3D reconstruction of particle tracks in a 2 mm thick CdTe hybrid pixel detector
Abstract
We demonstrate how the latest generation of hybrid pixel detectors of the Timepix family can be used to reconstruct 3 dimensional particle tracks on a microscopic scale, additionally determining the stopping power along the particles’ paths. In an experiment, a Timepix3 detector with a 2 mm thick planar CdTe sensor was irradiated in a 40 GeV/c pion beam and used in a similar way to a timeprojection chamber: The coordinates x and y were given by the trajectory projection (pixel pitch: \(55\,\upmu \hbox {m}\)), the zcoordinate was reconstructed from the charge carrier drift time measurement (time binning: 1.5625 ns). The achievable zresolution was studied at different bias voltages. Systematic inaccuracies due to an imprecise drift time model were determined and separated from the intrinsic uncertainty given by the time resolution. It was shown that a zresolution of \(60\,\upmu \hbox {m}\) could be achieved by a perfect modeling of the drift time. With the presented zreconstruction methodology, we studied the charge collection efficiency as a function of interaction depth, which was then used to apply a charge loss correction to the perpixel energy measurements. 3D event displays of pion, muon and electron tracks are shown.
1 Introduction
Early attempts to use pixelated detectors of Medipix/Timepix type for particle tracking were based purely on the analysis of the morphologic characteristics of 2D projections in the xyplane. The zcoordinate was determined by the entry and exit points, whereby the track broadening due to charge sharing gave further information about track orientation [1]. Later, Filipenko et al. [2] have shown that Timepix can be used similarly to a Time Projection Chamber (TPC) for a 3D track reconstruction. Using a 1 mm thick CdTe at very low reverse bias of \(\,\,80\,\hbox {V}\), they achieved a zresolution of \(60\,\upmu \hbox {m}\) (while the resolution in x and y was given by the pixel pitch of \(110\,\upmu \hbox {m}\)). Turecek et al. [3], Pacifico et al. [4], and Bergmann et al. [5] demonstrated and investigated the 3D track reconstruction capability of the latest generation of hybrid pixel detectors of the Medipix collaborations, Timepix3 [6], when used with a highly resistive planar silicon sensor. The latter has shown that a zresolution of \(29\,\upmu \hbox {m}\) can be achieved with a \(500\,\upmu \hbox {m}\) thick silicon sensor layer at a bias voltage of 130 V.
Compared with the typically gasfilled TPCs, Timepix detectors profit from the advantages of the semiconductor material, such as the higher density (by two orders of magnitude) and the approximately \(10\,\times \) lower energy needed to create free charge carriers, leading to the possibility to reduce the device dimension while providing precise spectroscopic information about the ionizing energy losses in the sensor. Compact semiconductor devices are typically also superior due to the significantly lower drift times giving an increased speed of operation.
Timepix particle trackers are compact, lightweight, portable and easy to use. They can be used in places where the available space is limited, and in situations where weight or power consumption matters. Such applications include space weather analyses [7], the determination of trapped particle directions in the VanAllen radiation belts [8, 9], monitoring of secondary radiation in hadron therapy [10], the study of the antiproton annihilation [4] and electron microscopy [11]. Especially, when equipped with CdTe or CdZnTe as sensor material Timepix detectors can be investigated for double beta decay experiments [12]. All of the above applications would profit significantly from a determination of the interaction depth in the sensor by improving particle discrimination, background event suppression, annihilation vertex reconstruction, impact angle or impact point determination. A practical example of improved particle discrimination is the characterization of mixed electronphoton radiation fields. Whereas in the 2D projections, electron and photon interactions are indistinguishable, 3D track reconstruction could provide means of separating them. Since photons have to be converted to electrons, photons generate tracks at random depths within the sensor. Electrons however are seen directly upon entering the sensitive volume. Besides, 3D particle tracking clearly allows a separation of penetrating and stopped particles.
In the presented work, we continue methodological development by systematically investigating the track reconstruction capabilities of a Timepix3 with a 2 mm thick CdTe sensor layer at different bias voltages. We show a 3D view of particle interactions seen in a 40 GeV/c pion beam at the SuperProtonSynchrotron (SPS) at CERN^{1} and illustrate the signatures of different types of interactions.
2 Timepix3
2.1 Basic facts
Timepix3 is the latest generation of hybrid pixel detectors of the Timepix family. A Timepix3 assembly consists of a sensor layer, which is bump bonded to the readout ASIC by the flipchip technology. In the presented work, a 2 mm thick CdTe sensor was used. This layer is divided into a square matrix of \(256 \times 256\) pixels. The pixel pitch (pixeltopixel distance) is \(55\,\upmu \hbox {m}\) thus forming a sensitive area of \(1.98\,\hbox {cm}^{2}\). The assembly, its readout (AdvaDAQ [3]) and the perpixel energy calibration coefficients were provided by ADVACAM s.r.o.^{2} In contrast to its predecessor Timepix [13], Timepix3 allows the measurement of the time of an interaction (timeofarrival) and energy deposition (by the timeoverthreshold) simultaneously in each individual pixel. It provides a datadriven readout scheme, i.e. that only the pixel registering an interaction is read out. The perpixel dead time is about 475 ns. The maximal achievable hit rate is \(40\,\hbox {Mpixel cm}^{2}\ \hbox {s}^{1}\).
2.2 Charge carrier motion
Ionizing radiation interacting in the sensor creates free charge carriers (electrons e and holes h), whose number is proportional to the amount of energy deposited in the sensor material. These charge carriers begin to drift through the sensor material due to an applied potential difference between the common backside contact (cathode) and the pixelated anode, the socalled bias voltage \(U_{\mathrm{bias}}\).
A lateral broadening of the initially created charge cloud is caused by diffusion and repulsion [16, 17, 18, 19]. It increases with increasing drift time, thus also with the distance to the pixel electrodes z, and, in the case of repulsion, with higher energy deposition. During the drift motions, charge carriers can recombine, so that the amount of induced charge is reduced.
2.3 Charge induction
2.4 Perpixel signal processing

The ToT is the time interval the voltage pulse is above the THL. This interval is sampled with a 40 MHz clock. Energy calibration is done pixel by pixel with Xrays of known energy;

The ToA is determined by the time when the signal crosses the THL on its upward slope. A continuously running clock of 40 MHz determines the base ToA value. To increase precision, an additional 640 MHz clock from a ring oscillator is used to sample the time of the THL crossing to the next rising edge of the base ToA clock. This way, a time binning of 1.5625 ns is achieved.
3 Reconstruction principles
In order to perform a 3D reconstruction of particle tracks, Timepix3 is used similarly to a TPC [5]. The crucial point of the reconstruction principle is thus the understanding of the measured “drift” times \(t_{\mathrm{drift,meas}.}\) in each pixel as a function of the interaction depth z. The drift time measured in pixel i is hereby given by the difference of the pixel’s time stamp \(t_{i}\) and the minimal time within the set of pixels forming a track \(t_{\mathrm{min, track}}\).
Due to charge induction, pulse shaping in the chargesensitive amplifier already starts before the charge carriers actually arrive at the collecting pixel electrodes. We refer to the time when the pulse shaping starts as \(t_{\mathrm{induction}}\). The duration from the start of the pulse shaping to the time when the hit is assigned is approximated by an offset \(t_{\mathrm{offset}}\) and, for low energy deposition, the delay due to timewalk \(t_{\mathrm{timewalk}}\). Figure 3 illustratively summarizes the situation.
The important parameter for zdetermination is thus \(t_{\mathrm{induction}}\). In Sect. 3.2, it is shown, that \(t_{\mathrm{induction}}\) depends on the interaction depth z and deposited energy \(E_{\mathrm{dep}}\). To properly determine the zcoordinate from the measured data, we thus calculated 2D lookup tables \(z_{\mathrm{lookup}}(t_{\mathrm{induction}},E_{\mathrm{dep}})\) describing the dependence of z not only on \(t_{\mathrm{induction}}\), but also on deposited energy \(E_{\mathrm{dep}}\).
 1.Evaluate the “rough” zcoordinate:where \(E_{\mathrm{meas},i}\) is the measured pixel energy deposition.$$\begin{aligned} z_{ \mathrm{rough}, i} = z_{\mathrm{lookup}} \left( t_{i}  t_{\mathrm{min, track}}, E_{\mathrm{meas},i} \right) , \end{aligned}$$(5)
 2.Correct for possible charge losses by dividing \(E_{\mathrm{meas},i}\) by the charge collection efficiency \(\varepsilon _{cc}(z)\):\(\varepsilon _{cc}(z)\) was determined from the experimental data as described in Sect. 5.5.$$\begin{aligned} E_{ \mathrm{corrected}, i} = \frac{ E_{\mathrm{meas},i}}{\varepsilon _{cc} \left( z_{ \mathrm{rough}, i} \right) }. \end{aligned}$$(6)
 3.Reevaluate the zcoordinate using the corrected energy \(E_{\mathrm{corrected},i}\):$$\begin{aligned} z_{ \mathrm{rec.}, i} = z_{\mathrm{lookup}} \left( t_{i}  t_{\mathrm{min, track}}, E_{\mathrm{corrected},i} \right) . \end{aligned}$$(7)
3.1 Timewalk correction
The pixel with the 30–32 keV measurement determines the reference time stamp \(t_{\mathrm{ref}}\). For each of the 3 other pixels, the delay due to the timewalk \(t_{i, \mathrm timewalk}\) is obtained by subtracting the pixel’s time stamp from the reference time: \(t_{i,\mathrm timewalk} = t_{i}  t_{\mathrm{ref}}\).
Figure 5a shows the scatter plot of measured pixel energies \(E_{i}\) versus their time delays \(t_{i, \mathrm timewalk}\) for 14,480 4pixel cluster events. The width of the timedelay distributions increases for energies closer to the threshold since fluctuations of the THL have a bigger effect on the measurement of the THL crossing when the slopes are less steep.
3.2 Modeling the time of induction
To understand the contribution of the charge induction process to the time measurement, the time dependence of the induced charge at the collecting pixel electrodes was calculated. Iteratively, the energy equivalent charge \(Q_{0}\), created at interaction depth \(z_{0}\) and time \(t_{0} = 0\), was drifted through the sensor volume. In each iteration i, the absolute time \(t_{i}\) was increased by \(\varDelta t = 0.3\,\hbox {ns}\) (\(t_{i} = t_{i1} + \varDelta t\)). The positions of electrons \(z_{\mathrm{e}}(t_{i})\) and holes \(z_{\mathrm{h}} (t_{i})\) were calculated using Eqs. 1 and 2, respectively, with the electric field from Eq. 3. Since the zdifferences are small, the electric field could be approximated by a constant, without significant loss of precision. The induced charge \(Q_{i}\) is given by the sum of the charges induced by electrons \(Q_{e, i}\) and holes \(Q_{h, i}\). Both quantities were calculated according to Eq. 4.
We now define \(t_{\mathrm{induction}}\) as the time when the induced charge reaches the THL level of 2.52 keV. As seen in Fig. 6, this means that higher energy deposition results in earlier hit assignment. Since the experimental approach for timewalk correction (see Sect. 3.1) was chosen, the time delays due to the induction process are automatically compensated for in the energy range below 30 keV. Thus, for lookup table calculation the energy range from 30 keV to 1 MeV was sufficient. An energy binning of 25 keV (giving a maximal uncertainty of \(10\,\upmu \hbox {m}\)) and a time binning of 0.3 ns (significantly below the Timepix3 time granularity) was used.
4 Experimental setup
5 Data analysis
In the following section, measured data are utilized to determine the zdependence on drift time, achievable zresolutions, and the depth dependent charge collection efficiency \(\varepsilon _{\mathrm{cc}}\).
The detector response in the form of the 2D projections of energy and time measurements is shown for an illustrative set of 100 detected particle tracks in Fig. 8. For further analysis, each individual event is analyzed separately.
5.1 Typical pion event
Figure 9 illustrates the detector response to a typical pion track passing through the sensor layer in the form of the perpixel energy deposit (ToT) and the relative time differences (\(\varDelta \hbox {ToA}\)). The bias was set at \(\,\,100\,\hbox {V}\).
The temporal profile, which is related to the charge carrier drift time \(t_{\mathrm{drift}}\) (see discussion in Sect. 3), increases almost linearly when following the particle trajectory. Higher time differences correlate with greater distances to the pixel electrodes. The energy depositions along the particle trajectory show a systematic decrease towards higher distances to the pixel electrodes. At greater distances, drift times are longer and the amount of material to be traversed by the charge carriers is bigger. This gives rise to charge carrier losses, for example due to recombination in trapping centres (e.g. crystal lattice defects). The charge collection (induction) efficiency \(\epsilon _{\mathrm{cc}}\) is thus lower at greater distance z to the pixel contact.
5.2 Principles of data evaluation
Boundary conditions used for track selection. The ranges correspond to required track widths \(\varDelta x\) and track heights \(\varDelta y\) of prototypical tracks used for analysis. The last column shows the amount of remaining tracks after the cuts were applied and their relative contribution to the entire data set
\(U_{\mathrm{bias}}\) [V]  \(\varDelta x\) [pixels]  \(\varDelta y\) [pixels]  Remaining tracks 

\(\,100\)  \(\left[ 30;37\right] \)  \(\left[ 0;3\right] \)  40992 (1%) 
\(\,200\)  \(\left[ 30;36\right] \)  \(\left[ 0;3\right] \)  51538 (2%) 
\(\,300\)  \(\left[ 30;36\right] \)  \(\left[ 0;3\right] \)  59209 (2%) 
\(\,400\)  \(\left[ 30;35\right] \)  \(\left[ 0;2\right] \)  28141 (2%) 
\(\,500\)  \(\left[ 30;35\right] \)  \(\left[ 0;2\right] \)  56821 (6%) 
 1.
The energy weighted coordinate \(y_{\mathrm{mean}}\), the minimal drift time \(t_{\mathrm{drift}}\), and the total energy \(E_{\mathrm{tot}}\) were calculated for each column x.
 2.
The entrance \(\mathbf {x}_{\mathrm{entry}} = (x_{\mathrm{entry}}, y_{\mathrm{mean, entry}})\) and exit \(\mathbf {x}_{\mathrm{exit}} = (x_{\mathrm{exit}}, y_{\mathrm{mean, exit}})\) points were determined from these average coordinates. The entry point is defined as the point at \(z = d\), the exit point is the point at \(z = 0\,\hbox {mm}\). The latter was determined in the same way as described in [5].
 3.Linear interpolation between \(\mathbf {x}_{\mathrm{entry}}\) and \(\mathbf {x}_{\mathrm{exit}}\) then yields the reference interaction depths:along the trajectory, where \(r_{xy} = \mathbf {x}  \mathbf {x}_{\mathrm{entry}}\) is the projected distance of point \(\mathbf {x}\) along the particle trajectory and \(L_{xy} = \mathbf {x}_{\mathrm{exit}}\mathbf {x}_{\mathrm{entry}}\) the projected track length. Charge sharing has been taken into account by subtracting half of the track width from its length.$$\begin{aligned} z_{\mathrm{geo.}}(r_{xy}) = \frac{d}{L_{xy}} \times r_{xy}, \end{aligned}$$(10)
5.3 zdependence on drift time
Figure 11 shows the zdependence on drift time. Therefore, the drift times were put to 32 equally distant depth of interaction bins. The lines indicate the behavior expected from the model derived in Sect. 3.2 for the energy bin 30–55 keV (corresponding to the average energy measured in the pixels). Overall, good agreement was found. At \(\,\,200\,\,\,\hbox {V}\) and \(\,\,100\,\,\hbox {V}\) deviations are observed. Possible explanations for the deviations are given in Sect. 5.4.
5.4 zresolution
To determine the achievable zresolution, \(z_{\mathrm{rec.}}\) was determined as described in Sect. 3 and compared to \(z_{\mathrm{geo.}}\). The comparison is shown for an event from the measurement at bias \(\,\,100\,\hbox {V}\) in Fig. 12. Here, the dispersion of the differences \(\varDelta z = z_{\mathrm{rec.}}  z_{\mathrm{geo.}}\) can be described by a gaussian with a \(\sigma _{\mathrm{z}}\) of \(45.3\,\upmu \hbox {m}\).
To study the depth dependence of the zresolution, the differences \(\varDelta z\) were determined and sorted into 32 equally distant interaction depth bins. In each bin, the \(\varDelta z\) distribution was fitted by a gaussian.
The gaussian widths \(\sigma _{z}\), shown in Fig. 13b, are related to the granularity of the drift time measurements. Given that drift times are lower at lower absolute values of bias voltages, sampling errors due to the timegranularity should be smaller. Overall, the expected behavior was found. However, there is no significant difference between the measurements at \(\,\,400\,\hbox {V}\) and \(\,\,500\,\hbox {V}\). Additionally, at intermediate zvalues, \(\sigma _{z}\) is higher at bias \(\,\,100\,\hbox {V}\) than at bias \(\,\,200\,\hbox {V}\). This indicates that other effects contribute. These could be variations of the timewalk correction parameters between individual pixels or local changes of drift times, e.g. due to inhomogeneities in the electric field.
Minimal and maximal values for the gaussian mean deviations \(\langle \varDelta z \rangle \) and maximum values of the widths \(\sigma _{z}\) at the different bias voltages investigated
Bias [V]  \(\langle \varDelta z \rangle \) [\(\upmu \hbox {m}\)]  \(\sigma _{z,\mathrm max}\) [\(\upmu \hbox {m}\)] 

\(\,100\)  [\(\) 45; 83]  61 
\(\,200\)  [4; 63]  59 
\(\,300\)  [\(\) 7; 31]  73 
\(\,400\)  [\(\) 29; 31]  82 
\(\,500\)  [\(\) 29; 48]  85 
5.5 Charge collection efficiency as a function of the depths
Results of the 3D line fit shown in Fig. 17a
Parameter  Value [\(\upmu \hbox {m}\)] 

\(x_{0}\)  \(3,132.85 \pm 0.37\) 
\(y_{0}\)  \(29.5 \pm 0.24\) 
dx  \(\,1.58919 \pm 0.00030\) 
dy  \(0.69220 \pm 0.00020\) 
6 3D reconstructed particle events
 Pions When the beam shutter is open, the majority of tracks relates to the interaction of 40 GeV/c pions. Pion events with outgoing \(\delta \)rays are shown in Figs. 15 and 16. The stopping power was determined by the total energy deposit (including the \(\delta \)ray) \(E_{\mathrm{dep}}\) divided by the density \(\rho _{\mathrm{CdTe}} = 5.85\,\nicefrac {\mathrm{g}}{\mathrm{cm}^{3}}\) [14] and the primary pion’s track length in the sensor L:In order to determine L, the iterative 3D Hough transform algorithm described in [25] was applied to the data. The algorithm returns a line parametrization in the form:$$\begin{aligned} \frac{dE}{dX} = \frac{E_{\mathrm{dep}}}{\rho _{\mathrm{CdTe}} \times L}. \end{aligned}$$(11)with the normalized directional vector \(\mathbf {u}\). L is thus given by evaluating the line parameterization at the entrance and exit points: \(L = \mathbf {r}(\lambda _{\mathrm{entry}})  \mathbf {r}(\lambda _{\mathrm{exit}})\).$$\begin{aligned} \mathbf {r}(\lambda ) = \mathbf {r}_{0} + \lambda \times \mathbf {u} =\begin{pmatrix} x_{0}\\ y_{0}\\ z_{0} \end{pmatrix} + \lambda \times \begin{pmatrix} dx \\ dy \\ dz \\ \end{pmatrix}, \end{aligned}$$(12)
 Muons: When the beam shutter is closed, pions are stopped so that only few muons per spill penetrate. The track shown in Fig. 17a was observed during interventions in the experimental area when the shutter was closed. We use this track to determine the precision of 3D trajectory reconstruction. Therefore, the line representation:with the four independent parameters \(x_{0}\), \(y_{0}\), dx and dy was fitted to the measured data. The distances of measured data points to the fit are shown in Fig. 17(b). Their distribution can be described by a gaussian with a \(\sigma \) of 59.4 \(\upmu \hbox {m}\). With the fit results summarized in Table 3, we find the uncertainty of the pivot point \(\mathbf {r}_{0}\) determination:$$\begin{aligned} \mathbf {r}(\lambda ) = \mathbf {r}_{0} + \lambda \times \mathbf {u} =\begin{pmatrix} x_{0}\\ y_{0}\\ 0 \end{pmatrix} + \lambda \times \begin{pmatrix} dx \\ dy \\ 1 \,\upmu \mathrm m \end{pmatrix} \end{aligned}$$(13)and the distance d dependent uncertainty caused by the directional vector:$$\begin{aligned} \varDelta r_{0} = \sqrt{\varDelta x_{0}^2+ \varDelta y_{0}^2} = 0.44\,\upmu \mathrm m, \end{aligned}$$(14)The precision as a function of the distance d can thus be estimated conservatively by:$$\begin{aligned} \varDelta dr = \frac{d}{\mathbf {u}} \times \sqrt{\varDelta dx^2 + \varDelta dy^2} = d \times 0.00018. \end{aligned}$$(15)Evaluating Eq. 16 for example at a distance of 1 m, we find a precision of \(\varDelta r(1\,\mathrm{m}) = 184\,\upmu \mathrm m\).$$\begin{aligned} \varDelta r(d) = \varDelta r_{0} + \varDelta u = 0.44\,\upmu \mathrm{m} + d \times 0.00018. \end{aligned}$$(16)

Electrons/positrons: Electron/positron tracks are characterized by curly paths through the sensor volume. Typical examples are depicted in Fig. 18. Whereas in Fig. 18a, an electron enters the sensor from the outside, the electrons/positrons in Fig. 18b and c were generated inside the sensor layer, e.g. as a result of \(\gamma \)interactions (Compton or photoelectric effect in the case of Fig. 18b and pairproduction in the case of Fig. 18c).

Fragmentation reactions Rarely, particle interaction in the medium causes a break up of a nucleus in the sensor medium. A fragmentation event was found in the measurement at \(\,\,100\,\,\,\hbox {V}\). It is illustrated in Fig. 19. Characteristic are tracks of different stopping power originating in the same point.

if a particle (almost) fully traverses the sensor, which is the case in Figs. 15, 16, 17a and 18b. In a practical use case, such events can be selected by requiring a maximal time difference within a track close to the drift times expected from the sensor thickness;

if the event geometry allows to make assumptions about entry or exit point(s), which is the case in Figs. 18c and 19, where it is unlikely that secondary particles all stop exactly at the same interaction depth.
7 Conclusion
The presented work described the application of Timepix3 for particle tracking on a microscopic scale. Particle interactions could be reconstructed in a 2 mm thick CdTe volume in 3D while simultaneously determining the energy deposition in the sensor medium along the particle trajectory. Timepix3 was therefore used in a similar way to a TPC: the x and y coordinates were given by the detector pixelation and the zcoordinate was determined from the charge carrier drift times. The presented analysis methods corrected the energy measurement for charge carrier losses during charge carrier drift motion.
The achievable zresolution was studied at different bias voltages. The effects of drift time model inaccuracies were separated from the uncertainties due to the time measurement. It was shown that a perfect modeling of the drift time in the sensor would provide a zresolution down to \(60\,\upmu \hbox {m}\). Thus, with the pixel pitch of \(55\,\upmu \hbox {m}\), a device equivalent to a voxel detector with voxel size \(55 \times 55 \times 60\,\upmu \hbox {m}^{3}\) could be created.
Event displays of 3D reconstructed particle interactions with different origins were presented. By 3D line fitting, the precision of particle trajectory reconstruction was determined as a function of distance to the detector.
Footnotes
 1.
Conseil Europeen pour la Recherche Nucleaire.
 2.
ADVACAM s.r.o., U Pergamenky 12, 170 00 Praha 7, Czech Republic, http://advacam.com/.
Notes
Acknowledgements
We would like to thank Lukas Tlustos for the useful discussion, ADVACAM s.r.o for lending us the detector for measurements, the AFP (ATLAS Forward Proton) detector group for allowing us a parasitic measurement and the Medipix collaboration for the development of the detector. The work was supported by the European Regional Development FundProjects “Van de Graaff Accelerator  a Tunable Source of Monoenergetic Neutrons and Light Ions” (No. CZ.02.1.01/0.0/0.0/16_013/0001785) and “Engineering applications of physics of microworld” (No. CZ.02.1.01/0.0/0.0/16_019/0000766). This research has further been supported by the Ministry of Education, Youth and Sports of the Czech Republic under the “RICE  New Technologies and Concepts for Smart Industrial Systems”, project No. LO1607.
References
 1.Z. Vykydal, J. Jakubek, T. Holy, S. Pospisil, in Proceedings of the 9th Conference, Villa Olmo, Como, ed. by M. Barone, E. Borchi, A. Gaddi, C. Leroy, L. Price, P.G. Rancoita, R. Ruchti (World Scientific Publishing, 2006), pp. 779–784Google Scholar
 2.M. Filipenko, T. Gleixner, G. Anton, T. Michel, Eur. Phys. J. C 74(8), 3013 (2014). https://doi.org/10.1140/epjc/s1005201430131 ADSCrossRefGoogle Scholar
 3.D. Turecek, J. Jakubek, P. Soukup, J. Instrum. 11(12), C12065 (2016). http://stacks.iop.org/17480221/11/i=12/a=C12065
 4.N. Pacifico, et al., Nuclear instruments and methods in physics research section A: accelerators, spectrometers, detectors and associated equipment 831, 12 (2016). https://doi.org/10.1016/j.nima.2016.03.057. http://www.sciencedirect.com/science/article/pii/S0168900216300808. Proceedings of the 10th International ’Hiroshima’ Symposium on the Development and Application of Semiconductor Tracking Detectors
 5.B. Bergmann, M. Pichotka, S. Pospisil, J. Vycpalek, P. Burian, P. Broulim, J. Jakubek, Eur. Phys. J. C 77(6), 421 (2017). https://doi.org/10.1140/epjc/s1005201749934 ADSCrossRefGoogle Scholar
 6.T. Poikela, J. Plosila, T. Westerlund, M. Campbell, M.D. Gaspari, X. Llopart, V. Gromov, R. Kluit, M. van Beuzekom, F. Zappon, V. Zivkovic, C. Brezina, K. Desch, Y. Fu, A. Kruth. J. Instrum. 9(05), C05013 (2014). http://stacks.iop.org/17480221/9/i=05/a=C05013
 7.C. Granja, S. Polansky, Z. Vykydal, S. Pospisil, A. Owens, Z. Kozacek, K. Mellab, M. Simcak. Planet. Space Sci. 125, 114 (2016). https://doi.org/10.1016/j.pss.2016.03.009. http://www.sciencedirect.com/science/article/pii/S0032063316300216
 8.S. Gohl, B. Bergmann, C. Granja, A. Owens, M. Pichotka, S. Polansky, S. Pospisil. J. Instrum. 11(11), C11023 (2016). http://stacks.iop.org/17480221/11/i=11/a=C11023
 9.S. Gohl, B. Bergmann, H. Evans, P. Nieminen, A. Owens, S. Posipsil. Adv. Space Res. (2018). https://doi.org/10.1016/j.asr.2018.11.016. http://www.sciencedirect.com/science/article/pii/S0273117718308706
 10.J. Jakubek, C. Granja, B. Hartmann, O. Jaekel, M. Martisikova, L. Opalka, S. Pospisil. J. Instrum. 6(12), C12010 (2011). http://stacks.iop.org/17480221/6/i=12/a=C12010
 11.R. van Gastel, I. Sikharulidze, S. Schramm, J. Abrahams, B. Poelsema, R. Tromp, S. van der Molen. Ultramicroscopy 110(1), 33 (2009). https://doi.org/10.1016/j.ultramic.2009.09.002. http://www.sciencedirect.com/science/article/pii/S0304399109001983
 12.T. Michel, T. Gleixner, J. Durst, M. Filipenko, S. Geißelsöder. Adv High Energy Phys. 2013, (2013). https://doi.org/10.1155/2013/105318
 13.X. Llopart, R. Ballabriga, M. Campbell, L. Tlustos, W. Wong. Nuclear Instrum. Methods Phys. Res. Sect. A Acceler. Spectrom. Detect. Assoc. Equip. 581(1–2), 485 (2007). https://doi.org/10.1016/j.nima.2007.08.079. http://www.sciencedirect.com/science/article/pii/S0168900207017020. VCI 2007 Proceedings of the 11th International Vienna Conference on Instrumentation
 14.A. Owens, Compound Semiconductor Radiation Detectors (CRC Press, Taylor & Francis Group, Suite, 2012)CrossRefGoogle Scholar
 15.J. Fink, H. Krüger, P. Lodomez, N. Wermes. Nucl. Instrum. Methods Phys. Res. Sect. A Acceler. Spectrom. Detect. Assoc. Equip. 560(2), 435 (2006). https://doi.org/10.1016/j.nima.2006.01.072. http://www.sciencedirect.com/science/article/pii/S0168900206001598
 16.M. Campbell, E. Heijne, T. Holy, J. Idarraga, J. Jakubek, C. Lebel, C. Leroy, X. Llopart, S. Pospisil, L. Tlustos, Z. Vykydal. Nucl. Instrum. Methods Phys. Res. Sect. A Acceler. Spectrom. Detect. Assoc. Equip. 591(1), 38 (2008). https://doi.org/10.1016/j.nima.2008.03.096. http://www.sciencedirect.com/science/article/pii/S0168900208003963. Radiation Imaging Detectors 2007
 17.J. Bouchami, A. Gutierrez, A. Houdayer, J. Idarraga, J. Jakubek, C. Lebel, C. Leroy, J.P. Martin, M. Platkevic, S. Pospisil. Nucl. Instrum. Methods Phys. Res. Sect. A Acceler. Spectrom. Detect. Assoc. Equip.607(1), 196 (2009). https://doi.org/10.1016/j.nima.2009.03.147. http://www.sciencedirect.com/science/article/pii/S016890020900641X. Radiation Imaging Detectors 2008
 18.H.G. Spieler, E.E. Haller, IEEE Trans. Nucl. Sci. 32(1), 419 (1985). https://doi.org/10.1109/TNS.1985.4336867 ADSCrossRefGoogle Scholar
 19.E. Gatti, A. Longoni, P. Rehak, M. Sampietro, Nucl. Instrum. Methods Phys. Res. A 253, 393 (1987)ADSCrossRefGoogle Scholar
 20.S. Ramo, in Proceedings of the I.R.E, vol. 27, 584–585. (1939) https://doi.org/10.1109/JRPROC.1939.228757
 21.W. Shockley, J. Appl. Phys. 9(10), 635 (1938). https://doi.org/10.1063/1.1710367 ADSCrossRefGoogle Scholar
 22.S. Del Sordo, L. Abbene, E. Caroli, A.M. Mancini, A. Zappettini, P. Ubertini, Sensors 9(5), 3491 (2009). https://doi.org/10.3390/s90503491. http://www.mdpi.com/14248220/9/5/3491
 23.W. Riegler, G.A. Rinella, Nucl. Instrum. Methods Phys. Res. Sect. A Acceler. Spectrom. Detect. Assoc. Equip. 767, 267 (2014). https://doi.org/10.1016/j.nima.2014.08.044. http://www.sciencedirect.com/science/article/pii/S0168900214009796
 24.E. Frojdh, M. Campbell, M.D. Gaspari, S. Kulis, X. Llopart, T. Poikela, L. Tlustos. J. Instrum. 10(01), C01039 (2015). http://stacks.iop.org/17480221/10/i=01/a=C01039
 25.C. Dalitz, T. Schramke, M. Jeltsch, Image Process. On Line 7, 184 (2017). https://doi.org/10.5201/ipol.2017.208 CrossRefGoogle Scholar
 26.M. Holik, J. Broulim, V. Georgiev, Y. Mora, J. Zich, in 2017 25th Telecommunication Forum (TELFOR), pp. 1–4 (2017) https://doi.org/10.1109/TELFOR.2017.8249416
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