Transition-Edge Sensors for cryogenic X-ray imaging spectrometers Luciano Gottardiand Stephen Smith

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Transition-Edge Sensors for cryogenic X-ray imaging

spectrometers

Luciano Gottardi∗and Stephen Smith

Abstract Large arrays of superconducting transition-edge sensor (TES) microcalorimeters are becoming

the key technology for future space-based X-ray observatories and ground-based experiments in the ﬁelds

of astrophysics, laboratory astrophysics, plasma physics, particle physics and material analysis. Thanks to

their sharp superconducting-to-normal transition, TESs can achieve very high sensitivity in detecting small

temperature changes at very low temperature. TES based X-ray detectors are non-dispersive spectrometers

bringing together high resolving power, imaging capability and high-quantum efﬁciency simultaneously. In

this chapter, we highlight the basic principles behind the operation and design of TESs, and their fundamen-

tal noise limits. We will further elaborate on the key fundamental physics processes that guide the design

and optimization of the detector. We will then describe pulse-processing and important calibration con-

siderations for space ﬂight instruments, before introducing novel multi-pixel TES designs and discussing

applications in future X-ray space missions over the coming decades.

Keywords

Key words: Imaging spectroscopy, transition-edge sensor, microcalorimeter array, superconductivity,

weak-link, X-ray astrophysics, laboratory astrophysics.

Luciano Gottardi

NWO-I/SRON Netherlands Institute for Space Research, Niels Bohrweg 4, 2333CA Leiden, The Netherlands. e-mail: l.

gottardi@sron.nl

Stephen Smith

NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA e-mail: stephen.j.smith@

nasa.gov

∗corresponding author

arXiv:2210.06617v1 [astro-ph.IM] 12 Oct 2022

Contents

Transition-Edge Sensors for cryogenic X-ray imaging spectrometers ...................... 1

Luciano Gottardi and Stephen Smith

Keywords......................................................................... 1

Introduction....................................................................... 3

Theoretical and Experimental Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

BasicPrinciples.............................................................. 4

TES Electrical and Thermal Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Negative Electrothermal Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

FundamentalNoiseSources ................................................... 8

Non-linearity................................................................ 10

PulseProcessing............................................................. 11

DetectorDesign ................................................................... 13

TESProperties .............................................................. 13

ThermalIsolation ............................................................ 14

Absorber Design and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

CurrentStateoftheArt ....................................................... 15

Physics of the Superconducting Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

The Superconducting Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Josephson Effects in DC and AC Biased TESs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Implication of the Weak-Link Behaviour on the Detector Noise . . . . . . . . . . . . . . . . . . . . . . 22

Detector Calibration Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

ResponseFunction ........................................................... 23

Energy Scale and Sensitivity to Environmental Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . 24

DriftCorrectionAlgorithms ................................................... 26

Multi-PixelTESs .................................................................. 26

Applications and Future Technology Needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Ground Based Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Next Generation Space Mission Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

References........................................................................ 32

Introduction

X-ray spectroscopy provides an excellent diagnostic probe of the energetics and physical conditions in

nearly all classes of cosmic objects throughout the observable universe. X-rays are emitted by various

high-energy processes. By observing their spectra we can obtain information about the temperature, elec-

tron density and ionic composition of hot plasma’s, and answer many questions across astrophysics (from

4 Contents

understanding turbulence in galaxy clusters to the accretion processes in binary systems or active galactic

nuclei.)

Microcalorimeters are non-dispersive thermal detectors that will provide the next major step in imaging

spectroscopy capabilities compared to gas proportional counters or charge coupled devices (CCD) which

have been extensively used in X-ray space instrumentation over the past several decades. Microcalorimeters

will full-ﬁll the needs of X-ray astrophysics in the 21st century, combining eV level energy resolution in the

soft X-ray energy range in large format imaging arrays with potentially 1000’s of pixels. With resolving

powers >1000, microcalorimeters are competitive with dispersive grating spectrometers, but with the

advantage of high collection efﬁciency. This enables efﬁcient observations of point sources and extended

sources with the same instrument. The sensor technology used in microcalorimeters can come in different

forms - silicon thermistors, transition-edge sensors (TESs) and magnetic microcalorimeters (MMCs) - but

the basic principle is the same. A microcalorimeter measures the temperature rise resulting from the energy

deposited by a single X-ray photon. The sensor transduces the change in temperature to an electrical signal

(either through a resistance change for thermistors and TESs or a change in magnetism for MMCs), from

which the photon energy can then be determined. In order to achieve resolving powers of ∼1000’s at keV

energies, extremely low detector noise is required, only achievable when operating at mK temperatures. The

potential power of microcalorimeters to revolutionize X-ray astrophysics has already been demonstrated

by the observation of the Perseus galaxy cluster by the Hitomi satellite’s Soft X-ray Imaging Spectrometer

(SXS) [63].

In this chapter, we describe microcalorimeters based around highly sensitive transition-edge-sensors

(TESs). TESs are next generation microcalorimeters based on a thin superconducting ﬁlm that is electri-

cally biased in the narrow region between superconducting (zero-resistance) state and the normal resistive

state. The transition region is typically only a few mK in width and as such, TES detectors are extremely

sensitive to temperature changes making them ideal detectors for high resolution X-ray spectroscopy. We

start by outlining the basic principles behind the operation and design of TESs, and their fundamental

noise limits. We will elaborate on the key fundamental physics effects that guide the design and optimiza-

tion of the TESs. We will then describe important calibration considerations for space ﬂight instruments.

We will continue by introducing novel multi-pixel TES designs and conclude the chapter by presenting the

applications in future X-ray space missions over the coming decades.

Theoretical and Experimental Background

Basic Principles

A TES-based X-ray detector is a thermal equilibrium calorimeter. It consists of three fundamental com-

ponents: an absorber with heat capacity C, a thermometer (the TES), and a weak thermal link, with a

conductivity Gbath, to the heat sink at temperature Tbath, which is below the operating temperature of the

device. Details on the design of each of these components is described in Section . A simpliﬁed scheme of

a TES calorimeter is shown in Fig. (1).

TESs are based on superconducting thin ﬁlms, voltage biased in the narrow transition region between

the onset of resistance and the fully normal state. A single photon deposits its energy Einto the absorber,

which converts it into heat. The temperature rise, proportional to the energy, causes a change in resistance

of the TES. The resistance change is determined by monitoring the current through the TES using a super-

conducting quantum interference device (SQUID) ammeter. Within this general description, there is room

for countless variations. Important device parameters such as the noise, Gbath and Care strongly dependent

on the operating temperature of the device. Thus, the transition temperature of the TES must be chosen

to achieve the desired energy resolution and response time, whilst being compatible with the instrument

cryogenic architecture. For typical astrophysics applications a transition temperature of below 100 mK is

ideal.

Contents 5

Thermal equilibrium detectors can achieve excellent energy resolution. A fundamental limit for the min-

imum energy resolution ∆Eoffered by a calorimeter is given by the random exchange of energy between

the detector and the thermal bath [105]. This thermodynamic limit is given by <∆E2

T D >=kBT2C. It de-

pends quadratically on the temperature Tof the calorimeter, linearly on the detector heat capacity C, and it

is independent on the thermal conductance Gbath of the thermal link.

Fig. 1 Schematic of a TES-based X-ray microcalorimeter. The TES is a very sensitive thermometer that detects the temper-

ature rise from the energy deposited in the absorber by an X-ray photon.

The ultimate sensitivity of a TES microcalorimeter depends on the shape of the TES superconducting-

to-normal transition and the intrinsic noise sources of the detector and the read-out circuit. The resistance,

R(T,I), of a TES is generally a function of both the temperature of the device, T, and the current ﬂowing

through it, I. For small changes about the equilibrium bias conditions (R0,T0,I0) the device resistance can

be expressed as

R(T,I)'R0+αR0

δT+βR0

δI.(1)

The two dimensionless parameters α=∂logR/∂logTand β=∂log R/∂logI, calculated at a constant

current and temperature respectively, are conveniently used to parameterize the current and temperature

sensitivity of the resistive transition at the operating point [94].

The energy resolution of an ideal TES calorimeter, limited only by the fundamental thermal ﬂuctuations

due to the exchange of energy between the calorimeter and the thermal bath, is given by [105]

∆E∝r4kBT2

α,(2)

where the logarithmic derivative of resistance α, introduced above, describes the steepness of the super-

conducting transition. By developing TESs with a large temperature sensitivity α, the photon energy can

be measured with a much higher resolution than the magnitude set by thermodynamic ﬂuctuations. Eq. (2)

tells us that low heat capacity devices, operating at very low temperature T0, could achieve very high energy

resolution. However, the value of C,αand T0are constrained by the maximum energy to be detected. For

high energetic photons, the temperature excursion could be so high to drive the TES in the normal state and

to saturate the detector. The saturation energy Esat is proportional to Esat ∝C/α, which effectively means

that the theoretical energy resolution ∆E∝√Esat .

A detail analysis of the noise, the electrothermal response and the ultimate sensitivity of a TES mi-

crocalorimeter will be presented in the following sections.

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Transition-EdgeSensorsforcryogenicX-rayimagingspectrometersLucianoGottardiandStephenSmithAbstractLargearraysofsuperconductingtransition-edgesensor(TES)microcalorimetersarebecomingthekeytechnologyforfuturespace-basedX-rayobservatoriesandground-basedexperimentsintheeldsofastrophysics,laboratoryastro...

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