Principle of microcalorimeters

A microcalorimeter is a new type of detector based on thermal signals, which was proposed by Moseley, Mather, and Dan McCammon in 1984 [39]. As shown in Fig. 1a, a microcalorimeter consists of four parts: an absorber, thermometer, thermal weak link, and heat sink. When the incident particle is stopped by the absorber, its kinetic energy is converted to thermal energy, causing a temperature increase in the absorber; $\delta T\infty \delta E/C$, where C is the heat capacity. Using a thermometer, $\delta R\infty \delta T$, the energy of the incident particle $\delta ER\times C$ can be inferred. Generally, the linear region of the detector is selected for the energy spectrum measurement, and thus, δE=k×δR×C. After calibration with the X-ray source, the slope k can be obtained. Thermodynamic fluctuation noise and Johnson noise are the main noise sources of microcalorimeters, and the readout system contributes little to the total noise. Thus, its energy resolution is mainly related to T, C, and the thermometer sensitivity. Unlike non-equilibrium detectors, the energy resolution of a TES ΔE_FWHM is independent of the X-ray energy E; $\delta E_{\text{F}WHM}\propto \sqrt{4k_{\text{B}}{T}_0{}^{2}C/{\alpha }_{\text{I}}}$, where α_I is the temperature coefficient of resistance [40]. According to this equation, to obtain a higher energy resolution, a lower temperature, smaller heat capacity, and higher α_I are required. Combining two factors, such as the cooling power of the cryogenic system and the performance of the energy spectrometer, a microcalorimeter generally operates at a temperature of 100 mK or lower. For the heat capacity, the absorber volume should be as small as possible to ensure sufficient quantum efficiency and detection area.

Fig. 1Full-screen View

Principle of microcalorimeters: (a) shows the main structure and working principle of microcalorimeters. It consists of four parts: an absorber, thermometer, thermal weak link, and heat sink. X-rays are absorbed and converted into thermal signals and then an electrical signal. The thermal signal will finally be conducted to the heat sink before returning to the equilibrium state to wait for the next incident particle. (b) shows the three thermometers that can be applied to microcalorimeters. Depending on the impedance and signal type of each thermometer, the type of signal amplifier is also different.

Depending on the type of thermometer, microcalorimeters are divided into three main types: semiconductor microcalorimeters [41], TES microcalorimeters [1], and metallic magnetic calorimeters (MMC) [42]. Semiconductor microcalorimeters use boron-doped silicon or transmuted germanium as temperature sensors with low sensitivity to changes in temperature. Owing to its large impedance, a JFET can be used as a signal amplifier. TESs have high temperature sensitivity. However, the transition edge is narrow; hence, it is prone to saturation and has relatively poor linearity. Because of its low impedance, a superconducting quantum interference device (SQUID) is required as a signal amplifier. MMC use paramagnetic materials as temperature sensors, have no saturation problems, and have good linearity. However, owing to its high heat capacity, it requires a lower operating temperature. In addition, it is difficult to multiplex the readout circuit; therefore, MMC are still under development.

Compared with semiconductor thermometers, the improvement in the temperature sensitivity by 10 to 100 times when using a TES makes it more flexible for structural design and material selection. For example, a high-specific-heat material, such as gold (Au), can be selected as the absorber. This change greatly improves the count rate and expands the range of material selection, allowing the use of microfabrication to obtain large arrays. The reduction in the heat capacity limitation of the absorber also makes it possible to bury the source in the absorber; therefore, several research institutes have used this feature to conduct neutrino mass measurement studies [43].

Selection of the absorber material was one of the main points of interest in this study. The time constant of a microcalorimeter can be expressed as τ=C/G, where G denotes the thermal conductance. Once the structure and working temperature are determined, the value of G is relatively fixed. According to this formula, a smaller heat capacity corresponds to a smaller time constant, and according to the expression for δE_FWHM, the smaller the heat capacity of the absorber, the higher the energy resolution. Therefore, a small heat capacity corresponds to a high time and energy resolution. The heat capacity of the absorber is C=c_v×S×H, where c_v is the specific heat capacity per unit volume, S is the area, and H is the thickness. For X-rays and γ-rays, the higher the energy, the stronger the transmission ability. After the upper limit of the expected energy E_max is determined, the thickness H_min corresponding to E_max and the predetermined quantum efficiency (such as 70%) can be calculated, and the maximum photosensitive area S_max can be obtained. To obtain a larger photosensitive area, the absorber should be chosen to achieve the best trade-off between high-Z and low-specific heat capacity. The specific heat capacity at extremely low temperatures is mainly contributed to by electrons and phonons; materials with higher specific heat capacities also have better conductivities. Therefore, from the perspective of maximizing the photosensitive area, it is desirable to use materials with lower electrical conductivities, such as semi-metals (for example, bismuth) or superconducting materials (for example, lead). To improve the conductance, a layer of Au or copper can be added to the absorber to improve the thermal conductivity.

Structure of a TES X/γ ray detector

TES X/γ ray detectors include a TES chip, input SQUID, and low-temperature block. The TES chip converts X-rays into current signals, and the input SQUID converts the current signals into voltage signals. The functions of the low-temperature block include low-temperature circuit connections, magnetic shielding, electromagnetic shielding, heat sinks, and infrared windows.

The typical structure of a TES sensor chip is shown in Fig. 2, where the silicon substrate is used as the support structure and heat sink, and the thickness of the silicon material is generally between 300 and 500 μM. Suspended silicon nitride is used as a thermally weak link structure, which can be realized by removing all backside silicon via deep silicon etching. The thickness of the silicon nitride is of the order of submicrometers. A molybdenum–copper bilayer superconducting material is used as a thermometer, and the total thickness is of the order of submicrometers. Superconducting materials, such as molybdenum or niobium, are used as wires with a typical thickness of the order of 100 nm. Using high-Z-value materials as the absorber, the thickness in the X-ray range is typically of the order of a few micrometers, whereas for γ-rays, it will reach the submillimeter level.

Fig. 2Full-screen View

(Color online) Typical structure of a TES chip, in which the silicon substrate is used as the support structure and heat sink, the suspended silicon nitride is used as the thermally weak link structure, a superconducting film is used as a thermometer, and a high-Z-value metal is used as the absorber. The figure on the left shows a typical structure for X-ray detectors, whereas the figure on the right shows a typical structure for γ-ray detectors.

The normal resistance of the TES chip used for X/γ ray detection is low, generally at the level of 10 mΩ; therefore, the input SQUID chip is used to convert the current signal into a voltage signal. A typical non-multiplexed SQUID structure is shown in Fig. 3. A single-stage SQUID comprises two Josephson junctions with the same structure. When the current in the TES changes, the voltage across the device changes, and the voltage signal is transmitted to the low-temperature signal amplifier through the cable for further amplification and feedback.

Fig. 3Full-screen View

Structure diagram of a single-stage SQUID, which consists of a ring-shaped superconducting coil and two Josephson junctions. The magnetic field generated by the current signal of the input coil will generate a voltage signal across the SQUID, while the magnetic field generated by the feedback coil is opposite to the direction of the input coil, making it work in the linear region [44].

The low-temperature block is responsible for electrically connecting the TES chip and input-SQUID and is also responsible for the thermal connection, refrigerator (cold head), and shielding of electromagnetic/magnetic fields. A low-temperature block is limited by the chip structure and its scientific applications, and its structure varies.

Auxiliary system of the TES X/γ ray detector

The detector requires a cryogenic system, low-temperature signal amplifier, and data acquisition and analysis system (DAQ) to realize energy spectrum measurement. The following is a brief introduction:

Cryogenic system: The refrigeration system provides low temperature, low vibration, low magnetic field, and low electromagnetic interference environments for the TES X-ray detector, mainly including the thermostat, temperature control system, vibration isolation structure, and magnetic/electromagnetic field shielding system. As mentioned above, the thermostat must reach a temperature of 100 mK or lower. To reduce the temperature fluctuation of a low-temperature X-ray detector, it is generally necessary to control the temperature fluctuation of the thermostat to the order of μK.

Low-temperature signal amplifier: Signal amplification systems based on non-multiplex SQUIDs generally use a SQUID array on a 4 K cold plate to further amplify the signal. Its main function is to suppress the noise of the operational amplifier in a room-temperature circuit. Figure 4 illustrates the principle of feedback amplification. The current signal δI_input first generates a magnetic field signal in the SQUID loop, and then forms a voltage signal. The voltage signal is further amplified by the 4 K SQUID array and operational amplifier at room temperature. The operational amplifier passes the signal through the resistor R_f to form a negative feedback, and the feedback coil forms a reverse-changing magnetic field in the SQUID loop, finally reaching a state where the feedback currents δI_f and δI_input are proportional to each other, δI_f=k_f×δI_input. The room-temperature terminal voltage signal is proportional to the low-temperature current signal δV_300K=δI_f×R_f=k_f×δI_input×R_f.

Fig. 4Full-screen View

Structure of the auxiliary system: The main structure of the auxiliary system is a set of dilution refrigerators. The low temperature block is installed on a 50 mK cold plate. X-rays are irradiated onto the TES X-ray detector through the X-ray window. The signal is amplified and transmitted from 4 K to 300 K by the low-temperature signal amplifier, which then reaches the DAQ.

DAQ: The data acquisition and analysis system includes an analog-to-digital conversion module (ADC), a waveform reconstruction module, and an energy spectrum analysis module.

TES X-ray detectors at ShanghaiTech University and the measured spectrum

Several sets of synchrotron radiation facilities and free-electron laser facilities have been constructed or are under construction around ShanghaiTech University; therefore, many beamline end stations are also being constructed simultaneously. To meet the energy spectrum measurement requirements of several end stations, ShanghaiTech University built a set of TES X-ray detectors for the X-ray band. The detectors use a 4×4 pixel TES sensor chip, and the area of a single pixel is approximately 0.5 mm×0.5 mm. The TES thin film is a molybdenum–copper bilayer film with a transition temperature of approximately 70 mK with molybdenum leads. The absorber layer is 2.4 μM-thick bismuth with a detection efficiency of 70% at 5.9 keV. The input SQUID chip uses a single-stage SQUID, and the refrigeration system has a minimum working temperature of 23 mK. The low-temperature amplifier adopts 16 SQUID arrays connected in series, and the room-temperature feedback amplifier circuit has a bandwidth of 1 MHz. An ADC board based on a PXIe chassis is used in the DAQ. After the signal is transmitted to the computer, the pulse height is fitted using offline software, the heights are calculated and calibrated, and the X-ray energy spectrum is finally obtained. After preliminary tests, the detector had an energy resolution of 5.2 eV at 5.9 keV. The energy spectrum and fitting curve are shown in Fig. 5.

Fig. 5Full-screen View

X-ray energy spectrum of an ⁵⁵Fe radioactive source. ⁵⁵Fe emits two X-ray spectral lines with energies of 5900 and 5890 eV, and the detector can clearly distinguish them. After fitting, the detector obtained an energy resolution of approximately 5.2 eV around 5900 eV with R_square=0.972 .

Two different cases are presented in this paper. In the first case, the composition of the sample was extremely complex, and the relative intensities of the spectral lines of many elements must be determined over a wide energy range. The second case is the measurement of impurity elements in high-purity samples, which required finding faint impurity spectral lines in a strong scattering background environment. In the first case, we used coins and stones as samples. In the second case, we used samples of high-purity (99.95%) niobium.

As shown in Fig. 6, X-rays from the Rh target tube irradiated the coins and stones, and the fluorescence spectrum was collected by the TES X-ray detector. The Rh target voltage was set to 15 kV. Because the K-absorption edge energy level of Rh is approximately 23 keV, the output X-ray is mainly generated by the bremsstrahlung process. The energy spectrum was relatively smooth, and the photon flux changed slowly with energy.

Fig. 6Full-screen View

(Color online) Energy spectrum obtained by irradiating complex composition materials, such as coins and stones, with an Rh target. The Kα and Kβ spectral lines of copper, zinc, nickel, iron, manganese, calcium, titanium, potassium, silicon, argon, and other elements can be clearly observed from the energy spectrum. Owing to the difference in composition, coins and stones exhibit clear differences in the relative intensities of the spectral lines.

The main content of the coin used for testing was brass, with a nickel-plated pattern in some areas. In the X-ray fluorescence spectrum, we observed clear Kα and Kβ spectral lines of copper, zinc, and nickel. At the same time, a lower content of iron and significantly lower content of manganese and silicon were found. Furthermore, clear L_α1 and L_β1 spectral lines of Rh were found, which originated from the reflection of the input X-ray by the coin. There were clear Ar Kα and Kβ spectral lines in the energy spectrum, which originated from argon in air.

The stone used for the test was red in color and had a high iron content. In the X-ray fluorescence spectrum, we observed clear Kα and Kβ spectral lines of iron, manganese, calcium, titanium, potassium, and silicon. At the same time, a lower iron content and lower levels of cerium, copper, zinc, and gallium were observed. In the spectrum, obvious Rh L_α1 and L_β1 spectral lines were seen, which originated from the reflection of the input X-ray by the stone. There were also clear Ar Kα and Kβ spectral lines.

The Au-target X-ray tube was irradiated with high-purity niobium. The Au target voltage was set to 15 kV. Because the L-absorption edge energy level of Au is lower than 15 keV, the X-ray output of the X-ray tube was mainly composed of a smooth energy spectrum generated by bremsstrahlung and a sharp characteristic peak.

In the X-ray fluorescence spectrum, the L characteristic line group of niobium was clearly observed. As shown in the enlarged subgraph of Fig. 7, L_{α 1}, L_{β 1}, L_{β 3}, L_{β 4}, and other spectral lines of niobium were observed. There were spectral lines around these that did not correspond to the database. The Kα and Kβ lines of Ar were also observed in the X-ray fluorescence spectrum. The Kα lines of low-content silicon, potassium, titanium, nickel, and copper shown in the energy spectrum indicate that these were the main components of impurities in the niobium metal. In the energy spectrum, we observed clear L_{α 1} and L_{β 1} spectral lines of Au and Kα lines of iron, which originated from the reflection of niobium from incoming X-rays. The ratios of the Kα and Kβ spectral lines of iron significantly deviated from the theoretical values; the detailed reasons for this must be further explored in future studies. Because the spectral lines of iron did not overlap with other spectral lines, they had no influence on the spectral analysis of the other elements.

Fig. 7Full-screen View

Energy spectrum obtained by irradiating high-purity niobium with an Au target X-ray tube. From the energy spectrum, L_{α 1}, L_{β 1}, L_{β 3}, and L_{β 4} of the niobium (Nb) lines can be clearly observed. On the energy spectrum, we can see the obvious L_{α 1} and L_{β 1} spectral lines of gold as well as the Kα line of iron.

In the energy spectrum of niobium, at the low-energy end of the L_{α 1}, L_{β 1} spectral lines of Au, and Kα of iron, bulge structures were observed. These structures were caused by Compton scattering when X-rays irradiated the sample, which eventually formed a bulge structure at the low-energy end of the elastic scattering peak. Because the Compton scattering bulge is always accompanied by an elastic scattering peak, its existence can be used to determine whether it corresponds to the elastic scattering peak or characteristic spectral line. For example, at the low-energy end of the spectral line of L_{α 1} of niobium, no bulge structure was observed; therefore, it can be assumed that L_{α 1} of niobium originated from niobium in the sample. At the low-energy end of the iron Kα spectral line, an obvious bulge structure was observed; hence, it can be concluded that most of the iron Kα spectral line did not originate from the sample, but from the iron-containing vacuum parts around the sample.

Fabrication of γ-ray detector based on the TES

To extend the measurement energy range to 100 keV or even 200 keV, the thickness of the absorber must be increased to the submillimeter level. A lead–tin alloy (63% Pb, 37% Sn) was used as the absorption material. The first reason for choosing this material is that it is superconducting with a small specific heat capacity at low temperatures [3]. Furthermore, lead and tin exhibit a strong absorption effect on X/γ-rays. The thermal transport process of the incident X-rays at different positions of the absorber is not the same, which causes X-rays with the same energy to generate different pulse shapes. To reduce this effect, the absorber was processed into a spherical shape. The spherical structure also reduces the bonding point area, which can reduce the difficulty of bonding. The fabrication process of the entire TES γ-ray sensor is shown in Fig. 8. First, a TES sensor array was prepared, and a small amount of epoxy resin was placed on the TES sensor; subsequently, the pre-processed lead–tin alloy balls were bonded using a robotic arm. After the epoxy resin was cured, the TES X-ray sensor mentioned in the previous chapter was replaced with the TES γ-ray sensor. Finally, a set of TES γ-ray detectors for γ-ray energy range was obtained.

Fig. 8Full-screen View

(Color online) Fabrication process of the TES γ-ray sensor: First, we prepare a TES sensor array, then place a small amount of epoxy resin on the TES sensor. Subsequently, the pre-processed lead–tin alloy balls are bonded by the robotic arm.

For the size and shape of the absorber, the absorbability of lead–tin alloys with different thicknesses to X-rays and γ-rays with different energies was calculated using the NIST database (PhysRefData). After preliminary calculations, a sphere with a diameter of 0.6 mm could obtain a high detection efficiency in most positions; therefore, the results presented in this paper are based on a lead–tin alloy absorber with a diameter of 0.6 mm. Figure 9 shows the absorption efficiency curves at different distances from the ball axis. It was observed that the position within 0.5 mm from the axis still had a high blocking ability, and the blocking ability sharply declined in the area beyond 0.5 mm.

Fig. 9Full-screen View

(Color online) Absorption efficiency at different distances from the ball axis. The diameter of the ball is 0.6 mm, and the material is a lead–tin alloy.

Brief description of the experimental setup

We used ²⁴¹Am as the γ-ray source. We coated ²⁴¹Am on a silver-plated metal sheet and then wrapped ²⁴¹Am with aluminum foil. This can effectively reduce the risk of ²⁴¹Am pollution to the surrounding environment while simultaneously reducing the signal intensity of α particles and β particles. The thickness of the aluminum foil was approximately 0.1 mm. This was placed inside the refrigerator 5 mm from the TES γ-ray detector, the surroundings were covered with lead, and then the dilution refrigerator was cooled. After the temperature reached approximately 23 mK, the temperature resistance(R–T) curve of the TES device was measured. The measured transition temperature was approximately 70 mK. Biasing the TES on the transition edge, the energy spectrum of the X-rays and γ-rays generated by the ²⁴¹Am source was measured.

Time constant and count rate

The response of the TES γ-ray detector to a single γ-ray is shown in Fig. 10. The width of the rising edge was approximately 0.2 ms, and the width of the falling edge was approximately 80 ms. The falling edge of the pulse signal decayed quasi-exponentially. Through fitting, the average time decay constant was τ = 8.54±0.06 ms. After 10 τ, the signals returned to the baseline level. According to the estimation of this time constant, the maximum count rate of a single pixel of the detector was approximately 10 CPS. This implies that the detector is not suitable for high-count-rate measurement scenarios.

Fig. 10Full-screen View

Left plot: R–T curve of the TES γ-ray detector. When collecting the energy spectrum, this is biased at the position of 1 mΩ. γ-rays will cause the temperature and resistance of the detector to rise. Right plot: Pulse signals generated by different energy X-rays and γ-rays have a rising edge width of approximately 0.2 ms and a falling edge width of approximately 80 ms. As shown in the zoomed-in image, the signal corresponding to the nuclear spectral line from ²⁴¹Am with an energy of 59.5 keV is most dense around 1.845 V.

Linear intervals and saturation energy

²⁴¹Am decays to Np after the emission of α particles with an energy of approximately 5 MeV and a γ-ray of 59.5 keV with 35.92% probability. When Np is excited, it emits a certain number of fluorescence lines corresponding to the K energy shell and L energy shell. Because there are supporting structures containing elements such as silver, copper, iron, and chromium around the source, the corresponding fluorescence lines can also be observed in the energy spectrum. The energy of each spectral line can be obtained by querying the X-ray fluorescence database http://bruceravel.github.io/demeter/(Demeter) and the manual for²⁴¹Am http://www.nucleide.org/DDEP_WG/introduction.pdf(nucleide.org). According to the settings of the experimental device, it was predicted that the number of pulses corresponding to 59.5 keV photons was the largest. It can be inferred from the right image of Fig. 10 that a pulse signal with a height of approximately 1.845 V corresponds to this energy. Through linear estimation, the energy spectrum was found with Kα of copper, L_{α 1}&L_{β 1} of Np, K_α1&K_α2&Kβ of silver, and 26.3 keV&59.5 keV nuclear transition lines of ²⁴¹Am. Using the pulse heights corresponding to these spectral lines to fit the energy values in the database, as shown in Fig. 11, there was a certain deviation in the fitting of one power function (R_square=0.9966), and the fitting effect of the quadratic function was excellent (R_square=1.000); therefore, the relationship between the pulse height and energy could be expressed by a quadratic function.

Fig. 11Full-screen View

There is a certain deviation in the fitting of the quadratic function, the fitting effect of the quadratic function is excellent, and R_square reaches 1.000.

It can be seen from the right plot of Fig. 10 that the falling edge of the pulse whose height was lower than 5.5 V decayed exponentially. When the incident particle energy was too high, the pulse appeared saturated with a flat top of approximately 5.5 V. After a certain period of time, it evolved into an equilibrium state at an exponential decay rate. It can be seen from Fig. 11 that the pulse height of 5.5 V corresponds to the energy of 220 keV. Therefore, the detector is suitable for γ-ray detection at energies lower than 220 keV.

Energy spectrum and resolution

The detected energy spectrum shown in Fig. 12 was obtained by accumulating the pulse height of each signal calibrated using the least squares fit "quadratic" model inferred by data in Fig. 11. Via Gaussian fitting, the detector had an energy resolution of 161.5 eV at 59.5 keV. However, at lower energies, such as 13.95 keV and 17.75 keV, the detector achieved energy resolutions of 71.6 eV and 69.1 eV. In theory, the energy resolution of TES γ-ray detectors should be independent of the photon energy. Therefore, the achieved results do not seem to be consistent with theoretical expectations. The reason for this phenomenon requires further analysis before conclusions can be drawn. In any case, a possible reasonable explanation for this inconsistency could be as follows: As described in the previous section, the detector was still linear at 59.5 keV; hence, the problem was unlikely to have been introduced by nonlinearity. As mentioned earlier, the higher the energy, the stronger the penetrating ability of the particle; therefore, the thermalization path of the 59.5 keV photon in the absorption body was significantly more complex than that of the 17.7 keV photon, which may be the main reason for this problem.

Fig. 12Full-screen View

Measured energy spectrum of Am241 exhibits spectral lines of Kα of copper, L_{α 1}&L_{β 1} of NP, K_α1&K_α2&Kβ of silver, and the 26.3 keV&59.5 keV nuclear transition lines of ²⁴¹Am.