Detectors Based on Scintillation

Tavernier, Stefaan

doi:10.1007/978-3-642-00829-0_6

Stefaan Tavernier²

7991 Accesses

Abstract

When ionising radiation interacts with matter it will excite or ionise a large number of molecules. When these molecules return to the ground state, this will sometimes give rise to the emission of photons in the visible or near to the visible energy range. This phenomenon has as scientific name ‘radioluminescence’, but it is more commonly called scintillation. Observation of the scintillation process was one of the first techniques used for the detection of ionising radiation. Rutherford used zinc sulphide scintillating crystals in his famous scattering experiment that showed that all the positive charge in atoms was concentrated in the nucleus. Today the use of scintillators is still one of the main methods for radiation detection.

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6.1 Introduction to Scintillators

When ionising radiation interacts with matter it will excite or ionise a large number of molecules. When these molecules return to the ground state, this will sometimes give rise to the emission of photons in the visible or near to the visible energy range. This phenomenon has as scientific name ‘radioluminescence’, but it is more commonly called scintillation. Observation of the scintillation process was one of the first techniques used for the detection of ionising radiation. Rutherford used zinc sulphide scintillating crystals in his famous scattering experiment that showed that all the positive charge in atoms was concentrated in the nucleus. Today the use of scintillators is still one of the main methods for radiation detection.

Many transparent materials will produce some small amount of scintillation light when hit by a high-energy particle or a high-energy photon, but usually this light signal is very weak. In a few materials, the conversion of the excitation energy into light is more efficient, and such materials are called scintillators. If the light emission continues for a long time after the excitation, i.e. much longer than 1 ms, this phenomenon is called phosphorescence rather than scintillation and the corresponding material is called a phosphor. Phosphors are often in the form of a thin layer of powder applied on a substrate. A different but related phenomenon is ‘photoluminescence’. This is the emission of visible or near to visible light under stimulation by light of a shorter wavelength. Photoluminescent materials are also often called phosphors, but sometimes these materials are also called wavelength shifters or fluors.

Scintillation and the Cherenkov effect both are light emission effects, but the physical mechanism is completely different. Cherenkov light is only produced when the velocity of the particle is larger than the velocity of light in the medium. Also for particles travelling at a speed close to the speed of light, the intensity of the Cherenkov light emission is typically a factor 100 lower than the light output of a good scintillator.

When an ionising particle interacts in matter it produces a number of free charges. In a gas, applying a modest electric field over the gas gap is sufficient to collect these charges. In a solid, it is very difficult to collect the charges. Only in very few materials, such as silicon or germanium, is it possible to obtain efficient charge collection. In a scintillator, the problem is avoided because the charges have only to travel to the nearest luminescence centre, often only a few atoms away. At the luminescence centre, the electrons give rise to photons. If the material is transparent, the light signal can then easily be extracted.

A scintillator should have the following properties to be useful as a detector for ionising radiation

the material should be transparent at the wavelength of the emitted scintillation light
the efficiency of light production should be large
the light pulses should be as short as possible and there should be little or no delayed light emission
the amount of light emitted should be proportional to the energy deposited by the ionising particle
the refractive index of the material should be close to 1.5 so that light can easily be extracted from the scintillator.

Other desirable properties of the material are that it should be chemically and mechanically stable, not too difficult to produce and not too expensive.

Scintillating materials broadly speaking fall into two classes: organic and inorganic scintillators. The physics of the scintillation mechanism, the properties and the applications of both types of scintillating materials are very different. Both types of materials are discussed in this chapter. From the application point of view the important difference is that organic scintillators contain, for the most part, atoms with a small atomic charge Z, and have therefore a long radiation length. Inorganic scintillators are interesting, mainly because many of them contain a large fraction of atoms with a high atomic charge Z and therefore these materials have a short radiation length. Because of this difference in radiation length, inorganic scintillators are mainly used for X- and gamma-ray detection, while organic scintillators are mainly used for charged particle tracking. Another important application of organic scintillators is as detectors for ‘fast neutrons’, i.e. for neutrons with energy between ≈10 keV and 10 MeV. This application depends on the elastic scattering of neutrons on the hydrogen nuclei in the scintillator and is discussed in Chap. 7.

Scintillation also occurs in some inorganic gases such as nitrogen and in some inorganic liquids such as liquid xenon. The nitrogen in air emits a green glow when excited by energetic charged particles. This phenomenon causes the Northern Lights when the stream of charged particles emitted by the Sun enters the Earth’s atmosphere near the poles.

6.2 Organic Scintillators

Three types of organic scintillators exist: organic crystals, organic liquids and plastic scintillators. Organic crystals such as anthracene and stilbene are efficient scintillators but, compared to plastic scintillators, they are expensive and difficult to use. Therefore these materials have fallen in disuse and will not be discussed further in these lecture notes.

Organic liquid scintillators are obtained by dissolving an organic scintillator in an appropriate solvent. Often a wavelength shifter is added to improve the transparency of the liquid for the scintillation light or to obtain a better match between the spectral sensitivity of the scintillator and the photodetector. Liquid scintillators are less expensive than other scintillators and are therefore used when the application requires a large volume of scintillator. It is also used to count radioactive material that can easily be dissolved in the liquid. This technique is used for counting low beta activity as for example when counting ¹⁴C for determining the age of archaeological samples.

The most widely used class of organic scintillators are the plastic scintillators. A plastic scintillator is made from a suitable polymerisable liquid, usually a liquid containing aromatic rings. Examples of such scintillating liquids are styrene and vinyltoluene. The base material in the plastic will scintillate in the UV, but the mean free path of the scintillation photons is only a few millimetres; therefore, a wavelength shifter, or fluor, needs to be added to the material. The fluor will absorb the primary UV scintillation light and emit it at a somewhat longer wavelength. At this longer wavelength the average mean free path of the photons is much larger. The concentration of the fluor in the scintillator is typically 1%. Sometimes, a second fluor is added at the ≈0.01% level to shift the emission to even longer wavelengths.

Plastic scintillators are often used because they are easily produced and can be shaped into whatever shape is required. In particular, they can be produced as large thin sheets or as fibres. A large number of different plastic scintillators are commercially available. Table 6.1 lists the main properties of one particular product, Kowaglass SCSN-32; these data are fairly typical of what can be achieved with plastic scintillators. An overview of the different organic scintillators available can be found in [5] in Chap. 1.

Table 6.1 Properties of the plastic scintillator Kowaglass SCSN-32

Full size table

The main application of organic scintillators is as detectors for charged particles. Because of the short decay time of the scintillator, this detector can provide good timing information. To obtain position information the scintillator needs to be divided into narrow strips and each strip connected to a photodetector; for this purpose, fibres made from scintillating materials are often used. These fibres are aligned in a plane and all bundled on a suitable photodetector that allows identification of the fibres with a signal.

The typical geometry of a plastic scintillator used for detecting charged particles is shown in Fig. 6.1 (a). The setup contains a sheet of scintillating plastic, a light guide and a photodetector. In many applications, one wants to read large sheets of plastic scintillator. Because of cost and for other reasons the sensitive area of the photodetector is usually much smaller than the area of the scintillator. One needs to make sure that a sufficient fraction of the scintillation photons arrives on the photodetector. The sheet of scintillator itself behaves as light guide and channels the light towards the four edges, using the effect of total internal reflection. Typically, each edge will receive about 10% of the scintillation light produced. A carefully shaped light guide brings the light from the edge of the scintillator to the photodetector using total internal reflection. The light guide is made of transparent plastic, usually polymethyl methacrylate (commonly called Plexiglas, Lucite or acrylic glass). The photodetector is usually a photomultiplier tube. It can be shown that the light guide will transmit light with good efficiency if the surface of the light guide in contact with the scintillator is the same as the surface of the light guide in contact with the photomultiplier. If the surface is smaller at the photodetector, the amount of light arriving at the photodetector is reduced in the ratio of these surfaces. This is a particular case of a general theorem in physics known as the Liouville theorem.

Because of this, the light collection efficiency can be very low if a large sheet of scintillating material is read by a small photodetector. A different approach to light collection is therefore often used and this method is shown in Fig. 6.1(b). In this method, a piece of transparent polymethyl methacrylate doped with a wavelength shifter is held against one edge of the scintillator. It is important that there is no optical contact between the scintillator and the wavelength shifter. The scintillation light is absorbed in the wavelength shifter and re-emitted at a longer wavelength. The direction of the photons emitted by the wavelength shifter is uncorrelated with the direction of the incoming scintillation light and again about 10% of this light is collected at each of the edges. If large sheets of scintillator are read with small photodetectors, this method of light collection is more efficient than the first method described.

6.3 Inorganic Scintillators

Inorganic scintillators are usually ionic crystals. The physical mechanism generating the light in an inorganic scintillator can best be explained with the help of the band model of a solid introduced in Chap. 6 and illustrated in Fig. 6.2. In this figure, the vertical axis represents the energy of the electron and the horizontal axis represents the position in the lattice along to one axis. The crystal has a valence band width, to first approximation, all energy levels occupied by one electron and a conduction band width to, first approximation, none of the energy levels occupied by an electron. Between the valence band and the conduction band there is an energy interval where there are no electron energy levels; an electron can never be in a stationary state with an energy corresponding to a point in this interval. If the ionic crystal is transparent to visible light, the band gap must be larger than ≈3 eV. In the simplest version of the model there is no way a crystal can emit light at a wavelength where the crystal is transparent. To make light emission possible we need luminescence centres that have localised levels in the crystal. Such localised levels can be intrinsically present in the material, but for the efficient scintillators these localised levels are provided by suitable dopant atoms introduced at the percent level in the host material. For the sake of definiteness, we will consider the case of a commonly used scintillator LSO. Similar considerations apply to other scintillators. Lutetium ortho-oxysilicate Lu₂SiO₅ (LSO) doped with cerium is an efficient scintillator. Neutral cerium has the electron configuration of xenon plus one electron in the 4f level, one electron in the 5d level and two electrons in the 6s level. When used as a dopant, cerium replaces lutetium in the lattice and will usually be in the Ce³⁺ ionisation state, hence only the 5d level is occupied by one electron. Inside an LSO host lattice the 4f and 5d levels are located near the bottom and the top of the band gap, respectively. The degeneracy of the 4f level is broken by spin-orbit coupling and the electron can have two possible energy values. The degeneracy of the 5d level is broken by the anisotropy of the host matrix and we have five possible values for the energy corresponding to the five possible values of the third component of the orbital angular momentum L _z. The Ce³⁺ ion therefore creates localised energy levels in the crystal as indicated in Fig. 6.2.

If a high-energy X-ray or one gamma ray interacts in the crystal, it will extract a deeply bound electron and raise it to an energy level in the valence band, or more often, to a significantly larger energy level. The electron will lose its extra energy by exciting further electrons and lifting them from the valence band or one of the deeper bands to the conduction band. Electrons from the outer bands fill the holes that are left in the core bands and the excess energy is again used to bring more electrons from the valence band to the conduction band. The net result is that one X-ray, or one gamma ray, produces a large number of holes in the conduction band and the same number of electrons in the valence band. These electrons sink to the bottom of the conduction band and the holes rise to the top of the valence band. All these happen in a very short time, in about 10⁻¹² s. The minimum energy needed to create one electron–hole pair is equal to the band gap energy E _g, but unavoidably some of the energy of the initial X-ray or gamma ray ends up being converted into phonons, i.e. thermal energy in the crystal. At the end of the cascade of events, the number of electron–hole pairs created is given by

$$N_{e - h} = \frac{{E_\gamma }}{{b\,\, E_g }}$$

In this equation, E _γ is the energy of the X-ray or the gamma ray and the parameter b has a value that depends on the nature of the host matrix. For crystals of interest, this number is typically ≈2.

To have an efficient scintillator, the electrons and the holes should reach the cerium luminescence centres. This migration of the charges is the least understood part of the scintillation process. Indeed, the band model where electrons and holes move freely in the lattice is a gross oversimplification. There are always imperfections in the crystals and these imperfections form traps that can capture the free charges and prevent them from reaching the luminescence centre. Many of these traps are shallow traps that correspond to a small binding energy. If the temperature is sufficiently high, the thermal energy will be sufficient to liberate the charge from the trap. The retention time will strongly depend on the temperature. If the electrons and holes are sufficiently free to move around, a hole will first ionise the cerium atom and form a Ce⁴⁺ and subsequently an electron is trapped in the 5d level. These capture processes are efficient if the lowest 4f level and the highest 5d level are close to the valence band and conduction band, respectively. This energy difference should be of the order of the energy of thermal agitations.

The electron captured by the 5d levels, quickly sinks to the lowest 5d level. The energy distance from this level to the 4f level is about 3 eV and this transition cannot happen by thermal agitation. The 5d → 4f transition is an allowed dipole transition and is therefore rather fast. In the case of cerium, this transition has a lifetime of the order of 40 ns, with the exact value depending on the host matrix.

The above model of the luminescence mechanism in inorganic scintillators obviously is incomplete. Indeed, it would seem that the light emitted by one luminescence centre will be absorbed by the other Ce³⁺ atoms in the crystal; hence, the crystal will not be transparent to its own scintillation light. The mechanism that avoids the above problem is called the ‘Stokes shift’ and it is explained in Fig. 6.3. When the electron of the Ce³⁺ final state is in the 4f state or in the 5d state, the spatial distribution of the charges is different. Therefore, the neighbouring ions have a different equilibrium position depending on the energy level of the electron.

For simplicity, I assume that the configuration of the ions round the luminescence centre can be described by a one-dimensional configuration coordinate as indicated in Fig. 6.3. Obviously, the configuration needs to be described by several variables, but with this simplification it is easier to explain the mechanism of the Stokes shift. Assume that the electron is in the 4f level. The lattice around the luminescence centre will find itself in the equilibrium position and this is the position where the energy of the electron takes the lowest value. If the electron absorbs a photon that rises it to the 5d level, at first the lattice remains in the geometry that corresponds to the electron in the 4f level. After the transition, the lattice relaxes and takes the geometry corresponding to the electron in the 5d level. This new geometry corresponds also to the minimum for the electron energy. If the electron jumps back to the ground level 4f, the energy of the emitted photon will be smaller than the energy used in the transition 4f → 5d. The energy difference between the absorbed photon and the emitted photon is called the Stokes shift. The corresponding absorption and the emission spectra of the crystal in function of the wavelength of the light are shown in Fig. 6.3(b). The distance between the edge of the absorption band and the maximum of the emission is the Stokes shift. Because of the thermal fluctuations in the crystal, the absorption peak is not very narrow and the band edge is not a sharp cut. Indeed, due to the thermal agitations, the configurations of the ions surrounding the luminescence centre are constantly fluctuating around the equilibrium position. The Stokes shift should be sufficiently large if the scintillator is to be transparent to its own scintillation light.

From the model described above it follows that the maximum number of photons, N _max, a scintillator can produce is given by

$$N_{\max } = \frac{{E_\gamma }}{{b \,\,E_g }}$$

Let us take as an example the scintillator CsI:Tl. In this scintillator, thallium (Tl+) dopants play the role of luminescence centres. The band gap in CsI is 6.2 eV and we predict, taking b = 2, a maximum light yield of 80,000 photons/MeV. Experimentally it is found that CsI:Tl scintillator produces about 60,000 scintillation photons/MeV. We conclude that both the transport of the electron–hole pairs to the luminescence centres and the efficiency of the luminescence centre in CsI:Tl are rather high at room temperature.

The decay time of a scintillator is determined by the lifetime of the excited level in the luminescence centre. This lifetime also depends on the host lattice, but this is not a very large effect. All cerium-doped scintillators have a decay time of the order of 40 ns. The probability to have a transition 5d → 4f is independent of how long the electrons are already in this level, we therefore expect an exponential decay of the scintillation light. In practice, the scintillation light emission often deviates significantly from a simple exponential decay. As an example, Fig. 6.4 shows the decay spectrum of CsI:Tl. In a logarithmic plot, we clearly see two exponential decay components. There are two possible explanations for this behaviour. There can be more than one type of luminescence centre in the crystal. These can be two truly different kinds of dopant atoms, but it can also be the same type of dopant sitting in a different lattice environment. The dopant atom can for example sit next to another lattice defect and this can completely change the decay characteristics of the luminescence centre. Another possible explanation is that the transport of the charges to the luminescence centre is hindered by the presence of traps. If either the electron or the holes are trapped in a defect that retains these charges with a lifetime much larger than the decay time of the luminescence centre, we will obtain a slow component in the decay spectrum as shown in Fig. 6.4. Traps with a rise time much shorter than the luminescence centre will affect the rising edge of the scintillation signal. Instead of a very sharp rising edge, we will see a much slower increase to the maximum value.

The scintillation properties of inorganic scintillators tend to have a strong dependence on the temperature. This is illustrated in Fig. 6.5. For many materials the light output first increases with temperature, reaches a maximum and then decreases again. For BGO, the maximum is reached at a temperature below 100 K; therefore, only the decreasing part of the curve is seen. This behaviour can be understood as follows. At low temperature the light yield is low because there will always be shallow traps that capture the electrons or the holes and prevent the charges from reaching the luminescence centre. With rising temperature, these traps are no longer able to retain the charges and the light yield increases. If the temperature increases further, we have the phenomenon called thermal quenching. This can be understood with the help of Fig. 6.3(a). The energy distance between the 4f and 5d levels depends on the configuration of the host matrix around the luminescence centre. This configuration is not constant due to the permanent thermal motion of the ions around the luminescence centre. At some values of the configuration coordinate the distance between the two energy levels becomes small and the electron can jump to the lower level without emission of an optical photon, but by interacting with the phonons in the lattice. This is a non-radiative transition. As the temperature increases, the probability of this happening increases and the light yield decreases.

Inorganic scintillators are mainly used as detectors for gamma rays, usually with the aim of measuring the energy of the gamma ray. A linear relation between the light yield and the energy of the gamma ray is, therefore, a desirable property of a scintillator. For many scintillators there are significant deviations from this linear relation as is illustrated in Fig. 6.6. When a gamma ray interacts in a scintillator crystal there are a large number of different ways to deposit its energy. It can deposit all its energy in one photoelectron, but it can also undergo one or more Compton interactions before losing all its energy in a final photoelectric effect. If the response of the scintillator is not linear, this will result in a light output of the scintillator that depends on the particular history of each gamma ray. This will degrade the energy resolution. This effect seriously limits the energy resolution that can be achieved with a scintillator for energies of the order of 1 MeV and less. At energies well above 1 MeV, these effects tend to become less important.

The response of a scintillator also tends to depend strongly on the energy loss density of the charged particles. Many scintillators have a strongly reduced sensitivity to energy deposited by alpha particles. The light yield for the same energy deposition by an alpha particle is usually several times smaller than for electrons.

Table 6.2 lists some commonly used inorganic scintillators. Each application has a different set of requirements for a scintillator. In some cases, a fast decay time is essential, in others a large light yield and in still other applications a short radiation length is the most desired property. What is the best scintillator depends on the application.

Table 6.2 Properties of some commonly used inorganic scintillators

Full size table

6.4 Photodetectors

Scintillators would not be very useful as detectors for subatomic particles without some device to convert the light signal into an electrical signal. Such a device is called a photodetector. Photomultiplier tubes were invented more than 70 years ago, but are still the most commonly used photodetector for reading out scintillators. This is due to the fact that the light pulses obtained from scintillators are usually very weak, often less than a few 100 photons. A photomultiplier has a very large internal gain, therefore even a few photons are sufficient to obtain a detectable signal. An amplifier can also be used for amplifying weak signals, but as will be shown in Chap. 8, amplifiers always have noise and this noise is amplified together with the signal one wants to observe. Electrical signals that are too small are therefore not observable. In recent years, several new types of photodetectors with internal gain have been developed. Some of these are quite promising and could possibly one day replace photomultiplier tubes. These devices are briefly discussed at the end of this section.

The photomultiplier tube. The first photomultiplier tube was produced by Zworykin in 1936. Modern photomultiplier tubes have much improved performance, but the basic principle of operation is still the same. For a more in dept review of photomultipliers and their use, See [11, 12, 13]. A photomultiplier tube is a vacuum tube, usually made of glass or at least with a glass window and with a photocathode and a number of metal dynodes inside the vacuum. The structure of a photomultiplier tube is schematically represented in Fig. 6.7(a). A photocathode is a thin layer of a compound that will emit electrons when absorbing photons with a wavelength in the visible or near to the visible region. The photocathode can be deposited on a metal electrode inside the tube, but more often the photocathode is deposited on the inside of the window of the photomultiplier tube. The photocathode is at some large negative potential, typically –2000 V. The dynodes are kept at potentials between –2000 V and 0 V, decreasing from –2000 V to 0 V in steps of typically 150 V. These voltages are nearly always obtained with a passive resistor chain as shown in Fig. 6.7(b). The last electrode, called the anode, is at ground potential. Sometimes one uses a different electrical layout with the cathode at ground potential and the anode at +2000 V. If a photon hits the photocathode, an electron is ejected from its surface. This electron will be attracted by the first dynode because this dynode is at a positive potential relative to the cathode and it will reach the surface of this dynode with a kinetic energy equal to the potential difference between the cathode and this first dynode. This kinetic energy is sufficient to extract several new electrons from this dynode. These few electrons, in turn, will be attracted by the next dynode and there again the number is multiplied. Of course, this multiplication process is efficient only if the shape of the dynodes is carefully optimised to provide efficient collection of the secondary electrons produced. The shape shown in Fig. 6.7 is only for illustration purposes and would not make an efficient photomultiplier tube. Figure 6.11 shows some more realistic dynode geometries. The electron multiplication step can be repeated many times, resulting in a very large total multiplication of the number of electrons, reaching 10⁶ or more. At some point the total number of electrons in the cloud is so large that the electric field is strongly affected by the corresponding space charge and the structure no longer multiplies. The number of electrons in each pulse can reach up to 10¹⁰ before serious problems due to space charge occur. The electrical output signal is taken from the anode, where all the electrons eventually arrive. The total transit time of an electron from the cathode to the anode is typically 20 ns, depending on the size of the tube. If the tube is optimised for timing, the complete electron cloud caused by one photoelectron will arrive on the cathode in a time interval of about 10 ns.

The first important step affecting the performance by the photomultiplier tube is the conversion of the photon into a photoelectron by the photoelectric effect in the cathode. The probability for a photon to give rise to a photoelectron is called the quantum efficiency.

Many materials display the photoelectric effect for UV photons, and usually the corresponding quantum efficiency is small. However, some semiconductor materials have a large quantum efficiency for photoemission in the visible region. A thin (a few 10 nm) layer of such a material is deposited by vacuum evaporation on the inside face of the photomultiplier tube window. The quantum efficiencies that can be obtained are shown in Fig. 6.8. The largest quantum efficiencies are obtained with K₂CsSb (bialkali photo-cathodes) and are 25−30% around 400 nm. Unfortunately, this high efficiency is obtained by choosing materials that very easily emit electrons from the conduction band. As a result, electrons will also be emitted in the absence of any illumination. These materials produce between 10² and 10⁴ thermal electrons per square centimetre at room temperature in the absence of any light stimulation. This dark current increases rapidly with temperature and can be a serious problem in certain applications. It should be mentioned that optical quality glass has a cut-off around 300 nm. Fused silica windows have a good light transmission down to 180 nm, but such PMTs are much more expensive.

The probability for producing a secondary electron on the dynode also depends strongly on the nature of the surface of this dynode. Gallium phosphide (GaP) heavily doped with p-type material such as zinc is particularly effective. Up to 25 secondary electrons can be produced by an electron with a kinetic energy of 200 eV. This number of secondary electrons is more or less Poisson distributed. If the multiplication factor on one dynode is d and assuming all dynodes to have the same multiplication factor, the total gain is d ^N, where N is the number of dynodes. The relative variance on the number of electrons produced (n _e) by one primary photoelectron can be shown to be given by (σ/n _e)² = 1/(d − 1) [11]. If a photomultiplier tube is illuminated with a weak light signal corresponding to only a few photoelectrons, a pulse height spectrum as shown in Fig. 6.9 is obtained. The first peak corresponds to events with one photoelectron, the second peak to events with two photoelectrons, etc. The peak corresponding to four photoelectrons is just visible.

Photomultiplier tubes come in many shapes and sizes. Figures 6.10 and 6.11 show a number of photomultiplier tubes and a few typical dynode geometries. In some applications, position information is highly desirable; therefore, position-sensitive photomultiplier tubes were developed. These are essentially of two types: multi-anode PMTs and true position-sensitive PMTs. In a multi-anode PMT, there are simply a large number of identical and independent amplifying structures, forming a collection of independent small PMTs inside one single vacuum enclosure, each PMT with its own readout anode, see Fig. 6.10(b). In a position-sensitive PMT, there are fewer anodes and the position is derived from a suitable ratio on the amplitudes of these anodes.

The photomultiplier tube is a very efficient instrument for observing and measuring weak and fast light pulses such as the light pulses caused by ionising radiation in a scintillator. However, there are a number of caveats when working with PMTs:

A PMT has an important dark current. In addition to the thermal dark current consisting of single electron pulses, there is also after-pulsing, i.e. pulses coming a fixed time after a true pulse. These after-pulses are caused by residual gas atoms in the tube. After being ionised these atoms can drift back towards the cathode and extract a large number of electrons at the same time. Unlike the thermal dark current pulses that are single electrons pulses, these after-pulses correspond to many primary photoelectrons and can easily be confused with true signal pulses. This problem tends to increase as the tube ages but is also present in new tubes.
PMTs, and particularly the larger ones, are extremely sensitive to magnetic fields. Even the Earth’s magnetic field is sufficient to seriously affect the operation of a large photomultiplier tube. Because of this, photomultiplier tubes are usually surrounded by μ-metal cylinders working as a shield against magnetic fields. These shields are sufficient to protect against the Earth’s magnetic field, but not against larger magnetic fields.
A PMT should never be exposed to daylight when under high voltage. Also when not under high voltage, the photocathode should never be exposed to very intense light such as direct sunlight.
When used at large gain and with fast pulses, the response of a photomultiplier tube becomes non-linear. This non-linear behaviour can have two causes: (a) too much current is drawn from some of the dynodes and their potential changes and (b) space charge effects. The potential of the dynodes can be stabilised by suitable design of the voltage divider. In Fig. 6.7(b), there are capacitors between the last three dynodes that will stabilise the potentials of these dynode to minimise this effect.

Silicon-based photodetectors. Another photodetector widely used in many applications is the silicon photodiode. In this detector, light is converted into electron–hole pairs in the depletion region. The mean free path of optical photons in silicon varies from 0.1 μm at 400 nm to 5 μm at 700 nm. The light must be able to reach the depletion region; hence, one of the electrodes, usually the p side, has to be as thin as possible and transparent to light. Silicon diodes are not expensive if the detector area is small, are insensitive to magnetic fields and have excellent quantum efficiency: around 60% at 400 nm, increasing to 80% at 800 nm. However, silicon diodes have no internal gain, and when used for the readout of scintillators give signals too small for most applications. Figure 6.12(a) shows the internal structure of a PIN photodiode.

An avalanche photodiode (APD) is a silicon photodiode with internal gain. To make an avalanche photodiode one must change the doping profile in a diode as illustrated in Fig. 6.12. In a reach-through type APD we first have a low field region, where the photons convert into electron–hole pairs, followed by a high field region, where the field is sufficient to cause electron multiplication. The drawback of this layout is that the large dark current in the drift region is also multiplied. If we make the drift region very thin, the dark current is reduced but the detector capacitance is increased. This is solved in the reverse type APD, where we have a drift region behind the application region to decrease the capacitance.

The structure of an APD is conceptually quite straightforward but, in practice, it is very difficult to realise. The reason is that for stable avalanche multiplication, it is essential that only one type of charges is multiplied, the other type being merely collected. In silicon, the difference between the mobility of electrons and holes is small and the field necessary to start electron multiplication is very close to the field where hole multiplication starts. In order to make a good APD, it is essential to be able to control the fields, and hence the purity of the material and the doping profiles, extremely well. Manufacturing techniques allowing this have only recently become available. In practice, APDs can only be used at a gain of the order of 100 and can only be made in small sizes. Moreover, APDs tend to be expensive, certainly if a large photosensitive surface is required.

A very interesting recent development is the so-called silicon PMT (SiPMT), also called ‘pixellised photodetector’ (PPD), illustrated in Fig. 6.13. This device makes it possible to obtain a gain of 10⁶ with silicon photodiodes. The idea is to subdivide the sensitive area of the photodetector in a large number of very small micro-pixels, typically measuring 50 × 50 μm². Each pixel works as a separate avalanche photodiode, but unlike in a normal APD, the electric field over the amplification region is made very large. As a result, the pixel-counter goes into discharge mode as soon as one electron–hole pair is formed.

A resistor between the micro-pixel and the power supply quenches the discharge. The separation between the individual pixels must guarantee that the discharge does not spread to the neighbouring pixels. The complete detector response remains linear with the light signal as long as only a small fraction of micro-pixels produce a signal. The quantum efficiency of a silicon PMT will certainly be less than what can be achieved with a PIN diode or an APD because of the unavoidable dead area between the micro-pixels. If the cross-talk between the pixels remains low, this type of detector will have an excess noise factor close to one. These devices are still under active development, but it seems likely that pure solid-state photodetectors with a gain of 10⁶ and with a quantum efficiency similar to that which can be achieved with a photomultiplier tube will soon be available commercially.

The hybrid photomultiplier tube. Another interesting recent development is the hybrid photomultiplier tube. This photodetector owes its name to the fact that it combines ideas borrowed from photomultiplier tubes with silicon photodetectors. The hybrid photomultiplier tube is illustrated in Fig. 6.14. It consists of a vacuum tube with a photocathode. In the vacuum, facing the photocathode there is a silicon diode with a geometry very similar to that of a PIN diode. Between the cathode and the diode a very large voltage difference is applied. Any photoelectron produced at the photocathode will be accelerated towards the diode and reach it with a large kinetic energy equal to the voltage difference. This energetic electron will create a number of electron–hole pairs equal to the kinetic energy divided by 3.62 eV. This kind of photodetector is good for determining the number of photoelectrons in any given pulse. Another advantage of this structure compared to a normal photomultiplier tube is that the silicon diode can easily be divided into a large number of pixels of arbitrary shape.

The drawback of hybrid photodetectors is that a large gain can only be achieved by using a very high voltage. To reach a gain of 10,000 it is necessary to apply 36,200 V. That is possible, but it is a significant technical complication and it makes the system both complicated to use and expensive.

The excess noise factor. In a photodetector with internal gain, the interactions of optical photons produce charges, and for each charge, the internal gain mechanism multiplies the number of charges. The number of primary charges in a photodetector is well described by the Poisson distribution law. However, all the charges are not multiplied by the same gain factor and this is an additional source of fluctuations in the output signal. The total signal S is given by the sum of a random number of terms and each term is itself a random variable

$$S = \sum\limits_i^{1...n} {x_i }$$

In this expression, x _i is a random variable describing the charge signal produced by one primary charge and the integer n is a random variable with a Poisson distribution of average value N, describing the number of primary charges. The quantity <x> is the internal gain factor of the photodetector. The following relations hold (see Exercise 3, Chap. 8):

$$\begin{array}{l} \left\langle S \right\rangle = N \left\langle x \right\rangle \\\\ \sigma ^2 \{ S\} = N \left\langle {x^2 } \right\rangle \\ \end{array}$$

This can also be written as

$$\begin{array}{l} \sigma^2 {\rm{\{ }}S{\rm{\} }}\, = N\left( {\sigma ^2 \{ x\}+ \langle x\rangle ^2 } \right) \\ \phantom{\sigma {\rm{\{ }}S{\rm{\} }}}\, =N \left\langle {x} \right\rangle ^2 \left[1 + \dfrac{{\sigma ^2 {\rm{\{ }}x{\rm{\} }}}}{{\langle x\rangle ^2 }}\right] \\\end{array}$$

We see that the variance of the output signal is exactly the variance that would be expected if the signal were only affected by Poisson fluctuations (N〈x〉²), multiplied by a factor independent of N. This factor is called the excess noise factor, and is usually denoted as F. It is unity if all the charges receive exactly the same multiplication. If the charge multiplication gives rise to an exponential distribution, F = 2. The noise equivalent number of photoelectrons, that is the number of photoelectrons that would give the same noise if all photoelectrons received the same gain, is given by N/F.

In comparing the merits of different photodetectors, the quantum efficiency divided by the excess noise factor is therefore the relevant quantity. The excess noise factor for photomultiplier tubes is in the range 1.2–2, depending mainly on the gain of the dynodes.

For APDs, the charge distribution of an avalanche produced by one primary charge is exponential at low gain. This is similar to the avalanche produced in a wire chamber. The excess noise factor is therefore ≈2 at moderate gain of less than 100. At higher gain the excess noise factor increases considerably. This is connected to the fact that in APDs both the electrons and the holes can contribute to the charge multiplication. SiPMs are still very new, but are expected to have a small excess noise factor. For hybrid photodetectors F ≈ 1.

6.5 Using Scintillators in the Nuclear Energy Range

The most important application of inorganic scintillators is as detectors for X-rays or gamma rays. The present section is devoted to the discussion of a number of issues related to the use of scintillators in the nuclear energy range.

If one wants to check for the presence of some radioactive material, observing the characteristic gamma emission is often a good way of doing so. For this application, it is desirable to have a large detection efficiency for the gamma rays, accurate determination of the energy of the gamma rays and the ability to identify gamma rays, also in the presence of many other gamma rays of similar energy. In other words, one needs to measure the best possible energy spectrum of the gamma radiation present.

All scintillators in Table 6.2 have a radiation length between 0.9 cm (e.g. BGO) and 2.6 cm (e.g. NaI). For gamma rays of more than 1 MeV, the mean free path is of the order of the radiation length. The piece of scintillator should hence be a few radiation lengths thick in order to have good detection efficiency. At energies much above 1 MeV, the scintillator should be much larger and this case is discussed in Sect. 6.6.

A gamma ray detector consists of a piece of scintillator material, a photodetector, usually a photomultiplier tube, and readout electronics. The readout system will register a pulse height spectrum and if all the gamma rays deposit all their energy in the scintillator, we will see a peak at the corresponding position. To collect as much light as possible, the scintillator is wrapped in some white reflecting material and a photodetector is pressed against one of its sides. Between the photodetector and the scintillator, it is usual to add a thin layer of transparent grease with a refractive index close to the refractive index of glass. This grease will make optical contact between the scintillator and the photomultiplier window. This considerably improves the collection of the scintillation light because it avoids the internal reflection in the scintillator side facing the photodetector. For a good light collection efficiency the sensitive area of the photodetector should be sufficiently large. If the scintillator is a cube, and if the photodetector covers one complete face of the cube, the light collection efficiency will typically be ≈50%. Figure 6.15 shows some commercial PMT–scintillator assemblies.

Assume that we have a piece of LSO scintillator measuring 5 × 5 × 5 cm³, with one face covered with a 2-inch photomultiplier tube with a photocathode quantum efficiency of 25%. For a 1 MeV gamma ray completely absorbed in the scintillator we expect 3750 photoelectrons in the pulse. The photomultiplier tube behaves like a current source with a capacitance in parallel (see Fig. 6.16). The capacitance shown in this figure represents the capacitance between anode and ground and this capacitance is typically of the order of 10 pF. The product C _a .Z _i gives the time constant of the readout and this time constant should be short compared to the decay time of the scintillator. In our example, this gives the condition Z _i < 1000 Ω. Often the signal is read directly with a 50 Ω cable. Assuming PMT gain is 10⁵, the output pulse will peak at 75 mV (see Exercise 1). This pulse amplitude is large enough to be comfortably visible above the noise in any modern electronic readout system.

To be able to determine the energy of each peak accurately and to be able to separate nearby peaks, it is essential that the width of each peak is as narrow as possible. Obviously this requires a light yield of the scintillator, and a light collection efficiency, that are homogeneous over the volume of the scintillator. Assuming a Poisson distribution with average N _e for the number of photoelectrons, the relative energy resolution FWHM of the scintillator will be given by

$${\rm{resolution \;\; FWHM[\% ]}} = {\rm{R}}_{{\rm{lightyield}}} = \frac{{100 \times 2.35}}{{\sqrt {N_e} }}$$

((6.1))

In our example of an LSO scintillator, we therefore expect an energy resolution of 3.8%.

However, also under optimal conditions, it turns out that the energy resolution is much worse than Eq. (6.1) predicts. This is mainly due to the non-linear response of the scintillator to the energy deposited. The resolution of a scintillator is well described by the quadratic sum of an intrinsic, energy-independent term and a light yield dependent term given by Eq. (6.1).

$$\begin{array}{l} R^2 = R_{{\rm{intrinsic}}}^2 + R_{{\rm{lightyield}}}^2 \\ {\rm{ }} \\ \end{array}$$

Table 6.3 gives the intrinsic energy resolutions for a few scintillator materials. At energies much above a few MeV, this equation no longer holds and this case will be considered in Sect. 6.6.

Table 6.3 Intrinsic resolutions for some scintillator materials

Full size table

If we irradiate a scintillator with a gamma ray beam with all gamma rays of the same energy, we not only obtain a peak corresponding to this energy, but also several other bands and peaks as shown in Fig. 6.17. In addition to the photopeak, i.e. the peak corresponding to events where all the energy is deposited in the scintillator, we also have a band corresponding to events where the gamma ray has undergone Compton scattering in the scintillator and where the scattered gamma ray escapes from the crystal. The shape of the Compton band can be obtained from Eqs. (2.10) and (2.11). The energy left in the scintillator is the energy of the recoil electron in the Compton interaction. This is simply the initial gamma energy minus the energy of the scattered photon. The maximum energy in the Compton band is obtained using Eq. (2.10), taking θ = 180°

$${\rm{maximum\, energy\, compton\, band}} = \raisebox{2.9pt}{--}{\rm{h}} \omega - \raisebox{2.9pt}{--}{\rm{h}} \omega ^{\prime}(\theta = 180^\circ ) = \raisebox{2.9pt}{--}{\rm{h}} \omega \frac{{2\raisebox{2.9pt}{--}{\rm{h}} \omega }}{{2\raisebox{2.9pt}{--}{\rm{h}} \omega + m_e c^{\rm{2}} }}$$

In Fig. 6.17, we also notice a peak at the energy of about 180 keV. The explanation of this peak is as follows. When this histogram was recorded, a ¹³⁷Cs source was used, and the source was next to the scintillator, on the opposite side of the PMT. Some of the 662 keV gamma rays emitted by the caesium source undergo Compton backscattering in the window of the PMT and the scintillator records the backscattered gamma rays. One can check that the value of this peak corresponds to the energy of backscattered gamma rays at 662 keV (184 keV).

Another spurious peak commonly encountered in gamma detection is the ‘escape peak’, see Fig. 6.18. The escape peak is caused by the following phenomenon. If a gamma ray interacts in a scintillator by photoelectric effect, the most probable electron to be involved in the interaction is the most deeply bound or K-shell electron. An outer electron quickly fills the vacancy thus left in the electron structure of the atom and the corresponding energy is emitted as an X-ray with an energy equal to the binding energy of this K-shell electron. Most of the time the scintillator immediately absorbs this X-ray, but sometimes, it can escape from the crystal. In the latter case, the total energy deposited in the crystal is the energy of the gamma ray minus the energy of the X-ray. These events will show up in the pulse height spectrum as second peak below the photoelectric peak.

Finally, gamma rays interacting in any other material present near the measurement setup can cause additional spurious peaks. If the primary gamma rays have a larger energy than 1.022 MeV, these gamma rays will create electron–positron pairs anywhere in the material surrounding the scintillator detector. When the positron annihilates, it gives rise to two gamma rays of 511 keV and these can also give rise to a peak in the pulse height spectrum. X-rays can also result from nuclear interactions of the gamma rays in the surrounding material.

All these spurious peaks can make the interpretation of a gamma ray pulse height spectrum quite complicated, certainly if gamma rays from several energies are present at the same time. This is illustrated in Fig. 6.19, which shows the pulse height spectrum for mono-energetic gamma rays in a NaI:Tl scintillator. An obvious way to avoid, or at least strongly suppress, most of these spurious peaks and bands is to use a well counter, i.e. a setup where the gamma source is completely surrounded by the scintillator. However, it is not always possible to put the source in a well counter, for example because the source is too large, its location is unknown, etc.

This section ends with a comparison of different methods commonly used for X-ray and gamma-ray detection. Proportional tubes with a gas filling containing mainly argon can be used to detect X-rays, but are limited to energies below 20 keV. With a gas filling containing mainly xenon, a reasonable detection efficiency can be obtained up to an energy of 100 keV. However, also for these low-energy X-rays it will take several centimetres of gas to have the same stopping power that can be achieved with only 100 μm of scintillator or germanium detector. At energies above 100 keV, only germanium detectors or scintillators have a sufficiently large stopping power to be useful for detecting gamma rays.

Comparing the energy resolution obtainable with scintillators with the energy resolution of germanium scintillators discussed in Chap. 5, we see that the energy resolution of germanium is at least a factor 10 better than even the best scintillator. This is illustrated in Fig. 6.20 showing the same gamma radiation field observed with a NaI:Tl scintillator and with a germanium detector. It may therefore seem that germanium detectors will nearly always be preferred over scintillators for gamma detection, but this is not at all the case. Germanium detectors are expensive and need to be cooled to the temperature of liquid nitrogen, which is a major complication. Moreover, germanium detectors are relatively slow since the signal formation requires the electrons to drift over the full length of the collection gap. Germanium detectors, therefore, cannot be used if either good time determination or large count rate is needed.

6.6 Applications of Scintillators in High-Energy Physics

An important type of detector for particles of high energy is the calorimeter. This type of detector measures the energy of a particle by totally absorbing the shower produced by this particle in a block of material. The energy of the particle is proportional to the amount of ionisation produced in the material. Calorimeters often use scintillators to measure the amount of ionisation. For an in-depth discussion of calorimeters, we refer the reader to [6, 7].

Electromagnetic calorimeters. Electromagnetic calorimeters are detectors for measuring the energy and the position of high-energy gamma rays or high-energy electrons and positrons. For the purpose of this discussion, high-energy means energy larger than 1 GeV. A gamma ray with this energy interacting in matter will initiate an avalanche consisting of a large number of electrons, positrons and secondary gamma rays. On average in about one radiation length the original gamma ray gives rise to an electron–positron pair. This electron and positron will create a large number of secondary gamma rays by bremsstrahlung. In one radiation length, an electron or a positron will radiate about half of its energy in this way. Many of these secondary gamma rays will again create electron–positrons pairs and these will again undergo bremsstrahlung, and so on. If the energy of the initial gamma ray is large enough, the number of particles in the shower will grow exponentially. However, at each step the average energy of the particles in the shower decreases and fewer of the secondary gamma rays have sufficient energy to produce electron–positron pairs. Moreover, below the critical energy, the electrons and positrons will lose more energy in ionisation than in bremsstrahlung and the production of additional gamma rays becomes less efficient. After a certain number of radiation lengths, the number of particles in the shower reaches a maximum and thereafter starts decreasing. Eventually, all electrons and positrons will have lost all their energy in ionisation and come to rest and all the gamma rays will be absorbed by photoelectric effect. The positrons will annihilate with electrons in two 511 keV gamma rays and these will also be absorbed.

The development of a shower is a complex process and only a detailed Monte Carlo simulation can provide a reliable quantitative description. Nevertheless, the following simple model gives a reasonable qualitative description of the shower development. The model assumes that in one radiation length a gamma ray will convert into one electron–positron pair and ignores the fluctuations on the conversion distance. The model furthermore assumes that in one radiation length an electron or a positron will emit one gamma ray with more energy than two times the electron mass. The model ignores the statistical fluctuations on the number of gamma rays and also ignores that the average number of such gamma rays depends on the energy of the electrons. This model of shower development is illustrated in Fig. 6.21(a). In this model, the total number of particles, i.e. the number of electrons, positrons and gamma rays with E > 2m _e, will increase with the depth in the material D as

$$N = 2^{D/X_0 }$$

The number of particles in the shower will increase exponentially until the average energy of the electrons becomes equal to the critical energy. At this point the shower has the maximum number of particles. We thus have

$$\begin{array}{l} N_{\max } = \dfrac{E}{{E_{c_{\vphantom{l}_{\vphantom{l}}}} }} = 2^{D_{\max } /X_0 } \\\noalign{} D_{\max } = \dfrac{{X_0 }}{{\ln 2}} \ln \dfrac{E}{{E_c }} \\ \end{array}$$

After this maximum, the number of particles in the shower decreases exponentially and the attenuation length of the number of particles is again of the order of the radiation length. Since the number of the particles in the shower increases exponentially with the energy of the incoming gamma ray, the length needed to fully absorb all the particles will also increase like ln(E/E _c). Experimentally, it is found that for a gamma ray of 10 GeV the number of particles in the shower reaches a maximum after about six radiation lengths and it takes a total of ≈25 radiation lengths of heavy material to absorb 99% of the shower energy.

The lateral, or sideways, development of the shower is mainly due to the multiple scattering of the electrons and positrons and scales with the ‘Molière radius’. The quantity Molière radius has the dimension of a length and it is characteristic for the medium in which the shower develops. Its value is close to [14 g/cm²]/density for most materials. In electromagnetic showers, 90 and 95% of the energy is deposited within one and two Molière radii, respectively.

If a gamma ray enters a sufficiently large block of scintillator material, all the energy of the initial particle is deposited as ionisation in the material. The total amount of ionisation is therefore proportional to the energy of the particle and the amount of scintillation light produced will also be proportional to the energy of the initial gamma ray. It should be mentioned that a high-energy electron or a high-energy positron will initiate a shower that looks exactly the same as a shower initiated by a high-energy gamma ray. The presence or absence of the incoming charged particle track at the starting point of the shower is the only difference between an electron-initiated shower and a gamma-initiated shower.

An electromagnetic calorimeter using inorganic scintillators typically has a large number of blocks of inorganic scintillator material with a geometry similar to what is shown in Fig. 6.21(b). The length of each scintillator block is typically equal to 25 radiation lengths. The width of each block is chosen to be less than the lateral extent of the shower to allow accurate determination of the centre of the shower, and therefore the impact point of the gamma ray.

The energy resolution attainable with an electromagnetic calorimeter is usually expressed as r.m.s. energy resolution, and its energy dependence can be parameterised as

$$\frac{{\sigma \{ E\} }}{E} = \sqrt {\frac{{a^2 }}{{E[{\rm{GeV}}]}} + b^2 }$$

((6.2))

In this equation, E[GeV] represents the energy of the initial gamma ray expressed in GeV. For a homogeneous crystal calorimeter the coefficients ‘a’ and ‘b’ are typically 0.02–0.03 and 0.005–0.01, respectively. The first term is the statistical term. One of the effects entering here is the fluctuation on the number of optical photons detected. The energy resolution due to the fluctuation on the number of detected photons is given by

$$\frac{{\sigma \{ E\} }}{E} = \frac{1}{{\sqrt {N_{p.e} } }} = \sqrt {\frac{{1/\varepsilon }}{{E[{\rm{GeV}}]}}}$$

where ɛ is the number of photoelectrons detected per GeV. However, there are several other effects contributing to the statistical term, e.g. leakage of a small fraction of the shower, photonuclear interactions in the shower, absorption of part of the shower in the dead material between two blocks of scintillating material.

The second term has to do with non-uniformities in the different components of the detector. Careful calibration is essential to keep this term small. To obtain the desired energy resolution, it is also essential that the signals from all the blocks containing parts of the same shower are added together.

Until now we have been considering electromagnetic calorimeters based on the use of large blocks of inorganic scintillating materials. Such detectors show excellent performance but are expensive. To reduce the cost one often uses sampling calorimeters. In a sampling calorimeter, different materials perform the function of absorbing the shower and the function of measuring the energy deposited. Such a sampling calorimeter typically is made from a large number of layers of some heavy material, usually lead, interleaved with active layers measuring the amount of ionisation present, often plastic scintillator sheets. In sampling calorimeters typically a few percent of the energy in the shower is actually sampled. As can be expected, the energy resolution that is obtained with a sampling calorimeter is significantly worse than what can be achieved with a homogeneous calorimeter. A crude estimate of the achievable energy resolution can be obtained as follows. Assume a sampling calorimeter where the thickness of the active layers is a small fraction of a radiation length and the thickness of the absorbers is of the order of one radiation length. In such a sampling calorimeter, one is essentially counting the number of charged tracks in each sample layer. The simple model of shower development discussed before, suggest that the number of tracks reaches a sharp maximum at the point of the maximum of the shower. The error on the number of charged tracks is therefore dominated by the error on the number of charged tracks at the maximum of the shower N _max = E/E _c. The error on the energy resolution of the sampling calorimeter is therefore approximately given by

$$\frac{{\sigma \{ E\} }}{E} \approx \sqrt {\frac{1}{{N_{\max } }}} \approx \sqrt {\frac{{E_c }}{E}}$$

For electromagnetic calorimeters where a few percent of the shower is sampled, the statistical term in Eq. (6.2) is typically ≈0.1.

For sampling the number of charges in a sampling calorimeter any method for measuring the amount of ionisation can be used. Sampling calorimeters have been built with scintillators, with gas ionisation chambers and with silicon detectors. A popular type of electromagnetic calorimeter uses liquid ionisation chambers for sampling the ionisation. The basic principle of operation of a liquid-filled ionisation chamber is the same as for a gas-filled ionisation chamber. The ionising charged particles produce electron-ion pairs in the liquid and the charges drift towards the electrodes under the influence of the applied electric field. In principle, many liquids could be used for this purpose, but in practice it turns out extremely difficult to obtain a liquid that is sufficiently pure to allow efficient charge collection. Liquefied noble gases, such as argon, krypton and xenon can more easily be purified than other liquids, because the chemical properties of such atoms are very different from the chemical properties of the impurities and because these gases are used at cryogenic temperatures, where most impurities just freeze out. Among the noble gases, argon has by far the lowest cost and is therefore the preferred choice. Electron drift velocities in liquid noble gases are a few 10⁵ cm/s at fields of interest, while positive ion velocities are only of the order of a few cm/s. Except if the detector were to be used at a rate of only a few Hz, the short signal integration time implies that only the electron signal will be seen.

As an example of a homogeneous electromagnetic calorimeter, I will briefly describe the electromagnetic calorimeter of the CMS detector. CMS is one of the very large detectors that were installed at the Large Hadron Collider of CERN in 2008. The main characteristics of the LHC accelerator were already presented in http://Sect. 3.5. Figure 6.22 shows a very schematic layout of the CMS detector. A detailed description of the CMS detector can be found in [8].

In the collision of high-energy protons, a large number of secondary particles is produced. The aim of the CMS detector is to observe as many of these particles as possible and determine their direction and their energy. The electromagnetic calorimeter of CMS is located inside a large cylindrical magnet just outside of the detector for charged particles (tracker). It is designed to measure the energy and the position of electrons, positrons and gamma rays. The layout of the device is schematically represented in Fig. 6.23. The electromagnetic calorimeter uses blocks of lead tungstate scintillator (PWO) 230 mm long and measuring 22 × 22 mm² at the front side and 26 × 26 cm² at the backside. The scintillator blocks in the endcaps are slightly larger. A length of 230 mm of PWO corresponds to 26 radiation lengths. A total of ≈80,000 such blocks of scintillator are arranged around the interaction point with the blocks always pointing with the long axis towards the interaction point. In fact, there is a small angle between the axis of the crystals and the line pointing towards the interaction point in order to prevent gamma rays from escaping detection by passing in the narrow gaps between adjacent crystals.

In CMS, PWO is chosen as a scintillator because of its short radiation length and short decay time. This scintillator has a rather low light yield, but at this high energy light yield is far less important than at lower energy. The scintillator blocks are long enough to fully contain the electromagnetic shower in the longitudinal direction, but the showers are wider than the blocks. Part of the shower will leak to the neighbouring blocks and it is necessary to sum the energy deposited in a 3 × 3 array of neighbouring blocks to get the correct value for total energy of the gamma ray. The spreading of the light over several blocks allows the determination the position of the gamma ray to a precision much better than the size of the blocks. In CMS, this accuracy is about 1 mm r.m.s. The light of the scintillator is read by avalanche photodiodes because the calorimeter is inside a strong magnetic field of 4 tesla, and this large field precludes the use of photomultiplier tubes. For the CMS electromagnetic calorimeter, the coefficients in the energy resolution formula (Eq. 6.2) are a = 3% and b = 0.5%.

Hadronic calorimeters. For detecting neutral hadrons one uses a device somewhat similar to the electromagnetic calorimeter just discussed. A hadron interacting in a block of material will undergo strong interactions with the nuclei in the material and in the collision produce a number of secondary hadrons, mainly protons, neutrons and π-mesons. Positively charged pions, negatively charged pions and neutral pions are produced roughly in equal numbers. The neutral pions decay after a few micrometer into two gamma rays. The other secondary hadrons will again interact, producing more protons, neutrons and π-mesons and so on. The phenomenon is similar to the electromagnetic avalanche induced by a high-energy gamma ray, with a few important differences, though.

For all heavy materials, the hadronic interaction length is much longer than the radiation length. The concept of hadronic interaction length was introduced in http://Sect. 2.5. For iron, copper and tungsten, the hadronic interaction length is 16.8, 15 and 9.6 cm, respectively, to be compared with 1.76, 1.43 and 0.35 cm, respectively, for the radiation length. To fully absorb most of the hadronic shower produced by a particle of 100 GeV, about 8–10 hadronic interaction lengths are needed. A hadronic calorimeter made entirely of inorganic scintillator such as PWO would need a ≈1.5 metre thick layer of scintillator and would be prohibitively expensive. A more cost-effective solution must be used and the hadron calorimeters are always sampling calorimeters with sheets of plastic scintillators as active material. To extract the light from the scintillator, wavelength shifting rods or wavelength shifting fibres are universally used. This readout method avoids the limitation imposed by the Liouville theorem as discussed in Sect. 6.2. The energy resolution that can be obtained with a hadronic calorimeter is typically given by

$$\frac{{\sigma \{ E\} }}{E} \approx \frac{{0.6}}{{\sqrt {E[{\rm{GeV}}]} }}$$

Notice that the energy resolution of a hadronic calorimeter is much worse than the energy resolution of an electromagnetic calorimeter. There are several reasons for this. First, a hadronic calorimeter is always a sampling calorimeter. A very important additional cause of degradation of the performance of a hadronic calorimeter has to do with the different response of the hadron calorimeter to the hadronic part of the shower and to the electromagnetic part of the shower. The reason for this difference is that of the order of 50% of the energy of the hadrons goes into breaking up the nuclei and into the energy of nuclear fragments. The energy used for breaking up the nuclei is lost, and the kinetic energy of the nuclear fragments is converted very inefficiently into scintillation light, such that this energy is also largely lost. The excited nuclei decay with a time constant that is large compared to the integration time of the signal, and this energy is therefore also lost. In the first interaction of the shower typically one third of the energy goes into the creation of neutral pions and these decay instantly into gamma rays and in this way give rise to electromagnetic showers. In all the subsequent hadronic interactions, additional neutral pions are produced, therefore the electromagnetic fraction increases with energy. This fraction varies from ≈30% at 10 GeV to ≈60% at 1 TeV. Moreover, this electromagnetic fraction is subject to large fluctuations and together with the different response of the calorimeter to the two components in the shower this degrades the energy resolution. This, in fact, is the main effect limiting the energy resolution of hadron calorimeters. A significant improvement in the resolution of hadronic calorimeters will only be possible with a much more sophisticated design that corrects for these effects.

Cosmic air showers. A somewhat different use of the scintillation effect is the observation of cosmic air showers. If a very high-energy cosmic ray enters the atmosphere, it will initiate an avalanche of secondary particles. These particles produce light by Cherenkov effect and by scintillation of the nitrogen in the air. For energies of ≈10¹⁴ eV and above the scintillation light produced in such air showers is sufficient to observe the light on a moonless night with a clear sky. A detector for high-energy cosmic air showers essentially consists of a parabolic mirror and a suitable photodetector. The optical quality of the mirror does not need to be comparable of what is needed for optical astronomy. The only function of the mirrors is to collect more light.

6.7 Applications of Scintillators in Medicine

Scintillators in radiology. Inorganic scintillators are also used extensively in X-ray imaging and in nuclear medicine. Imaging the inside of the human body with X-rays, called radiology, is the oldest medical imaging technique. X-ray imaging is based on the different absorption of X-rays in different body tissues. Figure 6.24 shows the linear attenuation coefficient in water and bone. The absorption in the soft tissues of the body is similar to the absorption in water.

We see that below 20 keV the mean free path of X-rays is less than 1 cm and therefore no useful images can be made with such X-rays, except when imaging small organs such as teeth. As the energy increases, the body becomes more transparent to X-rays, but the contrast also decreases. The useful energy range for medical X-ray imaging is therefore ≈20–80 keV.

In Fig. 6.24, we also show the linear attenuation coefficient for the inorganic scintillator CsI. It can be seen that in the region of interest, ≈150 μm of scintillator will stop about half of all X-rays.

Many years ago X-ray images were made using the direct interaction of X-rays in ordinary photographic emulsions, but the detection efficiency of the photographic film for X-rays is low and results in a correspondingly larger dose to the patient. Today, this method is still used in material testing where the dose is less important. It allows a better spatial resolution in the image than any other image recording method.

Until recently, most radiological imaging was done with the film-screen method. In this technique, a layer of scintillating powder, typically 300 μm thick, is applied on a plastic support. Such a layer of scintillator is usually called a phosphor. A photographic emulsion is applied against the phosphor screen. This photographic emulsion simply records the scintillation light produced by the X-rays in the phosphor screen. After development, the film contains the image. The scintillator materials used in this application are often different from the scintillators discussed previously since speed is not important here. A scintillator often used for this purpose is Gd₂O₂S:Tb and 10 photons/keV X-ray energy will reach the photographic emulsion. The film and screen assembly used in the film-screen method is illustrated in Fig. 6.25.

The film-screen method is more and more being replaced by a technique marketed under the name ‘computed radiography’. ‘Storage phosphor screen’ would be a more appropriate name. A storage phosphor screen looks similar to the screens used in the film screen method, but it uses a different type of phosphor that has the capability of ‘remembering’ the X-ray image. The physical principle behind the image storing property is explained in Fig. 6.26.

The most commonly used scintillator in storage phosphor screens is BaFBr doped with europium 2+ ions. In this scintillator, the Eu²⁺ ion has 4f and 5d energy levels in the band gap of the host material. It acts as luminescence centre and emits at 390 nm with a decay time of ≈1 μs. By suitable preparation of the material, it is possible to create many vacancies of the negative ion (fluor or bromine) in the BaFBr host lattice. Such vacancies act as electron traps and are called F-centres. The binding energy of the electrons in these traps is typically in the optical region; therefore, the presence of such traps will tend to colour the material. The name F-centre derives from ‘farbe-zentrum’ the German name for ‘colour centre’. This phenomenon causes many coloration effects in natural minerals.

In BaFBr, the binding energy of the electrons in the F-centre is ≈2 eV. If any X-ray interacts in the BaFBr:Eu²⁺, it will create a large number of electron–hole pairs. However, most of these electrons will never reach the luminescence centre because they are trapped in the F-centre. At room temperature electrons can remain trapped almost indefinitely. If one later illuminates the phosphor plate with photons of ≈2 eV (≈630 nm), the electrons will be liberated from the F-centres, reach the Eu²⁺ luminescence centres and emit scintillation light at 390 nm.

If a point on the surface of the storage phosphor screen is stimulated with light at 630 nm, the amount of light emitted at 390 nm will be proportional to the number of electrons trapped in F-centres at this point. This signal is proportional to the X-ray dose received at this point during the recording of the image.

The method to retrieve the stored image from a storage phosphor screen is illustrated in Fig. 6.27. A small light spot from a laser scans the surface of the X-ray storage phosphor image plate. An oscillating mirror causes the light spot to travel back and forth along a line. Optical fibres aligned along the line travelled by the light spot collect the photo-stimulated luminescence light emitted at 390 nm. These optical fibres guide the light to a photomultiplier tube. The stimulation light (630 nm) is stopped by means of an appropriate optical filter placed between the bundle of light guides and the photomultiplier. The scintillation light at 390 nm is not stopped by this filter and recorded by the photomultiplier tube. To scan the complete area of the plate, this plate is moving in a direction perpendicular to the laser line.

The main advantage of storage screens over the conventional film screen method is the larger dynamic range. In the film screen method, the image is recorded as variations in density (blackness), of the film. All irradiation levels above a certain value are black and can no longer be differentiated by the human eye, while all levels of irradiation below a certain level are seen as white and are also no longer differentiated. The dynamic range of this recording technique is limited to about a factor 100. With storage phosphor screens, the image is recorded electronically and a dynamic range of up to 10,000 is possible. When the image is printed on a film for inspection by a radiologist, the image processing software can adjust the density levels such that the information remains visible, also in the parts that would otherwise be too dark or too light.

It is expected that in the future the storage films will be replaced by a new technique called ‘digital radiography’ (DR). In DR, the X-ray image is recorded with the help of a phosphor layer in direct contact with a flat panel detector having a large number of small silicon photodetector pixels and with the circuitry allowing the readout of these pixels. The main difficulty in this technique is that for radiography it is necessary to have detectors that can record an image of 40 × 40 cm². The largest sizes of silicon monocrystals that are available have only 8 inch in diameter. The photodetectors pixels and readout circuitry must therefore be made in amorphous silicon. Amorphous silicon can be deposited by Chemical Vapour Deposition technique over large areas. This technique is aggressively being developed for the production of low-cost solar cells. Such amorphous silicon is less suitable for making electronic components than monocrystalline silicon, but the technology has now been improved to the point where suitable large panels with silicon photodetectors and the associated readout circuitry can be made.

One of the limitations of this technique, and of all other techniques using phosphor screens to convert the X-rays to light, is the spreading of the light in the phosphor layer. The light from an infinitely narrow X-ray beam will spread by diffusion in the phosphor layer and form a light spot with a diameter of the order of the thickness of the phosphor layer. It is therefore necessary to make a compromise between the detection efficiency and the spatial resolution. A peculiar property of CsI:Tl scintillator allows to overcome this limitation. Indeed CsI can be vapour deposited in a way as to form a layer of small microcolumns or needles. These needles behave like light guides channelling the light to the photodetector, and in this way strongly reduce the lateral spread of the light. Figure 6.28 shows micrographs of such a CsI layer.

An even more ambitious road towards DR is the so-called direct conversion X-ray imaging. In this approach, one is not using a phosphor for converting the X-ray energy to light, but directly records the ionisation left in some suitable material. Silicon cannot be used for this, because the stopping power is too low. The main difficulty is the fact that one needs to cover a surface of the order of 40 × 40 cm². With monocrystals such as Ga, this surface must be made from smaller detectors, and one has to deal with artefacts at the edges between the detectors. Selenium can be deposited as amorphous selenium over large surfaces and seems the most promising material to realise this kind of X-ray imaging detectors.

All presently used detectors in radiology integrate the signal because the event rate is too large to allow counting individual X-rays. However, counting individual X-rays would have the major advantage that it would be possible to select X-rays in certain energy windows. Developing systems that count individual X-rays and therefore would really deserve the name ‘digital’ are presently an active research field.

Scintillators in positron emission tomography. Another important medical application of scintillators is as gamma detectors in scintigraphy and in positron emission tomography (PET). Positron emission tomography is one of the powerful medical imaging techniques of nuclear medicine. In PET, a physiologically relevant compound is labelled with a positron-emitting isotope. The term ‘labelled’ means that a normally stable atom in the molecule is replaced by a radioactive isotope of the same element. The chemical properties of the labelled compound are identical to the properties of the natural one and this labelled compound will take part in all processes in the body exactly in the same way as the natural compound. At some point the radioactive isotope emits a positron and this positron has a kinetic energy of a few 100 keV. At this energy the range of the positron in the living tissue is usually less than 1 mm. After coming to rest, the positron annihilates into two nearly back-to-back gamma rays of 511 keV. The mean free path of gamma rays of 511 keV in the human body is about 10 cm. In many cases, the two gamma rays will leave the body without undergoing scattering, i.e. with their original direction unchanged. A PET scanner basically is a detector for gamma rays of 511 keV surrounding the patient. If two 511 keV gamma rays are detected at the same time, we assume that these come from the same annihilation event and we know that the annihilation and therefore the molecule containing the radioactive isotope was somewhere on the line joining the two detection points. From the observation of a large number of such annihilations it is possible to reconstruct the three-dimensional distribution in space of the annihilation events. That is the same as the three-dimensional distribution in space of the labelled molecules. PET is therefore a non-invasive technique that allows following the evolution of the labelled compound in the body. The value of PET lies in the very high sensitivity of this technique. Extremely small amounts of labelled compound are sufficient to obtain the desired information.

Modern PET scanners nearly all use scintillators in combination with photomultiplier tubes for the readout of the scintillation light. Table 6.4 lists some scintillators that are used in PET. The most important properties of a scintillator to be used in a PET scanner are that it must allow for a good time resolution, have a large stopping power and a good energy resolution. The time resolution is important because this ensures that the two gamma rays really come from the same annihilation event rather than from two unrelated annihilation events. The stopping power is important because this ensures a large detection efficiency and therefore that a large fraction of the annihilation events will be observed. The stopping power depends on the mean free path for gamma rays of 511 keV in the scintillator material and on the photofraction. The photofraction is the ratio of the cross section for photoelectric absorption over the total gamma interaction cross section. The mean free path of the gamma rays of 511 keV in tissue is about 10 cm. The Compton scattering cross section in living tissue is much larger than the photoelectric cross section. Therefore, a very large fraction of the positron annihilations are followed by the scattering of one, or both, of the 511 keV gamma rays in the body of the patient. If such events are detected, but not recognised as scatter events, the corresponding erroneous information is included in the image. Energy resolution of the scintillator is important because it allows rejecting such scatter events.

Table 6.4 Scintillators for positron emission tomography

Full size table

In its simplest geometry a PET scanner consists of rings of scintillator blocks each equipped with its photodetector surrounding the patient, as shown in Fig. 6.29. If one of the 511 keV gamma rays interacts in one of the scintillator blocks, the position accuracy on this interaction point is equal to the size of the block. One therefore is lead to use a large number of small scintillation blocks, each equipped with its own photodetector. Some PET systems indeed use this scheme. However, to reduce the cost, most commercial PET scanners use a system where one uses less photodetectors than crystals. A possible realisation of this detection method is illustrated in Fig. 6.30. In this design, groves are cut in a large piece of scintillator such that it is divided in 64 individual crystals and this block of scintillator is in contact with only four photomultiplier tubes. Notice that the groves cut in the scintillator do not go all the way to the bottom of the block. In this way, the light can spread over the four photomultiplier tubes with the distribution of the light depending on the position of the crystal where the gamma ray interacted. From the values for the ratios of the PM signal amplitudes, X and Y defined in Fig. 6.30, the crystal where the gamma ray interacted, can be identified. Notice that relation between values of (X-Y) and the crystal is not linear. The mapping between the values of (X-Y) and the crystal where the gamma ray interacted must be determined experimentally.

The most commonly used positron-emitting isotopes in PET are listed in Table 6.5. It can be seen that all these isotopes have a short lifetime. This is a desirable property, because in this way the activity naturally disappears from the body of the patient after the examination. However, because of this short lifetime, it is necessary to produce the isotope and incorporate it into a molecule of interest in a very short time, just before the examination. For carbon, nitrogen and oxygen, a cyclotron and chemical synthesis equipment at the hospital is necessary. For ¹⁸F a site within a few hours driving of the hospital is possible. Figure 6.31 shows an example of a commercial PET scanner.

Table 6.5 Most commonly used isotopes in PET

Full size table

Figure 6.32 illustrates the power of PET by showing PET scans of the brain for normal healthy volunteers. These subjects were injected with fluoro-desoxy-glucose (FDG). This is glucose where one oxygen atom was replaced by ¹⁸F. The compound is metabolically very similar to normal glucose. The glucose concentrates in areas where there is increased metabolic activity in the brain and this in turn shows up as an increased amount of radioactivity. The right-hand side of the figure shows four scans where the subject was given different kinds of auditory stimulation. With only verbal stimuli (a Sherlock Holmes story), the left-hand side of the brain appears more active; with non-verbal stimuli (a Brandenburg concerto) there is more activity in the right-hand side.

In the presently used commercial PET scanners the accuracy on the time difference between the two gamma rays is a few nanoseconds. This is sufficient for random coincidence rejection. However, if this timing accuracy could be improved to a value significantly better than 1 ns, it would be possible to use the timing information to localise the annihilation point along the line of flight of the two gamma rays. This information could be used to reduce the statistical noise in the image. Such systems are presently actively being developed.

6.8 Exercises

1.
Assume that a detector for gamma rays consisting of LSO scintillator and a photomultiplier tube. The signal is taken from the anode of the PMT with a 50 Ω coax cable and brought to an oscilloscope. The input impedance of the oscilloscope is 50 Ω and the gain of the PMT is 10⁵. What will be the signal amplitude when observing gamma rays of 1 MeV? Note: assume a light collection efficiency 50% and a photocathode quantum efficiency of 25%.
2.
Consider a source emitting gamma rays of 511 keV. Calculate the energy where you expect the backscatter peak in the pulse height spectrum.
3.
Consider a CsI:Tl scintillator. What fraction of the energy lost due to the interactions with the electrons in the material is converted to scintillation light?
4.
Consider a PIN diode with a quantum efficiency of Eff = 60%. Assume that it is exposed to a light flux of 1 μW at a wavelength of 565 nm. What will be the photocurrent?
5.
Consider a PET scanner with a solid angle covering around it centre point of Ω = 10%. Assume that the detection efficiency for a gamma ray of 511 keV and within the solid angle is Eff = 20%. Assume that you place a point source in its centre with an activity of 1 mCi. What will be the single count rate and the coincidence count rate?
6.
In several photodetectors, the charge multiplication gives rise to an exponential pulse height distribution for single primary charges. Show that in this case the excess noise factor equals 2.

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Fak. Wetenschappen, Dept. Natuurkunde (DNTK), Vrije Universiteit Brussel, Pleinlaan 2, 1050, Bruxelles, Belgium
Prof. Stefaan Tavernier

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Tavernier, S. (2009). Detectors Based on Scintillation. In: Experimental Techniques in Nuclear and Particle Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00829-0_6

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DOI: https://doi.org/10.1007/978-3-642-00829-0_6
Published: 14 September 2009
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Detectors Based on Scintillation

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6.1 Introduction to Scintillators

6.2 Organic Scintillators

6.3 Inorganic Scintillators

6.4 Photodetectors

6.5 Using Scintillators in the Nuclear Energy Range

6.6 Applications of Scintillators in High-Energy Physics

6.7 Applications of Scintillators in Medicine

6.8 Exercises

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