Prim ary I onization Track (Gases)

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2 Prim ary I onization Track (Gases) incoming particle ionization track Minimum- ionizing particles ( Sauli. IEEE+NSS ) ion/e - pairs Helium Argon Xenon DME GAS (STP) CH 4 de/dx (kev /cm ) n (ion pairs/ cm ) Oct 1 e - I + E n Linear Statistical ionization process: Poisson statistics Detection efficiency depends on average num ber < n> of ion pairs 1 e n GAS (STP) Helium Argon thickness 1 mm 45 mm 7 1 mm 91.8 mm 99.3 Higher for slower part icles

3 Free Charge Transport in Gases P( x) P( x) t x 1D Diffusion equation P(x)= (1/ N )dn/ dx dn dx 4Dt exp x 4D t x : x Dt rms N x Oct 1 3 t 1 > t x P( x) t > t 1 x v D 1 3 v Therm al velocities : 8kT 8 m 3 D( ion) D( e ) v D diffusion coefficient, < v> m ean speed m ean free path Maxwell+ Bolt zm ann velocity distribution Sm all ion m obility

4 Driven Charge Transport in Gases P( x) Electric field E = U/ x separates + / - charges 4 Oct 1 t x P( x) E t 1 > t x P( x) t > t 1 x dn N ( x w t ) exp dx 4Dt 4D t e w E drift v elocit y m v m ean collision tim e D kt e : w E m obility Cycle: accelerat ion scat t ering Drift and diffusion depend on field strength and gas pressure p (or ). x w w( E p); D D( E p)

5 I on Mobility GAS ION µ + (cm V -1 s +1 Ar Ar CH 4 CH Ar+CH 4 8+ CH I on m obility = w + / E I ndependent of field, for given gas at p,t= const. 5 Oct 1 Typical ion drift velocit ies (Ar+ CH 4 counters): w + ~ ( ) cm / s slow! E. McDaniel and E. Mason The mobility and diffusion of ions in gases (Wiley 1973)

6 Elect ron Transport Multiple scattering/ acceleration produces effective spectrum P( ) calculate effective and : e P 1 w E d D v P d 3 m v 3 Sim ulat ions v m Oct 1 6 w - ~ 1 3 w + Electron Transport: Frost et al., PR 17(196)161 V. Palladino et al., NIM 18(1975)33 G. Shultz et al., NIM 151(1978)413 S. Biagi, NIM A83(1989)716

7 Stability and Resolution Anisotropic diffusion in electric field (D perp > D par ). Electron capture by electro+negative gases, reduces energy resolution T dependence of drift: w/ w T/ T ~ 1-3 p dependence of drift: w/ w p/ p ~ Oct 1 Increasing E fields charge m ultiplication/ secondary+ ionization loss of resolution and linearity Townsend avalanches

8 Elect ronics: Charge Transport in Capacit ors q + conducting plates 8 q + U t Charges q + moving between parallel conducting plates of a capacitor influence t- dependent negative images q + on each plate. Oct 1 q + R e+ Electronics If connected to circuitry, current of e - would emerge from plate, in total proportionally to charge q +.

9 Signal Generation in I onization Counters Primary ionization: Gases I -3 ev/ip, Si: I 3.6 ev/ip Ge: I 3. ev/ip Capacitance C d x x Energy loss n= n I = n e = / I number of primary ion pairs n at x, t Force: F e = -eu / d = -F I Energy content of capacitor C: Oct 1 9 R C s U U(t) C 1) W t U U t CU U t ) W t n F x t x n F x t x 1) ) e e e I I I neu x I t x e t d w t t t W t ne U t w t w t t CU Cd t

10 Tim e- Dependent Signal Shape U t w t w t t t Cd w t 1 w t 3 Total signal: e & I com ponents Drift velocities (w + >, w - < ) 1 C U(t) Both components measure and depend on position of primary ion pairs Oct 1 C x d x = w - (t e -t ) Use electron component only for fast counting. t t e ~ s t I ~ m s t

11 Frisch Grid I on Cham bers 11 Oct 1 d x x d FG particle cathode Suppress position dependence of signal am plitude by shielding charge-collecting electrode from primary ionization track. I nsert wire m esh (Frisch grid) at position x FG held constant potential U FG. e - produce signal only when inside sensitive anode-fg volum e, ions are not seen. Anode/ FG signals out U t w t t t CdFG not x dependent. FG x-dependence used in drift cham bers.

12 Bragg- Curve Sam pling Count ers Sam pling I on cham ber with divided anodes 1 isobutane 5T Oct 1 E/ x x Sample Bragg energy-loss curve at different points along the particle trajectory improves particle identification.

13 I C Perform ance 13 Oct 1 E ( channels) I Cs have excellent resolution in E, Z, A of charged particles but are slow detectors. Gas I C need very stable HV and gas handling syst em s. Energy resolut ion F nip F I E residual (channels) F<1 Fano factor

14 Solid-State I C 14 Oct 1 i p Capacit ance Si C R. 3.7 n U c n p U(t) U U : pf m m pf m m E F Solids have larger density higher stopping power de/dx more ion pairs, better resolution, sm aller detectors (also more damage, max dose ~ 1 7 particles Sem iconductor n-, p-, i- types Si, Ge, GaAs,.. (for e -,lcp,, HI ) Band structure of solids: - E Conduction e - h + Valence + Bias voltage U creates charge- depleted zone Ionization lifts e - up to conduction band free charge carriers, produce U( t).

15 Particles and Holes in Sem i-conductors 15 Oct 1 C F V e h Conduction Band e - G h + Valence Band : f 1 exp e : f 1 exp h G kt kt Small gaps G (Ge) large thermal currents. Reduce by cooling. G 1 Fermion statistics: 3 m V ne f 3 e V volum e 3 m V n f n n for : f h 3 h e h F C G G C e 1 kt 5m ev G n n e e rm s 1 exp n n e h exp m kt 3 3 G kt 1 F V exp exp G kt!! G kt conduct ivit y at T

16 Sem iconduct or Junct ions and Barriers 16 Oct 1 Si Bloc e - Potential Donor Acceptor ions n p e - h + Similar: Homogeneous n(p)-type Si with reverse bias U also creates carrier-free space d n,p : up to 1mm possible. o + o + + o + o + o + o + + o + o + + o + o + o + o + + o + o + + o + o + o + o + + o o o o o o - - -o -o -o -o - o - o - - -o -o -o - o - o - o - - -o -o -o -o - o - o space charge d o o o o o o Need detector with no free carriers. Si: i-type (intrinsic),n-type, p-type by diffusing Li, e - donor (P, Sb, As), or acceptor ions into Si. Trick: Increase effective gap Junctions diffuse donors and acceptors into Si bloc from different ends. Diffusion at interface e - /h + annihilation space charge Contact Potential and zone deplet ed of free charge carriers Depletion zone can be increased by applying reverse bias pot ent ial 5 n, p n, p d U m k cm, U 5V d 7 m n, p

17 Surface Barrier Det ect ors E F Junction CB Semi conductor Metal VB Different Ferm i energies adjust to on contact. Thin m etal film on Si surface produces space charge, an effective barrier (contact potential) and depleted zone free of carriers. Apply reverse bias to increase depletion depth. Insulation 17 Oct 1 Ground +Bias Front: Au Back: Al evaporated electrodes Insulating Mount depleted dead layer Possible: depletion depth ~ 1 dead layer d d 1 V ~.5V/ Over-bias reduces d d Metal film Silicon wafer Metal case Connector ORTEC HI detector

18 Charge Collect ion Efficiency Heavy ions: E deposit > E app = apparent energy due to charge recom bination, trapping. Light ions E deposit E app Typical charge collection tim es: t~ (1-3)ns Moulton et al. E : E E PhD deposit app b( Z, A) a( Z, A) PhD deposit deposit Fit : E E 1 E 18 Oct 1 5 a( Z).3 1 Z.568 b( Z) 14.5 / Z.85 6 a( A) A.578 b( A) 8.4 / A.381 Affect also collection time lower signal rise time.

19 Position-Sensitive Sem iconductor Detectors Gerber et al., IEEE TNS- 4,18(1977) Double-sided x/y matrix detector, resistive readout. 19 Oct 1 y x Au Q R n- Si R R x ( L x ) Q Q Q Q n x n 1 Lx Lx y Q Q Q Q m 3 4 Ly Q Q Q Q Q E ( L y ) y L y m R ~ cm, 3 U 16V

20 Si-Strip Detectors 5 cm Typically (3-5) thick. Fully depleted, thin dead layer. Annular: 16 bins, 4 Micron Ltd.) Oct 1 circuit board Rectangular with 7 strips

21 Ge ray Detectors Ge detectors for -rays use p-i-n Ge junctions. Because of sm all gap E G, cool to -77 o C (LN ) Ge Cryostate (Canberra) Oct 1 1 Ge cryostate geometries (Canberra)

22 Properties of Ge Detectors: Energy Resolution Superior energy resolution, compared to NaI E E =1keV Oct 1 Size=dependent mall detection efficiencies of Ge detectors 1% solution: bundle in 4 -arrays Gam m asphere, EuroBall, Tessa,

23 Townsend Gas Avalanche Am plificat ion _ Radiation U M Nonlinear Region 3 d IC Region Oct 1 + U ~ kv/ cm I U Amplification M M n n ip 1 n ip i( t) dt ; nip prim ary IP : nm d 1. Townsend coef ficient

24 Avalanche Form at ion Townsend Coefficient Electron-ion pairs through gas ionization Elect r ons in out er shells ar e mor e r eadily removed, ionization energies are smaller for heavier elements. dn n dx x n( x) n e for const n( x) n exp ( x ) dx x

25 Parallel Plate Counters: t-resolution cathode - d~1/ sensitive layer e - anode + 5 R Oct 1 + Charges produced at different positions along the particle track are differently amplified. non-linearity n ip ( E) PPAC ff U ff PPAC PPACs used where time resolution important, U(p,f)f p

26 Sparking and Spark Count ers /p I mpact ionizat ion Pr obabilit y 6 Oct 1 Different cathode materials + Amplification by impact ionization d n e M n d 1 e 1 - d Pr event spar k by r educing for ions: collisions wit h lar ge or ganic molecules quenching d Sparking : e 1 p 1 3 (1 1 ) Torr

27 Avalanche Quenching A. Sharma and F. Sauli, Nucl. Instr. and Meth. A334(1993)4 7 Oct 1 in Argon Reduce and energy of ions by collisions with com plex organic m olecules (CH4, ). Excitation of rotations and vibrations already at low ion energies Organic vapors = self quenching CH 4

28 Effect ive I onizat ion Energies 8 Oct 1 Mean energy per ion pair larger than IP because of excitations Lar ge or ganic molecules have low-lying excited rotational states excit at ion wit hout ionizat ion t hr ough collisions quenching additives

29 Am plificat ion Count ers Single-wire gas counter signal gas C Oct 1 counter gas - U +

30 Proport ional Count er 3 Oct 1 R c counter gas Anode Wire - gas + e - q + R - U + R A R I C signal eu I R I Anode wir e: small r adius R A 5 m or less Volt age U E( r) (3-5) V Field at r from wire U ln( R R ) r C 1 Avalanche R I R A, sever al mean f r ee pat hs needed Pulse height mainly due t o posit ive ions (q + ) A

31 Pulse Shape U event 1 event event 4 t Pulse shape : time t, wire length L q t U ( t) ln(1 ) 4 L t t / CU, mobility w / E dielectric constant drift 31 Oct 1 event 1 event event 4 t long decay t ime of pulse pulse pile up, summar y inf or mat ion U C R dif f er ent iat e elect r onically, RCcir cuit r y in shaping amplif ier, individual inf or mat ion f or each event (= incoming par t icle)

32 Multi-Wire Proportional Counters Magic Gas: Ar( 7 5 % ), isobutane ( 4.5 % ), freon (.5%) HV:kV/cm (Charpak ) I m portant for detection of high-energy part icles, beam profile,.. Equipotential Lines 3 Oct 1 d ac Anode Wires Field at V ( x, y) U ln 4 sin x sinh y ( x, y) (,) C 4 d Capacitance C ; dac s d d s ln( d s) ac s Cathode Wire Planes s s Anode Wires Field strength close to anode wires: V(x,y) 1/ r

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