2. Oct 2001 W. Udo Schröder 2 Primary Ionization Track (Gases) incoming particle ionization track  ion/e - pairs Argon DME n (ion pairs/ cm ) 25 55 dE/dx (keV/cm) GAS (STP) 2.4 3.9 Xenon 6.7 44 CH 4 1.5 16 Helium 0.32 6 Minimum-ionizing particles (Sauli. IEEE+NSS 2002) Statistical ionization process: Poisson statistics Detection efficiency  depends on average number of ion pairs thickness  Argon GAS (STP) 1mm91.8 2mm 99.3 Helium 1mm45 2mm 70 Higher  for slower particles e-e- I+I+ E  n Linear

3. Oct 2001 W. Udo Schröder 3 Free Charge Transport in Gases x P(x) t0t0 x t 1 >t 0 x P(x) t 2 >t 1 1D Diffusion equation  P(x)=(1/N 0 )dN/dx D diffusion coefficient, mean speed   mean free path Thermal velocities : Maxwell+Boltzmann velocity distribution Small ion mobility

4. Oct 2001 W. Udo Schröder 4 Driven Charge Transport in Gases x P(x) t0t0 t 1 >t 0 x P(x) t 2 >t 1 Electric field E =  U/  x separates +/- charges x P(x) E x Cycle: acceleration – scattering Drift and diffusion depend on field strength and gas pressure p (or ).

5. Oct 2001 W. Udo Schröder 5 Ion Mobility GAS ION µ + (cm 2 V -1 s +1 ) @STP Ar Ar + 1.51 CH 4 CH 4 + 2.26 Ar+CH 4 80+20 CH 4 + 1.61 Ion mobility   = w + /E Independent of field, for given gas at p,T=const. Typical ion drift velocities (Ar+CH 4 counters): w + ~ (10 -2 – 10 -5 ) cm/s slow! E. McDaniel and E. Mason The mobility and diffusion of ions in gases (Wiley 1973)

6. Oct 2001 W. Udo Schröder 6 Electron Transport Multiple scattering/acceleration produces effective spectrum P()  calculate effective and  : Simulations http://consult.cern.ch/writeup/garfield/examples/gas/trans2000.html#elec Electron Transport: Frost et al., PR 127(1962)1621 V. Palladino et al., NIM 128(1975)323 G. Shultz et al., NIM 151(1978)413 S. Biagi, NIM A283(1989)716 w - ~ 10 3 w +

7. Oct 2001 W. Udo Schröder 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 ~ 10 -3 p dependence of drift: w/w  p/p ~ 10 -3 -10 -2 Increasing E fields  charge multiplication/secondary+ ionization  loss of resolution and linearity  Townsend avalanches

8. Oct 2001 W. Udo Schröder 8 Electronics: Charge Transport in Capacitors Charges q + moving between parallel conducting plates of a capacitor influence t- dependent negative images q + on each plate. t U If connected to circuitry, current of e - would emerge from plate, in total proportionally to charge q +. q+q+ q+q+ q+q+ conducting plates Electronics R e+e+

9. Oct 2001 W. Udo Schröder 9 Signal Generation in Ionization Counters Primary ionization: Gases I  20-30 eV/IP, Si: I  3.6 eV/IP Ge: I  3.0 eV/IP Energy loss  n= n I =n e = /I number of primary ion pairs n at x 0, t 0 Force: F e = -eU 0 /d = -F I Energy content of capacitor C: Capacitance C + - U0U0  U(t) 0 x0x0 x d R CsCs

10. Oct 2001 W. Udo Schröder 10 Time-Dependent Signal Shape t 0 t e ~s t I ~ms t U(t) Drift velocities (w + >0, w - <0) Total signal: e & I components Both components measure  and depend on position of primary ion pairs x 0 = w - (t e -t 0 ) Use electron component only for fast counting.

11. Oct 2001 W. Udo Schröder 11 Frisch Grid Ion Chambers 0 d FG x0x0 d x Anode/FG signals out cathode Suppress position dependence of signal amplitude by shielding charge-collecting electrode from primary ionization track. Insert wire mesh (Frisch grid) at position x FG held constant potential U FG. e - produce signal only when inside sensitive anode-FG volume, ions are not “seen”.  not x dependent. x-dependence used in “drift chambers”. particle

12. Oct 2001 W. Udo Schröder 12 isobutane 50T Bragg-Curve Sampling Counters Sampling Ion chamber with divided anodes E/x x Sample Bragg energy-loss curve at different points along the particle trajectory improves particle identification.

13. Oct 2001 W. Udo Schröder 13 IC Performance E residual (channels) E (channels) ICs have excellent resolution in E, Z, A of charged particles but are slow detectors. Gas IC need very stable HV and gas handling systems. Energy resolution F<1 Fano factor

14. Oct 2001 W. Udo Schröder 14 Solid-State IC Solids have larger density  higher stopping power dE/dx  more ion pairs, better resolution, smaller detectors (also more damage, max dose ~ 10 7 particles i Semiconductor n-, p-, i- types Si, Ge, GaAs,.. (for e -,lcp, , HI) Band structure of solids: E EFEF Valence Conduction + - e-e- h+h+ Ionization lifts e - up to conduction band  free charge carriers, produce U(t). Bias voltage U 0 creates charge-depleted zone U0U0 + + + - n p U(t) c R

15. Oct 2001 W. Udo Schröder 15 Particles and Holes in Semi-Conductors Fermion statistics: 0  FF Valence Band Conduction Band e-e- h+h+ GG VV CC Small gaps  G (Ge)  large thermal currents. Reduce by cooling.

16. Oct 2001 W. Udo Schröder 16 Semiconductor Junctions and Barriers 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 depleted of free charge carriers  Depletion zone can be increased by applying “reverse bias” potential Similar: Homogeneous n(p)-type Si with reverse bias U 0 also creates carrier-free space d n,p : up to 1mm possible. + + + + - - - - o o o n p e-e- h+h+ Donor Acceptor ions space charge Si Bloc e - Potential d

17. Oct 2001 W. Udo Schröder 17 Surface Barrier Detectors Metal film Silicon wafer Metal case Insulation Connector EFEF Junction Metal CB Semi conductor VB Different Fermi energies adjust to on contact. Thin metal 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. Ground +Bias Front: Au Back: Al evaporated electrodes Insulating Mount depleted dead layer Possible: depletion depth ~ 100 dead layer d d  1 V ~ 0.5V/ Over-bias reduces d d ORTEC HI detector

18. Oct 2001 W. Udo Schröder 18 Charge Collection Efficiency Heavy ions: E deposit > E app = apparent energy due to charge recombination, trapping. Light ions E deposit  E app Typical charge collection times: t~(10-30)ns Moulton et al. Affect also collection time  lower signal rise time.

19. Oct 2001 W. Udo Schröder 19 Ge ray Detectors Ge detectors for -rays use p-i-n Ge junctions. Because of small gap E G, cool to -77 o C (LN 2 ) Ge Cryostate (Canberra) Ge cryostate geometries (Canberra)

20. Oct 2001 W. Udo Schröder 20 Properties of Ge Detectors: Energy Resolution Size=dependent mall detection efficiencies of Ge detectors  10%  solution: bundle in 4- arrays GammaSphere, EuroBall, Tessa,… Superior energy resolution, compared to NaI E  ~ 0.5keV @ E  =100keV

21. Oct 2001 W. Udo Schröder 21 Townsend Gas Amplification Radiation U0U0 I d U0U0 M IC Region Non- linear Region Amplification M

22. Avalanche Formation Townsend Coefficient Electron-ion pairs through gas ionization Electrons in outer shells are more readily removed from atom. Ionization energies are smaller for heavier elements.

23. Oct 2001 W. Udo Schröder 23 Sparking and Spark Counters  /p  Impact ionization Probability  Prevent spark by reducing  for ions: collisions with large organic molecules  quenching d - +

24. Oct 2001 W. Udo Schröder 24 Avalanche Quenching in Argon A. Sharma and F. Sauli, Nucl. Instr. and Meth. A334(1993)420 Reduce and energy of ions by collisions with complex organic molecules (CH4, …). Excitation of rotations and vibrations already at low ion energies

25. Oct 2001 W. Udo Schröder 25 Effective Ionization Energies Mean energy per ion pair larger than IP because of excitations Large organic molecules have low-lying excited rotational states  excitation without ionization through collisions  quenching additives

26. Oct 2001 W. Udo Schröder 26 Amplification Counters Single-wire gas counter U0U0 C - - + + counter gas gas signal

27. Oct 2001 W. Udo Schröder 27 Proportional Counter Anode wire: small radius R A  50  m or less Voltage U 0  (300-500) V counter gas e - q + RARA RIRI eU I R I Anode Wire Avalanche R I  R A, several mean free paths needed Pulse height mainly due to positive ions (q + ) U0U0 C - - + + gas signal R RcRc

28. Oct 2001 W. Udo Schröder 28 Pulse Shape t t UU UU long decay time of pulse  pulse pile up, summary information differentiate electronically, RC- circuitry in shaping amplifier, individual information for each event (= incoming particle) R C event 1 event 2 event 4 event 1 event 2 event 4