Semiconductor (solid state) detectorszacek/detektory/semiconductor_det.pdf · Semiconductor (solid state) detectors 1. Introduction 2. Principle of semiconductors 3. Silicon detectors,

Semiconductor (solid state)

detectors 1. Introduction

2. Principle of semiconductors

3. Silicon detectors, p-n junction, depleted region, induced charge

4. energy measurement, germanium detectors

5. position measurement, silicon strip detectors, pixel detectors

silicon drift detectors

6. DEPFET

7. Photon detectors, APD, SiPM

8. 3D detectors

J. Žáček Experimentální metody jaderné a

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1. Introduction


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Principle of semiconductors


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hole conduction


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- E - 𝐸𝑓


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k ~8.6 x 10−5 𝑒𝑉 𝑇−1

electron concentration

g(E) - density of electron state in the conduction band

f(E) ⦁ g( E) – electron concentration

𝑬𝒄 lowest energy level in the conduction band

g(𝑬𝒄 ) ≡ 𝑵𝒄 density of electron states in the lowest energy level

approximation : f ≈ 𝒆− ( 𝑬−𝑬𝒇)/𝒌𝑻

electron concentration in the lowest energy level 𝒏𝒆 = 𝑵𝒄 𝒆−

𝑬𝒄 −𝑬𝒇

𝒌𝑻

hole concentration

𝑬𝑽 − 𝐡𝐢𝐠𝐡𝐞𝐬𝐭 𝐞𝐧𝐞𝐫𝐠𝐲 𝐥𝐞𝐯𝐞𝐥 𝐢𝐧 𝐭𝐡𝐞 𝐯𝐚𝐥𝐞𝐧𝐜𝐞 𝐛𝐚𝐧𝐝

𝑵𝑽 - density of hole state in the highest energy level of the valence band

hole concentration in the highest energy level 𝒏𝒉 = 𝑵𝑽 𝒆−

𝑬𝒇 −𝑬𝒗

𝒌𝑻


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Boltzmann constant k ≈ 8.6 ⦁ 10−5 eV ⦁ 𝐾−1

E-𝐸𝑓 ≈ 1 𝑒𝑉

𝐸𝑔 = 𝐸𝑐 - 𝐸𝑉


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𝑣𝑒 = μ𝑒 𝐸 𝑣ℎ = μℎ 𝐸

μ mobility, E external electric field

Current : J = e 𝑛𝑖 (μ𝑒 + μℎ ) 𝐸 = σ E, σ - conductivity R = 1/σ - resistivity

μ𝑒 μℎ

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i) Direct recombination

Recombination and trapping of the charge carriers

ii) Recombination resulting from impurities in the crystal

a)

b)

iii) Trapping resulting from impurities in the crystal

iv) Structural defects in the lattice


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3. Silicon semiconductors, p – n junction

Si:


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n- type semiconductor


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p- type semiconductor


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Approximation of charge densities

Concentration

of acceptors 𝑵𝑨 Concentration

of donors 𝑵𝑫

Maxwell equations:

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Using resistivity 𝑹𝒏of n-type

d= 𝟐 𝜺 𝑹𝒏 𝝁𝒆 𝑽𝟎

d= 𝟐 𝜺 𝑹𝒑 𝝁𝒉 𝑽𝟎

𝑹𝒏

𝑹𝒑𝑽𝟎

R

For R≈ 20 000 Ω , 𝑉0 = 1 V d= 75 μm

For reversed bias V= 𝑽𝟎 + 𝑽𝑩 ~ 50 − 100 V

d ~ 300 μm

R = 1/(e 𝑛𝑖 (μ𝑒 + μℎ ) ) in n-type, μℎ = 0 𝑛𝑖 = 𝑁𝐷


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𝑝+ over-dopped p-type

d

d

d

d


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depletion region HV

Ohmic contact : direct metal – p-type not possible, because of the barrier

between metal and p-type

instead heavily doped p-type 𝒑+ 𝐨𝐧 𝐭𝐡𝐞 𝐩 − 𝐭𝐲𝐩𝐞 𝐬𝐮𝐛𝐬𝐭𝐫𝐚𝐝𝐞

and then a metal

metal

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Induced charge

Q - charge in the depletion region

page 25:

but different coordinate frame,

zero at the junction

x ⟶ x - 𝑥𝑝 , 𝑥𝑝 ≡ d, E=-dV/dx

d - thickness of the depletion region

,resistivity R=1/( )

𝜏 = ε ⦁R

𝑡𝑑


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𝑞ℎ 𝑡 =

t ⟶ ∞ 𝑞ℎ =

𝑞𝑒 (𝑡𝑑) =

Induced charge at 𝑡𝑑

i.e. If x(t) =0

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Ex. /pair

a good preamplifier needed, low noice


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DC direct coupling, AC


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4. Energy measurement

Construction of p-n junctions

• Diffused junction diode: diffusion of donors to p-type at the temperature

1000 C

• Surface barrier junction: junction between a semiconductor and a

metal

n-type Si with Au, p-type Si with Al

sensitive to light

• Ion-implanted junctions: a substrate is bombarded by ions from an

accelerator

Depleted region small ⟹ energy measurement for low energies


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Guard ring


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in Si

particle energy ( MeV)

10 100


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Compensating materials developed to increase the depletion region

by lithium drifting process

known as p-i-n junction

Li diffused to p-type, a narrow n-type is created

electrons drifted to p-type, negative space charge

application of HV ⟶ positive Li ions drifted to p-type

for sufficient time to create

⟹ the same concentration of positive ions and electrons t ⟹ no space charge, i.e. compensated region

resistivity up to 100 000 Ω width of compensating region 10-15 mm Si(Li) , the noise is much greater then in normal Si cooling is needed


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Energy resolution

Fluctuation of energy losses in the depleted region

Landau fluctuation

, Δ𝐸𝑚.𝑝. most probable energy loss


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Germanium detectors suitable for γ detection,

Resolution at 1.33 Mev Ge detector 0.15 %

NaI 8 %

-

- High purity germanium (PHGe), depletion region~ cm, low temperature during

- measurement only


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Shape of Ge detectors - planar, circular shape, diameter 1-2 cm, volume 10-20 𝑐𝑚3

coaxial , volume up to 400 𝑐𝑚3


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5. Position measurement, silicon strip and pixel detectors

i) Manufacturing of Si strip detectors

ii) Microstrip detectors

iii) Position resolution

iv) Pixel detectors

v) Silicon drift detectors


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i)


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R

ii)


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iii)


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analog readout


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iv)


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Advantages and disadvantages


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v)


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Application of strip, pixel and pad detectors

Trackers: precise determination of particle tracks (strips or pixels)

Vertex detectors: in collider experiments, detectors situated around

the interaction vertex

Topology: sensors mounted on a planar carbon frames or cylindrical carbon frames

Calorimeters: as active layers in sampling calorimeters


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forward and backward silicon tracker of the H1 experiment

Collider HERA, DESY Hamburg, electrons (~26 GeV) vs protons (920 GeV)

several layers of circular planes equipted with strip sensors

Interaction vertex

Beam pipe

electrons

protons

Emitted particle

electronics

Si sensors

sensor

particle

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Pad silicon detectors for the readout of the

electromagnetic calorimeter CALICE

Si Si wafers 6 x 6 cm, 1 pad 1x1 cm, depletion

region 500 μm

calorimeter: absorber tungsten, active layers from Si wafers

electronic layer above active layer

(calorimeter for linear collider)

W - layer

Si wafers

readout board

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5. DEPFET

Bipolární

tranzistor:

Nepřipojený k obvodu Připojený k obvodu

emitor báze kolektor


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FET tranzistor

Polem řízené (neboli unipolární či FET) tranzistory spínají/omezují protékající proud

na základě toho, jaké napětí je na „drain“

řídicí se nazývá gate a značí se "G",

spínaný proud vstupuje do drainu "D" a

vystupuje z source "S". Tři jednotky FETu:

drain je zde jako kolektor, source jako emitor a gate jako báze


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FET

Proud teče mezi S a D mezi

nimiž je napětí.

Napětí na D mění vodivost

substrátu, tj proud teče/neteče

Zdroj proudu je S, výstupní proud

je v D.


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DEPFET je FET vytvořený na plně vyčerpanén substrátu. Působí současně jako

senzor a zesilovač

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Top gate

P –channel FET on a fully depleted n-bulk

𝑛+

n-Si


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electrons from photon are collected at the internal gate

the energy deposited by a photon is determined by the change of the FET conductivity


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clear mode - change of the FET conductivity,

This difference ~to the total amount of

collected charge


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7. Semiconductor photon detectors

APD - avalanche photodiode replace e.g. photomultipliers in calorimeters, very small devices,

can be connected with fibers

Usual photodiode PD


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avalanche photodiode


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HAPD - hybrid APD


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SiPM Silicon Photon Multipliers

1156 photodiodes on the area 1.1 x 1.1 𝑚𝑚2

depletion region


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SiPM detects individual photons, current ~ to the number of fired pixels

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Hadron calorimeter

Scintillation light from the tile is collected by a WLS fiber which is directly

connected to a SIPM.

WLS fibre

SiPM were first developed for the readout of scintillation light of the hadron

calorimeter within CALICE collaboration


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(pixel ≡ photodiode)

Pedestal ≡ noise


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3D detectors

Documents

Semiconductor (solid state) detectorszacek/detektory/semiconductor_det.pdf · Semiconductor (solid state) detectors 1. Introduction 2. Principle of semiconductors 3. Silicon detectors,