Low-threshold cryogenic calorimeters for sub-GeV dark-matter searches — including the 10 eV-threshold CRESST-III silicon detector — are limited by the low-energy excess (LEE), a steeply rising event rate below a few hundred eV that exceeds all known backgrounds. The CRESST-III silicon analysis excluded noise triggers, surface radioactivity, and scintillation light as dominant contributors, and subsequent work across CRESST, NUCLEUS, SuperCDMS, EDELWEISS and related experiments excluded any particle origin, localizing the cause in detector-intrinsic solid-state or instrumental processes. The open problem is to identify the microscopic mechanism(s) — candidate classes being stress relaxation at crystal-holder or crystal-sensor interfaces, dislocation-mediated relaxation of stressed sensor metallization, and defect-related athermal phonon bursts in the crystal bulk — and to establish the identification quantitatively, so that the excess can be mitigated at the detector level or subtracted in analysis. As of 2026 the problem is open: the leading hypotheses have partial and partially conflicting experimental support, and no mechanism is confirmed.

Background

Direct-detection experiments seek the rare elastic scattering of galactic dark matter particles off nuclei or electrons in a heavily shielded target. For dark-matter masses below a few GeV/c2c^2, recoil energies fall to the tens-of-eV scale or below, so the enabling technology is the cryogenic calorimeter: a dielectric or semiconductor crystal cooled to millikelvin temperatures, in which an energy deposition raises the absorber temperature by a fraction of a microkelvin, sensed by a transition-edge sensor (TES) — a superconducting film biased on its sharp resistive transition that converts a tiny temperature rise into a measurable electrical pulse. The CRESST-III silicon detector operated a 0.35 g Si wafer instrumented this way, achieving a nuclear-recoil energy resolution of (1.36±0.05)(1.36\pm 0.05) eV and a threshold of (10.0±0.2)(10.0\pm 0.2) eV — the lowest reported for a macroscopic particle detector — and set leading limits on spin-independent dark-matter-nucleus scattering for masses below about 160 MeV/c2c^2.

That sensitivity was capped not by radioactivity or electronic noise but by the low-energy excess (LEE): an event rate rising steeply as energy decreases below a few hundred eV, far above anything expected from known backgrounds, with pulse shapes indistinguishable from genuine particle recoils. The phenomenon is not specific to one device: comparable excesses appeared in the cryogenic phonon experiments EDELWEISS, NUCLEUS, SuperCDMS-CPD and TESSERACT, and — with a distinct, unrelated origin — in the charge-readout experiments SuperCDMS-HVeV, DAMIC and SENSEI. A community effort, the EXCESS workshop series, was formed to pool data and characterize the effect.

Systematic characterization has excluded whole classes of explanation. Excluded as dominant contributors: electronic-noise triggers (tested by running the optimum filter — the linear filter that maximizes signal-to-noise for the known pulse shape — on inverted baseline data); radioactive surface contamination (a coincidence cut with a facing instrumented crystal removes only about 1% of the low-energy events); scintillation or luminescence light; external radiation (the time evolution is the same above ground and underground); and any particle origin including dark matter (the rate decays at operating temperature with two time constants, partially resets after warming the cryostat to tens of kelvin, and — in double-TES detectors carrying two identical sensors on one crystal — splits into 'shared' events distributed over the substrate and 'singles' localized at one sensor, a topology no particle flux produces). What remains is detector-intrinsic solid-state physics: energy stored and intermittently released within the crystal, at its interfaces with holding structures and sensors, or in the sensor metallization itself.

Candidate mechanisms with partial support include: relaxation of shear stress at the crystal-sensor interface induced by thermal-expansion mismatch (favored by the CRESST double-TES observation of a sensor-localized component and by the warm-up reset); relaxation of the stressed aluminium films used for phonon collection through dislocation motion (dislocations are line defects in a crystal lattice; their motion releases stored elastic energy), consistent with 'single' events in the aluminium fins; and defect-related bursts of athermal phonons — vibrational excitations that have not yet thermalized with the crystal — originating in the bulk (supported by a measured linear scaling of the excess rate with substrate thickness in otherwise identical silicon detectors, and by pulse-shape anomalies in sapphire). These accounts conflict in emphasis — sensor-interface versus bulk — and none reproduces the full observed phenomenology (spectrum shape, two-component time decay, warm-up reset, cooldown-speed dependence, single/shared event topology, material dependence).

Resolving the LEE matters beyond a single experiment: it is the dominant background below roughly 100–200 eV for essentially every cryogenic dark-matter search and for coherent elastic neutrino-nucleus scattering (CEvNS) programs such as NUCLEUS and Ricochet; it currently forces multi-year 'waiting-time' strategies that simply outlast the slow decay of the excess; and the same unexplained phonon bursts have been linked to quasiparticle poisoning of superconducting qubits — the buildup of unpaired excitations that degrades qubit coherence. A 2025 community review of the field concluded that the nature of the underlying sources 'remains not fully understood'.

Problem Statement

The problem, as posed by the CRESST-III silicon result and inherited by the wider field, is to identify the physical mechanism(s) — solid-state or instrumental — responsible for the low-energy excess in low-threshold cryogenic phonon calorimeters, and to establish that identification quantitatively so that the excess can be mitigated or subtracted. Concretely, the target is the microscopic process (or set of processes, with their relative contributions by detector technology and target material) that produces events with the observed signature: particle-like pulse shapes, a rate rising steeply below a few hundred eV, decay over months of continuous operation with two time constants, partial reset after warm-up to tens of kelvin, dependence on cooldown speed but not on particle-background level or site, and the split — seen in double-TES detectors carrying two identical transition-edge sensors on one crystal — between sensor-localized and substrate-shared events. The identification is a physically motivated quantitative model of the mechanism(s) — whether a single mechanism or a small set of related effects with experiment-specific variations — that accounts for the observed LEE phenomenology in these detectors (spectral shape, rates, time evolution with partial warm-up reset, and the sensor-localized versus substrate-shared event populations), to the extent that the excess can be mitigated at the detector level or subtracted in analysis. Full elimination of the cause is the ideal aim, with mitigation at the detector level or subtraction in analysis where elimination is not achieved. The scope of this problem is the LEE in low-threshold cryogenic phonon calorimeters (CRESST, NUCLEUS, SuperCDMS-CPD, TESSERACT, the EDELWEISS heat-only excess, and comparable devices); the charge-readout excesses (SuperCDMS-HVeV, DAMIC, SENSEI) are outside its scope because their dominant sources are established to be distinct. (The same CRESST-III analysis also left a minor, separable open item — the origin of the (2.4±0.1)(2.4\pm 0.1) keV peak tentatively attributed to a double Si X-ray escape process — which remains unresolved but is not part of the completion boundary of this problem.)

References

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