a segmented silicon strip detector for photon-counting ...571537/fulltext01.pdfa segmented silicon...

A Segmented Silicon Strip Detector forPhoton-Counting Spectral Computed Tomography

CHENG XU

Doctoral ThesisStockholm, Sweden 2012

TRITA-FYS 2012:88ISSN 0280-316XISRN KTH/FYS/--12:88--SEISBN 978-91-7501-589-7

KTH FysikSE-106 91 Stockholm

SWEDEN

Akademisk avhandling som med tillstånd av Kungliga Tekniska högskolan fram-lägges till offentlig granskning för avläggande av teknologie doktorsexamen i fysikfredagen den 14 december 2012 klockan 13.15 i FA32, AlbaNova Universitetscent-rum, Kungliga Tekniska Högskolan, Stockholm.

© Cheng Xu, december 2012

Tryck: Universitetsservice US AB, typsatt i LATEX

iii

Abstract

Spectral computed tomography with energy-resolving detectors has a po-tential to improve the detectability of images and correspondingly reduce theradiation dose to patients by extracting and properly using the energy infor-mation in the broad x-ray spectrum. A silicon photon-counting detector hasbeen developed for spectral CT and it has successfully solved the problem ofhigh photon flux in clinical CT applications by adopting the segmented detec-tor structure and operating the detector in edge-on geometry. The detectorwas evaluated by both the simulation and measurements.

The effects of energy loss and charge sharing on the energy response of thissegmented silicon strip detector with different pixel sizes were investigatedby Monte Carlo simulation and a comparison to pixelated CdTe detectorsis presented. The validity of spherical approximations of initial charge cloudshape in silicon detectors was evaluated and a more accurate statistical modelhas been proposed.

A photon-counting energy-resolving application specific integrated circuit(ASIC) developed for spectral CT was characterized extensively by electricalpulses, pulsed laser and real x-ray photons from both the synchrotron and anx-ray tube. It has been demonstrated that the ASIC performs as designed. Anoise level of 1.09 keV RMS has been measured and a threshold dispersion of0.89 keV RMS has been determined. The count rate performance of the ASICin terms of count loss and energy resolution was evaluated by real x-rays andpromising results have been obtained.

The segmented silicon strip detector was evaluated using synchrotron ra-diation. An energy resolution of 16.1% has been determined with 22 keVphotons in the lowest flux limit, which deteriorates to 21.5% at an inputcount rate of 100 Mcps mm−2. The fraction of charge shared events has beenestimated and found to be 11.1% for 22 keV and 15.3% for 30 keV. A lowerfraction of charge shared events and an improved energy resolution can beexpected by applying a higher bias voltage to the detector.

Key words: photon counting, spectral computed tomography, silicon stripdetector, ASIC, energy resolution, cadmium telluride, charge sharing, MonteCarlo simulation, synchrotron

Publications

This thesis is based on the following papers:

I. C. Xu, M. Danielsson, and H. Bornefalk. Evaluation of energy loss and chargesharing in cadmium telluride detectors for photon-counting computed tomog-raphy. IEEE Trans. Nucl. Sci., 58(3):614–625, 2011.

II. C. Xu, M. Danielsson, and H. Bornefalk. Validity of spherical approximationsof initial charge cloud shape in silicon detectors. Nucl. Instr. and Meth. A,648:S190–S193, 2011.

III. C. Xu, M. Danielsson, S. Karlsson, C. Svensson, and H. Bornefalk. Prelim-inary evaluation of a silicon strip detector for photon-counting spectral CT.Nucl. Instr. and Meth. A, 677:45–51, 2012.

IV. C. Xu, M. Persson, H. Chen, S. Karlsson, M. Danielsson, C. Svensson, and H.Bornefalk. Evaluation of a second-generation ultra-fast energy-resolved ASICfor photon-counting spectral CT. IEEE Trans. Nucl. Sci., 2012. Accepted forpublication.

V. C. Xu, H. Chen, M. Persson, S. Karlsson, M. Danielsson, C. Svensson, and H.Bornefalk. Energy resolution of a segmented silicon strip detector for photon-counting spectral CT. Nucl. Instr. and Meth. A, 2012. Submitted for publi-cation.

Reprints were made with permission from the publishers.

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vi PUBLICATIONS

The author has contributed to the following publications, which are to some extentrelated to the thesis but not included.

• M. Yveborg, C. Xu, E. Fredenberg, and M. Danielsson. Photon-counting CTwith silicon detectors: feasibility for pediatric imaging. In J. Hsieh and E.Samei, editors, Proc. SPIE, Physics of Medical Imaging, volume 7258, 2009.

• H. Bornefalk, C. Xu, C. Svensson, and M. Danielsson. Design considerationsto overcome cross talk in a photon counting silicon strip detector for computedtomography. Nucl. Instr. and Meth. A, 621(1–3):371–378, 2010.

• H. Bornefalk, C. Xu, C. Svensson, and M. Danielsson. Simulation study of anenergy sensitive photon counting silicon strip detector for computed tomogra-phy: identifying strengths and weaknesses and developing work-arounds. InE. Samei and N. J. Pelc, editors, Proc. SPIE, Physics of Medical Imaging,volume 7622, 2010.

• C. Xu, M. Danielsson, S. Karlsson, C. Svensson, and H. Bornefalk. Per-formance characterization of a silicon strip detector for spectral computedtomography utilizing a laser testing system. In N. J. Pelc, E. Samei and R.M. Nishikawa, editors, Proc. SPIE, Physics of Medical Imaging, volume 7961,2011.

• P. Norlin, C. Xu, D. Perttu, M. Lundqvist, M. Åslund, and M. Bakowski,Evaluation of junction termination for silicon X-ray detectors. Nucl. Instr.and Meth. A, 648:S68–S71, 2011.

• M. Gustavsson, F. U. Amin, A. Björklid, A. Ehliar, C. Xu, and C. Svensson.A high-rate energy-resolving photon-counting ASIC for spectral computedtomography. IEEE Trans. Nucl. Sci., 59(1):30–39, 2012.

• C. Xu, M. Yveborg, H. Chen, M. Danielsson, S. Karlsson, C. Svensson, and H.Bornefalk. Evaluation of an ultra-fast photon-counting energy-resolved ASICfor spectral CT. In N. J. Pelc, R. M. Nishikawa, and B. R. Whiting, editors,Proc. SPIE, Physics of Medical Imaging, volume 8313, 2012.

• H. Bornefalk, C. Xu, M. Persson, S. Karlsson, C. Svensson, and M. Daniels-son. Effect of temperature variation on the energy response of a photoncounting silicon CT detector. IEEE Trans. Nucl. Sci., 2012. Submitted forpublication.

Contents

Publications v

Contents vii

1 Introduction 11.1 Computed Tomography . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Spectral Computed Tomography . . . . . . . . . . . . . . . . . . . . 21.3 Detector Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Contribution by Others . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Detector Simulation 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Detector Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4.1 Pixelated CdTe Detector . . . . . . . . . . . . . . . . . . . . 92.4.2 Segmented Silicon Strip Detector . . . . . . . . . . . . . . . . 142.4.3 Shape of Initial Charge Cloud in Silicon . . . . . . . . . . . . 14

3 ASIC Characterization 193.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Dead Time Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Characterization Methods . . . . . . . . . . . . . . . . . . . . . . . . 213.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4 Segmented Silicon Strip Detector 274.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Characterization Methods . . . . . . . . . . . . . . . . . . . . . . . . 284.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5 Conclusions 33

vii

viii CONTENTS

Acknowledgements 35

Bibliography 37

Chapter 1

Introduction

1.1 Computed Tomography

Computed tomography (CT), a widely used diagnostic imaging modality, producesdigital format images which represent the discrete slices of an imaged object bymeasuring the attenuated x-ray intensity and reconstructing the spatial distribu-tion of linear attenuation coefficients from a sufficient number of x-ray projectionstaken at different angles [1,2]. The invention of CT successfully overcomes the fun-damental limitation of conventional projection radiography, i.e. the superpositionof different anatomical structures, thus offering a much better visualization.

The first clinical CT image was acquired in 1972 [3]. Over the past four decades,CT has experienced an enormous improvement [2,4]. The CT scanner has evolvedfrom the pencil-beam geometry in the 1970s to today’s multi-slice spiral CT. Thecorresponding single slice image acquisition time has been reduced from 5 minutesto less than 1 second. CT has become one of the most important diagnostic imag-ing modalities. In addition to a wide range of routine applications, various newapplications have been exploited [1,2]. The integration of CT with other functionalimaging modalities, e.g. positron emission tomography (PET) and single photonemission computed tomography (SPECT), offers more possibilities [5, 6].

The use of CT has increased markedly since its introduction, around 70 millionCT scans were performed in the United States alone in 2007 [7], which also meansa noticeable increase in radiation dose to patients [8, 9], in particular for childrenwho are more sensitive to radiation than adults [10–13]. Although the estimatedrisks to individuals are small, the small risks combined with a large exposed pop-ulation could result in a potential public health risk and a remarkable number ofcancers; around 1.5 to 2.0% of all cancers in the United States might be caused bythe radiation from CT scans [7,8]. Simply replacing CT with other imaging modal-ities, such as magnetic resonance imaging (MRI), is not realistic for many commonimaging scenarios [14–16]. Several methods and strategies have been proposed toreduce or optimize the radiation dose from CT scanning [17–19], for example by

1

2 CHAPTER 1. INTRODUCTION

automatic exposure control [20]. The radiation dose can also be reduced by corre-spondingly improving the image quality with the development of new technology.The research interest of this thesis, photon-counting spectral CT, is one of thesenew technologies [21].

1.2 Spectral Computed Tomography

In clinical CT systems, the x-ray energy spectrum after passing through an ob-ject is polychromatic and x-ray photons of different energy have different contrastinformation as a result of the energy- and material-dependent linear attenuationcoefficients. The state-of-the-art CT with energy-integrating detectors simply inte-grates the broad energy spectrum reaching the detector regardless of the contrastinformation contained in different photon energies. The potential benefits of us-ing x-ray spectral information in medical imaging was realized early [22, 23], andthe corresponding applications in clinical CT has received increasing attenuationin recent years [24–27]. There are two main methods to fully exploit the spectralinformation of the transmitted x-ray energy spectrum through an examined ob-ject: energy weighting and material decomposition, both of which can improve thedetectability of CT images.

Energy weighting requires a photon-counting energy-resolving detector whichis capable of detecting the individual photons and measuring the correct photonenergies accordingly. An improved detectability can then be obtained by optimallyweighting the detected photons [23,28,29]. Different weighting methods have beenproposed (projection-, image- and task-based) and shown a significant performanceimprovement compared to the energy-integrating method [30–32].

The goal of material decomposition is to differentiate and characterize differentmaterials and tissues in an examined object by decomposing the energy-dependentlinear attenuation coefficients into a linear combination of energy-dependent basisfunctions and the corresponding basis set coefficients [22, 24, 26, 27, 33]. The beamhardening artifacts can also be eliminated as a result of having the entire energydependence of the linear attenuation coefficients. Two basis functions are enoughto approximate the linear attenuation coefficients of low atomic number materialswith high accuracy [22, 33]. K-edge imaging is feasible if more basis functionsare included to quantify the contrast agents (typically iodine and gadolinium withrelatively high k-edge energies) [26,27].

Several approachs have been developed to extract the x-ray spectral informa-tion in CT applications. Two dual-energy CT systems are commercially avail-able and have been used in clinical applications: the dual-source CT provided bySiemens [34–38] and the fast-kVp switching CT supplied by General Electric [39–44].Both systems exhibit promising potential in material decomposition, e.g. the differ-entiation of the distribution of contrast agent and characterization of renal stonesand calcified plaques in vessels [34, 35, 40]. However, the energy-integrating de-tectors are still used in these dual-energy CT systems and two energy spectra are

1.3. DETECTOR TECHNOLOGY 3

not entirely separated. The overlap in the energy spectra (i.e. an extra radiationdose), limited number of energy levels, scatter radiation between two detector sys-tems for dual-source CT [36], the mis-registration problem for fast-kVp switchingCT [45] are the corresponding drawbacks, which affect the effectiveness of spectralimaging and result in lower signal-difference-to-noise ratios (SDNR). The dual-layerdetector technique also suffers from the disadvantage of overlapped spectra [46–48].Another candidate technique for spectral CT, which attracts more attention re-cently, is to use photon-counting energy-resolving detectors with multi-energy binsand excellent energy-discrimination capability [Paper III, IV, V]. See next sectionfor a detailed description of photon-counting energy-resolving detectors.

1.3 Detector Technology

The detector is one of the most important components of a CT system. Two maindetector types are commonly used by almost all modern CT scanners: xenon filledionization chambers and scintillation detectors [1, 2]. The xenon ionization cham-bers are only installed in some low-end single-slice CT scanners due to the lowdetection efficiency and the difficulty to manufacture multiple detector rows. Mostof the CT scanners are equipped with scintillation detectors which consist of scin-tillators coupled to photodiodes. Gadolinium oxysulfide (GOS) ceramic, ultra fastceramic (UFC) and Gemstone are three scintillation materials used by the latesthigh-end CT scanners [38,44,49,50]. In scintillation detectors, an interacting x-rayphoton is first converted to scintillation lights in scintillators, then electron-holepairs are generated through the absorption of scintillation lights in photodiodes.All the detectors mentioned above integrate the energy deposited by the interact-ing photons over a certain exposure time and output a signal proportional to thetotal deposited energy, thus being called energy-integrating detectors. The energyinformation involved in the incident x-ray energy spectrum is simply lost as a resultof the energy-integrating process. Additionally, the electronic noise produced bydetector sensors and readout electronics is also integrated into the output signal,which degrades the SDNR of CT images.

The advances in semiconductor sensors and application specific integrated cir-cuits (ASICs) have made photon-counting spectral CT feasible. The x-ray photonsinteracting with the semiconductor sensors can be converted directly to electron-hole pairs without any inefficient intermediate processes, ensuring the superior in-trinsic energy resolution [51,52]. The high charge mobility and thus the short chargecollection time in semiconductor detectors is obviously another advantage for clini-cal CT systems which are usually running under extremely high photon fluxes, up toseveral million photons s−1 mm−2. In addition, an ultra-fast photon-counting ASICwith energy-discrimination capability is needed to process the photon-convertedpulses individually and retain good energy resolution [Paper III, IV]. The electronicnoise can be removed by setting a threshold above noise floor and the energy-discrimination capability can be accomplished by applying multiple thresholds.

4 CHAPTER 1. INTRODUCTION

Cadmium telluride (CdTe) and cadmium zinc telluride (CZT) are two candidatesemiconductor materials for photon-counting energy-resolving detectors [53, 54].Several evaluations including preclinical research have been performed to inves-tigate the spectral imaging capabilities of CT scanners based on CdTe/CZT de-tectors [55, 56]. However, the photon flux in the evaluations is far below the re-quirements of a CT system in clinical practice. Currently, the main method tomitigate the high photon flux problem for CdTe/CZT detectors is to decrease thepixel size [57,58], which also means an increased spectrum distortion as a result ofcharge sharing and fluorescence escape [Paper I]. In addition, a serious effect limitingthe use of CdTe/CZT detectors under high photon flux irradiation is polarization,i.e. the build-up of space charge in detectors, as a result of low hole mobility andhole trapping, which collapses the electric field, severely reduces the amplitude ofthe detected pulses and leads to a rapid decline of count rate at a critical photonflux [59]. A few other technologies for CdTe/CZT detectors, such as parallel driftstructure [60] and multiple-layers arrangement [61], are under investigation but arange of technical difficulties need to be solved [53].

The feasibility of using silicon as the sensor material for photon-counting spec-tral CT has been investigated previously [24,62]. The detector is a photon-countingsegmented silicon strip detector [Paper V]. The mature manufacturing technologyand low cost are the advantages of silicon detectors. The high mobility for bothelectrons and holes means less pulse pileup. The low detection efficiency of siliconfor high energy x-rays can be compensated for by operating the silicon strip de-tector in edge-on geometry. The detector strips are segmented along the photonincident direction with each segment connected to an individual ASIC channel. Asa result the count rate in each detector segment and the subsequent ASIC channelis reduced. The only possible limitation of using silicon for CT is the high frac-tion of Compton scattering for high energy photons. Previous studies have shownthat the effect of Compton scattering is manageable [24,62]. The detector and thecorresponding evaluations are described in Chapter 4.

1.4 Outline of the Thesis

The project to develop a novel segmented silicon strip detector for photon-countingspectral CT was started in 2008, and I have been involved in the project eversince. My research focuses mainly on the evaluation of the detector by simulationand measurements. After four years of work, five peer-reviewed articles have beenwritten based on the main research results, which are the basis of this thesis.

CdTe/CZT is the main competitor to silicon as a candidate detector materialfor photon-counting spectral CT. A simulation study was performed to investigatethe energy response of pixelated CdTe detectors as a function of pixel size and theresults are presented in Paper I. For comparison, a simulation of the segmentedsilicon strip detector was also carried out and the results are presented in Chap-ter 2. The purpose of such comparison between silicon and CdTe/CZT is to answer

1.5. CONTRIBUTION BY OTHERS 5

a question in this field “Why use silicon? Why not CdTe or CZT” from the per-spective of detector energy response by showing that the pixelated CdTe detectoralso suffers from severe spectrum distortion for small pixel sizes. As a by-productof the simulation work, Paper II evaluates the validity of spherical approximationsof initial charge clouds produced by x-ray photons in silicon detectors and proposesa more accurate statistical model. The characterizations of the first and secondgenerations of the ASIC are presented in Paper III and IV, respectively. Paper Vdescribes the evaluation of the first-version segmented silicon strip detector devel-oped for photon-counting spectral CT.

1.5 Contribution by Others

The author is the principal contributor to all the results presented in this the-sis. However, it should be recognized that some of the measurements dependedon the work carried out by others. The ASIC was designed by Christer Svenssonand collaborators at Linköping University. The mechanical components used in themeasurements were fabricated by Staffan Karlsson. The photon-counting CT imagepresented in Paper III was reconstructed by Mats Persson and the image acquisitionprogram was provided by Moa Yveborg. In Paper IV, the synchrotron measure-ments of the ASIC at the Diamond Light Source were carried out by Mats Persson,Staffan Karlsson, Hans Bornefalk and the author. In Paper V, the measurementsof the detector at the Elettra synchrotron were performed by Mats Persson, StaffanKarlsson, Han Chen and the author.

Chapter 2

Detector Simulation

2.1 Introduction

In a photon-counting energy-resolving detector, several physical effects lead to de-tected events with reduced energies, including Compton scattering, fluorescenceemission, charge diffusion, trapping of charge carriers and slow-hole-motion-inducedincomplete charge collection. Charge sharing is the result of the lost energy beingcollected by adjacent pixels, and the shared charge may give rise to double countsin adjacent pixels.

Improvement in image quality of a photon-counting x-ray imaging system can beaccomplished by weighting the detected photons to an optimal weighting scheme [28,29]. However, the magnitude of the improvement will be reduced as a result of thedeteriorated energy resolution of the detector caused by the various physical ef-fects mentioned above [63] and pulse pileup [64]. The distorted energy spectrumcaused by energy loss and charge sharing produces cupping artifacts and inaccu-rate CT numbers when applying optimal energy weighting schemes, also reducesthe benefits of contrast-to-noise ratio (CNR) improvement and shifts the estimatedattenuation coefficients of the investigated object [63]. Consequently, there is a needto better understand and investigate the energy loss and charge sharing effects inenergy-resolving detectors for photon-counting spectral CT.

The effects of energy loss and charge sharing on the response of pixelated CdTedetectors developed for photon-counting spectral CT were evaluated in Paper IIby simulating the photon transport and the charge-collection process with a MonteCarlo-based simulation. An evaluation on the segmented silicon strip detector ispresented in the thesis for comparison.

Spherical approximations have been used extensively in low-energy x-ray imag-ing to represent the initial charge cloud produced by photon interactions in silicondetectors [65–68]. However, for high-energy x-rays, where the initial charge distri-bution is as important as the charge diffusion process, the spherical approximationswill not result in a realistic detector response. Paper I evaluates the validity of the

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8 CHAPTER 2. DETECTOR SIMULATION

spherical approximations of initial charge cloud shape in silicon detectors, thenpresents a statistical model (bubble-line model) for photons in the upper energyrange of medical imaging.

2.2 Simulation Methods

The details of the simulation procedure are presented in Paper II. The interactionsof the incident photons with the detector volume and the transport of all the sec-ondary particles were traced by a Monte Carlo simulation code PENELOPE [69],and the deposited energies and corresponding coordinates along the tracks wererecorded. The energy tracks were then converted into electron-hole pairs by di-viding the deposited energies along the tracks by the ionization energy, 4.4 eV forCdTe and 3.6 eV for silicon.

The charge carriers get separated immediately after generation and drift in theelectric field. The currents induced on corresponding electrodes by the movementof charge carriers were calculated by the Shockley-Ramo theorem [70,71]

i(t) = −qN∑

j=1exp(−t/τ) ~Ewj(~rj(t))~vj(t) (2.1)

where q is the elementary charge, N is the number of charge carriers, t is the drifttime, ~rj determines the trajectory of a charge carrier, τ is the mean lifetime of thecharge carriers, ~Ewj is the weighting field that describes the electrostatic couplingbetween a charge carrier and the investigated electrode, and ~vj is the velocity ofthe carrier. The velocity of charge carriers is induced by both the drift underthe influence of electric field and the thermal diffusion of charge carriers, wherethe latter effect is the main cause of charge sharing during the charge collectionprocess. The diffusion effect was analyzed by the diffusion equation

P (dr) = 1√4πDdt

exp(− dr2

4Ddt ) (2.2)

where dr is the diffusing distance of a charge carrier in one direction randomlychosen from the Gaussian probability distribution P (dr) after a time step dt, andD is the diffusion coefficient given by D = µkT/q, with µ being the mobility of acharge carrier, k the Boltzmann constant and T the absolute temperature. Due tothe high purity of silicon detectors, the exponential component which represents thetrapping effect can be removed. The charge collected on an electrode was obtainedby integrating the induced current over a certain measurement time.

The electric potential in the detector volume was calculated numerically withthe Poisson equation

∇2ϕ = −qNε

(2.3)

2.3. DETECTOR GEOMETRIES 9

on a three-dimensional grid using the Successive Over-Relaxation method, whereε is the permittivity of the material, N is the acceptor concentration for p-typeCdTe or the donor concentration for n-type silicon, and ϕ is the electric potential.The weighting field was calculated from Laplace’s equation by setting the potentialof the investigated electrode biased at unit voltage and by grounding the otherelectrodes.

2.3 Detector Geometries

Three different pixel sizes were characterized for both the pixelated CdTe andsegmented silicon strip detectors, which are 1.0× 1.0 mm2, 0.5× 0.4 mm2 and0.3× 0.2 mm2, respectively. The detector thicknesses of the silicon detectors are1.0 mm, 0.5 mm and 0.3 mm, and the pixel pitches are 1.0 mm, 0.4 mm and 0.2 mmfor three different pixel geometries. By operating the silicon detectors in edge-ongeometry, a 1.4 mm long center segment was chosen as the investigated segmentaround which to model charge sharing to all eight neighboring detector segments. Abias voltage of 600 V was applied to the backside of the segmented silicon strip de-tector with a mid-sized pixel (i.e. 0.5× 0.4 mm2) and the bias voltage was adjustedto keep the average intensity of electric field identical for different pixel geometries,i.e. the bias voltages to the detectors with large and small pixel sizes were 1200and 360 V, respectively. The CdTe detectors were irradiated through the cathodeto reduce the drift distance of holes. The distance between anode and cathode was3.0 mm for all three pixel geometries and the bias voltage was –1000 V.

2.4 Results and Discussion

2.4.1 Pixelated CdTe DetectorThe trapping of charge carriers and slow-hole-motion-induced incomplete chargecollection were evaluated with an analytical model, assuming that interacting pho-tons deposit all energy as charges at points along the central axis of a pixel. Ageometrical consequence of this simplification is that it avoids charge sharing as aresult of diffusion, the initial charge cloud extent and fluorescence. The ratio of lostenergy to deposited energy as a function of the interaction depth in the detectorwas obtained and shown in Fig. 2.1(a). The corresponding values of the weightingpotential along the central axis of the investigated pixels are shown in Fig. 2.1(b).The weighting potentials concentrate around the detector anodes and the value ofweighting potential is lower in the smaller pixel. The energy loss increases whenthe photon interacts with the detector at a deeper level. The smaller pixel resultsin less energy loss at the same interaction depth as a result of the lower value ofthe weighting potential. This effect is called “small pixel effect” [72], which meansthat the small ratio of pixel size to thickness helps improve the charge-collectionefficiency and reduce the effect of poor hole collection.


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Figure 2.1: (a) The ratio of lost energy to deposited energy in a pixelated CdTedetector for three pixel sizes as a function of interaction depth along the centralaxis of the investigated pixels. (b) The distributions of weighting potential alongthe central axis.

For the following evaluations, the incident photon energy was sampled from a120 kVp tungsten anode x-ray spectrum [73] filtered by 2 mm aluminum and 0.1mm copper and passed through a model of human head. Fig. 2.2(a) shows thepercentages of double counts induced by fluorescence escape photons in the CdTedetectors. The percentages decrease with increasing threshold and become zero ataround 30 keV. Fig. 2.2(b) shows the percentages of double counts as a functionof the electronic threshold, taking into account all the physical effects in CdTe.The total double-counting percentages are high for all the pixel geometries at lowthresholds, and it is more than 100% for small pixels, indicating that the leakedcharge of a single interacting photon has the possibility of being shared by morethan one adjacent pixel as a result of fluorescence or of the diffusion to multipleadjacent pixels. The results explain why a standard threshold level in photon-counting CdTe detectors is relatively high. However, setting the threshold too highwill reduce the count efficiency as a result of energy loss of the primary photons.

The results of the energy-loss evaluation in CdTe are shown in Fig. 2.3(a).Nearly all events lose at least 1 keV and about 20%, 34%, and 52% of eventslose more than 10 keV for large, mid-sized, and small pixels, respectively. All threecurves have inflexions at around 24 keV, and the percentages of energy loss decreasemore at these inflexions as a result of the sudden disappearance of fluorescence inthis region. Fig. 2.3(b) shows the count efficiencies in CdTe detectors. The figureshows how the count efficiency is decreased with increased threshold and also howthe count efficiency varies with pixel size; the larger the pixel size, the higher thecount efficiency.

The total proportions of escaped fluorescence photons are 31.80%, 21.89% and

2.4. RESULTS AND DISCUSSION 11

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Figure 2.2: (a) Percentages of double counts induced by only escaped fluorescencephotons in a pixelated CdTe detector for three pixel geometries with an incidentx-ray spectrum of 120 kVp. (b) Amounts of double counts including all the effectsin CdTe with an incident x-ray spectrum of 120 kVp.

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Figure 2.3: (a) Percentages of events whose lost energy is larger than a certainenergy in pixelated CdTe detectors with primary x-ray energies from a 120 kVpspectrum. (b) Count efficiencies in pixelated CdTe detectors for the 120 kVp tung-sten spectrum.

13.46% of the number of primary interacting photons for small, mid-sized, andlarge pixels, respectively, and 26.54%, 16.46% and 7.94% of the escaped fluores-cence photons are reabsorbed by the surrounding pixels and contribute to chargesharing. The distributions of the positions of reabsorbed fluorescence photons inthe surrounding pixels of the detectors are shown in Fig. 2.4. The range of escaped


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Figure 2.4: Position distributions of escaped fluorescence photons that are reab-sorbed by surrounding pixels in a CdTe detector for three pixel geometries: (a)small, (b) mid-sized, and (c) large. The contour levels, 50%, 90%, 95% and 99%,respectively, indicate the amount of fluorescence photons which are reabsorbed in-side the corresponding contour lines.

fluorescence for smaller pixels is more than one pixel.Fig. 2.5 shows the distributions of collected energies in a CdTe detector for the

three pixel geometries with the corresponding incident monochromatic x-rays of60 keV and 100 keV. The energy of most of the collected events deviates from theactual energy of the incident photons, most notably in the photo peaks of all thespectra, which are shifted toward the lower-energy side, an effect caused mainly byincomplete charge collection. The amount of double counting is inversely relatedto pixel size; the photo peak is higher in a large pixel than in a smaller one. Thepeaks appear at around 35 keV and 75 keV for different incident energies producedby the escape of fluorescence photons between 20 keV and 32 keV. The asymmetricdistortion of photo peaks is caused by incomplete charge collection, a phenomenonknown as “hole tailing”. The tailing effect is also observed below the escape peaks.The tailing effect is more evident for 100 keV photons than for 60 keV photons as aresult of the longer drift time of holes arising from the deeper interaction positionsof high-energy photons. The same phenomenon explains why the photo peaks from100-keV photons are lower than those from 60-keV photons.

Fig. 2.6 shows the spectra of collected energies from the incident 120 kVp x-ray spectrum. Compared to the actual photon energy, the collected energies shifttoward the lower-energy side for all three pixel geometries. The energy shift ismore severe for the smaller pixels as a result of greater energy loss from chargesharing. A high number of double counts from other pixels was imported andlocated at the low-energy band, mainly below 60 keV on top of the collected energyspectra produced by primary photons in the investigated center pixel. The peaksnear 25 keV represent the fluorescence photons from surrounding pixels. Chargesharing is important in the loss of energy resolution. For small and mid-sized pixelsin Fig. 2.6, the events in the low-energy range introduced by charge sharing ofneighboring pixels are similar in frequency to those of primary events.


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(f)

Figure 2.5: Simulated collected energy spectra from CdTe detectors for incidentmonochromatic x-ray of 60 keV and 100 keV. The energy spectra of charge-sharedevents from neighboring pixels are shown separately, as dashed curves. (a) 60 keV,small pixel; (b) 60 keV, mid-sized pixel; (c) 60 keV, large pixel; (d) 100 keV, smallpixel; (e) 100 keV, mid-sized pixel; and (f) 100 keV, large pixel.

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(b)

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Co

un

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AB

C

D

(c)

Figure 2.6: Simulated energy spectra for an incident x-ray spectrum of 120 kVpin a CdTe detector for three pixel sizes: (a) small, (b) mid-sized and (c) large.Solid curves A: the distributions of actual photon energies; dashed curves B: thecollected energy spectra; dash-dot curves C: the energy spectra of double countsfrom neighboring pixels; dotted curves D: the superimposition of B and C.


2.4.2 Segmented Silicon Strip Detector

The fractions of double counts caused by diffusion and the initial charge carrierdistribution in silicon for three pixel geometries assuming an incident 120 kVp x-ray spectrum are shown in Fig. 2.7(a). The amount of double counting decreasesrapidly with increases in the electronic threshold and increases as pixel size isreduced. The value is around 4.5% for the smallest pixel at a threshold of 3 keVand well below 4% for all the geometries at the 5 keV threshold. The charge sharinginduced by Compton scattering shows a higher fraction of double counts for largerpixel sizes (Fig. 2.7(b)). The reason is that the thicker silicon wafer for larger pixelsize absorbs more scattered photons; however, most of the scattered photons escapefrom the detector wafer for all three geometries.

The total percentages of double counting are shown in Fig. 2.8(a). Because ofthe opposing signs of the effects from diffusion and Compton scattering, there areno obvious differences in the total amounts of double counting among the threegeometries. The count efficiencies of the segmented silicon strip detectors for thethree geometries do not differ noticeably (Fig. 2.8(b)). However, the count effi-ciencies decrease markedly when increasing the threshold slightly in the low-energyregion, implying that the threshold in the segmented silicon strip detector in CTapplications should be set as low as possible.

The above results show that for segmented silicon strip detector under the in-vestigated bias voltages, the amount of energy loss and charge sharing is almostindependent of the pixel size. Therefore, only the energy spectra of mid-sized pixelare shown in Fig. 2.9 for 60 keV monochromatic and 120 kVp polychromatic x-rays,respectively. In Fig. 2.9(a), the photo peak is very narrow and the peak widthis limited by the energy bin size in the simulation (0.5 keV) and by the statisti-cal fluctuation in the number of charge carriers initially released. The amount ofevents shared from neighboring segments is low and does not noticeably affect theenergy resolution. In Fig. 2.9(b), only a small amount of the high-energy chargeshared events are mixed with the useful counts. Most of the charge shared eventsare located in the low-energy region and can be eliminated by setting a properthreshold. As seen in Fig. 2.9(b), the collected energy spectrum deviates from theincident energy spectrum as a result of a high fraction of Compton scattering; morethan 60% of the interacting photons experienced Compton scattering for the 120kVp x-ray spectrum with the specific filtration and deposited only a small amountof the photon energy.

2.4.3 Shape of Initial Charge Cloud in Silicon

Fig. 2.10(a) shows the energy distributions of 1000 photons with 60-keV energybeing photo-absorbed 4 µm from the border between two neighboring pixels in asilicon strip detector [62]. For the same interaction position of incident photons,the spherical approximations always result in the similar collected energy in theinvestigated pixel, with an uncertainty induced by the statistical fluctuation of the


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Figure 2.7: (a) Percentages of double counts introduced by the initial charge distri-bution and charge diffusion in the silicon detector for three pixel geometries with anincident x-ray spectrum of 120 kVp. (b) Percentages of double counts introducedby Compton scattering in the silicon detector for three pixel geometries with 120kVp x-rays.

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un

t e

ffic

ien

cy (

%)

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Mid-sized pixel

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(b)

Figure 2.8: (a) The total amount of double counts in the segmented silicon stripdetector with an incident x-ray spectrum of 120 kVp. (b) Count efficiencies in asegmented silicon strip detector as a function of threshold for three pixel geometrieswith 120 kVp x-rays.

number of initially released charge carriers and the diffusion process. For MonteCarlo simulation, the direction of Monte Carlo simulated charged tracks is crucialand determines the energy of detected events. In addition to a peak located atthe energy of incident photons of 60 keV, other events were detected with variable


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Figure 2.9: Simulated collected energy spectra in silicon detectors with mid-sizedpixel for (a) 60 keV monochromatic energy and (b) 120 kVp x-ray beam. Solidcurve A: the distribution of actual photon energies; dashed curve B: the collectedenergy spectrum; dash-dot curve C: the energy spectrum of double counts fromneighboring pixels; dotted curve D: the superimposition of B and C.

0 20 40 60 800

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ba

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ty o

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(b)

Figure 2.10: (a) Distributions of collected energy inside a pixel when interactionsoccurred 4 µm from the neighboring pixel. All photons were assumed to deposit 60keV energy. (b) Probability of double counting as a function of interaction distancefrom the boundary of two neighboring pixels.

energy over the whole abscissa due to random distributions of individual tracks.Fig. 2.10(b) shows the probability of double counting as a function of interactiondistance from the border of two pixels. The deposited energy was assumed to be60 keV and the threshold is 5 keV, i.e. if the detected energy is less than 5 keV, theevent will not be registered. For spherical approximations, all the events will be


detected by the neighboring pixel if the interaction site is close to the border of twopixels and no events will be detected if the distance is increased further. As can beseen from the Monte Carlo simulation in Fig. 2.10(b), the charge sharing affects thedetector response up to 25 µm to the border in this case, which is underestimatedby spherical approximations.

A statistical model has been proposed to simulate the distribution of initialcharge cloud in silicon detectors for the photons in the energy range of medicalimaging. An initial charge cloud can be generated by sampling the center of gravityand the track size from statistical distributions derived from Monte Carlo gener-ated tracks and by distributing a certain fraction (68%) of the photon energy intoa bubble uniformly and by distributing the remaining energy uniformly along aline [Paper II]. Compared to the spherical approximations of initial charge cloud,the statistical model can simulate the detector response accurately and correspondsto the Monte Carlo simulation results.

Chapter 3

ASIC Characterization

3.1 Introduction

A clinical CT system is usually running under very high photon fluxes, up toseveral million photons s−1 mm−2, where the expected benefits available for photon-counting spectral CT would be removed by the deterioration of energy resolution asa result of pulse pileup [64]. Therefore, an ultra-fast application specific integratedcircuit (ASIC) is needed to mitigate pileup effect, and retain count rate linearityand energy resolution even under high photon flux. Two generations of an ultra-fastASIC have been developed for photon-counting spectral CT. Paper III and IV givea detailed description of these two generations of the ASIC and the correspondingcharacterizations.

The ASIC is designed to be used with the segmented silicon strip detector [PaperV]. The ASIC chip has 160 individual channels. Each channel consists of an analogchannel, 8 comparators, each with a threshold generated by a global 8-bit digital-to-analog converter (DAC) and a digital channel. The analog channel, illustrated inFig. 3.1, includes a charge sensitive amplifier (CSA), a pole-zero cancellation circuitand amplifier, a pulse shaping filter implemented as two Gm-C filters and an offsetcalibration circuit. The pulse shaping filter can be set to 4 different peaking times,10, 20, 40 and 60 ns. A previous work showed that the 40 ns peaking time isneeded to reject cross talk induced by charge collection in neighboring detectordiodes [62]. Therefore, only the measurements with this peaking time are discussedin this thesis.

A switched offset calibration mechanism was employed in the first generation ofthe ASIC to calibrate the analog channel before each measurement cycle to reducethreshold dispersion and to compensate for temperature variations. It is imple-mented as two feedback loops around each Gm-C filter, each creating a correctionvoltage on a capacitor, which is stable for a few hundred microseconds. The firstgeneration of the ASIC was evaluated in Paper III and the results showed that withthe switched offset calibration the channel-to-channel threshold dispersion was not

19

20 CHAPTER 3. ASIC CHARACTERIZATION

Cf

Detector CSA Differentiator

Cdet

Rf

Cs

Rs

Cpz

Rpz

PZC Circuit

Digital

block8 comparators

Vref0

Vref1

Vref7

Clk

Globally distributed programmable thresholds

Gm-C Filter

Figure 3.1: Schematic of the analog channel.

small enough and a rate-dependent DC offset was created. Therefore, in the secondgeneration of the ASIC [Paper IV], the switched offset calibration is replaced bya continuous-time nonlinear filter circuit, which is similar to the baseline holder(BLH) circuit [74].

The digital channel contains eight 8-bit counters associated with respectivecomparators and some timing circuits to manage measurement sequence and fil-ter reset [75]. In addition, there is a global digital part managing overall control,including DAC control and various configurations, and the readout process.

3.2 Dead Time Behavior

The count rate performance and dead time behavior of the detector are mainlydetermined by the timing circuits of the ASIC. After pulse shaping, any incomingpulse with amplitude higher than the lowest threshold is sampled at negative clockedges during a programmable time period (sample time TS) and the pulse height(i.e. the photon deposited energy) is detected by comparing with eight comparators.After the sample time, a filter reset function can be enabled to reduce the risk ofpulse pileup by forcing the remaining pulse to zero during another programmabletime period (reset time TR), which is achieved by shorting the capacitors in thetwo Gm-C filters. If the filter reset function is disabled the ASIC is simply haltedfor TR and a 2 clock-cycle internal delay (TD) until the pulse tail is skipped (belowthe lowest threshold) to avoid double counting of the same single pulse. Totally theASIC needs a detection period of TC = TS + TR + TD to record a count for boththe reset enabled and disabled modes.

When the filter reset function of the ASIC is enabled, the dead time behaviorof the ASIC approximates a nonparalyzable model [75]. However, when the filterreset function is disabled, none of the existing models can satisfactorily describe thedead time behavior of the ASIC. A semi-nonparalyzable dead time model has beendeveloped based on the principles of the ASIC timing for the filter reset disabled

3.3. CHARACTERIZATION METHODS 21

Events in detector

Pulses after shaping filter

Dead time behavior of the ASIC

TC τ

time

Threshold

Figure 3.2: Dead time behavior of the ASIC.

mode. Fig. 3.2 shows the schematic of this dead time model. In the model, eachpulse detection period TC is divided into two segments, a nonparalyzable time τand a semi-nonparalyzable time TC − τ . After the activation of a detection periodTC , any events occurring within the nonparalyzable time τ would be suppressedand have no effect on the dead time behavior of the detector. During the followingsemi-nonparalyzable time TC − τ , if one or more events occur and the pulse tail (acombined pulse if more than one event occurs) is higher than the lowest thresholdof the ASIC after passing through the current detection period TC , one and onlyone count can be observed due to the finite pulse length, and a new detection periodwill be activated when the current one is finished. An analytical formula has beenderived based on the above analysis (refer to Paper III for a detailed derivation)

m = n

exp (−n(TC − τ)) + nTC(3.1)

with n and m being the input and output count rates, respectively, of one ofthe ASIC channels. Eq. (3.1) approximates the nonparalyzable dead time modelm = n/(1+nτ) at low input count rates, and for high input count rates the outputcount rate m will reach a maximum value of 1/TC .

3.3 Characterization Methods

The characterization of the ASIC was performed on a test board (Fig. 3.3) with 64ASIC channels wire bonded to the central strips of a silicon strip sensor with 0.5mm thickness, 50 µm strip width and 11.3 mm strip length [76]. A bias voltageof 100 V was applied to the backside of the detector for the measurements in thisthesis. The detector was mounted in a light-tight box to prevent the disturbancesfrom natural light. The commands input, data output and the clock of the ASIC


Bias input

Sensor ASIC

Test MUX

Vddd Ground Vdda

Electrical pulse input

Figure 3.3: A photograph of the test board with 64 channels of the ASIC wirebonded to a 50 µm strip width silicon strip sensor.

were managed by a field-programmable gate array (FPGA) card via a low-voltagedifferential signaling (LVDS) interface.

The first generation of the ASIC was evaluated in Paper III with electricalpulses and a pulsed laser mainly to verify the functionality of the ASIC. For thesecond generation of the ASIC, a comprehensive characterization was carried outby synchrotron radiation at beamline B16 of the Diamond Light Source with differ-ent monochromatic energies and various photon fluxes [Paper IV]. The count rateperformance of the ASIC was also investigated with 120 kVp polychromatic x-raysproduced by a tungsten anode tube at different fluxes. During the evaluation withx-ray photons, the sensor was irradiated from the strip side to facilitate the ASICprotection and setup alignment.

The performance of the ASIC was characterized by threshold scanning. For acertain amount of the energy injected into the input of an ASIC channel, eitherthrough electrical pulses or laser or x-ray photons, the lowest threshold was fixedat a low value above noise floor to start sampling of the incoming pulses, the secondthreshold was scanned and all higher thresholds were evenly distributed above thescan range of the second threshold. The threshold offsets and noise levels (or RMSenergy resolution) of the ASIC were derived from the resulting S-curves. Afterobtaining the threshold offsets for different photon energies, the gain and thresholdoffset at zero keV of a certain ASIC channel were estimated by fitting a line to thethreshold offsets corresponding to different photon energies. For the sensor with50 µm strip width, the significant charge sharing effect makes the width of themeasured energy spectra much larger than the internal noise level of the ASIC.Therefore, a deconvolution procedure was adopted to remove the charge sharinginduced spectrum distortion and obtain the internal noise level of the ASIC bydeconvolving the measured spectrum with the simulated energy spectrum.


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Figure 3.4: Mimicking real measurement by spreading out all eight thresholds andsweeping the intensity of electrical pulses.


Fig. 3.4 shows the detector response produced by electrical pulses with the eightthresholds spread quasi-evenly across the whole DAC range and the intensity ofelectrical pulses swept from low to high, which clearly demonstrates the energyresolving capability of the ASIC.

Fig. 3.5(a) shows the gain value of the ASIC as a function of detector stripnumber. The average gain over 64 connected channels is 1.65 mV/keV, and thestandard deviation of gain values is 0.03 mV/keV, which gives a gain variation of2.0%. The central detector strips (also the central ASIC channels) show smallergain than the outer ones. A possible reason for this is a slightly lower transconduc-tance of the transistors in the filters of the central channels, which will influencethe gain through a mismatch in the time constants of the amplifier and the filters.The transconductances are controlled by a common bias voltage, generated by acentral current mirror. However, because of voltage drops in the ground distribu-tion network (which carries quite large currents from chip edges to the middle ofthe chip), we can expect a systematic error in the local bias voltages (measuredrelative to local ground), causing the observed gain variation. Fig. 3.5(b) shows thedistribution of threshold offsets at zero keV. The standard deviation of thresholdoffsets at zero keV is 1.47 mV (0.89 keV) which shows an improvement from thefirst generation of the ASIC with a value of 3.31 mV [Paper III].

Fig. 3.6(a) shows the noise level of the ASIC in mV as a function of strip numberfor two different CSA feedback resistance values measured with 15 keV photons at a


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Figure 3.5: (a) Gain variation of the ASIC showing the gain values for differentstrips. (b) Threshold offset at zero keV as a function of detector strip number. Thedashed line shows the average value and the dash-dot lines illustrate the dispersion(± standard deviation).

0 10 20 30 40 50 601.5

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ne

rgy r

eso

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Figure 3.6: (a) RMS noise level in mV as a function of strip number measured with15 keV photon energy. (b) RMS energy resolution of individual ASIC channels asa function of output count rate for 15 keV photons.

flux of 40 kcps where the pulse pileup effect is nearly negligible. The average noiselevel over 64 channels is 1.81 mV (1.09 keV) for 3.0 MΩ feedback resistance and 2.11mV (1.28 keV) for 0.7 MΩ. Measurements done at different photon energies indicatethat the noise level of the ASIC are almost independent of the incident photonenergy. Fig. 3.6(b) shows the values of RMS energy resolution of individual ASIC


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Figure 3.7: (a) Count rate linearity of an individual ASIC channel for 120 kVp x-rays with TC = 100 ns. (b) The energy spectra measured with the ASIC connectedto a 50 µm strip-width sensor for different photon interaction rates from 120 kVpx-rays.

channels as a function of output count rate. The energy resolution is deteriorateddue to the effect of pulse pileup when the count rate is increased. A linear fittingσ = ∆σ·m+σ0 was used to fit the RMS energy resolution of the ASIC as a functionof output count rate (m) for both 3.0 and 0.7 MΩ CSA feedback resistances, whereσ0 is the RMS energy resolution of the ASIC at zero output count rate and ∆σ isthe deterioration rate of the RMS energy resolution as a function of output countrate. The RMS energy resolution is 1.09 keV at zero output count rate for 3.0 MΩCSA feedback resistance, and it deteriorates as a function of output count rate at arate of 0.29 keV/Mcps. The RMS energy resolution at zero output count rate andthe deterioration rate are 1.27 keV and 0.32 keV/Mcps, respectively, for 0.7 MΩCSA feedback resistance.

Fig. 3.7(a) shows the output count rate of an ASIC channel as a function ofinput count rate with TC = 100 ns and the fitting with the semi-nonparalyzabledead time model (i.e. Eq. (3.1)). The average nonparalyzable dead time τ over all64 evaluated channels is −10.15 ± 3.62 ns for TC = 100 ns and 32.96 ± 5.24 nsfor TC = 120 ns. A possible reason for the negative value of τ with TC = 100 nsis that for polychromatic incident energy spectrum at high photon flux the eventswith energy below the lowest threshold might pile up on top of each other, activatea detection period and lead to an additional detectable count. There is also apossibility of double counting of the same single pulse for a short detection periodof TC .

Fig. 3.7(b) shows the measured energy spectra (average of 64 channels) underdifferent photon interaction rates in each silicon sensor strip from 50 kcps to 5 Mcps(equivalent to photon fluxes from 5 to 500 Mphotons s−1 mm−2 in the segmented


Figure 3.8: Photon-counting CT image obtained with the first generation of theASIC and 50 µm strip-width sensor. The radius of the plastic phantom is 4.5 mmand the diameters of the two holes are 2.5 and 1.6 mm, respectively.

silicon strip detector [Paper V]) with TC = 100 ns. For low photon fluxes withoutthe influence of pulse pileup, the distribution of deposited energies is highly skewedtowards low energies due to the short photon interaction length of 500 µm and thesevere charge sharing effect in the sensor with 50 µm strips. For higher photon fluxespileup skews the distribution towards higher energies, which is consistent with theincreased energy uncertainty with higher count rates of Fig. 3.6(b). However, forfluxes up to 150 Mphotons s−1 mm−2 the distortion is not severe, indicating thatthe energy resolution is retained to a large extent. The experiment was repeatedfor TC = 120 ns. The deterioration of the energy spectrum is a little faster thanthat with TC = 100 ns due to the longer detection period to detect each incomingevent, but for fluxes up to 150 Mphotons s−1 mm−2 the spectrum distortion is stillsmall.

A photon-counting CT image obtained with the first generation of the ASICand 50 µm strip sensor is shown in Fig. 3.8. The nearly ring free image demon-strates that, at least in pure photon-counting mode, the relatively large thresholddispersion in the first generation of the ASIC can be calibrated away. A betterimage quality is expected for the second generation of the ASIC which has lesschannel-to-channel threshold dispersion.

Chapter 4

Segmented Silicon Strip Detector

4.1 Introduction

Paper V describes a silicon photon-counting energy-resolving detector developedfor spectral CT. The detector modules are fabricated on high-resistivity n-typesilicon substrate with p-type electrodes implanted. With the silicon sensor as basesubstrate, a Multi-Chip Module (MCM) technology is employed to integrate theASICs and electric routing.

The detector width of 20 mm is divided into 50 strips with a strip pitch of 0.4mm. Like most of the other silicon strip detectors applied in high-energy physicsand particle physics, an edge-on geometry of the detector is adopted to provide along absorption path of 30 mm for high energy photons encountered in clinical CT(up to 120 keV). The detector thickness is 0.5 mm. Consequently, an x-ray entrance(i.e. pixel size) of 0.5 × 0.4 mm2 is constituted for each detector strip. In orderto mitigate the problem of high photon flux, each detector strip is divided into 16segments with exponentially increasing lengths along the x-ray incident directionensuring similar count rates in all 16 segments, which is achieved by implanting16 individual p-type electrodes instead of a whole strip electrode onto the siliconsubstrate, and each electrode is connected to an individual ASIC channel. Thecount rate in each segment and the corresponding ASIC channel is thus reducedby a factor of 80 compared to the incident photon flux per square millimeter persecond because of the segmented structure of the detector strips and the pixel sizeof 0.5 × 0.4 mm2. Fig. 4.1 shows a photograph of the detector module togetherwith a schematic illustation of two detector segments. Five 160-channel ASICs arestud bonded to each detector module using a flip-chip technology to manage 800detector elements on each detector module.

The first version of the detector module has been manufactured and the eval-uation has been carried out at the beamline SYRMEP of the Elettra synchrotronlight source. The results presented in Paper V shows how we solved the problem ofhigh photon flux for a clinical CT system with the segmented silicon strip detector.

27

28 CHAPTER 4. SEGMENTED SILICON STRIP DETECTOR

1

16

Se

gm

en

t

Strip 1 50

x-rays enter along this edge ASIC

D2

D1

D3

Front-side electrode

x-rays

(a) (b)

Figure 4.1: (a) A photograph of the detector module (MCM) with 50 strips, 16segments and five 160-channel ASICs bump bonded. The corresponding detectorelements managed by different ASICs are illustrated by thick white lines. (b) Amagnified view of two detector segments with detector thickness D1 = 0.5 mm,strip pitch D2 = 0.4 mm and electrode width D3 = 0.125 mm.

4.2 Characterization Methods

Paper V shows the detector evaluation performed at the beamline SYRMEP at theElettra synchrotron light source. The detector was aligned in edge-on geometry andan ionization chamber was positioned in front of the detector to monitor the time-dependent variation of photon flux. A thermocouple was attached to the detectorto record the temperature variation during the measurement. A bias voltage of160 V was applied to the backside of the detector. The gain, threshold offset,energy resolution and the amount of charge shared events were estimated using thethreshold scanning method.


The gain and threshold offset at zero keV were calibrated with four different photonenergies of 22, 26, 30 and 34.9 keV. A narrow beam of 6 mm width struck severalstrips of the detector edge-on. Since the low-energy photon beam only penetrateda few segments of the detector, the response of the first 4 segments were investi-gated based on the distribution of interacting photons in the detector. The average


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Outp

ut count ra

te p

er

segm

ent (k

cps)

Segment−1

Segment−2

Segment−3

Segment−4

Figure 4.2: Output count rate as a function of input count rate for the individualdetector elements of the first 4 segments with 22 keV incident photons. The dash-dot line is the ideal relationship between input and output count rates and thedashed curve illustrates the fit by the semi-nonparalyzable model (Eq. (3.1)).

gain over 44 evaluated detector elements is 1.65 mV/keV and the gain variationcalculated as the standard deviation divided by the mean is 3.7%. The standarddeviation of threshold offsets at zero keV is 2.36 mV (1.43 keV). The gain variationand threshold dispersion are larger than the results measured on the test boardwith only one ASIC mounted [Paper IV], probably caused by the non-uniformityof the power distribution to different ASICs on MCM.

Fig. 4.2 shows the output count rate as a function of input count rate forindividual detector elements measured with 22 keV photons. Fitting the semi-nonparalyzable model (Eq. (3.1)) to the measured relationship between input andoutput count rates gives an estimated nonparalyzable dead time of 79.8 ± 1.9 ns.Although the reset function of the ASIC was not enabled, the count rate perfor-mance of the detector is still very promising. The count rate performance of thedetector is a function of photon-deposited energy, setting of thresholds and, mostimportantly, the timing of the ASIC, and a significant improvement is expectedwith 120 kVp polychromatic x-rays [Paper IV].

Fig. 4.3 shows the RMS energy resolution (σ) in keV for individual detectorelements as a function of input count rate. The energy resolution of the detectorgradually deteriorates as the increase of photon flux due to the effect of pulse pileup.All the evaluated detector elements in the first segment, two in the third segmentand one in the fourth segment have higher noise levels than the other detectorelements, because part of the routing wires connecting these detector elements andthe ASICs is run in a metal layer with an insulator thickness of about 1.5 µm to

30 CHAPTER 4. SEGMENTED SILICON STRIP DETECTOR

101

102

103

104

1

1.5

2

2.5

3

3.5

4

Input count rate per segment (kcps)

RM

S e

nerg

y r

esolu

tion (

keV

)

Segment−1

Segment−2

Segment−3

Segment−4

Figure 4.3: RMS energy resolution versus input count rate for each detector segmentwith an incident photon energy of 22 keV and the linear fits.

the silicon substrate, smaller than the 10 µm insulator thickness for the wires ofthe other elements running in another metal layer, thus having higher capacitancesand easier to couple the noise from the diffused ground plane in the MCM. Alinear fit σ = ∆σ·n + σ0 was applied to the data set of each segment, with nbeing the input count rate, σ0 the RMS energy resolution at zero flux and ∆σ thedeterioration rate of the energy resolution for a single detector segment in units ofkeV/Mcps. The values of σ0 and ∆σ for the first 4 segments and the average valuesof the four segments are shown in Table. 4.1. An RMS energy resolution of 1.50 keVhas been determined with 22 keV photons at zero flux giving an energy resolution(FWHM/E) of 16.1%. Previous tests showed that the RMS energy resolutionwas quite independent of the incident photon energy [77], thus a superior energyresolution is expected for higher photon energies. The average deterioration rate ofthe energy resolution for each detector segment as a function of input count rate for22 keV photon energy is 0.41 keV/Mcps, which translates to a deterioration rate of5.13 eV mm2/Mcps for the studied detector layout with 16 depth segments and apixel size of 0.5 × 0.4 mm2. The energy resolution of the detector would be 21.5%for 22 keV photon energy at an input count rate of 100 Mcps mm−2.

The fraction of charge shared events was calculated and the results are presentedin Table. 4.2. A fraction of 11.1% of the interacting photons experienced chargesharing for the evaluated detector, and increased to 15.3% for 30 keV. As a resultof energy loss, these charge shared events distort the energy spectrum collectedby the detector, but they are still useful events if the system is operated in purephoton-counting mode. The energy leaked into the neighboring detector element


might be detected and result in noise counts if the leaked energy is higher than thelowest threshold of the neighboring detector element. Properly setting the thresholdcould help improve the system performance. Various effects result in charge sharedevents, including diffusion of charge carriers, distribution of initial charge cloudand Compton scattering. The diffusion effect was found to dominate the amountof charge shared events, thus the fraction of charge shared events is expected to bereduced by applying a higher bias voltage to the detector.

Table 4.1: The RMS energy resolution at zero flux (σ0) and the deterioration rateof the energy resolution (∆σ) for each detector segment for 22 keV photon energy.

∆σ (keV/Mcps) σ0 (keV)Segment-1 0.48 ± 0.02 1.85 ± 0.01Segment-2 0.31 ± 0.02 1.36 ± 0.01Segment-3 0.37 ± 0.07 1.40 ± 0.03Segment-4 0.48 ± 0.09 1.39 ± 0.02

Mean 0.41 ± 0.03 1.50 ± 0.01

Table 4.2: Fraction of charge shared events (%) for two photon energies and thefirst two detector segments.

Energy (keV) Segment-1 Segment-2 Mean22 9.8 ± 1.0 12.6 ± 1.0 11.1 ± 0.730 14.4 ± 0.8 16.2 ± 0.7 15.3 ± 0.5

Chapter 5

Conclusions

“Why use silicon? Why not CdTe or CZT?” This is a most frequently asked questionfrom the researchers who are developing photon-counting spectral CT based onCdTe/CZT detectors. I am not surprised at all to hear this due to the well-knownhigh-fraction Compton interactions in silicon in the energy range of x-ray CT.The answer to this question is obvious according to the evaluations and analysespresented in this thesis.

Actually silicon has properties which make it more attractive than CdTe/CZTas a candidate detector material for photon-counting spectral CT. The problem ofextremely high photon flux, what prevents a photon-counting energy-resolving de-tector from being used in a clinical CT system, can be properly solved by adopting asegmented detector structure and operating the detector in edge-on geometry. Thelow photon detection efficiency in silicon can be compensated for by increasing thedetector length. A previous study showed that the segmented silicon strip detectorcould perform comparably to the ideal energy-integrating detector for routine CTimaging tasks [24]. In addition, the energies deposited by photoelectric and Comp-ton interactions are well separated without an overlap, indicating that statisticalmethods can be applied to make maximum use of the energy information remainedin Compton events. The results presented in Chapter 2 further demonstrated thatthe pixel size of the investigated silicon detector could be reduced without the influ-ence of charge sharing by simply keeping the intensity of electric field for differentpixel sizes constant, which could help improve the spatial resolution of the systemin the future.

For CdTe/CZT detectors, the primary challenge is how to handle the high pho-ton flux encountered in clinical CT applications. Currently, no other way thandecreasing pixel size has been put into practice [57, 58, 78], which is not effectiveenough to fulfill the high flux requirements and also means an increased spectrumdistortion as a result of charge sharing and fluorescence escape, as demonstrated inPaper I. An edge-on multiple-layers arrangement which is similar to the detectorstructure presented in this thesis has been proposed in simulation [61], whereas

33

34 CHAPTER 5. CONCLUSIONS

the real implementation is much more difficult than that with silicon. Polarization,another serious limitation of CdTe/CZT detectors, caused by low hole mobility andhole trapping at high photon flux, is also difficult to be addressed even with edge-onmultiple-layers structure.

Both a novel detector structure and an ultra-fast ASIC are needed to developa CT scanner with photon-counting energy-resolving capabilities. A segmentedsilicon strip detector has been designed. By operating the detector in edge-ongeometry, the count rate in each detector segment and the corresponding ASICchannel can be reduced by a factor of 80 compared to the incident photon flux persquare millimeter per second with the 16 detector segments along the x-ray incidentdirection and a pixel size of 0.5 × 0.4 mm2.

An ultra-fast photon-counting energy-resolving ASIC has been developed toprocess the photon-converted pulses in each individual detector segment. The syn-chrotron measurement demonstrated that the ASIC performed as expected. Anoise level of 1.81 mV RMS (1.09 keV) has been measured, which is close to thesimulated value of 1.0 mV. A channel-to-channel threshold dispersion of 0.89 keVRMS can be calibrated away by using a novel compensation method [79]. The deadtime behavior of the ASIC approximates a nonparalyzable model in the filter resetenabled mode and follows a semi-nonparalyzable model when the filter reset is dis-abled. A promising count rate performance has been achieved in terms of the countrate linearity and energy resolution, i.e. the count loss and deterioration of energyresolution with the increase of photon flux are acceptable for the operational rangeof photon flux in clinical CT.

The first-version segmented silicon strip detector with 5 ASICs stud bondedwas characterized using synchrotron radiation. An energy resolution of 16.1% hasbeen determined with 22 keV photons at zero flux, which deteriorates to 21.5%at an input count rate of 100 Mcps mm−2 according to the deterioration rate ofRMS energy resolution of 5.13 eV mm2/Mcps. The noise level of this version of thedetector is higher than expected as a result of the imperfect ASIC power connectionand detector layout. Lowering the noise of the detector is an ongoing task which iscrucial for the performance of the whole CT system. The fraction of charge sharedevents has been estimated and found to be 11.1% for 22 keV and 15.3% for 30 keV.Since the diffusion of charge carriers dominates the amount of charge sharing, alower fraction of charge shared events and an improved energy resolution can beexpected by applying a higher bias voltage to the detector.

Acknowledgements

First of all, I would like to express my deepest gratitude to my supervisors, HansBornefalk and Mats Danielsson, for giving me the opportunity to work in thisexciting project. This thesis would not have been possible without your patientguidance and encouragement.

I would like to thank Christer Svensson for sharing expertise in electronics andfor valuable advice and discussions. I am sincerely grateful to all my colleagues inthe Physics of Medical Imaging group for all your help and support during thesefour years; Staffan Karlsson for help with mechanics, engineering and for variouspractical supports; Mats Persson for help with mathematics and data processing;Han Chen for numerous measurements; Peter Nillius for advice in Paper II; MoaYveborg for debugging the Python code; Erik Fredenberg for much help in the earlystages of my work; Björn Cederström, Sandra Tibbelin, Wujun Mi, Xuejin Liu, BenHuber and all former group members for creating such a good working atmosphere.

Special thanks go to my parents, my brother and my wife for your support.

35

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