利用锗内部放大技术对杂质离子电离产生的电荷直接检测MeV级暗物质资源-CSDN文库

Open

Access

153 浏览量 2020-04-17 09:02:22 上传评论收藏 1.09MB PDF 举报

资源推荐

资源详情

资源评论

Eur. Phys. J. C (2018) 78:187

https://doi.org/10.1140/epjc/s10052-018-5653-z

Regular Article - Experimental Physics

Direct detection of MeV-scale dark matter utilizing germanium

internal ampliﬁcation for the charge created by the ionization of

impurities

D.-M. Mei

1,2,a

, G.-J. Wang

,H.Mei

, G. Yang

,J.Liu

, M. Wagner

, R. Panth

, K. Kooi

, Y.-Y. Yang

,W.-Z.Wei

Department of Physics, The University of South Dakota, Vermillion, SD 57069, USA

School of Physics and Optoelectronic, Yangtze University, Jingzhou 434023, China

Received: 23 October 2017 / Accepted: 15 February 2018

Abstract Light, MeV-scale dark matter (DM) is an exciting

DM candidate that is undetectable by current experiments.

A germanium (Ge) detector utilizing internal charge ampli-

ﬁcation for the charge carriers created by the ionization of

impurities is a promising new technology with experimen-

tal sensitivity for detecting MeV-scale DM. We analyze the

physics mechanisms of the signal formation, charge creation,

charge internal ampliﬁcation, and the projected sensitivity

for directly detecting MeV-scale DM particles. We present a

design for a novel Ge detector at helium temperature (∼4K)

enabling ionization of impurities from DM impacts. With

large localized E-ﬁelds, the ionized excitations can be accel-

erated to kinetic energies larger than the Ge bandgap at which

point they can create additional electron–hole pairs, produc-

ing intrinsic ampliﬁcation to achieve an ultra-low energy

threshold of ∼ 0.1 eV for detecting low-mass DM parti-

cles in the MeV scale. Correspondingly, such a Ge detec-

tor with 1 kg-year exposure will have high sensitivity to a

DM-nucleon cross section of ∼ 5 × 10

−45

at a DM

mass of ∼ 10 MeV/c

and a DM-electron cross section of

∼ 5 × 10

−46

at a DM mass of ∼ 1MeV/c

1 Introduction

Observations from the 1930s [1] have led to the contem-

porary and shocking revelation that 96% of the matter and

energy in the universe neither emits nor absorbs electromag-

netic radiation [2,3]. Weakly Interacting Massive Particles

(WIMPs) [4] constitute a popular candidate for dark matter

(DM). These particles, with mass thought to be comparable

to heavy nuclei, have a feeble and extremely short range inter-

e-mail: [email protected]

action with atomic nuclei. While WIMPs appear to interact

with atomic nuclei very rarely, their collisions would cause

atoms to recoil at a velocity in the order of a thousand times

the speed of sound in air [5].

For over three decades, many experiments have conducted

searches for WIMPs using various targets [6–25]. These

experiments are all sensitive to WIMPs with masses greater

than a few GeV/c

. The best sensitivity for WIMPs masses

above 10 GeV/c

, with a minimum of 7.7 ×10

−47

for 35

GeV/c

at 90% conﬁdence level, is given by the most recent

results from XENON1T [23]. Despite great efforts have been

made, WIMPs remain undetected. More experiments will

soon come online [26–28]. The LZ experiment will push the

experimental sensitivity for WIMPs with masses greater than

10 GeV/c

very close to the boundary where neutrino induced

backgrounds begin to constrain the experimental sensitivity

[29,30].

In the past decade, light DM in the MeV-scale [31–34] has

risen to become an exciting DM candidate, even though its

low mass makes it unreachable by current experiments. The

detection of MeV-scale DM requires new detectors with an

extremely low-energy threshold (< 10 eV) since both elec-

tronic recoils and nuclear recoils induced by MeV-scale DM

are in the range of sub-eV to 100 eV [31]. Using the data

from the XENON10 experiment, the XENON Collaboration

was able to set the ﬁrst experimental limit on the MeV-scale

DM detection [35]. More recently, Kadribasic et al. have

proposed a method for using solid state detectors with direc-

tional sensitivity to DM interactions to detect low-mass DM

[36]. CRESST has achieved a threshold of 20 eV with a small

prototype sapphire detector [37]. DAMIC has claimed a sen-

sitivity to ionization < 12 eV with Si CCDs and considered

their method to be able to reach 1.2 eV [38].

DM coupling to visible matter is assumed through weak

and gravitational interactions [39,40]. A common search

123

187 Page 2 of 12 Eur. Phys. J. C (2018) 78:187

channel is the elastic scattering between incoming DM par-

ticles and target nuclei. Current direct detection experiments

search for nuclear recoils with the lowest accessible nuclear

recoil energy being around 1 keV [7,8,17,20]. This corre-

sponds to DM with masses greater than 6 GeV/c

.ForMeV-

scale DM, the average nuclear recoil energy gained from an

elastic scattering is:

= q

/2m

, (1)

which is the level of [31]:

 1 eV × (m

/100 MeV )

(10 GeV /m

), (2)

where q ∼ m

v is the momentum transferred, v ∼ 10

−3

is the DM velocity, c is the speed of light, m

is the mass

of DM, and m

is the mass of a nucleus. As can be seen,

this nuclear recoil energy is in the range of ∼ 1 eV and

well below the lowest threshold achieved in existing direct

detection experiments.

On the other hand, coupling between the incoming DM

and the orbital electrons is also possible [31,33,34]. In this

case, the total energy available in the scattering between DM

and electrons can be larger [31]:

tot

 m

/2  50 eV × (m

/100 MeV ). (3)

However, it is still in the level of ∼ 50 eV if m

is 100

MeV/c

. Consequently, conventional detector technology

does not allow for the detection of DM much below the GeV

mass scale. Direct detection of MeV-scale DM requires new

detectors with threshold as low as sub-eV to maximize the

capability of searches.

A promising technology for sensitivity to MeV-scale DM

is a germanium (Ge) detector which utilizes internal charge

ampliﬁcation for the charge carriers created by the ionization

of impurities. We describe the design of a novel Ge detec-

tor that develops ionization ampliﬁcation technology for Ge

in which very large localized E-ﬁelds are used to accelerate

ionized excitations produced by particle interaction to kinetic

energies larger than the Ge bandgap at which point they can

create additional electron–hole (e–h) pairs, producing inter-

nal ampliﬁcation. This ampliﬁed charge signal could then be

readout with standard high impedance JFET or HEMT [41]

based charge ampliﬁers. Such a system would potentially

be sensitive to single ionized excitations produced by DM

interactions with both nuclei and electrons. In addition, pur-

poseful doping of the Ge could lower the ionization threshold

by ∼×10 (∼ 0.1 eV), making the detector sensitive to 100

keV DM via electronic recoils.

2 The formation of signal

2.1 DM-nucleus and DM-electron elastic scattering

processes

The energy deposition between the incoming DM and a tar-

get nucleus or a bound electron through elastic scattering

can be calculated using the standard halo model [39,40]

assuming the velocity distribution of DM is approximately

Maxwellian, with v

rms

governed by the gravitational binding

and having a value  270 kms

−1

. The relative motion of the

solar system (v = 220 km s

−1

) through the DM halo is con-

sidered in the calculation. The energy deposition spectrum

arises due to kinematics of elastic scattering. In the center-

of-momentum frame, a DM particle scatters off a nucleus or

a bound electron through an angle θ, uniformly distributed

between 0 and 180

for the isotropic scattering that occurs

with zero-momentum transfer. The DM



s initial energy in

the laboratory frame can be expressed as: E

/2. The

nuclear recoil energy can be calculated as:

= E

4μ

χ N

(1 − cos θ)

, (4)

where μ

χ N

is the DM-nucleus reduced mass, μ

χ N

When a DM particle collides directly with a bound elec-

tron, exciting it to a higher energy level or an unbound state,

the calculation of electronic recoil energy is different from

that of a nuclear recoil [32]. Since electrons are in a bound

state, the electrons may have an arbitrarily high momentum

(albeit with low probability). During a collision between a

DM particle and a bound electron, the energy transferred to

the electron, ΔE

, can be related to the momentum lost by

the DM, q, via energy conservation [32]:

ΔE

= q · v −

2μ

χ N

. (5)

If one assumes an angle, α, between the momentum transfer

(q) and the velocity (v) of the DM particle, ΔE

can be

written as:

ΔE

= qvcos (α) −

2μ

χ N

. (6)

Taking into account a fact that ΔE

ef f

, the energy

transferred to electrons equals the squared momentum lost

by the DM particle divided by two times of the effective mass

of that atomic system, where m

is the mass of electron, then

Eq. 6 can be rewritten as:

ΔE

ef f

cos

(α)

(1 +

ef f

χ N

)

, (7)

123

Eur. Phys. J. C (2018) 78:187 Page 3 of 12 187

Tabl e 1 Effective nuclear charges for Ge electron conﬁguration

Electron conﬁguration Z

ef f

1s 31.294

2s 23.365

2p 28.082

3s 17.790

3p 17.014

4s 8.044

3d 16.251

4p 6.780

Fig. 1 The relative event rate as a function of recoil energy for DM

with masses between 0.1 MeV/c

to 1 GeV/c

where Z

ef f

is the effective number of orbital electrons (also

called effective nuclear charge) that participate in the DM-

electron scattering, which would interact with the entire

atomic system. The value of Z

ef f

corresponding to the elec-

tron conﬁguration, 1s

, is given by

Clementi et al. [42,43], as shown in Table 1.

Utilizing the electron conﬁguration of Ge and the values

of Z

ef f

in Table 1, the average value of Z

ef f

is determined to

be 18.989 for a Ge atom. Since an arbitrary-size momentum

transfer is possible, the largest allowed energy transfer is

found to be:

ΔE

≤

. (8)

The likelihood of actually obtaining a large enough q to excite

an electron depends on the effective atomic number,

ef f

and the incident angle of a DM particle.

With the standard halo model described above, the energy

deposition is simulated as shown in Fig. 1, which shows

the distributions of nuclear recoil energies induced by DM-

nucleus scattering and electronic recoil energies created by

DM-electron scattering with DM masses from 0.1 MeV/c

to1GeV/c

It is clear that the energy deposited by nuclear recoils is

mainly in the range of sub-eV to ∼100 eV. The dissipation

of such a small amount of energy in Ge is largely through

the emission of phonons. DM interacting with electrons can

lead to visible signals of ∼10 eV through the following chan-

nels: electron ionization and electronic excitation. Similar to

DM-nucleus scattering, the energy deposited by electronic

recoils is also in the range of sub-eV to ∼ 100 eV. Such a

small amount of energy is again largely dissipated through

the emission of phonons. Therefore, the detection of those

phonons is a major consideration for the design of the next

generation of Ge detectors.

2.2 The form of the detectable signature

The bandgap energy of Ge is 0.67 eV at room temperature

[44]. It increases slightly as temperature decreases [45]. The

band structure of Ge is an indirect bandgap, which means

that the minimum of conduction band and the maximum of

valance band lie at different momentum, k, values. When

an e–h pair is created in Ge, phonons must be involved to

conserve momentum [47]. Therefore, the average energy

expended per e–h pair in Ge at 77 K is ∼ 3 eV, much higher

than the bandgap energy of 0.73 eV [47] at the same temper-

ature.

Since the energy dissipation, induced by DM interactions

with a nucleus or an electron, is mainly released through

the emission of phonons, the energy of phonons (E

phonon

can be estimated through E

phonon

= hv

/a, where h is

the Planck constant, v

is the speed of sound in Ge, and

a (0.565 nm) is the lattice constant of Ge. The value of

the speed of sound in Ge depends on the polarization of

phonons and the orientation of Ge crystal. For a [100] Ge

crystal, v

=5.4× 10

m/s [49] for longitudinal acoustic

(LA) phonons and v

=3.58× 10

m/s for transverse acous-

tic (TA) phonons [50]. Therefore, E

phonon

can be 0.037 eV

for LA phonons and 0.026 eV for TA phonons, respectively.

These values agree with the early measurements made by

Brockhouse and Iyengar [51] and Others [52]. There are also

measured phonons in longitudinal optical (LO) and trans-

verse optical (TO) bench with energies up to 0.063 eV [51].

The energies of LA, TA, LO, and TO phonons are much less

than 3 eV required to generate an e–h pair at 77 K. Those

phonons are not capable of generating e–h pairs through exci-

tation of Ge atoms. Indirect detection of those phonons has

been demonstrated by CDMS [6], EDELWEISS [15] and

SuperCDMS [20] with threshold energy as low as ∼ 50 eV.

To access the large portion of the recoil energy spectra

shown in Fig. 1, a threshold energy of sub-eV is needed. This

can be obtained through excitation or ionization of impurities

naturally existing in a high-purity Ge detector with phonons.

The main impurities remaining in a high-purity p-type Ge

crystal after many passes of zone reﬁning and crystal growth

123

剩余11页未读，继续阅读

评论收藏

内容反馈

weixin_38698403

粉丝: 8
资源: 920

利用锗内部放大技术对杂质离子电离产生的电荷直接检测MeV级暗物质

通过太阳反射直接检测MeV级暗物质

促进辅助灭绝，获得宇宙学上安全的MeV级暗物质

直接偏转粒子暗物质

在地面以上运行的克级低温量热仪对MeV级暗物质的结果

MeV以下的热暗物质

MeV尺度暗物质的模型独立分析：宇宙学约束

SuperCDMS单电荷敏感检测器的第一个暗物质约束

中微子热通向亚MeV暗物质

MeV暗物质在21 cm吸收下可能的s波an灭

稀有液体直接检测中的单色暗中微子和增强暗物质

亚MeV暗物质的宇宙学

用费米变性材料检测超轻暗物质

使用原子钟和磁力计探索超轻至亚MeV暗物质窗口

通过非弹性宇宙射线碰撞检测暗物质

亚MeV自相互作用暗物质

使用轴离子拓扑反铁磁体检测暗物质的提案

SENSEI：表面运行对Sub-GeV暗物质的第一个直接检测约束

用极性材料中的光子检测轻暗物质

Qt 5实现串口调试助手 （源工程文件、0积分下载）

【SystemVerilog】路科验证V2学习笔记（全600页）.pdf

AutoSAR标准协议4.2.2

光伏-储能并网系统仿真.rar

XCP协议的规范文档

GD32替换STM32注意事项.pdf

NPPJSONViewer.zip

CANoe通过CAPL脚本实现自动测试

VS2015安装证书，JavaScript_ProjectSystem.msi，JavaScript_LanguageService.msi

蓝牙BLE协议中文版.pdf

最新资源

Qt 5实现串口调试助手（源工程文件、0积分下载）