Momentum Measurement in B Field Momentum is determined by measurement of track curvature κ = 1 ρ in B field: Measure sagitta s of the track. For the momentum component transverse to B field: = qbρ Units: [ GeV] = 0.3B[ T]ρ[ m] x 1 x 2 x 3 L 2 θ θ L 0.3B L --------- = sin-- -- (for small θ) θ -- = ------------------ ρ 2 2 ρ s ρ θ 1 cos-- 1 = ρ 1 1 -- θ2 ---- 2 2 4 = ρ---- θ2 8 For the simple case of three measurements: s = x 2 ( x 1 + x 3 ) 2 ds = dx 2 dx 1 2 dx 3 2 with σ( x) dx i uncorrelated error of single measurement: σ2 s σ 2 σ ( x) 2 ( x) 3 = + ------------- 2 = --σ 4 2 2 ( x) 0.3 ------ L2 B --------- 8 Relative Momentum Error σ( p For 3 points the relative momentum resolution is given by: T ) -------------- degrades linearly with transverse momentum improves linearly with increasing B field improves quadratically with radial extension of detector In the case of N equidistant measurements according to Gluckstern [NIM 24 (1963) 381]: σ( ) σκ ( ) σ( x) 720 -------------- = ----------- = ---------------------- (for, curvature ) κ 0.3BL 2 ----------------- N 10 κ = 1 ρ ( N + 4) Example: For = 1GeV, L = 1m, B = 1T, σ( x) = 200µm and N = 10 one gets: σ( ) -------------- 0.5% for s 3.5cm σ( ) Important track detector parameter: -------------- (%/GeV) 2 σ s = ---- = s 3 --σ ( x) 2 8 p ----------------- T 0.3BL 2 carsten.niebuhr@desy.de 1 Particle Detectors 2 carsten.niebuhr@desy.de 2 Particle Detectors 2 Contribution from Multiple Scattering First Track Detectors The contribution to the momentum error from MS is given by: σ( ) -------------- MS L' σ MS --------- 13.6 3 10 L' ------------------------z ----- ( s) 4 3 pβ X = ----------------- = ------------------------------------------------- 0 s 0.3BL 2 = z ( 8 ) for β 1 this part is momentum independent! 3 52.3 10 -------------------------------- βb LX 0 sinθ with L' = L sinθ = psinθ L θ total path L Until 1970: optical measurements using - bubble chambers - emulsions - spark chambers BEBC bubble chamber manual reconstruction The combined total momentum error is: σ ----- p 2 720 p ------------- -------------------- σx psinθ 2 3 52.3 10 2 = N + 4 0.3BL 2 + -------------------------------- βb LX 0 sinθ total hit resolution can handle only very low data rates + ( cotθσ θ ) 2 multiple scattering Example for momentum dependence of individual contributions θ resolution carsten.niebuhr@desy.de 3 Particle Detectors 2 carsten.niebuhr@desy.de 4 Particle Detectors 2
Gas Detectors Primary and Total Ionisation Yield in Gases Criteria for optimal momentum resolution: many measurement points large detector volume very good single point resolution as little multiple scattering as possible Gas Diensity ρ [g/cm 3 ] I 0 [ev] W [ev] n p [cm -1 ] n T [cm -1 ] H 2 8.99 x 10-5 15.4 37 5.2 9.2 He 1.78 x 10-4 24.6 41 5.9 7.8 N 2 1.23 x 10-3 15.5 35 10 56 O 2 1.43 x 10-3 12.2 31 22 73 @ STP Total number of produced electron-ion de ------ x E dx pairs: = ------- = ------------- with n T W i W i Gas detectors provide a good compromise and are used in most experiments. However: per cm in Argon only ca. 100 electron-ion pairs are produced by ionisation (see next page) this has to be compared with the noise of a typical amplifier of 1000 e- a very efficient amplification mechanism is needed carsten.niebuhr@desy.de 5 Particle Detectors 2 Ne 9.00 x 10-4 21.6 36 12 39 Ar 1.78 x 10-3 15.8 26 29 94 Kr 3.74 x 10-3 14.0 24 22 192 Xe 5.89 x 10-3 12.1 22 44 307 CO 2 1.98 x 10-3 13.7 33 34 91 CH 4 7.17 x 10-4 13.1 28 16 53 C 4 H 10 2.67 x 10-3 10.8 23 46 195 avg. ionisation pot. / shell elect. average energy loss./ion pair number primary electron-ion pairs total number electron-ion pairs E = total energy loss in x and W i = average energy loss per produced ion pair: n T 2 7 n p carsten.niebuhr@desy.de 6 Particle Detectors 2 Gas Amplification First Townsend Coefficient For cylindrical geometry: 1 Er ( ) -- r and r V( r) ln-- a the primary electrons drift towards the positive anode due to 1/r dependence the electric field close to very thin wires reaches values of E > kv/cm in between collisions with atoms electrons gain enough energy to ionize further gas molecules exponential increase in number of electron ion pairs very close (few µm) to the wire + simulated avalanche Number of electron ion pairs created per unit length in the avalanche per electron is given by the first Townsend coefficient α : σ [10 8 b] relation to cross section for ionisation: N A α = σ ion ----------- V Mol number of produced ions: nx ( ) = n 0 exp( α( E) x) the gas gain is given by: A ---- n = = exp α ( r ) dr n 0 with a anode diameter and r c distance to wire where avalanche starts example: Argon and E = 100eV: σ = 3x10-16 cm 2 α -1 1µm r c a E [ev] a/p [ion pairs /cm mm Hg] carsten.niebuhr@desy.de 7 Particle Detectors 2 carsten.niebuhr@desy.de 8 Particle Detectors 2
Avalanche Formation + + - - Signal Shape The signals which are induced on anode and cathode come from the fact that charges move Q in the electric field between the electrodes: dv = ------------ dv ------ dr lcv 0 dr Most of the electron-ion pairs are created very close to the anode wire electrons only move a short distance in the electric field: dr small due to transverse diffusion a droplet like avalanche develops around the anode electrons are collected very fast ( 1 ns) mobility of electrons 1000 times larger than for ions the cloud of positive ions remains and slowly drifts towards the cathode picture taken with cloud chamber in contrast the ions move all the way back to the cathode: dr much larger most of the signal is induced by the movement of the ions which takes very long usually the signal is electronically differentiated V max carsten.niebuhr@desy.de 9 Particle Detectors 2 carsten.niebuhr@desy.de 10 Particle Detectors 2 Modes of Operation of Gas Detectors Ionisation chamber: complete charge collection, but no charge amplification Proportional counter: above threshold voltage multiplication starts. Detected signal proportional to original ionization energy measurement (de/dx). Secondary avalanches have to be quenched. Gain 10 4-10 5 Region of limited proportionality: or streamer mode: strong photo emission secundary avalanches. Needs efficient quencher or pulsed HV. Gain upto 10 9, hence simple electronics sufficient Geiger-Müller counter: massive photo emission. Full length of anode wire affected. Stop discharge by HV break down. Strong quenchers needed. Number of electron ion pairs α e - Multi Wire Proportional Chamber Generalize principal of proportional tube to large area detector. Multi Wire Proportional Chamber: MWPC George Charpak 1968 anode wires act as independent detectors capacitive coupling of negative signal from avalanche forming anode wire to neighbours small compared to puls, which is generated by ions drifting towards cathode development in electronic: possibility to read many channels in parallel 10 6 tracks per second Breakthrough in detector development Nobelprice for physics 1992 carsten.niebuhr@desy.de 11 Particle Detectors 2 carsten.niebuhr@desy.de 12 Particle Detectors 2
MWPC Use of gold plated tungsten wires with diameter 15-30µm as anode wires. Chamber walls made from glas fiber material (rigid, low mass). Thin metal foil acting as cathode (typically d 50µm). Typical dimensions: d = 2mm, L = 4mm. Electrostatic potential in a planar MWPC given by: V( x, y) V(x,y) q πx ----------- 4 sin ----- 4πε 2 πy + ----- 0 d sinh2 d = ln y d resolution σ = d/ 12 electric field lines L Principal of a Driftchamber Measure arrival time t 1 of electrons at anode wire relative to reference t 0. external definition of time reference t 0 (here by fast scintillator signal) x-coordinate given by: x = t 1 t 0 v D ()t t d y x x E-field small E-field large drift region gas gain TDC: Time to Digital Converter if drift velocity v D constant over full drift distance: x = v D ( t 1 t 0 ) = v D t advantage of drift chambers: much larger sensitive volume per read out channel carsten.niebuhr@desy.de 13 Particle Detectors 2 carsten.niebuhr@desy.de 14 Particle Detectors 2 v drift vs E-Field in various Argon-Mixtures Examples for Cylindrical Driftchamber Geometries v drift [cm/µs] v drift [cm/µs] reduced E-field: E/p [V/cm mm Hg] strong dependence on the choice of the gas mixture details of the energy dependence of the ionisation cross section (Ramsauer minimum) result in a characteristic maximum of the E field dependence. for stable operation it is useful to operate in the maximum: typical drift velocities : v drift 2-10 cm/µs = 20-100 µm/ns dv -------------- drift = 0 de E [V/cm] at 1 atm Left-right ambiguity resolved by staggered wires cell of a "jet"-driftchamber carsten.niebuhr@desy.de 15 Particle Detectors 2 carsten.niebuhr@desy.de 16 Particle Detectors 2
Isochrones & Lorentzangle Intrinsic Position Resolution The intrinsic position resolution is influenced by three effects: statistics of primary ionisation: point of origin of primary cluster varys by 100µm Isochronen diffusion of electron cloud during it s drift to anode 1 2Dx - σ = ------ --------- n µe - Lorentz effect first electrons limitations in time resolution of whole chain of electronic signal processing - cabel - pulse shaping - definition of time refernce t 0 etc contributions to position resolution distance to wire plane carsten.niebuhr@desy.de 17 Particle Detectors 2 carsten.niebuhr@desy.de 18 Particle Detectors 2 Driftchambers during Construction Central Jet Chamber von H1 H1 Central Jet Chamber Cathode Supporting Rod Sense/Pot Cathode 15000 wires total force from wire tension 6 tons carsten.niebuhr@desy.de 19 Particle Detectors 2 carsten.niebuhr@desy.de 20 Particle Detectors 2
Options for Readout of Second Coordinate Time Projection Chamber Crossed Planes ambiguities Segmented Cathodes Q L Charge Divison, z-by-timing Z = +L/2 X Z O r(z = + L/2) α Y A L z 0 resistive wire, analog readout Stereo Wires z Q R In the seventies D.Nygren developed the Time Projection Chamber (TPC). large gas volume with one central electrode minimal amount of material electrons drift in strong electric field over distance of several meters to end walls where they can be registered for example with MWPCs - readout of anode wires and cathode pads x,y - drift time z - unambiguous 3d hit measurements diffusion strongly reduced, since E B electrons spiral around E-field lines: Larmor radius <1µm laser calibration for precise v D determination very good hit resolution and de/dx meas. analog readout Z = L/2 A1 σ z 0.1 mm Φ A 0 long drift times ( 40µs) - rate limitation - very good gas quality required carsten.niebuhr@desy.de 21 Particle Detectors 2 carsten.niebuhr@desy.de 22 Particle Detectors 2 Example ALEPH-TPC Gating in a TPC 5 m length achieved resolutions: σ rφ = 170 µm σ z = 740 µm r φ projection A specific problem in a TPC is presented by the ions drifting back to the central electrode. At high rates they disturbe the homogeneity of the electric field in the drift region. Solution by so-called gating : ions are collected on shielding grid only electrons from "interesting" tracks reach the amplification region; others are collected on gating grid this requires use of an external trigger 2.0 1.8 Gate closed (a) Gating grid closed Gate open 1.8 (b) Gating grid open 1.6 1.6 y (cm) 1.4 1.2 1.0 + + + gating grid gating grid shielding grid shielding grid y (cm) 1.4 1.2 1.0 0.8 anode wires 0.6 cathode plane 1.8 (b) Gating grid open anode wires cathode plane 0.8 0.6 0.4 0.6 0.4 0.2 0 0.2 0.4 0.6 x (cm) carsten.niebuhr@desy.de 23 Particle Detectors 2 carsten.niebuhr@desy.de 24 Particle Detectors 2
ALEPH TPC Event Aging Effects in Wire Chambers Deposits on anode wires Complex plasma-chemical reactions in the avalanche can lead to polymerisation This can make chambers unusable : inefficiency HV instabilities y x r z Measures against aging: carefully select materials for whole system highest gas quality - no impurities avoid excessive chamber currents carsten.niebuhr@desy.de 25 Particle Detectors 2 carsten.niebuhr@desy.de 26 Particle Detectors 2 Micro Strip Gas Chambers MSGC Gas Electron Multiplier GEM charged particle x-ray relative gain In the late 90 s developed by F.Sauli at CERN gas [ 3mm] electrons ions MWPC MSGC substrate 100µm 80µm 10µm [300µm] 10 3 10 4 10 5 10 6 10 7 rate (mm -2 s -1 ) typical gain of 10 3 at 500V can stack several stages on top af each other large total gain at relatively moderate HV Advantages very precise and small anode/cathode structures can be produced with lithographical methods very good position resolution high mechanical stability small drift distance for ions high rate capability Triple-Gem carsten.niebuhr@desy.de 27 Particle Detectors 2 carsten.niebuhr@desy.de 28 Particle Detectors 2
Semiconductors in the Periodic System Advantages of Silicon band gap E=1.12 ev III IV V energy needed per electron-hole pair: 3.6 ev (rest goes into phonons, for comparison 30eV for noble gas) high density: ρ = 2.33 g/cm 3 with de/dx min = 1.664 MeV/gcm -2 one obtains for 300µm thick Si-layer: N = 300 µm x 1.664 MeV/gcm -2 x 2.33 g/cm 3 /3.6 ev N 32000 electron-hole-pairs in 300 µm (MIP) good mechanical stability layers of this thickness can be made self supporting large mobility of charge carriers fast charge collection t 10ns no additional charge amplification mechanism neccessary carsten.niebuhr@desy.de 29 Particle Detectors 2 carsten.niebuhr@desy.de 30 Particle Detectors 2 Signal Generation in Silicon Doping of Semiconductors only at T=0 K the conduction band is completely empty distribution acccording to Fermi-Dirac statistics at room temperature we have n i n V n exp E C ----------- Gap i.e. a 2kT 10 = = 1.5 10 cm 3 fraction of 10-12 in conduction band (silicon 5x10 22 atoms/cm 3 ) E in this volume there are 4.5 x 10 8 free charge carriers in comparison to only 3.2 x 10 4 electron-hole pairs craeted for a MIP in order to detect this tiny signal the number of free charge carriers has to be reduced drastically. Options: - cooling - pn-junction in reverse bias conduction band - + valence band 1 cm 1 cm E Fermi 300µm By adding small amounts of impurities to semiconductors their conductivity can be changed drastically: E By adding elements from group V (donator, like As) one obtains n - type conduction band e valence band E Fermi donator level E By adding elements from group III (acceptor, like B) one obtains p - type conduction band valence band + acceptor level E Fermi carsten.niebuhr@desy.de 31 Particle Detectors 2 carsten.niebuhr@desy.de 32 Particle Detectors 2
Doping of Silicon pn - Junction Arsen atom diffusion of e - into p-zone diffusion of holes into n-zone n - type + p - type depletion zone asymmetry due to different level of doping Bor atom zone without free charge carriers carsten.niebuhr@desy.de 33 Particle Detectors 2 carsten.niebuhr@desy.de 34 Particle Detectors 2 Silicon Strip Detectors Double sided Readout 300 µm typical strip pitch d = 20-50 µm resolution σ 10µm Make use of drift electrons: second coordinate without additional dead material! carsten.niebuhr@desy.de 35 Particle Detectors 2 carsten.niebuhr@desy.de 36 Particle Detectors 2
Wafer for H1-CST p - side carsten.niebuhr@desy.de CST Ladders n - side 37 Par ticle Detectors 2 carsten.niebuhr@desy.de Zeus Micro Vertex Detektor 38 Par ticle Detectors 2 Charged Coupled Devices (CCD) 200.000 readout channels Advantage: - many detector channels can be readout with few readout channels Disadvantage: - small signal charge ( 2000e) cooling - long readout time (several 1000 transfers) - detector aktive during readout only applicable for low rate experiments e+e- experiments ε e.g. successfully used at SLD am SLD b-tagging at SLD 1996 VXD3: 307 x 106 pixel a 22 x 22 µm2 b-purity carsten.niebuhr@desy.de 39 Par ticle Detectors 2 carsten.niebuhr@desy.de 40 Par ticle Detectors 2
Silicon Pixel Detectors ATLAS Pixel Detector segmentation in both coordinates Matrix readout electronics with similar geometry connection by "Bump Bonding" use soft material like Indium or Gold complex readout architecture true 2D hits extensive use in LHC experiments Flip-Chiechnique carsten.niebuhr@desy.de 41 Particle Detectors 2 carsten.niebuhr@desy.de 42 Particle Detectors 2 Silicon Driftchambers Radiation Damage in Silicon Detectors Radiation hardness is a very important issue in particular at LHC bulk effects surface effects defects depend on particle type and particle energy potential readout-electrode decoupled from sensitive volume relatively small capacitance (low noise) resolution 10µm for 5-10cm drift distance de/dx measurement (STAR heavy-ion) drift velocity must be known very well not radiation hard Relevant quantities: fluence Φ = N A [cm -2 ] dose D = E m [Gy=J/kg] carsten.niebuhr@desy.de 43 Particle Detectors 2 carsten.niebuhr@desy.de 44 Particle Detectors 2
Consequences of Radiation Damage in Silicon Comparison of various Trackdetectors Increase of leakage current Change of depletion-voltage Detector type Positionresol. Deadtime electron. Advantage Problems [µm] [ms] readout Reduction of charge collection efficiency Counter measures: geometrically: develop sensors which can stand higher depletion voltages environment: cooling of sensors ( -10 C) - slows down "reverse annealing" - reduced leakage currents carsten.niebuhr@desy.de 45 Particle Detectors 2 carsten.niebuhr@desy.de 46 Particle Detectors 2