Charge Cloud Size Research Articles

Experimental Determination of the Charge Carrier Transport Models for Improving the Simulation of the HR GaAs:Cr Detectors' Response.

The response of Timepix3 detectors with 300 µm and 500 µm thick HR GaAs:Cr sensors was studied with particle beams at the Danish Centre for Particle Therapy in Aarhus, Denmark. Therefore, the detectors were irradiated at different angles with protons of 240 MeV. The precise per-pixel time and energy measurements were exploited in order to determine the charge carrier transport properties. Using the tracks left by the penetrating charged particles hitting the sensor at the grazing angle, we were able to determine the charge collection efficiency, the charge carrier drift times across the sensor thickness, the dependency of the electron, and for the first time, the hole drift velocity on the electric field. Moreover, extracting the dependence of the charge cloud size on the interaction depth for different bias voltages, it was possible to determine the dependence of the diffusion coefficient on the applied bias voltage. A good agreement was found with the previously reported values for n-type GaAs. The measurements were conducted for different detector assemblies to estimate the systematic differences between them, and to generalize the results. The experimental findings were implemented into the Allpix Squared simulation framework and validated by a comparison of the measurement and simulation for the 241Am γ-ray source.

Theoretical comparison and optimization of cadmium telluride and gallium arsenide photon-counting detectors for contrast-enhanced spectral mammography.

Most photon-counting detectors (PCDs) being developed use cadmium telluride (CdTe), which has nonoptimal characteristic x-ray emission with energies in the range used for breast imaging. New PCD using a gallium arsenide (GaAs) has been developed. Since GaAs has characteristic x-rays lower in energy than those of CdTe, it is hypothesized that this new PCD might be beneficial for spectral x-ray breast imaging. We performed simulations using realistic mammography x-ray spectra with both CdTe and GaAs PCDs. Five different experiments were conducted, each comparing the performance of CdTe and GaAs: (1) sensitivity of iodine quantification to charge cloud size and electronic noise, (2) effect of photon spectrum on iodine quantification, (3) effect of varying the number of energy bins, (4) a dose analysis to assess any possible dose reduction from using either detector, and (5) spectral performance of ideal CdTe and GaAs PCDs. For each study, 3 sets of 5000 noise realizations were used to calculate the Cramer-Rao lower bound (CRLB) of iodine quantification. For all spectra studied, GaAs gave a lower CRLB for iodine quantification, with 10 of the 12 spectra showing a statistically significant difference ( ). The photon energy spectrum that optimized iodine detection for both detector materials was the 40 kVp beam with 2-mm Al filtration, which produced CRLBs of and for CdTe and GaAs, respectively, when using five energy bins. GaAs is a promising detector material for contrast-enhanced spectral mammography that offers better spectral performance than CdTe.

Charge sharing simulations and measurements for digital algorithms aiming at subpixel resolution in photon counting pixel detectors

Hybrid pixel detectors are segmented devices used for X-ray detection that consist of a sensor attached to the readout electronics. Detectors working in single-photon counting mode process each incoming photon individually, have essentially infinite dynamic range, and by applying energy discrimination they provide noiseless imaging. To improve the resolution of the detector and allow operation with high-intensity photon fluxes, the pixel size is reduced. However, with decreasing pixel size, a charge sharing effect is more prominent. This leads to false event registration or omitting the event, and degradation of the energy resolution of the detector. Algorithms aiming at reducing the influence of charge sharing have already been implemented on-chip. However, the spatial resolution of the detector can be increased beyond the physical size of the pixel if the charge proportions collected by neighboring pixels are analyzed.The simulations show that charge cloud size referred to pixel size and noise are the key parameters that determine the accuracy of the subpixel algorithm. The article shows the concept of subpixel algorithm and the simulations for different detector parameters and approximation algorithms. The slanted-edge method was implemented to quantify the resolution of detectors consisting standard readout architecture. The chips were simulated and tested to verify the influence of different bias voltages, sensor materials, and thicknesses on charge sharing and as a consequence on the detector resolution. The simulated and measured edge spread functions were compared. The results show that the simulator can be used to describe the spatial resolution of the detectors, and can be used for further studies of the resolution of detectors with subpixel algorithm implemented.

Accurate contrast determination for X-ray speckle visibility spectroscopy.

X-ray speckle visibility spectroscopy using X-ray free-electron lasers has long been proposed as a probe of fast dynamics in noncrystalline materials. In this paper, numerical modeling is presented to show how the data interpretation of visibility spectroscopy can be impacted by the nonidealities of real-life X-ray detectors. Using simulated detector data, this work provides a detailed analysis of the systematic errors of several contrast extraction algorithms in the context of low-count-rate X-ray speckle visibility spectroscopy and their origins are discussed. Here, it was found that the finite detector charge cloud and pixel size lead to an unavoidable `degeneracy' in photon position determination, and that the contrasts extracted using different algorithms can all be corrected by a simple linear model. The results suggest that experimental calibration of the correction coefficient at the count rate of interest is possible and essential. Thisallows computationally lightweight algorithms to be implemented for on-the-fly analysis.

A spectroscopic Monte-Carlo model to simulate the response of pixelated CdTe based detectors

A fully spectroscopic Monte Carlo model has been developed to predict the spectroscopic performance of pixelated CdTe based detectors. The model incorporates photon attenuation by the photoelectric effect, Compton scattering and Rayleigh scattering. Charge transport equations are used to simulate the size of the electron cloud, approximated by a symmetrical two-dimensional Gaussian distribution, as it drifts to be read out at the detector anode. Direct comparisons are made between simulated data and experimentally acquired spectra from a 1 mm thick CdTe sensor coupled to the HEXITEC detector ASIC. The probability of an absorbed photon leading to charge sharing across pixels as a function of incoming photon energy is investigated. The charge cloud size was found to be dominated by cloud growth during drift for photon energies <100 keV. Furthermore, the portion of charge sharing events due to fluorescence from within the CdTe sensor is calculated—these events are distinguished from regular charge sharing events since their energy response differs. The model described is shown to give a good estimate of the total probability of charge sharing for energies up to 140 keV. CdTe sensor thickness, bias voltage, pixel size and electronic noise threshold can be adjusted to model a range of detector architectures.

A statistical field theory of salt solutions of ‘hairy’ dielectric particles

In this paper, we formulate a field-theoretical model of dilute salt solutions of electrically neutral spherical colloid particles. Each colloid particle consists of a ‘central’ charge that is situated at the center and compensating peripheral charges (grafted to it) that are fixed or fluctuating relative to the central charge. In the framework of the random phase approximation, we obtain a general expression for electrostatic free energy of solution and analyze it for different limiting cases. In the limit of infinite number of peripheral charges, when they can be modelled as a continual charged cloud, we obtain an asymptotic behavior of the electrostatic potential of a point-like test charge in a salt colloid solution at long distances, demonstrating the crossover from its monotonic decrease to damped oscillations with a certain wavelength. We show that the obtained crossover is determined by certain Fisher–Widom line. For the same limiting case, we obtain an analytical expression for the electrostatic free energy of a salt-free solution. In the case of nonzero salt concentration, we obtain analytical relations for the electrostatic free energy in two limiting regimes. Namely, when the ionic concentration is much higher than the colloid concentration and the effective size of charge cloud is much bigger than the screening lengths that are attributed to the salt ions and the central charges of colloid particles. The proposed theory could be useful for theoretical description of the phase behavior of salt solutions of metal-organic complexes and polymeric stars.

Measurement of Charge Cloud Size in X-Ray SOI Pixel Sensors

We report on a measurement of the size of charge clouds produced by X-ray photons in X-ray SOI (Silicon-On-Insulator) pixel sensor named XRPIX. We carry out a beam scanning experiment of XRPIX using a monochromatic X-ray beam at 5.0 keV collimated to $\sim 10$ $\mu$m with a 4-$\mu$m$\phi$ pinhole, and obtain the spatial distribution of single-pixel events at a sub-pixel scale. The standard deviation of charge clouds of 5.0 keV X-ray is estimated to be $\sigma_{\rm cloud} = 4.30 \pm 0.07$ $\mu$m. Compared to the detector response simulation, the estimated charge cloud size is well explained by a combination of photoelectron range, thermal diffusion, and Coulomb repulsion. Moreover, by analyzing the fraction of multi-pixel events in various energies, we find that the energy dependence of the charge cloud size is also consistent with the simulation.

A fitting model of the pixel response to monochromatic X-rays in photon counting detectors

We present a simple fitting model for the pixel response to monochromatic X-rays in single photon counting pixelated detectors that takes into account the 2D effects of the charge sharing and of the electronic noise on the photon counting process. It is based only on geometrical and physical parameters such as the pixel size, the charge cloud size at the pixel depth and the total electronic noise of the front-end circuitry. The equations describing the pixel point spread function and the integral pulse height spectrum are derived preserving the genuine 2D nature of the charge collection process. The fitting performances of the model has been assessed on a set of experimental integral pulse height spectra measured with an IBEX photon counting ASIC bonded to a 450μm thick Silicon sensor with 75μm×75μm pixel size, irradiated with monochromatic X-rays in the energy range 6–12.4 keV, with excellent agreement between model and measurement. The actual contributions of the charge sharing and of the electronic noise are identified and estimated. As a possible consequence, the model can be used to predict precisely the behavior of photon counting detection systems as a function of the design parameters.

Particle tracking with a Timepix based triple GEM detector

This paper details the response of a triple GEM detector with a 55 μmetre pitch pixelated ASIC for readout. The detector is operated as a micro TPC with 9.5 cm3 sensitive volume and characterized with a mixed beam of 120 GeV protons and positive pions. A process for reconstruction of incident particle tracks from individual ionization clusters is described and scans of the gain and drift fields are performed. The angular resolution of the measured tracks is characterized. Also, the readout was operated in a mixed mode where some pixels measure drift time and others charge. This was used to measure the energy deposition in the detector and the charge cloud size as a function of interaction depth. The future uses of the device, including in microdosimetry are discussed.

Imaging properties of a tetra wedge readout

The decoding principle of a tetra wedge anode, which is a development of the wedge and strip anode, is described. The influence of charge cloud size on decoding accuracy is studied using the Monte Carlo method. Simulation results show that the decoding error is large when the size of charge clouds collected by the anode is small. Thus, the charge clouds collected by the tetra wedge anode should reach a necessary size to ensure accurate decoding. Finally, using the ultraviolet photon counting imaging system, the linearity and the spatial resolution of the system are tested. Experimental results show that the system has a good linearity and the spatial resolution is better than 100 μm.

Influence of charge cloud size on performance of UV photon-counting imaging detector

The size of charge cloud is examined as a function of acceleration voltage, distance between MCP and anode, and MCP gain. The performance of photon counting imaging detector is significantly affected by charge cloud size. In this paper, the influence of charge cloud size on the performance of UV photon-counting imaging systems is investigated. Modulation distortion, "S" distortion and their cause are discussed. Then, Monte Carlo simulations for anode decode with different charge cloud sizes are carried out. And finally, the effects of acceleration voltage, distance between MCP and WSA, and MCP gain on the system performance are tested and some practical solutions of modulation and "S" distortion are suggested.

Spatial charge cloud size of microchannel plates

We examine the spatial evolution of charge clouds emitted by microchannel plates (MCPs). A model of this evolution is presented, along with a comparison to experimental results. We also present an experimental method to measure the charge cloud radius in which the radial charge cloud distribution is assumed to be Gaussian. When a charge cloud is released from the MCP, its initial size is determined by the number and distribution of excited channels. The size of the charge cloud is examined as a function acceleration voltage, distance between MCP and anode, and MCP bias voltage. Since electrons released from the MCP have various initial energies and angular divergence, the charge cloud size increases as it travels away from the MCP. Space charge effects also contribute to the growth of the charge cloud. The experimental results are in close agreement with our model, which includes these effects. From experiment, we also derive an approximate expression for charge cloud radius as a function of acceleration voltage and distance between MCP and anode. This expression can be used for the practical design and optimization of a position sensing system comprised of multiple anodes.

The direct measurement of the signal charge behavior in pnCCDs with subpixel resolution

In the MPI-Halbleiterlabor (MPI-HLL) we are developing fully depleted pn-type Charge Coupled Devices (pnCCD) with a thick radiation-sensitive region. Since 1997, the mesh experiment has been established as an unique technique to determine an X-ray interaction position with subpixel resolution. In order to investigate the signal charge behavior in pnCCDs, we performed the mesh experiment using various characteristic X-ray lines. Cu-L (0.9 keV), Al-K (1.5 keV) and Ti-K (4.5 keV) were used and the device operated under various conditions, e.g. register voltages. We obtained the restored pixel images for various X-ray event patterns. The photon entrance window of the back illuminated pnCCD shows highly uniform detection efficiency within a pixel. We measured the charge cloud size generated by an X-ray photon inside the CCD. The measured charge cloud sizes are around 6 μ m (rms) depending on the X-ray energy. The operation with different register conditions revealed asymmetries and regions with a weaker electric field around pixel boundaries.

The charge cloud shape generated by a Cu-K X-ray photon inside the CCD

An X-ray photon generates a finite size of charge cloud in a charge-coupled device (CCD). It forms various pattern of events, depending on the X-ray interaction position on the CCD. The mesh experiment is the only available method to determine the charge cloud shape, which depends on the incident X-ray energy. We employed a metal mesh of 13 μ m in thickness with many holes of 2 μ m diameter periodically spaced of 48 μ m . The valid energy range depends on the X-ray opacity of the metal. It has been thought to be limited to below 7.0 keV for the gold mesh employed. The new method is introduced to roughly estimate the X-ray interaction position to reduce ‘background’ events so that the energy range can be extended to 8.2 keV. Applying our method to Cu-K X-rays (8.04 keV), we measure the charge cloud size generated by Cu-K X-rays and find it to be bigger than that expected from a diffusion model in the depletion region of the CCD. This is due to the fact that the CCD employed has a depletion region of about 40 μ m that is much shorter than the attenuation length of Cu-K X-rays in Si.

DISSIPATION OF CHARGES IN SILICON NANOCRYSTALS EMBEDDED IN SiO2 DIELECTRIC FILMS: AN ELECTROSTATIC FORCE MICROSCOPY STUDY

In this paper, we report a mapping of charge transport in silicon nanocrystals ( nc - Si ) embedded in SiO 2 dielectric films with electrostatic force microscopy (EFM). By using contact EFM mode, positive and negative charges can be deposited on nc - Si . We found that the charge diffusion from the charged nc - Si to the surrounding neighboring uncharged nc - Si is the dominant mechanism during charge decay. A longer decay time was observed for a wider area of stored charge (i.e. 3 charged spots) due to the diffusion of charges being blocked by the surrounding charged nc - Si . This result is consistent with the increase of charge cloud size during the charge decay and the lower charge change percentage for 3 charged spots.

Influence of silicon-nanocrystal distribution in SiO2 matrix on charge injection and charge decay

Influence of distribution of silicon nanocrystals (nc-Si) embedded in SiO2 matrix on charge injection and charge decay of the nc-Si has been investigated with electrostatic force microscopy. For nc-Si distributing in the surface region, the size of charge cloud does not change with decay time, and neighboring charges have no influence on the charge decay. In contrast, for nc-Si distributing away from the surface, the size linearly increases with decay time, and the neighboring charges can either accelerate or resist the charge decay depending on their charge signs. In addition, the characteristic decay time for the first distribution is much shorter than that for the second distribution. These results provide an insight into the dissipation mechanism of the charges stored in the nc-Si.

Application of the Mesh Experiment for the Back-Illuminated Charge-Coupled Device: I. Experiment and the Charge Cloud Shape

We have employed a mesh experiment for back-illuminated (BI) charge-coupled devices (CCDs). BI CCDs possess the same structure as front-illuminated (FI) CCDs. Since X-ray photons enter from the back surface of the CCD, a primary charge cloud is formed far from the electrodes. The primary charge cloud expands through a diffusion process until it reaches the potential well that is just below the electrodes. Therefore, the diffusion time for the charge cloud produced is longer than that in the FI CCD, yielding a larger charge cloud size than expected. The mesh experiment enables us to specify the X-ray point of interaction with subpixel resolution. We measured a charge cloud shape produced in the BI CCD. We found that there are two components of the charge cloud shape having different sizes: a narrow component and a broad component. The size of the narrow component is 2.8–5.7 µm in units of standard deviation and strongly depends on the attenuation length of incident X-rays in Si. The shorter the attenuation length of the X-rays, the larger the charge cloud. This result is qualitatively consistent with a diffusion model inside the CCD. On the other hand, the size of the broad component is roughly constant at ≃13 µm and does not depend on X-ray energies. Judging from the design value of the CCD and the fraction of each component, we conclude that the narrow component has its origin in the depletion region whereas the broad component originates in the field-free region.

Application of a finite size of the charge cloud shape generated by an X-ray photon inside the CCD

A mesh experiment enables us to specify the X-ray landing position on a charge-coupled device (CCD) with subpixel resolution. By this experiment, we find that the final charge cloud shape generated by Ti–K X-ray photons ( 4.5 keV ) in the CCD is about 1.5×1.1 μm 2 (standard deviation). An X-ray photon photoabsorbed in the CCD generates a number of electrons, forming an X-ray event. It becomes up to a 4-pixel-split event since the pixel size of the CCD used ( 12 μm square pixel) is bigger than the charge cloud size. Using the mesh experiment, we can determine the X-ray landing position on the CCD. In this way, we can compare the estimated X-ray landing position with the actual landing position on the CCD. Employing the charge cloud shape, we can improve the position resolution of the X-ray CCD by referring to the X-ray event pattern. We find that the position accuracy of our method is about 1.0 μm . We discuss our method, comparing it with the charge centroid method.

Distortion of a charge cloud shape inside the CCD produced by an X-ray photon

A charge cloud produced by an X-ray photon in a charge coupled device (CCD) has a finite size. The size can be measured using a mesh experiment: the X-ray interaction position is restricted with subpixel precision by using the small mesh holes. This enables us to measure the charge cloud shape produced by an X-ray photon in the CCD. We measured charge cloud size for Al-K X-rays and for Mo-L X-rays. At both energies, we find the charge cloud shapes to be elongated perpendicular to the charge transfer direction. We confirmed the symmetric shape of the mesh hole both by SEM photography and by an experimental technique, and conclude that the elongation of the charge cloud shape is not an artifact of the experimental setup. We then applied an image restoration technique to directly measure the actual hole shape from the X-ray data. The inferred hole size is bigger than the geometrical shape due to diffraction of the incident X-rays by the mesh holes. We conclude that the distortion of the charge cloud shape is due to the asymmetry of the electric field in the CCD.

Direct measurement of the charge cloud size in SIS CCDs

We report here the method to measure the primary charge cloud size generated by X-ray photons in the CCD. If the incident X ray is photo-absorbed near the pixel boundary, the primary charge cloud splits into 2–4 pixels. We calculated the center of gravity of the split event weighted by the split charge. We found that the center of gravity is well-correlated with the X-ray interaction position. We analyzed the charge cloud size assuming either the Gaussian shape or the rectangular shape. From the analysis of the data using the model for the charge cloud shape, we measured a charge cloud size of 1∼2μm for X rays of Y L (1.9 keV), Ag L (3.0 keV) and Ti K (4.5keV). We also notice that we can determine the X-ray interaction position of the split event with an accuracy better than 1/10 of the pixel size.