Characterization of Germanium Detectors for the First Underground Laboratory in Mexico

This article reports the characterization of two High Purity Germanium detectors performed by extracting and comparing their efficiencies using experimental data and Monte Carlo simulations. The efficiencies were calculated for pointlike $\gamma$-ray sources as well as for extended calibration sources. Characteristics of the detectors such as energy linearity, energy resolution, and full energy peak efficiencies are reported from measurements performed on surface laboratories. The detectors will be deployed in a $\gamma$-ray assay facility that will be located in the first underground laboratory in Mexico, Laboratorio Subterr\'aneo de Mineral del Chico (LABChico), in the Comarca Minera UNESCO Global Geopark


Introduction
LABChico (Laboratorio Subterráneo de Mineral del Chico) will be an underground laboratory in a decommissioned silver mine from colonial times, at the Comarca Minera UNESCO Global Geopark [1], in the Mexican state of Hidalgo. The LABChico research program will focus on applications for environmental radiation monitoring, γ-ray assay and screening, as well as prototype design for detectors in underground astroparticle physics experiments, see [2][3][4][5][6][7] for some examples. This program requires a variety of state-of-the-art detector technologies which operate in a low radioactivity background environment, such as High Purity Germanium detectors. LABChico will be located at a depth of approximately 100 m of rock, 300 m.w.e. (meter water equivalent) overburden. The background cosmic ray flux is attenuated, from 1 muon/cm 2 /minute to approximately 1 muon/cm 2 /hour.
LABChico will consist of a 125 m 3 cavern with a usable surface area of 37 m 2 (including a platform), as well as a user/visitor center and storage facility outside the mine. The infrastructure will include ventilation and air conditioning (HVAC), electrical power, compressed air and networking. This work reports the characterization of two High Purity Germanium detectors that will be part of the LABChico underground facility.
This report is organized as follows. In section 2 the detectors characterization with radioactive sources is presented; energy calibration and resolution are reported in sections 2.1 and 2.2 respectively. The efficiency measurement is described in section 2.3. The simulation of the germanium detectors used in the efficiency measurement is described in section 3. The validation with extended sources is described in section 4.

Germanium detector characterization
The LABChico assay facility will initially consist of one High Purity Germanium detector manufactured by ORTEC, enclosed by a 5 inch thick lead shield. The detector has been characterized, for this work, at the Instituto de Ciencias Nucleares (ICN), Universidad Nacional Autónoma de México (UNAM) in Mexico City. This detector will be hereafter referred to as ICN-HPGe, see figure 1. The physics research and assay program will be complemented with a Broad Energy Germanium detector, located at the Instituto de Física (IF), also at UNAM in Mexico City, manufactured by Canberra. This detector will be hereafter referred to as IF-BEGe, see figure 2. Both laboratories are on surface (Mexico City altitude 2,250 meters above mean sea level).
Both detectors are cooled down using liquid nitrogen, in a 30 l cryogenic storage dewar. The ICN-HPGe has an operational bias of -3200 V, with a p-type structure and a coaxial closed vertical geometry. The data acquisition system (DAQ) consists of a PX5-HPGe multichannel analyzer (MCA) and the digital pulse processor (DPP) software analyzer provided by Amptek [8].
The dimensions of the internal components of the ICN-HPGe detector were estimated from X-ray images and by measuring the external parts of the device (see figure 1). The identified components included in the simulations (see figure 7, section 3) are: 1. Cryostat: an aluminium cylinder of 34.0 mm radius, 142.0 mm height and 500 µm thickness.
It contains the germanium crystal, contacts and endcap.
2. Outer contact: lithium cylinder of 700 µm thickness, surrounding the germanium crystal. 3. Dead layer: this is the part of the germanium crystal that is not sensitive to the incoming γ-rays. Its thickness was determined using Monte Carlo simulations as described in section 3.
4. Germanium crystal: a cylinder of 25.5 mm radius and 54.0 mm height with a cylindrical hole in the middle for the inner contact.
5. Endcap: made of carbon fiber with a 1.0 mm width aluminium window to allow low energy photons to interact with the sensitive crystal.
6. Thermal strap: an aluminum disc of 120 mm radius.
7. Electronics chamber: an aluminum cylinder of 39.0 mm radius, 70.0 mm height and 500 µm width that contains the preamplifier electronics.
8. Inner contact: a 0.3 µm inner contact of boron implanted ions.
9. Cold finger: an aluminum cylinder of 7.50 mm radius.
The IF-BEGe is a Canberra model BE2820 [9] with planar horizontal crystal configuration, 30 mm radius and 20 mm height, an operational bias of +3000 V, a DAQ consisting of a Pocket MCA 8000 A and the ADMCA software also provided by Amptek [8], see figure 2.
For the IF-BEGe detector the dimensions were obtained from the technical sheet provided by the manufacturer and also measuring the external parts of the device (see figure 2). The components identified and later included in the simulations (see figure 8, section 3) are: The main difference between the ICN-HPGe and the IF-BEGe detectors is the geometry of the germanium crystals. The ICN-HPGe has a bulletized coaxial crystal, that is, a crystal in which the corners facing the front of the detector have been rounded to avoid charge collection in regions where the electric field is weak [10]. The IF-BEGe detector has a planar crystal in which the applied electric field is more uniform than in a coaxial crystal. These differences have an effect in the charge collection produced by γ-ray interactions which become visible in the detector response.

Energy linearity
A set of pointlike radioactive sources, provided by Spectrum Techniques [11], described in Each source was deployed individually, at a distance of 25 cm from the detector endcap along its symmetry axis. The measurements with the ICN-HPGe detector were performed with the source and the detector enclosed by the lead shield, whereas the measurements with the IF-BEGe detector were performed without shield. A spectrum was acquired for each source; an example of the 137 Cs Right panel is a zoom around the peak corresponding to the 137 Cs photopeak, the red line is the fitted Gaussian function, the black line is the order one polynomial and the green line shows the fitted function composed by the sum of both, the fit is performed in a six sigma range about the photopeak mean.
spectrum is shown in figure 3, left panel. For each spectrum, the photopeak was fitted to a Gaussian plus a polynomial order one function using ROOT analysis tools [12]. The Gaussian mean fit parameter is the channel value associated to the γ-ray energy and its sigma is related to the detector energy resolution presented in section 2.2, see figure 3, right panel. The integral of the fitted linear function background model is subtracted from the total number of counts in a six sigma range about the mean. From this exercise with each spectrum the linear distribution of γ-ray energy vs. channel is obtained. The fit parameters of the energy response distributions shown in figure 4, are listed in table 21.
For the IF-BEGe detector, an extra two natural background radiation points ( 40 K 1.46 MeV and 214 Bi 1.76 MeV) are present in the spectrum and were included for the energy calibration, also 208 Tl peak is present at 2.6 MeV; these can be seen in the left panel of figure 3. Table 2. Fit parameters for the detector calibrations in figure 4, energy E as a function of the associated

Energy Resolution
After the energy scale calibration, the spectrum is fitted to a Gaussian function plus an order one polynomial with negative slope. The full width at half maximum (FWHM) is given as FW H M = 1For the IF-BEGe detector, if the b parameter is fixed to zero there is no significant change in the slope parameter m.
is the Gaussian fit parameter to each photopeak. The detector energy resolution is defined as the ratio of the FWHM to the true gamma peak energy, R = FW H M/E, the uncertainty in R is obtained from the uncertainty in σ and E, which are obtained from the fit2. This distribution is shown in figure 5 for both detectors, fitted to an empirical three parameter inverse square root function [13]: the best-fit values to the fitted parameters P 0 , P 1 and P 2 , in [keV], are listed in table 3.

Efficiency
Absolute efficiency, also known as full energy peak efficiency, is defined as the ratio of the number of counts detected in a peak to the total number emitted by the source, 2The errors in σ and E were augmented by a factor χ 2 /n.d.f. given by the fit to account for non-Gaussianities in the measured photopeaks when this number was greater than one, for χ 2 /n.d.f. smaller than one, this correction was not applied.

ICN-HPGe
IF-BEGe ]. The top panel shows the resolution curve vs. energy for the ICN-HPGe detector, and bottom panel the resolution curve for the IF-BEGe detector. The ICN-HPGe shows a better resolution performance compared to that of the IF-BEGe, which does not meet the expected resolution performance from factory settings [9], having almost twice the expected FWHM. The ICN-HPGe shows an energy resolution at 1.3 MeV compatible with values reported by ORTEC [14] for similar detectors. Fit parameters can be found in table 3 for both detectors. where N F E P is the full energy peak count rate in counts per second, P γ 3 is the emission probability of the γ-ray being measured, and N T OT is the total number of γ-rays emitted at the specific energy, which was corrected for decay from the date of preparation, see table 1.
The total number of counts in each full energy peak has been computed by integrating the fitted function in a standard interval of six times the standard deviation (see right panel of figure 3), which is symmetric about the mean of each photopeak. Counts below the straight line, used to fit The number of emitted γ-rays for each source is determined using the radioactive decay law and the age of the source. The half-life source values are presented in table 1 and the branching ratios for each γ-ray were taken from the National Laboratory Henri Becquerel decay tables [15]. Figure 6 shows the efficiency measurements for all photopeak energies at a distance of 25 cm. For the ICN-HPGe detector the expected behavior was observed: a fast rise of the efficiency from low energies up to a maximum expected around 100 keV, between the 109 Cd and 57 Co γ-rays, and then a slower steady decrease towards high energies, which is consistent with similar detectors by ORTEC [16] 4. Uncertainties in figure 6 are assessed assuming uncorrelated errors from branching ratios, half-lives of the isotopes [15], number of counts in the photopeak (statistical) and source activities (20 %).
Broad Energy Germanium detectors have a typical relative efficiency that can range from 9 % to up to 50 % depending on crystal volume and front face area [9]. For the IF-BEGe detector, model BE2820, a 13 % relative efficiency at 1332 keV from 60 Co is reported by Canberra [9]. For historical 4Due to a lack of documentation for the ICN-HPGe detector, a comparison of relative efficiency values with manufacturer specifications is not possible reasons, relative detection efficiency of germanium detectors is defined at 1.33 MeV relative to the absolute efficiency of a standard NaI(Tl) scintillator, this standard is a crystal of 3 in diameter and 3 in long using a 60 Co source placed 25 cm from the endcap face which value is 1.2×10 −3 [10]. The germanium detector full energy peak efficiency measured in this conditions divided by 1.2×10 −3 is the relative efficiency specification of germanium detectors. The 13 % relative efficiency value reported for the IF-BEGe detector is equivalent to a full energy peak efficiency of 0.0156 %, and the measured value, (0.0117 ± 0.0033) %, differs from the Canberra reported value by 25 %.

Monte Carlo simulations
Monte Carlo simulations for both detectors were performed using the simulation toolkit GEANT4 [17], 10.01.p03 version. The simulations included all the geometric elements that affect the propagation of γ-rays between the source and the germanium crystal.

ICN-HPGe
For the ICN-HPGe detector, the components listed in section 2 were included in the simulations (see figure 7). The preamplifier electronics (inside the electronics chamber) was not simulated.
There was no information available about the dead layer thickness surrounding the active volume of the germanium crystal. The X-ray images did not provide information about this parameter either. Dead layer thicknesses of the order of 0.75 mm have been measured for a similar coaxial vertical germanium detectors manufactured by ORTEC by bombarding its crystal with a collimated γ-ray source [18]. Having similar dimensions, the ICN-HPGe detector crystal was expected to have a dead layer of around the same order. Monte Carlo simulations with varying dead layer thicknesses were performed to estimate this parameter by comparing the measured and simulated pointlike source photopeak efficiencies, a best match was found at a dead layer thickness of 0.65 mm.

IF-BEGe
The IF-BEGe detector was simulated including the components and dimensions listed in section 2 (see figure 8). The dead layer thickness of the germanium crystal was modeled as 0.05 mm on the front, 1.45 mm on the sides and 2.8 mm on the back, after the study described in the following section.
A dead layer on the front side of the germanium crystal of 0.3 µm and 500 µm on the sides is reported by Canberra in the technical sheet of the IF-BEGe detector. These settings were used in the simulations as a first approach, pointlike γ-ray sources located 25 cm from the detector cryostat window were simulated. The efficiencies for these simulated sources were calculated similarly to those in section 2.3. A disagreement greater than 30 % was found when comparing the efficiencies obtained in the simulation with the experimental ones. Increasing the dead layer on the front side reported by the Canberra technical sheet up to two orders of magnitude was not sufficient to find an agreement between experimental data and the Monte Carlo simulations.
The discrepancy between data and simulated efficiencies could be explained if the crystal active volume had a major alteration with respect to that reported in the technical sheet. In order to explore this possibility, a crystal scan was performed following a similar method as in [19,20].
For the scan, a pointlike γ-ray source ( 109 Cd) was fixed on top of a mechanical translation stage, in order to move it in a plane parallel and 4 cm away from the frontal face of the germanium crystal. The length of the mechanical translation stage was such that the scan was performed along the diameter of the germanium crystal as shown in figure 9.
A lead collimator with an aperture of 4 mm diameter and 1 cm thickness was employed to obtain an homogeneous and focused γ-ray beam. A set of 33 measurements were taken along the horizontal axis, from left to right in steps of 1 mm, see figure 10. Runs of approximately one hour were taken for each position. A clear asymmetry can be seen in figure 10 between the left hand side and right hand side of the crystal with respect to its center. This was a clear indication that the sensitive volume of the germanium crystal is indeed most likely smaller than the one indicated in the technical sheet of the detector.
In order to find a better match between the experimental data and the simulation, the following procedure was performed. First, a 60 Co γ-ray source, placed 25 cm away from the cryostat window was simulated. Most of the γ-rays from such source reaching the germanium crystal volume will pass through most of this volume [21], if the crystal active volume is reduced in the Monte Carlo  simulation, it can match the experimental data, regardless of the dead layer thickness in the front crystal face. A sensitive volume reduction of ∼15 % was found to produce good agreement between the experimental and simulated data. The second step was to find the correct position of the sensitive volume in the crystal, that yields the dead layer thickness in the front side that matches the efficiency for a source with lower energy γ-rays. Simulating a 133 Ba source, also placed 25 cm away from the cryostat window, an agreement with the experimental data fixes a dead layer of 0.05 mm on the front face, 2.8 mm on the back and 1.45 mm on the sides of the crystal.  Figure 11. Background subtracted data and Monte Carlo simulation spectra comparison for a pointlike source with γ-rays at 835 keV (corresponding to a 54 Mn emission) pointlike source, located 25 cm away from the ICN-HPGe detector frontal face. An arbitrary normalization is used for qualitative comparison purposes.

Simulated efficiency and comparison to data
For both detectors, the sources 22 Na, 54 Mn, 57 Co, 60 Co, 65 Zn, 109 Cd and 133 Ba were simulated for comparison with experimental data, placed 25 cm away from the cryostat window of the detector. In the case of the IF-BEGe, the sources were simulated as ions with the GEANT4 General Particle Source and their decays with the Radioactive Decay Module [22]. For the ICN-HPGe, the simulations were performed emitting mono-energetic γ-rays corresponding to the emission energy of each isotope, see table 1. The deposited energy in the sensitive volume was computed adding up the deposited energy, via ionization processes, by all the secondary particles produced by the primary γ-ray. All information is stored in ROOT histograms [12]. For each primary γ-ray simulated, a count is stored in the corresponding deposited-energy bin. Figure 11 shows a comparison between a calibrated spectrum of a 54 Mn source and the Monte Carlo simulation for a pointlike source emitting γ-rays at 853 keV. The simulated spectrum reproduces with good agreement the experimental energy spectrum features such as energy resolution, photopeak, Compton continuum and Compton edge: maximum energy which can be transferred to an electron [10], escape peak at 511 keV has been removed by background subtraction. The energy resolution was introduced in the simulation following the empirical function obtained from experimental data, presented in section 2.2.
The full energy photopeak efficiencies are computed as in section 2.3, equation 2.2, comparing the number of counts in the fitted Gaussian photopeak to the original number of simulated primary γ-rays. The comparison to the experimental data is shown in figure 6. For both detectors, the efficiencies from the simulations are in agreement with the experimental efficiencies within uncertainties. The shapes of the curves drawn by the experimental data and Monte Carlo simulations of the detectors reflect the differences between these two. The curve for the ICN-HPGe is what is expected from a p-type coaxial detector, having a maximum in efficiency around 100 keV. On the other hand, the IF-BEGe detector does not show a maximum, as expected from a planar type detector [10]. The efficiency of both detectors decreases with the energy since the higher energy γ-rays need more sensitive volume for multiple interactions to be fully absorbed.

Validation with extended calibration sources.
In order to measure the activity in a given sample, the efficiency calibration with pointlike γ-ray sources is not sufficient, since full energy peak efficiency is a geometrically dependent quantity. Instead, an extended source efficiency is required, for the geometry of a given extended source, e.g. a sample vial. This is described for each detector in the following subsections. For practical reasons, each detector was validated with different extended sources; for the ICN-HPGe detector, a potassium chloride (KCl) solution was used while for the IF-BEGe detector, a 210 Pb solution was used.

ICN-HPGe detector characterization validation
The simulation of the ICN-HPGe detector was validated using water samples with a salt substitute containing KCl at different concentrations. Five samples of Novoxal brand KCl based salt substitute diluted in injectable water (sterile water used for medical applications) at different concentrations were prepared in cylindrical polypropylene containers of 600 ml volume. Figure 12 (top) shows the sample container geometry together with the ICN-HPGe cryostat in the Monte Carlo simulation.
In order to determine the 40 K isotope concentration per gram of salt, a background spectrum of the container with no diluted salt is recorded and subtracted from the spectra of the salt solution samples. Then, the remaining number of counts in the photopeak is determined following the same methodology as in the pointlike source case.
The geometry of the sample was implemented in the simulation, as shown in figure 12 (top). The γ-rays emission from active 40 K nuclei within the sample was incorporated in the simulation by sampling random points inside the physical volume of the solution and shooting mono-energetic and isotropic γ-rays with energy 1460 keV, the most probable γ-rays channel of 40 K. The efficiency is calculated as the ratio of the number of γ-rays counted inside the 40 K photopeak to those initially emitted. As the concentration approaches zero, the number of emitter centers from the solution approaches zero, but the efficiency approaches a finite value, corresponding to the probability of detecting 1460 keV γ-rays emitted from within the container inner volume when it is filled only with water.
Higher concentrations of KCl salt lead to a self-absorption effect of the γ-rays in the samples. This effect is clearly seen in the computed 1460 keV photopeak efficiencies for different concentrations, as shown in figure 12 (bottom). With these simulated efficiencies the activity of the extended sources were determined to obtain the masses of 40 K in the samples.
From the experimental data and Monte Carlo simulations, the concentration ratio of 40 K per mass of diluted potassium salt (PS) was obtained as η s = 0.0324 ± 0.0028 mg[ 40 K]/g [PS]. From the Novoxal label information, in which there is 309.33 mg of pure potassium per salt gram, and taking into account the natural abundance of the 40 K (0.012 %), the ratio η l = (0.0361 ± 0.0018) mg[ 40 K]/g[PS] was obtained. Both results are compatible within errors, validating the measurement and the Monte Carlo simulation. This comparison assumes an uncertainty of 5 % of the potassium concentration in the salt and a 20 % systematic uncertainty is estimated in the simulated efficiency.

IF-BEGe detector 210 Pb calibrated samples
For the Monte Carlo simulation validation of the IF-BEGe detector, five calibrated liquid samples of 210 Pb in a solution of deionized water were used. This samples were prepared at Royal Holloway, University of London (RHUL) and measured with a broad energy germanium detector in Boulby Underground Germanium Suite (BUGS) [23] in the UK. These samples were shipped to Mexico and independently measured with the IF-BEGe detector.
The response of the Boulby BEGe P-type detector, with a 60% relative efficiency and 0.9 kg crystal weight used in this study is characterized using the method discussed in [23]. An extended IAEA-385 [24] sample with known 210 Pb contamination is placed on the front face of the detector and the response to this is used to tune a GEANT4 simulation of the experimental setup. Using the simulation, the detector efficiency was determined at the 46.5 keV 210 Pb peak. The extended sources were assayed on the Boulby BEGe P-type detector and their activities were determined.
The activities measured at BUGS are compared with those measured with the IF-BEGe detector, as a cross-check to evaluate the IF-BEGe detector performance and also to validate the Monte Carlo simulation of the extended source. The IF-BEGe efficiency at lower energies was evaluated using X-rays from a pointlike 109 Cd source. The agreement between the experimental data and Monte Carlo simulations is 10 % at 25 keV.
For the measurement of the 210 Pb calibrated sample using the IF-BEGe detector, the containers were held inside of a Marinelli beaker, which maximizes the solid-angle coverage of the detector by the sample (both containers made out of polyethylene). The experimental setup was enclosed by a 14 cm thick lead shield, purged with the nitrogen gas from the detector dewar. After ∼ 24 hours of exposure time, the 46.5 keV peak was clearly identified. The γ-rays were counted as in section 2.3. Figure 13 shows the Monte Carlo simulation of the experimental configuration of the IF-BEGe detector with the 210 Pb calibrated sample. Since the position of the water container inside the Marinelli beaker could be shifted during experiment, as the lid of the beaker was closed, a systematic uncertainties study was performed. The nominal value for the measurement was taken in the position in which the axes of symmetry of the beaker and water container are aligned among themselves and with the detector symmetry axis. Then, the position of the water container in the simulation was shifted up +4 mm and down −4 mm with respect to the Marinelli beaker (which was the maximum space available for movement between the containers), maintaining their axes parallel. From this study, a 14 % systematic uncertainty was obtained.
With the efficiency computed from the Monte Carlo simulation and the γ-ray events from the experimental data, the activities of each 210 Pb sample were computed. The results are listed in   [23], and the last column shows the measurement reported using the IF-BEGe detector.

Conclusions
The High Purity Germanium detectors described in this work are part of the detector suite planned for the first underground laboratory in Mexico. The energy linearity, energy resolution and full energy peak efficiency of the detectors, in conjunction with the low radioactive background provided by the mine environment, will allow the study of a wide range of samples with low radioactive content. These detectors will be used for experiments in nuclear and astroparticle physics, biology and geology. Other applications of the facility in mining heritage, among other areas of the physical and social sciences are under development.
The energy scale and resolution of the ICN-HPGe and IF-BEGe detectors were obtained over the energy range relevant to low-background astroparticle experiments and environmental radiation studies. The detection efficiency was quantified in this energy range using a suite of radioactive sources. From a scan to the IF-BEGe crystal, an alteration in its active volume was found. Simulations considering this alteration were performed, to find the optimal configuration, matching the measured detector efficiencies within uncertainties. The detector characterization and simulation results were validated through tests with externally-calibrated KCl and 210 Pb sources. This work presents the first step towards establishing the performance of the LABChico radio-assay capabilities.