-ray and γ-ray spectrometers based on AlInP photodiodes with increased quantum detection efficiency and improved energy resolution is reported. The spectroscopic responses of two AlInP p+–i–n+ mesa photodiodes (10 μm i layer, the thickest so far reported) were investigated at photon energies from 4.95 to 88.03 keV; the detectors and preamplifier were operated at 30 °C. Energy resolutions (full width at half maximum) of 750 ± 40 eV and 850 ± 30 eV at 4.95 keV were achieved with the two detectors. The energy resolution deteriorated with increasing photon energy; this was in accordance with the increasing Fano noise with energy and suggested negligible incomplete charge collection noise across the photon energy range investigated. The measured voltage output of each spectrometer was found to be linear as a function of incident x-ray photon energy. The count rate (measured at 8.63 keV) was also found to linearly increase with incoming x-ray photon flux for the investigated spectrometers. These results, which were obtained using the thickest AlInP photodiodes produced so far, suggest that AlInP detectors are highly promising candidates for future uncooled x-ray and γ-ray spectrometers.

X-ray spectroscopy with an AlInP photodiode

Abstract A custom-made Al 0.52 In 0.48 P p + -i-n + circular mesa X-ray photodiode ( 200 μ m diameter; 2 μ m i layer thickness) has been investigated for its use in photon counting X-ray spectroscopy within the energy range 4.95 keV to 21.17 keV. This is the widest energy range so far used to characterize an AlInP X-ray detector. High-purity X-ray fluorescence calibration samples were excited by a Mo target X-ray tube to give characteristic energy photons with which to illuminate the detector. X-ray fluorescence spectra were accumulated with the Al 0.52 In 0.48 P X-ray detector coupled to a custom-made charge-sensitive preamplifier (both operated at a temperature of 30 °C ± 2 °C). The charge output linearly increased with X-ray photon energy. The energy resolution (Full Width at Half Maximum, FWHM) degraded from 0.99 keV ± 0.02 keV (80 e − rms) at 4.95 keV to 1.12 keV ± 0.02 keV (89 e − rms) at 21.17 keV. The increase of the FWHM with increased energy exceeded the increase expected as a consequence of Fano noise. Hence, the presence of energy dependent incomplete charge collection noise was suggested. The count rate linearly increased with increasing incident X-ray flux across the investigated flux range, up to ∼ 3 . 8 × 105 photons s−1 cm−2.

Energy response characterization of InGaP X-ray detectors

Two custom-made In0.5Ga0.5P p+-i-n+ circular mesa spectroscopic X-ray photodiodes with different diameters (200 μm and 400 μm) and a 5 μm i layer have been characterized for their response to X-ray photons within the energy range 4.95 keV to 21.17 keV. The photodiodes, operating uncooled at 30 °C, were coupled, in turn, to the same custom-made charge-sensitive preamplifier. X-ray fluorescence spectra of high-purity calibration foils excited by a Mo target X-ray tube were accumulated. The energy resolution (Full Width at Half Maximum) increased from 0.79 ± 0.02 keV at 4.95 keV to 0.83 ± 0.02 keV at 21.17 keV, and from 1.12 ± 0.02 keV at 4.95 keV to 1.15 ± 0.02 keV at 21.17 keV, when using the 200 μm and 400 μm diameter devices, respectively. Energy resolution broadening with increasing energy was attributed to increasing Fano noise (negligible incomplete charge collection noise was suggested); for the first time, the Fano factor for In0.5Ga0.5P was experimentally determined to be 0.13, suggesting a Fano limited energy resolution of 145 eV at 5.9 keV. The charge output of each system had a linear relationship with photon energy, across the investigated energy range. The count rate of both spectroscopic systems increased linearly with varying X-ray tube current up to ∼105 photons s−1 cm−2 incident photon fluences. The development of In0.5Ga0.5P based spectrometers is particularly important for hard X/γ-ray astronomy, due to the material’s large linear X-ray and γ-ray absorption coefficients and the ability to operate uncooled at high temperatures.

Simulation of charge sharing in the Caliste-SO detector

Caliste-SO is CdTe X-ray pixelated detector employed in STIX telescope which is one of the instruments on-board Solar Orbiter mission. In such type of detectors charge sharing between adjacent pixels is expected. The effect can affect measured spectra which requires the development of dedicated method for scientific data processing. In this article, we present simulations of the charge sharing with regard to incoming photon energy. We define two processes causing charge sharing: fluorescence and movement of charge cloud. First type was calculated using Geant4 toolkit to determine the response of the detector. Additionally we prepared dedicated software written in Interactive Data Language (IDL) to calculate instrumental effects: Fano and electronic noise, charge loss and properties of the entrance window. To calculate second type of charge sharing we calculated movement of charge cloud in the crystal using Fick’s second law. Our simulation shows that for Caliste-SO detectors charge sharing strongly depends on energy of incoming photon. The fraction of events classified as double counts is nearly 6% for 150 keV photons. Furthermore, we calculated the charge sharing for the Caliste64 detector. For this case our result is confirmed by laboratory measurements.

Ion mobility spectrometer with orthogonal X-Ray source for increased sensitivity

Ion mobility spectrometers (IMS) are compact devices for extremely sensitive detection of proton and electron affine volatile compounds down to low pptv concentrations within less than a second. The measuring principle requires ionization of the target analyte. Most IMS employ radioactive electron sources, such as 63Ni or 3H. These radioactive materials suffer from legal restrictions limiting the fields of application. Furthermore, the electron emission has a predetermined intensity and cannot be controlled or disabled. In a previous work, we replaced the axially mounted 3H source of our ion mobility spectrometer with a commercially available X-ray source operated at low acceleration voltage of 4.5 kV to be applicable in most application without legal restrictions. However, the high penetration depth of the radiation together with the statistical behavior of the X-ray ionization process led to an increase of Fano noise and thus a limited signal-to-noise ratio. Therefore, the X-ray source is now mounted orthogonal to the drift tube in order to avoid Fano noise. Here, we compare the analytical performance of this orthogonal setup with the axially mounted X-ray source. The noise level is significantly reduced. This improves the signal-to-noise ratio from 700 with the axially placed source to more than 3000 with the orthogonally placed source, while the resolving power still remains at R = 100. Furthermore, typical limits of detection for some model substances in the low pptv range in positive and negative ion mode are given.

Prototype GaAs X‐ray detector and preamplifier electronics for a deep seabed mineral XRF spectrometer

Work towards developing a prototype GaAs based X‐ray fluorescence spectrometer focusing on the detector‐preamplifier system for in situ characterisation of deep seabed minerals is presented. Such an instrument could be useful for marine geology and provide insight into hydrothermal processes. It would also be beneficial for deep sea mining applications. The GaAs photodiode was electrically characterised at 4 °C (ambient seawater temperature) and 33 °C. A system energy resolution (full width at half maximum) at 5.9 keV of 580 eV at 4°C, limited by the dielectric noise, broadening to 680 eV at 33°C, was recorded. The spectral performance of the system was characterised across the energy range 4.95 keV to 21.17 keV, at 33°C, using high‐purity X‐ray fluorescence calibration samples excited by a Mo target X‐ray tube. The charge output from the system was found to be linear with incident photon energy. The energy resolution was found to broaden from 695 eV at 4.95 keV to 735 eV at 21.17 keV, attributed to the increasing Fano noise with energy. The same X‐ray tube was used to fluoresce an unprepared manganese nodule (revealing the presence of Mn, Fe, Ni, Cu, Zn, Pb, Sr, and Mo) and a black smoker hydrothermal vent sample (containing Fe, Co, Ni, Cu, Zn, Pb, and Mo). Such a spectrometer may also find use in future space missions to study the hydrothermal vents that are believed to exist in the oceans of Jupiter's moon Europa.

Geant4 simulations of STIX Caliste-SO detector's response to solar X-ray radiation

AbstractSpectrometer/Telescope for Imaging X-rays (STIX) is a part of Solar Orbiter (SO) science payload. SO will be launched in October 2018, and after three years of cruise phase, it will reach orbit with perihelion distance of 0.3 a.u. STIX is a Fourier imager equipped with pairs of grids that comprise the flare hard X-ray tomograph. Similar imager types were already used in the past (eq. RHESSI, Yohkoh/HXT), but STIX will incorporate Moiré modulation and a new type of pixelized detectors with CdTe sensor. We developed a method of modeling these detectors' response matrix (DRM) using the Geant4 simulations of X-ray photons interactions with CdTe crystals. Taking into account known detector effects (Fano noise, hole tailing etc.) we modeled the resulting spectra with high accuracy. Comparison of Caliste-SO laboratory measurements of 241Am decay spectrum with our results shows a very good agreement. The modeling based on the Geant4 simulations significantly improves our understanding of detector response to X-ray photons. Developed methodology gives opportunity for detailed simulation of whole instrument response with complicated geometry and secondary radiation from cosmic ray particles taken into account. Moreover, we are developing the Geant4 simulations of aging effects which decrease detector's performance.

Characterization of GaAs mesa photodiodes with X-ray and γ-ray photons

Results characterizing the performance of prototype thin (3µm i layer) GaAs p+–i–n+ mesa photodiodes (one 200µm diameter and one 400µm diameter device) are presented showing the spectral performance of the devices at photon energies from 4.95keV (V Kα1 X-ray fluorescence) to 59.5keV (241Am γ-ray emission). The devices were operated uncooled at +33.3°C. The energy resolution (full width half maximum) was measured to vary from 780eV at 4.95keV to 950eV at 59.5keV for the 200µm diameter diode, and from 1.08keV at 4.95keV to 1.33keV at 59.5keV for the 400µm diameter diode. The increased broadening of FWHM with increasing photon energy was found to be greater than can be explained by the expected energy dependence of the Fano noise, but the peak charge output from the devices varied linearly (R2200µm=0.99998, R2400µm=0.999998) with incident photon energy.

A multi-energy (2–60 keV) calibration of200 μ m and 400 μm diameter spectroscopic GaAs X-ray photodiodes

Thin (2 μm active layer) spectroscopic p+-i-n+ GaAs X-ray photodiodes of circular mesa geometry (200 μm and 400 μm diameter; one representative diode of each diameter) have been characterised for their energy response using high-purity X-ray fluorescence calibration samples excited by an X-ray tube, giving energies between 2.1 keV (Au Mα1) and 21.18 keV (Pd Kα1), and an 241Am radioisotope γ-ray source (26.3 keV, 59.5 keV). The photodiodes were operated uncooled at +33°C. The 200 μm diameter device's energy resolution (FWHM) was found to be constant (0.79 keV) and primarily limited by electronics noise at energies between 2.1 keV and 21.18 keV, but it broadened to 0.85 keV at 26.3 keV, and to 1 keV at 59.5 keV. The 400 μm diameter device's energy resolution (FWHM) was constant (1.1 keV) for photon energies between 4.95 keV and 9.89 keV, but increased to 1.15 keV at 16.62 keV, 1.25 keV at 21.18 keV, 1.3 keV at 26.3 keV and 1.66 keV at 59.5 keV. The broadening of energy resolution (FWHM) observed in both cases is greater than can be attributed solely to increasing Fano noise and is hypothesised to be at least in part due to energy dependent charge trapping. However, for both types of device, the peak charge output from the devices was found to be linearly (R2 ⩾ 0.9999) dependent on incident X-ray energy.

Adaptation Improves Neural Coding Efficiency Despite Increasing Correlations in Variability

Exposure of cortical cells to sustained sensory stimuli results in changes in the neuronal response function. This phenomenon, known as adaptation, is a common feature across sensory modalities. Here, we quantified the functional effect of adaptation on the ensemble activity of cortical neurons in the rat whisker-barrel system. A multishank array of electrodes was used to allow simultaneous sampling of neuronal activity. We characterized the response of neurons to sinusoidal whisker vibrations of varying amplitude in three states of adaptation. The adaptors produced a systematic rightward shift in the neuronal response function. Consistently, mutual information revealed that peak discrimination performance was not aligned to the adaptor but to test amplitudes 3-9 μm higher. Stimulus presentation reduced single neuron trial-to-trial response variability (captured by Fano factor) and correlations in the population response variability (noise correlation). We found that these two types of variability were inversely proportional to the average firing rate regardless of the adaptation state. Adaptation transferred the neuronal operating regime to lower rates with higher Fano factor and noise correlations. Noise correlations were positive and in the direction of signal, and thus detrimental to coding efficiency. Interestingly, across all population sizes, the net effect of adaptation was to increase the total information despite increasing the noise correlation between neurons.

Quantum Efficiency and Quantum Yield of an HgCdTe Infrared Sensor Array

ABSTRACTWe measure the quantum efficiency and quantum yield of an H2RG HgCdTe near-infrared sensor array. Using a blackbody, narrowband filters, and a pinhole camera to provide a calibrated irradiance on the HgCdTe sensor, we determine a 2 σ lower limit of 85% for the quantum efficiency averaged over the array and over three observed wavelengths, 3.38, 3.9, and 4.5 μm. The peak quantum efficiency occurs near the center of the sensor and is unity within measurement uncertainty (5%). By substituting a calibrated PbSe diode for the H2RG sensor, we verify the methods and equipment at the three wavelengths, 3.38, 3.9, and 4.5 μm. Accurate measurement of the quantum efficiency requires a well-calibrated system gain, the determination of which is complicated by interpixel capacitance, which correlates noise between adjacent pixels. If unaccounted for, the correlation induced by interpixel capacitance would cause the system gain and hence the quantum efficiency to be overestimated by ∼20%. We accurately measure the interpixel capacitance using the autocorrelation method of Brown, Schubnell, and Tarlé and by a method described in this paper that uses post-readout binning. The two methods yield consistent results, but the binning method is more robust than the autocorrelation method in the presence of electromagnetic interference. The interpixel capacitance we measure for the H2RG-S010 sensor is similar to that of another epoxy-backfilled H2RG sensor tested recently by Brown, Schubnell, and Tarlé. Using the same PbSe diode to calibrate the quantum efficiency of the 5.5-μm-cutoff H2RG sensor from 0.7 μm to 6.0 μm, and correcting for the interpixel capacitance, we derive implausible quantum efficiencies greater than unity between 1.4 μm and 2.4 μm that we cannot explain. The apparent system gain, measured at many monochromatic wavelengths with the usual variance-versus-mean photon-transfer analysis of flat-field images, is a function of wavelength for wavelengths less than 2 μm, which we interpret as evidence for quantum yield larger than unity, i.e., more than one electron being produced by each photon detected by the sensor. We derive the effects of Fano noise and quantum yield on the photon-transfer curve.

The spectral response of silicon X-ray detectors

A discrete analytic calculation of the spectral response of silicon drift detectors for X-rays is presented. The results are compared with measurements at BESSY II using monochromatic synchrotron radiation in the energy range from 0.2 to 2 keV. All Gaussian features (main, escape, and Al fluorescence peak) as well as the background are included in the model. The peak intensities are calculated from energy dependent probability distributions. The non-Gaussian background is produced by charge-loss in the entrance window. The charge loss of energetic photo and Auger electrons and the diffusion of low-energy secondary electrons into the aluminum dead layer are considered. The secondary electrons disperse in a Gaussian charge distribution with the width σ sec , which is the only free parameter of the model. All collected charge is summed up for every possible process and convoluted with electronic and Fano noise, yielding the energy distribution of the background. Its intensity is given by the probability of the process. This method generates all observed spectral background features using a single fundamental calculation scheme. It can, in principle, be applied to any type of semiconductor detector. The calculations are in very good agreement with the measurements.

Next generation of pnCCDs for X-ray spectroscopy and imaging

A special type of charge-coupled device, the pnCCD, has been developed in the nineties as focal-plane detector for the X-ray astronomy mission XMM-Newton of the European Space Agency. The pnCCD detector has been in operation since the satellite launch in 1999. It is performing up to date spectroscopy of X-rays in combination with imaging and high time resolution. The excellent performance of the flight camera is still maintained; in particular, the energy resolution has been nearly constant since launch. In order to satisfy the requirements of future X-ray astronomy missions as well as those of ground-based experiments, a new type of pnCCD has been developed. The ‘frame store pnCCD’ shows various optimizations in device design and fabrication process. Devices with up to 256×512 pixels have been fabricated in 2004 and recently tested. Simultaneously, a programmable analog signal processor for the readout of the CCD signals, the DUO CAMEX, has been developed. The readout noise of the new detector has a value of 2 electrons ENC which is less than half of the figure of the XMM-Newton pnCCD. We measured an energy resolution that is close to the theoretical limit given by the Fano noise. In particular the low-energy response of the new devices was substantially improved. The quantum efficiency for X-rays is at least 90% in the entire energy band from 0.3 keV up to 11 keV. This is due to the ultra-thin photon entrance window as well as the full depletion of the 450 μm thick back-illuminated pnCCD. The position resolution is better than the pixel sizes of 75 μm×75 μm or 51 μm×51 μm because the signal charge is spread over up to four pixels which allows a more accurate event position determination. ‘Out of time’ events are substantially reduced to the order of 0.1% by operating the pnCCD in frame store mode. Higher operating temperatures, e.g. −20 °C, are possible due to the smaller thermally generated dark-current level of the new devices and the operation at higher frame rates. Low power consumption applications like for the ROSITA X-ray astronomy mission with low frame rates of, e.g. 20 images/s, as well as high frame rate applications, e.g. 200 images/s, are possible with the same device.

Carrier dynamics and resolution of co-planar grid radiation detectors

Co-planar grid detectors utilizing single carrier sensing techniques, offer a practical solution for developing compound semiconductor gamma-ray detectors with high resolving power. We present an analytical model for describing the response of co-planar grid detector. The response of a co-planar grid detector is shown to be affected by intrinsic lateral inhomogeneity, which is inherent to its design. We evaluate the effect of both lateral and bulk inhomogeneities and show that the resolution of a co-planar grid detector is dominated by inhomogeneous broadening of the signal and not by Fano or electronic noise.

Compound semiconductor radiation detectors

We discuss the potential benefits of using compound semiconductors for the detection of X- and γ-ray radiation. While Si and Ge have become detection standards for energy dispersive spectroscopy in the laboratory, their use for an increasing range of applications is becoming marginalized by one or more of their physical limitations; namely the need for ancillary cooling systems or bulky cryogenics, their modest stopping powers and radiation intolerance. Compound semiconductors encompass such a wide range of physical properties that it is technically feasible to engineer a material to any application. Wide band-gap compounds offer the ability to operate in a wide range of thermal and radiation environments, whilst still maintaining sub-keV spectral resolution at hard X-ray wavelengths. Narrow band-gap materials, on the other hand, offer the potential of exceeding the spectral resolution of both Si and Ge, by as much as a factor of 3. Assuming that the total system noise can be reduced to a level commensurate with Fano noise, spectroscopic detectors could work in the XUV, effectively bridging the gap between the ultraviolet and soft X-ray wavebands. Thus, in principle, compound semiconductor detectors can provide continuous spectroscopic coverage from the far infrared through to γ-ray wavelengths. However, while they are routinely used at infrared and optical wavelengths, in other bands, their development has been plagued by material and fabrication problems. This is particularly true at hard X- and γ-ray wavelengths, where only a few compounds (e.g., GaAs, CdZnTe and HgI2) have evolved sufficiently to produce working detection systems. In this paper, we examine the current status of research in compound semiconductors and by a careful examination of material properties and future requirements, recommend a number of compounds for further development. In the longer term, when material problems are sufficiently under control, we believe the future lies in the development of heterostructures and inserted interface layers to overcome contacting problems and quantum heterostructures and superlattices to facilitate low-noise readout.

High resolution x-ray spectroscopy using GaAs arrays

We have produced a number of small format gallium arsenide (GaAs) arrays to address the material, electronic, and technological problems that need to be solved in order to develop mega pixel, Fano-limited spectroscopic x-ray imagers. Results will be presented of a series of x-ray measurements carried out on a prototype 5×5 array, fabricated from 40 μm thick epitaxial GaAs. The device has pixel sizes of 200×200 μm2 and pitch 250 μm. As a preliminary investigation of performance, two pixels have been instrumented. Measurements from 5.9 to 98 keV were carried out both in our laboratory and at the Hamburger Synchrotronstrahlungslabor research facility in Hamburg, Germany. Both pixels were found to be remarkably uniform, both in their spectral and spatial response to x-rays. The average nonlinearity in the spectral response is <1% across the energy range 5.9–98 keV. Using a 12 keV, 20×20 μm2 pencil beam, the spatial uniformity was found to be better than 98% over the entire pixel surfaces, consistent with the statistical precision of the measurement. The energy resolution at −40 °C is 400 eV full width at half maximum (FWHM) at 5.9 keV rising to 700 eV FWHM at 98 keV. No difference in energy resolution was found between full area and pencil beam illumination. An analysis of the resolution function has shown that the detector is dominated by electronic noise at low energies and Fano noise at energies above 30 keV. By best-fitting the expected resolution function to the entire data set, we derive a Fano factor of 0.140±0.05, together with a charge transport factor as low as 1.4×10−3. Further improvement in the resolution function has been achieved by replacing the conventional resistive feedback preamplifiers with a new resistorless design, which provides a lower component of electronic noise. In this case, a resolution of 266 eV FWHM at 5.9 keV has been achieved at room temperature (23 °C) and 219 eV FWHM with only modest cooling (−31 °C). The expected Fano noise at this energy is ∼140 eV.

Monte Carlo simulation of the X-ray response of a germanium microstrip detector with energy and position resolution

We present Monte Carlo computer simulations of the X-ray response of a micro-strip germanium detector over the energy range 30–100 keV. The detector consists of a linear array of lithographically defined 150 μm wide strips on a high purity monolithic germanium crystal of 6 mm thickness. The simulation code is divided into two parts. We first consider a 10 μm wide X-ray beam striking the detector surface at normal incidence and compute the interaction processes possible for each photon. Photon scattering and absorption inside the detector crystal are simulated using the EGS4 code with the LSCAT extension for low energies. A history of events is created of the deposited energies which is read by the second part of the code which computes the energy histogram for each detector strip. Appropriate algorithms are introduced to account for lateral charge spreading occurring during charge carrier drift to the detector surface, and Fano and preamplifier electronic noise contributions. Computed spectra for different energies and beam positions are presented and compared with the experimental results obtained at the European Synchrotron Radiation Facility (ESRF), where the detector was scanned with a micro-beam of monochromatic photons. The remarkable agreement between the computed and measured data is discussed, and we show that consideration of charge diffusion and the resultant signal splitting between adjacent strips is essential to explain the observed results. We also comment upon the relevance of phenomena neglected in our model, such as secondary electron transport and charge trapping.

Resolution degradation in X-ray detectors based on superconducting tunnel junctions

Despite considerable progress over the past years, the detection of medium-energy X-ray photons (E>1 keV) with STJs near the energy-resolution limit, set by the Fano and tunnel noise, remains an elusive goal. There is presently little doubt that the spatially inhomogeneous response of the STJ is responsible for the degradation of the energy resolution. We review several proposed mechanisms against experimental data for Nb- and Ta-based STJs, of various sizes and in single or array-format. We argue against a single mechanism behind the resolution degradation. The experimental results presented here support a model in which quasi-particles are lost at the edges of the STJ, but also indicate that losses into the leads seriously degrade the energy resolution. Finally, an example is given of how fabrication details may play a role as well.

Performance of the pn-CCD X-ray detector system designed for the XMM satellite mission

The pn-CCD detector system is designed as a focal plane instrument for the European Photon Imaging Camera (EPIC) on the X-ray Multi Mirror mission (XMM) of the European Space Agency. This satellite will be launched by the end of this century. The sensitive area of the detector consists of a 6 × 6 cm 2 array of 12 pn-CCDs monolithically integrated on a single silicon wafer. The detector has been optimized for high-resolution X-ray spectroscopy between 100 eV and 15 keV with simultaneous good quantum efficiency for the investigation of faint objects. A fast readout achieves excellent time resolution for the observation of pulsed X-ray sources. The relevant performance parameters reflecting the state of the detector development are presented. Energy resolution reaches the theoretical limits given by the Fano noise. Due to a thin entrance window and full depletion of the device the quantum efficiency is better than 80% over a wide energy range. Evidence for radiation hardness and background rejection capability will also be provided.