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Advanced DePFET concepts: Quadropix
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Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Advanced DePFET concepts: Quadropix Alexander Baehr a, *, A. Feller b , P. Lechner a , J. Ninkovic a , R. Richter a , F. Schopper a , J. Treis a a b
Semiconductor Laboratory of the Max Planck Society, Otto-Hahn-Ring 6, 81739 Munich, Germany Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Goettingen, Germany
a r t i c l e
i n f o
Keywords: Imaging Optical polarimetry Semiconductor APS
a b s t r a c t Currently several development activities for the European Solar Telescope (EST) are ongoing, one of these is Getting Ready for EST (GREST), a venture for the development of new sensor and detector technologies for EST. Among other objectives, EST will perform time resolved, high precision polarimetric imaging. These measurements require detector systems that are capable of detecting even smallest changes in the polarization of light. At the MPG-HLL we developed a sensor concept for such a system, the Quadropix DEPFET. These devices offer in-situ storage of up to four independent images without reducing the sensors fill-factor. For polarimetric applications this properties can be used for polarimetry measurements at high modulation frequencies. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The European Solar Telescope (EST) [1] is a next generation largeaperture solar telescope. Several development activities for EST are currently ongoing. Among other objectives, EST will perform time resolved, high precision polarimetric imaging that can be used to determine the magnetic fields in the solar atmosphere and their fundamental role in the physical processes taking place. High precision polarimetry requires a modulator that encodes the polarimetric information into an intensity modulation. To cancel the influence of e.g. air turbulences, the typical modulation frequency is of the order of 10–40 kHz. The full polarization information can be retrieved through 4 modulation images. High precision polarimetric measurements require detector systems that are capable of detecting even smallest changes in the polarization. At the MPG-HLL we developed a sensor concept for such a system the Quadropix DEPFET. These devices offer in-situ storage of image information without reducing the sensors fill-factor. The foreseen switching time between different sub-images is of the order of 100 ns. At a modulation frequency of 10 kHz the sub-images will be switched every 100 μs. The matrix interconnection provides 2 readout channels per pixel that can be read simultaneously. Tests on devices with similar gate extension have shown that clear time below 200 are possible [2]. Using a Veritas 2.1 readout ASIC, readout times of 2.5 μs can be achieved [2]. For a 1k × 1k pixel matrix as planned for EST, two sub-images will be read within 2.5 ms and the information of all 4 sub-images is processed every 5 ms. For the operation of the sensor, different schemes are possible. In the
most simple, the sensor would be illuminated for several ms using a high polarimetric modulation frequency. Using an external shutter, the illumination would be stopped and the sensor can be read out. In a more advanced scheme modulation and readout are interleaved, i.e. the sensor is simultaneously illuminated with the modulated signal and read out. In this case an additional shutter is obsolete. The feasibility of the readout modes will be part of future works. 2. DePFET The Depleted P-channel Field Effect Transistor (DePFET) is a FieldEffect-Transistor (FET) built on a highly resistive n-doped silicon bulk as shown in Fig. 1(a). The device is sidewards depleted and sensitive over the complete bulk thickness. A deep n-implant, most pronounced below the MOS-gate, forms a potential minimum for electrons. Charge collected in this internal gate causes a proportional modulation of the transistors channel conductivity. In addition to the MOS-transistor, every DePFET has a clear-structure, built of clear-gate and clear, to remove collected charge carriers. Simplified, the DePFETs internal gate can be seen as a collection node for generated charge as shown in Fig. 1(b). 3. Quadropix A Quadropix superpixel consists of 4 DePFET subpixels as shown in Fig. 2(a). Two DePFETs of a superpixel share a source node and the clear
* Corresponding author.
E-mail address: [email protected] (A. Baehr). https://doi.org/10.1016/j.nima.2017.10.048 Received 30 September 2017; Received in revised form 17 October 2017; Accepted 17 October 2017 Available online xxxx 0168-9002/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.
A. Baehr et al.
Nuclear Inst. and Methods in Physics Research, A (
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Fig. 1. The DePFET is a p-MOS-transistor built on a highly resistive n-doped bulk as shown in the cutaway in (a). Charge generated in the bulk will be collected in a deep-n implant below the MOS-gate and modulate the transistors channel conductivity. Simplified the internal gate, serves as collection node for incident charge carriers.
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Fig. 2. A Quadropix consists of four DePFETs that together form a single superpixel as shown in (a). Depending on the voltage applied to the 4 drain nodes, charge will only be collected in one of the four subpixels as indicated in (b).
structure. The gates as well as drain nodes are controlled individually for each subpixel. The basic principle is to modify the potential distribution within the bulk through the applied drain voltages such, that charge generated in the bulk is collected in only one of the four internal gates as indicated in Fig. 2(b).
heavily influenced by the applied backside voltage and bulk-doping variations [3,4]. To study the influence of the backside voltage on the three presented layouts, charge was injected in a point like area at the backside of the device opposite to the sensitive DePFET. During the following drift, most of the charge will be collected only in the sensitive DePFET. Depending on the applied backside voltage however, a small fraction will also be collected in the supposedly insensitive sub-pixels. The charge fraction collected within the sensitive pixel is shown in Fig. 3(b). For all three layouts, a window of operation for the backside contact can be found. It ranges from the point of full depletion until the backside voltage at which a significant fraction (fraction of 5 ⋅ 10−3 of the signal charge) is collected in the insensitive DePFETs. This operation window is about 2 V for the standard layout. The changes introduced for ‘‘mod DN’’ and ‘‘adj geom’’ devices increase the operation window to 5 V and 10 V respectively.
3.1. Single pixel simulation The operational parameters of three different superpixel layouts have been studied using 3 dimensional electrical device simulations done with Synopsis TCAD. The first layout, herein called ‘‘standard’’, is an approximation of available prototype devices. The only change of the second layout is an extension of the deep-n implant that also forms the internal gate (herein called ‘‘mod DN’’). It is extended to cover a larger area of the pixel in that way reducing the focusing onto the central pixel part and improving the separation between the single internal gates. The identical gate structures are shown in Fig. 2(a). The last design, herein referred to as adjusted geometry ‘‘adj geom’’ also includes a change of the geometry. By rotating the clear contacts, the size of the internal gates is reduced and the area of the drain-nodes maximized. These changes further improve the separation between the internal gates. The layout of the third device is shown in Fig. 3(a). In all cases, the simulation covers an area of 60 × 60 × 350 μm3 . It was repeatedly shown that the function of devices that rely on the redirection of charge by the electric field within the bulk are
3.2. 3 × 3 pixel matrix simulation It was expected that the charge collected within a superpixel will change with respect to the applied bias voltage i.e. the sensitive subpixel and the charge generation point within the bulk. A small pixel array built of devices of the standard layout was simulated to study this effect. The simulated array has a pixel size of 60 × 60 μm2 . To reduce the amount of contacts required for the complete pixel array, adjacent subpixels of 2
Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.
A. Baehr et al.
Nuclear Inst. and Methods in Physics Research, A (
(a)
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Fig. 3. By rotating the clear-nodes and reducing the size of the external gates as shown in (a) the operation window for the backside voltage can be enhanced largely. The operation window for the standard layout, a layout with an adapted deep-n implant and the layout with adjusted clear structure are shown in (b).
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Fig. 4. To evaluate the influence of the asymmetric potentials, a pixel array of 3 × 3 pixels was simulated. The resulting potential distribution is shown in (a). Due to the asymmetry the charge collected within one pixel also shows an asymmetry as can be seen in (b).
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Fig. 5. By reducing the bulk thickness from 350 μm to 50, the asymmetry in the charge collection is largely reduced (see (a)). The asymmetry can be further reduced by a focussing implant on the backside of the sensor. This results in the charge collection shown in (b).
different superpixels share their drain contacts. The addressing of gate, clear-gate and clear is done row-wise while the readout is supposed to be done column-wise in parallel. This operation leads the potential distribution shown in Fig. 4(a). This dependency of the potentials can be seen as a change of the pixels borders within the sensor. If unknown and not corrected for, this effect limits the capabilities of the Quadropix devices for polarimetric imaging. The available prototype devices are available with different bulk thicknesses. During the drift through the device the initial charge cloud expands by diffusion and electrostatic repulsion. The effect was studied by simulating a bulk thickness of 350 μm and 50 μm, representing the available prototypes. For a bulk thickness of 350 μm and a bulk doping concentration of 1 ⋅ 1012 ∕cm3 the comparably long drift time (of the order of 10 ns) in combination with
the spatial distribution of the superpixels potential leads to the charge collection shown in Fig. 4(b). Here, the charge collection for the central pixel for different positions of charge injection is shown. The central superpixel extends from 1 to 2 on both 𝑥- and 𝑦-axis. As the simulation indicates, the pixel border is blurred into the bottom left direction. This is also the direction of the sensitive subpixel respectively the positive drain. The same layout has been simulated with a bulk thickness of 50 μm and a doping concentration of 2 ⋅ 1013 ∕cm3 . While the charge sharing is still blurred into the direction of the positive drain node as shown in Fig. 5(a), the reduced bulk thickness limits the spread of the charge cloud and the influence of the sensitive subpixel on the chargesharing is strongly reduced. Furthermore, the thin pixel array has been simulated with a structured focusing deep-n implant in a depth of 6 μm 3
Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.
A. Baehr et al.
Nuclear Inst. and Methods in Physics Research, A (
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Fig. 6. The asymmetry caused by the potential distribution within the Quadropixel also affects the polarimetric performance. Based on the electrical simulations from the previous section and the resulting charge collection the polarimetric crosstalk for point excitations can be calculated. The results for excitation in the pixel center and off center are shown in (a) and (b) for a thick bulk and in (c) and (d) for a thin bulk with focussing implant.
below the backside contact and a gap of 10 μm between two pixels. The implant is aligned to the pixel structure on the frontside. The charge collection for the two thin matrices are shown in Fig. 5(a) (thin) and (b) (thin and focussed). As shown the focussing further improves the charge collection and mitigates the blurring effect caused by the Quadropix concept. In addition to charge collection within the sensitive subpixel, a fraction of the injected charge may also be collected in the insensitive subpixels. At the simulated bias point, an average fraction of about 2 ⋅ 10−4 is collected in the insensitive subpixels for the thick device. For the thin device this value is below 5 ⋅ 10−5 . Both a different bias point as well as an optimization of the device geometry (as indicated in the previous section) should further reduce these values.
then 𝑞𝐴,𝑖𝑗 =
𝛥𝑡 d𝑥 d𝑦 𝐼(𝑥, 𝑦) 𝑅𝐴,𝑖𝑗 (𝑥, 𝑦), 4 ∬
(1)
where 𝐼 is the intensity distribution on the sensor (in photons per unit area and time), and where 𝑅𝐴,𝑖𝑗 (𝑥, 𝑦) = [𝑅𝐴,𝐴,𝑖𝑗 + 𝑅𝐴,𝐵,𝑖𝑗 + 𝑅𝐴,𝐶,𝑖𝑗 + 𝑅𝐴,𝐷,𝑖𝑗 ](𝑥, 𝑦)
(2)
is the total response of the subpixel, including the responses 𝑅𝐴,𝐴,𝑖𝑗 , 𝑅𝐴,𝐵,𝑖𝑗 , 𝑅𝐴,𝐶,𝑖𝑗 and 𝑅𝐴,𝐷,𝑖𝑗 of the subpixel in sensor states A to D. In the same way we obtain the number of photo-electrons 𝑞𝐵,𝑖𝑗 , 𝑞𝐶,𝑖𝑗 , 𝑞𝐷,𝑖𝑗 collected in the other subpixels of superpixel (𝑖, 𝑗). Here we assume that both the intensity distribution and the sensor response are constant in time, which in practice is the case (to sufficient precision) at modulation frequencies of order 10 kHz or higher. The 4 × 4 modulation matrix 𝑂 relates the incoming polarization state, in terms of Stokes parameters 𝐼, 𝑄, 𝑈 , 𝑉 to the photo-electrons 𝑞𝐴 , … , 𝑞𝐷 collected in the 4 subpixels:
4. Theoretical polarimetric performance The asymmetry of the superpixels charge collection leads to four distinct states of the sensor. Let us define state A as the sensor state with subpixels A sensitive. In the same way we can define the remaining 3 sensor states B to D, with the corresponding subpixels sensitive. During a full polarization modulation cycle of duration 𝛥𝑡 these 4 sensor states are successively active, one state at a time during a quarter cycle each. Let us further define the response of a given subpixel as the amount of electrons collected in the subpixel per incident photon. The number of photo-electrons 𝑞𝐴,𝑖𝑗 collected in subpixel 𝐴 of superpixel (𝑖, 𝑗) during a full polarization modulation cycle is
⎛ 𝑞𝐴 ⎞ ⎛𝐼 ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ 𝑞𝐵 ⎟ = 𝑂 ⎜ 𝑄 ⎟ . ⎜𝑞𝐶 ⎟ ⎜𝑈 ⎟ ⎜𝑞 ⎟ ⎜𝑉 ⎟ ⎝ 𝐷⎠ ⎝ ⎠
(3)
4
Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.
A. Baehr et al.
Nuclear Inst. and Methods in Physics Research, A (
An example normalized modulation matrix of an ideal, 4-state balanced modulation scheme is 1 1 ⎛1 √1 √ √ ⎞ ⎜ 3 3 3 ⎟ ⎟ ⎜ ⎜1 √1 − √1 − √1 ⎟ ⎟ ⎜ 3 3 3⎟ (4) 𝑂=⎜ 1 1 1 ⎟ ⎜ √ ⎟ ⎜1 − √ − √ 3 3 3 ⎟ ⎜ ⎜ 1 ⎟ 1 1 √ −√ ⎟ ⎜1 − √ ⎝ 3 3 3⎠
𝐷 = 𝑂−1
–
correction is applied. For the thin pixel array with focussing implant, the polarization crosstalk reduced drastically into the range of a few 10−4 for charge generated in the pixel center and a few 10−3 for charge generated in the pixel corner. 5. Summary At the MPG-HLL we developed the Quadropix, a novel sensor concept providing in-situ storage for 4 images. These devices provide full fill factor, high modulation speed, low read noise and fast frame rates. Although the number of controlled nodes increases by a factor of four per pixel, the chosen interconnections scheme increases the number of required contacts only by about a factor of two. The here shown simulations indicate the full functionality of these devices. The polarimetric performance requires further investigation. However, it is already obvious that thinning and a focussing backside implant would largely benefit the sensors performance. Thinning itself has been established in the semiconductor lab [5]. A thin entrance window technology for thinned wafers however, is not yet available. This is going to be part of future developments. Tests of the fabricated prototypes (64 × 32 pixels) have started.
with the corresponding demodulation matrix 1 1 1 ⎞ ⎛ 1 √ √ ⎟ ⎜√ √ 3 − 3 − 3⎟ 1⎜ 3 √ √ √ ⎟. = ⎜√ 4⎜ 3 − 3 − 3 3⎟ √ √ √ ⎟ ⎜√ ⎝ 3 − 3 3 − 3⎠
)
(5)
The dependence of the spatial distribution of the subpixel responses on the sensor state can lead to small deviations in the elements of the real modulation matrix. When applying the nominal demodulation matrix to the measurements, the actual matrix product 𝐷 ⋅ 𝑂, which relates the incoming to the measured Stokes parameters is then different from the expected identity matrix. The non-zero non-diagonal matrix elements are called polarization crosstalk. For an application in the EST the goal is to reduce the polarization crosstalk to values below 0.01% for the first column of 𝐷 ⋅ 𝑂 (Stokes I to Q, U, V crosstalk) and to values below 0.1% for the matrix elements of 𝐷 ⋅ 𝑂, representing crosstalk between Stokes Q, U and V. Using the simulated charge collection functions for the thick and thin pixel arrays, the expected I to Q, U, V polarization crosstalk for point-like unpolarized excitations has been calculated. This was done first for excitation in the pixel center and secondly for an excitation 10 μm from the pixel corner. The results are shown in Fig. 6(a) for the thick pixel array with charge generated in the center and (b) for charge generated off center. The calculated values for the thin pixel array with focussing implant can be found in Fig. 6(c) for the case of central charge injection and (d) for off center injection. For the thick pixel array, a polarization crosstalk in the percentage range has to be expected if no
Acknowledgment This work has been supported by the Horizon 2020 project ‘‘Getting Ready for EST (GREST)’’ no. 653982. References [1] S.A. Matthews, M. Collados, M. Mathioudakis, R. Erdelyi, The European solar telescope (EST), Proc. SPIE 9908 (2016) 990809. http://dx.doi.org/10.1117/12. 2234145. [2] W. Treberspurg, Studies of prototype DEPFET sensors for the wide field imager of athena, Proc. SPIE 10397-0U (2017). [3] A. Bähr, et al., Spectral performance of DEPFET and gateable DEPFET macropixel devices, JINST 9 (2014). http://dx.doi.org/10.1088/1748-0221/9/03/P03018. [4] Johannes Müller-Seidlitz, et al., Spectroscopic performance of DEPFET active pixel sensor prototypes suitable for the high count rate athena WFI detector, Proc. SPIE 9905 (2016) 990567. [5] F. Mueller, Some aspects of the pixel vertex detector (PXD) at belle II, JINST 9 (10) (2014) Rainer Richter, 2010, Belle II, Technical Design Report, vol (2009) pg.
5
Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.
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Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Advanced DePFET concepts: Quadropix Alexander Baehr a, *, A. Feller b , P. Lechner a , J. Ninkovic a , R. Richter a , F. Schopper a , J. Treis a a b
Semiconductor Laboratory of the Max Planck Society, Otto-Hahn-Ring 6, 81739 Munich, Germany Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Goettingen, Germany
a r t i c l e
i n f o
Keywords: Imaging Optical polarimetry Semiconductor APS
a b s t r a c t Currently several development activities for the European Solar Telescope (EST) are ongoing, one of these is Getting Ready for EST (GREST), a venture for the development of new sensor and detector technologies for EST. Among other objectives, EST will perform time resolved, high precision polarimetric imaging. These measurements require detector systems that are capable of detecting even smallest changes in the polarization of light. At the MPG-HLL we developed a sensor concept for such a system, the Quadropix DEPFET. These devices offer in-situ storage of up to four independent images without reducing the sensors fill-factor. For polarimetric applications this properties can be used for polarimetry measurements at high modulation frequencies. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The European Solar Telescope (EST) [1] is a next generation largeaperture solar telescope. Several development activities for EST are currently ongoing. Among other objectives, EST will perform time resolved, high precision polarimetric imaging that can be used to determine the magnetic fields in the solar atmosphere and their fundamental role in the physical processes taking place. High precision polarimetry requires a modulator that encodes the polarimetric information into an intensity modulation. To cancel the influence of e.g. air turbulences, the typical modulation frequency is of the order of 10–40 kHz. The full polarization information can be retrieved through 4 modulation images. High precision polarimetric measurements require detector systems that are capable of detecting even smallest changes in the polarization. At the MPG-HLL we developed a sensor concept for such a system the Quadropix DEPFET. These devices offer in-situ storage of image information without reducing the sensors fill-factor. The foreseen switching time between different sub-images is of the order of 100 ns. At a modulation frequency of 10 kHz the sub-images will be switched every 100 μs. The matrix interconnection provides 2 readout channels per pixel that can be read simultaneously. Tests on devices with similar gate extension have shown that clear time below 200 are possible [2]. Using a Veritas 2.1 readout ASIC, readout times of 2.5 μs can be achieved [2]. For a 1k × 1k pixel matrix as planned for EST, two sub-images will be read within 2.5 ms and the information of all 4 sub-images is processed every 5 ms. For the operation of the sensor, different schemes are possible. In the
most simple, the sensor would be illuminated for several ms using a high polarimetric modulation frequency. Using an external shutter, the illumination would be stopped and the sensor can be read out. In a more advanced scheme modulation and readout are interleaved, i.e. the sensor is simultaneously illuminated with the modulated signal and read out. In this case an additional shutter is obsolete. The feasibility of the readout modes will be part of future works. 2. DePFET The Depleted P-channel Field Effect Transistor (DePFET) is a FieldEffect-Transistor (FET) built on a highly resistive n-doped silicon bulk as shown in Fig. 1(a). The device is sidewards depleted and sensitive over the complete bulk thickness. A deep n-implant, most pronounced below the MOS-gate, forms a potential minimum for electrons. Charge collected in this internal gate causes a proportional modulation of the transistors channel conductivity. In addition to the MOS-transistor, every DePFET has a clear-structure, built of clear-gate and clear, to remove collected charge carriers. Simplified, the DePFETs internal gate can be seen as a collection node for generated charge as shown in Fig. 1(b). 3. Quadropix A Quadropix superpixel consists of 4 DePFET subpixels as shown in Fig. 2(a). Two DePFETs of a superpixel share a source node and the clear
* Corresponding author.
E-mail address: [email protected] (A. Baehr). https://doi.org/10.1016/j.nima.2017.10.048 Received 30 September 2017; Received in revised form 17 October 2017; Accepted 17 October 2017 Available online xxxx 0168-9002/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.
A. Baehr et al.
Nuclear Inst. and Methods in Physics Research, A (
(a)
)
–
(b)
Fig. 1. The DePFET is a p-MOS-transistor built on a highly resistive n-doped bulk as shown in the cutaway in (a). Charge generated in the bulk will be collected in a deep-n implant below the MOS-gate and modulate the transistors channel conductivity. Simplified the internal gate, serves as collection node for incident charge carriers.
(a)
(b)
Fig. 2. A Quadropix consists of four DePFETs that together form a single superpixel as shown in (a). Depending on the voltage applied to the 4 drain nodes, charge will only be collected in one of the four subpixels as indicated in (b).
structure. The gates as well as drain nodes are controlled individually for each subpixel. The basic principle is to modify the potential distribution within the bulk through the applied drain voltages such, that charge generated in the bulk is collected in only one of the four internal gates as indicated in Fig. 2(b).
heavily influenced by the applied backside voltage and bulk-doping variations [3,4]. To study the influence of the backside voltage on the three presented layouts, charge was injected in a point like area at the backside of the device opposite to the sensitive DePFET. During the following drift, most of the charge will be collected only in the sensitive DePFET. Depending on the applied backside voltage however, a small fraction will also be collected in the supposedly insensitive sub-pixels. The charge fraction collected within the sensitive pixel is shown in Fig. 3(b). For all three layouts, a window of operation for the backside contact can be found. It ranges from the point of full depletion until the backside voltage at which a significant fraction (fraction of 5 ⋅ 10−3 of the signal charge) is collected in the insensitive DePFETs. This operation window is about 2 V for the standard layout. The changes introduced for ‘‘mod DN’’ and ‘‘adj geom’’ devices increase the operation window to 5 V and 10 V respectively.
3.1. Single pixel simulation The operational parameters of three different superpixel layouts have been studied using 3 dimensional electrical device simulations done with Synopsis TCAD. The first layout, herein called ‘‘standard’’, is an approximation of available prototype devices. The only change of the second layout is an extension of the deep-n implant that also forms the internal gate (herein called ‘‘mod DN’’). It is extended to cover a larger area of the pixel in that way reducing the focusing onto the central pixel part and improving the separation between the single internal gates. The identical gate structures are shown in Fig. 2(a). The last design, herein referred to as adjusted geometry ‘‘adj geom’’ also includes a change of the geometry. By rotating the clear contacts, the size of the internal gates is reduced and the area of the drain-nodes maximized. These changes further improve the separation between the internal gates. The layout of the third device is shown in Fig. 3(a). In all cases, the simulation covers an area of 60 × 60 × 350 μm3 . It was repeatedly shown that the function of devices that rely on the redirection of charge by the electric field within the bulk are
3.2. 3 × 3 pixel matrix simulation It was expected that the charge collected within a superpixel will change with respect to the applied bias voltage i.e. the sensitive subpixel and the charge generation point within the bulk. A small pixel array built of devices of the standard layout was simulated to study this effect. The simulated array has a pixel size of 60 × 60 μm2 . To reduce the amount of contacts required for the complete pixel array, adjacent subpixels of 2
Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.
A. Baehr et al.
Nuclear Inst. and Methods in Physics Research, A (
(a)
)
–
(b)
Fig. 3. By rotating the clear-nodes and reducing the size of the external gates as shown in (a) the operation window for the backside voltage can be enhanced largely. The operation window for the standard layout, a layout with an adapted deep-n implant and the layout with adjusted clear structure are shown in (b).
(a)
(b)
Fig. 4. To evaluate the influence of the asymmetric potentials, a pixel array of 3 × 3 pixels was simulated. The resulting potential distribution is shown in (a). Due to the asymmetry the charge collected within one pixel also shows an asymmetry as can be seen in (b).
(a)
(b)
Fig. 5. By reducing the bulk thickness from 350 μm to 50, the asymmetry in the charge collection is largely reduced (see (a)). The asymmetry can be further reduced by a focussing implant on the backside of the sensor. This results in the charge collection shown in (b).
different superpixels share their drain contacts. The addressing of gate, clear-gate and clear is done row-wise while the readout is supposed to be done column-wise in parallel. This operation leads the potential distribution shown in Fig. 4(a). This dependency of the potentials can be seen as a change of the pixels borders within the sensor. If unknown and not corrected for, this effect limits the capabilities of the Quadropix devices for polarimetric imaging. The available prototype devices are available with different bulk thicknesses. During the drift through the device the initial charge cloud expands by diffusion and electrostatic repulsion. The effect was studied by simulating a bulk thickness of 350 μm and 50 μm, representing the available prototypes. For a bulk thickness of 350 μm and a bulk doping concentration of 1 ⋅ 1012 ∕cm3 the comparably long drift time (of the order of 10 ns) in combination with
the spatial distribution of the superpixels potential leads to the charge collection shown in Fig. 4(b). Here, the charge collection for the central pixel for different positions of charge injection is shown. The central superpixel extends from 1 to 2 on both 𝑥- and 𝑦-axis. As the simulation indicates, the pixel border is blurred into the bottom left direction. This is also the direction of the sensitive subpixel respectively the positive drain. The same layout has been simulated with a bulk thickness of 50 μm and a doping concentration of 2 ⋅ 1013 ∕cm3 . While the charge sharing is still blurred into the direction of the positive drain node as shown in Fig. 5(a), the reduced bulk thickness limits the spread of the charge cloud and the influence of the sensitive subpixel on the chargesharing is strongly reduced. Furthermore, the thin pixel array has been simulated with a structured focusing deep-n implant in a depth of 6 μm 3
Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.
A. Baehr et al.
Nuclear Inst. and Methods in Physics Research, A (
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)
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(b)
(c)
(d)
Fig. 6. The asymmetry caused by the potential distribution within the Quadropixel also affects the polarimetric performance. Based on the electrical simulations from the previous section and the resulting charge collection the polarimetric crosstalk for point excitations can be calculated. The results for excitation in the pixel center and off center are shown in (a) and (b) for a thick bulk and in (c) and (d) for a thin bulk with focussing implant.
below the backside contact and a gap of 10 μm between two pixels. The implant is aligned to the pixel structure on the frontside. The charge collection for the two thin matrices are shown in Fig. 5(a) (thin) and (b) (thin and focussed). As shown the focussing further improves the charge collection and mitigates the blurring effect caused by the Quadropix concept. In addition to charge collection within the sensitive subpixel, a fraction of the injected charge may also be collected in the insensitive subpixels. At the simulated bias point, an average fraction of about 2 ⋅ 10−4 is collected in the insensitive subpixels for the thick device. For the thin device this value is below 5 ⋅ 10−5 . Both a different bias point as well as an optimization of the device geometry (as indicated in the previous section) should further reduce these values.
then 𝑞𝐴,𝑖𝑗 =
𝛥𝑡 d𝑥 d𝑦 𝐼(𝑥, 𝑦) 𝑅𝐴,𝑖𝑗 (𝑥, 𝑦), 4 ∬
(1)
where 𝐼 is the intensity distribution on the sensor (in photons per unit area and time), and where 𝑅𝐴,𝑖𝑗 (𝑥, 𝑦) = [𝑅𝐴,𝐴,𝑖𝑗 + 𝑅𝐴,𝐵,𝑖𝑗 + 𝑅𝐴,𝐶,𝑖𝑗 + 𝑅𝐴,𝐷,𝑖𝑗 ](𝑥, 𝑦)
(2)
is the total response of the subpixel, including the responses 𝑅𝐴,𝐴,𝑖𝑗 , 𝑅𝐴,𝐵,𝑖𝑗 , 𝑅𝐴,𝐶,𝑖𝑗 and 𝑅𝐴,𝐷,𝑖𝑗 of the subpixel in sensor states A to D. In the same way we obtain the number of photo-electrons 𝑞𝐵,𝑖𝑗 , 𝑞𝐶,𝑖𝑗 , 𝑞𝐷,𝑖𝑗 collected in the other subpixels of superpixel (𝑖, 𝑗). Here we assume that both the intensity distribution and the sensor response are constant in time, which in practice is the case (to sufficient precision) at modulation frequencies of order 10 kHz or higher. The 4 × 4 modulation matrix 𝑂 relates the incoming polarization state, in terms of Stokes parameters 𝐼, 𝑄, 𝑈 , 𝑉 to the photo-electrons 𝑞𝐴 , … , 𝑞𝐷 collected in the 4 subpixels:
4. Theoretical polarimetric performance The asymmetry of the superpixels charge collection leads to four distinct states of the sensor. Let us define state A as the sensor state with subpixels A sensitive. In the same way we can define the remaining 3 sensor states B to D, with the corresponding subpixels sensitive. During a full polarization modulation cycle of duration 𝛥𝑡 these 4 sensor states are successively active, one state at a time during a quarter cycle each. Let us further define the response of a given subpixel as the amount of electrons collected in the subpixel per incident photon. The number of photo-electrons 𝑞𝐴,𝑖𝑗 collected in subpixel 𝐴 of superpixel (𝑖, 𝑗) during a full polarization modulation cycle is
⎛ 𝑞𝐴 ⎞ ⎛𝐼 ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ 𝑞𝐵 ⎟ = 𝑂 ⎜ 𝑄 ⎟ . ⎜𝑞𝐶 ⎟ ⎜𝑈 ⎟ ⎜𝑞 ⎟ ⎜𝑉 ⎟ ⎝ 𝐷⎠ ⎝ ⎠
(3)
4
Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.
A. Baehr et al.
Nuclear Inst. and Methods in Physics Research, A (
An example normalized modulation matrix of an ideal, 4-state balanced modulation scheme is 1 1 ⎛1 √1 √ √ ⎞ ⎜ 3 3 3 ⎟ ⎟ ⎜ ⎜1 √1 − √1 − √1 ⎟ ⎟ ⎜ 3 3 3⎟ (4) 𝑂=⎜ 1 1 1 ⎟ ⎜ √ ⎟ ⎜1 − √ − √ 3 3 3 ⎟ ⎜ ⎜ 1 ⎟ 1 1 √ −√ ⎟ ⎜1 − √ ⎝ 3 3 3⎠
𝐷 = 𝑂−1
–
correction is applied. For the thin pixel array with focussing implant, the polarization crosstalk reduced drastically into the range of a few 10−4 for charge generated in the pixel center and a few 10−3 for charge generated in the pixel corner. 5. Summary At the MPG-HLL we developed the Quadropix, a novel sensor concept providing in-situ storage for 4 images. These devices provide full fill factor, high modulation speed, low read noise and fast frame rates. Although the number of controlled nodes increases by a factor of four per pixel, the chosen interconnections scheme increases the number of required contacts only by about a factor of two. The here shown simulations indicate the full functionality of these devices. The polarimetric performance requires further investigation. However, it is already obvious that thinning and a focussing backside implant would largely benefit the sensors performance. Thinning itself has been established in the semiconductor lab [5]. A thin entrance window technology for thinned wafers however, is not yet available. This is going to be part of future developments. Tests of the fabricated prototypes (64 × 32 pixels) have started.
with the corresponding demodulation matrix 1 1 1 ⎞ ⎛ 1 √ √ ⎟ ⎜√ √ 3 − 3 − 3⎟ 1⎜ 3 √ √ √ ⎟. = ⎜√ 4⎜ 3 − 3 − 3 3⎟ √ √ √ ⎟ ⎜√ ⎝ 3 − 3 3 − 3⎠
)
(5)
The dependence of the spatial distribution of the subpixel responses on the sensor state can lead to small deviations in the elements of the real modulation matrix. When applying the nominal demodulation matrix to the measurements, the actual matrix product 𝐷 ⋅ 𝑂, which relates the incoming to the measured Stokes parameters is then different from the expected identity matrix. The non-zero non-diagonal matrix elements are called polarization crosstalk. For an application in the EST the goal is to reduce the polarization crosstalk to values below 0.01% for the first column of 𝐷 ⋅ 𝑂 (Stokes I to Q, U, V crosstalk) and to values below 0.1% for the matrix elements of 𝐷 ⋅ 𝑂, representing crosstalk between Stokes Q, U and V. Using the simulated charge collection functions for the thick and thin pixel arrays, the expected I to Q, U, V polarization crosstalk for point-like unpolarized excitations has been calculated. This was done first for excitation in the pixel center and secondly for an excitation 10 μm from the pixel corner. The results are shown in Fig. 6(a) for the thick pixel array with charge generated in the center and (b) for charge generated off center. The calculated values for the thin pixel array with focussing implant can be found in Fig. 6(c) for the case of central charge injection and (d) for off center injection. For the thick pixel array, a polarization crosstalk in the percentage range has to be expected if no
Acknowledgment This work has been supported by the Horizon 2020 project ‘‘Getting Ready for EST (GREST)’’ no. 653982. References [1] S.A. Matthews, M. Collados, M. Mathioudakis, R. Erdelyi, The European solar telescope (EST), Proc. SPIE 9908 (2016) 990809. http://dx.doi.org/10.1117/12. 2234145. [2] W. Treberspurg, Studies of prototype DEPFET sensors for the wide field imager of athena, Proc. SPIE 10397-0U (2017). [3] A. Bähr, et al., Spectral performance of DEPFET and gateable DEPFET macropixel devices, JINST 9 (2014). http://dx.doi.org/10.1088/1748-0221/9/03/P03018. [4] Johannes Müller-Seidlitz, et al., Spectroscopic performance of DEPFET active pixel sensor prototypes suitable for the high count rate athena WFI detector, Proc. SPIE 9905 (2016) 990567. [5] F. Mueller, Some aspects of the pixel vertex detector (PXD) at belle II, JINST 9 (10) (2014) Rainer Richter, 2010, Belle II, Technical Design Report, vol (2009) pg.
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Please cite this article in press as: A. Baehr, et al., Advanced DePFET concepts: Quadropix, Nuclear Inst. and Methods in Physics Research, A (2017), https://doi.org/10.1016/j.nima.2017.10.048.