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Charge sharing suppression using pixel-to-pixel communication in photon counting X-ray imaging systems
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 576 (2007) 243–247 www.elsevier.com/locate/nima
Charge sharing suppression using pixel-to-pixel communication in photon counting X-ray imaging systems H.-E. Nilssona,, B. Norlina, C. Fro¨jdha, L. Tlustosb a
Mid-Sweden University, Department of Information Technology and Media, 851 70 Sundsvall, Sweden b CERN, ETT/TT, 1211 Geneva 23, Switzerland Available online 6 February 2007
Abstract In planar silicon detector structures, the charge sharing between pixels is one limiting factor for colour X-ray imaging using integrated photon counting pixel detectors. 3D detector structures have been proposed as one solution to this problem. However, there are also readout system solutions to the problem, i.e., introducing pixel-to-pixel communication and distributed charge summing in the readout electronics. In this work, different charge summing schemes are evaluated using Monte Carlo simulation techniques. The increase in electronic noise introduced by the charge summing is one of the most severe problems. A proper selection of summing scheme is necessary to obtain an efficient system. r 2007 Elsevier B.V. All rights reserved. PACS: 07.07.Df; 07.05.Tp; 07.85.Fv; 85.60.Gz Keywords: Monte Carlo simulation; X-ray imaging; Photon counting
1. Introduction Charge sharing limits the energy resolution in integrated photon counting pixel detectors such as the MEDIPIX2 system [1]. This problem becomes severe in silicon detectors as pixel dimensions reach below 100 mm. Charge from a single-photon absorption event that is shared between pixels will show up in the spectrum as several photon absorptions with lower energy than the true event. Thus, it provides a distortion of the energy spectra. Fig. 1 compares the energy spectrum of a standard dental X-ray source with that recorded by a MEDIPIX2 [1] pixel detector (55 mm 55 mm pixel size and a 300 mm thick silicon detector). The difference between the true spectrum of the X-ray source and the recorded spectrum is very large due to charge sharing. One way to overcome the charge sharing problem, using pixel signal processing, was presented by Llopart et al. [1] in 2002. The suggested method requires additional signal processing electronics in each pixel. The additional signalCorresponding author.
E-mail address: [email protected] (H.-E. Nilsson). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.01.160
processing unit should determine in which pixel all the charge from an absorption event should be summed. The summation should be done with as little additional noise contribution as possible. Summing of charges will always provide additional noise according to a square root relation (noise increases as the square root of the number of contributions summed). In order to understand better how this type of signal processing (distributed decisionmaking) will affect the detector system, a system level Monte Carlo simulation of the MEDIPIX2 system [1] has been developed. This simulation tool has been used to compare different signal-processing schemes and how these will affect the energy resolution of the system. 2. Numerical model The numerical model is based on detailed charge transport modelling of the charge diffusion in the detector. The charge transport simulations were made using our inhouse full band self-consistent ensemble Monte Carlo device simulator (GEMS) [2], where the trajectory of each electron and hole has been recorded for a large set of absorption events. Cylindrical coordinates were used in
ARTICLE IN PRESS 244
H.-E. Nilsson et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 243–247
p+
n-
Fig. 2. Structure used in the simulation.
Fig. 1. Comparison of the measured energy spectrum extracted from threshold scans on the MEDIPIX2 system and the actual spectrum of the dental X-ray tube used.
accounting for 3D electrostatic effects in the 2D charge transport simulations. The charge transport simulations were used to extract the charge spread at the surface of the detector as a function of the position of the absorption. The data for the charge spread is then used in a system level Monte Carlo simulator to simulate the imaging performance of the detector system. In Fig. 2, the planar detector structure studied in this work is presented. For a more detailed description regarding the simulation technique, see Ref. [2]. Over-depletion of the detector has been modelled using a scaling rule developed from the charge spread expression derived in Ref. [3]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kB T W Dx ¼ 4 ln q2 N W y0
Fig. 3. Comparison between simulation model and measurement (MEDIPIX2 system, 25 V bias, dental X-ray source).
(1)
where T is the temperature, N the doping level, W the depletion width, q the elementary charge, e is the dielectric constant, kB is Planck’s constant and y0 is the position from the surface at which the photon was absorbed. The scaling of the charge cloud needed to compensate for the over-depletion can be written as Dxover ¼ Dxnorm
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lnð1 ðy0 =W over ÞÞ lnð1 ðy0 =W norm Þ
(2)
where Wnorm is the depletion width without over-depletion and Wover is what the depletion width would be for a thicker detector for the higher voltage. In Figs. 3 and 4, we have compared simulated and measured energy spectra for 25 and 100 V bias, respectively. The results demonstrate the accuracy of the model and show that the simulation model can be used to estimate the effect of different charge summing algorithms on the energy resolution.
Fig. 4. Comparison between simulation model and measurement (MEDIPIX2 system, 100 V bias, dental X-ray source).
3. Charge assignment schemes In Figs. 5–8, we present the charge assignment schemes studied in this work. The pictures include a schematic
ARTICLE IN PRESS H.-E. Nilsson et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 243–247
2 X
1
3
Fig. 5. Three pixel summing configuration (3PS).
1
2 X
245
requires a simple interpolation transformation in order to be transferred to a standard image format. Table 1 presents the equivalent area and radius as well as the theoretical limit for the increase in noise due to the charge summing. The charge assignment algorithm starts by determining the pixel with the highest signal value (centre pixel). In the case of non-symmetric configurations such as the three pixel summing (3PS) and the four pixel summing (4PS) an additional logic step is needed to determine which set of neighbours should be summed. The 3PS has six possible summing configurations (see Fig. 9) and the 4PS has four possible summing configurations (see Fig. 10). Note that the 4PS configuration shown in Fig. 10 is the only configuration that for all possible absorption positions covers the entire charge cloud (radius of approximately 40 mm) at 30 keV in a 300 mm thick silicon detector.
4
3
Table 1 Increase in noise and equivalent pixel area (55 mm 55 mm pixels) due to charge summing Fig. 6. Four pixel summing configuration (4PS).
1 2
3 X
Configuration
Increase in noise
Summed area (mm2)
Covered area (mm2)
1 3 4 5 7
1.0 1.73 2.0 2.24 2.65
3025 9075 12,100 15,125 21,175
3025 21,175 27,225 15,125 21,175
pixel pixel pixel pixel pixel
summing summing summing summing
4
5 1
4
Fig. 7. Five pixel summing configuration (5PS).
X
5
2 3
6
2 1
3 4
5
X
Fig. 9. Different possibilities for the charge assignment in the 3PS configuration.
7
6 1
2
Fig. 8. Seven pixel summing configuration (7PS).
X
picture of charge assignment for an absorption event in the centre of the pixel cluster configured to record the event. The pixel layout is based on two different designs of the pixel matrix; the normal 2D pixel layout (Figs. 6 and 7) and a 2D Odd Column Shifted Matrix, OCSM (shift of half a pixel height see Figs. 5 and 8). Note that the OCSM layout
3
4
Fig. 10. Different possibilities for the charge assignment in the 4PS configuration.
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In the case of the 3PS schemes presented in Fig. 9, a cloud radius of only 27 mm is completely covered by the scheme. In both of these statements, the pixel size has been assumed to be 55 mm 55 mm. 4. Simulation results All the assignment schemes have advantages and disadvantages. The lower the number of neighbours, the better from a noise perspective. However, the scheme with the smallest number of neighbours also has the largest loss of carriers, which results in the largest energy tail towards low energies. A larger number of summing neighbours provide a more complicated charge assignment algorithm and suffers from the largest electronic noise distortion. In order to understand the trade off that is needed, we have simulated each scheme for a mono-energetic source of 30 keV. The bias condition is the worst case with no overdepletion (25 V bias). In Figs. 11 and 12, the simulated energy spectrum is presented for an assumed electronic noise of 10 and 100 EHP, respectively. The 4PS algorithm is the best in terms of suppressing charge sharing and still providing reasonable noise levels. The main reason for the better performance is that the configuration covers a larger area than all the other configurations, while in the summation only four pixels are included (see Table 1). All the proposed summing configurations provide significantly better peak amplitude. The width of the peak is directly linked to the amount of noise added in the summation. The best performance is given by the 4PS algorithm due to the largest sensing area (9 pixels, see Fig. 10) and at the same time, the reasonably low number of pixels used in the summation (4 pixels). A possible drawback with the 4 pixel summation is that it demands more logic to sense all 9 pixels in order to select the 4 pixels with the highest signal contribution. The standard config-
Fig. 12. Simulated energy spectra for different charge assignment schemes assuming a mono-energetic 30 keV X-ray source. The assumed electronic noise-level is 100 electrons.
Fig. 13. Simulated energy spectra for the two proposed summing strategies for the 3PS configuration. A mono-energetic 30 keV X-ray source and an electronic noise-level 100 EHP are assumed.
Fig. 11. Simulated energy spectra for different charge assignment schemes assuming a mono-energetic 30 keV X-ray source. The assumed electronic noise-level is 10 electrons.
uration shows a very pronounced charge sharing tail towards lower energies. The electronic noise-level in each pixel of the MEDIPIX2 system is approximately 100 electrons. The same noise level has been applied in the simulation to the signal recorded in each pixel by summing a normally distributed elementary charge contribution with a standard deviation of 100. According to theory [4], the full-width of the peak at half-maximum (FWHM) should then be 851 eV. Our simulations show good agreement with this theory. For example, the 4PS scheme FWHM is 1700 eV, which divided by the square root of 4 yields a contribution of 850 eV from each pixel. Thus, the energy resolution is no longer limited by charge sharing but rather limited by the electronic noise in the pixels. Another important noise source adding to the
ARTICLE IN PRESS H.-E. Nilsson et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 243–247
electronic noise in the pixels results from threshold variations, which can seriously degrade the system in energy-sensitive imaging configurations. This has not been considered in the simulations since this noise will affect all pixel summing schemes in the same way. An alternative simplification is to use the 3PS configuration with the same summing strategy as for the 4PS configuration. In this case, the summing is done according to the 1, 3, 4, 6 cluster shown in Fig. 9. Thus, we deliberately neglect the case when the charge in clusters 2 and 5 is the largest. In Fig. 13, the result of this approximation is compared to the result for the full solution of the 3PS algorithm. 5. Conclusions Different readout system solutions to the problem of charge sharing in photon counting X-ray imaging detectors have been studied. The solutions are all based on different schemes for pixel-to-pixel communication and distributed charge summing in the readout electronics. Five different charge summing schemes have been evaluated; two
247
versions of a 3PS solution, one 4PS solution, one 5 pixel summing solution and one 7 pixel summing solution. The scheme covering the largest search area combined with a minimized pixel summation over 4 pixels shows the best characteristics. For 30 keV, approximately 100% of the charge cloud is collected within a radius of 40 mm from the surface projection of the absorption position (for a 300 mm thick silicon detector). Thus, the charge summing configuration that covers this area for all possible cases will be the best solution. The only scheme providing this area coverage in a 55 mm 55 mm pixel system is the 4PS configuration. References [1] X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, E. Pernigotti, IEEE Trans. Nucl. Sci. NS-49 (2002) 2279. [2] H.-E. Nilsson, E. Dubaric, M. Hjelm, K. Bertilsson, Nucl. Instr. and Meth. A 487 (2002) 151. [3] H.-E. Nilsson, C. Fro¨jdh, E. Dubaric, IEEE Trans. Nucl. Sci. NS-51 (2004) 1636. [4] G.K. Knoll, Radiation Detection and Measurement, third ed, Wiley, New York, 1999, p. 630.
Nuclear Instruments and Methods in Physics Research A 576 (2007) 243–247 www.elsevier.com/locate/nima
Charge sharing suppression using pixel-to-pixel communication in photon counting X-ray imaging systems H.-E. Nilssona,, B. Norlina, C. Fro¨jdha, L. Tlustosb a
Mid-Sweden University, Department of Information Technology and Media, 851 70 Sundsvall, Sweden b CERN, ETT/TT, 1211 Geneva 23, Switzerland Available online 6 February 2007
Abstract In planar silicon detector structures, the charge sharing between pixels is one limiting factor for colour X-ray imaging using integrated photon counting pixel detectors. 3D detector structures have been proposed as one solution to this problem. However, there are also readout system solutions to the problem, i.e., introducing pixel-to-pixel communication and distributed charge summing in the readout electronics. In this work, different charge summing schemes are evaluated using Monte Carlo simulation techniques. The increase in electronic noise introduced by the charge summing is one of the most severe problems. A proper selection of summing scheme is necessary to obtain an efficient system. r 2007 Elsevier B.V. All rights reserved. PACS: 07.07.Df; 07.05.Tp; 07.85.Fv; 85.60.Gz Keywords: Monte Carlo simulation; X-ray imaging; Photon counting
1. Introduction Charge sharing limits the energy resolution in integrated photon counting pixel detectors such as the MEDIPIX2 system [1]. This problem becomes severe in silicon detectors as pixel dimensions reach below 100 mm. Charge from a single-photon absorption event that is shared between pixels will show up in the spectrum as several photon absorptions with lower energy than the true event. Thus, it provides a distortion of the energy spectra. Fig. 1 compares the energy spectrum of a standard dental X-ray source with that recorded by a MEDIPIX2 [1] pixel detector (55 mm 55 mm pixel size and a 300 mm thick silicon detector). The difference between the true spectrum of the X-ray source and the recorded spectrum is very large due to charge sharing. One way to overcome the charge sharing problem, using pixel signal processing, was presented by Llopart et al. [1] in 2002. The suggested method requires additional signal processing electronics in each pixel. The additional signalCorresponding author.
E-mail address: [email protected] (H.-E. Nilsson). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.01.160
processing unit should determine in which pixel all the charge from an absorption event should be summed. The summation should be done with as little additional noise contribution as possible. Summing of charges will always provide additional noise according to a square root relation (noise increases as the square root of the number of contributions summed). In order to understand better how this type of signal processing (distributed decisionmaking) will affect the detector system, a system level Monte Carlo simulation of the MEDIPIX2 system [1] has been developed. This simulation tool has been used to compare different signal-processing schemes and how these will affect the energy resolution of the system. 2. Numerical model The numerical model is based on detailed charge transport modelling of the charge diffusion in the detector. The charge transport simulations were made using our inhouse full band self-consistent ensemble Monte Carlo device simulator (GEMS) [2], where the trajectory of each electron and hole has been recorded for a large set of absorption events. Cylindrical coordinates were used in
ARTICLE IN PRESS 244
H.-E. Nilsson et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 243–247
p+
n-
Fig. 2. Structure used in the simulation.
Fig. 1. Comparison of the measured energy spectrum extracted from threshold scans on the MEDIPIX2 system and the actual spectrum of the dental X-ray tube used.
accounting for 3D electrostatic effects in the 2D charge transport simulations. The charge transport simulations were used to extract the charge spread at the surface of the detector as a function of the position of the absorption. The data for the charge spread is then used in a system level Monte Carlo simulator to simulate the imaging performance of the detector system. In Fig. 2, the planar detector structure studied in this work is presented. For a more detailed description regarding the simulation technique, see Ref. [2]. Over-depletion of the detector has been modelled using a scaling rule developed from the charge spread expression derived in Ref. [3]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kB T W Dx ¼ 4 ln q2 N W y0
Fig. 3. Comparison between simulation model and measurement (MEDIPIX2 system, 25 V bias, dental X-ray source).
(1)
where T is the temperature, N the doping level, W the depletion width, q the elementary charge, e is the dielectric constant, kB is Planck’s constant and y0 is the position from the surface at which the photon was absorbed. The scaling of the charge cloud needed to compensate for the over-depletion can be written as Dxover ¼ Dxnorm
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lnð1 ðy0 =W over ÞÞ lnð1 ðy0 =W norm Þ
(2)
where Wnorm is the depletion width without over-depletion and Wover is what the depletion width would be for a thicker detector for the higher voltage. In Figs. 3 and 4, we have compared simulated and measured energy spectra for 25 and 100 V bias, respectively. The results demonstrate the accuracy of the model and show that the simulation model can be used to estimate the effect of different charge summing algorithms on the energy resolution.
Fig. 4. Comparison between simulation model and measurement (MEDIPIX2 system, 100 V bias, dental X-ray source).
3. Charge assignment schemes In Figs. 5–8, we present the charge assignment schemes studied in this work. The pictures include a schematic
ARTICLE IN PRESS H.-E. Nilsson et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 243–247
2 X
1
3
Fig. 5. Three pixel summing configuration (3PS).
1
2 X
245
requires a simple interpolation transformation in order to be transferred to a standard image format. Table 1 presents the equivalent area and radius as well as the theoretical limit for the increase in noise due to the charge summing. The charge assignment algorithm starts by determining the pixel with the highest signal value (centre pixel). In the case of non-symmetric configurations such as the three pixel summing (3PS) and the four pixel summing (4PS) an additional logic step is needed to determine which set of neighbours should be summed. The 3PS has six possible summing configurations (see Fig. 9) and the 4PS has four possible summing configurations (see Fig. 10). Note that the 4PS configuration shown in Fig. 10 is the only configuration that for all possible absorption positions covers the entire charge cloud (radius of approximately 40 mm) at 30 keV in a 300 mm thick silicon detector.
4
3
Table 1 Increase in noise and equivalent pixel area (55 mm 55 mm pixels) due to charge summing Fig. 6. Four pixel summing configuration (4PS).
1 2
3 X
Configuration
Increase in noise
Summed area (mm2)
Covered area (mm2)
1 3 4 5 7
1.0 1.73 2.0 2.24 2.65
3025 9075 12,100 15,125 21,175
3025 21,175 27,225 15,125 21,175
pixel pixel pixel pixel pixel
summing summing summing summing
4
5 1
4
Fig. 7. Five pixel summing configuration (5PS).
X
5
2 3
6
2 1
3 4
5
X
Fig. 9. Different possibilities for the charge assignment in the 3PS configuration.
7
6 1
2
Fig. 8. Seven pixel summing configuration (7PS).
X
picture of charge assignment for an absorption event in the centre of the pixel cluster configured to record the event. The pixel layout is based on two different designs of the pixel matrix; the normal 2D pixel layout (Figs. 6 and 7) and a 2D Odd Column Shifted Matrix, OCSM (shift of half a pixel height see Figs. 5 and 8). Note that the OCSM layout
3
4
Fig. 10. Different possibilities for the charge assignment in the 4PS configuration.
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H.-E. Nilsson et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 243–247
In the case of the 3PS schemes presented in Fig. 9, a cloud radius of only 27 mm is completely covered by the scheme. In both of these statements, the pixel size has been assumed to be 55 mm 55 mm. 4. Simulation results All the assignment schemes have advantages and disadvantages. The lower the number of neighbours, the better from a noise perspective. However, the scheme with the smallest number of neighbours also has the largest loss of carriers, which results in the largest energy tail towards low energies. A larger number of summing neighbours provide a more complicated charge assignment algorithm and suffers from the largest electronic noise distortion. In order to understand the trade off that is needed, we have simulated each scheme for a mono-energetic source of 30 keV. The bias condition is the worst case with no overdepletion (25 V bias). In Figs. 11 and 12, the simulated energy spectrum is presented for an assumed electronic noise of 10 and 100 EHP, respectively. The 4PS algorithm is the best in terms of suppressing charge sharing and still providing reasonable noise levels. The main reason for the better performance is that the configuration covers a larger area than all the other configurations, while in the summation only four pixels are included (see Table 1). All the proposed summing configurations provide significantly better peak amplitude. The width of the peak is directly linked to the amount of noise added in the summation. The best performance is given by the 4PS algorithm due to the largest sensing area (9 pixels, see Fig. 10) and at the same time, the reasonably low number of pixels used in the summation (4 pixels). A possible drawback with the 4 pixel summation is that it demands more logic to sense all 9 pixels in order to select the 4 pixels with the highest signal contribution. The standard config-
Fig. 12. Simulated energy spectra for different charge assignment schemes assuming a mono-energetic 30 keV X-ray source. The assumed electronic noise-level is 100 electrons.
Fig. 13. Simulated energy spectra for the two proposed summing strategies for the 3PS configuration. A mono-energetic 30 keV X-ray source and an electronic noise-level 100 EHP are assumed.
Fig. 11. Simulated energy spectra for different charge assignment schemes assuming a mono-energetic 30 keV X-ray source. The assumed electronic noise-level is 10 electrons.
uration shows a very pronounced charge sharing tail towards lower energies. The electronic noise-level in each pixel of the MEDIPIX2 system is approximately 100 electrons. The same noise level has been applied in the simulation to the signal recorded in each pixel by summing a normally distributed elementary charge contribution with a standard deviation of 100. According to theory [4], the full-width of the peak at half-maximum (FWHM) should then be 851 eV. Our simulations show good agreement with this theory. For example, the 4PS scheme FWHM is 1700 eV, which divided by the square root of 4 yields a contribution of 850 eV from each pixel. Thus, the energy resolution is no longer limited by charge sharing but rather limited by the electronic noise in the pixels. Another important noise source adding to the
ARTICLE IN PRESS H.-E. Nilsson et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 243–247
electronic noise in the pixels results from threshold variations, which can seriously degrade the system in energy-sensitive imaging configurations. This has not been considered in the simulations since this noise will affect all pixel summing schemes in the same way. An alternative simplification is to use the 3PS configuration with the same summing strategy as for the 4PS configuration. In this case, the summing is done according to the 1, 3, 4, 6 cluster shown in Fig. 9. Thus, we deliberately neglect the case when the charge in clusters 2 and 5 is the largest. In Fig. 13, the result of this approximation is compared to the result for the full solution of the 3PS algorithm. 5. Conclusions Different readout system solutions to the problem of charge sharing in photon counting X-ray imaging detectors have been studied. The solutions are all based on different schemes for pixel-to-pixel communication and distributed charge summing in the readout electronics. Five different charge summing schemes have been evaluated; two
247
versions of a 3PS solution, one 4PS solution, one 5 pixel summing solution and one 7 pixel summing solution. The scheme covering the largest search area combined with a minimized pixel summation over 4 pixels shows the best characteristics. For 30 keV, approximately 100% of the charge cloud is collected within a radius of 40 mm from the surface projection of the absorption position (for a 300 mm thick silicon detector). Thus, the charge summing configuration that covers this area for all possible cases will be the best solution. The only scheme providing this area coverage in a 55 mm 55 mm pixel system is the 4PS configuration. References [1] X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, E. Pernigotti, IEEE Trans. Nucl. Sci. NS-49 (2002) 2279. [2] H.-E. Nilsson, E. Dubaric, M. Hjelm, K. Bertilsson, Nucl. Instr. and Meth. A 487 (2002) 151. [3] H.-E. Nilsson, C. Fro¨jdh, E. Dubaric, IEEE Trans. Nucl. Sci. NS-51 (2004) 1636. [4] G.K. Knoll, Radiation Detection and Measurement, third ed, Wiley, New York, 1999, p. 630.