Lecture 4. Detectors for Ionizing Particles

Transcription

1 Lecture 4 Detectors for Ionizing Particles

2 Introduction Overview of detector systems Sources of radiation Radioactive decay Cosmic Radiation Accelerators Content Interaction of Radiation with Matter General principles Charged particles heavy charged particles electrons Neutral particles Photons Neutrons Neutrinos Definitions Detectors for Ionizing Particles Principles of ionizing detectors Semiconductor detectors Semiconductor basics Sensor concepts

3 Semiconductor detectors Different detector materials Readout electronics Gas detectors Principles Detector concepts Scintillation detectors General characteristics Organic materials Inorganic materials Light output response Content Velocity Determination in Dielectric Media Cerenkov detectors Cerenkov radiation Cerenkov detectors Transition Radiation detectors Phenomenology of Transition Radiation Detection of Transition Radiation Complex Detector Systems Particle Identification with Combined Detector Information Tracking

4 Review of Previous Lecture

5 Absorption of Photons Photoelectric effect: Compton scattering Pair production near nuclei

6 Interaction of Neutrons No electric charge è no Coulomb interaction Only strong force with nuclei in matter High energy neutrons have to come within cm of the nucleus è very penetrating Several different interaction processes: Elastic scattering: Principal mechanism of energy loss in the range of MeV Inelastic scattering: Nucleus is left in an excited state which later decays by radiative emission. Energy of neutron has to be high enough for excitation (typically > 1 MeV) Radiative neutron capture: cross section 1/v è only takes place for slow neutrons, resonance peaks superimposed Other nuclear reaction: caption of neutron + emission of charged particle, typically in the range of ev to kev, cross section 1/v + resonances Fission: most likely at thermal energies High energy hadron shower production: only for very high energy neutrons (> 100 MeV)

7 Neutrino Measuring Techniques Radio chemical method Detection via radioactive reaction products Only sensitve on ν e!! Measurement of the partner lepton Sensitive on ν e and ν µ (+ ν τ ) Momentum of ν has to be sufficient Elastic Scattering Detection of the scattered electron Deuteron breaking Detection of the nucleons

8 Start of Lecture 4 Definitions Semiconductor Detectors

9 Sensitivity is the minimum magnitude of input signal required to produce a specified output signal having a specified signal-to-noise ratio Usually given by: the cross section for ionization reactions in the detector the detector mass the inherent detector noise the protective material surrounding the detector determines the probability that (part of) the energy of the incoming radiation is transformed in the form of ionization signal > noise entrance threshold

10 Energy Resolution Width of the probability distribution function of the measured observable for a given physical value For detectors designed to measure the energy of the incident radiation the energy resolution is the most important quantity The resolution is quantified in terms of the full width at half maximum of the peak: R = Δ FWHM E / E = 2.35 σ(e) / E Two peaks closer together than the FWHM are usually considered not resolvable ΔE includes all type of noise sources: ( ) 2 ( ) 2 ( ) 2 ( ) 2 ΔE = ΔE + ΔE + ΔE +... stat det elect

11 Energy Resolution and Fano Factor The mean number of ionizing events J is given by the mean energy required to produce an ionization w (w > B.E.): J = E / w w depends on the material To calculate the fluctuations one would typically take the Poisson distribution which yields: var = J This implies that the ionization processes are all statistically independent, which is not true U. Fano calculated the variance for large J and found: var = σ 2 = FJ F is the Fano factor describing the deviation of the variance from a Poisson distribution This gives for the resolution: FJ R = 2.35 = J Fw E For F = 1 the variance is the same as the Poisson distribution

12 The Fano Factor Because the Fano factor describes corrections in the statistical fluctuations in the process of ionization it gives the best energy resolution a detector can reach It is material dependent and varies strongly: scintillators 1 gases < 1 semiconductors 0.1 (theoretically) Measuring the Fano factor not easy because all other noise sources have to be reduced è typically an upper limit for the Fano factor is given F is in addition a function of the temperature and, below 1 kev, also of the energy of the incoming particle

13 Detector Response In general the detector response describes the dependence of the expectation value of a measured quantity on the physical quantity Ideally the relation between the physical quantity and the measured quantity is linear (this is not necessary but makes life easier) Due to the limited resolution of the detector the result will always convoluted with the resolution Be careful: the response of a detector may vary with the type of radiation it detects

14 The Response Function Spectrum of pulse heights observed from the detector for a monoenergetic beam Ideal case: delta function and linear behavior for different energies è 1-to-1 correspondence between the measured quantity and the particles physical quantity Typically (much) more complicated: e.g.: electrons on a thick detector: main component: Gaussian distribution some electrons scatter out of detector è low energetic tail bremsstrahlung à photons leave detector è low energetic tail e.g.: photons on the same detector: è next page

15 The Response Function Superposition of photoelectric effect, Compton scattering and pair production Response function for a germanium detector and an organic scintillator detector for 661 kev gamma rays PH( E) = S( E') R( E, E') de' PH: pulse height distribution, R(E,E ) response function, S(E ) incident spectrum, E incident energy

16 Response Time Time between the arrival of the particle and the signal formation Important for dedicated time measurements (e.g. time-of-flight detectors) Must be considered when triggering on events in different detector components

17 Dead Time Finite time required by a detector to process an event, during which no additional signal can be registered Two cases: detector is insensitive à non-extendable/paralyzable dead time detector stays sensitive à extendable or paralyzable dead time (e.g. rate of a Geiger-Müller counter drops at at very high dosis)

18 Dead time Non-extendable dead time: mt = k + mkτ k T m = 1 ( k T ) τ m: true count rate, T: measuring time, k: measured counts, τ: dead time Extendable dead time: P(t): distribution of time intervals between random events with rate m P( t) = mexp( mt) only events arriving later than τ are recorded P( t > τ ) = m exp( mt) dt = exp( mτ ) τ k = mt exp( mτ )

19 Measuring dead time Two-source technique (for the non-extended case): f n n 1 1/ 2 + n R = 1 R 2 1/ 2 1/ 2τ R = 1 R 12 12τ τ = Large errors (5-10%) Experimentally difficult 12 R 1 R R R Better: use of two oscillators: f1 + = 1/ T Non-extendable dead time f 2 2 f1 f2τ for for < τ < T R1 R2 = + τ 1 Rτ 1 R τ [ R R / 2 T / 2 < τ < T ( R12 R R R R f f = 0 1 )( R + f R 2 )] 1/ 2 Extendable dead time 2 f1 f2τ for for 0 < τ < T T < τ with T: period of faster osc. τ = t m R1 + R2 2 R R 1 2 R 12 Equal for f < (2τ) -1

20 Two definitions: absolute efficiency E tot intrinsic efficiency E int Detector Efficiency E tot Example: cylindrical detector with a point source at a distance d on the axis of the detector P( θ) dω = dω / 4π x dω de tot = 1 exp λ 4π If x does not vary too much : E tot E int E geom = efficiency acceptance events registered events emitted by source events registered E int = events impinging on detector

21 Semiconductor Detectors

22 Insulator Semiconductor - Conductor 10-3 to 10 8 Ωcm

23 IV IV-IV III-V II-VI IV-VI Si SiC AlAs CdS PbS Ge AlSb CdSe PbTe yellow=most common Semiconductors Period II III IV V VI 2 Boron Carbon Nitrogen 3 Magnesium Aluminium Silicon Phosphorus Sulfur 4 Zinc Gallium Germanium Arsenic Selenium 5 Cadmium Indium Tin Antimony Tellurium 6 Mercury Lead BN GaAs GaP GaSb InAs InP InSb CdTe ZnS ZnSe ZnTe CdZnTe HgCdTe

24 Semiconductor Detectors A semiconductor detector is a solid state ionization chamber Gas Semiconductor Z E(e/ion) creation ev ev specific density 0.17 (He) 0.9 (Ne) g l (Si) 5.3 (Ge) g cm -3 pairs per length 100 e/ions per cm 100 e/h per µm e mobility O(1000 cm 2 /Vs) cm 2 /Vs ion(hole) mobility 1 2 cm 2 /Vs cm 2 /Vs

25 Semiconductors suited for Detectors

26 Lattices face centred cubic (fcc): diamond lattice (Si,Ge): cubic face centered lattice all atoms identical zinc blende lattice (GaAs): cubic face centered lattice different Atoms (Ga, As)

27 Energy bands I energy at r 0 E tot à min Degeneration of energy levels for close distances valence level e.g. p-level e.g. s-level r = distance between atoms

28 Energy bands II semi conductors metals band gap

29 Energy bands III Insulator Semi-conductor Conductor conduction band (empty) valence band (filled) E g ~10eV conduction band (empty) valence band (filled) E g ~1eV conduction band valence band type 1 type 2 conduction band part. filled Fermi-Dirac Statistics: room temperature 1/40 ev

30 Auger effect Auger effect: an electron from a higher shell to a vacant electronic state and ejecting an electron from the same higher shell. è Only levels near the edge are important

31 Brillouin zone Within a lattice the free electrons see the potential of the atoms For electrons all k-values are allowed but when the k meets the Bragg condition an interaction with the lattice happens Trick: create Brillouin zone: reciprocal lattice in k-space All k-vectors sitting at the boundary of the Brillouin zone fulfill Bragg condition

32 Effective mass Brillouin zones Simplified picture The electron wave function is reflected at the Brillouin boundaries è stationary wave with two solutions of the Schrödinger equation è forbidden areas Dispersion relation of a free electron gas 2 is not valid anymore E =! 2m k 2 Transition from true mass of electron to effective mass: 1 m * = 1 2 µν! dk µ dkν m* curvature of E(k) à m* < 0 possible d 2 E Tensor Equation of motion: * F = m v! g

33 Effective mass m e* /m e m h* /m e Si Ge GaAs

34 Direct and indirect semiconductors indirect e.g. Si, Ge direct e.g. GaAs to produce e/h must change E AND k narow minimum è m * small (0.07) several k-values for the same energy value possible à bands overlap in k-space k wide minimum è m * large (0.20) note: for the conduction mechanism only levels near the edges of the bands are important

35 Intrinsic conductivity at T > 0 a lattice bond can break valence electron becomes free leaves a hole behind this is a VB à CB transition the e - can move freely in CB the hole at position A is filled by an e - leaving another hole hole has effectively moved from A à B hole moves freely as well e - and hole move freely through the lattice as particles with different effective mass.

36 Density of states I

37 Density of states II

38 Density of states III

39 Carrier Concentration The number of free electrons can be calculated by the density of states in the conduction band Z(E) with the probability of their occupation given by the Fermi-Dirac function F(E): n = Z ( E ) F ( E )de Ec 0 with: F (E) = 1 1+ e ( E E F ) / kt e ( E E F ) / kt concentration of free electrons: 3/ 2 2π mn kt ( E E ) / kt n = 2 e C F 2!!h#!! " $ NC concentration of free holes: 3/ 2 2π m p kt ( EF EV ) / kt e p = 2 2 h!!#!! " $ NV with: EF the Fermi level mn (mp) the effective mass of the electrons and holes NC (NV) the effective density of states 2m * Z ( E )de = 4π 2 h 3 2 E de

40 Fermi level The product of electron and hole concentration is independent of the Fermi level: np = n 2 E i = NCNVe g / kt with E g = E C - E V This leads to intrinsic carrier concentration for silicon at 300 K to be: n i 10 3 = cm The intrinsic Fermi level is: E i = E 2 g 3kT + 4 m ln m p n Doping with donor or acceptor atoms changes the Fermi level: N N D E = + F Ei kt ln A E = F Ei kt ln ni ni

41 Doping of Semiconductors Electron Configuration for Si: K 2 L 8 M by bonding 8 group E g 1 ev n-type (donor) P, As, Sb 5 electrons in the M-shell 1 electron with binding energy mev p-type (acceptor) B, Al, Ga 3 electrons in the M-shell 1 electron missing

42 Doping n i = 1.45 x cm -3 typically n - = cm -3 n = cm -3 n + = cm -3

43 Donor and acceptor Levels

44 Donor and acceptor Levels

45 Donor and acceptor Levels

46 Ionisation energies for impurities states in the band gap E C Si ΔE E V E C GaAs ΔE E V

47 Drift of e and h in semiconductors drift velocity as a function of electric field strength saturation at ~10 7 cm/s v drift remember v = µ(e) E always! E(V/cm) typical Si - detector 100 V / 300 µm

48 Mobility as a function of temperature µ n (cm 2 /Vs) T 3/2 T -3/2 T(K) scattering at impurities scattering on lattice higher temp more lattice vibrations lower mobility

49 Try to make a detector Take a Si crystal of mm 3 volume resistivity Ge 0.49 Ωm at 300K Si some 100 Ωm due to impurities ~ free carriers A minimum ionizing particle would produce ~ e-h pairs

50 Get rid of free carriers

51 Get rid of free carriers Have to reduce the number of free carriers. Freeze out: Mobility, µ, conductivity, σ, majority [donors (e) acceptors (holes)] and minority [donors (holes) acceptors (e)] carrier concentration as function of temperature. n i is the intrinsic carrier density. or depletion

52 pn - junction p n

53 pn junction as particle detector p + n - thin, highly doped p + (~10 19 cm -3 ) layer on lightly doped n - (~10 12 cm -3 ) substrate Space charge region N x = A de dx p N D x 1 = ρ( x) ε n neutrality cond. Maxwell Electric field!! E( x) en ε = + en ε A D ( x + x ( x x p n ) ) for for x p < x < 0 0 < x < x n Potential 2 2 ( N x N x ) e V bi = A p + 2 ε D n

54 pn junction under reverse bias (V ext ) 1. V bi! V bi + V ext 2. no thermal equilibrium => E F (n) E F (p) no bias Hole current Electron current p n forward bias Depletion region Depl. I p n reverse bias Depl. I

55 pn junction as particle detector Depletion zone grows from the junction into the lower doped bulk

56 Rules for junctions The chemical potential µ = ( F/ N) U,T, where F = free energy, U=inner energy, T = temperature, N = particle number, is a measure of the particle concentration in an ensemble. When µ=const. everywhere in the device there is no net diffusion, i.e. thermal equilibrium is established 1) Temperature and Chemical Potential (µ=e F ) are uniform over the device after equilibrium is established 2) Far away from the junction the bulk properties must be recovered (i.e. bands bend in junction regions only) 3) For homojunctions (e.g. pn) only: In the junction region the bands are simply connected without discontinuities

57 Metal-semiconductor junction metal semiconductor note work function Φ M depends on type of metal Φ S depends on doping χ S = electron affinity = E vac E C is independent of doping Schottky Contact =potential barrier i.e eφ S < eφ m

58 Metal-semiconductor junction Ohmic Contact =very thin potential barrier when E F (s.c.) E C (s.c.) N D (cm -3 ) tunneling R C (Ωcm 2 ) achieved by high doping (>10 19 cm -3 )

59 MOS structure - I

60 MOS structure II

61 End of the lecture