6.2 Spatial and Readout Split
6.2.2 Charge Collection and Distribution
Besides the actual penetration depth of the incident X-ray photon, also its location in the sensor plane and the arrival time are generated using Monte Carlo methods. For this x, y and t coordinates, uniformly distributed random variables are used. They are distributed in the interval [0,1) and can be redistributed later according to the desired sensor geometry and applied timing. The pixel size, the number of pixels – quadric pixels and sensors are assumed – can be defined. The further development of the charge cloud depends on the time it takes to reach the front side of the sensor. A simple two dimensional electric field is applied to calculate the drift times. The solution of the one-dimensional Poisson equation (eq. (2.13)) is a parabola[72] that describes the one dimensional electrostatic potential in z direction with the boundary conditions defined by the applied voltages at the front and the back side, UF and UB.
Φ (z) =−qND 2s z 2+qN Dds 2s + UB−UF ds z+UF (6.2)
The thickness of the sensor is ds. To obtain a sideward drift at the potential minimum in z, the front side voltage UF is implemented as a radial dependent function. With the electron mobility as further input parameter, the velocity a test particle is accelerated to in the electrostatic potential, can be calculated. The time it needs from the interaction position of the incident X-ray photon to the point at which a significant sideward drift towards the pixel centre starts is used to calculate the charge cloud expansion.[73] Parts of the charge
6.2 Spatial and Readout Split 89 0 2 4 6 10−4 10−3 10−2 10−1 100 Measurements Energy (keV) No rmalised Counts
10 µs Window: Storage,150 µm non-Storage,130 µm
0 2 4 6
Simulations
Energy (keV)
Full Frame: Storage,150 µm non-Storage,130 µm non-Storage,75 µm
Figure 6.7:On the left, measurements with existing devices at a readout speed of 5 µsper row and
10 µsframe are shown. The simulations on the right consider only charge loss at the entrance window, the charge distribution over the pixels of different sizes and the different readout effects of storage and non-storage devices. The DEPFET is assumed to be perfect. Therefore, charge loss or an incomplete clear in the DEPFET as visible in the measurements is not included. As input, only characteristic radiation from manganese, silver, aluminium and silicon is used, while the measurements show some further emission lines from heavier elements. The difference between the non-storage and the storage DEPFETs is underestimated by the simulations as clearly visible for the short frame rates.
cloud that cross pixel borders are assigned to those pixels. Split events are formed. For the sideward drift towards the potential minimum inzat the pixel centre, a linear potential and, therefore, constant electric field and velocity is assumed. The missing distance towards the surface is modelled with an exponential function. The total charge collection time results in a charge cloud spread[73] that is converted to a spread in time. Although a Gaussian distribution is only a rough approximation,[55] it is used to describe the charge cloud which is then convoluted with the readout scheme of the desired sensor type. It is demonstrated in Fig. 6.6 for a non-storage and a storage DEPFET.
At the end, offset and noise – common mode separately – can be added by defining the expectation value and standard deviation of their Gaussian shaped distribution. Since these numbers can be obtained from actual measurements, all other steps of the calculation of the charge cloud splitting over the pixels and in time can be verified. The output of the simula- tion is stored in the format that is also used for the measurements taken in the laboratory and can be analysed with the same offline analysis.[104] Measurements from three different sensors were taken for comparison. As shown in Fig. 6.7, the sensor background is not only caused by the energy misfits – as expected – but also by the pixel size. Since no charge loss in the DEPFET is considered in the simulations, the charge loss to adjacent pixels below the noise threshold degrades the spectrum, too. The higher background in the measurements
row n-1 row n row n+1 row n+2 (a) row n-1 row n row n+1 row n+2 (b)
Figure 6.8: (a) Readout of different rows in the rolling shutter mode as presented in section 4.2.
(b)Full parallel continuous readout. Each pixel has to be connected to a separate readout channel and is turned on all the time. Since it is the fastest possible readout, a DEPFET with storage is essential to omit energy misfits which would appear most of the time otherwise.
compared to the simulations originates from the assumption of a perfect DEPFET. Charge loss – also visible at the manganese peaks – is not present in the simulations. Neverthe- less, with the Python scripts, it is possible to generate spectra that cannot be obtained by measurements with the existing devices. Furthermore, all parameters can be kept constantly while only one feature, like the storage, is changed to investigate their influence on a spec- trum. As a further test, the fast window mode measurements were simulated. A comparison to the measured spectra demonstrates, that the energy misfits generated by a non-storage DEPFET are underestimated. That may originate from a charge cloud that has a larger temporal spread than assumed in the simulation.
The change from the rolling shutter operation of the present samples to a full parallel readout is one case that can be simulated and not yet measured. The different readout schemes are depicted in Fig. 6.8. The exposure time texp shrinks to the length of the readout cycle of one pixel. It increases nmisfit to about 30 %. Nevertheless, also the voltage at the drain contacts of the Infinipix have to be switched after each of the short exposure times. Due to the finite switching time of the drain regions and the finite size of the charge cloud, the probability of an inter-frame splitting of an event, nsplit, increases at the same order of magnitude. It can be expected, that the differences in the spectra are small. But while energy misfits during the first integration cannot be recognised or corrected, split events between two consecutive frames can be recombined. It is the same as the recombination of split charge clouds between multiple pixels of the same frame, but in a further dimension. Since an appropriate inter-frame split recombination has not yet been available in the analysis tools and its implementation in the complex event recognition would go beyond the scope of this thesis, it can be simulated by assuming an infinitesimal charge cloud arriving at the front side. Although there will be a degradation during the recombination of the events like it is visible in a worse energy resolution for multiples compared to single events, the advantage
6.2 Spatial and Readout Split 91 0 2 4 6 10−3 10−2 10−1 100 Readout Crosstalk Al K Mn K- α Mn K- β Mn K- α Si Escap e peak Measurement Energy (keV) No rmalised Counts
All Valid Patterns
0 2 4 6 10−5 10−4 10−3 10−2 10−1 100 Simulations Energy (keV) No rma lised Counts No Split Events Inter-Frame Splits Energy Misfits
Figure 6.9:A spectrum of all valid events normalised to the55Mn K-αpeak for a measurement with 1 µsper row taken with a linear gate device from the Athena prototype production is shown. Crosstalk visible below1 keVis a result of a not completely settled source node. It vanishes if the drain current readout is used for such a measurement. On the right, simulations of a non-storage DEPFET (green) and a storage DEPFET with (red) and without inter-frame splits (turquoise) are presented. All three cases are simulated for a pixel size of130 µm.
of an implemented storage can be shown.
The linear gates enable a shorter clear time and, due to smaller capacitances, reduced settling times. Since the gate dimensions of the Athena prototypes are even smaller, a further increased readout speed is possible. Preserving a still good spectral performance, a readout time of 1 µs per row resulted in a noise of 3.5 e- ENC and an energy resolution of about 150 eV FWHMat5.9 keV. The spectrum is shown on the left in Fig. 6.9. Due to a relatively short settling of the source node of250 ns, crosstalk effects are visible below1 keV. Not yet fully understood, they seem to be the result of an interaction between the source potential and the readout ASIC. If the drain current readout is used which does not need a settling process at the sensor, the low energetic features can be omitted. It is not shown since the drain current readout has not yet been possible with the Infinipix and the present readout ASIC (see section 4.2.3).
Applying the same timing conditions as in the 1 µs-measurement, but for a full parallel readout with this non-storage DEPFET, the resulting simulated spectrum worsens drastically. It leads to a very high sensor-generated background between the event and the noise peak. From the comparison shown in Fig. 6.7 one can assume that it will be even worse for a real measurement. Emission lines with low intensities are almost not visible. The storage DEPFET creates a slightly smaller sensor background. Weaker emission lines are more pronounced. Omitting inter-frame split events as a first approximation for a recombination in the feature, the spectral quality increases drastically. For these simulations, a perfect entrance window was set which allows for such weak contributions to the valley. But measurements
with pnCCDs show[79] that an extremely low flat shelf is possible. The last uncertainty is the quality of a potential inter-frame split recombination which needs to be implemented in the future to finally verify the advantages of DEPFETs with storage as soon as they are available as full parallel readout devices.
Chapter 7
Conclusions and Future Prospects
First instruments for space science are and will be equipped with DEPFETs, a concept for an active pixel sensor, improving the time resolution and omitting the disadvantages of CCDs like out-of-time events and potential charge loss during the transfer towards the readout node. However, a DEPFET delivers false energy information if the charge cloud generated by an incident photon approaches during the readout. In case of a full parallel readout, about 30 %of all events would be affected. The implementation of a storage that separates the charge collection and the readout spatially can solve this problem. One solution for this approach is the so-called Infinipix DEPFET.
The DEPFET active pixel sensors that I investigated and which are composed of 32×32 pixels of the Infinipix type are the first linear gate DEPFETs on matrix scale tested for spectroscopic purposes. Including the storage functionality, my measurements show a very promising performance with better results than achieved by previous DEPFET productions. In contrast to the Cut Gate design, shorter and narrower gates are feasible which has been limited by the necessary steering lines and vias before. As a result of the smaller gate dimensions, the capacity of the internal gate is reduced and the gain is increased which leads to a better noise performance and a more complete clear process. In addition, the processing time per row can be increased significantly. The Infinipix DEPFET exists in three layout variants which I investigated to determine potential weak spots that need to be optimised. A detailed table of the differences is presented in section 5.6. The main outcome of my measurements is the requirement of large drain regions for a robust functionality of the Infinipix principle. At the present layout, the size of the drain regions is coupled to the width of the DEPFET gate. Since the gate width also scales with the maximum distance in the internal gate to the clear region, narrow gates are needed to perform an efficient clear process of the collected charge carriers with respect to completeness and timing. With the present Infinipix devices with narrow gates I obtained an energy resolution of(123.61±0.07) eV FWHMfor single events ((127.40±0.07) eV FWHM for all valid events) at the Mn K-α emission line energy of 5.895 keV, operated at a readout speed of 5 µs per row. The noise performance at 220 Kis at (2.333±0.004) e- ENC. The lower limit achievable in theory for the energy resolution with this noise component is 121.2 eV FWHM for events appearing in only one pixel.
The decoupling of the size of the drain region and the gate width in the layout of the Infinipix was addressed by simulations. I tested different layouts (see Fig. 6.1). They all showed an improved robustness against intrinsic bulk doping variations that limit the operation voltage at the back side contact. I proposed the most simple layout adaption for fabrication. It is shown in more detail in section 7.1.2. The disadvantages like a worse clear performance seem to be negligible according to the results of my simulations.
With a further simulation based on Monte Carlo methods I implemented in Python scripts, the influence of the entrance window, the pixel size and the readout scheme on the background generated by the sensor itself was investigated. I could show that in a first approximation, the obtained spectral features can be reduced to these three effects. In addition, an outlook on the future full-parallel readout was possible. Assuming an optimised entrance window and a functioning inter-frame split recombination in the offline analysis tools, the difference in the sensor background between a non-storage and a storage DEPFET is up to the order of three magnitudes. It allows for the investigation of weak spectral features even in the combination with a high time resolution.