**Fig. 20.8** Schematic representation of the divergent-beam weighted back-projection: The magenta points at seven different positions on each of the represented LOR's are visual guides to indicate how the sampling fraction varies as a function of the distance to the X-ray source, justifying the need for a distance-dependent weighting function in the backprojection algorithm (from [15])

#### **<IP_ADDRESS> Design of Modern CT Scanners**

The most recent advance in CT scanning is the introduction of multi-slice helical scanning, sometimes known as spiral CT. A volume of tissue, e.g. the thorax or abdomen, is scanned by moving the patient continuously through the gantry of the scanner while the X-ray tube and detectors rotate continuously. The multislice systems offer the advantage over single-slice systems of being able to acquire information about the same volume in a shorter time, or alternatively to scan larger volumes in the same time or scan the same volume but obtaining thinner slices for better z-axis resolution. Helical CT has improved over the past years with faster gantry rotation, more powerful X-ray tubes, and improved interpolation algorithms [16].

The introduction of multi ring detectors and cone beam reconstruction algorithms have enabled the simultaneous acquisition of multiple slices: 4 slices in 1998, 16 slices 3 years later, 64 slices at the end of 2004, and up to 128 slices for the last generation scanners. Coupled with continuous increase of the gantry rotational speed (1.5 rotations per second in 1998, about 3 rotations per second in 2004) multislice acquisition is allowing shorter scan times (important for trauma patients, patients with limited ability to cooperate, pediatric cases and CT angiography),

**Fig. 20.9** Siemens Somaton 64 without cover and multislice CT block-diagram

extended longitudinal scan range (for combined chest abdomen scans, such as in oncological staging) and/or improved longitudinal resolution (typically 0.5 mm per slice). It has further improved the performance of the existing applications such as angiography and detection of lung and liver lesions as well as paved the way to the introduction of new ones, most notably in cardiology, where high quality images can be obtained in 10–20 heartbeats or in a single breath-hold only.

A third-generation multislice CT scanner and a block-diagram is shown in Fig. 20.9. The slip-ring technology was introduced at the end of 1980s and allowed the spiral scanning mode, when the X-ray tube and 2D arc of multislice detector system are rotated continuously around the patient while the scanning table is translated through the rotating gantry. The scan parameters, selected by the radiologist, define the X-ray tube protocol, X-ray collimation, patient table motion, data acquisition, and reconstruction parameters.

The scanner can be designed for a fixed slice collimation. It is however desirable, although more challenging, to design the detector in such a way as to meet the clinical requirement of different slice collimations adjustable to the diagnostic needs. There are basically two different approaches, the matrix detector with elements of a fixed size or the adaptive array principle (Fig. 20.10). As shown in the figure for a 16 slice array in an expanded way the cone beam geometry introduces a smearing over the field of view, which Increases the slice thickness on the edges of the cone compared to the centre.

There is therefore no need to have the same number of detector elements in the centre and in the periphery of the detector.

Most of the modern CT scanners have multiple, up to 128, detector rings, or slices. Typical CT scanners have a field of view FOV = 50 cm, and a spatial resolution of 0.5 mm in the middle of the FOV. Therefore, each detector ring houses more than 1000 detector elements per slice. The electronic channels amplify and filter the detector current and measure the filtered current at small time interval, called "view time" Tw, which is the time in which the disc rotates approximately one 1/4 to 1/3 of a degree. Since the rotational speed of modern CT scanners

**Fig. 20.10** Principle of the matrix detector (left) and of the Adaptive Array Detector (right)

can be as high as 3 or even 4 rotations per seconds, Tw can be as short as about 250 μs. At a typical focal spot-detector distance of 1000 mm, the exposure rate at the detector can reach ~0.1 Gy/s. Single detector channel detects up to 300,000 Xray photons per sample at 3000 Hz acquisition rate. At such high photon fluxes, the detector cannot be operated in counting mode, and the majority of medical X-ray CT scanners operates in current measurement or integration mode.

One of the most widely used CT scanner, the Siemens SOMATOM Sensation 64 [17], is using a scintillating ceramics detector head. The X-ray focal spot is switched in two different positions during a view time, to reduce the aliasing of sampled data in the translational direction, i.e. along the z-axis. Consequently, the readout electronics must sample and measure the input signal two times in each view time. This machine uses an adaptive array detector with 40 detector rows in the longitudinal direction. The 32 central rows have a slice width of 0.6 mm in the centre of the field of view, whereas four detector rows on each side (in the penumbra of the collimated X-ray source) have a slice width of 1.2 mm. The slice widths being determined at the isocentre the actual detector size is about twice as large, due to the geometrical magnification (Fig. 20.11). Acquisition of 64 slices per rotation is possible through the use of a special X-ray tube with a flying spot capability (Fig. 20.12). The electron focal spot is wobbled between two different positions of a tilted anode plate by an variable electromagnetic field, resulting in a motion of the X-ray beam in the longitudinal direction. The amplitude of this periodic motion is adjusted in such a way that two subsequent readings are shifted by half a slice width in the longitudinal direction.

In general, it should be remembered that the performance factors of image quality, dose and speed can each only be improved at the expense of the other parameters. High contrast resolution in the final image is affected by noise, matrix size and contrast. Low contrast detection is affected by the size of the object, windowing and image noise. Image noise itself is affected by exposure factors, detection efficiency, slice width and, most critically, by the algorithms used in the reconstructions.

**Fig. 20.11** Adaptive array detector with 32 slices of 0.6 mm in the central part, resulting in 64 slices with 0.3 mm sampling at the isocentre (Courtesy Siemens Medical Solutions)

**Fig. 20.12** Schematic drawing of a rotating envelope X-ray tube (Siemens STRATON, Forchheim, Germany) with z-flying spot technique (Courtesy Siemens Medical Solutions)

It must be noted that for modern scanners the X-ray tube operates with a higher duty cycle: heat output and heat dissipation are therefore a concern in the design of such multislice CT-scanners.

Another important trade-off is related to the radiation exposure of the patient. The continuing quest for better spatial resolution imposes ever smaller detector sizes. As the area of each detector cell decreases, the amount of X-rays incident on the detector decreases, leading to an increase in statistical noise. Retaining the original signal/noise ratio (and therefore the same level of contrast detection power) requires an increase in the number of X-rays and hence patient radiation dose. There is, therefore, a balance to be struck between radiation dose and resolution.

Recent developments are aiming at further decreasing the scan time and, most importantly, reducing the dose exposure to the patient. This is achieved by the introduction of the dual X-ray technology, with two X-ray sources of different energy (typically 80 kV and 140 kV) and selective photon shield for better spectral separation. Combined with two 128 slices detector panels and a rotation speed of 0.28 s, the SOMATOM Definition Flash Spiral from Siemens achieves ultrafast image acquisition (not necessitating a breath hold) with an dose exposure approaching 1 mSv for a number of protocols, to be compared to 20 mSv 10 years ago (https://www.healthcare.siemens.com/computed-tomography/ dual-source-ct/somatom-definition-flash/technical-specifications). A summary of the recent progress and new trends in CT imaging can be found in [18, 19].

### *20.2.4 Future of X-Ray Imaging*

X-ray imaging is the historical imaging modality since the discovery of X-rays and the pioneering work of W. Roentgen in 1895. It is still the most widely used imaging diagnostic tool for physicians with nearly half a billion X-ray exams performed every year worldwide.

One major thrust for the future X-ray imaging devices is to obtain higher resolution data at a faster rate. For instance, cardiac applications would substantially benefit from CT scanners able to acquire heart images in one heartbeat or less so that motion artifacts can be minimized. One direction being pursued are scanners featuring multiple X-ray tube/data acquisition combinations operating simultaneously. Moreover, tubes incorporating a smaller focal spot are being introduced, enabling higher spatial resolution (up to around 25 line pairs per cm). Various other medical applications, such as surgical ones or the rapidly developing interventional radiography, would substantially benefit from CT scanners able to perform acquisitions at both normal and ultra-high spatial resolutions, as those required in fluoroscopic procedures. Ultra-high resolution can be achieved by substantially shrinking the physical size of both the focal spot and detector elements. Similar trends to reduce the pixel dimensions are observed for two-dimensional detector arrays used in digital radiography. This results in a considerable increase in the number of pixels and increases the complexity of the acquisition system in CT and planar digital radiography (see Sects. <IP_ADDRESS> and <IP_ADDRESS>).

Present X-ray imaging only provides morphologic information but no information about the physiology of the organs under examination. However ongoing research suggests that information about the pathology of a tissue is conveyed not only by its overall X-ray attenuation, but also by its selective absorption at different X-ray beam wavelengths. This opens a new and exciting field: exploiting the new singly photon counting techniques for studying tissue pathologies with Xray spectral images (see Sects. <IP_ADDRESS> and <IP_ADDRESS>).

#### **<IP_ADDRESS> Indirect Detection with Phosphor Screen**

The choice of the scintillating material is of course the key for a higher segmentation of a new generation of X-ray devices, as the pixel size is determined by mechanical properties of the crystal like hardness, cleavage, mechanical processing yield

**Fig. 20.13** Column structure of vapor deposited CsI(Tl). Columns have a typical diameter of 10 μm and a length of 500 μm

and cost. Large efforts have been devoted recently on specific technologies to develop a solid-state dynamic X-ray sensor with digital readout for matrixes manufacturing with sub-millimeter resolution. So called columnar structure screens were developed [20]. The rapid progress on position sensitive photomultipliers (PSPMT), Silicon photodiodes with different designs and Geiger mode Silicon photomultipliers (SiPMT) open attractive possibilities for pixel based arrays. The current design is based on large a-Si photodiodes (substrate) coupled to a CsI(Tl) layer. The scintillator layer growth is nucleated on the pattern substrate and transferred to a columnar system separated with grain boundaries as seen in Fig. 20.13. Each CsI(Tl) column is not only a scintillation pixel but also a light guide. This guide prevents or at least strongly suppresses the radial light spread and might be the way to obtain very high spatial resolution. Columnar structure growth technique allows to get 3–5 μm diameter columns and the pixel size is defined by the Si pad size as seen from Fig. 20.14. Currently, flat panels with dimensions up to 40 × 40 cm2 are developed to image the human chest.

It should be noted that it is possible to use non-pixilated screens for low energy X-rays. If X-rays are absorbed in a very thin crystal layer, the angle of the emitted light is small (for the thin film) and the crosstalk to the neighbor photo-receiver is negligible maintaining therefore a good spatial resolution. The search for materials for such applications is now of very high importance.

**Fig. 20.14** Integrated columnar CsI(Tl) and a-Si photodiode readout for new generation X-ray flat panel (Courtesy J.A. Seibert, UC Davis Medical Centre, CA, USA)

**Fig. 20.15** Direct conversion detector for new generation X-ray flat panel (Courtesy J.A. Seibert, UC Davis Medical Centre, CA, USA)

#### **<IP_ADDRESS> Direct Conversion Screen**

Another even more radical departure from the present X-ray detector technology may be the use of high-density room temperature semiconductors.

As shown in Fig. 20.15, direct detection flat panel technology is based on a uniform layer of X-ray sensitive photoconductor, e.g., amorphous selenium (a-Se) to directly convert incident X-rays to charge, which is subsequently electronically read out by a two-dimensional array of Thin-Film-Transistors (TFT). During readout, the scanning control circuit generates pulses to turn on the TFTs one row at a time, and transfers the image charge from the pixel to external charge sensitive amplifiers. They are shared by all the pixels in the same column. Each row of the detector typically takes about 20 μs to read out. Hence a detector with 1000 × 1000 pixels can be read out in real-time (i.e., 30 frames/s).

A challenge for this approach is the practical implementation of the complex pixel design over a large area with consistent and uniform imaging performance. The problem of charge collection efficiency and speed for materials with high Z and sufficient thickness remains a major concern. Substantial technical problems must be resolved before these technologies will be implemented in commercial X-ray devices.

#### **<IP_ADDRESS> Single Photon Counting**

The impressive CT images shown in the literature (Fig. 20.4) require several tens to 100 times higher X-ray exposures compared to standard radiography (typically 20–50 mSv as compared to 0.1 mSv). On the other hand, the enormous research effort on particle detectors has led to the development of digital X-ray detectors with very small pixels, based on silicon (Medipix) [21] and on gaseous detectors (GEM, Micromegas) [22]. The major and unique feature of these devices is their capability to work in single photon counting mode up to very high rates. Excellent high contrast images can therefore be obtained with X-ray doses up to 10 times smaller than for standard X-ray systems working in current mode.

There are a number of advantages of counting systems over current mode systems, such as:

This results in much better image contrast performance and significantly lower doses as shown in Fig. 20.16 in a comparative study of the signal-to-noise ratio for a 2 mm thick tumour as a function of the X-ray tube current for different mammography systems. The Medipix single photon counting device achieves the same image quality as the best commercial mammograph working in current mode for typically half the dose.

#### **<IP_ADDRESS> Spectral X-Ray Imaging**

The introduction of hybrid pixel detectors in X-ray imaging**,** where the sensor array and the matching read-out chip are processed independently and are connected together only in the final step, has allowed high dynamic, noise free images to be recorded on the basis of single photon counting techniques [25]. Moreover, among the most promising recent developments in CT is the use of spectral information to improve contrast discrimination, by acquiring data with different energy thresholds. In traditional CT imaging, the overall attenuation of X-ray intensity is measured by the detector, but the detected X-rays are not spectrally resolved. This introduces a bias in the images because the absorption of X-rays by different materials depends on the X-ray energy. A significant amount of information can therefore be gained by including spectral data in the CT reconstruction process. Based on differences in X-ray absorption, different materials can be distinguished and quantified with a single spectral CT scan.

Two principal methods provide spectral CT data. The first method, dualenergy (DE) CT, uses X-ray sources with two different energy spectra and energy integrating X-ray detectors. The second method uses a single X-ray source but has energy-resolving detectors (photon counting detectors) that measure the energy of each detected photons. DE CT is currently used clinically and has been successful in improving imaging for a variety of applications.

While the soft tissue attenuation coefficient is rather wavelength independent, the photoelectric effect in high atomic Z materials strongly depends on X-ray energy. This feature can be exploited by using contrast agents containing such high Z elements. The attenuation coefficient of such substances (calcium in bone, iodine, gold) will show significant differences if the two energy spectra are recorded on either side of the K-edge for these heavy elements. The large increase in attenuation at energies above the K-edge leads to large signal differences between the two scans. By combining data from the two energy sets, these high Z materials can be distinguished and quantified. Figure 20.17 shows scans of a mice after injection

**Fig. 20.17** Coronal slices of a sacrificed mouse after injection of an iodinated contrast agent. From left to right: slice reconstructed in the energy window just below the iodine K-edge, in the energy window just above the iodine K-edge and K-edge image (subtraction of the first slice from the second one). Zooms of two ribs and the ureter are also shown (from [26])

of a iodinated contrast agent. The difference between the scan taken in an energy window just below the iodine K-edge (left) and the scan taken in an energy window just above the K-edge (centre) shows the iodine concentration in some parts of the kidneys. More information can be found in [26].

### **20.3 Single Photon (SPECT) and Positron (PET) Emission Tomography**

### *20.3.1 SPECT and PET Working Principle*

Nuclear medicine relies on using radioactive molecules administered to a patient for diagnostic or therapeutic purposes. Radioactive molecules behave in vivo the same way as their non-radioactive "natural" equivalent involved in the metabolic or molecular processes under study. Nuclear medicine is used daily in oncology, cardiology, neurology, paediatrics, rheumatology or orthopaedics for diagnosis and therapy.

A new and recent concept is molecular imaging. It provides the ability to visualize and quantitatively measure in-vivo the activity of different biological and cellular processes activated or depressed in some pathologies.

The working principle of emission tomography is to image γ rays emitted by the radiotracers injected into the patient. Contrary to X-ray CT and standard nuclear magnetic resonance, which provide very precise images of the anatomy of organs, nuclear molecular imaging modalities give in vivo access to the quantitative functioning of these organs.

#### **<IP_ADDRESS> SPECT**

In Single Photon Emission Computed Tomography (SPECT) a molecule involved in the metabolism of the patient is labeled by a single photon emitter (usually 99Tc emitting one 140 keV γ ray). After injection, this molecule concentrates preferentially in the organs or tumours where this metabolic function is active and allows their imaging through the reconstruction of the γ ray emitting points. The most popular technique is based on the "Anger logic", where γ rays are directed through a multi-hole collimator to a large slab of Sodium Iodide (NaI) or Cesium Iodide (CsI) scintillator. The coordinates of the interaction point are then determined by comparing the signals from a set of photomultipliers (PMT) coupled to the crystal, by the centre of gravity method (Fig. 20.18). This technique, called scintigraphy, is still largely used in many hospitals and medical imaging labs, but suffers from a relatively poor space resolution, of the order of a few centimeters.

More recent detector designs are based on discrete scintillating pixels coupled to multichannel photodetectors, such as multianode photomultipliers or avalanche photodiode matrices. But the most impressive progress has been made on the collimator, which is the main limiting factor for the spatial resolution and the sensitivity of SPECT devices. Several configurations have been studied:

The best results so far are achieved with multi-pinhole configurations, for which sub-millimeter spatial resolution and sensitivities at the level of 1 cps/KBq have been obtained on small animal imaging SPECT cameras. The counterpart of using collimators, and particularly pinholes, is a reduction of the overall sensitivity of the SPECT camera. For clinical applications a compromise needs to be found between sensitivity and spatial resolution.

The spatial resolution is usually given by the Full Width at Half Maximum (FWHM) of the so-called point spread function (PSF):

$$FWHM = \frac{D}{L} \left( z\_0 + L + B \right)$$

**Fig. 20.18** Principle of an Anger camera

where D and L are the collimator hole diameter and length, z0 is the distance from the γ-ray source to the collimator entrance and B is the distance between the collimator back face and the image plane in the crystal.

The collimator introduces an important loss of efficiency by a factor of 103 to 104. The resulting efficiency is given by the following formula:

$$\eta = \varepsilon \left(\frac{a\_{hole}}{a\_{cell}}\right) \left(\frac{a\_{hole}}{4\pi L^2}\right)$$

where ahole and acell are the collimator hole and cell area respectively and *ε* is the γ detection efficiency in the scintillator.

#### **<IP_ADDRESS> PET**

In the case of Positron Emission Tomography (PET) the functional molecules are labeled with a β+ emitter generally produced in a cyclotron. These PET tracers, injected into the patient, simulate natural sugars, proteins, water and oxygen presence, circulation and accumulation in the human body. Once fixed in the organ or the tumour, the molecule emits positrons, which annihilate very quickly on contact with the tissue, emitting two gamma photons located on the same axis called the line of response (LOR)—but in opposite directions, with a precise energy of 511 keV each (Fig. 20.19).

The coincidence detection scheme introduces therefore an electronic collimation, which greatly enhances the background rejection as compared to SPECT. Moreover, the line of interaction being precisely determined by the two detectors hit in coincidence, there is no need for a collimator system, which severely reduces the sensitivity of SPECT cameras. In order to simplify and reduce the image reconstruction time the first generation PET scanners used septa to restrict the acquisition to transversal slices through the patient in a so called 2D acquisition mode. The slices were then combined off line for a 3D image reconstruction. Modern PET scanners benefit from the considerable progress in computer power and directly acquire data in 3D mode without septa (i.e. recording all the LORs independent of their direction relative to the scanner axis), which results in a significant gain in sensitivity.

Positron scatters in

e + e +

e e – +

e + e +

511 keV Annihilation

**Fig. 20.19** Principle of a PET scanner

**Fig. 20.20** The readout quadrant-sharing scheme for the CTI (now Siemens) and for the General Electrics PET scanners

Until recently, as a result of a compromise between performance and cost, PET scanners were using partially segmented BGO crystals readout by groups of four PMT's (quadrant-sharing scheme), allowing a reconstruction precision of the order of 4–5 mm (Fig. 20.20). Modern machines are going progressively to higher segmentation of the crystals and of the readout to achieve higher spatial resolution. Resolutions of the order of 1 mm have been reached at least for small dedicated machines, such as breast imaging devices or for small animals.

Positron Emission Tomography measures the uptake of the tracer in different organs or tumours and generates an image of cellular biological activities with a much higher sensitivity than any other functional imaging modality. The PET images can be used to quantitatively measure many processes, including sugar metabolism, blood flow and perfusion, oxygen consumption etc. Moreover, specialized PET scanners designed for experimental small animal studies (mouse, rat, rabbit) are powerful tools for fundamental research in disease models, new therapeutic approaches and pharmacological developments. The most commonly used radio-isotopes are 18F with a lifetime of 109.8 min, 11C (20.4 min), 13N (10 min) and 15O (2.1 min), the last three ones being among the basic building blocks of organic systems and therefore being easily introduced chemically in molecules involved in metabolic or pharmaceutical reactions. A typical example is FDG (18F labeled fluorodeoxyglucose), which allows monitoring the energetic consumption of the cells in different parts of the body. FDG is a glucose analog, where a hydroxyl group has been substituted by a 18F atom. Once phosphorylated by the hexokinase enzyme into FDG-6-phosphate, it remains trapped in the cell, where it accumulates. The interest in labeled glucose lies in the fact that tumour cells are characterized by an increase of glycolisis and expression of glucose transporters, such as GLUT-1, as compared to healthy tissues. This increase of FDG metabolism allows detecting tumours and related metastases through their abnormally high glucose concentration and therefore increased γ-ray activity.

PET has a very high sensitivity, at the picomolar level, which makes it one of the essential tools of molecular imaging with applications in many areas such as expression and occupancy of therapeutic molecular targets, pharmacokinetics and pharmacodynamics, mechanisms of therapeutic action and functional response to therapy.

### *20.3.2 Detector Challenges for Modern Nuclear Medicine*

The spectacular development of in-vivo molecular imaging will allow in the near future bridging the gap between post-genomics research and physiology and opening interesting perspectives for new diagnostic and therapeutic strategies for many diseases. Nuclear medicine and particularly PET imaging are already playing and will play an increasing role in molecular imaging [27, 28]. Constant progress in the medical and biological fields implies that imaging performances have to be continuously improved. In order to fulfill the needs of quantitative cell and molecular imaging, of dynamic studies over a certain time and of individualized therapy focusing on the patient's genotype, major technical improvements [29] will be necessary, comparable to those in large particle detectors, in order to deal with:

The challenge for functional isotopic imaging lays in its capacity to identify the specific molecular pathways in action in a metabolic process and to quantitatively measure their relative metabolic activity. To achieve this, it is necessary to improve both the imaging system's spatial resolution, that is, its capacity to discriminate two separate objects, and the measurement's signal to noise ratio, that is, how precisely a metabolic agent's concentration in a body area can be determined. The precision of the concentration measurement depends mainly, but not only, on the imaging system's sensitivity, and therefore its capacity to accumulate the statistics needed to tomographically reconstruct the radiopharmaceutical tracer distribution. Moreover, the location of this metabolic activity must be precisely associated to the organs or parts of the organs under examination. This explains the increasing demand for combining functional and anatomical imaging devices.

The perspectives to develop isotopic imaging with multimodality and multifunctional capability revolve around three goals:

#### **<IP_ADDRESS> Improving Sensitivity and Specificity**

Sensitivity is defined as the ratio of the detected number of radioactive decays and the radioactivity injected into the patient and fixed on the organ under study. It reaches at best 10% in the case of PET scans on small animals, and a few percent only in the case of whole body PET. The main losses arise from poor geometrical acceptance, gaps between crystals, rejection of Compton events due to partial conversion of the γ-ray in the crystal and electronics dead time. Moreover, whole body PET scanners visualize only the patient's thorax in one acquisition run, which is sometimes a limiting factor, for instance in oncological studies of bone metastases in limbs. In the last few years, the use of faster scintillating crystals and electronics and improved geometrical acceptance has allowed to reach the abovementioned sensitivity levels.

However, sensitivity has to be further improved for several reasons. First, examination durations have to be shortened. Today, a whole body scan lasts between 10 and 20 min. It would be desirable to reduce this time to a few minutes to improve the patients' comfort. It would also increase the exploitation of costly equipment and infrastructures with a significant impact on the cost of examinations. Shorter acquisition times would also improve the image quality because the impact of the patient's natural movements—breathing and cardiac activity, digestive bolus, etc. would be reduced. Quicker metabolic processes could be followed, which are crucial for pharmacokinetic studies.

There is a strong interplay between sensitivity and spatial resolution, since the signal-to-noise ratio per voxel is the relevant image quality factor. Doubling the linear spatial resolution (i.e. reducing the volume by a factor 8), requires a 16 times (because it requires two detector pixels to identify one voxel) higher noise equivalent rate if the statistical quality of the image is to be maintained. The acquisition time of an image depends on many factors, which all influence the noise-equivalent measurement of the imaging system and of the radioactivity administered to the patient. Some of the relevant parameters are: the imaging system's geometrical acceptance; the efficiency and energy resolution, improving the energy selection of events and hence discriminating in a coincidence system the diffused events; the time resolution allowing to reduce the width of the coincidence window and rejecting random coincidences more efficiently; dead time of the detectors.

Increasingly, specific molecular signatures for the major diseases are being evaluated to devise individually targeted therapies adapted to the patient's genotype. This requires ever more performing equipment and more specific protocols. Indeed, it is highly desirable to study different molecular pathways simultaneously and to record the intensity, the range, the localization and the temporal development of various biochemical processes in their natural environment in the human body. In this way, the nature of the pathology can be established, at least partially, through molecular imaging, using an array of radiopharmaceuticals giving information on cell proliferation (FLT), on energetic metabolism (FDG) or on aminoacid synthesis (methionine) in the various tissues. For multitracer analysis of various biochemical or pathophysiological processes several radioactive tracers have to be administered.

**Fig. 20.21** Conventional PET scanner (**a**) and Total-Body PET (TB-PET) scanner (**b**). From [30]

In order to keep the doses tolerable for the patient, high-sensitivity PET scanners have to be developed, which would also open new prospects for young or pregnant women and for children.

The obvious approach for increasing the sensitivity is to increase the geometrical acceptance of the scanner. In some cases, developing dedicated equipment might be the right solution to study an organ (brain, breast, prostate) in a more efficient and optimized way. In this case the detectors can be placed closer to the organ under study, increasing therefore the geometrical acceptance of the events.

Until recently the length of the detector cylinder, or length of the system's sensitive volume ("field of view"), has remained essentially at the level of 15–18 cm (Fig. 20.21a), resulting in a very small geometric efficiency ≤0.2. Several static views need therefore to be acquired to perform a "whole body" scan, i.e. from the head to the pelvis. This procedure presents major limitations, as the acquisition time increases in proportion to the number of views. A "standard study" with the injection of 10 mCi of 18F-FDG takes about 3 min per view and, therefore, approximately 20 min per entire study.

A few year ago, the EXPLORER consortium (http://explorer.ucdavis.edu) had launched the concept of a Total-Body PET scanner (TB-PET) to realize the full potential of PET—extending the FOV to cover the entire length of the body (Fig. 20.21b).

In TB-PET, the vast majority of the emitted photons could be captured. This step change in technological evolution would mean simultaneous coverage of all the tissues and organs in the body, with an overall >40-fold gain in effective sensitivity and a >6-fold increase in signal-to-noise ratio compared with whole-body imaging on current PET scanners. The challenge of funding the construction of the first prototype machine, an expensive novel device, was successfully overcome in September 2015 through funding from the NIH Transformative Research Award program, which recognizes high-risk, high-reward, paradigm-shifting innovative research [30].

To further improve sensitivity, we need denser and faster scintillating crystals or direct conversion materials, more compact and adaptable geometries, lower-noise and faster acquisition electronics, more parallelized acquisition architecture with integrated processing power, and at least partial use of the information included in the events diffused in the patient or in the detector. Potential progress in these fields are described in the next paragraphs.

Another promising way to significantly increase the sensitivity is to push the limits of time-of-flight PET scanners, as will be explained in Sect. <IP_ADDRESS>.

#### **<IP_ADDRESS> Improving Spatial Resolution**

Spatial resolution reaches 1.5–2 mm at the centre of the field of view of small animal PETs, but worsens off-axis. Modern technologies have allowed to reach a 1 mm resolution for small animals PETs or for scanners dedicated to specific organs, and a 4–5 mm resolution for whole body scanners.

Good spatial resolution is obviously of value for the study of small animals, but also for humans: increasingly smaller structures which are involved in specific metabolic processes can thus be visualized. Anatomical localization can also be more precise and combining CT or MRI information can be improved. But it is in the field of quantification that the improvement potential is likely to be the most significant. By reducing the blurring caused by insufficient spatial resolution (also called partial volume effect), the dynamic sensitivity of the radiotracer's concentration measurement, also called Standard Uptake Value (SUV), can be significantly improved.

There are four factors, which limit a PET camera's spatial resolution:

(LOR) in opposite directions. In practice the positron is not at rest when it is annihilated, which causes an average non-collinearity of the two gamma photons of about 0.25◦. The error in the reconstruction of the emission point varies like the square of the scanner's radius. This error is reduced in equipment dedicated to the study of specific organs whose detectors can come as close as possible to the areas to be studied.

Another solution is to determine the γ conversion point in the crystal by means of a light sharing scheme with readout at both ends of the crystal. This solution has been chosen for 20 mm long LSO crystals in the ClearPEM®, a dedicated PET scanner for breast imaging [32].

#### **<IP_ADDRESS> Improving Time Resolution**

Time-of-flight reconstruction can significantly reduce the signal to noise ratio in PET scanners, by constraining the annihilation point to a shorter segment on each LOR, with an uncertainty given by:

$$
\Delta x = \frac{c}{2} \Delta t
$$

where *Δx* is the position error, *c* is the speed of light, and *Δt* is the timing error.

**Fig. 20.22** Illustration of the parallax error for off centre events

**Fig. 20.23** Spatial resolution with and without phoswich for the ClearPET® (Courtesy Crystal Clear collaboration)

Until recently, PET scanners did not have any Time-of-Flight (TOF) capability to localize the position of the positron decay along the line of response (LOR) of the two γ-rays. Developments in fast scintillation crystals, photodetectors and electronics have open the way to TOFPET scanners with coincidence time resolution (CTR) improving progressively from 500–600 ps to 249 ps as recently announced by Siemens for their Biograph-Vision scanner. Pushing the limits of TOFPET techniques is motivated by the perspective for a significant improvement in the image signal-to-noise ratio (SNR), resulting in a corresponding clinical sensitivity increase and dose reduction, as given by the following equation:

$$SNR\_{TOF} \left/ \_{SNR\_{NONTOF}} = \sqrt{\frac{2D}{c.CTR}}\right.$$

where

D is the diameter of the Field of View (FOV), c is the speed of light in vacuum CTR is the Coincidence Time Resolution

Breaking significantly the 100 ps barrier, would dramatically improve the SNR (Fig. 20.24) and significantly remove artefacts affecting tomographic reconstruction in the case of partial angular coverage. This will open the field to a larger variety of organ-specific imaging devices as well as to imaging-assisted minimally invasive endoscopy.

Ultimately, a time resolution of 10 ps would lead to an uncertainty of only 1.5 mm for a given positron disintegration along the corresponding line of response (LOR). This is the order of accuracy achieved in today's very best small animal or organ

**Fig. 20.24** Signal to Noise Ratio improvement as compared to non TOFPET as a function of the Coincidence Time Resolution for three different diameters of the Field of View (FOV)

specific PETs. The processing time of tomographic back-projection or iterative reconstruction algorithms would be considerably reduced, as true 3D information would be directly available for each decay event [33]. The possibility to see in real time the accumulation of the events during the acquisition could introduce a paradigm shift in routine clinical protocols, allowing in particular adapting the acquisition time to what is really observed and not to some predetermined evaluation. Moreover, such a timing resolution would allow recording the full sequence of all γ-ray interactions inside the scanner, including Compton interactions, like in a 3D movie, opening the way to the integration of at least a fraction of the Compton events in the image reconstruction, further improving the sensitivity.

To improve time resolution scintillating crystals with short decay time and fast treatment and acquisition electronics are needed. This has a double impact on image quality:

In PET, the random event rate for an individual LOR is given by:

$$\mathcal{R} = 2R\_1R\_2\Delta T$$

where *R* is the random event rate for that chord, *R*1 and *R*2 are the single event rates for two detector elements that form that chord, and *T* is the width of the coincidence gate. The total number of random events in the image is the sum over all the chords, thus is proportional to *T*. The mean contribution to the image from random events can be measured and subtracted, but the noise resulting from the statistical variations in this rate remains. The residual noise from random coincidences is usually estimated using the noise equivalent count rate (NECR) [34], a common figure of merit for comparing tomograph performance. The NECR is given by:

$$NECR = \frac{T^2}{T + S + 2R}$$

where *NECR* is the noise equivalent count rate, *T* is the true coincidence event rate, *S* is the scattered event rate, and *R* is random event rate. The noise equivalent count (NEC) metric is designed to obey counting statistics; that is, the NEC variance is equal to the NEC. Although the magnitude of the NECR is very sensitive to the source and camera geometries, this formalism is useful for predicting how changes in the trues, randoms, and scatters affect the image quality. Figure 20.25 shows such examples of NEC curves measured with a 20 cm long 20 cm diameter phantom

for a commercial PET scanner (ECAT EXAT HR from Siemens). The NEC value first increases linearly with the injected activity. It then progressively saturates and slowly decreases when the electronics dead time becomes significant as compared to the event rate. The importance of reducing the coincidence gate is evident from these plots.

### *20.3.3 Current and Future Technical Approaches*

In the last few years, there have been noticeable improvements in commercial imaging equipment, with increased level of pixellization, better angular coverage, faster crystals, higher degree of integration of electronics with increased built-in functionality, more efficient reconstruction algorithms. Further progress is expected if medical imaging, and particularly nuclear imaging, can take advantage of significant technological advances in other fields like telecommunications or particle detectors.

Developments proceed along the following lines:

#### **<IP_ADDRESS> Conversion Materials and Metamaterials**

The scintillating crystals used in PET scanners have to be dense, with a high atomic number, so as to optimize detection efficiency, and fast, in order to reduce dead time. The previous generation of PET scanners were using BGO crystal arrays, which have the advantage of being very dense (7.1 g/cm3) and of having the highest atomic number known to this day for a scintillator (75), and therefore a high photoelectric conversion efficiency. Their main flaw is a slow decay time (300 ns) of the scintillating light. As a result, these scanners work with a limited sensitivity of about 1000 kcps/mCi/ml with a coincidence window of about 10–12 ns and a proportion of diffused events of more than 30%.

A new generation of scanners is now using LSO (Lutetium oxyorthosilicate) crystals [35], about 10 times faster than BGO and in some cases, the capability of determining the interaction depth in the crystals thanks to phoswich technology or double readout schemes. Combining these developments with progress in readout electronics and data acquisition, a gain in sensitivity by about one order of magnitude and in spatial resolution by a factor 2 or 3 has been achieved.

In the last 10 years, many groups, among them the Crystal Clear collaboration [36], have devoted a large effort on pluridisciplinary work to develop new scintillating materials meeting the demands for increasingly efficient detectors in physics and medical imaging. The most attractive scintillating crystals currently available or being developed for nuclear medicine are presented in Table 20.3. Cadmium Tungstate (CWO) and two ceramics compositions used for CT scanners are also mentioned for comparison. Figure 20.26 shows some pictures of the growth of LuAP ingots and pixel production developed in this context [37] for the preparation of phoswich pixels in combination with LSO for the ClearPET small animal PET scanner.

Other attractive crystals presently being developed are from the Lathanum halide group [38]. LaBr3:Ce for instance has a higher light yield than CsI:Tl with more than 60,000 photons/MeV. The combination of high scintillation efficiency and good low energy linearity gives this crystal an unprecedented energy resolution (about 3% measured with avalanche photodiodes for 511 keV photons) and excellent timing properties.

Contrary to scintillators, semi-conductors convert the energy of the gamma photons to electric charge carriers (electrons and holes), which are directly collected on electrodes. However, most of the semi-conducting materials known today and used industrially, such as silicon, are not dense enough and do not have sufficient stopping power for 511 keV gammas (density 2.33 g/cm3 and atomic number 14, as compared, for instance, to BGO density, 7.13 g/cm3, and average atomic number,

**Table 20.3** Scintillators already used or in development for medical imaging

Particularly attractive parameters are marked in bold

**Fig. 20.26** LuYAP crystals produced in Bogoroditsk, Russia (Courtesy Crystal Clear, CERN)

75). This technique is nevertheless used in single photon X-ray imaging and makes the acquisition of high resolution and high contrast digital images possible [39].

For gamma imaging, multi-layer systems could be considered, but to this day integrating a huge number of channels in these conditions has not been solved, especially in terms of connectivity. Yet interesting solutions to these problems have recently become available through recent developments on pixel detectors for tracking devices. For example, using bump-bonding techniques semiconductors are coupled directly to their readout electronics. It has also become possible to integrate the semiconductor directly with ASIC readout chips and to read a large number of channels on a very small surface quickly and with low noise.

New semiconducting materials, denser than silicon, are also being developed: Gallium Arsenide (GaAs) [40], with a density of 5.32 g/cm3 and an average atomic number of 31, Cadmium Telluride (CdTe), with a density of 5.85 g/cm3 or Cadmium and Zinc Telluride (CdZnTe, or CZT) [41], with a density of 5.78 g/cm3 but whose atomic number is higher, 49 instead of 32. One of these materials is particularly attractive because of its density and high atomic number: Mercuric Iodide (HgI2). With a density of 6.4 g/cm3 and an average atomic number of 62, it nearly equals the stopping power of the best scintillating crystals (BGO, LSO and LuAP). It is unfortunately very difficult to grow in reasonable size and consistent quality.

One remaining problem for these materials is the limited charge collection speed and efficiency, which requires well designed geometries with small drift regions and optimized, cost effective production technologies with a very good control of charge carriers traps.

As shown in [33], the ambitious target of a few tens of picoseconds Time-of-Flight resolution can only be met with scintillators exhibiting a very fast rise time in the scintillation process and the possibility to combine standard scintillation processes with a few hundreds of prompt photons generated by another mechanism. One of the very attractive mechanisms for the production of sub-ns scintillation processes is related to quantum confinement in nanocrystals, as explained in [42, 43].

The challenge is to optimize the design of a metamaterial combining the high density and stopping power (small radiation and interaction lengths, small Moliere radius, high photoelectric fraction) of already well known scintillators (LSO, L(Y,G)SO, PWO, BGO, LuAG, YAG, GGAG, Lu(Y)AP, etc *...*) to the ultrafast (<1 ns) light emission of nanocrystals. Different solutions are presently under study for an optimal combination of these two classes of materials, solving at the same time the problem of light transport by the use of photonic fibers, as proposed in [44].

#### **<IP_ADDRESS> Photodetectors**

In nuclear medicine the basic technique to detect ionizing radiation uses scintillators to convert X- or gamma-rays into light and then into an electric signal by a photodetector. Until recently, the standard commercial imaging cameras were equipped with photomultiplier tubes (PMT) used as light sensors. However, these technologically mature products are approaching their limits in terms of dimension, efficiency and cost. However, their sensitivity to magnetic fields prevents their use in combined PET/MRI devices. The trend toward larger numbers of scintillating pixels of increasingly smaller size will limit their use in the future.

New compact photodetectors have been developed over the last two decades, for instance hybrid photodetectors (HPD), photodiodes and avalanche photodiodes, thanks to which sensitivity, spatial resolution and immunity to magnetic field could be significantly improved. Arrays of avalanche photodiodes have been considered for hybrid PET/MRI scanners and several prototypes dedicated to brain and breast imaging have been built.

Avalanche photodiodes suffer however, a number of drawbacks, such as a limited gain of a few hundred, a large excess noise factor and relatively poor timing characteristics preventing their use in PET Time-of-Flight systems. For these reasons the intense ongoing R&D activity on multipixel Geiger mode avalanche photodiodes (also called Silicon Photomultipliers or SiPM) is followed with particular attention. Their working principle is based on the segmentation of the large coupling area with the scintillating crystal into a large number of small avalanche photodiode cells working in Geiger mode and connected in parallel via individual quenching resistors. The first devices of this type were developed in the late 1990s in Russia and since then several designs have been realized [44, 45].

The cells in a SiPM are all identical with dimensions ranging from 7 × 7 to 70 × 70 μm2. Each cell operates as an independent photon counter in Geiger-mode when the bias voltage is 10–20% higher than the breakdown voltage and behaves as a binary device since the signal from a cell always has the same shape and amplitude.

The gain is similar to the one of a photomultiplier, in the range of 105 to 107. Since each cell acts as a digital single photon counter the excess noise factor is very small. The light yield is directly given by the number of fired cells. This assumption is of course valid only, if crosstalk between individual cells can be eliminated, which has been solved by the use of trenches between the pixels.

Present SiPMs have a dead-time per cell of the order of several μs. For the device to be linear to the light response of fast scintillators having a decay time in the ns range, the number of cells must be larger than the maximum number of photons per event. This requires SiPM to have a cell density above 1000 cells/mm2. SiPMs with 100–10,000 cells/mm2 are currently available.

The overall efficiency of the device depends on the quantum efficiency of each individual cell, which is wavelength dependent but is now reaching 60–65% at the emission wavelength of LSO, and with the geometrical acceptance due to the dead space between the cells, which ranges between 20% and 70% depending on the design.

One of the most promising features of SiPMs for medical imaging applications is related to their excellent timing resolution. The active layer of silicon in a SiPM is very thin (2–4 μm), the avalanche breakdown process is fast and the signal amplitude is large. Impressive timing resolution of about 10 ps for single photons have been reported. For a system of a SiPM and a LYSO crystal with dimensions of 2 × 2 × 3 mm3, 2 × 2 × 10 mm3 and 2 × 2 × 20 mm3, a time resolution of 73 ps, 100 ps and 122 ps FWHM respectively has been measured for 511 keV X-rays [46].

#### **<IP_ADDRESS> Highly Integrated Low Noise Front-End Electronics**

The large number of readout channels requires highly integrated low-noise and highspeed readout electronics, typically using integrated circuits of the VLSI CMOS type [47]. Institutes of particles physics are experienced in designing and integrating large numbers of multichannel and multifunction low noise and fast electronics into complex detector systems.

Medical imaging should also benefit from the progress in large-scale integration of electronic channels with complex functions and highly segmented sensors. The concept of a hybrid detector, in which each pixel is integrated directly to its readout electronics opens totally new perspectives in the conception and architecture of new imaging systems.

### **<IP_ADDRESS> Highly Parallelized and Intelligent Data Acquisition System (DAQ)**

The data acquisition system has a double function: first, it has to discriminate between the interesting events—coming from real X- or γ-ray interactions—and the various types of background, and, secondly, it has to transfer data to the computer(s) where these events will be processed. In medical imaging, most of the "real events" are triggered by the time and amplitude analysis of each sensor. In this acquisition system, data are selected, standardized, organized, corrected, processed with more or less complex algorithms and finally presented as an image file.

In data acquisition system with conventional architecture, data are treated sequentially. A new event is only accepted, once the processing of the previous event is completed; pile-up is thus avoided, but dead time occurs at each treatment stage affecting the data collection efficiency and coming from three main sources: first, the sensor and the electronic pulse generation system, second, the analog-todigital conversion of this signal, and third, the logic treatment (in general, the major one).

Although pipeline architectures could be seen as more complex and more expensive than conventional ones, improvements in electronics (ASIC and FPGA) in terms of integration and cost suggest that in a very close future medical imaging devices entirely based on this concept might be designed. Similarly, progress in data transfer speed between the electronic system and the analysis system is no more a limiting factor for data transfer at the 1 Gbit/s level. Finally, with the parallelization of processors in cheap PC clusters (processor farms), adequate processing power is now available.

In the future, data acquisition system will no longer be a limiting factor in medical imaging.

#### **<IP_ADDRESS> Simulation Software**

Monte Carlo simulation methods are an essential tool for developing new detectors in medical imaging.

Versatile generic simulation tools have been developed for particles physics, for instance Geant4 and FLUKA at CERN and INFN, EGS4 at SLAC or MCNP at Los Alamos National Laboratory. More recently, the development of Geant4 has made it possible to include efficient geometrical modelling and visualisation tools. GATE [48] was developed on this basis to simulate PET and SPECT imaging devices; it is a simulation platform written specifically to model imaging systems, through which time-dependent phenomena—detector motion, decrease in isotope radioactivity, dead time phenomena—can be followed. This new simulation tool, developed, validated and documented by the OpenGATE collaboration regrouping about 20 laboratories of medical and particles physics, is freely available on the Internet and is currently used by a community of more than 200 scientists and industry worldwide.

### *20.3.4 Image Reconstruction Algorithms*

The data provided by transmission and emission tomography make it possible to reconstruct projections of the image, which are then combined to images thanks to tomographic reconstruction methods [49]. There are two possible approaches to deal with tomographic reconstruction problems. The first one is analytical and consists in treating the measured projections as if they were perfect mathematical projections. In this case, it is necessary to make a number of hypotheses on linearity and continuity, but the data, often incomplete and noisy, will not always fulfil these requirements and give rise to artefacts. The second approach is phenomenological. It consists in modelling the measuring process using a probability matrix, which has to be inverted through iterative algebraic techniques. Such algorithms iterate a process aiming at optimising an objective function, for instance the verisimilitude function coming from the Poissonian nature of the data recorded by the tomograph. This is the case for instance of the maximum likelihood expectation maximization (MLEM) algorithm and its variant using ordered subsets expectation maximization (OSEM). These iteration methods are less demanding on the geometry of the detector, and do not require a complete set of projections. On the other hand, they require high calculation power. Fortunately, in the near future the Grid or Cloud will provide considerable and massively distributed computing resources. The quality of the results of an iterative process are more difficult to evaluate than the results of an analytical one. Monte Carlo simulation is often a key element to study and optimise these algorithms.

### **20.4 Multimodality**

### *20.4.1 Need for a Multimodal Approach*

SPECT or PET scanners allow localizing radiotracers uptakes in the human body and are, as such, very powerful tools for basic research in cognitive sciences, for

**Fig. 20.27** Primary lung cancer imaged with a PET/CT scanner. A large lung tumour, which appears on CT as a uniformly attenuating hypo dense mass (left), has a rim of FDG activity and a necrotic centre revealed by PET (middle). The combined image (right) allows a precise localization of the active parts of the tumour (Courtesy Dave Townsend, University of Tennessee)

clinical oncology and cardiology and for kinetic pharmaceutical studies. However, they do not deliver precise anatomical images, like MRI or X-ray CT for instance. Whilst effective software image fusion techniques exist there is a great deal of interest in performing functional and anatomical studies as simultaneously as possible in order to improve registration accuracy and to resolve the logistical problems associated with software registration.

Modern scanners combine the very high sensitivity of PET for metabolic imaging with the high spatial resolution anatomic information delivered by X-ray CT or another anatomical modality. Indeed, the majority of PET and SPECT systems currently being installed now incorporate a CT scanner in the same gantry, so that functional and anatomical images can be performed in rapid succession. Features identified with PET or SPECT can then be accurately localized via the CT scan. The CT data can also be used to determine the photon attenuation correction, an advantage, in particular for overweight patients. These machines provide impressive images giving the very precise localization of the metabolic activity of organs and tumours (Fig. 20.27).

The development of bimodal acquisition systems, for metabolic, functional and anatomical data, like PET/CT combined scanners [27]—several thousand machines exist as of today—, is radically modifying the patients care thanks to increased precision in diagnosis. This approach also decreases significantly the number of imaging scans for a patient.

Combined PET/CT imaging brings additional benefits in the planning of radiotherapy, which is a promising area for research and clinical applications. The principle of radiation therapies is to modulate the intensity according to the spatial distribution of the area to be treated (Intensity-Modulated Radiation Therapy, IMRT). The combination of PET images, which provide information on the metabolic extension and heterogeneity of tumoural tissues, and CT images, which provide precise structural information and location of the tumour, helps defining an irradiation map to focus the therapy on the particularly active areas of the tumour.

Multimodality has become an intensive research area, the challenge being to take the best advantage in the combination of anatomic and functional information by optimizing the choice of the imaging modalities as a function of the application domain. The progress in SiPM technology has opened the way for a vibrant field of development for PET/MRI systems, in particular for brain studies, taking advantage of the high functional sensitivity of the PET and of the very good soft tissue contrast capability of the MRI. Similarly, coupling optical fluorescence methods and PET or SPECT is very attractive for studying biologic processes on small animals. In another domain a Cerimed [50] collaboration has designed a PET/SPECT/Ultrasound dedicated breast imaging camera allowing to simultaneously access a variety of parameters on breast tumours such as energetic metabolism of cells, response to specific hormonal ligands (herceptin, bombesin), echogenecity, elastometry, Doppler, and to correlate them in order to optimize the treatment plan of the patients.

Finally, the combination of PET and SPECT imaging associated to the labeling of various ligands signaling different molecular pathways opens the way to multifunctional imaging. Such an approach could prove useful for identifying the molecular profiling of a tumour in a single exam. It would also allow the simultaneous recording of the expression of several neurotransmitters under specific stimuli, a very powerful approach in cognitive sciences.

### *20.4.2 Outlook: Towards Integrated Morphologic and Functional Imaging*

Biological systems are so complex that there is an important need to develop imaging modalities capable of simultaneously recording different molecular pathways in a quantitative and dynamic manner. Helping to address this issue, multi-parametric molecular imaging involves combining the excellent sensitivity and specificity of molecular imaging (PET or SPECT) with a complementary high-spatial resolution imaging modality (CT, MRI or ultrasound).

The most frequently used equipment combines a PET scanner and an X-ray CT. At present, these combined systems are large, consisting of independent scanners mounted in-line in a common gantry, not generally mounted on the same rotary holder. This results in some imprecision in the image fusion process due to external and internal movements of the patient. CT data provide crucial information for the correction of the unavoidable attenuation factors from the patient's body in PET images and for improving image quality by decreasing the influence of artefacts. Partial volume effects are caused by PET's limited spatial resolution, which dilutes information from small hot spots onto a larger area because of the blurring of the image. CT information, which provides much more precise anatomical information, helps to correct, at least partially, these negative effects. This correction is difficult if both imaging systems acquire data in distinct, poorly correlated spaces. In the case of attenuation and partial volume correction, it is crucial to record both data sets as simultaneously as possible so as to guarantee good image superposition. A major challenge is to further integrate the readout of X-rays and γ-rays. Simultaneous recording of anatomical (CT) and functional (PET and/or SPECT) information by the same reading head is in principle possible thanks to progress in microelectronics. The large functionality of modern ASIC's makes it possible to develop electronic readout channels able to count each individual event, well suited for CT, PET and SPECT signal treatment. This is a particularly interesting perspective, because it would make it possible to correct attenuation and partial volume parameters more precisely.

Another way of obtaining images associating anatomical and functional information is to merge MRI and PET images. Again both data sets have to be acquired as simultaneously as possible, even if a universal acquisition system cannot be considered here because of the fundamental differences between these two modalities. The PET/MRI approach is particularly promising for brain studies. Indeed, MRI gives much better images than CT for the soft brain tissues behind the skull.

Besides, BOLD contrast MRI, which relies on the variation of blood oxygenation level, is promising as a tracer of neuronal activity in functional MRI imaging. Combining this approach with PET functional imaging using various ligands (dopamine, serotonine, acetylcholine, glutamates, opiates, etc.) opens the way to a better understanding of fundamental neurotransmission mechanisms in the brain.

However, a number of significant technological problems arise from recording almost simultaneously MRI and PET images; these problems are mainly caused by the presence of powerful magnetic fields in MRI, with a high homogeneity requirement. To combine the two systems, innovative technologies are needed. The development of SiPM matrices has solved the problem of photodetectors having to be immune to the magnetic field. Moreover, they are extremely compact and require an operating voltage of only a few hundred volts. However, a number of other constraints remain: in a PET/MRI system conducting or ferromagnetic materials must also be carefully avoided because they would alter the homogeneity of the MRI magnetic field. Other technical difficulties, which have to be solved are linked to gradient coils and to MRI's radiofrequency fields, which require effective shielding for PET parts against Eddie currents and electromagnetic noise.

Thanks to multiparametric molecular imaging, a radical shift is currently taking place in the way diseases are managed: from the present onefitsall approach to one that delivers medical care tailored to the needs of individual patients. This includes the detection of disease predisposition, early diagnosis, prognosis assessment, measurement of drug efficacy and disease monitoring. Thus, the introduction of personalized medicine requires an unprecedented effort to develop new technologies in fields of diagnostic and image-guided therapeutic medicine (theranostics) including pathology and imaging. Such imaging tools should characterize diseases and assess treatment efficacy, with the added advantage of non-invasive monitoring at multiple time points. The recent explosion of molecular biology and imaging technologies is now allowing simultaneous quantitative and dynamic characterization of several biological processes inside the body at the molecular and genetic level. This exciting new field will transform the future of medicine on a massive scale and will have an enormous impact on the advancement of targeted therapies for personalized medicine.

### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Chapter 21 Solid State Detectors for High Radiation Environments**

**Gregor Kramberger**

### **21.1 Introduction**

The solid state particle detectors emerged in 1950 [1]. Initially Si and Ge detectors operated as junction diodes were used for charged particle detection and *γ* spectroscopy measurements (Chap. 5). Although these detectors are superior to gaseous detectors in many respects, being a crystalline medium meant that they are susceptible to radiation damage. Unlike in gaseous detectors where the detection media can be exchanged the semiconductor crystals have to retain their detection properties over the entire envisaged period of operation. The particle detection capabilities and the energy resolution degrade gradually with irradiation, which limits their lifetime.

A large majority of present high energy experiments uses position sensitive silicon detectors which became widely available after the introduction of planar process in 1980 [2]. Their goal is achieving desired position resolution with as few read out channels as possible, while keeping detection efficiency close to 100%. At the present and particularly future experiments high particle rates close to the interaction point require very fine segmentation and high position resolution of detectors in order to be able to associate hits with tracks.

In the future a precise timing information associated with a track and even with each sensor hit may be required to cope with large multiplicity of tracks. The sensor hits and associated tracks will be therefore separated not only spatially, but also in time allowing easier assignation of tracks to different collisions occurring within each colliding particles bunch crossing.

G. Kramberger (-)

Experimental Particle Physics, Jožef Stefan Institute, Ljubljana, Slovenia e-mail<EMAIL_ADDRESS>
High particle rates cause radiation effects. The most important is the damage of the crystal lattice which leads to the degradation of the measured charge after passage of ionizing radiation. At the same time the noise may increase for various reasons thus significantly reducing the signal-to-noise ratio. Consequently the detection efficiency, energy, and position resolution may degrade to the level where the detectors become unusable. Extensive research was made in the last decades to understand the damage in silicon detectors and to manipulate the properties of silicon aiming at radiation-harder detectors. The research was not only limited to silicon but alternative semiconductor materials were considered.

It is not only the bulk crystal that is affected by irradiation, but also the surface. The radiation effects at the silicon—silicon oxide interface not only change the performance of silicon detectors, but are the main reason for radiation damage of electronics. The latter was often considered a bigger problem than the radiation damage of detectors, particularly in environments where the ionization dose was large (e.g. synchrotron radiation). With the advent of deep sub-micron CMOS processes, electronics was thought to became intrinsically radiation hard and no special radiation hardening processes would be required. An important contribution to the radiation hard electronics was also introduction of radiation-tolerate design rules. However, for very small feature sizes, e.g. very deep sub-micron processes, such as 0.130, 0.065μm, radiation hardness of electronics, rather than sensors, could become a limiting factor at harshest radiation environments.

On the other hand the effects of radiation damage were exploited for dose measurements. Active dosimeters appeared for both measurements of ionizing and non-ionizing energy losses in silicon crystal such as *p*−*i*−*n* diodes [3] and radiation sensitive field effect transistors [4].

### **21.2 High Radiation Environments**

The radiation environments differ in composition and energies of the particles producing the radiation damage. Although the particles that are to be detected contribute largely to the damage it is often the background particles that dominate. As will be described later the damage depends on the type of the particle. While X-rays alter the properties of the detector surface they can not displace the semiconductor atoms from the lattice. On the other hand neutron irradiation affects only the lattice and energetic charged hadrons and leptons damage both the lattice and the surface. The difference in damage creation and its effects to detector operation will be discussed later. First we review the radiation environments where particle detectors are employed.

**Collider Experiments** In general there are three major types of accelerators with respect to collision particles: hadron (*p* − *p*, *p*¯ − *p*, heavy ions), lepton (*e*+ − *e*−, eventually μ+ − μ−) and lepton-hadron (*e*+*,*− − *p*). The flux of particles traversing the detectors is given by the particles originating from the collisions (*φcoll*) and secondary radiation that originates from the spectrometer or the accelerator (*φsec*)

$$
\phi = \phi\_{coll} + \phi\_{sec},
\tag{21.1}
$$

The flux of particles crossing the detectors is much larger at hadron colliders than at lepton colliders, owing to a difference in total cross-section *σtot* of colliding particles. The radiation environment at lepton colliders is dominated by e± from Bhaba scattering. Consequently the radiation damage of detectors at hadron colliders is much more severe than at lepton colliders.

A significant secondary irradiation, particularly at high luminosity colliders, can arise from back-scattered neutrons originating in breakup of nuclei in calorimeters and other parts of spectrometers after interaction with highly energetic hadrons. The secondary radiation originating from the accelerator such as synchrotron radiation, beam-gas interactions or halo particles scraping the collimators should be small but can represent in case of an accident a significant contribution to the total fluence (integral of flux = 0 *φ dt*) of particles traversing the detectors.

The required radiation tolerance/hardness of vertex detectors at different colliders is given in the Table 21.1. Placing of the detectors in the spectrometer determines their exposure. The *φcoll* decreases quadratically with the distance from the interaction point. The large cross-section for soft collisions result in larger *φcoll* at small angles with respect to beam. Large *φcoll* at small angles is also characteristic for asymmetrical beams (energy, particle) or fixed target experiments. A particle fluence profile for ATLAS experiment [5] at the Large Hadron Collider (LHC) is shown in Fig. 21.1. The dominating particles are at small radii mainly pions and protons originating from collisions and "albedo" neutrons from the calorimeters for *R >* 20 cm.

**Table 21.1** The review of basic parameters of some accelerators and required radiation hardness of the most exposed detectors for the entire operation period

The total cross-section without Bhaba scattering is given for *e*+ − *e*− accelerators

**Fig. 21.1** Yearly fluence profile in ATLAS experiment at LHC design luminosity. The radiation damage caused by different particles was used to normalize the fluences (see next section for *eq* ). The arrows denote the location of the pixel and strip detectors (SCT)

The choice of detector technology at a given radius depends on the ability to retain the detection efficiency and position resolution at required levels. At the same time the material budget should be kept low in order not to spoil the tracking performance. At many experiments the most exposed detectors are beam position/condition and radiation monitors (Chap. 18).

#### **Space Applications**

Particle detectors are an important constituent of many space missions. They are mainly used as spectrometers, visible light detectors and charged particle trackers. The radiation fields are far less severe than that at accelerators experiments, but the detectors and the information that they provide can be far more susceptible to the radiation effects (e.g. CCD, DEPFet, Si-drift detectors). The origin of radiation in space comes from three sources:

**Fig. 21.2** (**a**) Galactic cosmic ray particle spectra and their modification by solar activity [6]. (**b**) Equatorial electron and proton flux vs. the distance from the Earth's center. Each curve gives the total flux above the specified threshold [7]

subsequent coronal mass ejections. These solar particles comprise both protons and heavier ions with variable composition from event to event. Energies typically range up to several hundred MeV and occasional events produce particles of several GeV. Although such events are rare, typically one per month and lasting several hours to days, the flux integrals as large as 1010 cm−2 for protons with energy *>*1 MeV were measured.

• **Radiation belts;** The charged particles trapped in the Earth's magnetic field form so called Van Allen's belts. The inner belt extends to 2.5 Earth radii and comprises protons up to 600 MeV and electrons up to several MeV. The outer belt extends to 10 Earth radii where there are mainly electrons and soft protons (0.1–100 MeV). The fluxes of electrons and protons trapped in the radiation belts are shown in Fig. 21.2b. The sharp fall of flux at high energies makes shielding very effective.

#### **Environmental Applications**

### **21.3 Damage Mechanism in Solid State Detectors and Electronics**

As radiation (photons, leptons, hadrons) passes through material, it loses energy by interaction with the electrons and nuclei of the material atoms. The effects produced in the material are dependent on the energy-loss processes and the details of the material structure. The damage in semiconductor detectors can be divided into bulk and surface damage.

### *21.3.1 Bulk Damage*

The interaction with electrons results in creation of electron-hole pairs (ionizing energy loss, ionizing dose) that does not affect the lattice and causes no bulk damage. The bulk damage in crystalline and poly-crystalline material is a consequence of displacement of lattice atoms by impinging particles, due to elastic scattering on a nuclei and nuclear reactions. In order to produce Primary Knocked off Atom (PKA) the transfer of kinetic energy should be sufficient. Approximately 25 eV of recoil energy is required for example in silicon. The displaced atom may come to rest in a interstitial position (I), leaving a vacancy (V) at its original location. If the kinetic energy of the recoiling atom is sufficient (∼5 keV in Si [8]) it can displace further atoms, creating a dense agglomeration of defects at the end of the primary PKA track. Such disordered regions are referred to as defect clusters.

Most of the resulting vacancies and interstitials recombine while others diffuse away and eventually create stable defects with impurity atoms and other vacancies or interstitials. Those defects disturb the lattice periodicity and give rise to energy levels in the band-gap, which alter the properties of the semiconductor. In most semiconductor materials the cross-section for nuclear reaction is much smaller than

**Table 21.2** Material properties of some semiconductors used as ionizing particle detectors

for elastic scattering, hence the creation rate of defects, resulting from nuclear reactions, is usually more than two orders of magnitude lower when compared to creation rates of defects originating from displaced silicon atoms.

The energy *Ep* required for an incoming particle of mass *mp* to produce PKAs and clusters with a creation threshold *Eth* can be calculated from non-relativistic collision kinematics as

$$E\_p = E\_{lh} \frac{(m\_p + m\_l)^2}{4 \, m\_p \, m\_l},\tag{21.2}$$

where the lattice atom has a mass *ml*. In silicon a neutron needs at least 175 eV to produce a PKA and 35 keV to form a cluster. For an electron a relativistic kinematics should be used giving 260 keV and 8 MeV. It should be noted that the radiation damage caused by *γ* -rays from radioactive decays is primarily due to the interaction of Compton electrons with a maximum energy well below the one required for cluster production. The bulk damage is therefore exclusively due to point defects. As the thresholds are of the same order also in other semiconductor materials (see Table 21.2 ) similar conclusions are valid.

A part of vacancies and interstitials formed immediately after irradiation can recombine, while others diffuse away and eventually recombine or react with other defects or impurities. The defects can evolve in time. They can either dissociate or react with each other and form new defects. The evolution of defects is described by first order dynamics in case of dissociation (Eq. (21.3)) or second order dynamics for reactions of two defects (Eq. (21.4)):

$$X \to Y \quad , \quad \frac{dN\_Y}{dt} = -\frac{dN\_X}{dt} = k\_1^Y N\_Y \tag{21.3}$$

972 G. Kramberger

$$dX\_A + X\_B \to Y \quad , \quad \frac{dN\_Y}{dt} = -\frac{dN\_{X\_A}}{dt} = -\frac{dN\_{X\_B}}{dt} = k\_2^Y N\_{X\_A} N\_{X\_B} \tag{21.4}$$

where *kY* 1*,*2 denotes the reaction constants. The Eq. (21.4) turns into a first order process in cases when one type of the reacting defects is present in much larger quantities than the other. The solution of Eq. (21.3) is exponential with

$$N\_Y = N\_X^0 \left( 1 - \exp\left(-\frac{t}{\tau\_1^Y}\right) \right) \quad , \quad N\_X = N\_X^0 \exp\left(-\frac{t}{\tau\_1^Y}\right), \quad \tau\_1^Y = \frac{1}{k\_1^Y} \tag{21.5}$$

with *N*0 *X* denoting the initial concentration of defects *X* proportional to the fluence. The solution of the Eq. (21.4) for (*N*0 *XA > N*0 *XB* ) is given by

$$N\_{Y}(t) = N\_{X\_{B}}^{0} \frac{1 - e^{-k\_{2}^{Y}I(N\_{X\_{A}}^{0} - N\_{X\_{B}}^{0})}}{1 - (N\_{X\_{B}}^{0}/N\_{X\_{A}}^{0})e^{-k\_{2}^{Y}I(N\_{X\_{A}}^{0} - N\_{X\_{B}}^{0})}} \ . \tag{21.6}$$

In the case of two defects with similar initial concentrations *N*0 *XA* = *N*0 *XB* = *N*0 *X* or a reaction between defects of the same type one obtains

$$N\_X(t) = \frac{N\_X^0}{1 + N\_X^0 k\_2^Y t} = \frac{N\_X^0}{1 + t/\tau\_2^Y} \quad , \tau\_2^Y = \frac{1}{k\_2^Y N\_X^0} \tag{21.7}$$

$$N\_Y(t) = N\_X^0 - N\_X(t) = N\_X^0(1 - \frac{1}{1 + t/\tau\_2^Y}).\tag{21.8}$$

From Eqs. (21.3) and (21.4) it can be seen that for first order reactions, the rate depends linearly on defect concentration while for second order reactions the dependence is quadratic.

Since the energy needed for breaking up the defect (dissociation) or forming a new defect is supplied by the lattice vibrations, the reaction constant is strongly temperature dependent. The lattice atom vibration energy is governed by the Maxwell-Boltzmann distribution. The probability of sufficient energy transfer from lattice vibration to the defect is therefore exponential with temperature (*T* ). If the reaction rate given by the Arrhenius relation is known at *T*0 then the rate at *T*1 is calculated as:

$$k\_{1,2}^Y \propto \exp\left(-\frac{E\_a}{k\_B T}\right) \quad \implies \quad \frac{\mathbf{r}\_{1,2}^Y(T\_0)}{\mathbf{r}\_{1,2}^Y(T\_1)} = \frac{k\_{1,2}^Y(T\_1)}{k\_{1,2}^Y(T\_0)} = \exp[\frac{E\_a}{k\_B}\left(\frac{1}{T\_0} - \frac{1}{T\_1}\right)],\tag{21.9}$$

where *Ea* is the energy required for defect dissociation or formation.

#### **<IP_ADDRESS> Non-Ionizing-Energy-Loss Hypothesis of Damage Effects**

The energy loss of impinging particles suffered in a process of displacing lattice atoms is called non-ionizing energy loss—NIEL. First experimental findings have led to the assumption that damage effects produced in the semiconductor bulk by energetic particles may be described as being proportional to non-ionizing energy loss, which is referred to as the NIEL-scaling hypothesis. According to it any displacement damage induced change in the material properties scales with the amount of energy imparted in displacing collisions, irrespective of the spatial distribution of the defects in a PKA cascade and irrespective of the various annealing sequences taking place after the initial damage [10].

The non-ionizing energy deposit in a unit cell of the target nuclei (*ρdis*) exposed to the fluence of particles with energy *E* can be calculated as

$$
\rho\_{dis} = D(E) \cdot \Phi,\tag{21.10}
$$

where *D(E)* [9] is so-called displacement damage function, sometimes also referred to as damage cross-section. For a spectrum of particles the contributions to the *ρdis* for each energy should be summed:

$$
\rho\_{dis} = \int\_0^\infty \frac{d\Phi(E)}{dE} D(E) dE. \tag{21.11}
$$

According to NIEL hypothesis *ρdis* determines the damage effects. The damage efficiency of any particle spectrum *d/dE* can therefore be expressed as that of an equivalent 1 MeV neutron fluence. The equivalent fluence of 1 MeV neutrons *eq* is calculated as

$$\Phi\_{eq} = \kappa \text{ } \Phi = \frac{\rho\_{dis}}{D\_n(\text{l } \text{MeV})} \tag{21.12}$$

*κ* = 1 *Dn(*1 MeV*)* · 0 ∞ 0 *D(E) d dE (E) dE* 0 ∞ 0 *d dE (E) dE ,* (21.13)

where *κ* is so called hardness factor for that particle spectrum and *Dn(*1 MeV*)* the *D* for 1 MeV neutrons, 95 MeV mb for Si and 10 MeV mb for diamond [12]. The displacement damage cross-section for pions, protons, electrons and neutrons in silicon is shown in Fig. 21.3. The hardness factors for most commonly used irradiation facilities are given in the Table 21.3.

The NIEL hypothesis is violated in silicon for highly energetic charged hadrons. In addition to the hard core nuclear interactions, being dominant for neutrons, charged hadron reactions are also subjected to Coulomb interactions leading to low energy recoils below the threshold for cluster creation. In this case the damage is a mixture of homogeneously distributed point defects and clusters. This distinct

**Fig. 21.3** Non Ionizing Energy Loss NIEL for different particles in silicon [11]. The insert shows magnified *D(E)* for most damaging particles at LHC

**Table 21.3** Measured hardness factors of commonly used irradiation particles

a KIT, Germany and University of Birmingham, UK

b CYRIC, Japan

c LANL, USA

d CERN, Switzerland

e PSI, Switzerland

f JSI, Slovenia

difference between neutron and proton induced damage is depicted in Fig. 21.4. Different impurities (e.g. O,C) are homogeneously distributed over the volume and the probability for such an impurity to form a defect complex with vacancy or interstitial is much larger if the latter are also homogeneously distributed. Hence, the defects formed after irradiation and consequently the lattice properties can be different for various irradiation particles at equal NIEL. It should be emphasized again that the NIEL scaling can only be regarded as a rough approximation as it disregards the specific effects resulting from the energy distribution of the respective recoils.

#### **<IP_ADDRESS> Impact on Bulk Damage on Detector Performance**

As already mentioned the defects in the semiconductor lattice give rise to energy levels (states) in the band gap affecting the operation of semiconductor detector mainly in three ways as shown in Fig. 21.5.

**Fig. 21.4** Initial distribution of vacancies produced by 10 MeV protons (left), 23 GeV protons (middle) and 1 MeV neutrons (right). The plots are projections over 1 μm of depth (z) and correspond to a fluence of 1014 cm−2 [10]

**Fig. 21.5** Consequences of deep energy levels to operation of semiconductor detectors: (**a**) charged defects alter the space charge and therefore the electric field, (**b**) defects can trap and detrap free carriers and (**c**) defects act as generation-recombination centers. Electrons and holes are denoted by e and h

• Some of the defects can be charged which leads to (Chap. 5) (Fig. 21.5a) changes in the electric field. For semiconductor detectors this may result in loss of the depleted (active) region requiring an increase of the applied bias. The bias voltage is however limited by the device break down. The space charge is calculated as a difference in concentration of charged donors and charged acceptors,

$$N\_{eff} = \sum\_{donors} N\_l \left(1 - P\_l\right) - \sum\_{acepeters} N\_l \left| P\_l \right. \tag{21.14}$$

where *Nt* denotes the concentration of deep traps and *Pt* the probability of a trap being occupied by an electron. The traps continuously emit and capture carriers. The difference in emission and capture rate is called the excess rate. In a stationary state the occupation probability is constant, therefore excess rates of holes and electrons for a given trap have to be equal. The derivation of occupation probability from this condition can be found in any solid state physics text book. As the *Pt* is needed for calculation of detector properties we will just state the result:

$$P\_I = \left[\frac{c\_p \ p + \epsilon\_n}{c\_n n + \epsilon\_p} + 1\right]^{-1},\tag{21.15}$$

$$c\_{n,p} = \upsilon\_{lh\_{\varepsilon,h}} \sigma\_{l\_{\varepsilon,h}}, \epsilon\_{n,p} = n\_l \ c\_{n,p} \ \exp\left(\pm \frac{E\_l - E\_l}{k\_B \ T}\right). \tag{21.16}$$

where *cn,p* is the capture coefficient and *n,p* emission rate of electrons and holes, respectively. The concentration of free electrons and holes is denoted by *n* and *p* and their thermal velocity by *vthe,h* . The capture coefficients and emission rates depend on trap and semiconductor properties. The carrier capture cross-section is given by *σte,h* and the level in the band gap by *Et* . The Fermi level and free carrier concentration in intrinsic semiconductor are denoted by *Ei* and *ni*. They occupation probability depends on temperature only for levels close to middle of the band-gap. The exponential term in Eq. (21.15) prevails once *Et* is few *kB T* away from the *Ei*. If follows from here that only donors in the upper part of the band gap and acceptors in lower part of the band gap contribute to the space charge.

• The states can act as trapping centers for the drifting charge generated by the particles we want to detect (Fig. 21.5b). If trapped charges remain trapped and do not complete the drift within the integration time of the read-out electronics they are lost for the measurement, which leads to smaller signal.

The probability for electrons and holes to be trapped at the trap *t* can be calculated as

$$\frac{1}{\tau\_{tr\_\ell}^I} = c\_n \left(1 - P\_l\right) N\_l, \quad \frac{1}{\tau\_{tr\_h}^I} = c\_p \ P\_l N\_l. \tag{21.17}$$

The trapping time *τ t t re,h* represents the mean time that a free carrier spends in the part of the detector before being trapped by *t*. According to Eq. (21.17) electron traps have energy levels in the upper part of the band gap (*Pt* ≈ 0), while hole traps have energy levels in the lower part of the band gap (*Pt* ≈ 1).

To get the effective trapping probability 1*/τeff e,h* for electrons and holes one has to sum over the trapping probabilities of all traps with emission times (1*/n,p*) longer than integration time of the electronics:

$$\frac{1}{\pi\_{eff\_\epsilon}} = \sum\_{l}^{defects} c\_{l\iota} \left(1 - P\_l\right) N\_l,\tag{21.18}$$

#### 21 Solid State Detectors for High Radiation Environments 977

$$\frac{1}{\pi\_{eff\_h}} = \sum\_{t}^{defects} c\_p \, P\_t \, N\_t. \tag{21.19}$$

The emission times decrease with distance from the mid-gap and become at certain energy level short enough not to be included in the Eq. (21.19). The traps close to the mid-gap have therefore a dominant contribution to the effective trapping times.

• States close to the mid-gap region also act as generation-recombination centers (Fig. 21.5c). The thermally generated electron hole pairs are separated in the electric field before they can recombine, which gives rise to the bulk generation current. The increase of current leads to the increase of noise and power dissipation.

The generation current can be calculated with the assumption of equal generation rates *Gt* = *Gn* = *Gp* of electrons and holes in thermal equilibrium:

$$G\_{l} = N\_{l}P\_{l} \epsilon\_{n} = N\_{l} \frac{\epsilon\_{n} \left(\epsilon\_{p} + c\_{n}n\right)}{\epsilon\_{n} + \epsilon\_{p} + c\_{p} \left|p + c\_{n}n\right|}\tag{21.20}$$

$$G\_l = N\_l \frac{1}{1/\epsilon\_n + 1/\epsilon\_p} \quad \text{for} \quad n, p \approx 0. \tag{21.21}$$

Both carrier types generated in the active volume drift to the opposite electrodes. The current density, albeit different for holes and electrons, is constant everywhere in the detector. The measured current is therefore calculated as

$$I = \,e\_0 \, w \, S \sum\_{l}^{defects} \, G\_l \tag{21.22}$$

where *w* denotes the active thickness and S the active surface of the detector. It follows from Eq. (21.21) that only the levels close to mid-gap *Ei* ∼ *Et* contribute significantly to the current. If traps are far from the mid-gap, emission times are either very long or very short.

Apart from the changes in the depletion region, the properties of the non-depleted silicon bulk are also affected by irradiation. The resistivity of the bulk increases. The increase depends on both initial dopant concentration as well as on irradiation fluence. The minority carrier lifetime also decreases as 1*/τr* ∝ and reaches values of few tens ns at = 1014 cm−2 and below ns at  *>* 1016 cm−2 [13].

Recent measurements [14] also show that mobility of free carriers is affected by radiation. The concentration of defects, not only electrically active, is high enough to affect the low field mobility. A significant decrease of low field mobility was observed at fluences of *eq >* 5 · 1015 cm−2.

Although silicon detectors are by far the most widely used there are other semiconductor detectors which can be used in high radiation fields and have a higher PKA displacement energy. The material properties of different semiconductors used as particle detectors are summarized in Table 21.2.

Effects of irradiation on detector performance strongly depend on the choice of material. In wide band gap semiconductors for example the rate of thermally generated carriers will be small even if states close to mid-gap are present in abundant concentrations due to small intrinsic carrier concentration. Thus the leakage current increase is negligible. If the drift velocity is large and charge collection time is short then the increase of trapping probability will be less important. The small dielectric constant reduces the capacitance of a detector leading to lower noise, which can partially compensate for larger e-h pair creation energy. The choice of the semiconductor detector for a specific application is often governed by a compromise in semiconductor properties. Also availability, reliability and experience play an important role. In this respect diamond is the choice of detector material next to silicon.

#### **<IP_ADDRESS> Most Important Defects in Silicon**

A lot of effort was invested over the R&D phases of LHC/HL-LHC in identifying the defects responsible for changes in performance of silicon detectors. A comprehensive list of defects identified by so called "microscopic" techniques such as Deep Level Transient Spectroscopy (DLTS) or Thermally Stimulated Current (TSC) can be found in [15]. The summary plot with the most important defects is shown in Fig. 21.6. The effects for which they are mainly responsible will be addressed in

**Fig. 21.6** A schematic view of known defects and their main effects on the detector performance. The defect charge state is given in brackets. For the defects with unknown chemical composition the temperature at which electron -E or hole-H traps were identified with DLTS/TSC techniques is used. The near mid-gap H levels are likely multivacancy complexes

the following sections. Note, that for only few identified energy levels the chemical composition of the corresponding defects is known.

### *21.3.2 Surface Damage*

The semiconductor detector bulk needs to form a contact with readout electronics. The contacts used, either Ohmic or Schottky, as well as the rest of the surface are prone to changes due to irradiation. The description of surface radiation damage given here will be focused on the border of silicon bulk and oxide (Chap. 5). The surface damage affects the electrical properties of the detectors such as interelectrode resistance, inter-electrode capacitance and dark current. It is particularly important for sensors where charge flow is close to the surface, such as 3D-Si detectors, CCDs, Active CMOS Pixel Detectors and MOS-FET transistors.

The surface of particle detectors is usually passivated by thermal oxidation [16]. The oxide isolates and stabilizes the crystal surface with respect to chemical and electrical reactivity. The cross-section of the device surface is generally divided into silicon/oxide interface and oxide bulk depicted in Fig. 21.7. The border region between oxide and silicon crystal is characterized by a large defect density due to bond stress. In general surface defects can be caused by growth and irradiation. According to their position in the oxide the traps are divided in the oxide bulk traps (OT), border traps (BT) and interface traps (IT). The latter two are located close to the interface and can exchange charges with underlying silicon (switching traps). The oxide traps are mostly donors, which is the reason that net oxide charge

**Fig. 21.7** Schematic view of the surface of a silicon detector according to [17]; (**a**) surface regions (**b**) trap locations (**c**) states (**d**) oxide charges

density is always positive. The most important oxide defects are trivalent Si (≡ Si·, donor), interstitial oxygen (OI, donor) and non-bridging oxygen (≡ Si–O·, acceptor). Other important defects include hydrogen related defects (all donors) [18]. Hydrogen is particularly important since it passivates the dangling bonds by attaching to them. The build-up of interface traps is not fully understand yet and there are different models explaining it [18, 19]. The bulk and interface traps formed during processing of the oxide can be passivated by annealing (350–500 ◦C) in hydrogen rich environment.

If the creation of e–h pair in the silicon bulk is completely reversible process, it is not in SiO2 and at the interface. Ionizing radiation has a significant impact on the defect generation and activation. The damage mainly manifests itself as a regeneration process of already present but deactivated defects. Hence the processing of the oxide, preparation and temperature treatments (annealing) impacts the performance after irradiation.

Although the underlying physics of formation is not yet fully understood, it is assumed that radiation ionizes oxide bulk defects that remain charged

$$\text{Si} \cdot + \text{radiation} \rightarrow \text{Si}^+ + \text{e}^- \tag{21.23}$$

or free holes are trapped by passivated defects

$$\text{Ol} + \text{h} \rightarrow \text{Ol}^+.\tag{21.24}$$

Similarly to oxide bulk damage the interface state density also increases with irradiation. After [20] the interface states are generated by breaking up the bonds between surface silicon atoms (Si*s*) and hydrogen, due to hole trapping at the interface (Si*s*-H+h→Si*s*·+H+; Si*s*-H+h→Si+ *s* +H· followed by Si+ *s* +e− →Si*s*· ). The dangling bonds enable surface silicon atoms to react with the underlying silicon and induce different states in the silicon band-gap. The state build-up can continue over a long period of time after exposure to radiation.

The electrons are much more mobile in the oxide (*μe(*20 ◦C*)* ∼ 20 cm2/Vs) and are in the presence of electric field promptly swept away, while holes (μ*h(*20 ◦C*)* = 10−4−10−11 cm2/Vs ) slowly drift to the interface. The absence of electric field in the oxide is therefore beneficial as the recombination can take place in the oxide bulk as well as at the interface.

#### **<IP_ADDRESS> Impact of Surface Damage on Device Properties**

Positive Oxide Charge

As shown by many experiments the exposure to ionizing radiation causes an increase of positive space charge. The different contributions to the oxide charge are shown in Fig. 21.7. Apart from the oxide traps and mobile ion impurities also trapped holes at interface states contribute to the positive oxide charge. An

**Fig. 21.8** (**a**) Oxide charge measured from a change in flat band voltage for silicon gated diodes [21] after irradiation with 20 keV electron and *γ* -rays from 60Co. (**b**) Dependence of flat band voltage on oxide thickness [22]. (**c**) Recent measurements to very large doses for samples with different producer/orientation/oxide thickness [23].

effective net sheet charge (surface density) in the oxide *Nox* is calculated as the sum of all contributions. It has been shown that under bias the oxide charge density increases with irradiation up to few kGy where it starts to exhibit saturation. In an unbiased devices saturation occurs at significantly larger doses up to few 10 kGy (see Fig. 21.8) [21]. The saturation sheet charge depends on thickness of the oxide and is of order *Nox* = 1012 cm−2. Latest measurements show an increase of oxide charge, although at a much slower rate, up to the doses of 1 GGy (see Fig. 21.8c).

The positive oxide charge attracts electrons which can form a conductive layer underneath the surface. The resistivity between the nearby *n*+ contacts can therefore decrease producing a short circuit. A *p*+ implant is therefore commonly used to cut these conductive paths. A more novel approach is to use a moderate *p* implant over the whole surface (*p*-spray [24]). The p-spray dose must be sufficiently high (≈1011−1013 ions/cm2; the same order as *Nox*) to prevent decrease of inter-strip resistivity and not too high to cause early breakdowns. Very often both methods are used together.

In very thin oxides the tunneling of electrons from nearby electrodes occurs. The oxide traps get passivated, by reversing the reactions described by Eqs. (21.23), (21.24). Thinning down the oxide therefore reduces the *Nox* (see Fig. 21.8b)[22], which makes the device more radiation hard. The flat band voltage which should follow the *VFB* ∝ *d*2, if the oxide charge is uniform, shows a steep decrease in thin oxide films *<*20 nm. The importance of this effect will be discussed in section on radiation hard electronics.

#### Surface Generation Current

Interface states act as charge carrier generation centers. As soon as the silicon surface is depleted, the thermally generated carries are separated in electric field and contribute to the dark current of a nearby *p* − *n* junction or a MOS transistor. This current is called interface generation current and is calculated as

$$I\_{o\chi} = e\_0 n\_i \ S\_s \ v\_{surf} \tag{21.25}$$

where *vsurf* is the surface recombination velocity and *Ss* the depleted silicon surface area. The surface recombination velocity is directly proportional to the density of interface states. The density of states rather than discrete states is used as experimentally it is impossible to distinguish between different trap levels [25]. The increase of surface current and surface recombination velocity with irradiation is shown in Fig. 21.9.

#### Trapping

The interface states act as trapping centers for the charge drifting close to silicon surface in analogous way to trapping of drifting carries in the bulk. Equation 21.17 is multiplied with an exponential term exp*e*0 *<ψ> kB T* to take into account the average band bending *<ψ>* close to the surface.

### **21.4 Detector Technologies**

### *21.4.1 Design Considerations*

The design of the detector should minimize the radiation effects most crucial for the successful operation of the detector while retaining the required functionality. The material and operational conditions determine to a large extent the radiation hardness of a detector. However, some of the radiation effects can be reduced by

**Fig. 21.9** (**a**) The increase of surface current density (surface recombination velocity) after 20 keV electron and 60Co irradiations for biased and unbiased gate. (**b**) Surface current density after 12 keV X-rays irradiations of different samples to very high doses [23]

a choice of the read-out electrodes and detector geometry. At the new accelerator experiments the largest obstacle is the radiation-provoked decrease of measured charge and increase of noise. The consequent degradation of signal-to-noise ratio can lead to the loss of detection efficiency up to the level where successful operation of the detectors is no longer possible.

In terms of charge collection the radiation hard detector design follows directly from the calculation of the induced charge *Q*. The current induced (*I* ) by a motion of charge *q* in the detector is given by Shockley-Ramo's theorem [26] and is discussed in the section on signal processing. The charge induced in the electrodes is given by the difference in the weighting potential (*Uw*) traversed by the drifting charge (Chap. 10, Eq. 10.2):

$$\mathcal{Q}(t) = q[U\_w(\tilde{r}(t)) - U\_w(\tilde{r}\_0)],\tag{21.26}$$

where *r* 0 and *r* denote position at the both ends of the traversed path. The distinct difference in weighting potential for a pixel detector and simple pad detector is shown in Fig. 21.10 and discussed in section 6.2.2.

For an electron hole pair the induced charge is a sum of both contributions *Qe*−*h* = *Qe* + *Qh*. A track of an ionizing particle therefore induces the charge *Qt*

$$\mathcal{Q}^{t} = \sum\_{\text{all pairs}} \mathcal{Q}\_{\varepsilon} + \mathcal{Q}\_{h} = \mathcal{Q}\_{\varepsilon}^{t} + \mathcal{Q}\_{h}^{t},\tag{21.27}$$

$$\mathcal{Q}\_{e,h}^{l} = \mp e\_0 \sum\_{l}^{e,h} U\_w(\vec{r\_l}) - U\_w(\vec{r\_{l,0}}).\tag{21.28}$$

If all carries complete the drift on the sensing electrode *Uw(r i)* = 1 if on nonsensing *Uw(r i)* = 0. In the absence of trapping and homogeneous ionization the sum in Eq. (21.28) becomes integral which can be easily calculated. For the track through the center of the pixel shown in Fig. 21.10 the contribution of electrons drifting to sensing electrode is *Qt e/Qt* = 0*.*82, which is significantly larger than *Qt e/Qt* = 0*.*5 for pad detectors. The fact that in segmented devices one carrier type contributes more to the total induced charge, can have important consequences after irradiation if the difference in mobility or/and trapping probability is large for electrons and holes.

If carriers are trapped and not released in time to finish the drift within the integration time of the amplifier (*tint*) then *Uw(ri)* = 1*,* 0. Using *ve,h* = μ*e,hE* and *q* = *e*0 exp −*t τeff,e,h* the Eqs. (21.28), Eq. 1 (Section 6) turn to

$$\mathcal{Q}\_{e,h}^{t} = \mp e\_0 \sum\_{l}^{e,h} \int\_0^{t\_{l\text{int}}} \exp\left(\frac{-t}{\tau\_{eff,e,h}}\right) \mu\_{e,h}(E) \left[\vec{E}(\vec{r}\_l) \cdot \vec{E}\_w(\vec{r}\_l)\right] dt,\tag{21.29}$$

where μ*e,h* represents carrier mobility. Three conclusions can be drawn without actually solving the Eq. (21.29) for a given detector and charge particle track:

**Fig. 21.10** (**a**) A schematic picture of the ATLAS pixel detector with pixel dimensions of 400×50 μm2. The hit pixel for which the *Uw* was calculated is shaded. Neighbors are denoted by the corresponding numbers. (**b**) The weighting potential along the axis through the center of the hit pixel and through the center of the three closest neighbors. For comparison *Uw* of a pad detector is also shown

electric field around the read-out electrodes, where *Ew* is large (large *E* · *E w*). Operation of partially depleted detectors therefore requires that the junction grows from the segmented side. Growth of depletion region from the back of the detector, shown in Fig. 21.10, would result in smaller induced charge in hit pixel than expected from the thickness of the active region.

• A detector design where the number of generated e–h pairs is disentangled from their drift time is optimized for large induced charge.

**Fig. 21.11** Explanation of trapping induced charge sharing

As *Uw* depends on the geometry only it is obvious that it is possible to optimize the electrode design for maximum signal. However, as the paramount parameter for any detector is its signal-over-noise ratio, the optimization should also include the inter-strip capacitance and leakage current of electrode both affecting the noise.

Charge collection in segmented devices leads to "signal cross-talk" as described in the section on Signal processing 6.2.1. The bi-polar current pulses in the neighboring electrodes (see e.g. *Uw* in Fig. 21.10) yield zero net charge for integration time larger than the drift time (see Signal processing Fig. 6.2). In irradiated detector some of the carriers are trapped and do not complete their drift. Therefore the integrals of the bipolar pulses do not vanish. A significant amount of charge can appear in the neighbors adding to the usual charge shared by diffusion (see explanation in Fig. 21.11). Unlike diffusion, where the polarity of the induced charge is equal for all electrodes, the trapping can result in charges of both polarities. If electrodes collect carriers with smaller μ · *τeff* , the polarity of the charge is the same for all electrodes. Otherwise the polarity of the charge induced in the neighbors is of opposite sign compared to the hit electrode [27, 28]

The effect can be used to enhance the spatial resolution due to larger charge sharing at the expense of smaller charge collection efficiency or vice versa.

**Fig. 21.12** Schematic view of (**a**) *p*+ −*n*−*n*+ and (**b**) *n*+ −*n*−*p*+, *n*+ −*p* −*p*+ strip detectors (AC coupled)

### *21.4.2 Silicon Detectors*

Silicon is by far the most widely used semiconductor detector material. A large majority of silicon particle detectors exploit the asymmetric *p* − *n* junction bias in the reverse mode as a basic element. Up to recently the detector grade silicon was produced by the so called float zone (FZ) technique, where concentration of impurities and dopants can be precisely controlled to very low values (∼1011 cm−3). The step further in radiation hardening of silicon detectors was the enrichment of the float zone silicon through oxygen diffusion (DOFZ). Recently, detectors were processed on Czochralski1 and epitaxially grown silicon and are in some respects radiation harder than float zone detectors.

Most of the detectors used up to now were made on *n*-type silicon with *p*+ readout electrodes (see Fig. 21.12a), which collect holes. Electrons have larger *μ τeff* in silicon, hence *n*+ readout electrodes are more appropriate for high radiation environments where the loss of charge collection efficiency is the major problem. They are mostly realized by segmentation of *n*+ side of the *n*-type bulk (see Fig. 21.12b), which however requires more complex processing on both detector sides. The double sided processing can be avoided by using *p*-type bulk material with *n*+ electrodes [29]. This is the preferred choice silicon detector type at HL-LHC.

#### **<IP_ADDRESS> Effective Doping Concentration**

The defects produced by irradiation lead to change of the effective doping concentration. The main radiation induced defects responsible for the change of effective dopant concentration can be found in Fig. 21.6 and consist of both donors and acceptors.

1If magnetic field is used to control the melt flow in crucible the process is called Magnetic-Czochralski.

**Fig. 21.13** (**a**) Effective doping concentration in standard silicon, measured immediately after neutron irradiation [30] (**b**) Evolution of *Neff* evolution with time after irradiation [31]

It is a well established, that irradiation by any particle introduces effectively negative space charge in detectors processed on float zone silicon, which is most commonly used. The change in effective doping concentration is reflected in the full depletion voltage *Vf d* , needed to establish the electric field in the entire detector:

$$V\_{fd} = \frac{e\_0 \left| N\_{eff} \right| W^2}{2\epsilon\_0 \epsilon}. \tag{21.30}$$

The *Vf d* of initially *n*-type detectors (*p*+ −*n*−*n*+), therefore decreases to the point, where the negative space charge prevails, so called space charge sign inversion point (SCSI). The *Neff* turns to negative and depleted region grows from the *n*+ contact at the back. The *Vf d* thereafter continues to increase with fluence beyond any tolerable value, which is usually set by the breakdown of a device (see Fig. 21.13a). The space charge of *p*-type detectors (*n*+ − *p* − *p*+) remains negative with irradiation so that the main junction stays always at the front *n*+ − *p* contact.

For both detector types not only deep radiation induced defects are created, but also initial shallow dopants are electrically deactivated (removed)—so called initial dopant removal. The initial dopant removal impacts to large extent the performance of some detector technologies such as Low Gain Avalanche Detectors and depleted CMOS detectors, which will be reviewed later.

#### Evolution of Effective Dopant Concentration—Hamburg Model

After the irradiation the defects responsible for space charge evolve with time according to defect dynamics described by Eqs. (21.3), (21.4). The time scale of these processes varies from days to years already at close to room temperatures which makes the annealing studies lengthy procedures. At elevated temperature the underlying defect kinetics can be accelerated, and thus the simulation of the damage investigation at real experiments spanning several years is possible in weeks.

The radiation induced change in the effective doping concentration is due to historical reasons defined as *Neff* = *Neff,*0 − *Neff (t)*, where *Neff,*0 denotes the initial doping concentration. The fact that the radiation introduced space charge is negative means that *Neff* is positive. The evolution of *Neff* after irradiation is shown in Fig. 21.13b. *Neff* initially decreases, reaches its minimum and then starts to increase. The measured evolution can be described by a so called Hamburg model, which assumes three defects [31] all of them obeying first order kinetics (see Eq. (21.3)). The initial decrease of *Neff* is associated with decay of effective acceptors (*Na*). After a few days at room temperature a plateau, determined by defects stable in time (*Nc*), is reached. At late stages of annealing effective acceptors are formed again (*NY* ) over approximately a year at room temperature. The corresponding equations are:

$$
\Delta N\_{eff} = N\_{eff,0} - N\_{eff} = N\_a(\Phi, t) + N\_c + N\_\circ(\Phi, t) \tag{21.31}
$$

$$
\Delta N\_{eff} = \mathcal{g}\_a \Phi\_{eq} \exp\left(-\frac{t}{\tau\_a}\right) + N\_c + \mathcal{g}\_Y \Phi\_{eq} (1 - \exp\left(-\frac{t}{\tau\_{ra}}\right)) \quad (21.32)
$$

$$N\_c = \pm N\_{ld}(1 - \eta(1 - \exp(-c \cdot \Phi\_{eq}))) + \mathcal{g}\_c \Phi\_{eq},\tag{21.33}$$

where *ga*, *gc* and *gY* describe the introduction rates of defects responsible for the corresponding part of the damage and *τa* and *τra* the time constants of initial and late stages of annealing.

The **stable part** of the damage incorporates also **initial dopant removal**, where ±*Nid* (negative/positive sign for donors/acceptors) denotes the concentration of initial dopants, *η* fraction of removed dopants and *c* the removal constant. Displacement of the initial dopant from the lattice site, deactivates it. Once in the interstitial position, initial dopants (mainly boron and phosphorous) can react with other defects leading to possibly new electrically active defects. The new defects formed can also be charged, hence the removal can be partial, i.e. *Nid* = *Neff,*0 [32, 33]. For example, the interstitial boron can undergo different reactions with impurities forming both donor and acceptor like defects [32]. As the reactions can take place also with impurities the removal rate depends on their concentration.

The initial donor (phosphorous) removal was intensively studied for high resistivity *p*+ − *n* − *n*+ detectors [34], where initial donor removal is attributed to formation of electrically inactive Vacancy-Phosphorous (V-P) complex. The rate of removal was found to depend on initial concentration with *Nid* × *c* ≈ 0*.*008 cm−1. The reason for such relation is unclear. It was observed that donor removal is complete for charge hadron irradiated detectors while around half of the initial donors remain effectively active after neutron irradiations (*η* ∼ 0*.*45 − 0*.*7).

The initial acceptor (boron) removal was much less studied in the *n*+ − *p* − *p*+ particle detectors, more for solar cells [35]. The required radiation hardness of *p*type detectors for HL-LHC is such that deep acceptors exceed the concentration of

**Fig. 21.14** Initial acceptor removal rate dependence on initial dopant concentration. The data were obtained from measurements with different detectors/technology: pad diodes (float zone and epitaxial), depleted (HV) CMOS and LGADs. The red markers show neutron irradiations and the blue markers show fast charged hadron irradiations. The red and blue arrows guide the eye. Data from Refs. [36–41]

The uncertainty in the parameters is of order 10% and mainly comes from variation of silicon materials used

initial ones by far, hence their removal was not in focus. However, new detector technologies (LGAD, depleted CMOS) with significant/dominant concentration of initial dopants also after foreseen fluences, triggered extensive studies of initial acceptor removal. Similarly to donor removal *c* was found to depend on initial concentration as shown in Fig. 21.14. The rate of removal is around two times larger for fast charged hadrons and only for large initial dopant concentrations the removal is complete (*η* ≈ 1).

The **parameters of the Hamburg model** related to radiation induced defects (deep traps) are given in the Table 21.4 and are valid for *p*- and *n*-type silicon detectors. For reasons that will be explained later, the model parameters are also shown for FZ detectors which were deliberately enriched by oxygen.

The time constants of initial (*τa*) and late stage annealing (*τra*) can be scaled to different annealing temperatures by using Eq. (21.9). The activation energies for initial and long term annealing are *Era* ≈ 1*.*31 eV and *Ea* ≈ 1*.*1 eV [34].

After around 80 min annealing at 60 ◦C *Na, Ny Nc* and *Neff* is almost entirely due to stable defects. If the initial dopant removal is complete or initial dopant concentration is small (with respect to to deep defects) the effective doping concentration is given by a simple relation |*Neff* | ≈ *gc* · *eq* .

Often the irradiations follow the planned operation scenario. For example at LHC the detectors are operated at *T* ≈ −10◦C for 1/3 of the year then stored for few weeks at close to room temperature and the rest of the year at *T* ≈ −10◦C. The corresponding temperature history of a whole year can be compressed roughly to 4 min at 80◦C. The whole period of operation therefore consists of multiple irradiation and annealing steps, which is also referred to as CERN scenario [34].

The parameters of Hamburg model are used to predict the evolution of full depletion voltage of silicon pixel (*n*+ − *n* − *p*+) and strip detectors (*p*+ − *n* − *n*+) at LHC experiments. The agreement of predictions with measurements during LHC operation was good, as shown on few examples in Fig. 21.15.

**Fig. 21.15** The agreement of predicted and measured *Vf d* for (**a**) LHCb Velo detector [42], (**b**) ATLAS-Insertable B layer pixel detector [43] (**c**) CMS—strip detectors in the outer region [44]. For (**b**) the prediction is denoted by black dots and measurements as bars with different colors

As can be seen in Figs. 21.15, the agreement of Hamburg model with measurements is reasonable and allows for predictions of operation up to the end of their lifetime at LHC. It is evident that careful planning of maintenance and technical stops is required to keep *Vf d* as low as possible. Even though oxygen rich silicon was used for ATLAS pixel detectors, they will be operated under-depleted at least for some time at the end of LHC operation. The depleted region after space charge inversion grows from the pixel side and for *Vbias < Vf d* the detector performance is similar to that of somewhat thinner detector, still providing efficient tracking.

On the other hand irradiated strip detectors at LHC (*p*+ − *n* − *n*+) require at all times *Vbias > Vf d* as the region around the strips needs to be depleted for achieving sufficient charge collection efficiency. The maximum bias voltage for e.g. ATLAS strip detectors is set to 450 V, which is sufficient for full depletion over the entire operation program before the HL-LHC upgrade. Standard float zone detectors are used for the fact that the larger fraction of damage is coming from neutrons and oxygenated detectors would therefore offer no significant advantage.

#### Defect Engineering

The radiation tolerance of silicon can be improved by adequate defect engineering. Defect engineering involves the deliberate addition of impurities in order to reduce the radiation induced formation of electrically active defects or to manipulate the defect kinetics in such a way that less harmful defects are finally created. It has been established that enhanced concentration of oxygen in FZ detectors reduces the introduction rate of stable defects by factor of ∼3 after charged hadron irradiations (see Table 21.4). The most likely explanation is that oxygen acts like a trap for vacancies (formation of an uncharged V-O complex) and therefore prevents formation of charged multi-vacancy complexes. In addition, Oxygen is also related to formation of deep donors (see Fig. 21.6).

On the opposite carbon enhances the concentration of vacancies as it traps interstitial silicon atoms and reduces the recombination. Since the concentration of oxygen is not high enough in the disordered regions-clusters, it has little or no effect after neutron irradiations. Different stable damage in neutron and charged hadron irradiated detectors at equal NIEL is an evidence of NIEL hypothesis violation. The diffusion oxygenated float zone detectors are used for the inner-most tracking detectors at LHC, where significant reduction of *Vf d* is required as shown in Fig. 21.15.

The oxygen concentration in DOFZ detectors is around 2·1017 cm−3, which is up to an order of magnitude lower than the oxygen concentration in Czochralski (Cz) silicon. They have only recently become available as detector grade material with resistivity (*>*1 kcm) high enough to allow production of 300μm thick detectors [45]. The increase of *Vf d* after irradiation was found to be smaller or equal to that of DOFZ detectors as shown in Fig. 21.16a. Moreover, for *n*-type Cz detectors (less evident in *p*-type Cz) stable donors (*gc* ∼ −5 · 10−3 cm−1) are introduced instead of acceptors after fast charged hadron and *γ* -ray irradiations. The oxygen in form

**Fig. 21.16** (**a**) Influence of carbon and oxygen enrichment and wafer growth on the change of *Neff* as function of fluence. (**b**) Annealing of the Magnetic Cz-*n* type (MCz) and diffusion oxygenated samples after 2 · 1014 cm−2. Also shown are thin epitaxial and standard FZ detectors irradiated to fluences around 1015 cm−2. Note the typical behavior of detectors with positive space charge for epitaxial and MCz detectors

of a dimer [O2*i*], which is more abundant in Cz than FZ detectors, is likely to be responsible. It is a precursor for formation of radiation induced shallow donors (thermal donors) [46]. The reverse annealing in Cz detectors has approximately the same amplitude as in FZ but is delayed to such extent that may not even play an important role at future experiments. The different sign of *gc* and *gY* produce a different shape of *Neff* annealing curve (see Fig. 21.16). During the short term annealing the *Vf d* increases and then starts to decrease as acceptors formed during late stages of annealing compensate the stable donors. Eventually the acceptors prevail and the *Vf d* starts to increase again.

Another interesting material is epitaxial silicon grown on low resistivity Cz substrate [47]. Stable donors are introduced after charge hadron irradiation with rates depending on the thickness of the epitaxial layer (*gc* = −4 · 10−3to − 2 · 10−2 cm−1, for thickness of 150–25μm). They exhibit also the smallest increase of |*Neff* | after neutron irradiations, but are only available in thicknesses up to 150μm.

#### Control of Space Charge

The opposite sign of *gc* and *gY* and |*gY* | *>* |*gc*| opens a possibility to control *Vf d* with a proper operation scenario and to keep it low enough to assure good charge collection (see Fig. 21.16b).

This has been demonstrated with thin epitaxial detectors which were irradiated in steps to *eq* = 1016 cm−2 and annealed for 50 min at 80◦C during the steps which is roughly equivalent to room temperature storage during non-operation periods at LHC or HL-LHC (see Fig. 21.17) [48]. The compensation of stable donors by acceptors activated during the irradiation steps resulted in lower *Vf d* after *eq* = 1016 cm−2 than the initial *Vf d* . Allowing detectors to anneal at room temperature during non-operation periods has also a beneficial effect on leakage current and trapping probability as will be shown later.

The use of silicon material with opposite sign of stable damage for neutrons and charged hadrons can be beneficial in radiation fields with both neutron and charged hadron content. The stable acceptors introduced by neutron irradiation compensate stable donors from charged hadron irradiations and lead to reduction of *Vf d* as demonstrated in [49]. An example is shown in Fig. 21.17b for MCz *n*-type pad detectors which were irradiated by 23 GeV protons (open symbols) and then by neutrons (solid symbols). The additional neutron irradiation decreases the *Vf d* .