# Development of metallic magnetic calorimeters for x-ray metrology applications

Matias Rodrigues, Martin Loidl, E. Leblanc, Jacques Bouchard, Andreas

Fleischmann, Christian Enss

► To cite this version:

Matias Rodrigues, Martin Loidl, E. Leblanc, Jacques Bouchard, Andreas Fleischmann, et al. Development of metallic magnetic calorimeters for x-ray metrology applications. X-Ray Spectrometry, 2008, 37 (3), pp.255-259. 10.1002/xrs.1009 . cea-05469372v2

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# Development of metallic magnetic calorimeters for x-ray metrology applications

M. Rodrigues,¹ M. Loidl,¹ E. Leblanc,¹ J. Bouchard,¹ A. Fleischmann² and C. Enss²

¹ LNE-LNHB, CEA Saclay, 91 191 Gif-sur-Yvette, France

² Kirchhoff Institut fur Physik, Universität Heidelberg, IF 227, 69120 Heidelberg, Germany

We are developing metallic magnetic calorimeters operating at very low temperatures for applications in the field of ionizing radiation metrology. The main aim of this development is to enhance the accuracy of atomic and nuclear data determination, in particular x-ray and gamma ray emission probabilities. The energy resolution of metallic magnetic calorimeters is much better than that of the commonly used semiconductor detectors, enabling the separation of lines of very close energies. We have chosen gold, a high Z material, for the detector absorber. This favors photoelectric absorption, and the quantum efficiency can be made close to unity. We first describe the detection principle including the detector read-out system. Following, we present the conception, first prototypes and experimental results of two x-ray and gamma ray detectors for the energy ranges 1–20 keV and 20–200 keV.

## INTRODUCTION

Ionizing radiations are naturally present in our environment or may result from human activities. X-ray and gamma rays are used in numerous fields of research and industry, to take advantage of their energy or to trace, qualitatively or quantitatively, a given isotope. Many applications strongly rely on the comprehension of photon emission processes.

One example is ionizing radiation metrology. Standardization of radioactive sources often requires an accurate knowledge of x-ray and gamma ray emission probabilities. In the case of materials analysis, x-ray fluorescence can be used to determine the abundances of elements. Another industrial application concerns nuclear medicine. When radio-pharmaceuticals are injected into the body for treatment or diagnosis, it is of prime importance to precisely determine the dose delivered to the patient in order to minimize secondary effects. Better monitoring of nuclear waste generated by industry and in the nuclear fuel cycle depends on a more precise determination of atomic and nuclear data. In environmental survey, x-rays and low-energy gamma rays are commonly used to establish isotopic ratios of actinides. Atmospheric physics and chemistry make use of spectroscopic data analysis for pollution studies. For astrophysical applications, precise emission intensities are required to determine the quantities of certain elements in regions of star formation, or in intergalactic material.

To satisfy atomic data needs, one of the goals of the French institute of ionizing radiation metrology, Laboratoire National Henri Becquerel (LNHB), is to improve the accuracy of x-ray and gamma ray emission probabilities. Measurements of these emissions are commonly performed with germanium or silicon semiconductor detectors. This technique is well established and highly reliable; however, it is limited for two reasons. Firstly, the detection efficiency of these detectors is energy dependent. Since the detection efficiency is often determined using emission intensities of x-ray and gamma rays, any measurement relies on the initial knowledge of atomic data. Secondly, the energy resolution of semiconductor detectors is intrinsically limited due to their detection principle. In many cases, it does not allow to separate the numerous x-ray and gamma ray lines associated with photon emission in the energy range 1–200 keV. The fitting procedures used to determine the intensities of strongly overlapping lines increase the total uncertainty on emission probabilities.

The requirements on the detector for precisely establishing x-ray and gamma ray emission probabilities are on the one hand a good energy resolution (less than 10 eV for 1–20 keV photons and less than 200 eV for 20–200 keV photons), on the other hand a high quantum efficiency (high Z material and high photoelectric absorption). The LNHB is developing metallic magnetic calorimeters (MMC) for x-ray and gamma ray metrology with the aim to combine a good energy resolution and a high quantum efficiency for 1–200 keV photons.

## OPERATING PRINCIPLE OF METALLIC MAGNETIC CALORIMETERS

A calorimetric detector for single photon detection is based on the measurement of the temperature rise $\Delta T$ caused by the absorption of a photon with an energy $E$ in the detector. The temperature is monitored by a temperature sensor that is thermally coupled to the absorber. A weaker thermal coupling of the ensemble absorber–temperature sensor to a thermal bath—brings the detector back to its initial temperature after each photon interaction. The signal amplitude is proportional to $\Delta T = E/C_{total}$, where $C_{total}$ is the total heat capacity of the calorimeter. The heat capacity strongly decreases with temperature. This implies to operate the detector at very low temperatures (less than 100 mK). For an overview of cryogenic detectors, see Refs 1 and 2.

A metallic magnetic calorimeter consists of a metallic absorber and a metallic paramagnetic temperature sensor composed of a few hundred ppm of erbium in a gold lattice (Au : Er). The erbium spins interact with an external magnetic field, resulting in a magnetization $M$ that strongly depends on temperature (Fig. 1).

The result of a photon interaction in the absorber is a reduction of the sensor magnetization. The sensor is magnetically coupled to a DC superconducting quantum interference device SQUID magnetometer. The quantity measured by the SQUID is a magnetic flux change $\delta\phi$ proportional to the deposited energy.

There are mainly two ways to couple the sensor to the SQUID:

* If the sensor is small enough it can be placed directly in the SQUID loop. The flux change is given by:

$$ \delta\phi = G\mu_0 \frac{V}{r} \frac{\partial M}{\partial T} \frac{E}{C_{total}} $$
where r is the radius of SQUID loop, V the volume of the sensor, μ₀ the permeability of the free space, and ∂M/∂T the dependence of the sensor magnetization upon temperature. The dimensionless factor G depends on the geometry of the sensor with respect to the SQUID loop and is of the order of unity.

* A larger sensor can be read out by a pick-up coil that is coupled to the SQUID via an input coil (superconducting flux transformer). This configuration adds an inductive coupling factor:

$$ \delta\phi = n \frac{M_{in}}{L_{P} + L_{in}} G\mu_{0} \frac{V}{r} \frac{\partial M}{\partial T} \frac{E}{C_{total}} $$

where r and G refer in this case to the pick-up coil, M_in denotes the mutual inductance between the input coil and the SQUID and n the number of windings of the pick-up coil. L_P and L_in are the pick-up coil inductance and the input coil inductance, respectively.

A disadvantage of transformer-coupled sensor read-out is a somewhat higher noise level. Referred to the pick-up coil, for the optimal configuration, where L_P = L_in, it is larger than the SQUID noise by a factor 2.³

The signal shape can be described when the energy transfers are considered. When a photon interacts in the metallic absorber, its energy is transferred to the conduction electrons. The resulting heat diffuses in the entire detector volume. The diffusion time is one of the components of the signal rise time and depends on the volume. It can range from ~0.1 µs to a few 10 µs for the detector dimensions discussed in this article. The other contribution to the rise time is the relaxation time between the conduction electrons and the Er spins. It is described by the Korringa relation and is less than 1 µs at 50 mK.⁴ The signal decay time corresponds to the return of the detector to thermal equilibrium. It is given by τd = C_total/G_bath, where G_bath denotes the thermal conductivity of the thermal link between detector and thermal bath (Fig. 1).

The energy resolution of semiconductor, scintillating and ionization detectors is limited by the statistical fluctuations of the number of excited states that contribute to the signal. This number is determined by the mean energy required for the creation of an excited state. The energy required to excite a spin in a magnetic calorimeter is by several orders of magnitude smaller than the excitation energies in the conventional detectors mentioned above. The energy resolution of magnetic calorimeters is therefore not limited by the statistics of the carriers of information.

The fundamental limit of the energy resolution of a MMC is set by thermodynamic fluctuations of energy between the detector and the thermal bath. Another intrinsic contribution to the total energy resolution comes from magnetic noise generated by the random thermal motion of conduction electrons in the detector itself (magnetic Johnson noise). The noise power of both the energy fluctuations and the magnetic Johnson noise is proportional to the operating temperature. This turns out to be another reason to operate the detector at very low temperature. Additional noise arises from the SQUID, the SQUID electronics, variations of the detector temperature and mechanical vibrations.

## TWO-STAGE SQUID SYSTEM

A SQUID can be described as a converter of magnetic flux to voltage. It is a very sensitive device, but its response is a periodic function of flux. A feedback system is used to fix an operating point in this function in order to linearize the response.

To improve the total noise of the SQUID read-out system including the electronics, we are using a two-stage SQUID setup, represented in Fig. 2. SQUID 1 acts as a magnetometer reading out the sensor. It is inductively coupled to SQUID 2 through a

$$ G_{\phi} = \frac{M_{in,2}}{R_{dyn,2} + R_{g}} V_{\phi,1} $$

resistor R_g of a few ohms and an input coil. SQUID 2 acts as a low noise preamplifier with a gain expressed by:⁵

where M_in,2 is the mutual inductance between the input coil and SQUID 2 and Rdyn,2 the dynamic resistance of SQUID 2. V_φ,1 = ∂V/∂φ,1 is the transfer coefficient at the working point of SQUID 1. The resistance R_g permits to adjust the flux gain between the two SQUIDs in order not to have multiple working points. In such a configuration the voltage noise contribution of the room temperature amplifier is greatly reduced.

<figure><img src="image_2.png" /><figcaption>Figure 1. Scheme of the detection principle.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2. Scheme of the two-stage SQUID setup.</figcaption></figure>
# DESIGN OF A METALLIC MAGNETIC CALORIMETER FOR 1–20 keV X-RAY SPECTROMETRY

We have designed a metallic magnetic calorimeter dedicated to the determination of x-ray emission probabilities in the energy range 1–20 keV. Our aim is to have a photon absorption efficiency greater than 99.9% in the considered energy range. In this case, the detector essentially measures absolute intensities; it does not need to be calibrated in efficiency and the measured intensities do not need to be corrected for efficiency. This is achieved by using a gold absorber of 50 µm thickness. In order to keep the total heat capacity of the detector small enough for an energy resolution better than 50 eV, we have fixed the diameter of the absorber to 250 µm.

The sensor parameters that maximize the signal-to-noise ratio of a MMC3 with the absorber described above (heat capacity 3.5 * $10^{-12}$ J/K at 20 mK) are a diameter of 44 µm, a height of 11 µm, an erbium concentration of 890 ppm and a magnetic field of 6.2 mT for an operating temperature of 20 mK. A sensor of this diameter can be placed directly in the sensing loop of a commercially available SQUID, offering the advantages of ease of realization and a very efficient coupling between the paramagnetic sensor and the SQUID as compared to coupling via a flux transformer. At present, we are using a SQUID with a loop diameter of 50 µm for sensor read-out. Adjusting the sensor dimensions and the magnetic field, the signal-to-noise ratio compared to the optimal case will only be reduced by a few percent.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Left: Cross sectional view of the MMC for 1–20 keV x-ray spectrometry. Middle: Detector holder ready to place the Au:Er temperature sensor. Right: Detector integrated with source and collimator.</figcaption></figure>

## First step of realization

As a first step, we have realized a Au:Er sensor of 50 µm diameter and an erbium concentration of 900 ppm. As it is being used without an additional absorber in a first attempt, we have increased its height to 25 µm in order to have a fairly high quantum efficiency (98% for 20 keV photons). We have fixed it inside the loop of SQUID 1 with a small quantity of vacuum grease. The SQUID carrying the Au:Er sensor was mounted in the center of a lead ring and a superconducting coil next to the ring (Fig. 3). The magnetic field used to magnetize the sensor is first created by injecting a current into the coil. The field is then being maintained by the lead ring that is superconducting at temperatures less than 7.2 K, and the current injection is turned off. We have mounted a 55Fe source and a collimator in front of the sensor and shielded the ensemble from external magnetic fields by a superconducting lead cylinder. The detector was mounted in our dilution refrigerator and cooled to 17 mK. The temperature was stabilized to within ±4 µK. For signal read-out, we have used a two-stage SQUID configuration as discussed in the previous section.

Each photon detection results in a pulse of an amplitude of ~80 mV/keV at the output of the SQUID electronics. The measured signal rise time of ~2 µs is limited by the wiring and the SQUID electronics. The thermal coupling of the detector to the bath, limited by the use of vacuum grease, is very weak, resulting in a very long signal decay time of 135 ms.

During first measurements carried out with this detector, the room temperature SQUID electronics generated abnor mal oscillations at various frequencies that strongly degraded the acquired data. Nevertheless, we recorded a preliminary spectrum of the 55Fe source (Fig. 4).

The main peak (Mn Kα) consists of two lines separated by 11.1 eV. We fit the spectrum with a software developed by LNHB.⁶ We used a Voigt function (Gaussian convoluted with a Lorentz function taking account of the natural width of the lines). The fit shows that the peaks exhibit a tail toward low energies whose origin is not yet understood. The energy resolution determined graphically as the full width at half maximum of the total Kα peak indicates that the energy resolution of the detector is less than 40 eV. We expect to substantially improve our energy resolution since the obtained value is far from the resolution one can expect for the given experimental setup. The theoretical limit of energy resolution is given by thermodynamic noise. Calculated for a detector with an absorber of the dimensions indicated above, it corresponds to an energy resolution of the order of 1 eV (FWHM) at 20 mK. Taking into account the other noise contributions mentioned in the Operating Principle Section, the final expected energy resolution should be of the order of a few eV.

# A METALLIC MAGNETIC CALORIMETER FOR 20–200 keV X-RAY AND GAMMA SPECTROMETRY

In a first approach, we decided to build a detector with a simple geometry, similar to the one described in Ref. 4. But in our configuration we have used a two-stage SQUID system as described in earlier. The present detector consists of a Au:Er sensor with a diameter of 420 µm and a height of 390 µm containing 600 ppm of Er. The detection efficiency by photoelectric absorption for 100 keV photons, as
<figure><img src="image_5.png" /><figcaption>**Figure 4.** First recorded spectrum of a <sup>55</sup>Fe source.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Cross sectional view of the MMC prototype for 20–200 keV x-ray and gamma spectrometry.</figcaption></figure>

determined with the Beer-Lambert approximation, is about 97%. For this prototype (Fig. 5), we did not use an additional absorber. The sensor has a large diameter, therefore it is inductively coupled to SQUID 1 via a superconducting flux transformer with a pick-up coil of 18 turns.

The heat capacity of the detector is about $5 \times 10^{-9}$ J/K, more than two orders of magnitude larger than that of the 1–20 keV detector. Therefore, a much stronger thermal coupling between the detector and the bath is needed to achieve a reasonably short decay time. The thermal link consists in a gold foil ultrasonically bonded both to the sensor and to the bath.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Typical pulse, resulting from the absorption of a 59.54 keV photon in the detector.</figcaption></figure>

A <sup>241</sup>Am source was mounted in front of the detector. To avoid events in the pick-up coil or in the thermal link, a gold collimator with a diameter of 300 µm and a thickness of 1 mm was placed between the source and the detector. The detector was operated at 20 mK. The magnetic field of 3 mT is created by a superconducting coil that permits to run a persistent current in the coil. A superconducting heat switch is used to interrupt the injected current while maintaining the persistent current.

The output signal exhibits a rise time of 26 µs. This intrinsic rise time is not altered by the electronics. The decay time has two exponential components. The fast decay time is due to an additional heat capacity in the Au : Er material.4 The long decay time, corresponding to the return to the equilibrium temperature, is about 30 ms. A typical pulse after analogical filtering is illustrated in Fig. 6.

Given the relatively large sensor volume, the contribution of magnetic Johnson noise is comparable with the thermodynamic noise for this detector. With the two-stage SQUID read-out, the SQUID noise is not likely to be a major contribution. Considering these noise sources, an energy resolution less than 200 eV is expected in the overall energy range. But in this experiment, the energy resolution was degraded mainly by temperature fluctuations and instabilities of the SQUID working point. Unexpected power dissipation in a filter resistor on the chip of SQUID 1 (at 20 mK) is the main reason of these instabilities. In the next experiment the onchip filter will be removed; we have implemented an efficient filter on the 1 K stage of the refrigerator.

## CONCLUSIONS AND PERSPECTIVES

First results obtained with the MMC dedicated to the energy range 1–20 keV are promising, although the broadening of the lines in the first spectrum is non Gaussian and remains to be understood. The energy resolution is partially limited by an abnormal noise contribution of the present SQUID electronics. We have just received a new electronics that will soon be tested. The next step in the development will be the realization of a detector including a gold absorber of a larger active area and a quantum efficiency greater than 99.9% for 1–20 keV photons.

Concerning the MMC dedicated to the energy range 20–200 keV, a new read-out SQUID will be implemented without an on-chip filter in order to have a stable operating temperature and thus a stable SQUID working point. We expect to improve the energy resolution to less than 200 eV.
Regarding the field of XRF and synchrotron applications, some ample developments have already been done with other kinds of cryogenic detectors (TES and STJ).⁷ The detector is mounted inside the cryostat and held at the end of a cold finger, separated from the sample by an IR blocking window.

The count rate and the solid angle of cryogenic detectors are smaller than those of semiconductor detectors, but can be increased by using detector arrays. The great advantage of these cryogenic detectors is the energy resolution, which is typically about 10 eV and in some cases about 3 eV. The energy range is 1–10 keV. Hence, cryogenic detectors offer a good compromise between good energy resolution and high detection efficiency. The magnetic calorimeter is a promising technology to extend the energy range to hard x-rays with a very good linearity.

## REFERENCES

1. Enss C (ed.). Cryogenic Particle Detectors, Topics Applied Physics 99. Springer: Berlin/Heidelberg, 2005.

2. Ohkubo M, Mitsuda K, Takahashi H. (eds.). In Proceedings of 11th International Workshop on Low Temperature Detectors, Nucl. Instr. & Meth. A 559/2, 2006.

3. Fleischmann A, Enss C, Seidel G. Nucl. Instrum. Methods A. 2005; 559.

4. Enss C, Fleischmann A, Horst K, Schonefeld J, Sollner J, Adams JS, Huang YH, Kim YH, Seidel GM. J. Low. Temp. Phys. 2000; 121: 137.

5. Drung D, Muck M. SQUID electronics. In "The SQUID Handbook—Vol. I: Fundamentals and Technology of SQUIDs and SQUID Systems, Clarke J, Braginski Al (eds). Wiley-VCH, Weinheim, Germany.

6. Ruellan H, Lepy MC, Plagnard J. Présentation du logiciel COLEGRAM, Note technique LPRI/95/016, 1995; (in French).

7. Friedrich S. J. Synchrotron Radiat. 2006; 13: 159.