#
Development of ^{222}Rn Emanation Sources with Integrated Quasi 2π Active Monitoring

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## Abstract

**:**

^{222}Rn emanation is presented. The technique is based on the integration of a

^{222}Rn source, directly, with an α-particle detector, which allows the residual

^{222}Rn to be continuously monitored. Preparation of the device entails thermal physical vapor deposition of

^{226}RaCl

_{2}directly onto the surface of a commercially available ion implanted Si-diode detector, resulting in a thin-layer geometry. This enables continuous collection of well resolved α-particle spectra of the nuclei, decaying within the deposited layer, with a detection efficiency of approximately 0.5 in a quasi 2π geometry. The continuously sampled α-particle spectra are used to derive the emanation by statistical inversion. It is possible to achieve this with high temporal resolution due to the small background and the high counting efficiency of the presented technique. The emanation derived in this way exhibits a dependence on the relative humidity of up to 15% in the range from 20% rH to 90% rH. Traceability to the SI is provided by employing defined solid-angle α-particle spectrometry to characterize the counting efficiency of the modified detectors. The presented technique is demonstrated to apply to a range covering the release of at least 1 to 210

^{222}Rn atoms per second, and it results in SI-traceable emanation values with a combined standard uncertainty not exceeding 2%. This provides a pathway for the realization of reference atmospheres covering typical environmental

^{222}Rn levels and thus drastically improves the realization and the dissemination of the derived unit of the activity concentration concerning

^{222}Rn in air.

## 1. Introduction

#### 1.1. Background and Motivation

^{222}Rn is a naturally occurring radioactive noble gas, generated in the decay chain of primordial

^{238}U, and is thus released from soil to the atmosphere through diffusion processes.

^{222}Rn can be accumulated inside buildings and has been estimated to be the second most important cause of lung cancer. It is also the most relevant contributor to the average effective dose from natural sources experienced by the general public [1,2,3], which is why radon measurements are of interest for public health, radiation protection, and associated legislation. Moreover, in the environmental sciences,

^{222}Rn, in ambient air, was found to be an interesting proxy for mixing processes and terrestrial influence, so the measurement of its concentration finds a multitude of applications [4,5,6,7,8,9,10,11,12,13]. Activity concentrations of

^{222}Rn in outdoor air are in the order of a few Bq⋅m

^{−3}. The implementation of large-scale

^{222}Rn monitoring networks, to provide concentration data for the environmental sciences, and ensuring their comparability requires calibration techniques, for radon monitors in this concentration range, that are traceable to the international system of units (SI), as addressed in the project 19ENV01 traceRadon [14].

^{−3}for

^{222}Rn in air, with a small uncertainty over the required range, in a way that is traceable to the SI. For calibrations at such remarkably low activity concentrations, decaying reference atmospheres of

^{222}Rn, e.g., produced by the method of Picolo et al. [15], are generally unsuitable for statistical reasons. Relatively recently, an alternative was found in the use of so-called

^{222}Rn emanation sources [16,17,18], which are

^{226}Ra sources constructed with such physicochemical properties that a known or measurable amount of

^{222}Rn is released per unit time, which enables calibration at static or even dynamic activity concentrations. Since the processes resulting in this release are generally linked to the physicochemical properties of the source material, the

^{222}Rn emanation from such sources must be expected to vary with environmental parameters such as humidity, temperature, and pressure. The correlation of emanation with these parameters has previously been reported for a variety of different materials, e.g., in [19,20,21]. It is, therefore, of interest to construct

^{222}Rn sources whose emanation can be monitored during operation to account for these factors, especially in the case of in-field calibrations of ambient level

^{222}Rn monitors, where the exact control of all relevant climatic parameters is not feasible. In the following we present a new method of construction of such sources, specifically designed to overcome the challenges that result from the considerably low activity range of

^{226}Ra that is needed to realize reference atmospheres in the outdoor concentration range by combining the

^{222}Rn source and detector into one system. The full traceability chain to the SI, regarding determination of the

^{222}Rn delivery by this system, is laid down, along with a discussion of possible causes for systematic bias and the limits of the presented technique. Additionally, a data analysis method, enabling the estimation of near real-time values of

^{222}Rn released from the system (in terms of atoms per unit time) through statistical inversion, is briefly presented, which is tightly coupled with its design and is applied to provide emanation estimates in times of non-steady-state situations.

#### 1.2. Theoretical Considerations for ^{222}Rn Emanation Standards for Outdoor Activity Concentrations

^{222}Rn emanation from solid sources (in a primary way, i.e., not using

^{222}Rn concentration measurement devices that require calibration) rely on measuring activity ratios of

^{226}Ra and the residual γ-ray emitting

^{222}Rn progeny,

^{214}Pb and

^{214}Bi, inside an emanation source to deduce the steady-state release of

^{222}Rn or, equivalently, a partitioning coefficient of

^{222}Rn between the free volume and the source volume [16,18,22]. The basis of this method is the conservation of the total amount of

^{222}Rn nuclei that are generated by the source, which can either emanate from the source or decay within the source, which is expressed by the following first order kinetics.

^{222}Rn atoms per unit time and $A$ denote the activities of the respective nuclides in the emanation source.

^{222}Rn and

^{226}Ra activity of an emanation source allows one to estimate $\eta $, e.g., trivially in the steady-state of $\frac{\mathrm{d}{A}_{Rn-222}}{\mathrm{d}t}=0$.

^{222}Rn progeny

^{214}Pb and

^{214}Bi are not readily efficient enough to provide good temporal resolution of this method, especially regarding the real-time monitoring and considering the ubiquitous Poisson noise. A more direct, and much more sensitive, method entails the direct measurement of

^{222}Rn that remains in the emanation source, henceforth referred to as residual

^{222}Rn, through detection of its α-particles. However, with conventional α-particle spectrometry techniques, this is only possible in vacuo, e.g., [23], and thus, it is generally not useful to investigate emanation behavior directly under ambient conditions. This is due to the rapid energy loss of α-particles in any type of material, which leads to the significant distortion of α-particles spectra, recorded at a finite distance between the source and the detector, at ambient pressure. In such a spectrum, the contributions of

^{226}Ra and

^{222}Rn would no longer be well resolved, at which point the measurement of residual

^{222}Rn is not reliable.

^{222}Rn is to minimize the source-detector distance, i.e., ultimately, by direct construction of the source on, or even within, an α-particle spectrometric detector. Such a setup will henceforth be referred to as the Integrated

^{222}Rn Source/Detector (IRSD) and is proposed, discussed, and implemented within this work for the first time. It is schematically depicted in Figure 1. Typically, an α-particle spectrometer, such as the one used for the IRSD, is made up of an n-type silicon wafer that is p-doped at its entrance window, nowadays commonly through ion implantation, which results in entrance windows on the order of 50 nm thickness. To operate such a detector, the resultant p/n-junction is reversely biased from a backside ohmic contact to form a depletion layer of minimal free charge carriers. Due to their high interaction probability with matter, α-particles, which enter this layer of few 0.1 mm in thickness, are detected with practically unity probability, resulting in an electrical impulse that is proportional to the incident α-particle energy. Therefore, the theoretical detection probability in this configuration is 50% resulting from the 2π sr solid-angle subtended by the detector. Moreover, the typical background in α-particle spectrometry is orders of magnitude smaller than in any γ-ray spectrometric setup, and considering that the latter requires bulky lead shielding, emanation sources monitored by α-particle spectrometry are strongly preferred for the realization of in-field calibration procedures. In addition, α-particle spectrometers are typically a factor of 10 to 100 cheaper than γ-ray spectrometers. For these reasons, α-particle spectrometry is the superior choice for the purpose of monitoring the amount of residual

^{222}Rn.

^{226}Ra layer must be as thin as possible to minimize the variance in the energy loss of traversing α-particles. As a result of the variance in the energy loss, peaks in α-particle spectra generally show a left-handed (low energy) tailing that can lead to considerable overlap in the spectra and, thus, to significant difficulty of their analysis. Especially at such an infinitesimally small source-detector distance, the variance in the path length of α-particles entering the depletion layer through absorbing intermediate matter is high. Thus, pronounced low energy tailing of peaks in spectra, recorded in such a configuration results and methods to construct such a device must be chosen considering the mass of deposited impurities. Correspondingly, the analysis of α-particle spectra, which entails the determination of peak areas, must be carried out considering both the significance of the tailing and the specific nuclide composition at hand.

^{226}Ra for the construction of the IRSD, the

^{222}Rn nuclei are released by two distinct processes. After the α-decay of

^{226}Ra, the

^{222}Rn nucleus carries a recoil energy of 86 keV on average, which is enough to overcome the binding energy of chemical bonds, electrostatic attraction, and other adsorption forces and to penetrate few nm of a solid material and several 10 µm of ambient pressure air [24]. Hence, the generated

^{222}Rn is, in part, released directly as a result of this recoil energy. Since the recoiling takes place isotropically, in a random direction, a fraction of up to 50% of the generated

^{222}Rn nuclei are implanted into the first few nm of the silicon detector. These

^{222}Rn nuclei may be subsequently released through a diffusion process, which supposedly depends strongly on the chemical composition of the radium layer and the temperature. Analogous displacement occurs for

^{218}Po and

^{214}Po, both of which are nuclei that result directly, and indirectly, from an α-decay within the decay chain of

^{226}Ra.

^{226}Ra, onto commercially available Si-detectors. Specific analytical techniques, which are detailed in Section 2, have been developed to best utilize the data that can be obtained by operation of the resultant IRSD to measure and, hence, to standardize the amount of emanating

^{222}Rn, even in non-steady state situations.

## 2. Materials and Methods

#### 2.1. Construction of ^{226}Ra Modified Ion-Implanted Si-Diode Detectors

^{226}Ra containing thin-layer directly onto commercially available implanted Si-diode detectors (e.g., Mirion PIPS

^{®}series, Ametek Ortec ULTRA

^{®}series) to implement the IRSD. It was built from standard conflat-flange components (316L stainless steel) with copper seals. The unit is equipped with a sample holder for mounting the detector to be modified with a

^{226}Ra layer (the future IRSD) at a nominal distance of 35 mm from the opening of a tantalum tube (EVOCHEM Advanced Materials) of approximately 25 mm length and 4 mm inner diameter. The tantalum tube was heated resistively, using powers up to 120 W DC, estimated (Stefan–Boltzmann law) to roughly correspond to a temperature of 1500 K in steady-state. The sample holder features a stainless-steel aperture system to confine the deposited

^{226}Ra layer by shadowing with a diameter of (20.0 ± 0.1) mm to minimize possible edge effects on the approx. 25 mm active diameter of the Si detectors. The aperture is tubular and elongated to the level of the opening of the tantalum tube to avoid contamination of the vacuum chamber as much as possible, presuming molecular flow and line-of-sight deposition. The aperture system was cleaned of

^{226}Ra with diluted HCl when the built-up contamination was found to be too large. Chamber pressure was maintained at around 10

^{−4}Pa when the unit was operating using a membrane- and a turbomolecular pump (Pfeiffer vacuum HiPace80), while at ambient temperature, pressures as low as 5 × 10

^{−6}Pa were attained.

_{2}would show reasonably high vapor pressure at 1300 K, similar to BaCl

_{2}, with reportedly around 1 Pa to 10 Pa in this range [25,26], making it very feasible to evaporate, or even sublime, this radium compound at pressures in the order of 10

^{−4}Pa to 10

^{−3}Pa. Supposedly, RaCl

_{2}exists as a gas-phase molecule, and therefore, the species deposited using the present method is presumed to be RaCl

_{2}, which is thought to form its dihydrate upon contact with ambient moisture. Nonetheless, the sub-halide RaF of radium has been reported and investigated for radium recently [27], and the sub-halides are well known to exist for barium in the form of BaF and BaCl, which is why a mixture of radium from decomposition, radium chloride, and radium subchloride might be deposited using this method. Due to the chemical reactivity of some of the deposited species, it is expected that the chemical composition changes upon first exposure to the atmosphere.

^{226}RaCl

_{2}for the outlined thermal-PVD process, a PTB standard solution, nominally 71 kBq RaCl

_{2}(

^{226}RaCl

_{2}in 0.1 HCl with 0.5% m/m BaCl

_{2}), was converted into the nitrate and purified from its Ba

^{2+}carrier through extraction chromatography with Sr-Resin

^{®}[28] (4,4′(5″)-di-tertbutyl-di-cyclohexano-18-crown-6 in 1-butanol dispersed on SiO

_{2}-particles). This step was deemed necessary to reduce the amount of BaCl

_{2}present and, hence, to minimize the amount of deposited material on the future IRSDs. The chromatography was monitored by the addition of nominally 13 kBq

^{133}Ba as a radiotracer. Resultant

^{133}Ba-free fractions were pooled and converted back into the chloride by addition, and subsequent evaporation, of conc. HCl and aliquoted for later use. This method was previously used in the production of reduced carrier

^{226}Ra solutions in [16], with optimized conditions based on [29]. ICP-MS was used to determine that the residual amount of Ba

^{2+}was on the same order as the content of

^{226}Ra

^{2+}(concerning atom numbers). For each deposition, an aliquot of this solution was transferred to a 0.5 mL conical bottom polyethylene flask, evaporated to dryness, and taken up in a suitably small volume (e.g., 0.1 mL) of 0.5 M HCl (Methanol was also tested, but it was found to lead to considerable losses by wall-attached or undissolved

^{226}Ra) to allow for transfer into the tubular tantalum evaporation source in which the solution was allowed to dry. For the removal of crystal water from the resultant

^{226}RaCl

_{2}-dihydrate in the tube, the heating power was maintained at 20 W for the first 30 min of each deposition. Power was subsequently increased to a maximum of 120 W over 20 min. Deposition efficiencies, on the order of 15%, were experienced for this specific setup (including losses from solution transfer), mainly caused by the specific deposition geometry. However, a non-negligible gross-alpha count rate was observed in close proximity to the tantalum tube orifice, likely attributable to the

^{226}Ra that did not make its way out of the tube. This might be due to the formation of highly non-volatile tantalates or chloro-tantalates.

^{226}Ra activity and the counting efficiency for

^{226}Ra were determined, as presented, in Section 2.4. Before the deposition onto detectors was carried out, bare prime-grade polished 1” p-type Si-wafers were modified with

^{226}RaCl

_{2}on the order of 10 Bq to be investigated by scanning electron microscopy (SEM, Thermo Fisher Scientific Verios G4, through-lens secondary electron detector).

^{226}Ra, released into the solid-angle subtended by the future IRSD. This geometry is, thus, presumed to result in increased deposition efficiency at the cost of reduced uniformity.

#### 2.2. Operation of Integrated ^{222}Rn Sources/Detectors

^{226}Ra activity of the respective IRSD. The bias voltage was chosen according to the manufacturer’s specifications. For general spectrum acquisition, the humidity and temperature of the environment were not controlled. However, two IRSDs were also operated in a nominal 50 L closed volume in which the temperature, relative humidity, and pressure were recorded. At specific times, the relative humidity in this volume was changed by the introduction of warm water or by flushing with laboratory air to investigate the dependence of the emanation of each IRSD on the relative humidity. In this case, the method described in Section 2.5 was used to calculate the emanation based on time-series of collected α-particle spectra.

#### 2.3. Autoradiography

^{238}Pu reference point sources and a 3d printed holder were used to place the

^{238}Pu sources rectangularly around the respective IRSD. The images of the

^{238}Pu sources created on the radiography film were used to position a 140 × 140 grid of (0.2⋅0.2) mm

^{2}pixels over which the readout was conducted. The grid was placed in such a way that it was centered with respect to the

^{238}Pu sources and, due to the sample holder, also with respect to the outer diameter of the IRSD housing. The IRSDs were placed directly on top of the film, resulting in a displacement of the active surface of the detectors of approximately 1 mm from the radiography film because of the recess in the detector housing (Figure 3a).

#### 2.4. Alpha-Particle Spectrometry under Defined Solid-Angle

#### 2.4.1. General Defined Solid-Angle Setup

^{226}Ra activity, traceably to the SI, which was subsequently used to calibrate the counting efficiency of each IRSD by comparison of the IRSD α-particle spectrum with the determined value of its

^{226}Ra activity. In this way, traceability to the SI is established.

^{−1}Pa. Spectra of the reference DSA detector, as well as the IRSDs, were each recorded over integration times that were chosen concerning each IRSD’s

^{226}Ra activity. However, spectra obtained were summed up for data analysis, neglecting possible gain-shifts. Total measurement times were adjusted concerning each deposited activity.

#### 2.4.2. Calculation of Geometrical Efficiency

#### 2.4.3. Peak Area Analysis

^{226}Ra,

^{222}Rn,

^{218}Po, and

^{214}Po) to the depletion layer (Figure 1) and their respective decay characteristics, each peak was found to be slightly differently tailed, and hence, a simple restriction to shared tailing parameters, commonly applied in α-particle spectrometry, was found to lead to insufficiently well modeled tailing. To account for this, a special regression technique was developed that allows for differently tailed peaks, while maintaining reasonable convergence speed and robustness, considering the high number of required parameters. This is achieved by ${\ell}^{2}$-regularization of the tailing parameters, keeping them somewhat similar but not entirely shared among the peaks of each nuclide in the decay chain. Physically, this is motivated by the fact that the tailing is supposed to be similar, due to the relative similarity of the α-particle energies and the relatively small deviation in the effective path length through all absorbing layers. Specific details of this modeling procedure are given in Appendix A.

#### 2.5. Estimation of ^{222}Rn Emanation from Spectral Time-Series

^{222}Rn activity retained in the IRSDs must follow first-order continuity, accounting for the emanation of

^{222}Rn from the deposited layer, $\eta $, in terms of emanating

^{222}Rn atoms per unit time.

^{222}Rn activity, ${A}_{Rn-222}\left(t\right)$, and the

^{226}Ra activity, ${A}_{Ra-226}\left(t\right)$, are accessible through the analysis of the peak areas. The estimation of $\eta $ (or derived quantities such as the emanation coefficient), based on those time-series, is an inverse problem unless a steady-state of $\frac{\mathrm{d}{A}_{Rn-222}}{\mathrm{d}t}=0$ has been reached. The observed version of ${A}_{Rn-222}\left(t\right)$ is given by the discretized convolution of $\eta $, with the impulse-response defined by the radioactive kinetics. In previous work [35,36], we developed and presented a deconvolution technique that allows the probability density function (PDF) of a discretized version of $\eta \left(t\right)$ to be estimated, including the propagation of systematic uncertainty, using the supporting measurements of the residual

^{222}Rn activity in the source.

^{222}Rn and

^{226}Ra, the time-offset between each spectrum and their live times, a prior of the initial state, as well as an estimate of the PDF of the counting efficiency vector $\mathit{\epsilon}=\left[\begin{array}{c}{\epsilon}_{Rn-222}\\ {\epsilon}_{Ra-226}\end{array}\right]$. Necessary inference equations are given in Appendix B, and for a detailed presentation of the algorithm, the reader is directed to [35,36]. The uncertainty in $\mathit{\epsilon}$ is propagated across the model using a sigma point method, as described in Appendix B. In steady-state situations, where $\frac{\mathrm{d}{A}_{Rn-222}}{\mathrm{d}t}=0$, $\eta $ is simply given by the solution of Equation (1), using the components of the counting efficiency vector $\mathit{\epsilon}$ and the count rates of the respective nuclides as

## 3. Results and Discussion

#### 3.1. Morphological Characterization

^{226}Ra [16], where much more voluminous deposits were observed. Given that similar amounts of

^{226}Ra were deposited in both studies, it is suggested that the present method produces considerably cleaner deposits.

^{226}RaCl

_{2}, Figure 3a), most likely, it is composed almost entirely of other materials. This includes impurities present in the obtained

^{226}RaCl

_{2}solution, impurities introduced by all the solvents used, and impurities from the chamber materials at the respective deposition conditions. In the future, some of these impurities could potentially be avoided by a refined process, involving a mechanical shutter and feedback temperature control, to avoid contamination with readily volatile species. Nonetheless, the DSA α-particle setup showed a FWHM of only around 15 keV for the 4.78 MeV emission of

^{226}Ra, where, previously, around 20 keV was measured for electrodeposited and around 16 keV for ion implanted

^{226}Ra with the same setup [16,23], indicating relatively small α-particle energy loss within the deposited layer.

^{226}RaCl

_{2}, hinting at the inhomogeneity of the deposit. This is more clearly evident in Figure 3b, a typical digital autoradiograph, obtained as explained in Section 2.3. The deposits of smaller activities, shown in Table 1, were initially not visible to the naked eye. However, they turned irreversibly slightly pale white upon exposure to very humid air. The deposits were found to be soluble in water, which means that IRSDs formed in this way should not be operated in condensing atmospheres.

#### 3.2. Typical α-Particle Spectrum Features of the IRSD

^{226}Ra emission was found to be between 21 keV and 40 keV in the IRSD α-particle spectrum. While the observed FWHM are close to the manufacturer’s specifications (between 17 keV and 20 keV), pronounced low-energy tailing of the peaks can be identified that results from the high variability of the α-particle energy loss in the dead-layer (p-doped region) and deposited layers, as stated in Section 1.2.

^{210}Po,

^{222}Rn,

^{218}Po, and

^{214}Po, respectively, appear below a threshold of 4.8 MeV in the spectrum, i.e., the

^{226}Ra region. Considering that, due to emanation, the amount of

^{222}Rn and progeny present in the layers is around 50% of the amount of

^{226}Ra, while

^{210}Po is not present in significant quantities, this yields a maximum deviation of only 1.25% in the

^{226}Ra area determination if the tailing contributions were entirely ignored.

^{210}Po are also present. In general, the

^{210}Po is introduced from

^{210}Po in the original

^{226}Ra solution, but it will also grow in slowly over time.

^{214}Po and

^{218}Po peaks of the spectrum show higher energy satellites with increasing energy shift between the main progeny peak and the satellite peaks in the order (

^{222}Rn) <

^{218}Po <

^{214}Po. An unresolved satellite peak might be present below the

^{222}Rn peak, since this peak appears much broader than the main

^{226}Ra emission. Due to the varying energy shift increasing along the decay chain, these satellites are thought to be related to the self-implantation of

^{222}Rn and the short-lived progeny (SLP)

^{218}Po and

^{214}Po, as shown schematically in Figure 1. As a result,

^{222}Rn and SLP are either present in the material deposited on the detector or injected into the p-doped region of the IRSD, due to their recoil, which is thought to cause the varying energy shift. In addition, some of the recoil energy might be detected in coincidence with the α-particle under some circumstances, i.e., injection of SLP to within the depletion zone. However, the energy shifts observed are on the order of 10 keV to 30 keV, while the coincidence of the α-particle, with the full recoil energy, would result in peak shifts of up to 200 keV. This indicates that

^{218}Po and

^{214}Po do not get implanted past the dead-layer to within the depletion zone.

^{226}Ra,

^{222}Rn, and

^{218}Po peaks can also be identified, attributable to random α-e and α-photon coincidences, while the usual pronounced right-handed tailing of the

^{214}Po peak is due to the α-β true coincidence with the

^{214}Bi β-particle, caused by the particularly small half-life of

^{214}Po.

^{214}Po and

^{218}Po peak areas are smaller than the

^{222}Rn peak area under all observed circumstances. The deviation of those two peaks from one another, and especially from the

^{222}Rn peak area, was found to be dependent on the pressure of the environment as shown in Figure 6, depicting a time-series of the initial ingrowth of count-rates of the different nuclei in the deposited layer under reduced pressure and ambient conditions. Under ambient conditions,

^{218}Po and

^{214}Po count rates are observed to be approximately 1% to 2% lower than the

^{222}Rn count rate. This can be explained by

^{218}Po and

^{214}Pb recoiling that leads to the additional ejection of

^{218}Po and

^{214}Pb, Figure 1. The mean free path of those nuclei in ambient pressure air is on the order of 100 nm, suppressing the recoiling strongly, where

^{218}Po and

^{214}Pb that lost enough energy, in proximity to the deposited layer, potentially remain adsorbed. However, some recoiling can still be observed, even in ambient pressure air. Due to this disturbance, with potential pressure sensitivity, the SLP peak areas were not further used to assess the activity of

^{222}Rn remaining in the IRSD.

#### 3.3. Efficiency Calibration

^{226}Ra in each detector’s spectrum (DSA detector and IRSD), as determined by the regression models in Section 2.4.2. The counting efficiency of the IRSDs is hence given by

^{226}Ra counting efficiencies is given in Table 1, and the deposited

^{226}Ra activity was determined analogously. Considering the uncertainty of this method, the counting efficiencies observed were generally very close to 0.5, with a maximum observed relative deviation of 1.6%. It is presumed that the deviation from the 2π sr geometrical efficiency, 0.5, results from backscattering and self-absorption losses in the deposited layer and the dead-layer of the IRSD. Since the covariance matrix estimate of the peak areas from the inverted Hessian of the regression procedure, outlined in Section 2.4.3, can lead to underestimation of the uncertainty due to non-stochastic residuals and amplification of numerical errors, and based upon the observations in Section 3.2, an additional normally distributed uncertainty, with a standard deviation of 0.3% for each peak area, was introduced to account for possible shortcomings of the modeling procedure. This value is based on the estimated tailing contributions of the short-lived progeny. As pointed out in earlier work, the contribution of scattered particles to the peak areas introduces an uncertainty of approximately 0.2% [16,37]. It is worthy to note that the backscattering causes an anti-correlation of the scattering bias of the DSA peak area and the IRSD peak area. However, this is intentionally not corrected to deduce the counting efficiency of the IRSD resulting from all effects. Due to layer areal density and random coincidence, the effective counting efficiency is expected to decrease with increasing

^{226}Ra activity. However, in the investigated activity range this effect could not significantly be observed. Generally, uncertainty on the order of 1% in the counting efficiency or equivalently deposited activity was achieved using this method which is dominated by the uncertainty in the solid-angle resulting from the distance measurement of the recessed Si-surface of the IRSD relative to the standard geometry. An uncertainty budget is given as an example in Table 2 for the determination of the efficiency of the IRSD, with approx. 2 Bq

^{226}Ra, where the least counting statistics were accumulated.

^{222}Rn and SLP that resides within the IRSD, since the recoiling of

^{222}Rn and SLP nuclei from the IRSD causes implantation into the geometrical components and the detector of the DSA setup. The emission of α-particles from those recoil implanted nuclides thus contributes to the peak areas of each detector to varying degrees. Due to this, no attempt was made to derive the

^{222}Rn and progeny efficiency separately, and for the following, it is assumed that the

^{222}Rn and

^{226}Ra counting efficiencies are close to each other. Since the energy of the emitted α-particles of both nuclides are relatively similar, it is assumed that the backscattering and absorption losses are also similar. However, the recoiling causes slight displacement of the positional distribution of the

^{222}Rn nuclei to the

^{226}Ra positions, thereby possibly introducing a slight difference in the true counting efficiency. To model this effect, we assumed, in the following, that the counting efficiency of

^{226}Ra and

^{222}Rn is given by a multivariate normal distribution with a high correlation coefficient. However, for the following analyses using the counting efficiency, the peak-areas of

^{222}Rn and

^{226}Ra are thought to be anti-correlated, which has the opposite effect, and hence, a relatively balanced correlation coefficient of 0.6 was chosen to approximately model both effects.

#### 3.4. Estimation of ^{222}Rn Emanation from IRSD Time-Series and its Humidity Dependence

^{222}Rn in non-steady-state situations is estimated using the SLDS-deconvolution approach of the observed counts time-series, which is evaluated from the IRSD spectrometric time-series using the methods outlined in Section 2.4.3. The statistical uncertainty of the determined peak areas is estimated, recursively, alongside the prediction step of the filtering algorithm (Section 2.5, [36], Appendix B), accounting approximately for possible tailing contributions, as well as the Poisson statistics, as

^{222}Rn retained within the IRSD is buried in the silicon wafer, such as in Figure 1, some of it is evidently loosely adsorbed to the surface or within the

^{226}RaCl

_{2}layer. Those

^{222}Rn nuclei can evidently be desorbed in response to a change in relative humidity (Figure 7 10 d and Figure 8 30 d), such that the activity of retained

^{222}Rn quickly drops, resulting in a peak in the emanation. If the release of those

^{222}Rn nuclei, however, is not enough to reach the equilibrium point, a characteristic decay period of the retained

^{222}Rn nuclei, with the kinetics of the radioactive decay, follows. Conversely, during a change from high to low emanation, the only way for the activity of retained

^{222}Rn to reach equilibrium is the ingrowth from the

^{226}Ra decay, since back-diffusion evidently does not occur (Figure 7, >80 d), which follows a characteristic ingrowth curve. Additionally, the change of the effective emanation conditions can follow its own dynamics, as during the initial rise in Figure 7. Given that the rate of re-equilibration of the device depends on the state it was previously in, hysteresis may occur. Nonetheless, it is shown in Figure 7 that the emanation from the IRSD recovers its initial value after exposure to more humid air.

## 4. Conclusions

^{222}Rn from a solid source of

^{226}Ra. For the first time, a complete approach based on a unique combination of a

^{222}Rn source with a spectrometric detector, the IRSD, was presented. This allows the continuous monitoring of the residual amount of

^{222}Rn in the source by highly efficient, direct α-particle measurements under ambient conditions, which drastically improves the reliability under changing operational characteristics and environmental parameters. Additionally, the direct measurement of the α-particles, emitted by the residual

^{222}Rn, specifically enabled by the design of the IRSD, alleviates some of the sources for systematic uncertainty of previous γ-ray spectrometry based approaches [16,18] while providing a means of achieving unmatched counting efficiency at a negligible background. As was demonstrated,

^{222}Rn is not necessarily in secular equilibrium with the short-lived progeny in a thin-layer, which could result in a bias of approximately 2% if γ-spectrometry of

^{214}Pb and

^{214}Bi was applied as a monitoring tool instead.

^{222}Rn emanation terms (corresponding to a single

^{222}Rn atom released per second) allows refining calibration procedures in the future, e.g., by down-scaling of reference volumes, injection of collected amounts of

^{222}Rn directly into measurement systems, reductions of flow rates, and other, similar methods. Thereby, the definition of the unit Bq⋅m

^{−3}can be realized by integrating the radioactive decay kinetics, driven by the derived emanation source terms ranging from 2 µBq⋅s

^{−1}to 440 µBq⋅s

^{−1}, with a combined uncertainty not exceeding 2% and thus, providing one of the most advanced techniques of low-level

^{222}Rn standardization to this end. The application of the IRSD setup thus allows one to realize and disseminate reference atmospheres of

^{222}Rn in the ambient concentration range, traceable to the SI.

^{226}Ra activity IRSD, while the higher activity ones did not begin to show significant losses from random coincidence and self-absorption.

^{226}Ra than those used in this study. Moreover, the

^{210}Po peak is a disturbance in the spectra that were collected, and hence, the ingrowth of

^{210}Po will additionally degrade the information that can be inferred from the spectra or, at least, increase the uncertainty of the determined emanation. Due to the relatively long half-life of intermediate

^{210}Pb, however, this process takes place on the scale of tens of years. Currently, the technique is only applied at PTB, and this first presentation of it serves as a proof of principle and to lay down the traceability chain to the SI. However, continuous production of IRSD of different activity, for dissemination and potential future replacements, by the PTB is limited to a low volume of devices. Due to the relative simplicity of the process to create an IRSD, using relatively low-cost and rugged components, supply of such setups can, potentially, be realized in the future by an implementation in industry to disseminate the unit Bq⋅m

^{−3}, concerning

^{222}Rn in the air, in the presented way.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

^{2})erfc(x)), which was computed by Chebyshev approximation [38]. Flipping the sign on $x$ and $\mathsf{\mu}$, Equation (A1) is similarly used to represent right tailed Gaussians.

**A**is a vector containing the peak-areas and $R$ is a matrix made up of the peak-shapes as the column vectors. The modeled spectrum is thus given by the linear-combination of the column-vectors of $R$,

**A**is given as the solution to the weighted, linear least-squares problem

**S**.

^{214}Po alpha-beta true coincidence region, Figure 5.) are excluded from the regularization function to obtain better results. Due to true coincidence effects already pointed out in earlier work on

^{226}Ra α-particle spectrometry [42], the right-handed tails of the lower energy

^{226}Ra emission were also excluded from the regularization procedure due to the pronounced α-e true coincidence resulting from the high counting efficiency and the highly converted levels in the decay of

^{226}Ra [42]. For each peak, a total of 6 left-handed and 2 right-handed tailing terms were used, which provided good deconvolution results.

**R**, the best fitting

**A**is implicitly found during each iteration of the chosen non-linear optimization procedure.

**R**matrix,

## Appendix B

${F}_{a}={\mathrm{e}}^{Ka}$ | ${U}_{a}={{\displaystyle \int}}_{0}^{a}{\mathrm{e}}^{K\left(a-\tau \right)}\mathit{L}{\mathit{L}}^{T}{\mathrm{e}}^{{K}^{T}\left(a-\tau \right)}\mathrm{d}\tau $ |

${M}_{r}={{\displaystyle \int}}_{0}^{r}{\mathrm{e}}^{K\tau}\mathrm{d}\tau $ | ${C}_{r}={{\displaystyle \int}}_{0}^{r}{{\displaystyle \int}}_{\tau}^{r}{\mathrm{e}}^{K\left(r-\tau \right)}\mathit{L}{\mathit{L}}^{T}{\mathrm{e}}^{{K}^{T}\left(a-\tau \right)}\mathrm{d}a\mathrm{d}\tau $ |

${B}_{r}={{\displaystyle \int}}_{0}^{r}{{\displaystyle \int}}_{\tau}^{r}{{\displaystyle \int}}_{\tau}^{r}{\mathrm{e}}^{K\left(a-\tau \right)}\mathit{L}{\mathit{L}}^{T}{\mathrm{e}}^{{K}^{T}\left(b-\tau \right)}\mathrm{d}a\mathrm{d}b\mathrm{d}\tau $ |

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**Figure 1.**Schematic of silicon detector, modified with a thin layer of

^{226}Ra (IRSD). The silicon detector is made up of n-type silicon and a p-doped front side contact. Reverse biasing of the p/n-junction results in a depletion layer of several 0.1 mm thickness, which is the sensitive detection volume. The

^{222}Rn emanation mechanisms of recoiling and diffusion are depicted, as well as the spatial displacement of progeny along the decay chain. Details are given in the text.

**Figure 2.**Schematic drawing of the custom thermal-PVD setup used in this work. Drawing not to scale. Details of the setup are described in Section 2.1.

**Figure 3.**(

**a**) shows a photograph of an IRSD based on a 450 mm

^{2}Canberra PIPS

^{®}detector, modified with a layer containing 440 Bq

^{226}RaCl

_{2}. (

**b**) shows a digital autoradiograph obtained from such a deposit where the inner diameter of the recessed Si-surface is given in yellow and the diameter of the shadowing aperture is given in red.

**Figure 4.**Secondary-electron SEM Images (through-lens detector) of thermal-PVD

^{226}RaCl

_{2}on a bare 1” prime Si-wafer at different magnifications: (

**a**) 1500×, (

**b**) 100,000×, (

**c**) 100×. Length of bar: (

**a**) 30 μm (

**b**) 500 nm, (

**c**) 500 μm.

**Figure 5.**Typical α-particle spectrum obtained with a 442 Bq

^{226}Ra IRSD (modified Canberra PIPS

^{®}detector of nominal 100 μm depletion depth, 450 mm

^{2}active area), over the first 6 · 10

^{5}s after modification and regression results, according to Section 2.4.3. The 4.8 MeV

^{226}Ra emission shows a FWHM of approx. 21 keV and a FWTM of approx. 48 keV. Progeny peaks appear slightly shifted to higher energies (wrt. the energy calibration obtained from the

^{226}Ra emissions).

**Figure 6.**Ingrowth of α-particle count rates of an IRSD after initial

^{226}Ra deposition at reduced and ambient pressure.

**Figure 7.**SLDS-deconvolution result for a IRSD of approx. 160 Bq

^{226}Ra. Black dots represent the determined peak areas of a set of approx. 15,000 spectra, taken over 110 days at a sampling interval of 600 s of

^{222}Rn and

^{226}Ra, respectively. Red curves represent the smoothed results for the residual

^{222}Rn- and

^{226}Ra activities and the deconvolved time-series of the emanation $\eta $, according to Section 2.5. Shaded areas represent the 1$\sigma $ credible intervals, almost entirely caused by the systematic uncertainty.

**Figure 8.**SLDS-deconvolution result for an IRSD of approx. 65 Bq

^{226}Ra. Black dots represent the determined peak areas of a set of approx. 9000 spectra, taken over 65 days at a sampling interval of 600 s of

^{222}Rn and

^{226}Ra, respectively. Red curves represent the smoothed results for the residual

^{222}Rn- and

^{226}Ra activities and the deconvolved time-series of the emanation $\eta $, according to Section 2.5. Shaded areas represent the 1$\sigma $ credible intervals, almost entirely caused by the systematic uncertainty.

Detector Type | Active Area/Depletion Depth | A(^{226}Ra)/Bq | ${\mathit{\epsilon}}_{\mathit{R}\mathit{a}-226}/\mathbf{cps}\text{}\mathbf{Bq}{-}^{1}$ | $\mathbf{Observed}\text{}\mathbf{Mean}\text{}\mathsf{\eta}$ |
---|---|---|---|---|

Mirion PIPS^{®} | 450 mm^{2}/300 μm | 1.91 ± 0.02 | 0.502 ± 0.006 | 0.999 ± 0.017 |

Ametek Ortec ULTRA^{®} | 450 mm^{2}/300 μm | 66.4 ± 0.5 | 0.494 ± 0.004 | Figure 8 |

Mirion PIPS^{®} | 450 mm^{2}/300 μm | 158.6 ± 1.7 | 0.494 ± 0.005 | Figure 7 |

Mirion PIPS^{®} | 450 mm^{2}/100 μm | 442 ± 4 | 0.492 ± 0.005 | 209 ± 4 |

Description and Type | Value and Uncertainty | Rel. Uncertainty | Rel. Contribution |
---|---|---|---|

Solid angle (systematic) | $(0.00940\text{}\pm \text{}0.00006)\text{}4\mathsf{\pi}$ sr | 0.6% | 28.4% |

Backscattering_{DSA} (systematic) | 1 ± 0.002 | 0.2% | 3% |

Tailing_{DSA} (systematic) | 1 ± 0.003 | 0.3% | 6.7% |

Tailing_{Si} (systematic) | 1 ± 0.003 | 0.3% | 6.7% |

^{226}Ra rate_{DSA} (stochastic) | $(0.01796\text{}\pm \text{}0.00015)\text{}{\mathrm{s}}^{-1}$ | 0.8% | 55.1% |

^{226}Ra rate_{Si} (stochastic) | $(0.9595\text{}\pm \text{}0.0004)\text{}{\mathrm{s}}^{-1}$ | 0.04% | 0.1% |

${\epsilon}_{Ra-226}$ | 0.502 ± 0.006 | 1.2% |

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**MDPI and ACS Style**

Mertes, F.; Röttger, S.; Röttger, A.
Development of ^{222}Rn Emanation Sources with Integrated Quasi 2π Active Monitoring. *Int. J. Environ. Res. Public Health* **2022**, *19*, 840.
https://doi.org/10.3390/ijerph19020840

**AMA Style**

Mertes F, Röttger S, Röttger A.
Development of ^{222}Rn Emanation Sources with Integrated Quasi 2π Active Monitoring. *International Journal of Environmental Research and Public Health*. 2022; 19(2):840.
https://doi.org/10.3390/ijerph19020840

**Chicago/Turabian Style**

Mertes, Florian, Stefan Röttger, and Annette Röttger.
2022. "Development of ^{222}Rn Emanation Sources with Integrated Quasi 2π Active Monitoring" *International Journal of Environmental Research and Public Health* 19, no. 2: 840.
https://doi.org/10.3390/ijerph19020840