Radiation Measurement Systems Semiconductor Detectors Ho Kyung Kim Pusan National University Semiconductors Differences btwn semiconductor & gas as a material for radiation detectors Higher (1,000 ) Free charge carriers (electron-hole pairs) inside Leakage current origin of detector noise Cooling, blocking contact, wide bandgap materials Differences btwn semiconductor & all other radiation detector materials Low W-value Low statistical noise N = E W σ N = FN 1 W Detector Gas Scintillator Semiconductor W-value (ev) 30 40 ~100 2.96 (Ge @ 77 K) 3.76 (Si @ 77 K) 3.62 (Si @ 300 K) Best for radiation spectroscopy 2 1
How to make Si wafers 3 Band structure for electron energies 4 2
Charge carriers Thermal excitation 5 Intrinsic semiconductors n = concentration of electrons in conduction band p = concentration of holes in valence band For intrinsic materials: 1.5 10 10 cm -3 2.4 10 13 cm -3 n i = p i Ge 2.4 10 13 cm -3 < 10-5 cm -3 6 3
Donor Donor impurity (e.g., phosphor) occupying a substitutional site in a Si crystal & the corresponding donor levels created in the Si bandgap 7 Because of small energy gap between donor sites and conduction band, nearly all donor electrons are thermally elevated to conduction band 8 4
n-type semiconductors Add donor impurities: N D n i Then, n N D To maintain equilibrium: n p = κ(= n i p i ) As a consequence: n n i electrons become majority carriers p p i holes become minority carriers 9 Acceptor Acceptor impurity (e.g., boron) occupying a substitutional site in a Si crystal & the corresponding acceptor levels created in the Si bandgap 10 5
Because of small energy difference between acceptor levels and valence band, nearly all are filled leaving holes in valence band 11 p-type semiconductors Add donor impurities: N A p i Then, p N A To maintain equilibrium: n p = κ(= n i p i ) As a consequence: p p i holes become majority carriers n n i electrons become minority carriers 12 6
Compensated semiconductors N D = N D (= N Li ) n = n i & p = p i Can be produced thru lithium ion drifting into p-type semiconductors Drifting temp. = ~40 C, time = ~days or weeks Drifting is easier in Ge (10 15 mm in Ge, 5 10 mm in Si) Ge(Li) should be always kept at low temp. Si(Li) can be stored at room temp. Can be produced by neutron doping 1 28 0 n + Si 29 P + e 14 15 1 0 13 Charge-carrier concentration Heavily-doped semiconductors High electrical conductivity Often denoted by n + or p + 14 7
Charge-carrier migration under E-field At low to moderate E-field v e = μ e ε v h = μ h ε Mobility ( ) values in Si (cm 2 /V s) 77 K 300 K Electrons 21,000 1,350 Holes 11,000 480 15 Drift velocities 16 8
Trapping & recombination Deep impurities Can trap carriers and effectively remove them from collected charges May promote recombination with carriers of opposite sign Measure of purity Carrier lifetime Trapping length 17 Principle of semiconductor detectors Let s attempt to make semiconductor ionization chamber by pure Si A = = 5 10 4 -cm 18 9
Leakage vs. signal current Leakage (dark) current (DC) I leak = A V ρ d = 1 cm2 500 V 5 10 4 Ω cm 0.1 cm = 0.1 A Signal current (pulse) For a collection of 10 5 e-h pairs (300 kev) w/i 10 ns I sig = Q = 105 1.6 10 19 C = 10 6 A t C 10 8 s 19 Signal-to-noise ratio (SNR) Signal in unit of e-h pairs 10 5 e-h pairs collected over 10-8 s Number of leakage current electrons collected over the same time n leak = I leak t C = 0.1 A 10 8 s = 6 e 1.6 10 19 C 109 electrons It's fluctuation, σ leak = n leak = 8 10 4 electrons SNR, S N = n sig σ leak = 105 8 10 4 1 To achieve SNR = 10 3, need to reduce leakage by 10 6! 20 10
Sources of leakage current Leakage current (I = V/R) injected from contacts e.g., I leak = A V = 1 cm2 500 V = 0.1 A ρ d 5 10 4 Ω cm 0.1 cm Can be avoided by using blocking contacts Thermally-generated charge carriers Can be reduced by cooling or wider bandgap materials Equilibrium levels kept low by rapid sweep-out (n= ) 21 Thermally generated carriers Let n(t) be the free carrier concentration at time t and if loss of carriers are due to extraction & recombination; dn(t) n t G T k n t p t dt τ n t = G T τ eff At equilibrium, n eq = τ eff G(T) I leak = q G(T) This thermal generation current is much smaller than the injection current without blocking contact 22 11
Thermally generated carriers in the depletion region In the region between blocking contacts, the electric field causes rapid collection of charge carriers in typically ~10 9 to 10 8 s Carriers are regenerated thermally but much more slowly Time to thermal equilibrium may be ~10 4 to 10 3 s The equilibrium concentration of carriers therefore is drastically lowered roughly by the ratio between these characteristic times The region becomes depleted in charge carriers, and leakage current is suppressed by the similar ratio 23 Electrical contacts Blocking contact prevents leakage across the bulk 24 12
How to make blocking contacts Need low leakage current, but also need high bias for fast collection of e-h pairs Reverse-biased diode (blocking contact) Schottky junction diode High work-function metal (e.g., Pt, Pb) + semiconductor (n-layer) Poor blocking (not used) PN junction diode p-doped layer + n-doped layer 25 Doping of n-type impurities into the p-type semiconductor Space charge Electric potential Electric field 26 13
Depletion region Region of no mobile charge carriers Two regions of ionized dopants (N D + & N A ) Thickness: Inversely proportional to the square root of doping density Proportional to the square root of the applied reverse bias voltage Non-zero E-field within it Increase with the reverse bias Only sensitive region for radiation detection 27 Abrupt junction model Note the idealized space-charge distribution Charge balance: N D a = N A b ρ x = en D ( a < x 0) en D (0 < x 0) Note that Poisson s eq. to obtain the potential φ: 2 φ = ρ ε d2 φ = ρ(x) (1-D form) dx 2 ε Electric field ε = φ ε x = dφ dx 28 14
= en D ε dx 2 d2 φ + en D ε ( a < x 0) (0 < x 0) First integration w/ the boundary conditions: dφ( a) dx = dφ(b) = 0 dx dφ = en D (x + a) ( a < x 0) ε dx + en D (x b) (0 < x 0) ε 29 Second integration w/ the boundary conditions: φ a = V & φ b = 0 φ x = en D 2ε + en D ε x + a 2 + V ( a < x 0) x b 2 (0 < x 0) 30 15
Boundary at x = 0: V en Da 2 Charge balance: N D a = N A b 2ε = en Db 2 2ε Then, the depletion width: d = a + b = 2ε e N A +N D N A N D V Assuming that N D N A b a then we have d b d 2ε en A V V = V b + V c V b V b bias voltage V c = kt e ln N AN D n i 2 built-in potential 31 Summary Depletion width (N = lower dopant concentration) d 2εV b en Full depletion bias voltage V d enx2 2ε Capacitance with an area A C = ε A εen A d 2V b Max. E-field ε max 2V b 2eNV b d ε 32 16
How to obtain large active-area volume detector? Semiconductor ion chamber Impractical due to large leakage current Blocking contact is required Simple junction diode (e.g., p-n, Schottky) Small natural depletion width (at zero bias) High reverse bias is required Large active volume (e.g., p-i-n structure) Ultra refined material (n i ~ 10 9 cm -3 ) Compensated material 33 Producing intrinsic material Extreme refining Reduce absolute impurity levels to less than 10 10 cm -3 Possible only in Ge (not in Si) Compensation Balance concentrations of donors & acceptors Carried out by drifting lithium ions in either Ge or Si 34 17
Types of semiconductor detectors Junction, surface barrier & ion-implanted detectors Thin Si detector (partially or fully depleted) Charged particle spectroscopy High purity germanium detectors (HPGe) Fully depleted thick detectors Gamma-ray spectroscopy Lithium-drifted silicon detectors [Si(Li)] Fully depleted thick detectors X-ray spectroscopy 35 General properties of semiconductor detectors General properties Similar to gas-filled ionization chamber Direct ionization along the radiation path Electron & hole collection by E-field btwn electrodes No multiplication of charge carriers # of e-h pairs produced = E W 36 18
Signal process Generation of charge carriers: N = E W Drift of charge carriers: v j = μ j ε Detector current: J = env e + qpv p Incomplete charge collection: Q C = η C Q 0 Output signal from the charge-sensitive preamplifier: V p = Q C C f Output signal from the shaping amplifier: V 0 J V p V 0 37 Factors affecting pulse rise time V p Charge-carrier transit time t = d v drift Preamplifier response time t Plasma time HCP s produce dense plasma state of e-h pairs 1 5 ns dispersion time (ambipolar diffusion) 38 19
Pulse-height loss Ideally, the signal pulse-height after the shaping time is V 0 = G Q 0 C = G e E WC In reality: V = G t V p t = V 0 V Causes of pulse-height defect (loss) Entrance window or dead layer Recombination & trapping Ballistic deficit Energy loss thru nuclear collision 39 Entrance window or dead layer E loss in the dead layer t: E 0 = de 0 dx t E loss for an angle of incidence θ E(θ) = E 0 cos θ Difference btwn the measured pulse heights E = E 0 E 0 E 0 E θ = E 0 1 cos θ 1 Plot E as a function 1 cos θ 1, which should be a straight line whose slope = E 0 Then, t = E 0 de 0 dx using tabular data for de 0 dx 40 20
Pulse-height saturation Loss due to recombination & trapping Variation w/ V b V 0 Depletion width d V b Recombination & trapping Higher E-field will increase drift velocity so that it will lower recombination & trapping Peak E-field dependence on V b» Partially depleted detectors ε = V b d V b» Fully depleted detectors ε = V b V x b V b 41 Columnar recombination For HCP s Plasam column is made along the track of HCP s Thanks to no E-field inside of plasma, e-h pairs will recombine more Important in fission fragment measurement Tilted biasing of the detector w/ an angle of incidence may reduce some recombination Si surface-barrier detector HCP Si 42 21
Ballistic deficit Preamplifier integration time is very long >> carrier transit time For spectroscopy, pulse shape is determined by the shaping amplifier If the pulse shaping time < carrier transit time, the ballistic deficit occurs I d V p τ p V 0 Ballistic deficit τ t c t t c t τ t 43 Detector noise sources FWHM of peak: W T 2 = W D 2 + W E 2 Statistical noise W D due to the statistics of e-h pair generation Electronic noise (system noise) W E Amplifier noise Detector noise sources» Bulk leakage current» Surface leakage current» Trapping & detraping» Series (contact) resistance (Johnson) noise» Incomplete charge collection 44 22
Thin silicon detectors Diffused junction detectors 45 Surface barrier detectors Au onto n-type Si produces thin Schottky barrier 46 23
Fully depleted SBD 47 Ion implanted detectors Mono-energetic ions have well-defined range Can closely control thickness & concentration profile of implanted layer 48 24
Field and contacts 49 Charged particle spectroscopy w/ Si detectors Need the depletion width greater than the ptl range Simple peak response function Si detectors are nearly always chosen operated at room temp. Theoretical limits in energy resolution R lim = 2.35 F N = 2.35 Fw E = 0.06 % for -ptl s from 241 Am (5.486 MeV) W lim = 2.35 FEw = 2.35 (0.11) (5.486 MeV) (3.62 ev) = 3.5 kev More conventional expression for Si detectors In commercially available small (ion-implanted) Si detectors, however, the energy resolution tends to be no better than about 10 kev (at this -ptl energy) The discrepancy may be due to fluctuations in the ptl energy loss due to nuclear recoils, charge loss in surface dead layers, etc. 50 25
Si surface-barrier detector 51 Particle identifier telescope (PIT) t Bethe s formula: de = C mz 2 dx 1 ln C E 2 E E C 1 mz 2 E = de dx E m t for t ptl range Multiplier spectrum (or distribution) (p = E E) For protons: mz 2 = 1 For alphas: mz 2 = 16 E E 52 26
High purity germanium detectors Start w/ ultra-pure Ge (~10 10 cm -3 p- or n-type impurity) Fabricate n + & p + contacts on opposite surfaces Apply reverse bias to the p-n + or n-p + junction 53 Planar vs. coaxial configurations wraparound electrode X or rays 54 27
E-fields in two configurations Ge(Li) w/ the same size 55 Cryostat & dewar Vacuum cryostat Ge crystal Cold finger 56 28
Pulse shape of HPGe Larger distance leads to longer charge collection time ~100 ns for a detector w/ a thickness of 1 cm operated at E = ~10 5 V/m (v drift = 10 5 m/s) Different interaction positions lead to variable pulse shapes Affect: Accuracy of timing measurements Mim. electronic shaping time needed for good energy resolution 57 Assumption for the pulse shape For each pulse, e-h pairs are created at a single point Negligible trapping & detrapping Full E-field exists everywhere w/i intrinsic region Both electrons & holes reach the saturated drift velocity 58 29
Pulse shape from the planar HPGe Shape of the leading edge of the output pulse Q(t) for various interaction points Initial slope of all pulses is the same, corresponding to the period when both electrons & holes are drifting 59 Pulse shape from the coaxial HPGe 60 30
Energy resolution W T 2 = W D 2 + W X 2 + W E 2 W D 2 = 2.35 2 FEw: inherent statistical fluctuation in # of charge carriers W D = 2.35 FEw = 2.35 (0.08) (1.333 MeV) (2.96 ev) = 1.32 kev for 60 Co Best W T of ~1.7 kev w/ small coaxial Ge detectors W X 2 : due to incomplete charge collection Assuming that recombination & trapping disappear (W D = 0) at infinitely strong E-field W E 2 : due to all electronic components Can be directly measured by connecting pulse generator to the preamplifier test pulse input The extrapolated values on the ordinate (or intercept) indicate W D W D 61 Radiation damage Damage due to gamma rays (fast electrons) is normally not significant Damage due to fast neutrons (recoiled nuclei) creates traps for holes Begin to deteriorate energy resolution at fluence levels above 10 9 n/cm 2 Long-term degradation For HPGe detectors, the accumulated damage can be annealed away by temporarily heating the detector 62 31
Gamma-ray spectroscopy Germanium detectors Modest detection efficiency (Z = 32) Excellent energy resolution NaI(Tl) scintillation detectors Good detection efficiency High-Z (53) & Large sizes Poor energy resolution 63 Gamma-ray spectra from HPGe compared w/ NaI(Tl) Much sharper peaks More prominent x-ray escape peaks (at low E ) More prominent single & double escape peaks (at high E ) Lower photofraction Smaller photopeak area 64 32
Spectrum measured w/ a p-type HPGe for 60 Co 1 Characteristic x rays from Pb shield K 1 = K 1 L 3 = 88 13.04 = 74.9 kev K 2 = K 1 L 2 = 88 15.2 = 72.8 kev K 1 = K 1 M 3 = 88 3.066 = 84.9 kev L 1 = L 3 M 5 = 13.04 2.484 = 10.6 kev 2 Backscatter around ~250 kev 3 Due to 1332 kev; why so small & why not for 1173 kev? 4 Annihilation radiation from Pb shield 5 Compton edges 6 Full-energy peaks (or photopeaks) 7 1460 kev from the background 8 Shoulder from the summing of two 1173 kev thru pile-up 9 Sum peaks 10 2614 kev from 228 Th in the background 1 2 3 4 3 5 6 7 8 9 9 10 9 65 Photofraction Ratio of the area under the photopeak to that under the entire response function A measure of the prob. that a gamma ray that undergoes interaction of any kind within the detector ultimately deposits its full energy C P FWHM Peak-to-Compton ratio Ratio of the count in the highest photopeak channel to the count in a typical channel of the Compton continuum associated w/ that peak A measure of the combined effects of detector energy resolution & photofraction Inversely proportional to the FWHM for detectors w/ equal photofraction Typ. 50 75 from coaxial Ge detectors for 1332 kev from 60 Co peak area P FWHM photofraction = Compton area C peak to Compton ratio = P C photofraction FWHM 66 33
Methods for continuum reduction Anticoincidence Compton rejection 60 Co Continuum suppressed 67 Sum-coincidence mode Ge(Li) 68 34
Pair spectrometer Ge(Li) + two NaI(Tl) 69 Calibration curve Sources of non-linearity Charge trapping Recombination 70 35
Detection efficiency Relative efficiency Commonly quoted by vendors Absolute peak efficiency normalized by that of a 3 3 NaI(Tl) scintillator at 1.33 MeV gamma-ray energy Typ. 20 70% Available < 150% Caused by the attenuation due to different contact thicknesses 71 Lithium-drifted detectors Ge(Li) Used since early 1960 s for gamma-ray spectroscopy Now largely replaced by HPGe Must be cooled continuously to prevent lithium redistribution Not popular anymore Si(Li) Low-Z (14) Si restricts applications to electron & x-ray spectroscopy Normally cooled continuously Planar configuration Not needed large volume for electrons or x rays 72 36
Dopant compensation To achieve the intrinsic or compensated region Bulk compensation of the material is impractical Use instead the ion-drifting technique in which a residual acceptor impurity is exactly matched by Li donor atoms 73 Lithium-drifted p-i-n junction configuration 74 37
Li-drifted Si detector, Si(Li) X-ray spectroscopy 75 Escape peak to full-energy peak ratio Decreases w/ increasing incident photon E because of deeper penetration of incident radiation 76 38
Energy resolution W T 2 = W D 2 + W X 2 + W E 2 W D = 2.35 FEw = 2.35 (0.11) (5.9 KeV) (3.76 ev) = 116 ev for 55 Fe Typ. W T = 116 ev for commercially available small-area Si(Li) detectors 77 Photopeak efficiency 78 39
Electron spectroscopy Low-Z (14) Mim. backscattering Little bremsstrahlung Need an intrinsic thickness greater than the range of highest energy electrons to be measured for max. full energy absorption 79 Other semiconductor detectors General requirements Large bandgap To allow room-temp. operation But, may bring a high W-value High Z-value To permit applications to gamma-ray spectroscopy High electron/hole mobility & lifetime For good energy resolution 80 40
81 82 41
CdZnTe or CZT Made by high-pressure vertical Bridgman method Cd 1-x Zn x Te where x = 0.04 0.2 Bandgap energy = 1.53 1.64 ev e = 1350 cm 2 /V s h = 120 cm 2 /V s 83 Charge-loss compensation Most charge loss is due to trapping of holes When interaction position is such that the hole motion contributes the majority of the pulse amplitude, the pulse rise time is slow due to the low hole mobility The above observations suggest that slowly rising pulses are likely to be deficient in amplitude Make use of empirical amplitude vs. rise time behavior to make up the loss for slow pulses 84 42
Single-carrier approach Frisch grid to utilize single carrier for signal generation Frisch grid is actually realized w/ interdigitated electrode sets Depth of interaction is determined from the ratio of anode and cathode signal Energy resolution of ~2% @ 662 kev in 1-cm 3 CZT Pixellated design to use the small pixel effect Complex electronic readouts make signal processing challenging Energy resolution of ~1.5% @ 662 kev in 1-cm 3 CZT Nonuniform charge collection efficiency across the crystal area that often arise due to variations in the concentration of charge traps or crystal imperfections CZT w/ coplanar grid electrodes 85 Coplanar grid electrodes (a) Schematic drawing of a coplanar-grid detector (b) Calculated induced charge signals on the collecting grid (cg) and non-collecting grid (ncg) as a function of the position of a drifting charge Q originating near the fullarea cathode and ultimately collected by the collecting grid as illustrated in (a). The detector was assumed to be 1 cm thick and infinite in size in the lateral dimensions, and the line width of the grid electrode was 0.25 mm with a gap spacing of 0.25 mm. Charge trapping was not included in the calculation. The region of the detector in which the drifting charge produces the greatest change in the induced charge signals is defined as the near-grid region, whereas the remainder of the detector volume is referred to as the far-grid region. (c) Difference between the collecting- and non-collecting-grid signals for various values of the relative gain G of ncg. 86 43
Special semiconductor detectors 87 Photoconductive detectors Photoconductor: injecting (ohmic) contacts for both sides Photocurrent: additional current over steady dark current Photoconductive gain: G = μτε = lifetime = τ = a L drift time τ c b current A a b Radiation or light time 88 44
1-D position-sensitive detectors Resistive charge division Energy signal at cathode Anode signal for position at divided anode Position resolution = 0.5 1 mm 89 Si microstrip detectors Similar to gas microstrip proportional counters 2-D positioning Typ. pitch = ~50 m Equiv. noise = ~1500 e = 4.5 kev in Si 90 45
Linear Si drift detectors Drift time determines the y position Electrons formed by the radiation are initially drawn to a potential min. near the center of the wafer. They are then transported parallel to the surfaces by a potential gradient btwn the surface strips and collected at an anode near the edge of the wafer Position resolution = ~4 m in 1 size Segmented anodes determine the x position 91 Cylindrical drift detectors Electrons are collected by the anode ring Radial position is measured Good energy resolution = 225 kev @ 5.9 kev High counting rate due to small stray capacitance to preamp. 92 46
Thick film semiconductor x-ray imagers 93 Charge-coupled devices 2-D image from each shot are repeatedly measured (fps) Pixel dimension = 25 150 m 94 47
Pixel detectors Arrays of individual small detectors and preamps Equiv. noise = ~100 e = 300 ev in Si 95 48