1 INTRODUCTION Energy loss due to defect creation in solid state detectors Matti Heikinheimo1 Sebastian Sassi1 Kimmo Tuominen1 Kai Nordlund1and Nader

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1 INTRODUCTION

Energy loss due to defect creation in solid state detectors

Matti Heikinheimo1?, Sebastian Sassi1, Kimmo Tuominen1, Kai Nordlund1and Nader

Mirabolfathi2

1Helsinki Institute of Physics and Department of Physics, University of Helsinki,

P.O.Box 64, FI-00014 University of Helsinki, Finland

2Department of Physics and Astronomy and the Mitchell Institute for Fundamental Physics and

Astronomy, Texas A&M University, College Station, TX 77843, USA

* matti.heikinheimo@helsinki.ﬁ

October 5, 2022

14th International Conference on Identiﬁcation of Dark Matter

Vienna, Austria, 18-22 July 2022

doi:10.21468/SciPostPhysProc.?

Abstract

The threshold displacement energy in solid state detector materials varies from several eV

to ®100 eV. If a stable or long lived defect is created as a result of a nuclear recoil event,

some part of the recoil energy is stored in the deformed lattice and is therefore not observ-

able in a phonon detector. Thus, an accurate model of this effect is necessary for precise

calibration of the recoil energy measurement in low threshold phonon detectors. Further-

more, the sharpness of the defect creation threshold varies between materials. For a hard

material such as diamond, the sharp threshold will cause a sudden onset of the energy loss

effect, resulting in a prominent peak in the observed recoil spectrum just below the thresh-

old displacement energy. We describe how this effect can be used to discriminate between

nuclear and electron recoils using just the measured recoil spectrum.

1 Introduction

Direct detection of low mass dark matter requires detectors sensitive to recoil energies well be-

low the keV scale. Phonon-mediated detectors with O(eV) resolution are the most appropriate

detectors for this purpose. Phonons are among the lowest energy quantum excitations (compred

to e.g. ionization and scintillation) that can be detected after particle interactions. In addition to

their excellent signal to noise, phonon-mediated detectors offer an interaction-type independent

(nuclear or electron recoil) energy measurement. Many groups have recently achieved energy

resolution within the O(eV) scale [1–3].

Recently several experiments [4–13]have observed a steeply rising event rate at low energies,

Er®1000 eV. The origin of these events is currently unknown, and understanding their physical

character is a question of great interest for both the DM and coherent neutrino scattering experi-

ments [14]. Most of the anticipated background sources, such as photons or electrons, would give

arXiv:2210.01550v1 [physics.ins-det] 4 Oct 2022

2 ENERGY LOSS

Al2O3

50 100 150 200

rec

[

]

Eloss [eV]

Figure 1: Energy loss, averaged over recoil direction, as a function of the recoil energy

in silicon, germanium, sapphire and diamond. The ﬁgure has appeared before in [20].

rise to electron recoils. Therefore the identiﬁcation of the nuclear/electron recoil character of

these events would add an important piece of information towards understanding and mitigating

this background.

Nuclear recoils at these energies can result in lattice defects, while electron recoils are not

expected to do so. The formation of defects stores a part of the recoil energy in the crystal, resulting

in a quenching of the measured energy in phonons. At higher recoil energy this quenching factor

becomes approximately constant and can be absorbed in the calibration of the energy scale, but

for recoil energies close to the threshold displacement energy the effect can be highly nonlinear,

affecting not just the overall energy calibration but also the shape of the measured recoil spectrum

[15,16]. In diamond, the energy loss effect turns on sharply at ¦30 eV. The affected recoil events

are shifted towards lower enegy, resulting in a peak in the observed spectrum around ∼30 eV, and

a dip around ∼60 eV, compared to the underlying true recoil spectrum. Gram scale diamond based

detectors are expected to offer a resolution that is superior to the existing technologies [17,18].

In the following we will describe how the energy loss induced peak in the nuclear recoil spectrum

in a diamond detector can be utilized to test if the observed spectrum originates from nuclear

recoils.

2 Energy loss

The energy stored in the crystal lattice as a function of the nuclear recoil direction and energy were

obtained from molecular dynamics (MD) simulations, described in [16]. We have simulated multi-

ple materials, for which the numerical results can be obtained from online repository1. The energy

loss averaged over the recoil direction is shown in ﬁgure 1for four detector materials, namely sil-

icon (Si), germanium (Ge), sapphire (Al2O3) and diamond (C). The sharp, nonlinear threshold

in diamond is evident in the ﬁgure, while sapphire shows almost linear behaviour throughout the

energy range. Silicon and germanium feature nonlinear threshold behaviour, but at lower ener-

gies compared to diamond, and with a much smaller step in the stored energy. Therefore, the

resulting effect on the observed spectrum should be largest for diamond, and almost negligible

for the other materials.

1https://github.com/sebsassi/elosssim

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1INTRODUCTIONEnergylossduetodefectcreationinsolidstatedetectorsMattiHeikinheimo1?,SebastianSassi1,KimmoTuominen1,KaiNordlund1andNaderMirabolfathi21HelsinkiInstituteofPhysicsandDepartmentofPhysics,UniversityofHelsinki,P.O.Box64,FI-00014UniversityofHelsinki,Finland2DepartmentofPhysicsandAstronomyandth...

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1 INTRODUCTION Energy loss due to defect creation in solid state detectors Matti Heikinheimo1 Sebastian Sassi1 Kimmo Tuominen1 Kai Nordlund1and Nader

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