Summary

This document provides an overview of semiconductor diode detectors, covering their properties, configurations, and applications. It details the use of these detectors in various fields of physics, including nuclear physics and particle physics. The material is suitable for an undergraduate-level physics course.

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Semiconductor Diode Detectors Semiconductor Properties Ionizing Radiation in Semiconductors Semiconductors as Radiation Detectors Semiconductor Detector Configurations Operational Characteristics Applications of Silicon Diode Detectors Germanium Gamma-ray Detecto...

Semiconductor Diode Detectors Semiconductor Properties Ionizing Radiation in Semiconductors Semiconductors as Radiation Detectors Semiconductor Detector Configurations Operational Characteristics Applications of Silicon Diode Detectors Germanium Gamma-ray Detectors Lithium Drifted Silicon Detectors cfr. Knoll, Chapter 11, 12 & 13 Solid detection medium: density ~1000x higher than for a gas → small detector dimensions Scintillation counters (solid): ~100eV needed for one information carrier (photo- electron) and number of carriers usually ~few thousand only → statistical fluctuations limit energy resolution Semiconductor diode detectors yield much larger number of charge carriers for a given incident radiation event → best energy resolution in routine use Features of “semiconductor diode detectors” or “solid-state detectors”: - information carriers: electron – hole pairs (similar to electron-ion pairs) - superior energy resolution - compact size - relatively fast timing characteristics - effective thickness can be varied - drawbacks: limitation to small sizes, relative high susceptibility to radiation-induced damage, cost 2/65 Use of Solid State Detectors Nuclear Physics o Energy measurement of charged particles (up to a few MeV) o Gamma spectroscopy (precision measurement of photon energies Particle Physics o Tracking and vertexing o Beam condition monitoring Satellite Experiments o Tracking, particle identification Security, medicine, biology … 3/65 Semiconductor Properties Band structure in solids isolated atoms: only discrete electron energy levels solid state material: atomic levels merge into energy bands, i.e. periodic lattice of crystalline materials establishes allowed energy bands for electrons - Valence band: outer shell electrons bound to specific lattice sites - Conduction band: electrons free to mitigate through the crystal 4/65 Size of bandgap determines type of material, i.e. metals: conduction and valence band overlap insulators: bandgap > 5 eV Semiconductors: bandgap ~eV Without thermal excitation, valence band is completely full and conduction band is empty for insulators and semiconductors Highest occupied band in metals is not full, i.e. electrons can easily migrate Examples of elemental semiconductors Silicon: standard material for vertex and tracking detectors in high energy physics; can be operated at room temperature; synergies with micro-electronics industry Germanium: used in nuclear physics, due to small band gap (0.66 eV) needs cooling (usually done with liquid nitrogen at 77 K) Diamond (Chemical Vapor Deposition synthetic diamond or single crystal): large band gap (~5.5 eV); requires no depletion zone; very radiation hard; drawback is a low signal and high cost 5/65 Charge carriers At non-zero temperature, valence electrons can gain thermal energy, leave the covalent bonding site and drift through the crystal, i.e. excitation process creates electron in conduction band and hole in valence band Probability per unit time that an electron-hole pair is thermally generated is given by: T = absolute temperature 3/2  Eg  Eg = bandgap energy = p (T ) CT exp  −  k = Boltzmann constant  2 kT  C = proportionality const. charact. of material In absence of an applied electric field: thermally created electron-hole pairs ultimately recombine; an equilibrium is established in which the concentration of electron-hole pairs observed at any given time is proportional to the rate of formation; strong temperature dependence After formation, electron and hole take part in random thermal motion away from point of origin; distribution of charges (for single point of origin): kT σ = 2 Dt with D µ D = diffusion constant; kT/e=0.0253V at 20°C e 6/65 Migration of charge carriers in an electric field When an electric field is applied to semiconductor material, electrons and holes undergo a net migration, i.e. combination of random thermal velocity and net drift velocity parallel to the electric field At low to moderate electric fields: drift velocity ν is proportional to applied field E; mobility µ can be defined by vh = µ h E ve = µ e E In semiconductor materials the mobility of the electrons and holes are roughly of the same order ( electrons, ions in gases) At higher electric fields, drift velocity reaches saturation velocity Saturation velocity ~107 cm/s, i.e. for typical dimensions of 0.1 cm, the charge collection takes < 10 ns → semiconductor detectors can be among the fastest-responding of all radiation detector types Diffusion causes spread in arrival position (typ. < 100 µm) and collection time (typ. < 1 ns) 7/65 8/65 Temperature dependence saturation velocity 9/65 Effect of impurities or dopants Intrinsic semiconductors Intrinsic semiconductor: completely pure semiconductor, electron-hole pairs caused by thermal excitation only, i.e. #electrons in conduction band = #holes in valence band In practice virtually impossible to achieve, i.e. electrical properties are determined by small residual level of impurities Assume equilibrium (thermal excitation + recombination); intrinsic carrier densities: ni = p i e.g. 1.5∙1010/cm3 for Si and 2.4∙1013/cm3 for Ge Flow of both negatively charged electrons and positively charged holes contributes to conductivity metallic conductors where only electrons contribute 10/65 Conductivity (or its inverse, i.e. resistivity ρ) is determined by intrinsic charge carrier densities and electron/hole mobility AV AV A = semiconductor surface area I or ρ = ( unit Ω ⋅ m ) t = semiconductor thickness ρt It V = applied voltage Net current is I = I e + I h = Ani e(ν e +ν h ) V = Ani eE ( µe += µh ) Ani e ( µe + µh ) t 1 → resistivity is ρ = eni ( µ e + µ h ) e.g. for intrinsic Si at room temperature: 1 ρ= (1.6 ×10−19 C )(1.5 ×1010 / cm3 )(1350 + 480)cm 2 / Vs V s cm ρ= 2.3 ×105 = 230000 Ω cm C (realistic value due to residual impurities: 50000 Ω.cm) 11/65 Impurity or extrinsic semiconductors Majority of charge carriers provided by extra impurity atoms at lattice sites 12/65 Compound semiconductors consist of two (binary semiconductors) or more atomic elements; depending on the column in the periodic system of elements one differentiates between e.g. III-IV, III-V, IV-V, II-VI and IV-IV (e.g. SiGe, SiC) compounds Important III-V compounds: - GaAs: faster and probably more radiation resistant than Si; drawback is less experience in industry and cost - GaP, GaSb, InP, InAs, InSb, InAlP Important II-VI compounds: - CdTe: High atomic number Z (48+52), i.e. very efficient to detect photons - ZnS, ZnSe, ZnTe, CdS, CdSe, Cd1-xZnxTe, Cd1-xZnxSe Different properties (bandgap, electron mobility, breakdown voltage, thermal stability …) allow different applications in e.g. solar cells, LEDs, high-speed or high-power electronics, opto-electronics … 13/65 n-type semiconductors: Si as example (tetravalent), with pentavalent (Group V element) impurities (~few/million or less), occuping substitutional sites in lattice Left-over lightly bound electron can easily promote to conduction band without leaving a hole → “Donor impurities” Extra electrons are not part of the lattice and occupy energy levels in forbidden gap, i.e. electron energy levels near the top of the band gap so that electrons can more easily be excited into the conduction band; fermi level EF moves up (because of the increased electron population in the conduction band) 14/65 Usually, concentration of impurities ND is large compared to #electrons expected in conduction band for intrinsic material, hence n ≅ N D while np = ni pi (increased amount of e- increases recombination) e.g. Si at room temperature ni=pi=1010 cm-3; adding donor impurity 1017 atoms/cm3 gives n=1017 cm-3, p=103 cm-3 → Number of charge carriers is much larger, from 2x1010 to 1017 cm-3, such that the conductivity is much larger compared to intrinsic material, but charge neutrality is still maintained because of the ionized donor impurities, which however cannot migrate (like holes can) Net effect in n-type material is to have #conduction electrons >> #holes compared to intrinsic material, hence electrical conductivity is driven by flow of electrons, i.e. electrons are majority carriers, holes are minority carriers Resistivity can be computed from dopant concentration and mobility of majority carriers, e.g. Si with ND = 1013/cm3 1 1 ρ = = = 463 Ω cm eN D µe (1, 6 ×10 C )(10 / cm )(1350 cm / V s ) −19 13 3 2 i.e. much lower compared to intrinsic material ! 15/65 p-type semiconductors: Si as example, with trivalent (Group III element) impurities occupying substitutional sites One unsaturated covalent bond represents a hole, slightly different from regular hole, i.e. electrons filling the hole will form covalent bonding where one atom is trivalent impurity, and are less firmly attached compared typical electrons “Acceptor impurities” create electron sites close to bottom of forbidden band gap, i.e. large fraction of acceptor sites filled with thermally excited valence band electrons, leaving behind holes; fermi level EF moves down (because of increased hole population in the valence band) 16/65 If concentration of acceptor impurities NA is large compared to intrinsic holes concentration: p ≅ NA with np = ni pi In p-type materials, holes are majority carriers, electrons are minority carriers Filled acceptor sites represent fixed negative charges balancing positive charge of majority holes; resistivity decreases tremendously 17/65 Examples of Si doped with different elements (III-IV and IV-V compounds) Effect of temperature Electron density in conduction band - in pure Si (dashed) - in Si doped with As (1016/cm3) 18/65 Electron vs. hole concentrations in a semiconductor: Total charge carrier density (electrons+holes) is lowest for intrinsic material; minimum conductivity if mobility is similar for both types of charge carriers Presence of either donors or acceptors will raise majority carrier concentration by an absolute amount that is larger than amount of decrease of minority carrier concentration 19/65 Electrical conductivity can serve as measure of impurity level of semiconductors Si resistivity levels of ~50.000 Ωcm can be achieved with advanced purification methods ( 200.000 Ωcm theoretical value) 20/65 Compensated material Donor and acceptor impurities are present in equal concentration Has some of the properties of an intrinsic semiconductor, i.e. electrons from donor impurities captured by acceptor sites Designated i Heavily doped material Thin layers of semiconductor material with unusually high concentration of impurities: n+, p+ Often used in making electrical contact with semiconductor devices because the low minority carrier density allows their application as “blocking” contacts 21/65 Trapping and recombination Electrons and holes in a semiconductor will tend to migrate either spontaneously or under influence of applied electric field, until they are collected at an electrode or recombination takes place Lifetimes 10-3-10-4s are observed, dominated by low level of remaining impurities (theoretical lifetime for pure semiconductors much longer …) Deep impurities (e.g. Au, Zn, Cd …) introduce energy levels near the middle of the forbidden gap ( shallow impurities), acting as trapping centers for charge carriers → time delay often sufficient to prevent carrier contributing to the measured pulse Recombination centers are capable of capturing both majority and minority carriers, causing them to annihilate, e.g. impurity level near center of forbidden gap might first capture a conduction electron and slightly later a hole from the valence band, with the electron filling the hole; recombination through such centers is more common than direct recombination across full bandgap 22/65 → Both trapping and recombination contribute to loss of charge carriers and tend to reduce their average lifetime in the crystal; for materials serving as radiation detector, collection times (commonly 10-7 to 10-8 s) should be short compared to mean lifetime of charge carriers (10-5 s or longer is sufficient) → Trapping length within material is mean distance traveled before trapping or recombination, and should be long compared to physical dimension over which charge needs to be collected Note that structural defects within the crystal can also lead to trapping and charge carrier loss (point defects, line defects, dislocations …) 23/65 Ionizing Radiation in Semiconductors The ionization energy Charged particle passing through semiconductor → direct or indirect production of many electron-hole pairs along track of particle Ionization energy ε observed to be largely independent of energy of incident radiation, i.e. #electron-hole pairs incident energy slight dependence on nature of incident radiation (protons, alpha, heavy ions, fission fragments), temperature and energy of radiation Doping atoms (low doping levels) have no effect on interaction probabilities or stopping power, i.e. identical for p- or n-type material E.g. Si ε = 3 eV ( 30 eV gaseous detectors) , i.e. statistical fluctuations in number of carriers smaller than for other detectors (limiting resol. for medium to high energies), larger charge per pulse leads to better signal to noise ratio (limiting resol. for low energies) 24/65 The Fano factor Fluctuations in number of charge carriers affects energy resolution As for gas counters, observed statistical fluctuations in semiconductors are smaller than expected if formation of charge carriers were a Poisson process In case of Poisson model, all events along track are considered independent and #electron-hole pairs (and its variance) equals to E/ε observed statistical variance Fano factor F≡ E /ε i.e. good energy resolution requires small F F ~ 0.1 for Si and Ge 25/65 Semiconductors as Radiation Detectors Pulse formation Equal numbers of electrons and holes are formed within few picoseconds; assume all from single point Drift in opposite directions due to electric field Different, but relatively close charge collecting times, i.e. hole mobility within factor 2-3 equal to electron mobility ( electron/ions in gaseous detectors) Si and Ge counters rely on complete integration of current due to both electrons and holes ! 26/65 Leakage current Created electrical charges must be collected at either boundary of semiconductor material; to create an electric field large enough in a semiconductor detector a voltage of typically hundreds or thousands of volts must be imposed → a steady state leakage current will be observed, even in absence of ionizing radiation Fluctuations in leakage current represents significant source of noise and will tend to mask small signal currents from ionizing events Example: Leakage current of 0.1 A can be expected if 500 V is  ρt  R=  applied over a 1 mm thick, very pure Si disc (ρ ~ 50.000 Ωcm)  A having a 1 cm surface area and ohmic contacts 2 Peak currents of the order of 10-6 A for pulse of 105 charge carriers → It is essential to reduce bulk leakage current through use of blocking contacts; in critical applications the leakage current must not exceed 10-9 A At these levels, leakage across surface of semiconductor can become more significant than bulk leakage, i.e. avoid surface contaminations ! 27/65 Blocking contacts With ohmic contacts (in which charges of either sign can flow freely) connected to a detection circuit, equilibrium charge carrier concentrations will be maintained, but they give rise to too high steady-state leakage currents to be of practical use as detectors Instead, noninjecting or blocking electrodes are universally employed, i.e. charge carriers removed by electric field are not replaced at opposite electrode and their overall concentration will drop → leakage current can be reduced sufficiently to allow detection of added current pulse due to ionizing particle Most appropriate type of blocking contacts are the two sides of a p-n semiconductor junction, i.e. it is difficult to inject electrons from p side (free electrons relatively scarce minority carriers) or holes from n side (holes are minority carriers) 28/65 The semiconductor junction Basic junction properties p-n junction is formed by bringing together n- and p-type material in good thermodynamic contact → Discontinuity in conduction electron concentration at junction causes diffusion of conduction electrons into p-side (leaving behind immobile, positively ionized donor impurities) and of holes into n-side (leaving behind immobile acceptor sites that picked up an extra electron) → Build-up of net negative charge in p-side and positive charge in n-side; accumulated charge forms an electric field that stops further diffusion and brings the system into equilibrium 29/65 Depletion region has suppressed concentrations of electrons and holes, and can act as detector medium, i.e. electron-hole pairs are swept out of the depletion region by the electric field, and their motion constitutes a basic electrical signal Thermal generation of charge carriers in depletion zone (→ generation current); swept away within few ns, i.e. much faster than time to establish equilibrium Junction is formed in one single crystal by causing change in impurities from one side of the junction to the other Example: start with p-type crystal doped uniformly (NA); exposure with n- type impurity vapor diffusing into crystal (ND), converting one side into n- type material 30/65 Depletion region (i.e. region of charge imbalance) extends into n- and p-region of junction; extend of this region depends on donor and acceptor concentrations Electric potential ϕ (→ contact potential VC) and electric field across junction d 2ϕ ρ ( x) dϕ = − E ( x) = − dx 2 ε dx (Poisson’s equation in 1 dim.; ε = dielectric constant of medium) 31/65 Biasing the p-n junction Forward bias Reverse bias 32/65 Reverse biasing Contact potential ~1V across unbiased junction is too low to let charges move fast → easily lost due to trapping and recombination, i.e. poor resolution External voltage applied to cause p-n junction to be reverse biased (~diode), i.e. negative voltage to p-side wrt. n- side → Natural potential difference across junction gets enhanced; minority carriers are attracted across junction, giving a small reverse current due to their low concentration p-n junction serves as rectifying element, i.e. relatively free flow in one direction (forward biasing), while presenting large resistance in opposite direction (reverse biasing) 33/65 Properties of the reverse bias junction Applied voltage will appear across depletion zone (high resistivity compared to normal p- or n-material) and accentuate the potential difference across junction → space charge will extend over larger distance on either side of junction; bias voltage usually >> contact potential Ionized donor sites Filled acceptor sites Partially or fully depleted detectors NDa=Nab 1/ 2 Width d of the depleted region:  2εV  d=a+b d ≅  N lower dopant level of the two  eN  (either of donors or acceptors); d ≅ (2εV µρ d )1/2 µ mobility of majority carrier; ρd resistivity doped semicond. 1/2 → high purity detectors best ε eε N  C= ≅  → note V dependence ! d  2V  1/2 2V  2VNe  Small detector capacitance Emax ≅ =  needed for good energy resolution d  ε  Max. E-field occurs at transition between p- and n-material; typ. 106-107 V/m; operating voltage must be kept below the breakdown voltage 34/65 Interrelation between Si junction detector parameters Short summary: Reversed biased p-n junction is an attractive radiation detector because charge carriers created within depletion region can be quickly and efficiently collected Width of depletion area represents active detector volume and depends on reverse bias in partially depleted detectors Variable active volume of semiconductor junctions is unique among radiation detectors Capacitance of partially depleted detector also varies with applied voltage 35/65 Semiconductor Detector Configurations Diffused junction detectors Homogeneous p-type crystal → treatment with n-type vapor (typ. phosphorus), converting region near surface into n-type; typical depths of diffused layer 0.1-2.0 µm Due to heavily doped n-type surface, depletion region extends primarily into p-side → surface layer remains outside depletion region, i.e. dead layer acting like an entrance window, is a disadvantage for particle detection Ion implanted layers Expose surface of semiconductor to a beam of accelerator produced ions, i.e. ion implantation to form n+ or p+ layers (for example P or B ions) Monoenergetic ions have well-defined range in semiconductor material, i.e. concentration profile can be controlled by changing ion energy 36/65 Surface barrier detectors Role of p-type material can be assumed by high density of electron traps formed at surface of an n-type crystal, i.e. metal-semiconductor contact or Schottky Junction Empirical procedure: etching of surface, followed by evaporation of a thin gold layer (~20nm) for electrical contact Very thin dead layers Disadvantage is sensitivity to light, causing very high noise levels (thin entrance window optically transparent, i.e. photons can reach active volume; 2-4 eV energy of visible light photons is larger than band gap) 37/65 Fully depleted detectors If reverse bias voltage is increased large enough, depletion region extends across entire thickness of silicon wafer → preferred configuration Usual case: one side heavily doped n+ or p+ layer, or surface barrier, and high-purity, mildly n or p type semiconductor (often denoted as ν or π) on other side of junction → thick depletion zone with low impurity concentration Due to large difference in doping level, depletion region extends only into high-purity side; heavily doped layer can be kept very thin and acts as entrance window eNT 2 Extend of Depletion voltage Vd = depletion 2ε region (T = wafer thickness) Undepleted, insensitive Over-depleted detector : V >> Vd region i.e. high electric field everywhere in active volume → preferred case 38/65 Fully-depleted detector at lowest possible voltage: highest purity wafer (n- or p-type) + rectifying contact + blocking contact; E-field max. at rectifying contact intrinsic or compensated material wafer; uniform E-Field, detector fully depleted even for low applied voltage Fully depleted detectors useful as transmission detectors (of energy loss): - Dead layers must be as small as possible - Wafer thickness must be kept uniform to avoid energy loss variations - Dead layer in partially depleted configurations represents a source of thermal noise, and due to the low E-field charge carrier velocity is low causing deteriorating timing characteristics - Active volume and capacitance independent of applied voltage Available purity of semiconductor drives max. possible wafer thickness, i.e. several cm for Ge, several mm for Si (higher impurity level than Ge) 39/65 Passivated planar detectors Newest method of fabricating silicon junction detectors: combination of ion implantation and photolitography Can be used to produce complex electrode geometries 40/65 Operation Characteristics Leakage current Reverse bias voltage applied to junction detector gives fraction of µA leakage current, originating from both bulk volume and detector surface: - Small minority carrier current across junction (majority carriers are repelled away from junction), roughly proportional to junction area - Thermal generation of electron-hole pairs within depletion region, can be reduced by cooling (esp. for Ge with its low gap energy) - Surface leakage effects at edges of junction, depending on e.g. encapsulation, humidity, contamination …; with planar fabrication junction edges are buried within wafer leading to reduced leakage Bias voltage is usually supplied to detector via a large-value series resistor (e.g. RC circuit for signal integration) → large leakage currents can reduce voltage over detector itself Monitoring of leaking current is common practice (and allows to detect abnormal detector behavior or damage …) 41/65 Changes with detector bias voltage For low bias voltage and electric field, pulse height from radiations that are fully stopped in depletion layer continues to rise with applied voltage, which is due to incomplete charge collection (trapping and recombination) Fraction of charge that escapes collection decreases with increasing electric field, until saturation region is reached, i.e. pulse height no longer changes with increasing bias voltage For sufficiently high electric fields multiplication effects can be induced similar to ion saturation and gas multiplication in gas-filled chambers 42/65 Pulse rise time Semiconductor diode detectors are generally among the fastest of all commonly used radiation detectors; pulse rise time of order 10ns or less Charge transit time, i.e. time of migration of electrons and holes formed by incident radiation across depletion region → rise time output pulse limited by time required for complete charge migration from point of formation to opposite sides of depletion zone - Fully depleted detectors, i.e. fixed depletion width: transit time decreases as bias voltage (electric field) is increased - Partially depleted detectors more complex: larger bias voltage increases both electric field and distance over which charge must be collected; electric field (and electron & hole drift velocity) also not uniform Plasma time, for heavy charged particles (α, fission frag.) creating sufficiently high density of electron-hole pairs to form plasma-like cloud → shielding of interior of cloud such that only outer edge of charge cloud feels electric field and starts migrating immediately - Plasma time is roughly time required for charge cloud to disperse to the point where regular charge collection proceeds 43/65 Entrance window or dead layer Particle energy loss before reaching active volume can be significant, i.e. dead layer includes metallic electrode and indeterminate thickness of silicon below with inefficient charge collection; can depend on bias voltage → Can in principle be determined by varying the angle of incidence of a monoenergetic charged particle radiation dE ∆E0 - incidence angle zero: ∆E0 = 0 t ; angle θ: ∆E (θ ) = (t = thickness of dead layer) dx cos(θ )  1  → difference is: E ' = ( E0 − ∆E0 ) − ( E0 − ∆E (θ )) = ∆E0  − 1  cos θ  → extract ΔE0 from plot of E’ as function of (1/cosθ -1), and use dE0/dx known from tables to determine thickness t Energy loss could depend on angle (e.g. angular dep. of recombination wrt. electric field direction, i.e. more recombination parallel to E-field) Typ. energy loss values: 100nm of Si gives 4 keV for 1 MeV protons, 14 keV for 5 MeV α-particles, several hundred keV for fission fragments 44/65 Channeling Particles that travel parallel to crystal planes can, on average, show a rate of energy loss that is lower than that for particles directed in some arbitrary direction To minimize tendency for channeling, silicon is cut such that crystal orientation is perpendicular to wafer surface (and channeling would happen for particles parallel to surface) Energy calibration Semiconductor diode detectors respond very linearly when applied for fast electrons or light ions (protons, α-particles …) and energy calibration is similar within ~1% or less Most common calibration source is 241Am, giving α’s of 5.486 MeV (85%) and 5.443 MeV (13%) 45/65 Pulse height defect Pulse height observed for heavy ions is substantially less than that for light ions of the same energy → pulse height defect is defined as difference between true and measured energy of the heavy ion: - Energy loss of ion in entrance window and dead layer: in contrast to light ions, dE/dx max. at start of their range - Energy loss by other mechanisms than electronic collisions, e.g. nuclear collisions, where low velocity recoil nuclei have low probability for electronic interactions - High rate of recombination in dense plasma along ion track; could be decreased with higher bias voltage and may depend on orientation wrt. electric field Radiation damage will increase pulse height defect due to increased level of trapping and recombination 46/65 Applications of Silicon Diode Detectors General charged particle spectroscopy Used often for heavy charged particle detection Semiconductor detectors often provide advantages in several key areas: - exceptionally good energy resolution - good stability and freedom from drift - excellent timing characteristics - very thin entrance windows - simplicity of operation Relatively small size can be advantage but also limitation in case large surface area is needed - commercially available up to ~20cm2, while usual size 1-5cm2 - depletion depth up to 5mm, while usually heavy ion range → single, full-energy peak; [for fully depleted detector, depletion depth = wafer thickness; for partially depleted detector, depletion depth is bias voltage dependent] 47/65 Alpha particle spectroscopy Silicon diodes at room temperature are near-ideal for α’s and light ions; performance of detectors often tested using α-sources, e.g. 241Am If noise from preamplifier or other electronics is smaller than inherent energy resolution, then limiting resolution is: F Fε =Rlim 2.35 = 2.35 N E FWHM lim (in units of energy) = 2.35 FEε → e.g. for Si: F = 0.11, ε = 3.62 eV, and E = 5.486 MeV: FWHM lim = 3.47 keV In reality: 8-10 keV resolution → partial energy transfer to recoil nuclei that create only few e-h pairs (e.g. 3.5 keV FWHM contribution for 6 MeV α’s) → incomplete charge collection, energy loss variation in dead layers, electronic noise 48/65 Energy loss measurements – Particle identification If dE/dx is of interest instead of full energy E, thin detectors compared with particle range are used; #charge carriers for thickness Δt : (dE/dx)Δt/ε → ΔE transmission detectors: - thin film scintillators (energy resolution not good) - thin semiconductor detectors (can be made as thin as 10µm) - ionization chambers or proportional counters Particle identifier telescope: - Transmission detector in coincidence with normal silicon diode or “thick detector”, i.e. simultaneous measurement of ΔE and E 49/65 For non-relativistic particles, Bethe’s formula gives: dE mz 2  E  m = particle mass = C1 ln  C2  dx E  m ze = particle charge → E(dE/dx) is only mildly dependent on E, but is a sensitive indicator of mz2, i.e. product of pulse amplitudes of both detectors can be used to identify particle type (if energy of incident radiation is similar) 50/65 Alternative approach based on fact that range R and energy E for a wide variety of particles is related by power-law approximation: R( E ) = aE b → If the incident particle deposits an energy ∆E in the transmission detector of thickness ∆t and the remainder of its energy Er in the thick detector, then ∆t = R( E r + ∆E ) − R( E r ) ∆t = ( E r + ∆E ) b − E rb a a is constant for given particle type and ~1/mz2; b is almost constant if ions of similar mass are involved (e.g. b = 1.73 for protons, 1.65 for carbon ions), i.e. choose a reasonable value for b and measure a “brute force” approach is to use tables of actual energy loss data … Fundamental limit of the (ΔE,E) measurements to distinguish particle types is set by fluctuations in the ΔE signal produced by energy straggling 51/65 Germanium Gamma-Ray Detectors Using Si or Ge at normal semiconductor purities, depletion depths >2- 3mm are difficult to achieve; for more penetrating radiations like gamma- rays, the active volume and thus the maximum depletion depth must be large enough 1/2  2εV  Depletion thickness d =   eN  → 1) Reducing N to 1010 atoms/cm3, would give d = 10mm for V < 1000 V for Ge; however, this corresponds to 1 part in 1012 impurity concentration, which seems about the present limit for ultrapure Ge (not reached for Si), i.e. intrinsic Ge or high-purity Ge (HPGe) 2) Use of compensated material in which residual impurities are balanced by an equal amount dopant atoms of opposite type; after crystal has been grown, use of lithium ion drifting to produce Ge(Li) detectors: residual acceptor impurities are exactly balanced over a thickness of up to 2 cm by addition of interstitial lithium donor atoms Ge(Li) detectors became commercially available in 1960s; replaced by HPGe in 1980s 52/65 Configurations of germanium detectors High-purity Germanium (HPGe) Detector Fabrication Starting material is bulk germanium intended for semiconductor industry (i.e. high purity already); further processing using zone refining technique, i.e. impurity levels progressively reduced by local heating and slowly passing melted zone from one end to the other; can yield impurity level of 109 atoms/cm3 Planar configuration p-type high-purity Ge + n+ contact (Li evaporation or direct implantation) + non-injecting p+ contact (ion implantation) or metal-semiconductor surface barrier n+-π-p+ or n+-ν-p+ or compensated configuration When fully depleted with large overvoltage, electric field almost uniform 53/65 Coaxial configuration Active volume planar config. limited to ~10-30cm3, depl. depth ~1-2cm, due to limited size (~few cm diameter) of crystal from which the wafer is cut; larger volumes (up to 800 cm3) starting with cylindrical crystal Closed-ended coaxial config. avoids issue with surface leakage current and provides planar front entrance window; however, electric field no longer perfectly radial (→ bulletizing may help to avoid low-field regions); well config. allows access to central hole (for e.g. sources) Preferred config. has rectifying contact on outer surface (lower depletion voltage, and higher E-field in outer regions where most of the detector volume is) 54/65 Germanium crystal growth [G. Wang et al, J. Phys.: Conf. Ser. 606 (2015) 012012] 99.99999999999% Germanium crystal from Canberra purity Germanium Semiconductor (CSI) crystals from Umicore 55/65 Germanium detector operational characteristics Detector cryostat and dewar Due to small bandgap (0.7 eV) room-temperature operation of Ge detectors is impossible → cooling to 77 K through the use of insulated dewar with reservoir of liquid nitrogen in thermal contact with detector For Ge(Li) low temperature must be maintained continuously to prevent catastrophic redistribution of drifted Li at room temperature; Li drifting is eliminated in HPGe and they can be kept at room temperature in between uses Detector housed in vacuum-tight cryostat to inhibit thermal conductivity between crystal and surrounding air Thin end window located near crystal to minimize attenuation of gamma rays before entering the germanium 56/65 Ge detectors universally fitted with interlock to prevent application of detector HV before reaching low temperature (excessively high leakage current will likely destroy input FET of preamplifier); preamplifier incorporated in cryostat package (input stages also cooled to reduce electronic noise) 57/65 Energy resolution Ge detectors have superior energy resolution compared to NaI(Tl) scintillators Overall energy resolution determined by 3 factors: - inherent statistical spread in #charge carriers - variations in charge collection efficiency - electronic noise which of these dominate depends on radiation energy and on size and inherent detector quality 58/65 Pulse shape and timing properties Assuming the equivalent circuit of measuring electronics presents a large time constant compared with the largest rise time produced by the detector, the leading edge of signal pulse is entirely determined by details of charge collection process within detector For low electric fields, drift velocity increases linearly with field (see slide 9), but saturates at sufficiently high fields; for electrons in Ge at 77K, saturated drift velocity ≈ 105 m/s for field of ~105 V/m; similar for holes but minimum field of 3x105 V/m required Limiting factors for ultimate time resolution: - Charge collection is inherently slow; 100 ns needed to travel 1 cm, i.e. pulse rise times typically several hundred nanoseconds, much larger than for fast detectors (e.g. organic scintillators) - Pulse rise time from Ge detectors can change substantially from event to event, depending on position where electron-hole pairs are created within active volume 59/65 Similar analysis of leading edge pulse shape as for gas-filled ion chambers, however, positive and negative charge carriers (electrons & holes) now have similar mobilities Calculation of pulse shape with following common assumptions: 1. All charge carriers are created at a fixed position x from the anode within the detector active volume 2. Trapping and detrapping (release) of charge carriers are ignored 3. All charge carriers are assumed to be generated entirely within the active volume of the detector where the electric field has its full expectation value 4. The electric field within the active volume of the detector is sufficiently high to cause saturation of drift velocities 1 1 CV02 = q0ε vet + q0ε vh t + CVch2 2 2 1 ) q0ε ( ve + vh )t C (V02 − Vch2 = 2 V0 ε = d 1 C (V0 + Vch )(V0 −=  V0  Vch ) q0   ( ve + vh )t 2 d  60/65 1 V  C (V0 + Vch )(V0 −= Vch ) q0  0  ( ve + vh )t 2 d  VR =V0 − Vch V0 + Vch ≅ 2V0 1  V0  (2V0 )(VR ) q0   ( ve + vh )t C= 2 d  q0 = VR ( ve + vh ) t dC Corresponding induced charge: q0 Q =ind CV = R (ve + vh )t d q0 = (electron drift distance + hole drift distance) d 61/65 te = electron collection time = x/ve, where ve is the saturation electron velocity th = hole collection time = (d-x)/vh, where vh is the saturation hole velocity 1) t < th and t < te  ve vh  Q (t ) q0  t + t  = d d   x vh  2) te < t < th Q (t ) q0  + t  = d d   ve (d − x )  3) th < t < te Q (t ) q0  t + =   d d  4) t > th and t > te Q (t ) = q0 62/65 63/65 Gamma-ray spectroscopy with germanium detectors Response function Lower atomic number Z of Ge and smaller typical active volume compared with NaI scintillators lead to differences in pulse height spectrum: - Photoelectric cross section factor 10-20 lower compared to NaI - Full-energy peak more likely to consist of multiple interactions 64/65 [Lithium Drifted Silicon Detectors] Si of highest currently available purity: depletion depth is limited to 1–2mm → Si(Li): compensated or “intrinsic” silicon layer 5 -10 mm through lithium drifting; thickness limited by the distance over which Li drifting can be carried out successfully not widely used in general gamma-ray spectroscopy (Si: Z = 14 only, compared to Ge: Z = 32, i.e. photoelectric cross section factor 50 lower for typical gamma-ray energies) detection of very low-energy gamma rays or X-rays, i.e. reasonable probability for photoelectric absorption (larger Si transparency for high- energy gamma rays helps) detection of beta particles (lower Z helps to have fewer electrons backscattering from detector without depositing their full energy) Si has larger bandgap compared to Ge, i.e. thermally generated leakage current at any given temperature will be lower 65/65

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