Characterization of a Germanium Detector by Means of Experimental Measurements and GEANT4 Monte Carlo Simulations

A HPGe detector was modelled and characterized by means of experimental measurements and Monte Carlo simulations. The simulation based on Monte Carlo GEANT4 was used to characterize the potential dead layer/inactive materials and Full Energy Peak Efficiency (FEPE). The calibration of FEPE for the HPGe detector was conducted in the γ-ray energy range from 88 keV to 1332 keV, using eight standard point sources of gamma radiation: 137Cs, 133Ba, 109Cd, 65Zn, 60Co, 57Co, 54Mn, and 22Na. The efficiency dependence curves were obtained by changing the source to detector distance from 8 cm to 12 cm. a remarkable similarity in FEPE for low energy measurements ranging from 88 keV to 122 keV was obtained between the simulation results and the experimental measurements.


Introduction
Nuclear applications have made significant advancements in various areas, including nuclear medicine, beam radiotherapy, and spectroscopy [1]- [4].Gamma spectroscopy is an analytical technique used to identify radionuclides by analyzing the energy spectrum of emitted gamma radiation [5], [6].There are three major kinds of detectors utilized for measuring gamma radiation: gas-filled, scintillation, and semiconductor detectors.The High Purity Germanium (HPGe) detector is among the most commonly employed semiconductor materials for radiation measurements [5], [7].It consists of cylindrical crystals housed within a vacuum-tight cryostat.Unlike other detectors, semiconductor detectors like HPGe provide high resolution, making them reliable in accurately distinguishing the energy levels of radiation.Currently, gamma spectroscopy finds wide application in various scientific fields, such as studying soil hydrodynamics and air pollution.
With the advancement of computer technology, the program of Monte Carlo, such as GEANT4, has been created for simulation of radiation-matter interactions.GEANT4 is a versatile toolkit that includes tracking, geometry, physics models, and scoring functionalities [8].Its physics processes cover a wide range of applications, from photon optics to high level of energy particles in the Large Hadron Collider (LHC) [9].GEANT4 simulations also contribute significantly to advancing the understanding of detectors.By modeling various parameters like detector materials, sizes, and shapes, we can study the detector's efficiency, and energy response under different experimental conditions.
Utilizing GEANT4 simulation allowed us to determine radiation characteristics and detector responses that may not be easily achievable through experimental methods alone.In this study, we aim to use GEANT4 to assess the efficiency of full-energy peak of the HPGe detector at different distances and compare it with experimental measurements.Additionally, the simulation will be utilized to determine the the dead layer thickness of the HPGe material, which can impact low energy gamma measurements.

Efficiency Calculation
The efficiency of a gamma detector depends on several factors, including radiation energy, detector volume, direction of incident radiation, and distance between source and detector [5].Generally, the detector intrinsic efficiency is the comparison of recorded pulses to the amount of gamma rays that reach the detector, while absolute efficiency is the ratio of recorded pulses to the amount of gamma emission of the source in all directions.In most cases, intrinsic efficiency is considered constant for a given detector and energy.The efficiency equation can be described as follows:

𝐺 = 𝛺 4𝜋
(2) The interval time between the manufacture time and the measurement time  : Ratio of branching of the source characteristic gamma-ray Full Energy Peak Efficiency (FEPE) is obtained by calculating the ratio of gamma-ray detections recorded at the Full Energy Peak (FEP) to the amount of incident gamma-ray photons entering the detector.The FEPE was calculated as [10], Where: : the FEPE   : the net area counts of the peak  : the source activity at the time of measurement (Bq)  : the emission intensity of gamma-ray  : the duration of measurement (sec)

Experimental Set Up
For this work, we used an ORTEC High Purity Germanium (HPGe) detector model GEM-S5020 with a cryostat CFG-SV-70, serial number 57-P51571.Multichannel Analyzer (MCA) ORTEC model DSPEC-LF SN 17213942 with 4095 channels setting was used for amplitude analysis.Background measurements were taken without any sources and subtracted from the source measurements to obtain the actual source measurement.Gamma-ray reference standard sources from Oak-Ridge, TN 37830 USA model RSS 8-UN with a plastic disc shape were used.Table 1 shows the radionuclides used, including 137 Cs, 133 Ba, 109 Cd, 65 Zn, 60 Co, 57 Co, 54 Mn, 22 Na, covering an energy range of approximately 80 keV to 1333 keV.The energies of gamma-ray and emission intensities were referenced from the database Laboratoire National Henri Becquerel (LnHB) [11].
The standard sources were positioned at certain distances of 8 cm, 10 cm, and 12 cm from the cap of detector.Each measurement lasted one hour.An energy calibration was performed to adjust channels to energies using sources with known emission energy as references.The gamma souces used for this study were described in Table 1.

Simulation
In this work, we utilized GEANT4 version 10.05.p01 to simulate the HPGe detector response.The GEANT4 simulation uses C++ programming language with three basic defined classes: detector construction, physics list, and primary generator.User action classes such as Run Action, Event Action, and Stepping Action were also used to obtain necessary information of the simulation.The simulation employed modular physics lists G4Radioactivedecay and G4EmStandardPhysics to simulate physical processes.General Particle Source was used to implement the point source of radioactivity through a class of primary generator, enabling particle generation using macro commands.
The interaction of gammas with material, involving photoelectric effect, Compton scattering, and electron positron pair production, was determined to simulate the process of physical interaction.GEANT4 tracked particle movements, energy deposition, and generation of secondary particles when particles interacted with the detector material.Energy deposition information represented the signal received by the actual detector.Angular distribution of isotropic was used to handle the directions of particles coming from the source.A visualization of the GEANT4 simulation is depicted in Figure 1.The Stepping Action class was used to record deposited energy in the specified material at each step.The sum of deposited energy in one event was calculated using the class of Event Action.The class of Run Action plotted a spectrum with deposited energy and number of counts.Spectra of simulation were scaled to the activity of each source used in each experimental measurement.
Knowledge of detector geometry was essential for subsequent calculations.To verify the geometric dimension and discover unidentified details of the detector structure, X-ray imaging was used, as shown in Figure 2. Through the class of detector construction, the geometric dimension was implemented in the simulation.
We used the GEANT4 simulation to determine if there was a dead layer in the HPGe detector material.The dead layer is significant in low energy gamma measurements since most gamma energies can be absorbed in the outer layer of the detector, which is the part that first interacts with gamma radiation.The simulation for estimating the dead layer involved creating a dead layer with a thickness varying from 0 mm to 1 mm on the outer layer of the detector material.After determining the estimated dead layer thickness, we simulated GEANT4 for the detector geometry equipped with the estimated dead layer, as shown in Figure 3.A radioactive source was simulated and placed at specified distances of 8 cm, 10 cm, and 12 cm from the top of the detector cover, corresponding to the experimental measurements.

Energy Calibration
One crucial step in gamma spectroscopy measurements is the calibration of gamma ray energy.We performed the calibration of the HPGe detector using standard radionuclide sources, as shown in Table 1.The energy calibration curve is depicted in Figure 4, which establishes the relationship between energy and channel.

Efficiency by Experimental Measurement
For efficiency calculation of the HPGe detector, we used experimental data from a standard source with known energies.The efficiency graph, shown in Figure 5, plots the FEPE as a function of energy of emitted gamma ray from the used radionuclide source.Different distances are taken into account, and it can be observed that as the distance increases, the FEPE curves decrease due to lower detection probability.These findings align with previous studies [10], [20], [21].

Efficiency by Simulation
On the other hand, the detector efficiency resulted from the Monte Carlo -GEANT4 simulation was performed by first determining the dead layer in the HPGe detector material.A dead layer occurs due to surface damage, where a certain thickness of material does not function as a radiation detector.The estimated dead layer thickness obtained is 0.7 mm, as shown in Table 2 and Figure 6.Using the GEANT4 simulation, we obtained the detector efficiency, as displayed in Figure 7.The simulation indicates that the efficiency data (FEPE) remains relatively consistent in the low energy range of 88 keV -122 keV.Above this energy, the simulation data exhibits higher efficiency values compared to the experimental measurement.This can be attributed to various factors, including losses due to electronic processing instruments.Additionally, the simulation only considers Germanium (Ge) material, while actual measurements involve an aluminum protective layer, a window cover layer, and other components.Furthermore, shielding and the precise measurement of the depth of electrical contact on the detector are not calculated in the GEANT4 simulation.Notwithstanding these differences, the measurement and simulation results exhibit similar patterns in their spectra.

Conclusion
The Monte Carlo -GEANT4 simulation has successfully characterized the HPGe ORTEC GEM-S5020 detector based on efficiency values.The efficiency of various radionuclide sources, such as Cs-137, Co-60, Co-57, Mn-54, Cd-109, Ba-133, Zn-65, and Na-22, was simulated according to the results of experimental measurements at distances of 8 cm, 10 cm, and 12 cm.Efficiency measurements provide valuable insights into the detector's ability to detect the gamma radiation interaction with material based on its detector geometry (volume) and the radiation source distance.The experimental measurements and the GEANT4 simulations demonstrated a remarkable similarity in Full Energy Peak Efficiency (FEPE) for low energy measurements ranging from 88 keV to 122 keV.Additionally, the simulation served as a tool to identify the presence of a dead layer with a certain thickness.This simulation lays the foundation for future works aimed at developing more accurate applications, particularly for irregular volumes.

Figure 1 .
Figure 1.GEANT4 simulation of 500 events of gamma radiation, showing gamma rays in green color.

Figure 2 .
Figure 2. The result of X-ray imaging of the Germanium detector.

Figure 3 .
Figure 3. Illustration of dead layer in the HPGe detector.

Figure 4 .
Figure 4. Curve of energy calibration of the HPGe detector.

Figure 5 .
Figure 5. Efficiency of full energy peak of the Germanium detector by experimental measurements at three specified distances.

Figure 6 .
Figure 6.Estimation of dead layer thickness

Figure 7 .
Figure 7.The efficiency of full energy peak of the Germanium detector by GEANT4 simulation at three specified distances.

Table 1 .
Information of the Gamma-Ray Sources utilized in the measurement.

Table 2 .
Result of dead layer estimation