Dirac materials and narrow- gap semiconductors for keV-MeV - - PowerPoint PPT Presentation

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Dirac materials and narrow- gap semiconductors for keV-MeV - - PowerPoint PPT Presentation

Jan 19, 2023 232 likes •372 views

Dirac materials and narrow- gap semiconductors for keV-MeV freeze-in DM Yoni Kahn, KICP/UIUC In collaboration with: UIUC: P. Abbamonte, J. Eckstein, J. Filippini, F. Mahmood, D. Van Harlingen, L. Wagner, J. Zuo Brookhaven: Q. Li, G.

slide-1
SLIDE 1

Dirac materials and narrow- gap semiconductors for 
 keV-MeV freeze-in DM

Yoni Kahn, KICP/UIUC

In collaboration with:
 UIUC: P. Abbamonte, J. Eckstein, J. Filippini, F. Mahmood, 


  • D. Van Harlingen, L. Wagner, J. Zuo

Brookhaven: Q. Li, G. Gu Fermilab: A. Para, P. Rubinov

slide-2
SLIDE 2

Concept: DM-electron scattering at low gap energies

  • We are going after DM-electron

scattering (c.f. Tongyan’s talk on Wed.) at the freeze-in target (c.f. all the Tues. afternoon theory talks) in the mass range 
 20 keV — 1 MeV

  • Need materials with ~30 meV excitation

energy for the lowest-mass DM

  • We will use charge amplification rather

than phonon detection - energy threshold is set by material rather than detector

  • One of our proposed materials (ZrTe5) is

highly anisotropic, leading to strong daily and annual modulations which can help mitigate isotropic backgrounds

0:00h 12:00h N

Dark Matter Wind

wide open
 parameter space!

slide-3
SLIDE 3

Detection by charge avalanche

Y Γ Z T S R

  • 1.5
  • 1
  • 0.5

0.5 1 E-EF (eV)

(a) (b

χ χ

k k0 = k + q

insulating
 sample a)

  • r

depletion p-type n-type b)

ZrTe5 band diagram

Operates like an APD or a SiPM (c.f. Claudio’s talk on Tues.):
 e-h pair created in insulating layer is accelerated, impact ionization leads to
 charge cascade: mA for exponential gain, 10-100 e for linear gain

+10-100 V +10-100 V 0 V 0 V

1 − 300 µm

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1 − 10 µm

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slide-4
SLIDE 4

What is a Dirac material?

ZrTe5 is a “Dirac material” with highly anisotropic band structure

k E(k) = ± q v2

F,xk2 x + v2 F,yk2 y + v2 F,zk2 z + ∆2

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Like a rescaled relativistic (“Dirac”)
 electron if space were anisotropic DM has a quadratic dispersion,
 so solving energy-momentum 
 conservation with a linear dispersion 
 leads to curious effects:

vmin(|q|, !`,`+q) = q v2

F,?(` + q)2 ? + v2 F,z(`z + qz)2 +

q v2

F,?`2 ? + v2 F,z`2 z

|q| + |q| 2mχ !

No scattering if DM is 
 slower than vF, but this depends


  • n direction of q!


Strong directional dependence

2∆ ∼ 30 meV

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vF,z ⇠ 6.5 ⇥ 10−4 c ⌧ vF,x, vF,y

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vF,x ∼ vF,y ∼ 1.6 × 10−3 c

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slide-5
SLIDE 5

Importance of the dielectric function

R ∼ Z d3q dΦ|FDM(q)|2|Fmed(q)|2|fexcit.(q)|2

χ χ e e A0

1 q2 − m2

A0 → 1

q2

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for

m2

A0 ⌧ q2

<latexit sha1_base64="+Uar6DfLTB/fEMxIChOuYZSZSk=">AB+XicdVDLSsNAFJ3UV62vqEs3g0V0VZIY2rqrunFZwT6gTcNkOm2HziRxZlIoX/ixoUibv0Td/6Nk7aCih64cDjnXu69J4gZlcqyPozcyura+kZ+s7C1vbO7Z+4fNGWUCEwaOGKRaAdIEkZD0lBUMdKOBUE8YKQVjK8zvzUhQtIovFPTmHgcDUM6oBgpLfmyf308nTWc2CXMXjfc3yzaJUuqmXHLUOrZFkV27Ez4lTcxfaWslQBEvUfO9249wkmoMENSdmwrVl6KhKYkVmhm0gSIzxGQ9LRNEScSC+dXz6DJ1rpw0EkdIUKztXvEyniUk5oDs5UiP528vEv7xOogZVL6VhnCgS4sWiQcKgimAWA+xTQbBiU0QFlTfCvEICYSVDqugQ/j6FP5Pmk7J1vzWLdaulnHkwRE4BmfABhVQAzegDhoAgwl4AE/g2UiNR+PFeF205ozlzCH4AePtEzoWkr4=</latexit><latexit sha1_base64="+Uar6DfLTB/fEMxIChOuYZSZSk=">AB+XicdVDLSsNAFJ3UV62vqEs3g0V0VZIY2rqrunFZwT6gTcNkOm2HziRxZlIoX/ixoUibv0Td/6Nk7aCih64cDjnXu69J4gZlcqyPozcyura+kZ+s7C1vbO7Z+4fNGWUCEwaOGKRaAdIEkZD0lBUMdKOBUE8YKQVjK8zvzUhQtIovFPTmHgcDUM6oBgpLfmyf308nTWc2CXMXjfc3yzaJUuqmXHLUOrZFkV27Ez4lTcxfaWslQBEvUfO9249wkmoMENSdmwrVl6KhKYkVmhm0gSIzxGQ9LRNEScSC+dXz6DJ1rpw0EkdIUKztXvEyniUk5oDs5UiP528vEv7xOogZVL6VhnCgS4sWiQcKgimAWA+xTQbBiU0QFlTfCvEICYSVDqugQ/j6FP5Pmk7J1vzWLdaulnHkwRE4BmfABhVQAzegDhoAgwl4AE/g2UiNR+PFeF205ozlzCH4AePtEzoWkr4=</latexit><latexit sha1_base64="+Uar6DfLTB/fEMxIChOuYZSZSk=">AB+XicdVDLSsNAFJ3UV62vqEs3g0V0VZIY2rqrunFZwT6gTcNkOm2HziRxZlIoX/ixoUibv0Td/6Nk7aCih64cDjnXu69J4gZlcqyPozcyura+kZ+s7C1vbO7Z+4fNGWUCEwaOGKRaAdIEkZD0lBUMdKOBUE8YKQVjK8zvzUhQtIovFPTmHgcDUM6oBgpLfmyf308nTWc2CXMXjfc3yzaJUuqmXHLUOrZFkV27Ez4lTcxfaWslQBEvUfO9249wkmoMENSdmwrVl6KhKYkVmhm0gSIzxGQ9LRNEScSC+dXz6DJ1rpw0EkdIUKztXvEyniUk5oDs5UiP528vEv7xOogZVL6VhnCgS4sWiQcKgimAWA+xTQbBiU0QFlTfCvEICYSVDqugQ/j6FP5Pmk7J1vzWLdaulnHkwRE4BmfABhVQAzegDhoAgwl4AE/g2UiNR+PFeF205ozlzCH4AePtEzoWkr4=</latexit><latexit sha1_base64="+Uar6DfLTB/fEMxIChOuYZSZSk=">AB+XicdVDLSsNAFJ3UV62vqEs3g0V0VZIY2rqrunFZwT6gTcNkOm2HziRxZlIoX/ixoUibv0Td/6Nk7aCih64cDjnXu69J4gZlcqyPozcyura+kZ+s7C1vbO7Z+4fNGWUCEwaOGKRaAdIEkZD0lBUMdKOBUE8YKQVjK8zvzUhQtIovFPTmHgcDUM6oBgpLfmyf308nTWc2CXMXjfc3yzaJUuqmXHLUOrZFkV27Ez4lTcxfaWslQBEvUfO9249wkmoMENSdmwrVl6KhKYkVmhm0gSIzxGQ9LRNEScSC+dXz6DJ1rpw0EkdIUKztXvEyniUk5oDs5UiP528vEv7xOogZVL6VhnCgS4sWiQcKgimAWA+xTQbBiU0QFlTfCvEICYSVDqugQ/j6FP5Pmk7J1vzWLdaulnHkwRE4BmfABhVQAzegDhoAgwl4AE/g2UiNR+PFeF205ozlzCH4AePtEzoWkr4=</latexit>

q ∼ mDMvDM ∼ eV

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Ultralight dark photon mediator:

slide-6
SLIDE 6

Importance of the dielectric function

χ χ e e A0

1 q2 − m2

A0 → 1

q2

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for

m2

A0 ⌧ q2

<latexit sha1_base64="+Uar6DfLTB/fEMxIChOuYZSZSk=">AB+XicdVDLSsNAFJ3UV62vqEs3g0V0VZIY2rqrunFZwT6gTcNkOm2HziRxZlIoX/ixoUibv0Td/6Nk7aCih64cDjnXu69J4gZlcqyPozcyura+kZ+s7C1vbO7Z+4fNGWUCEwaOGKRaAdIEkZD0lBUMdKOBUE8YKQVjK8zvzUhQtIovFPTmHgcDUM6oBgpLfmyf308nTWc2CXMXjfc3yzaJUuqmXHLUOrZFkV27Ez4lTcxfaWslQBEvUfO9249wkmoMENSdmwrVl6KhKYkVmhm0gSIzxGQ9LRNEScSC+dXz6DJ1rpw0EkdIUKztXvEyniUk5oDs5UiP528vEv7xOogZVL6VhnCgS4sWiQcKgimAWA+xTQbBiU0QFlTfCvEICYSVDqugQ/j6FP5Pmk7J1vzWLdaulnHkwRE4BmfABhVQAzegDhoAgwl4AE/g2UiNR+PFeF205ozlzCH4AePtEzoWkr4=</latexit><latexit sha1_base64="+Uar6DfLTB/fEMxIChOuYZSZSk=">AB+XicdVDLSsNAFJ3UV62vqEs3g0V0VZIY2rqrunFZwT6gTcNkOm2HziRxZlIoX/ixoUibv0Td/6Nk7aCih64cDjnXu69J4gZlcqyPozcyura+kZ+s7C1vbO7Z+4fNGWUCEwaOGKRaAdIEkZD0lBUMdKOBUE8YKQVjK8zvzUhQtIovFPTmHgcDUM6oBgpLfmyf308nTWc2CXMXjfc3yzaJUuqmXHLUOrZFkV27Ez4lTcxfaWslQBEvUfO9249wkmoMENSdmwrVl6KhKYkVmhm0gSIzxGQ9LRNEScSC+dXz6DJ1rpw0EkdIUKztXvEyniUk5oDs5UiP528vEv7xOogZVL6VhnCgS4sWiQcKgimAWA+xTQbBiU0QFlTfCvEICYSVDqugQ/j6FP5Pmk7J1vzWLdaulnHkwRE4BmfABhVQAzegDhoAgwl4AE/g2UiNR+PFeF205ozlzCH4AePtEzoWkr4=</latexit><latexit sha1_base64="+Uar6DfLTB/fEMxIChOuYZSZSk=">AB+XicdVDLSsNAFJ3UV62vqEs3g0V0VZIY2rqrunFZwT6gTcNkOm2HziRxZlIoX/ixoUibv0Td/6Nk7aCih64cDjnXu69J4gZlcqyPozcyura+kZ+s7C1vbO7Z+4fNGWUCEwaOGKRaAdIEkZD0lBUMdKOBUE8YKQVjK8zvzUhQtIovFPTmHgcDUM6oBgpLfmyf308nTWc2CXMXjfc3yzaJUuqmXHLUOrZFkV27Ez4lTcxfaWslQBEvUfO9249wkmoMENSdmwrVl6KhKYkVmhm0gSIzxGQ9LRNEScSC+dXz6DJ1rpw0EkdIUKztXvEyniUk5oDs5UiP528vEv7xOogZVL6VhnCgS4sWiQcKgimAWA+xTQbBiU0QFlTfCvEICYSVDqugQ/j6FP5Pmk7J1vzWLdaulnHkwRE4BmfABhVQAzegDhoAgwl4AE/g2UiNR+PFeF205ozlzCH4AePtEzoWkr4=</latexit><latexit sha1_base64="+Uar6DfLTB/fEMxIChOuYZSZSk=">AB+XicdVDLSsNAFJ3UV62vqEs3g0V0VZIY2rqrunFZwT6gTcNkOm2HziRxZlIoX/ixoUibv0Td/6Nk7aCih64cDjnXu69J4gZlcqyPozcyura+kZ+s7C1vbO7Z+4fNGWUCEwaOGKRaAdIEkZD0lBUMdKOBUE8YKQVjK8zvzUhQtIovFPTmHgcDUM6oBgpLfmyf308nTWc2CXMXjfc3yzaJUuqmXHLUOrZFkV27Ez4lTcxfaWslQBEvUfO9249wkmoMENSdmwrVl6KhKYkVmhm0gSIzxGQ9LRNEScSC+dXz6DJ1rpw0EkdIUKztXvEyniUk5oDs5UiP528vEv7xOogZVL6VhnCgS4sWiQcKgimAWA+xTQbBiU0QFlTfCvEICYSVDqugQ/j6FP5Pmk7J1vzWLdaulnHkwRE4BmfABhVQAzegDhoAgwl4AE/g2UiNR+PFeF205ozlzCH4AePtEzoWkr4=</latexit>

q ∼ mDMvDM ∼ eV

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1 q2 → 1 q2 − Π(q)

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If material has strong response to EM fields (e.g. metal), mediator picks up large effective mass, suppressing rate.
 In narrow-gap semiconductors, this does not happen

R ∼ Z d3q dΦ|FDM(q)|2|Fmed(q)|2|fexcit.(q)|2

not in vacuum!

Ultralight dark photon mediator:

slide-7
SLIDE 7

Importance of the dielectric function

R ∼ Z d3q dΦ|FDM(q)|2|Fmed(q)|2|fexcit.(q)|2

Ultralight dark photon mediator: This is a key material property — and UIUC has the tools to measure it!

momentum-resolved electron energy-loss spectroscopy (M-EELS)

|FDM|2|Fmed(q)|2|fexcit.(q)|2 = |h f|eiq·x| ii|2 (q2 Π(q))2 ⌘ 1 q4 Im ✓ 1 ✏(q) ◆

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slide-8
SLIDE 8

Projected sensitivity

  • Parameters for ZrTe5 which determine

DM rate are band structure (Fermi velocities and gap) and dielectric function: we use the measured value for the former and calculated value for the latter

  • Obtaining a mg sample is easy,

challenge will be placing the Fermi level in the gap and/or making a p-n junction

  • Dark rate is the largest expected

background by far for such a low- mass detector with no radioisotopes

  • Even with dark rates of Hz, can

achieve first ever limits on DM below 500 keV!

nderstanding these tuning parameters’ – – under i nt. r- t- to de- he al ke

− 𝑌 − 𝑍

  • 𝑙𝑑 = 0.454 Å−1

(a)

(based on YK, Griffin, Hochberg, Lisanti, Zurek, et al., PRD 2018 [1708.08929])

slide-9
SLIDE 9

Status of R&D

2. Near-term Technology R&D

2.a R&D Goals

Our R&D goals can be separated into two main categories: materials properties and device
  • prototyping. In detail, our goals are:
  • 1. Characterize the materials properties of ZrTe5 relevant for electronic excitation induced by
keV dark matter scattering. This includes:
  • Measuring the gap ∆ with time-resolved angle-resolved photoemission spectroscopy
(ARPES) and IR absorption;
  • Measuring the Fermi velocities vx, vy, vz near the Dirac point with ARPES, verifying
anisotropy;
  • Measuring the q = 0 part of the dielectric function, ✏(0, !), with time-domain THz
spectroscopy (TDTS);
  • Measuring the dielectric function ✏(q, !) for q ∼ O(10 − 100) eV and ! ∼ O(10 −
100) meV with momentum-resolved electron energy-loss spectroscopy (M-EELS), veri- fying scaling with q and anisotropy;
  • Determining the effect of strain and/or doping on the Fermi level and the gap, using
both molecular beam epitaxy (MBE) and bulk crystal growth techniques;
  • Opto-electronic measurements with IR photon absorption and time-resolved ARPES to
determine the carrier lifetime for electrons and holes in ZrTe5, and comparison with corresponding theory calculations;
  • Opto-electronic measurements with IR photon absorption to determine impact ionization
efficiency for electrons and holes, and comparison with corresponding theory calculations;
  • Measuring the breakdown voltage of ZrTe5 as a function of sample thickness and tem-
perature. A successful R&D process will result in a mg-scale sample of ZrTe5 which is insulating at 300 mK, for which all of the above properties have been measured at temperatures from 1.6 K to 20 K.
  • 2. Identify the key technical issues driving the design of an avalanche detector with an O(10)
meV gap. As a first step, we plan to design and test an avalanche device made from the commercially-available narrow-gap semiconductor InSb, for which functioning APDs have already been demonstrated [41, 42, 43] to identify any general issues with lowering the gap below the O(1 eV) typical of APDs or SPADs in common
  • use. The band structure and materials properties of InSb are much closer to silicon with
the exception of the smaller gap, which will allow us to draw on existing technology for commercially-available SPADs and isolate any issues resulting from the smaller gap as opposed to the Dirac band structure of ZrTe5. These include a measurement of dark current as a function of temperature, the optimal bias voltage to minimize the effects of Zener tunneling while still allowing sufficient carrier multiplication for an avalanche, and calibration with an
  • ptical parametric oscillator at 500 meV photon energies.

We submitted a BRN proposal on the R&D track

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measure material properties
 (does ZrTe5 behave in the wild 
 like we calculate it to behave?)

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practice making an APD


  • ut of another, 


commercially-available
 narrow-gap semiconductor

slide-10
SLIDE 10

ZrTe5 state of the art

  • Gap is ~20 meV at 4.5 K, band

structure is very close to linear near BZ center

  • ~50 mg single crystals can be

grown at Brookhaven

  • Fermi level can be manipulated

with epitaxial strain and/or Te concentration

  • Need to measure dielectric

function and Fermi velocities in an insulating sample: UIUC
 has expertise and machinery
 to do this

nderstanding these tuning parameters’ – –

− 𝑌 − 𝑍

  • 𝑙𝑑 = 0.454 Å−1

a) b) c)

slide-11
SLIDE 11

In the meantime: InSb APD

  • Making an avalanche device out of a

new material is hard. Practice on an easier material

  • InSb has a gap of ~235 meV and was

first made into an APD in 1967 (!!)

  • Large gap isn’t great for lightest DM,

but still sensitive to DM down to 200 keV

  • To do: make our own device at UIUC,

test at Fermilab, calculate DM sensitivity

  • Novel elements: cryogenic

temperatures, SQUID current sensor readout in linear gain mode

4 2
  • 2
  • 4
  • 6

K Γ L W X Γ

Energy [ E-Ef (eV) ] E0 E’0 ∆SO ∆’SO Σ4 Σ3 Σ4 Σ3 Σ4 Σ3 Σ4 Σ3 (c) JOURNAL OF APPLIED PHYSICS VOLUME 38, NUMBER 11 OCTOBER 1967

Noise and Multiplication Measurements in InSb Avalanche Photodiodes

  • R. D. BAERTSCH
General Electric Research and Development Center, Schenectady, New York (Received 15 May 1967) Multiplication and noise measurements on InSb avalanche photodiodes have been made from 77° to 125°K. For the diodes studied, the electron ionization rate is much larger than the hole ionization rate and depends only weakly on the field for fields between 5X loa and 1()4 V
  • fcm. The electron ionization rate in-
creases and the breakdown voltage decreases with increasing temperature. The dependence of the ionization rate on field and temperature is explained by the weak dependence of the distribution function on field for high fields. The noise measurements are consistent with McIntyre's theory providing that the electron ionization rate is much greater than the hole ionization rate. A current-controlled negative resistance is
  • bserved in InSb avalanche diodes at breakdown.
  • I. INTRODUCTION
Improvements in the signal-to-noise ratio in an avalanching silicon diode used as a broadband detector for high-frequency modulated light were reported by Johnson.! It was thought at that time that the state analog of the photomultiplier had been discovered. The calculations of the noise generated in an avalanch- ing photodiode by Tager2 and McIntyre3 showed, how- ever, that the noise associated with avalanche multi- plication increases more rapidly than the signal. Thus the gain in signal obtained in an avalanche photodiode is only useful if the system under consideration is limited by amplifier noise or the thermal noise of the diode load resistance. This limitation is obtained only in broadband systems. The noise generated in an avalanche photodiode depends critically on the ratio of a to (3, the electron and hole ionization coefficients, respectively.3-6 The least noise is obtained if the ratio of the ionization rates is very large and the primary photocurrent is carried by the carrier with the higher ionization rate. .The maximum frequency response of an avalanche photo- diode is also obtained if the ratio of the ionization rates is large.7 The ratio of the electron to hole ionization rates in silicon varies between 10 and 50 depending on the elec- tric field,S while in germanium the hole ionization rate is a factor of two larger than the electron ionization rate.9 1 K. M. Johnson, IEEE Trans. Electron. Dev. ED 12, 5S (1965) . 2 A. S. Tager, Soviet Phys.-Solid State 8, 1919 (1965). 3 R. J. McIntyre, IEEE Trans Electron. Dev. ED 13, 164 (1966) . 4 H. Melchoir and L. K. Anderson, 1965 Intern. Electron Devices Meeting, Washington, D.C. 5 R. D. Baertsch, IEEE Trans. Electron. Dev. ED 13, 383 (1966) . 6 R. D. Baertsch, IEEE Trans. Electron. Dev. ED 13, 987 (1966) . 7 R. B. Emmons and G. Lucovsky, IEEE Trans. Electron.
  • Dev. ED 13, 297 (1966).
8 C. A. Lee, R. A. Logan, R. L. Batdorf, J. J. Kleimack, and
  • W. Wiegmann, Phys. Rev. 134, A761 (1964).
9 S. L. Miller, Phys. Rev. 99, 1234 (1955). The measurements in GaAsI0,l1 and GaP12 show the hole ionization rate to be equal to the electron ioni- zation rate. This paper reports on measurements of ionization rates and noise in InSb avalanche photodiodes at tem- peratures from 77° to 125°K. From the temperature and field dependence of the ionization rate some sug- gestions as to the distribution function of hot electrons in InSb for very high fields are made. The calculation of the ionization rates from the multiplication data is given in the Appendix.
  • II. DEVICE FABRICATION
Single-crystal n-type indium antimonide with a con- centration of approximately 2 X 1014 donors/ cm3 was sawed into slices 1 mm thick and oriented in the (100)
  • plane. The slices were chemically polished in a meth-
anol-bromine solution in contact with a rotating wheel covered with a fine polishing paper.I3 The polished slices were sealed in an evacuated quartz tube with an indium-candmium alloy and diffused at 400°C for 60 to 200 h. The slices were then back lapped and etched to a thickness of 150 }J., and cleaved along the [110J directions into dice approximately 1 mm on a side. The dice were alloyed to a gold-plated Kovar header with pure tin. A platinum wire was soldered to the player with pure indium. Care was taken that the indium did not alloy through the p layer which was 3 to 6}J. thick. A portion of the p layer was masked with Apiezon W black wax and a mesa was etched electrolytically in
  • NaOH. A final clean-up etch was used to restore surface
stoichiometry.14 In some cases the diode was then anodized in a solu- tion of O.lN KOH to form a passivating oxide film over the diode. In other cases silicon monoxide was evapo- 10 R. A. Logan, A. G. Chynoewth, and B. G. Cohen, Phys.
  • Rev. 128, 2518 (1961).
11 C. R. Crowell and S. M. Sze, App!. Phys. Letters 9, 242 (1966) . 12 R. A. Logan and H. G. White, J. App!. Phys. 36, 3945 (1965). 13 M. V. Sullivan and G. A. Kolb, J. Electrochem. Soc. 110 585 (1963). ' 14 H. L. Henneke, J. App!. Phys. 36, 2967 (1965). 4267

*

0.00 0.02 0.04 0.06 0.08 0.10 q (˚ A−1) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 E (eV) InSb 200 keV DM 400 keV DM
slide-12
SLIDE 12

Future prospects (i.e. years 3-4 of our proposal)

  • Optimize readout: exponential or

linear gain? Impact ionization efficiency? Quenching circuit?
 Temperature dependence of afterpulsing?

  • Prototype calibration with CO2 laser

(117 meV) at 300 mK

  • Background mitigation strategy:

exploit daily and annual modulations

  • Dark rate measurements with goal
  • f 1/day at 10 mK for 1g target

mass after isotropic background subtraction

Absorption |q| ω