Tracking detectors for the LHC Peter Kluit (NIKHEF)
Overview lectures part I Principles of gaseous and solid state tracking detectors Tracking detectors at the LHC Drift chambers Silicon detectors Modeling of a silicon detector Peter Kluit 2
Overview lectures part II Tracker design and performance Momentum and impact parameter measurement Optimization of tracker design and G4 simulation Track reconstruction and fitting Principles and basic ideas Pattern recognition Track fitting Physics applications Primary and secondary vertex reconstruction Invariant mass reconstruction b-tagging Peter Kluit 3
Principles of tracking detectors Detect and reconstruct the trajectory of charged particles: determine direction and momentum minimize the distortion of the trajectory Gaseous detectors and thin layers of solid state detectors Contrast to calorimeter: particles are stopped Peter Kluit 4
Some history Tracking detectors Wilson cloud chamber ~1912 Nuclear emulsion Cloud chamber Bubble chamber Spark chamber Streamer chamber Peter Kluit 5
LHC experiments LHCb ATLAS/CMS/LHCb/ALICE Silicon detectors: vertex (locator) and tracker (SCT) gaseous detectors: TRT, Outer tracker,tpc ALICE Peter Kluit 6
Interaction of charged particles with matter Coulomb scattering An incoming particle with charge z interacts with a target of nuclear charge Z. The cross-section for this e.m. process is: 2 dσ 2 m c 1 P e = 4zZr Rutherford e 4 dω βp sin θ 2 Multiple Scattering Sufficiently thick material layer: L r plane θ plane θ plane 13.6 MeV θ 0 = z x/ X 0 X βcp Peter Kluit 7 0 θ 0 X 0 Radiation length Gaussian sin -4 (θ/2) ( 1+ 0.20 ln( x/ )) 0
Energy loss Collisions with the atomic electrons of the absorber material: e.g. e -> e +γ If E, p high enough ionisation only Bethe Bloch: de dx = 4πN A 2 2 2 2 2 2 Z 1 1 2mec γ β max 2 δ r m c z ln T β e e p/m A 2 2 2 β I 2 Peter Kluit 8
Gaseous detectors Fast charged particles ionize the atoms of a gas: Primary Ionization 10-40 pairs/cm Total Ionization total n primary Often the resulting primary electron will have enough kinetic energy to ionize other atoms Gives rise to non-gaussian Landau distribution: More collisions more Gaussian n 3 4 de/dx ~ dn/dx Peter Kluit 9
Proportional Counter Cylindrical field geometry: E cathode gas b E threshold E ( r) V ( r) = = CV 2πε 0 CV 2πε 0 0 0 1 r ln r a a anode 1/r C = capacitance / unit length a r Field near wire is sufficiently high to get large amplification: exponential increase of number of electron-ion pairs Peter Kluit 10
Signal formation Signal induction both on anode and cathode due to moving charges from electrons and ions: Q dv ind = lcv 0 dv dr dr Electrons contribute only very little to detected signal (few %). Ions have to drift back to cathode, i.e. dr is big. Signal duration limited by total ion drift time! Need electronic signal differentiation Peter Kluit 11
MWPC/Drift chamber Multi wire proportional chamber (MWPC) (G. Charpak et al. 1968, Nobel prize 1992) Typical parameters: L=5 mm, d=1 mm, a wire =20 µm scintillator DELAY Stop TDC Start Drift chamber Measure arrival time of electrons at sense wire relative to a time t 0 drift anode x = vd ( t) dt low field region drift high field region gas amplification Peter Kluit 12
Drift and diffusion in gasses Undergoing multiple collisions, an originally localized ensemble of charges will diffuse: dn σ N x = ( t ) = 1 4π Dt 2 Dt e ( x 2 or 4 Dt ) D dx = In presence of E field: D D(x,t) eτ v D = µ E µ = (mobility) m With E B fields (in e.g.tpc) reduced to: D eb DT( B) = ω = 2 2 1+ω τ m σ 2 x 2t ( t ) σ x D: Diffusion coefficient Peter Kluit 13 t
Time Projection Chamber: 3D tracking z from drift time x-y from wires and segmented cathode of MWPC de/dx information PEP-4 TPC Drift over long distances Diffusion significantly reduced by B-field Space charge problem from positive ions, drifting back to midwall gating σ Rφ = 173 µm ALEPH TPC σ z = 740 µm Ø 3.6m L=4.4 m Gate open Gate closed Peter Kluit 14
Outlook tracking detectors Discussed classical gaseous detectors from proportional chamber MWPC/drift chamber Time Projection Chamber Now present silicon detectors Microstrip detector Pixel detector Modeling a silicon detector Peter Kluit 15
Principles of a silicon detector p-n junction Typical layout of a strip sensor depth 285µm pitch 80µm width 10µm V=200-350 V Operating principle: track creates 30,000 e-hole pairs (~100 /µm) create a depleted zone where e-hole pairs move freely by applying a reverse bias voltage and measure the current Peter Kluit 16
Principle of P-N junction: diode diffusion of e- into p holes into n thin depletion zone no free charge carriers potential stops diffusion P doped bulk material: majority carriers electrons (add donors eg As) N majority holes (add acceptors eg B) Apply a reverse bias V: depletion zone gets extended over the full junction Track gives e-hole pairs Electrons drift towards the n- side, the holes towards the p- side detectable current Peter Kluit 17
Silicon Pixel detectors Measures a 3D point in space Segment silicon to form matrix Readout electronics with same geometry Connection by bump bonding techniques Peter Kluit 18
Characteristics of Silicon detectors Relative high number of electrons but no charge multiplication Integrate electronics on chip (see pixel) Fine granularity ~100 µm pitch and high resolution Fast charge collection ~10 ns Rigidity of silicon: self-supporting Large detectors (still) expensive Peter Kluit 19
Silicon vertex detector DELPHI Strips 50 µm RΦ 44-176 µm z Pixels 330 x 330 µm 2 1033 mm, 10º q 170º Hit resolution 10 µm RΦ Peter Kluit 20
Modeling a silicon strip detector Field lines in a strip detector depth 285µm pitch 80µm width 10µm V=200-350 V N bulk detector Assumes no space charge and no B field Holes run to strip, electrons to backplane strip Peter Kluit 21
Velocity v = µ E Collection times µ e =1350 cm 2 /Vs µ h =480 cm 2 /Vs Collection time electrons ~5 ns holes ~10 ns Tail from low field region between strips electrons holes E x Peter Kluit 22 x
Induction current in a sensor n Moving charge induces a current I = q v grad Vind (Ramo s Theorem) Vind calculated v=1 on strip, 0 on rest Most current induced at large gradients: around 20 µm from strip n NB: same applies to signal induction gaseous detectors n Peter Kluit 23
Hole current Electron current arbr units Electron and hole induced currents Generated electron-holes pairs at x=0 uniform in z=0-285 µm Electrons: most signal from small z values; 35% of signal Holes: most signal from large z values; 65% of signal Peter Kluit 24
Gaseous-silicon detector Timepix: combination of a Micromegas with a pixel read-out (Medipix chip) R&D stage for TPC at linear collider: Replace read-out pads at endplate Peter Kluit 25