Low-energy background in low-temperature solid-state detectors, microcracking and microscopic
mechanisms of inelastic deformation of single crystals
Low-temperature solid-state detectors use different single-crystal sensors: Si, Ge, SiO2, CaWO4, etc.,
cooled to 10-50 mK temperatures. Experiments look for signatures of nuclear recoils in these crystals
using a thermometer attached to the crystal and looking for the temperature spikes, or a superconducting
hot phonon sensor/ microbolometer on the surface of the crystal (or array of hot phonon sensors) and
looking for the appearance of hot phonon pulses. In parallel, one can look for the emission of photons
(scintillation) and electrons/conductivity pulses in the crystal. All types of detectors demonstrate excess
low-energy background raising sharply as the energy of the event goes below approximately 10-1
eV[5,6,7] (we will not discuss here questions of recoil energy calibration). In many experiments, the
intensity of the low-energy background increases with the increase of thermomechanical stress in the
crystal, and additional experiments verify this observation. The other statement is that excess background
decreases slowly after the initial cool-down of the detector on a time scale of weeks or months. This
relaxation can restart after warming up to several K temperatures- not all the way to room temperature.
The above properties of excess backgrounds were attributed to microcracking (see [7] for example) -a
process of relief of mechanical stress produced during cool-down by the differences in thermal expansion
of materials.
Microscopic mechanisms of small inelastic deformation (flow) of single-crystal samples (Si and Ge most
often) were studied under different load conditions, including inhomogeneous loading and micro-
indentations [10,11]. It was found that flow has a form of small steps, each consisting of transformation in
a microscopic volume of material. These transformations can be changes in crystallographic structure,
chemical transformations, the appearance of the twin boundaries, sliding plains, appearance and motion of
dislocations. These transformations are dissipative events and should result in heat or hot phonon
productions. In many cases, the formation and movement of defects, dislocations, etc., in dielectrics,
semiconductors, and metal samples can be accompanied by photon emission and electrons from the
sample's surface [12,13]. As we can see, "microcracking" likely has the same meaning as inelastic
deformation /flow of crystal material. Thus, the low-energy background we see is a natural relaxation
process of mechanical stress release in single crystals and solids in general. As a term, "microcracking"
could be misleading, as the production and motion of defects in the crystal are not immediately leading to
mechanical breaking or failure. The Inelastic deformation of metals has similar mechanisms, but the
limits of plasticity (ductility) can be much more significant for metals.
Below we will discuss other relaxation processes in solids that can generate small discrete energy release
events. We argue that the observed excess low-energy backgrounds are a cumulative effect of various
glass-like relaxation processes.
Relaxation processes in glasses and Excess low-energy backgrounds in low-temperature solid-state
detectors
At temperatures below the glass transition, amorphous (disordered) materials are out of mechanical and
thermodynamic equilibrium; relaxation processes in the glass state (response to force or other stimuli)
became long and dependent on the internal state of the material (i.e., history-dependent). When one
applies force for some time and then removes it, slow "back-relaxation" can be present. Such effects mean
energy accumulation and releases can be present when the system demonstrates glass-like relaxation
properties.
At low temperatures, many subsystems in materials demonstrate complex and history-dependent
relaxation properties. Here we provide multiple references on low-temperature physics papers: charges
localized on boundaries and interphases in SQUIDs [14], the motion of charges in dielectric substrate
probed by single-electron transistor on the surface [15], magnetic moments of impurities in
superconductors [16]. The glass-like properties of the relaxation processes become more pronounced with