**3. Technology, material, geometry, and performance of HPGe gamma-ray detectors**

Focusing on photon energy resolution criterion, HPGe still provides one of the best results. With a good quality material, the energy resolution is very close to the Fano limit [21, 22]. To obtain this, the readout electronics must be low noise. Historically, the front-end transistor was a JFET cooled to the temperature of the detector (77 K, liquid nitrogen temperature) [9, 23]. This reduced the energy resolution to less than 1 keV for 1 MeV photons. It would now be possible to use very low-noise room temperature CMOS μ electronic circuits [24] to match the low-noise specifications required for γ-ray spectrometry. The front-end readout electronics for these detectors is usually a charge-sensitive device, which is necessary for spectrometric measurements for which the generated charge is proportional to the energy deposited in the detectors. These CSA (charge-sensitive amplifiers) have an integrating pole followed by filtering stage (usually based on derivation-integration schemes for optimal filtering). This is done by a so-called shaper in order to optimize the signal/noise ratio and to reduce event pile up through fast operation. This channel is however slow (a few μs), so it may be supplemented by a fast currentsensitive channel, for coincidence, veto (anticoincidence) or timing purposes.

Because a typical size of a HPGe detector is not optimum for timing measurements, the resolution obtained with a CFD (Constant Fraction Discriminator) is close to 400 ps [25], which is a high value compared with other fast detectors (PM or APD). In fact, this value was measured for a planar germanium detector of a volume of a few cubic centimeters, and it would be even higher for standard coaxial HPGe detectors.

#### **3.1 Starting material**

In order to reach optimum resolution of semiconductor detectors, the crystal defect density should be decreased, in particular for those that are electrically active. This has become possible when defect and impurity control in the process of crystal growth has reached a sufficient level of reliability. In addition to point defects and impurities, dislocations play a major role as they behave like a sink for impurities [1, 9, 12]. They can currently be revealed by chemical crystal etching. The pits observed using optical microscopes are related to dislocations, which allows determining the etch-pit density. These dislocations induce a broad DLTS signal in n-type high purity material [3]. These are moderately deep donor states

*Use of Gamma Radiation Techniques in Peaceful Applications*

n = Z × <sup>ρ</sup>\_\_

become dominant. In the intermediate energy range, Compton effect dominates, hence the absorption of the photon becomes a multistep process with Compton electrons (<1 MeV) being absorbed after traveling a short distance, while Compton photons are created and absorbed in subsequent steps. One should note that some photons can escape the detecting medium and consequently do not contribute to a full-energy peak. These induce a signal background (Compton background) that is particularly large in low volume detectors. Techniques exist to mitigate this drawback using a secondary detector surrounding the primary one. This secondary detector is referred to as a Compton shield [17]. This anticoincidence scheme with these two detectors eliminates the un-absorbed photon events. This shows that for high detection efficiency, a relatively large volume of the detector is necessary for γ-ray spectroscopy. This is much different for γ-ray tracking is, when detector granularity is required. Time coincidence between events in neighboring detectors is the way to proceed to identify the particles. The probability of interaction with the electrons of the solid through Compton effect increases when the density of electrons n increases, being roughly proportional to it. If ρ is the mass density of the solid and A the mass number, the average electron density is proportional to ρ/A, which is the atomic density, multiplied by Z, the number of electrons per atom [16].

This shows that as the Z/A ratio is constant, it is reasonable to use very dense media. Hence, it proves that germanium is a better choice than silicon for this purpose, as would be CdTe or GaAs, if the defect concentration could be reduced to an acceptable level. We will discuss the problem of defects in the following paragraph. Present-day experiments benefit from simulation codes such as GEANT4 or others [18] for their design. HPGe γ-ray detectors are no exception. The other process that becomes important at higher photon energy is the electron-positron pair creation, which may appear at energies above 1022 keV. This kind of interaction is related to γ-nuclear coupling, where the γ-photon interacts with the nucleus resulting in a creation of a e−/e+ pair with a total kinetic energy equal to Ek = Eγ − 1.022 MeV (Ek is the kinetic energy of the e = e− pair, and Eγ is the energy of the incident gamma photon). Subsequently, the positron may annihilate with an electron in the material, which leads to the production of two γ-rays of 511 keV that may (but not have to) be absorbed in the detecting material through Compton or photoelectric effect processes. As one or both 511-keV photons may escape from the detector with no energy deposition, satellite peaks appear in the measured energy spectrum, called escape peaks and separated from the total absorption peak by a 511 keV energy difference (or 1022 keV for double escape). Again, some discrimination is possible to avoid this effect, although one should be interested in visualizing the different peaks to investigate how the incident particle has interacted with the detector medium. The e + e- pair creation is most important at energies above 10 MeV [16], which shows that HPGe is not a good choice for very energetic photons such as cosmic radiation or those generated by high-energy accelerators (~1 GeV) since huge monocrystals would be required to provide a significant detection efficiency. This is hardly possible, with the largest commercially available HPGe crystals weighing 1–2 kg (larger crystals have been grown for specific applications) and having a diameter of a few centimeters. If we consider photofission [19], it has been reported that it occurs in natural lead for 10 MeV range photons. However, as the dependence on the fissility parameter is sublinear in logarithmic scale, it should be considered as being very weak for a germanium nucleus. Let us compare with lead, the fissility parameters read:

<sup>A</sup> (3)

**70**

Z2

⁄

<sup>A</sup> = 32.5 for Pb <sup>Z</sup><sup>2</sup>

⁄

<sup>A</sup> = 14 for Ge (4)

with carrier capture cross section of the order of 10<sup>−</sup>13 cm−<sup>2</sup> or more. The peak is at 50–60 K for a large emission rate window (56 s<sup>−</sup><sup>1</sup> ) [3]. This means that at 77 K, the emission rate is large enough to have no marked effect on carrier trapping as the electrons are released with a time constant that is low compared with the drift time. With σn higher than 10<sup>−</sup>13 cm−<sup>2</sup> , which is the case with a filling pulse shorter than 1 ms in duration (with a 1010 cm−<sup>3</sup> carrier concentration, and 106 cm s<sup>−</sup><sup>1</sup> of thermal velocity at 50 K, in our DLTS measurements), the emission rate at 77 K exceeds the capture rate for an activation energy of 100 meV. The other fact is that the DLTS signal fades away above 65 K, so the contribution of the dislocation band should be low as long as the concentration remains at a reasonable level. This gives a rule of thumb [2] for the dislocation density that should not exceed 104 cm<sup>−</sup><sup>2</sup> and should be above 102 cm<sup>−</sup><sup>2</sup> for detector-grade material, at least for the material used in the 1980s–1990s. If the dislocation density is too low, the deep impurities such as those related with copper (substitutional or bound with hydrogen) will be higher, as they cannot precipitate onto the dislocation lines and have a higher density than isolated impurities. They give rise to deep hole traps that affect greatly the hole transport even at 77 K. These traps have an activation energy higher than 0.160 eV and capture cross sections above 10<sup>−</sup>13 cm−<sup>2</sup> , (similar to coulombic/attractive centers) with concentrations reaching 109 cm<sup>−</sup><sup>3</sup> .
