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Semiconductor detectors properties of semiconductors p-i-n diode - - PowerPoint PPT Presentation

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Semiconductor detectors properties of semiconductors p-i-n diode interface metal-semiconductor measurements of energy space sensitive detectors radiation damage in detectors Literatura: W.R.Leo: Techniques for Nucear and

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SLIDE 1
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 1

Semiconductor detectors

  • properties of semiconductors
  • p-i-n diode
  • interface metal-semiconductor
  • measurements of energy
  • space sensitive detectors
  • radiation damage in detectors

Literatura:

W.R.Leo: Techniques for Nucear and Particle Physics Experiments

  • H. Spieler: Semiconductor Detector Systems
  • G. Lutz: Semiconductor Radiation Detectors

S.M. Sze: Physics of Semiconductor Devices Glenn F. Knoll: Radiation Detection and Measurement

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 2

  • Energy resolution of a detector

depends on statistical fluctuation in the number of free charge carriers that are generated during particle interaction with the detector material

  • Low energy needed for generation
  • f free charge carriers → good

resolution

  • Gas based detectors: a few 10eV,

scintillators: from a few 100 do to 1000 eV

  • Semiconductors: a few eV!

Why semiconductors?

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 3

Comparison: radiation spectrum as measured with a Ge (semiconductor) in NaI (scintillation) detector

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SLIDE 4
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 4

good energy resolution → easier signal/background sepairstion

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SLIDE 5
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 5

Principle of operation:

Semiconductor detector operates just like an ionisation chamber: a particle, which we want to detect, produces a free electron – hole pair by exciting an electron from the valence band: electron hole Eg forbidden band, width Eg conduction band valence band

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 6

Drift velocity in electric field:

E vd × = µ

E vd ⋅ = µ

µ mobility different for electrons and for holes!

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SLIDE 7
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 7

properties of semiconductors

ρ [kg dm-3] ε Eg [eV] µe [cm2V-1s-1] µh [cm2V-1s-1] Si 2.33 11.9 1.12 1500 450 Ge 5.32 16 0.66 3900 1900 C 3.51 5.7 5.47 4500 3800 GaAs 5.32 13.1 1.42 8500 400 SiC 3.1 9.7 3.26 700 GaN 6.1 9.0 3.49 2000 CdTe 6.06 1.7 1200 50

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 8

n - concentration of conduction electrons p - concentration of holes

∫

=

t c

E E

dE E F E N n ) ( ) (

N(E) density of states ) exp( 1 1 ) ( kT E E E F

F

− + = Fermi-Dirac distribution EF Fermi energy level Pure semiconductor Neutrality: n=p

) ln( 4 3 2

e h v c F

m m kT E E E + + =

ratio of effective masses of holes and electrons

Intrinsic (pure) semiconductor (no impurities)

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SLIDE 9

Semiconductor detectors 9

) exp( ) ) ( exp( ) ) ( exp(

2

kT E N N n p n kT E E N p kT E E N n

g v c i

v F v F c c

− = = × − − × = − − × = ) 2 exp( kT E N N n

g v e i

− =

[ ] [ ]

3 22 3 13 3 10

atoms 10

  • f
  • ut

10 4 . 2 10 4 . 1

− − −

× = × = cm Ge cm n Si cm n

i i

Ec energy of the bottom of conduction band Ev energy of the top of the valence band Eg =Ec-Ev width of the forbidden band Nc, Nv: effective density of states in the conduction and valence bands At room themperature: ni number density of free charge carriers in an intrinsic semiconductor (only for electrons and holes)

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SLIDE 10
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 10

Properties of semiconductors are modified if we add impurities

  • Donor levels → neutral, if occupied

charged +, if not occupied

  • Acceptor levels → neutral, if not occupied

chargedi -, if occupied shallow acceptors – close to the valence band (e.g. three-valent atoms in Si – examples B, Al) shallow donors – close to the conduction band (e.g. five-valent atoms in Si – examples P, As)

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SLIDE 11
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 11

n-tip semiconductor, with added donors p-tip semiconductor, with added acceptors Binding energy of a shallow donor state is smaller because of a smaller effective mass and because of the diectric constant

eV m m eV

eff

025 . 6 . 13

0 ≈

⋅ ε

for Si In most cases it can be assumed that all shallow donors (acceptors) are ionized since they are far from the Fermi level. Neutrality:

D A

N p N n + = +

As a result, the Fermi level gets shifted:

) ln( ) ln(

i A F i i D i F

n N kT E E n N kT E E = − = −

if ND » NA , n type semiconductor if NA » ND , p type semiconductor

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SLIDE 12
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 12

Properties of semiconductors with imputies (doped semiconductors)

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 13

Resistivity of semiconductors

E vd × = µ

cm 47 cm 230k : tor semiconduc intrinsic re, temperatu room at ) ( 1 Ω = Ω = + = ⋅ ⋅ + ⋅ ⋅ = = × =

Ge Si h e d d

ρ p n e p v e n v e E E j

h e

ρ µ µ ρ ρ σ Charge drift in electric fieldu E, µ mobility specific resistivity

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 14

p-n structure

At the p-n interface we have an inhomogenous concentration

  • f electrons and holes  difussion of

electrons in the p direction, and of holes into the n direction At the interface we get electric field

(Gauss law)

Potential difference Vbi = built-in voltage difference,

  • rder of magnitude 0.6V

To the signal only those charges can contribute that were produced in the depleted region with a non-zero electric field  The depleted region should cover most

  • f the detector volume!

2

ln

i d a bi

n N N q kT V =

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SLIDE 15
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 15

How to excrease the size of the depleted region: apply external voltage Vbias

  • if the potencial barrier is increased, the depleted region

increases  larger active volume of the detector – voltage in the reverse direction

  • if the potencial barrier decreases, the active volume is

reduced, we get a larger current, voltage is in the conduction direction. The height of the potential barrier: VB= Vbias+ Vbi How large is the depleted region (xp+xn)? Neutrality: Na xp = Nd xn For the electric field we have the Poisson equation:

, 2 2

εε εε ρ

d a e

N e dx V d = − =

) ( e ) ( ≤ ≤ − +    ≤ ≤ −   − = x x x x N x x x x N e dx dV

p p a n n d

εε εε The electric field varies linearly, potential quadratically on the coordinate

+ Vbias

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 16

( )

2 / 1 2 / 1 2 / 1 2 / 1 2 / 1

2 : y resistivit spec. the

  • f

in terms 2 : example ) ( 2 ) / 1 ( 2 ) ) / 1 ( 2 (

bias e n d bias n d a d a d a bias p n d a a bias p a d d bias n

V d N e V x d N N N N N N e V x x d N N N e V x N N N e V x µ ρ εε ρ εε εε εε εε ≈         ≈ ≈ ⇒ >>         + = + =         + = + =

increases as Vbias

1/2

example: silicon      = type

  • p

m ) 0.32( type

  • n

m ) ( 53 .

2 / 1 p 2 / 1

µ ρ µ ρ

bias bias n

V V d if ρ=20000kΩcm and Vbias=1 V → d~75µm

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SLIDE 17
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 17

Leakage current

= current in the reverse direction difussion current:

  • difussion of minority carriers into the region with electric field
  • current of majority carriers with large enough thermic energy, such

that they overcome the potencial barrier generation current: generation of free carriers with the thermal excitation in the depleted layer

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 18

The probability of excitation is dramatically increased in the presence of intermediate levels.

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 19

generation current:

traps

  • f

ion concentrat ) 2 exp(

2 t g t gen

N kT E T N j − ∝

→ high T – high generation current → wider forbidden band Eg , lower generation current Consequence: some detectors have to be cooled (Ge based, radiation damaged silicon detectors)

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 20

metal-semiconductor interface (Schottky barrier)

Χ electron affinity Φ work function Assumption Φm >Φs Vbi = Φm- Φs

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 21

No external voltage voltage in the conduction direction voltage in the reverse direction Ohmic contact: high concentration of impurities → thin barrier → tuneling

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 22

Manufacturing of semiconductor detectorjev

1. manufacturing of monocrystals in form of a cylinder:

  • Czochralski (Cz) method

Liquid silicon is in contact with the vessel – higher concentration of impurities

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 23

Float zone method: No contact of the liquid semiconductor with the walls – higher purity of the material.

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 24

Photolitography for pattern fabrication

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SLIDE 25

June 5-8, 2006 Course at University of Tokyo

50 cm 20 cm

Two coordinates measured at the same time Typical strip pitch ~50µm, resolution about ~15 µm

pitch

Typical tracking device in particle physics: silicon strip detector

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 26

Signal development in a semiconductor detector

1. interaction of particles with matter (generation of electron – hole pairs) 2. drift of charges in electric field causes an induced current on the electrodes (signal) – similar as in the ionisation detector

96 . 6 . 1 1 1) Z particle, ionizing (minimum M.I.P. for

2

≈ = ≈ = ∝      

−

c v gcm MeV dx dE A Z dx dE

ion

β ρ ρ

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SLIDE 27

Signal development

For an electron-hole pair created at x0 in p-n detector, p-doped and higly n doped (n+)

             − − − = − =      − = − = = = <                 − = − − =         = = − = = = = − = − = = τ τ τ µ µ µ τ τ µ µ τ µ µ τ µ µ µ µ ρ ρεε τ τ µ εε t x d e x t x d e t Q t x t x x E v dt dx x d t x d e x t x d e t Q t x t x x E v dt dx eN x E x eN E qdx dQd

h h e h h e e h e h e e h A h A

exp 1 ) ) ( ( ) ( exp ) ( : holes ln for t 1

  • exp

) ) ( ( ) ( exp ) ( : electrons 1 and with , 1

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SLIDE 28

Signal development 2

Relation between charge carrier propagation and induced current: detector volume V=S*d n = concentration of carriers I=j*S current through surface S I=e0*v*n*S For a single drifting electron: n*V=n*S*d=1 n*S=1/d and therefore for a single drifting electron we get: I=e0*v/d and dQ*d = e0*dx

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SLIDE 29

Signal development 3

For an electron-hole pair created at x0

             − − − = − = <                 − = − − = τ µ µ τ τ µ µ t x d e x t x d e t Q x d t x d e x t x d e t Q

e e h h e e

exp 1 ) ) ( ( ) ( : holes ln for t 1

  • exp

) ) ( ( ) ( : electrons

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SLIDE 30
  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 30

Number of pairs/cm ε (eV)

Si

3.87 1.07 106 3.61

Ge

7.26 2.44 106 2.98

C

3.95 0.246 106 16

gas

~keV/cm a few 100 ~30

Scint.

~300- 1000/ph.e.

[ ]

cm MeV dx dE / /

Si on average ~100 electron-hole pairs /µm

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SLIDE 31

Semiconductor detectors 31

Radiation damage

Damage caused by:

  • Bulk effect: lattice damage, vacancies and interstitials
  • Surface effects: Oxide trap charges, interface traps.
  • C. oram, Academic training, CERN, 2002

J

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SLIDE 32

Semiconductor detectors 32

Main radiation induced macroscopic changes

How to mitigate these effects?

  • Geometry: build sensors such that they stand high depletion voltage (500V)
  • Environment: keep sensors at low temperature (< -10ºC)  Slower reverse
  • annealing. Lower leakage current.
  • C. oram, Academic training, CERN, 2002

J

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 33

Absorption of gamma rays

  • Photoeffect

) ( 1 ) ( 1

2 5 2 2 / 7 5

c m E E Z c m E E E Z

e ph e K ph

>> ∝ < < ∝

γ γ γ

σ σ

γ

  • Compton scattering

Z ∝ σ

  • Pair production

2

Z ∝ σ

gamma ray photo-electron

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 34

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 35

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 36

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SLIDE 37

Germanium detectors

  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 37

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 38

Energy resolution of gamma detectors

Depends on the statistical fluctuation in the number of generated electron-hole pairs. If all energy of the particle gets absorbed in the detector – E0 (e.g. gamma ray gets absorbed via photoeffect, and the photoelectron is stopped):

  • n average we get

generated pairs

_ i i

E N ε =

εi ~ 3.6eV for Si ~ 2.98 eV for Ge Average energy needed to create an e-h pair

gamma ray photo-electron

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 39

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 40

If we have a large number of independent events with a small probability (generation of electron-hole pairs) → binominal distribution → Poisson

i

N

__

= σ

Standard deviation – r.m.s. (root mean square): The measured resolution is actually better than predicted by Poisson statistics

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 41

  • Reason: the generated pairs e-h are not really independent since there is
  • nly a fixed amount of energy available (photoelectron looses all energy).
  • Photoelectron looses energy in two ways:
  • pair generation (Ei ~ 1.2 eV per pair in Si)
  • excitation of the crystal (phonons) Ex ~0.04 eV for Si

_ _ _ _

deviation standard

i i x x i x

N N N N = = σ σ

Average number of crystal excitations Average number of generated pairs Since the available energy is fixed (monoenergetic photoelectrons): Ei = energy needed to excite an electron to the valence band (=Eg)

_ x i x i x x i i x x i i

N E E E E N E N E = ⇒ = ⇒ ∆ − = ∆ σ σ σ

Width of the energy loss distribution

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  • V. Cindro and P. Križan,

IJS and FMF Semiconductor detectors 42

_ _ _ _ _ _ _ _

) 1 (

  • f

use make

i i i i x i i i i x i i i x i x i i x x x i i

N F E E E N E N E N E E E E E N E E N E N E N E = − = ⇒ = − = − = ⇒ = + ε σ ε σ

F Fano factor – improvement in resolution F ~ 0.1 for silicon