Active optical thermal feedback for stabilizing cryogenic detector temperature

Sergey V. Uchaikin 1

Shamil H. Sultanov 2,3,4✉ Emailssultanov@mail.ru

Xiaofeng Zhou 2,3

Pavel F. Baranov 5

Valery N. Borikov 5

Jianguang Wei 2,3

1 Dark Matter Axion Group (DMAG), Institute for Basic Science (IBS) Creation Hall, 193 Munji- ro, Yuseong-gu 34051 Daejeon Republic of Korea

State Key Laboratory of Continental Shale Oil Northeast Petroleum University 163318 Daqing Heilongjiang China

3 Heilongjiang China Russia Joint Laboratory of Efficient Development of Hard-to-Recover Hydrocarbon Reserves (International Cooperation) Northeast Petroleum University 163318 Daqing China

4 Ufa State Oil Technical University (USPTU) Kosmonavtov Str 1 450064 Ufa, Bashkortostan Russian Federation

5 School of Non-Destructive Testing National Research Tomsk Polytechnic University (TPU) Lenina Ave 40 634050 Tomsk Russian Federation

Sergey V. Uchaikin ¹, Shamil H. Sultanov^2,3,4*, Xiaofeng Zhou^2,3+, Pavel F. Baranov⁵, Valery N. Borikov⁵, Jianguang Wei^2,3+

1Dark Matter Axion Group (DMAG), Institute for Basic Science (IBS), Creation Hall, 193 Munji-ro, Yuseong-gu, 34051, Daejeon, Republic of Korea

2State Key Laboratory of Continental Shale Oil, Northeast Petroleum University, Daqing, Heilongjiang 163318, China

3Heilongjiang China Russia Joint Laboratory of Efficient Development of Hard-to-Recover Hydrocarbon Reserves (International Cooperation), Northeast Petroleum University, Daqing, 163318, China2

4Ufa State Oil Technical University (USPTU), Kosmonavtov Str 1, Ufa, 450064, Bashkortostan, Russian Federation

5School of Non-Destructive Testing, National Research Tomsk Polytechnic University (TPU), Lenina Ave 40, Tomsk, 634050, Russian Federation

*corresponding ssultanov@mail.ru

Xiaofeng Zhou and Jianguang Wei contributed equally to this work.

ABSTRACT

Cryogenic calorimeters with superconducting phase-transition thermometers are highly sensitive particle detectors. In these systems, particle interactions in the absorber are measured via temperature changes detected by the thermometer. However, performance can degrade due to absorber temperature change, which reduce the detector’s count rate. Active thermal feedback is used for a massive detectors which characteristics are limited from heater inertia. Here, we introduce an active optical thermal feedback (OTF) mechanism that avoid using resistive heater and stabilizes the detector’s operating temperature. This stabilization is achieved through controlled heating provided by a light source, enhancing the detector’s count rate and linearity. Experimental results demonstrate that the OTF significantly reduces thermal effects.

Introduction

The massive transition-edge sensor (TES) is renowned for its exceptional sensitivity (see, for example, [1]). It consists of a thin superconducting film deposited on a crystal substrate. These detectors operate at temperatures near the superconducting transition of the film, where a small temperature variation induces a significant change in resistance. TESs are intensively used in fundamental research areas such as dark matter searches, double beta decay, and other experiments [2, 3], as well as in practical applications like mass spectrometry [4, 5].

To increase sensitivity, these detectors operate at cryogenic temperatures where thermal phenomena, such as the thermal component of the signal, emerge and significantly reduce the count rate. The count rate is constrained by substrate heating, which introduces a long thermal component into the output signal [6]. In some applications, where events are not rare or where background noise is substantial before rejection, the count rate of the detector becomes a critical performance parameter. Additionally, TESs face challenges, including limited dynamic range and linearity due to the finite width and irregularity of the superconducting transition.

Keywords: cryogenic detector, TES, active thermal feedback, optical thermal feedback, thermal component.

1.1. Electrothermal Feedback (ETF)

Electrothermal feedback (ETF) is a widely used technique to enhance the performance of TESs [7, 8]. By leveraging the Joule heating of the thermometer, ETF stabilizes the thermometer’s temperature. When the TES is voltage-biased, it can self-regulate within the transition temperature range. A modified approach [9] incorporates the voltage bias source into the feedback loop, further enhancing performance. However, at massive detector operation at low temperature due to critical current effects in the superconducting film the ETF is not very effective [10].

1.2. Active Thermal Feedback (ATF)

Active thermal feedback (ATF), described in [11, 10], involves attaching a heater to the thermometer, such as a nonsuperconducting gold-bonded wire or a normal thin film deposited on the TES substrate. During operation, the temperature of the sample holder is maintained well below the thermometer’s superconducting transition temperature.

In this setup, the heater current is controlled using a PID controller connected to the output of the thermometer’s SQUID readout, with a square root circuit included to linearize the heater’s response to current (Fig. 1). When events occur, and phonons from the absorber are deposited in the thermometer, the feedback reduces the heater power accordingly. ATF stabilizes the thermometer’s working temperature, improving the linearity and count rate of slower detectors [11].

However, the speed of ATF is limited by the thermal inertia of the heater. For instance, experimental results [12] show that, due to heater inertia, ATF does not always reduce the output pulse height as conventional feedback mechanisms might. Another issue arises when a film heater is deposited on the absorber, as part of the power penetrates into the absorber, creating its own thermal effects.

Fig. 1

Block diagram of the Active Thermal Feedback (ATF) system. Key components include: Ce, the heat capacitance of the thermometer; G, the thermal conductance from the thermometer to the bath; K, the transformation coefficient from temperature change to SQUID output; kF, the feedback coefficient; τH, the heater time constant; QX and QF, the input and feedback thermal flows, respectively; QG, the thermal flow from the detector to the bath via the bonding wire (heater); ∆T, the temperature change of the thermometer; V, the output voltage; and s, the Laplace parameter.

Key components include: Ce, the heat capacitance of the thermometer; G, the thermal conductance from the thermometer to the bath; K, the transformation coefficient from temperature change to SQUID output; kF, the feedback coefficient; τH, the heater time constant; QX and QF, the input and feedback thermal flows, respectively; QG, the thermal flow from the detector to the bath via the bonding wire (heater); ∆T, the temperature change of the thermometer; V, the output voltage; and s, the Laplace parameter.

2. Active Optical Thermal Feedback

In this work, we develop the concept of active optical thermal feedback (OTF) as proposed in [13]. Unlike approaches that use a resistive heater, the OTF employs light from a relatively fast illumination source to heat the thermometer film (Fig. 2). This method minimizes thermal inertia and provides faster thermal control.

The illumination source is implemented using a light-emitting diode (LED), which can be positioned within the refrigerator at a 4 K temperature stage. This setup allows efficient heat transfer to the thermometer film without significant delays, making it particularly suited for stabilizing the operating temperature of cryogenic detectors.

Fig. 2

Block diagram of the Active Optical Thermal Feedback (OTF) system. Com- pared to Fig. 1, the resistive heater, represented by 1/(1 + sτH ), is replaced by an LED light source. Additionally, a light attenuator (ATT) is introduced to regulate the power of the light heating. The thick arrows indicate the path of the light within the system.

3. OTF Circuit

The active optical thermal feedback (OTF) system utilizes an SFH756 LED transmitter from Infineon Technologies as the light source [14]. This LED emits red light with a wavelength of approximately 650 nm. The luminous power, QLED, generated by the LED is a function of its current, ILED. However, this relationship can be nonlinear and is influenced by LED temperature changes.

To ensure the feedback circuit operates linearly and minimizes thermal effects on the LED, we designed a specialized circuit and a light splitter- attenuator (LSA) (Fig. 3). In this circuit, the relationship between QLED and its components, QPH1 and QF, is defined by a LSA design and is proportional to coefficients KPH1 and KOTF, respectively. Here, QPH1 represents the power absorbed by the photodiode PH1, while QF corresponds to the power absorbed by the TES’s thermal resistance, Rth. Therefore, Eqs. (1) and (2):

$\:{K}_{PH1}=\frac{{Q}_{PH1}}{{Q}_{LED}}$

$\:{K}_{OTF}=\frac{{Q}_{F}}{{Q}_{LED}}$

This configuration ensures precise control and stability of the feedback system.

Fig. 3

The OTF circuit. The LED, photodiode (PH1 ), the splitter (blue arrows) and SQUID are positioned on the 4 K stage of the refrigerator, while the TES (Rth) and the reference resistor (Rref) are located on the mixing chamber (MXC) stage of the dilution refrigerator. To mitigate the capacitance effect of the input cable, the noninverting input of operational amplifier U3 is shielded and connected as a guard [15]. Thick arrows indicate the path of the LED’s light.

The signal from the output of the SQUID amplifier passes through the PID controller, which is also used to adjust the feedback depth. The output voltage from the PID controller, VF, is applied to the input of the unity-gain operational amplifier (OA) U1. The amplifier U1 also features a secondary input, TEST, which allows heating pulses to be applied for testing and TES calibration purposes. The output of OA U1 drives OA U2, which supplies the LED current, ILED, through a current-limiting resistor. This current generates light power, QLED, from the LED.

A significant portion of the LED’s light power, QPH1, is captured by the photodiode PH1 (SFH250 from Infineon Technologies [14]). The photodiode produces a photocurrent, IPH1 = ρPH1QPH1, where ρPH1 is the photodetector responsivity (in A/W). This current flows through the resistor RPH1, which is connected to the noninverting input of OA U3. Consequently, the output voltage of OA U3, VU3, can be expressed as Eq. (3):

$\:{V}_{U3}={I}_{PH1}\bullet\:{R}_{1}={P}_{PH1}\bullet\:{Q}_{PH1}\bullet\:{R}_{1\:}={P}_{PH1}\bullet\:{K}_{PH1}\bullet\:{Q}_{LED}\bullet\:{R}_{1},\:\:V$

The operational amplifier (OA) U2 provides sufficient LED current, ILED, to maintain the voltage, VU3, at its inverting input (2) equal to the voltage, VF, at its noninverting input (3). Considering VU3 ≈ VF and Eq. (2), we can express by Eq. (4):

$\:{Q}_{F}=\frac{{K}_{OTF}}{{K}_{PH1}}\:\bullet\:\frac{1}{{P}_{PH1}\bullet\:{R}_{1}}{V}_{F}$

,W (4)

A linearity test of the circuit was conducted using an additional setup shown in Fig. 4. In the experiment, the light was split into approximately two equal parts. As a result, KPH1 during the test is half of its value during OTF operation with the TES. The LED and the photodiode PH1 are positioned on the 4 K stage of the refrigerator. One portion of the LED light passes through an optical fiber to photodiode PH1, while the other portion is guided through a separate optical fiber to photodiode PH2. Photodiode PH2 is kept at 50K stage of the fridge temperature to ensure its responsivity, ρPH2, remains unaffected by the temperature variations because of self-heating.

The photodiode PH2 is connected to a voltage follower, U4. The output of U4 is given by Eq. (5):

$\:{V}_{U4}={P}_{PH2}\bullet\:{K}_{PH2}\bullet\:{Q}_{LED}\bullet\:{R}_{2}\bullet\:V$

Fig. 4

Linearity test circuit for the OTF system shown in Fig. 3. The circuit is designed to evaluate the linearity of the OTF setup under experimental conditions. Thick arrows indicate the path of the LED light as it is split and directed toward photodiodes PH1 and PH2.

The transfer gain from the input voltage, VF, to the output voltage, VU4, is Eq. (6):

$\:\frac{{V}_{U4}}{{V}_{F}}\:\approx\:\frac{{V}_{U4}}{{V}_{U3}}=\frac{{\rho\:}_{PH2}}{{\rho\:}_{PH1}}\:\bullet\:\frac{{K}_{PH2}}{{K}_{PH2}}\bullet\:\frac{{R}_{2}}{{R}_{1}}$

As demonstrated, VU4 is also independent of the LED current.

The results of the linearity test are shown in Fig. 5. The circuit’s dynamic range is approximately 60 dB with nonlinearity not exceeding 0.5%. No deviation from the curve in Fig. 5 was observed when the 4 K stage temperature was varied between 4 K and 10 K.

In the experiment with the detector, only a small percentage (approximately 0.05% to 0.1%) of the LED light is directed into the fiber, where it heats the TES. A special LSA, shown in Fig. 6, was developed to reduce the illumination of the detector. In the LSA, a tiny fraction of the light exits the fiber through a small hole in the fiber wall. This light is then directed through additional fibers to the MXC stage of the refrigerator, where it illuminates the TES from the film side.

Fig. 5

Result of the linearity test for the OTF circuit shown in Fig. 5.

Methods and results

To validate the active optical thermal feedback (OTF) concept, we used a detector based on an iridium film. The detector is built on a sapphire crystal substrate with dimensions of 3 mm × 3 mm × 0.5 mm. One side of the substrate is fully covered by the Ir film, which has a critical temperature of 142 mK. The design of the detector follows the specifications described in [16]. Two aluminum pads are sputtered onto the edges of the film, and a gold pad is placed in the center (Fig. 7). The Al pads serve as electrical leads for the TES, while the Au pad is used for thermalization. The operating temperature is maintained using a dilution refrigerator.

Fig. 6

The LSA designed to reduce the power of the light source. The left-hand photo shows the LED and photodetector, enclosed in black and grey plastic housings, respectively. A plastic optical fiber connects the LED to the photodetector PH1. A window is made in the middle of the fiber, where a second fiber is attached. The other end of the second fiber illuminates the TES. The right-hand photo displays the covered attenuator.

To measure the resistance of the TES, we use a current-bias readout circuit, shown in Fig. 3. The change in the TES resistance Rth affects the branching current between Rth and a reference resistor Rref. For small temperature changes in the TES, the readout circuit provides a quasi-linear response to the SQUID amplifier. The current change is detected by a two-stage SQUID amplifier [17].

The reference resistor Rref is a 100 mΩ standard foil FPR resistor from Riedon, with the resistive element bonded to a copper plate using Emerson and Cuming Stycast 2850FT. All connections in the readout circuit are made from twisted NbTi superconducting wires, shielded by Nb tubes. The TES sample holder and reference resistor are located on the MXC stage of the refrigerator.

To minimize the inductance of the readout wires, the SQUID is mounted on the MXC plate through a plastic washer and thermalized to a 4 K plate with a copper wire. The inductances of the SQUID input coil and the wire are Lin = 110 nH and LW = 30 nH, respectively. The average film resistance is approximately 150 mΩ, so the time constant of the readout circuit is Eq. (7):

$\:{\tau\:}_{RO}=\frac{{L}_{IN}+{L}_{W}}{{R}_{th}+{R}_{ref}}=\frac{110\:nH+30nH}{150\:m\varOmega\:+100m\varOmega\:}=0.56\:\mu\:s$

The current for the readout circuit is supplied by a floating current source.

Fig. 7

Schematic of the TES assembly. The diagram illustrates the layout of the iridium (Ir) film on the sapphire substrate, with aluminum (Al) pads for electrical leads and a gold (Au) pad for thermalization.

The current leads are filtered using RC low-pass filters located on the 4 K stage of the refrigerator. Grounding of the input circuit is achieved through a gold wire bonded to the gold pad of the TES, which is also used for the thermalization of the TES.

The transmitter, photodiode, and attenuator are placed on the 4 K stage of the dilution refrigerator. Both the transmitter and the photodiode are housed in plastic enclosures, which create a temperature difference between the LED chip and the base temperature of the refrigerator due to self-heating. This temperature difference allows the diodes to operate reliably at low temperatures. Light between the attenuator and the detector is transmitted via optical fiber, which is bent several times to block infrared photons at the 4 K temperature.

In the OTF circuit operation, the temperature of the MXC stage increases from a base temperature of approximately 12 mK up to 30 mK. The TES sample holder’s temperature is stabilized by a PID controller at 40 mK. This temperature increase is a result of the LED-generated light being absorbed by the TES. Reflected light heats other parts of the MXC stage, but this effect can be minimized using an TES-reflecting covering [18].

During measurements, the optical heater bias is applied to heat the thermometer within its transition range. To simulate a particle impact on the TES, 200 ns pulses are applied to the TEST input of the OTF electronics (Fig. 3).

The output of the SQUID electronics is digitized using a 12-bit, 10 Mbs ADC and stored on a laptop.

Without the OTF, the output of the TES is a pulse with a short rise time and a long decay time, as shown by the red curve in Fig. 8. The decay time consists of two time constants: τfast ≈ 180 µs and τslow ≈ 1200 µs. With the OTF (blue curve in Fig. 8), the fast decay time τfast is reduced by approximately a factor of 10, and the slow component is eliminated. The rise time remains limited by the SQUID amplifier and its input circuit and does not change. The pulse height is reduced by about a factor of two.

Fig. 8

Detector pulses. The red and blue curves represent the output voltage of the SQUID amplifier without and with the OTF, respectively. The left and right graphs show the same pulses on different time scales.

Discussion

We propose a technique for stabilizing the temperature of massive cryo- genic detectors based on the transition edge sensor using active optical thermal feedback. Our experimental results demonstrate that it is possible to eliminate the need for an inertial resistive heater, thereby improving the dynamic characteristics of thermal feedback through light-based heating of the TES. The OTF successfully eliminates the thermal component of the TES response.

Materials and Data Availability Statement

All data generated or analyzed during this study are included in this published article.

Author Contribution

Sergey V. Uchaikin and Shamil H. Sultanov participated in developing the research idea, defining the problem, reviewing the scientific literature, and analyzing the results. Pavel F. Baranov and Valery N. Borikov analyzed the obtained results, determined their reliability, and validated the mathematical and physical models of the processes. Xiaofeng Zhou and Jianguang Wei conducted the overall scientific analysis of the problem, analyzed the obtained results, and drafted the article. All authors reviewed the manuscript.

Data Availability

All data generated or analyzed during this study are included in this published article.

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Funding

This work is supported in part by the Institute for Basic Science (IBS- R017-D1) and by the Ministry of Science and Higher Education of the Russian Federation under agreement No. 075-15-2022-297 within the framework of the development program for a world-class Research Center.

Author contributions statement

Additional information

The authors declare no conflict of interest.

Yes