Characterization of a pnCCD for applications with synchrotron radiation

Nuclear Instruments and Methods in Physics Research A 711 (2013) 132–142

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Characterization of a pnCCD for applications with synchrotron radiation S. Send a,n, A. Abboud a, R. Hartmann b, M. Huth b, W. Leitenberger c, N. Pashniak a, J. Schmidt b, a,b,d ¨ , U. Pietsch a L. Struder a

University of Siegen, Department of Physics, Walter-Flex-Straße 3, 57068 Siegen, Germany PNSensor GmbH, R¨ omerstraße 28, 80803 M¨ unchen, Germany c University of Potsdam, Department of Physics, Karl-Liebknecht-Straße 24/25, 14476 Potsdam, Germany d Max-Planck-Institut f¨ ur extraterrestrische Physik, Giessenbachstraße, 85748 Garching, Germany b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 December 2012 Received in revised form 14 January 2013 Accepted 16 January 2013 Available online 7 February 2013

In this work we study the response of a pnCCD by means of X-ray spectroscopy in the energy range between 6 keV and 20 keV and by Laue diffraction techniques. The analyses include measurements of characteristic detector parameters like energy resolution, count rate capability and effects of different gain settings. The limit of a single photon counting operation in white beam X-ray diffraction experiments is discussed with regard to the occurrence of pile-up events, for which the energy information about individual photons is lost. In case of monochromatic illumination the pnCCD can be used as a fast conventional CCD with a charge handling capacity (CHC) of about 300,000 electrons per pixel. If the CHC is exceeded, any surplus charge will spill to neighboring pixels perpendicular to the transfer direction due to electrostatic repulsion. The possibilities of increasing the number of storable electrons are investigated for different voltage settings by exposing a single pixel with X-rays generated by a microfocus X-ray source. The pixel binning mode is tested as an alternative approach that enables a pnCCD operation with significantly shorter readout times. & 2013 Elsevier B.V. All rights reserved.

Keywords: pnCCD X-ray spectroscopy X-ray imaging Energy-dispersive Laue diffraction

1. Introduction The development and continuous improvement of the pnCCD (pn-junction charge coupled device) offers a variety of new possibilities to detect photons in X-ray diffraction experiments. In contrast to conventional position-sensitive detectors and CCD area detectors the pnCCD allows a time-resolved, simultaneous position- and energy-dispersive detection of X-rays. Originally the pnCCD was invented and fabricated at the Halbleiterlabor of the Max-Planck-Institut (MPI-HLL) with high technological effort for applications in X-ray astronomy. Its performance was successfully demonstrated within the scope of XMM-Newton [18] and will be used for the eROSITA satellite mission to be launched in 2014. Recently, synchronizing the cycle time to the repetition rates of free electron lasers, the pnCCD was utilized to detect intense soft X-ray pulses at FLASH and LCLS [19]. For these purposes the system serves as a flexible large area detector with the capability to both resolving single photons in the spectroscopic operation mode and counting photons with a high dynamic range in the imaging mode. Within a collaboration between the University of Siegen, the MPI-HLL and PNSensor GmbH pnCCD devices had been applied

n

Corresponding author. Tel.: þ49 271 740 3766; fax: þ 49 271 740 3763. E-mail address: [email protected] (S. Send).

0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.01.044

in various X-ray diffraction experiments with white synchrotron radiation. The one-shot availability of structural information was demonstrated by static reflectivity measurements [9] and energydispersive Laue diffraction techniques [15,16] exploiting the threedimensional resolution of the pnCCD in case of experiments with a stationary sample. An example of a time-resolved detection of interdiffusion processes in multilayers across characteristic absorption edges of the sample is given in [1]. Presently the University of Siegen is equipped with an 8.3 cm2 pnCCD camera, primarily developed for the X-ray satellite mission eROSITA [10], as depicted in Fig. 1. The on-chip electronics of this device contains an additional transistor that enables an active reset of all pnCCD channels after readout of the anodes0 charge signals and finally an enhancement of the count rate capability of a single pixel. The gain mode of the system can be chosen by defining the amplifiers0 gains within the CAMEX and the sampling number within the MCDS filter (multicorrelated double sampling, [13]). The analog signals are digitized by one 14-bit ADC per CAMEX and transferred via an optical fiber link to a Linux-based platform used for data acquisition and to control the pnCCD operation voltages. In this paper the performance of an eROSITA pnCCD test module with 128  128 pixels will be discussed for applications with synchrotron radiation. At first the characterization includes a simulation of the quantum efficiency and an investigation of the energy resolution by means of fluorescence spectroscopy in the hard X-ray regime

S. Send et al. / Nuclear Instruments and Methods in Physics Research A 711 (2013) 132–142

Fig. 1. Geometrical layout of the eROSITA pnCCD with frame store operation. The detector unit and the on-chip electronics are mounted on a carrier ceramic. The column-parallel readout of the image is performed by three CAMEX chips with 128 channels each [10].

between 6 keV and 20 keV. Analyzing the pnCCD response we will show that photons can be counted with a reduced but still sufficient energy resolution at low gain respectively high dynamic range settings. Subsequently the restriction of the SPC is motivated and quantified with respect to clusters developing in the case of high local count rates within Laue diffraction experiments. In the following part the dynamic range of the system is measured in the standard operation mode in terms of the CHC using the monochromatic (111) reflection of a Si crystal. Further studies on the capability of CHC enhancement are discussed for different back voltage settings by exposing a single pixel with intense X-rays generated by a microfocus X-ray source. Finally we show possibilities to extend the dynamic range of the pnCCD by testing an alternative operation mode with reduced readout times based on pixel binning. In general the obtained results will be helpful to understand the properties of the pnCCD in real X-ray diffraction experiments in order to make it more suitable for users at synchrotron facilities. Considering the system performance, especially as far as cluster development and CHC analyses are concerned, experimental conditions can be defined and optimized for particular applications.

2. The pnCCD detector The concept of the pnCCD as an energy-resolving area detector is based on the principle of sideward depletion in high resistivity

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silicon [5] allowing for an efficient combination of high X-ray detection efficiency, low noise level and fast readout. The first pnCCD systems fabricated for X-ray astronomy were full frame pnCCDs consisting of a single image area for incident X-rays [18]. Within further developments a higher detector performance could be achieved by adding an adjacent shielded frame store area to the image area to obtain the so-called frame store pnCCD [11]. The advantage of a frame store pnCCD compared to a conventional full frame pnCCD is a reduced probability for outof-time events. In full frame mode line-wise readout of the accumulated image is performed within a few milliseconds per frame leading to a substantial probability for the occurrence of out-of-time events depending on the incident photon flux. Those events arise, if incident X-rays interact with the detector material during readout, and are consequently assigned with an incorrect row index. In frame store mode only the fraction of X-ray photons which hit the image area of the detector during the fast transfer have a corrupt position information regarding the transfer direction. Therefor we use the pnCCD with frame buffer readout for applications with highly brilliant synchrotron radiation. The detector module of a frame store pnCCD with back side illumination is subdivided into an image area and a shielded frame store area with the same number of pixels. The sensitive volume of the chip consists of a fully sideward depleted, weekly n-doped Si bulk of 450 mm thickness. For the investigated energy range below 30 keV the cross section of photoelectric effect in Si is dominant compared to that of Compton scattering. Each photon interacting with the detector material in the image area creates a number of electron–hole pairs proportional to its energy. The electrons are separated from the holes by means of an electric field generated by an external back contact voltage and drift into quadratic pixels at the front side where they are stored in potential minima at a depth of about 8 mm below the surface. During the drift the charge cloud extends due to diffusion and electrostatic repulsion of the electrons. Each of the pnCCD channels is terminated with an anode allowing a parallel readout of complete columns. After a fast three-phase transfer to the frame store region the charge content of the accumulated image is shifted to the anodes and read out row-wise with a low noise level and a typical frame rate below 200 Hz. Throughout the readout time the image area is again sensitive for entering photons. The probability to detect an out-of-time event in frame store operation is given by the ratio of the transfer time between image area and frame store area and the cycle time. In the case of a pnCCD module with 128  128 pixels of 75  75 mm2 quadratic size the signal charges are shifted within about 77 ms (600 ns per line) into the frame store area. For typical cycle times of about of 5 ms the fraction of out-of-time events is less than 2%. After amplification by the on-chip electronics, the signal is filtered and multiplexed to optionally one or more output nodes by means of a CAMEX amplifier array. As long as the system is operated in the single photon counting mode (SPC) each registered event can be analyzed by measuring the number of electrons generated at a certain position within the detector volume during exposure time. The information about single photons delivered by the system is provided by two pixel directions, an energy and a time coordinate. A safe separation of different photons avoiding pile-up effects requires that the average count rate within the detector plane is much less than one photon per pixel and frame. In this case the pnCCD data pattern consists of single events where the signal charge is completely collected in one pixel and split events (double, triple and quadruple events), where the electrons split over at most four pixels. Split events occur if the interaction point within the detector is located close to the corner of a pixel. Typical charge cloud radii are about 10 mm depending on the number of generated electrons, i.e. the energy of the incident

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photon, and therefore influence the split statistics. The best possible energy resolution of the system can be obtained from single events, as the signal amplitudes of split events contain noise contributions of more than 1 pixel. On the other hand, calculating the center of mass of a split event, the position information is more accurate than in case of single events. Consequently, the position resolution of the pnCCD can be improved to the subpixel regime by means of appropriate analyses of split events [7]. In a new approach a position determination with an accuracy of below 2 mm was achieved for quadruple events [2]. In order to suppress thermally generated leakage current the pnCCD was cooled to a temperature of about 70 1C. Therefore the detector was installed inside a vacuum chamber that was kept at a pressure of 10–6 mbar. The X-rays enter the chamber through a Kapton foil of 200 mm thickness. Additionally a graphite-coated Al layer (thickness 20 mm) of high purity (4 99.999%) was added to ensure that no optical light can reach the detector. For applications in the soft X-ray region, the Kapton foil can be replaced by a thin Be window of a few mm thickness.

3. System characterization 3.1. Quantum efficiency The quantum efficiency (QE) of a semiconductor radiation detector is defined as the probability to detect an incident X-ray photon. Therefore the photon has to interact within the active Si bulk and generate signal charges. In the hard X-ray regime the QE of the pnCCD depends strongly on the X-ray energy, the effective thickness of the detector module and the choice of the housing window. For soft X-rays with energies below 1 keV also absorption effects within the thin entrance window of the pnCCD have to be considered (Fig. 2, left hand side). In a simple model the real experimental situation can be considered as depicted in the upper right part of Fig. 2: An X-ray photon, e.g. diffracted by a crystal, enters the detector unit at a certain incident angle 2y between the path direction of the photon and the normal of the detector plane. Only if the photon is not absorbed within the housing window it can reach the sensitive volume and produce a signal. In our setup the environment between the entrance window of the vacuum chamber and the detector module is evacuated to a pressure

below 10  6 mbar and therefore does not lead to significant absorption. Consequently, the QE of this system can be described according to [12] by Q EðE,2yÞ ¼ ð1expðmSi dSi =cos 2yÞÞexpðmW dW =cos 2yÞ

ð1Þ

with mSi being the energy-dependent linear attenuation coefficient of the Si layer, dSi its thickness and dSi/cos 2y is the effective maximum path length of the photon within the detector module. The corresponding contribution of the housing window (denoted with index w) is to be understood as a composition of various materials with different absorption behavior. In this sense the first term in Eq. (1) is the probability that the photon is absorbed by the Si bulk and the second one that it is not absorbed within the housing window. In a more accurate approach for low energetic photons metallization on the detector surface (Al, SiO2) leading to dead layers have to be taken into account as well. However, such effects play a minor role in case of hard X-rays and are not further considered here. In order to numerically simulate the expected QE of the pnCCD we used the linear attenuation coefficients of Si and the various window materials with their respective thicknesses in Eq. (1) and compared the obtained QE curve with that of an ideal (windowless) pnCCD with the same thickness of 450 mm. The results are shown in Fig. 2, right hand side within an energy range up to 50 keV for the case of normal incidence (2y ¼01). In the X-ray regime below 8 keV the ideal pnCCD is fully sensitive with a QE of nearly 100%. For hard X-ray energies above 10 keV the finite device thickness leads to an exponential decay of the QE curve. In contrast the used pnCCD detector module exhibits a maximum QE of about 78% at 11 keV. Due to the presence of the relatively thick housing window photons with energies below 3.5 keV are completely absorbed before they can reach the detector volume. In this way the sensitivity of the pnCCD could be well tuned to the experimental conditions at the white beam EDR beamline of the storage ring BESSY II, at which most of the measurements were performed: The shape of the calculated QE curve is comparable to the energy spectrum of the bending magnet after penetration through an air path of about 1 m length. Moreover, the vanishing QE at low X-ray energies prevents an unwanted background due to fluorescence radiation from air. Towards harder X-ray energies above 25 keV the QE of the used system and the ideal pnCCD do not differ, i.e. absorption effects within the housing window are

Fig. 2. Left hand side: quantum efficiency of a pnCCD in the energy range between 0.1 keV and 25 keV. The upper graph shows the intrinsic QE of the detector, while the lower curve shows the QE for a pnCCD with an applied optical and UV blocking filter. Right hand side: the housing window of the used pnCCD system containing a Kapton foil of 200 mm thickness and an additional Al layer of 20 mm thickness leads to significant absorption of soft X-rays. In the upper right part the geometrical conditions for the simulation of photons entering a semiconductor radiation detector are illustrated.

S. Send et al. / Nuclear Instruments and Methods in Physics Research A 711 (2013) 132–142

negligible in this case. Taking into account estimated uncertainties concerning various layer thicknesses and inhomogeneities of the housing window the relative accuracy of the obtained QE values is better than 2%. The calculated QE curves show that the pnCCD with its technical realization can be used for energy-dispersive X-ray diffraction experiments with synchrotron radiation in a wide energy range starting at about 3.5 keV. In white beam applications the integrated diffraction signals generated by a sample have to be normalized to the QE values in order to obtain real scattered intensities. In principle the QE of the used pnCCD module can be enhanced by using a Kapton housing window with a smaller thickness of about 100 mm and optimizing the routes to achieve light-tightness [6]. 3.2. Energy resolution The energy resolution of the pnCCD was measured for hard X-rays in the energy range between 6 keV and 20 keV at the white beam EDR beamline of BESSY II by means of fluorescence spectroscopy. Illuminating different metallic samples with white synchrotron radiation we could analyze characteristic fluorescence radiation distributed homogenously within the detector plane. The samples typically consisted of thin foils containing Fe, Cu, Pb and Mo. In another experiment the Rb line of a pine wood sample treated with RbOH served as an energy calibration signal. In all cases the element specific fluorescence lines were accompanied by a weak background continuum produced by air-scattered photons. For each measurement the pnCCD raw data sets contained 300 dark frames recorded in the absence of X-rays and 20,000 signal frames with the fluorescent samples exposed to white synchrotron radiation. Using a readout frequency of 200 Hz in frame store operation which is in accordance with a complete exposure time of 100 s, the photon rate in the active pnCCD area was about 100 events per frame at a storage ring current of 200 mA. Noise, offset and common mode were calculated from the dark frames and subtracted from the real photon events accumulated in the signal frames, as described in Andritschke et al. [3]. For all measurements presented in this paper the mean detector noise s including electronic and thermal noise contributions corresponds to an equivalent noise charge of 8 e– (rms) per pixel. In a final step of the data analysis the pattern recombination to individual photon hits, characterized by an integrated signal amplitude and two center of mass coordinates in case of split events, is performed with a user-defined threshold ns. Events with a signal amplitude below the selected threshold are not considered for further data treatment. For applications with synchrotron radiation n is usually chosen to be an integer value between 4 and 8. The choice of n does not only affect the distribution of split events but also the energy resolution itself. In order to obtain gain and charge transfer inefficiency (CTI) correction factors quantifying the inhomogeneities between different pnCCD channels a Gaussian with linear background was fitted to the amplitude distribution in the vicinity of the fluorescence energy. By means of a column-by-column analysis of the recorded pulse height spectra the average gain and the deviations of the individual channels0 gains could be determined. For the presented measurement the dispersion of these gain values about the mean gain is below 2%. CTI correction factors were extracted by fitting the peak position shift along the rows, according to the model described in Andritschke et al. [3], leading to an average CTI of 3  10–6. Applying the calculated gain and CTI factors to each individual event and taking into account single and double events with a splitting parallel to the transfer direction of the accumulated image the FWHM of the particular fluorescence line was finally

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obtained. According to the limited ADC range the highest possible gain mode was selected (1/16 of the maximum gain of 2.56 ADU/eV) to ensure that energies between 6 keV and 20 keV including pile-up could be detected safely. Table 1 gives an overview of the possible pnCCD gain modes in case of 8-fold CDS with their noise levels, pulse heights of CuKa radiation (E¼8041 eV) and dynamic ranges. Fig. 3 shows the measured FWHM of the corresponding single peaks for various characteristic energies emitted by the illuminated samples using an event threshold of 6s. With respect to further quantitative analyses the PbLa and MoKa lines were excluded due to the spectral overlaps of PbLa1 with PbLa2 and MoKa1 with MoKa2 leading to a significant broadening of the energy peaks. The remaining widths of the Fe, Cu, Pb, Rb and Mo fluorescence lines were fitted by means of a power function of the form FWHM(E)p(E0 þE)c where E0 and c are constants. Hence we obtained c¼0.42470.092 which is in good agreement with the expected behavior of a semiconductor radiation detector [17],   FE 1=2 FWHMðEÞ ¼ 2:355w ENC 2 þ w

ð2Þ

Here F ¼0.115 is the Fano factor of Si, w¼3.65 eV the electron– hole pair creation energy in Si and 2.355 the conversion factor between the standard deviation of a Gaussian and the FWHM. The first term includes all electronic and thermal noise components of the detector given by the equivalent noise charge ENC. The second term accounts for statistical fluctuations of the number of created electron–hole pairs (Fano noise) depending on the incident Table 1 Gain modes of the pnCCD and related performance parameters. The dynamic range for a particular experiment is determined by the maximum energy that can be detected per frame within a single pixel without exceeding the ADC range. Gain [ADU/ eV]

Gain/max. gain

2.56

1/1

1.28 0.64 0.16 0.04 0.02 0.01

1/2 1/4 1/16 1/64 1/128 1/256

s [e–]

8.2 8.2 8.2 9.3 18.7 36.8 65.6

Pulse height (CuKa) [ADU]

Not measurable 10,044 5019 1300 332 169 83

Max. energy per pixel [keV]

5.6 11.2 22.4 89.6 358.4 716.8 1433.6

Fig. 3. Energy resolution of the pnCCD for different fluorescence energies at a signal threshold of 6 s described by the FWHM of the individual peaks containing only single events. The gain was set to 1/16 of the highest gain. The solid curve is a least-squares fit through the data.

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photon energy. With a gain setting of 1/16 the maximum achievable energy resolution of the pnCCD at a signal threshold of 6 s is limited by ENC  13

ð3Þ

The fitted value of the effective ENC also includes a noise component caused by possible misinterpretations of individual events within the pnCCD data pattern concerning the correct analysis of split events. The pattern form of a certain event depends on the threshold level. In case of a double event, where the signal charge is spread over two neighboring pixels with a low amplitude in one of the pixels, the lower amplitude might fall below threshold and thus be cut from the event. Therefore the event is counted as a single event with a too low charge content increasing the FWHM of the fluorescence line. Further studies on the influence of different threshold settings on the energy resolution of the pnCCD revealed that compared with the data of Fig. 3 the FWHM was reduced by about 20 eV at an event threshold of 4 s. In this case the single peak of CuKa radiation with an energy of 8041 eV could be resolved with 195 eV (FWHM). The standard deviation of the corresponding Gaussian is about 83 eV and enables a relative energy resolution in the order of 1% being sufficient for many applications with synchrotron radiation. In contrast to eROSITA pnCCD systems fabricated for X-ray astronomy with a typical ENC below 3 e– (rms) per pixel [14] the device which is used here is optimized for the detection of higher count rates based on a large dynamic range rather than to ensure the best possible energy resolution. The simultaneous position and energy resolution of the pnCCD was used for fast analyses of crystalline materials by means of energy-dispersive Laue diffraction with white synchrotron radiation. This method has the clear advantage that the crystallographic unit cell of the sample can be extracted within a single X-ray exposure of the arbitrarily oriented crystal by resolving both the Laue spots0 positions and energies and analyzing the information in reciprocal space coordinates, as described in detail in Send et al. [16]. In this case the unit cell parameters are accessible without any a priori information about the sample itself. Fig. 4 shows a Laue pattern of a tetragonal hen egg-white lysozyme single crystal recorded by an eROSITA pnCCD module with 384  384 pixels. The average lattice parameters obtained ˚ c¼(37.9 70.9) A˚ from this measurement are a¼(79.1 71.6) A, and a ¼ b ¼ g ¼(89.5 73.1)1 in good agreement with the expected structure of hen egg-white lysozyme.

Fig. 4. Laue pattern of a hen egg-white lysozyme crystal. The Laue spot energies were detected between 9 keV and 25 keV.

3.3. Dynamic range The dynamic range of the pnCCD is limited by the input ADC range and the selected gain of the front-end electronics. Depending on the experimental conditions the amplification stages of the system can be adjusted by the user. At the end of data acquisition the raw amplitudes of a frame are digitized by a 14-bit ADC providing a scale of about 0y14,300 arbitrary digital units (ADU). With the choice of the gain the signal pulse height belonging to a particular X-ray energy is well defined as a result of the amplification process. For a specific operation mode the overall gain is given by the ratio between the mean amplitude of a photon (in ADU) and its energy (in eV). Especially in the measurements of energy resolution described in Section 3.2 the covered amplitude range extended from 1040 ADU (FeKa, E¼6400 eV) to 3200 ADU (MoKb, E¼19,644 eV) according to an average gain of 0.16 ADU/eV. The different gain settings are realized through switched capacitors in the CAMEX ASIC after the first amplification of the on-chip JFETs of the pnCCD. Both, the pnCCDs JFETs and the first CAMEX amplifier are responsible for the noise of the system at highest gain. Typically a signal-to-noise ratio of 300:1 is provided

Fig. 5. FWHM of single peaks for different fluorescence energies as a function of the selected gain. The data were taken with 8-fold correlated double sampling and six different gain settings for the CAMEX amplifiers. Again, a signal threshold of 6 s was used for data analysis and event recombination.

for 6 keV X-rays. The signal-to-noise ratio decreases with lower gain because the corresponding signal decreases, whereas the noise of the pnCCD0 s front-end stays constant. Therefore the relative energy resolution decreases. In the high gain mode the contribution of the CAMEX to the total noise is approximately 0.5–1 e– (rms), the on-chip JFET typically contributes 3–5 e– (rms). In the lowest gain mode (1/256 of the maximum gain) the signalto-noise ratio can therefore be reduced to about 100:1 dominated by the CAMEX contributions. This leads to a total system noise equivalent to 600 to 900 eV (FWHM). In the lowest gain mode one pixel is able to store approximately 1.1 MeV of photon energy, the dynamic range is 1500:1–2000:1. The results shown in Fig. 5 also depend on the monochromacity and the intensity of the incident

S. Send et al. / Nuclear Instruments and Methods in Physics Research A 711 (2013) 132–142

photon beam, the selected event thresholds and the specific experimental and instrumental background. In X-ray spectroscopy, where the position and energy information of every single photon is of interest, the pnCCD is operated in a high gain mode to achieve the best possible energy resolution. As discussed previously in this case SPC conditions have to be fulfilled to guarantee a sufficiently low probability for spatial overlaps of different charge clouds. On the other hand the gain has to be selected in such a way that the energy range of interest is completely covered by the range of the ADC including the detection property of pile-up events. For example the highest possible gain to detect RbKb radiation (E¼14,978 eV) with 8-fold correlated double sampling and without event pile-up recognition is 0.64 ADU/eV leading to a signal pulse height of about 9600 ADU and a maximum detectable energy of about 22,000 eV per pixel. For X-ray imaging techniques, in contrast to spectroscopic applications, integrated intensities produced by many photons per pixel incident on the detector within the integration time are of interest. In X-ray imaging the determination of absolute photon numbers relies on the correct interpretation of pile-up events for which the position and energy information about individual photons cannot be conserved, as described in Section 3.4. For that purpose a low gain mode has to be selected in order to be able to detect as many photons per pixel as possible without exceeding the ADC limit. Quantitative analyses of the pnCCD response in case of homogeneous illumination with fluorescence radiation of different energies show that the energy resolution of the system decreases towards low gains (Fig. 5). By reducing the gain of the CAMEX amplifiers this noise contribution increases compared to the noise at the highest gain, while on the other hand the dynamic range is enhanced. Consequently, in the imaging mode using a low gain of 0.01 ADU/eV, the FWHM of the RbKb single peak after gain and CTI corrections could not be smaller than about 650 eV. Up to higher energies in the order of SnKa (E¼25,192 eV) the line width already reaches the 1 keV regime. However, in this gain mode, a single pixel is able to deal with a total deposited X-ray energy above 1 MeV without losing the amplitude information, as discussed in Section 3.5. At small energies the marked broadening of fluorescence peaks results in a spectral overlap of FeKa and FeKb for gain values below 0.04 ADU/ eV. In this case the corresponding lines could no longer be separated properly, so that the FWHM could not be defined for individual peaks. The same effect was observed for CuKa and CuKb lines overlapping at the minimum gain of 0.01 ADU/eV.

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of pile-up events can be distinguished, depending on the interaction points of the participating photons within the Si bulk: If the spatial distance between two (or more) generated charge clouds is sufficiently smaller than the pixel size, the pattern measured at the front side can be a single or a valid split event in terms of SPC, also referred to as event pile-up. If the interaction points are well separated from each other with distance in the order of the pixel size, the pattern can be an invalid split event. However, in many cases with high local count rates the charge clouds generated by several different photons overlap in such a way that the detected pattern spreads over more than four pixels to create big cluster events, also referred to as pattern pile-up. Consequently, for event as well as pattern pile-up, the precise position and energy information about the individual photons cannot be conserved. In case of a monochromatic illumination of the pnCCD the numbers of photons recorded within a sufficiently large number of pnCCD frames follow a Poisson distribution with mean value l depending on the incident intensity and the quantum efficiency of the pnCCD, i.e. the photons0 energy. Hence, the statistical probability Pk(l) to detect k photons during one integration cycle is given by [4] Pk ðlÞ ¼

lk k!

el

ð4Þ

If the illuminated area contains only one pixel or a few adjoined pixels, the pile-up probability Ppile-up corresponds to the probability to measure overlapping charge clouds generated by two or more photons, Ppileup ðlÞ ¼

1 X lk l e ¼ 1ð1þ lÞel k! k¼2

ð5Þ

At low average count rates l o0.1 the pile-up probability is below 0.5% so that position and energy of individual photons can be discriminated. Above l ¼0.1 the function of Eq. (5) exhibits a strongly rising behavior before it converges to unity in the range of l 410 (Fig. 6). In this case the pnCCD data volume contains enhanced contributions of pile-up events, i.e. the system effectively acts as an integrating X-ray detector. The pnCCD response at high average count rates, for which in the hard X-ray regime

3.4. Single photon counting capabilities The results concerning energy resolution and effects of gain selection which are presented in Sections 3.2 and 3.3 are based on investigations of individual photon hits within the pnCCD plane. Quantitative analyses were restricted to single events with the smallest noise contribution. However, these considerations are only valid as long as there are no spatially overlapping electrons generated by different photons (pile-up events), i.e. as long as a safe SPC operation is ensured by the experimental conditions. Previous studies have shown that for homogenous illumination of the pnCCD the fraction of pile-up events of the total data pattern is negligible, if not more than about 3% of the pixel area is filled with electrons during one integration cycle. Under these circumstances the pnCCD allows simultaneous position-, energy- and timeresolved X-ray spectroscopy with white synchrotron radiation. A variety of other applications, e.g. X-ray imaging techniques, rely on a detector system being capable to accumulate photons with good statistics. Then, the local count rates within the detector plane typically exceed the SPC limit and pile-up events are the major contribution to the recorded data set. In general, two classes

Fig. 6. Pile-up probability within a single pixel as function of the mean count rate according to Eq. (5). A safe SPC operation for spectroscopic applications can only be possible, if the probability to detect spatially overlapping charge clouds is sufficiently small, i.e. if l o0.1. Towards higher local count rates the signal amplitudes generated by different photons are integrated. Then the pnCCD, operated in the imaging mode, serves as a fast conventional CCD without energy resolution.

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Fig. 7. Spatial distribution of signal amplitudes within the (105) reflection of g-LiAlO2 (spot energy 21.3 keV) in a linear color scale of calibrated energies (in keV). In all the depicted cases the integrated signal amplitudes of individual clusters are integer multiples of the spot energy. The white numbers indicate the number of photons that generated the observed clusters. (a) Two spatially separated single events of 21.3 keV fulfilling SPC conditions. (b–d) Cluster events of various sizes and shapes generated by overlapping charge clouds belonging to different photon hits. The pixel with the highest signal amplitude in (d) is an event pile-up of two 21.3 keV photons with a total energy of 42.6 keV.

the pixels’ saturation limit is typically reached at l ¼100, will be investigated in Section 3.5. If the incident beam is polychromatic, the pile-up probability can be generalized directly from Eq. (5) to P pileup ðLÞ ¼ 1ð1 þ LÞeL

ð6Þ

where

L¼

n X

li

ð7Þ

i¼1

Here the white beam with average count rate L is considered to be a composition of many monochromatic beams with different energies, each of them following Poisson statistics with an individual mean value li. The occurrence of event pile-up and pattern pile-up was studied within an energy-dispersive Laue diffraction experiment using a pnCCD module with 256  256 pixels both in the image area and in the frame store area. For that purpose a tetragonal gLiAlO2 crystal was exposed to white synchrotron radiation at the

EDR beamline of BESSY II. By means of the pnCCD the positions and energies of various Laue spots were measured simultaneously and used for lattice determination and indexing of the Laue pattern, as described in Send et al. [15]. The reflections of the sample were spread over a quadratic area of about 7  7 pixels according to the incident beam size of 0.5  0.5 mm2. Under the experimental conditions the energy spectra within the recorded Laue spots were generated by a monochromatic signal diffracted by the crystal and a suppressed white background as a result of scattering at air molecules. If background contributions are negligible and different harmonics of the considered reflection are not present, the number of photons per frame located within the spot area follows Poisson statistics according to Eq. (4). In the described experiment the most intense Laue spot in the recorded Laue pattern of g-LiAlO2 was the (105) reflection with an energy of 21.3 keV and a scattering angle of 27.91. Normalizing its integrated intensity to the number of accumulated signal frames the average count rate per frame corresponded to a Poisson mean value of about 7.3 leading to a high statistical probability for pattern pile-up within the spot. By means of a frame-wise

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Fig. 8. Measured signals of 11.1 keV photons in the vicinity of the central pixel as a function of count rate. If the CHC of the illuminated pixel is exceeded, surplus charges spill over to adjacent pixels perpendicular to the transfer direction first. The signal amplitudes of different images shown in a linear color scale are not normalized to each other.

analysis of the spatial amplitude distributions the occurring event patterns could be classified in terms of individual photon hits fulfilling SPC conditions and pile-up events. Fig. 7 shows examples of four different patterns detected within a 16  16 pixel area surrounding the (105) spot obtained after noise, offset and common mode subtraction, gain and CTI correction and conversion into calibrated energies (in keV). In Fig. 7(a) where two single events are spatially separated the energies of the individual photons can be determined with a high resolution. If the charge clouds generated by more than one photon overlap, they generate pattern pile-up which results in cluster events of arbitrary sizes and shapes (Fig. 7(b–d)). In the example of Fig. 7(b) two clusters containing the amplitudes of three and four photons were recorded, accompanied by a double event belonging to a single photon in the lower part of the spot. If higher photon numbers are involved in a particular event, clusters with complex shapes extending over large pixel areas within the pnCCD plane can be formed, as depicted in Fig. 7(c) and (d). Because of the experimental conditions for energy-dispersive Laue diffraction of g-LiAlO2 with a relatively large beam size and an attenuated primary beam intensity pattern pile-up is the dominant effect compared to event pile-up. Although the information about single photons is lost in case of pile-up, the number of detected photons generating a particular cluster can be found by integrating the individual signal amplitudes within the cluster area and dividing it by the spot energy obtained from single hits, if only photons with the same energy overlapped. In general, pileup events generated by photons with different energies cannot be resolved in this way. An approach, where such types of events are treated by means of statistical methods will be discussed within a future work based on Laue diffraction experiments at macromolecular crystals described in Send et al. [16]. 3.5. Charge handling capacity Especially for time-resolved measurements, e.g. with respect to the detection of structural phase transitions within crystalline materials, the dynamic range of the pnCCD is of great importance. In contrast to spectroscopic applications relying on a precise energy resolution of individual photons, the time evolution of a particular diffraction signal is of major interest. Therefore it is desirable that as many photons as possible can be detected in a

single pixel with good counting statistics. In the simplest situation the illumination of a single crystal with white X-rays gives rise to Bragg reflections of well defined and measurable energies. In general the image of a Laue spot within the pnCCD plane consists of pile-up events generated by a Poisson distributed number of photons depending on the incident beam intensity and size. The dynamic range of the pnCCD is determined by the readout time and the detectable photon flux per pixel according to the maximum number of electrons that can be stored within a pixel. In order to study the pnCCD response at different count rates the (111) reflection of a cubic Si(111)-crystal was excited by exposing the sample with a white synchrotron beam. In the chosen geometry the angle of incidence referred to the crystal surface amounted 10.31 giving rise to a spot energy of 11.1 keV measured by the pnCCD at a gain of 0.64 ADU/eV. Under the experimental conditions the contributions of higher harmonics of the selected reflection, i.e. (222) and (333) with energies of 22.2 keV and 33.3 keV, are strongly suppressed and therefore negligible. In this sense the Laue spot on the detector can be considered as a sharp monochromatic signal, for which the integrated intensity is given by the ratio between the accumulated signal amplitude and the signal amplitude of one single 11.1 keV photon. The diffracted beam was guided through a pinhole of 15 mm diameter located close to the housing window in order to confine the incident photon flux to the center of 1 pixel. Taking into account the geometry of the used experimental setup and the enhanced divergence of the reflected beam compared to the primary beam the radius of the spot area covered within this pixel was less than 20 mm. Moreover the detector plane was oriented perpendicular to the diffracted beam to ensure that photons enter the pnCCD at normal incidence. Consequently, with respect to the data shown in Fig. 2, the quantum efficiency of the pnCCD detector system amounted about 78% for this experiment. The intensity of the primary synchrotron beam with a quadratic size of 0.1  0.1 mm2 could be varied over three orders of magnitude by means of a flexible absorber system containing Al layers of various thicknesses between 0.1 mm and 1.5 mm. Prior to quantitative measurements of the charge handling capacity (CHC), pulse height and line width of single photon events were studied for low average count rates of a few counts per frame (cpf). Under these conditions the individual single

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Fig. 9. Column profiles profiles of the charge distributions of Fig. 8 after conversion from signal amplitudes into real photon numbers. The maximum number of electrons per pixel corresponds to approx. 100 X-ray photons with an energy of 11.1 keV.

photon peak at 80 ADU could be resolved with an FWHM of about 10 ADU being sufficient to separate pile-up signals of different orders from each other and to assign the correct photon numbers to each peak. For higher incident photon fluxes recorded event patterns are depicted in Fig. 8 for various average count rates. The images comprise an area of 19  7 pixels (horizontal  vertical) in the vicinity of the illuminated pixel. If the number of generated electrons within one pixel is below its CHC, all signal charges are stored completely within the pixel. A stepwise increment of the primary beam intensity up to count rates of 1420 cpf led to a successive broadening of the measured signal perpendicular to the transfer direction. As soon as a pixel is completely filled with electrons any additional charge deposited within this pixel spills over to neighboring pixels due to electrostatic repulsion of the electrons. The confinement of the signal charges within a pixel in transfer direction is determined through the reverse biased p þ shift registers and their external voltages. In the standard transfer depth of the pnCCD of about 8 mm the barriers for electrons are typically DV¼3.5 V. In the direction perpendicular to the charge transfer the electron potential well is generated by implanted channel stops. Under standard operation conditions the threshold seen by the electrons varies between DV ¼2 V and 2.5 V. Electrons therefore escape first across this weakest barrier perpendicular to the transfer direction. Confinement in the depth of the pnCCD is determined by the offset of the p þ shift registers and the depletion voltage on the p þ back side voltage. The potential confinement in this direction is substantially higher than in the two directions parallel to the surface discussed above. In principle, despite the loss of position information about individual photons in horizontal direction, the interaction point of the intense X-ray beam can be reconstructed as the center of mass of the measured pattern with a time resolution given by the readout frequency of the pnCCD. In order to analyze the spatial charge distributions of Fig. 8 in a more quantitative way column profiles were extracted for various count rates to determine the mean CHC of a pixel. By normalizing the corresponding pulse heights to the signal amplitude of a single 11.1 keV photon the profiles depicted in Fig. 9 were obtained. The successive filling of additional pixels in row direction due to enhanced incident photon fluxes results in a saturation of those pixels, so that the average signal amplitude per pixel becomes constant. Intensity enhancement up to an average count

rate of 1420 cpf does not change the measured signal amplitudes of already saturated pixels any further. Maximum detectable amplitudes within neighboring pixels show only slight fluctuations in a range of 2% around the mean CHC. The mean value can be interpreted as the average maximum number of photons with the given energy that can be recorded in a single pixel at the saturation limit. For experimental situations with an average count rate of 1420 X-ray photons with 11.1 keV energy incident on one single pixel the charge spilling extends over a wide range in horizontal direction, so that 5 pixels on both sides of the center pixel are saturated. The measured amplitude of these pixels is equivalent to 100 11.1 keV X-ray photons. Apart from statistical fluctuations in the process of electron–hole pair creation in Si, one 11.1 keV photon creates 3041 signal electrons within the detector volume (3.65 eV per electron–hole pair). Consequently, the maximum average number of electrons stored within the pixels of the pnCCD can be estimated by CHC ¼

100  11:1keV  300000e 3:65eV=e

ð8Þ

Taking into account the relative errors of this measurement (about 0.4% for the mean value of the accumulated photon number and 0.9% for the spot energy) the relative accuracy of the obtained CHC value is better than 1%. The single-pixel CHC corresponds to a total deposited energy of 1.11 MeV and, in case of the Si(111) reflection, to an integral count rate of 20,000 cps per pixel at a frame rate of 200 Hz. Obviously the maximum detectable flux without losing position resolution is inversely proportional to the incident photon energy. Possibilities to expand the count rate capability for particular experiments by means of pixel binning ensure a faster readout of the pnCCD image and are discussed in Section 3.6. The single-pixel CHC has been determined for two different operating modes of the pnCCD, namely in a high-resolution mode for spectroscopic applications (spectroscopy mode), and in a dedicated imaging mode. In the latter mode, operating voltages and detector timing are optimized to allow for a maximum number of electrons being stored within one pixel [8]. In order to study the effect of different operating modes in a quantitative way the pnCCD was exposed to an intense monochromatic X-ray beam generated by a 30 W microfocus X-ray tube (INCOATEC ImS

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Fig. 10. Influence of the pnCCD operating mode on the focal spot signal of the ImS source. (a) X-ray spectroscopy mode. (b) X-ray imaging mode. The different spatial charge distributions shown in a linear color scale are not normalized to each other.

source) equipped with a Cu anode. The ImS source delivers CuKa radiation focused by a MONTEL Quazar multilayer system down to a focal spot diameter of 56 mm with a maximum usable photon flux of about 3  108 cps. According to the data shown in Fig. 2 CuKa radiation is recorded with a reduced quantum efficiency of about 65%. For this experiment one single pixel was illuminated with an incident X-ray flux of 3.5  106 cps corresponding to an average measurable count rate of 11,400 cpf at a frame rate of 200 Hz. In the spectroscopy operation mode the incident X-ray flux leads to massive charge spilling in row direction extending over an area of 49  3 pixels (Fig. 10(a)). The spatial charge distribution is inhomogeneous but relatively symmetric around a maximum close to the center pixel. Owing to the successive enhancement of the back side potential and the accordingly deeper potential well more electrons can be stored within the center pixel reducing the horizontal spread of the signal stepwise. In the final configuration, optimized for imaging, the extension of the charge distribution within the focal spot of the X-ray source could be decreased to about 5 pixels in horizontal direction (Fig. 10(b)). Charge spilling effects at high photon fluxes are a constraint to be considered in X-ray diffraction experiments with synchrotron radiation. For applications relying on Laue techniques at inorganic crystals giving rise to intense Bragg reflections the exceeding of the single-pixel CHC degrades the position resolution of the pnCCD. A dedicated operation mode for X-ray imaging experiments helps to confine the spilled electrons within smaller pixel areas. Under these conditions the measurement of Laue spot energies is possible by means of X-ray exposures with sufficiently low count rates, for which the pile-up probability of different photons is negligible. On the other hand, applying an appropriate background correction, integrated spot intensities can be extracted from high count rate experiments with improved statistics. In the sense that structural information is quantitatively available, selecting the pnCCD operation mode according to the experimental conditions is beneficial for X-ray imaging techniques.

3.6. Time resolution In the case of static X-ray diffraction experiments the information about single photons delivered by the pnCCD comprises threedimensional data sets spanned by two spatial and the energy coordinates. The achievable resolution within this data volume is given by the energy and position resolution of the system. Assigning center of mass coordinates to individual events and applying well known relationships between the X-ray energy and the generated charge cloud size split events can be identified with a significantly better position resolution than the pixel size [7,2]. However, if the arrival time of single photons is of interest as well, the data volume becomes effectively four-dimensional. The additional time coordinate is usually characterized by a frame index enumerating the recorded frames in which a certain number of events occurred. In that sense the time resolution of the pnCCD is given by the time difference between two subsequent images. In the standard operation mode of the pnCCD full images are read out with a frequency of 200 Hz corresponding to a time resolution of 5 ms. An example of structural phase transitions, where the fourdimensional resolution of the pnCCD was exploited to measure

dynamic interdiffusion processes in FePt multilayers across the PtL edges, is described in Abboud et al. [1]. Within a further experiment the so-called ‘on-chip pixel binning’, also referred to as timing mode [18], was tested. By sacrificing spatial resolution in one direction (transfer direction), the signal of n pixels is accumulated and read out, thus forming so-called macro-lines of n-times the pixel width. Since leakage current is negligible at operating temperatures below  60 1C, this process can be regarded as noiseless summing of pixel contents. The spatial resolution in the other direction remains unaffected by this method. Starting with a readout time of 5 ms (200 Hz frame rate) of the entire sensitive area, the pnCCD could be read out at higher speeds of about 370 Hz, 700 Hz, 1200 Hz and 2000 Hz in case of 2-fold, 4-fold, 8-fold and 16-fold binning respectively. Using Fe55 as a calibration source it was verified that the energy resolution remains at a constant value, as expected. The success of a scattering experiment at a polymer film of P3HT solved in chloroform (2 mg/ml) and grown on a Si/SiO2 substrate was relying on the feasibility of this operating mode. The integrated signal of the (100) Bragg peak was recorded in reflection geometry with the sample exposed to intense CuKa radiation delivered by the ImS laboratory X-ray source. The obtained accumulated images are depicted in Fig. 11 with the pnCCD operated in the standard mode (Fig. 11(a)) and in the pixel binning mode for increasing values of n (Fig. 11(b–d)). Obviously, the enhanced degree of binning leads to a compression of the diffraction signal in transfer direction, but enables a gain in readout speed by about one order of magnitude and finally in the achievable dynamic range for the experiment. In this sense, using 8-fold binning structural phase transitions can be recorded with a time resolution below 1 ms.

4. Summary and conclusions In this paper we investigated the performance of a frame store pnCCD detector system in the hard X-ray regime for X-ray spectroscopy and X-ray imaging with synchrotron radiation at the example of an eROSITA test chip with 128  128 pixels of 75  75 mm2 size. The QE of the device was simulated taking into account the thickness of the absorbing Si bulk and the housing window of the detector chamber. The calculations show that under the given conditions the detector is sensitive to X-ray energies above 3.5 keV with a maximum QE of about 78% at 11 keV. In principle the sensitivity of the used pnCCD system can be enhanced by choosing a thinner housing window including Kapton and Al layers of smaller thicknesses. The measurements of detector parameters being relevant for synchrotron applications were performed by means of fluorescence spectroscopy and Laue diffraction techniques using white synchrotron radiation and monochromatic X-rays delivered by an INCOATEC ImS source. In a medium gain mode FeKa radiation could be resolved with an FWHM of about 200 eV for single events at a typical signal threshold of 6s being comparable with the energy resolution achieved by conventional energy-dispersive detectors. Owing to the limited ADC range the capability to record high local photon fluxes requires a low gain selection leading to a broadening of the line energy peak.

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Fig. 11. (1 0 0) reflection of the P3HT sample measured for different binning modes: (a) no binning (image size: 128  128 pixels, frame rate: 200 Hz); (b) 2-fold binning (128  64 pixels, 370 Hz); (c) 4-fold binning (128  32 pixels, 700 Hz) and (d) 8-fold binning (128  16 pixels, 1200 Hz).

In general two different X-ray detection modes of the pnCCD defined by the conditions of a particular experiment have to be distinguished: single photon counting and photon integration. In the case of sufficiently low local intensities within the pnCCD plane the event patterns generated by incident X-rays are spatially separated. Then, the positions, energies and arrival times of individual photons can be measured simultaneously and the pnCCD acts like a fourdimensional X-ray detector for spectroscopic applications. If the event density is higher, charge clouds generated by different photons can overlap as a result of enhanced pile-up probability giving rise to cluster development. This effect was described for a Laue diffraction experiment at a g-LiAlO2 crystal by means of a frame-wise analysis of the spatial amplitude distributions within the (105) reflection. As discussed exemplarily for a few event patterns of various sizes and shapes the information about single photons is lost in case of event and pattern pile-up. However, if the cluster contains only signals of monochromatic X-rays, the number of involved photons can be found by integrating the recorded amplitudes and normalizing to the spot energy obtained from single hits. The dynamic range of the pnCCD is determined by the CHC, i.e. the maximum number of electrons that can be stored within a pixel. Under standard operation conditions the mean CHC amounts about 300,000 e– measured by exposing one single pixel to monochromatic X-rays of a Si(111) reflection. If the CHC is exceeded the surplus charges spill over to neighboring pixels perpendicular to the transfer direction owing to electrostatic repulsion of the electrons. In this case an extension of the signal in transfer direction is suppressed by horizontal potential barriers between two adjacent pnCCD rows. Further investigations of the pnCCD response using CuKa radiation of an ImS X-ray source showed that a higher back side potential results in a minor spilling effect. For X-ray imaging applications the pnCCD operated at an enhanced back contact voltage provides good opportunities to detect intense diffraction signals of the sample. The second possibility to increase the dynamic range of the pnCCD is to reduce the cycle time required to shift one accumulated image to the frame store area and to read it out. In order to achieve a shorter readout time the pixel binning mode was tested within a diffraction experiment at P3HT films. It could be demonstrated that by binning of a user-defined number of rows the time resolution of the pnCCD improves markedly. The described method delivered a frame rate enhancement from 200 Hz in the standard mode up to 2000 Hz for 16-fold binning. In this sense the pnCCD operated in the pixel binning mode enables measurements of structural phase transitions on a time scale of sub-milliseconds.

Acknowledgment This work was supported by BMBF Verbundforschung, Project number 05K10PSB. We gratefully acknowledge the financial support.

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