Silicon Detectors How They Work Rainer Wallny Silicon

Silicon Detectors – How They Work Rainer Wallny Silicon Detector Workshop at UCSB May 11 th, 2006 Slides ruthlessly stolen from: Paula Collins, CERN Alan Honma, CERN Christian Joram, CERN Michael Moll, CERN Steve Worm, RAL

Outline o o Why Silicon ? Semiconductor Basics – Band-gap, PN junction – Silicon strip detectors Some Technicalities - Wafer Production - Wire Bonding o o Radiation Damage – Effect on Vd – Effect on Leakage Currents o 11/26/2020 Conclusions 2

Tracking Chambers with Solid Media o Ionization chamber medium could be gas, liquid, or solid – Some technologies (ie. bubble chambers) not applicable in collider environments o Gas Liquid Solid Density Low Moderate High Atomic number Low Moderate Ionization Energy Moderate Low Signal Speed Moderate Fast High-precision tracking advantages with solid media – Easily ionized, relatively large amount of charge – Locally high density means less charge spreading – Fast readout possible “Solid-state detectors require high-technology devices built by specialists and appear as black boxes with unchangeable characteristics. ” -Tom Ferbel, 1987 11/26/2020 3 3

Why Silicon? o Electrical properties are good – Forms a native oxide with excellent electrical properties – Ionization energy is small enough for easy ionization, yet large enough to maintain a low dark current o Mechanical properties are good – Easily patterned and read out at small dimensions – Can be operated in air and at room temperature – Can assemble into complex geometries o Availability and experience – Significant industrial experience and commercial applications – Readily available at your nearest beach 11/26/2020 4 4

The Idea is Not Quite New … Semiconductors used since 50’s for energy measurement in nuclear physics o Precision position measurements up until 70’s done with emulsions or bubble chambers -> limited rates, no triggering o Traditional gas detectors: limited to 50 -100 μm o First silicon usage for precision position measurement: NA 11 at CERN, 1981 11/26/2020 5

Pioneering Silicon Strip Detectors E 706 (FNAL 1987) NA 11 (CERN 1981) sensor o 24 x 36 mm 2 active area o 8 layers of silicon o 1 m 2 readout electronics! fan out to readout electronics o 50 x 50 mm 2 active area Silicon sensor and readout electronics technology closely coupled with electronics miniaturization (transistors, ICs, ASICs …) silicon quickly took off … 11/26/2020 6 6

Contemporary Silicon Modules CDF SVX IIa half-ladder: two silicon sensors with readout electronics (SVX 3 b analog readout chip) mounted on first sensor ATLAS SCT barrel module: four silicon sensors with center-tapped readout electronics (ABCD binary readout chip) Silicon sensor and readout chip development intimately related BUT will concentrate on silicon only here … 11/26/2020 7 7

Large ‘Contemporary’ Silicon Systems DELPHI (1996) ~ 1. 8 m 2 silicon area 175 000 readout channels CMS Silicon Tracker (~2007) ~12, 000 modules ~ 223 m 2 silicon area CDF SVX IIa (2001 -) ~25, 000 silicon wafers ~ 11 m 2 silicon area ~ 10 M readout channels ~ 750 000 readout channels 11/26/2020 8 8

New Production Paradigm evolution : DELPHI (888 detectors, 8 geometries) CDF (8000 sensors, 8 geometries) CMS (25000 sensors, 15 geometries) Each sensor treated individually, nurtured into life in many hours of careful handling Systematic assembly line production with decent QA systems P. Collins, Warwick 2006 11/26/2020 9

‘Moore’s Law’ for Silicon Detector Systems Moore’s Law: Exponential growth of sensitive area and number of electronic channels with time (from Computer Science: doubling of IC integration capacity every 18 months) 11/26/2020 10

Large Silicon Detector Systems …. LEP Tevatron Whoops… 11/26/2020 LHC P. Collins, ICHEP 2002 11

The Basics …… 11/26/2020 12

Semiconductor Basics – Band Gap o In a gas, electron energy levels are discrete. In a solid, energy levels split and form a nearly-continuous band. 11/26/2020 o If the gap is large, the solid is an insulator. If there is no gap, it is a conductor. A semiconductor results when the gap is small. o For silicon, the band gap is 1. 1 e. V, but it takes 3. 6 e. V to ionize an atom. The rest of the energy goes to phonon exitations (heat). 13

Semiconductor Basics – Principle of Operation - Basic motivation: charged particle position measurement - Use ionization signal (d. E/dx) left behind by charged particle passage + _ + _ - In a semiconductor, ionization produces electron hole pairs - Electric fields drift electrons and holes to oppositely electrodes BUT: - In pure intrinsic (undoped) silicon, many more free charge carriers than those produced by a charged particle. Have 4. 5 x 108 free charge carriers; only 3. 2 x 104 produced by MIP - Electron –hole pairs quickly re-combine … Need to deplete free charge carriers and separate e-holes ‘quickly’! 11/26/2020 14

Doping Silicon n-type: • In an n-type semiconductor, negative charge carriers (electrons) are obtained by adding impurities of donor ions (eg. Phosphorus (type V)) • Donors introduce energy levels close to conduction band thus almost fully ionized => Fermi Level near CB p-type: • In a p-type semiconductor, positive charge carriers (holes) are obtained by adding impurities of acceptor ions (eg. Boron (type III)) Electrons are the majority carriers. Holes are the majority carriers. 11/26/2020 • Acceptors introduce energy levels close to valence band thus ‘absorb’ electrons from. VB, creating holes => Fermi Level near VB. 15

The pn-Junction Exploit the properties of a p-n junction (diode) to collect ionization charges p + + + + – + +– + ++ – + – – – + n When brought together to form a junction, a gradient of electron and hole densities results in a diffuse migration of majority carriers across the junction. Migration leaves a region of net charge of opposite sign on each side, called the depletion region (depleted of charge carriers). Electric field set up prevents further migration of carriers resulting in potential difference Vbi Another way to look at it: Fermi-Levels need to be adjusted so thus energy bands get distorted => potential Vbi Funky cartoon from Brazil: http: //www. agostinhorosa. com. br/artigos/transistor-6. html 11/26/2020 16

pn - Junction o p-type and n-type doped silicon forms a region that is depleted of free charge carriers p + + o o ++ + + +– + + The depleted region contains a non-zero fixed charge and an electric field. In the depletion zone, electron – hole pairs won’t recombine but rather drift along field lines Dopant concentration Artificially increasing this depleted region by applying a reversed bias voltage allow charge collection from a larger volume Electric field 11/26/2020 n – – + – – – + Space charge density Carrier density Electric potential 17

How to Build a Silicon Detector If we make the p-n junction at the surface of a silicon wafer with the bulk being n-type (you could also do it the opposite way), we then need to extend the depletion region throughout the n bulk to get maximum charge collection by applying a reverse bias voltage. p p p n – h+ e- + 11/26/2020 18

Properties of the Depletion Zone – Depletion width is a function of the bulk resistivity , charge carrier mobility and the magnitude of reverse bias voltage Vb: w = 2 Vb Depletion zone – Vb + w d undepleted zone where = 1/ q N for doped material where N is the doping concentration and q is the charge of the electron and is the carrier mobility (v= E) – The bias voltage needed to completely deplete a device of thickness d is called the depletion voltage, Vd Vd = d 2 /(2 ) – Need a higher voltage to fully deplete a low resistivity material. – A higher voltage is needed for a p-type bulk since the carrier mobility of holes is lower than for electrons (450 vs 1350 cm 2/ V·s) 11/26/2020 19

Properties of the Depletion Zone (cont’d) – One normally measures the depletion behavior (finds the depletion voltage) by measuring the capacitance versus reverse bias voltage. The capacitance is simply the parallel plate capacity of the depletion zone. C = A / 2 Vb capacitance vs voltage 1/C 2 vs voltage Vd 11/26/2020 20

Leakage Current - Two main sources of (unwanted) current flow in reversed-biased diode: – Diffusion current, charge generated in undepleted zone adjacent to depletion zone diffuses into depletion zone (otherwise would quickly recombine) negligible in a fully depleted device – Generation current Jg, charge generated in depletion zone by defects/contaminants Jg exp(-b/k. T) Exponential dependence on temperature due to thermal dependence of e-h pair creation by defects in bulk. Rate is determined by nature and concentration of defects. 11/26/2020 21 21

Bias Resistor and AC Coupling – Need to isolate strips from each other and collect/measure charge on each strip => high impedance bias connection (resistor or equivalent) – Usually want to AC (capacitatively) couple input amplifier to avoid large DC input from leakage current. – Both of these structures are often integrated directly on the silicon sensor. – Bias resistors via deposition of doped polycrystalline silicon, and capacitors + via metal readout lines over the implants but separated by an insulating dielectric layer (Si. O 2 , Si 3 N 4). 11/26/2020 h+ e- 22

The Charge Signal • Collected charge usually given for Minimum Ionizing Particle (MIP) Most probable charge ≈ 0. 7 x mean Mean charge d. E/dx)Si = 3. 88 Me. V/cm, for 300 m thick = 116 ke. V This is mean loss, for silicon detectors use most probable loss (0. 7 mean) = 81 ke. V 3. 6 e. V needed to make e-h pair Collected charge 22500 e (=3. 6 f. C) 11/26/2020 23

But There Is Noizzzzzz …. . Landau distribution has significant low energy tail which becomes even lower with noise broadening. noise distribution Landau distribution with noise Noise sources: o Capacitance ENC ~ Cd o Leakage Current ENC ~ √ I o Thermal Noise ENC ~ √( k. T/R) One usually has low occupancy in silicon sensors �most channels have no signal. Don’t want noise to produce fake hits so need to cut high above noise tail to define good hits. But if too high you lose efficiency for real signals. Figure of Merit: Signal-to-Noise Ratio S/N. Typical Values ~ 10 -15, people get nervous below 10. Radiation Damage can degrade the S/N. Thus S/N determines detector lifetime in radiation environment. 11/26/2020 24

Charge Collection and Diffusion – Drift velocity of charge carriers v = E, so drift time, td = d/v = d/ E – Typical values: d=300 m, E= 2. 5 k. V/cm, e= 1350; h= 450 cm 2 / V·s, gives: td(e)= 9 ns , td(h)= 27 ns – Diffusion of charge “cloud” caused by scattering of drifting charge carriers, radius of distribution after time td: = 2 D td , where D is the diffusion constant, D = k. T/q – Typical charge radius: ≈ 6 m – Charge Radius determines ‘Charge Sharing’, i. e. deposition of charge on several strips. 11/26/2020 25

Double Sided Detectors Why not get a 2 nd coordinate by measuring position of the (electron) charge collected on the opposite face? BUT: Unlike the face with the p-strips, nothing prevents horizontal charge spread on back face. n-strips alone are not sufficient to isolate the charge because of an electron accumulation layer produced by the positively charged Si. O 2 layer on the surface. p+ p+ p+ n-bulk n n n SOLUTION: • Put p-strips in between the n-strips. p+ p+ OR • Put “field plates” (metal over oxide) over the n-strips n-bulk and apply a potential to repel the electrons. n n n + 11/26/2020 + + 26

Guard Rings and Avalanche Breakdown We have treated the silicon strip device as having infinite area, but it has edges. What happens at the edges? Single guard ring structure – Voltage drop between biasing ring and edge, top edge at backplane voltage. – Typically n-type implants put around edge of the device and a proper distance maintained between p bias ring and edge ring. – Usually one or more “guard” rings (left floating) to assure continuous potential drop over this region. – Defects or oxide charge build-up in this region could lead to additional leakage current contributions – If one increases the bias voltage, eventually the field is high enough to initiate avalanche multiplication. This usually occurs around 30 V/ m (compared to a typical operating field of <1 V/ m). Local defects and inhomogeneities could result in fields approaching the breakdown point. –. 11/26/2020 27 27

Some Technicalities …… 11/26/2020 28

Material: Float Zone Silicon (FZ) Float Zone process Mono-crystalline Ingot Using a single Si crystal seed, melt the vertically oriented rod onto the seed using RF power and “pull” the single crystal ingot Poly silicon rod Wafer production Slicing, lapping, etching, polishing RF Heating coil Single crystal silicon Oxygen enrichment (DOFZ) Oxidation of wafer at high temperatures 11/26/2020 29

Czochralski silicon (Cz) & Epitaxial silicon (EPI) Czochralski silicon o o Pull Si-crystal from a Si-melt contained in a silica crucible while rotating. Silica crucible is dissolving oxygen into the melt high concentration of O in CZ Material used by IC industry (cheap) Czochralski Growth Recent developments (~2 years) made CZ available in sufficiently high purity (resistivity) to allow for use as particle detector. Epitaxial silicon o o o 11/26/2020 Chemical-Vapor Deposition (CVD) of Silicon CZ silicon substrate used in-diffusion of oxygen growth rate about 1 m/min excellent homogeneity of resistivity up to 150 m thick layers produced price depending on thickness of epi-layer but not extending ~ 3 x price of FZ wafer 30

Wafer Processing (1) 1) Start with n-doped silicon wafer, ≈ 1 -10 k cm n-Si Si. O 2 2) 3) Oxidation at 800 – 1200 0 C Photolithography (= mask align + photo-resist layer + developing) followed by etching to make windows in oxide UV light etch mask Photo-resist 11/26/2020 31

Wafer Processing (2) B 4) Doping by ion implantation (or by diffusion) As 5) p+ p+ Annealing (healing of crystal lattice) at 600 0 C n+ Al 6) Photolithography followed by Al metallization over implanted strips and over backplane usually by evaporation. Simple DC-coupled silicon strip detector 11/26/2020 32

Bringing It All Together • Connectivity technology: some of the possibilities – High density interconnects (HDI): industry standard and custom cables, usually flexible kapton/copper with miniature connectors. – Soldering still standard for surface mount components, packaged chips and some cables. Conductive adhesives are often a viable low temperature alternative, especially for delicate substrates. – Wire bonding: the standard method for connecting sensors to each other and to the front-end chips. Usually employed for all connections of the front-end chips and bare die ASICs. A “mature” technology (has been around for about 40 years). OPAL (LEP) module ~200 wire bonds 11/26/2020 4 x 640 wire bonds Total ~2700 wire bonds 33

Wire Bonding • Uses ultrasonic power to vibrate needle-like tool on top of wire. Friction welds wire to metallized substrate underneath. • Can easily handle 80 m pitch in a single row and 40 m in two staggered rows (typical FE chip input pitch is 44 m). • Generally use 25 m diameter aluminium wire and bond to aluminium pads (chips) or gold pads (hybrid substrates). • Heavily used in industry (PC processors) but not with such thin wire or small pitch. Electron micrograph of bond “foot” Microscope view of wire bonds connecting sensor to fan-out circuit 11/26/2020 34

Radiation Damage … 11/26/2020 35

Radiation Damage in Silicon Sensors Two general types of radiation damage to the detector materials: Bulk (Crystal) damage due to Non Ionizing Energy Loss (NIEL) - displacement damage, built up of crystal defects – I. Change of effective doping concentration (higher depletion voltage, under- depletion) II. Increase of leakage current (increase of shot noise, thermal runaway) III. Increase of charge carrier trapping (loss of charge) Surface damage due to Ionizing Energy Loss (IEL) - accumulation of positive in the oxide (Si. O 2) and the Si/Si. O 2 interface – affects: interstrip capacitance (noise factor), breakdown behavior, … Impact on detector performance and Charge Collection Efficiency (depending on detector type and geometry and readout electronics!) Sensors can fail from radiation damage by virtue of… – – – Noise too high to effectively operate Depletion voltage too high to deplete Loss of inter-strip isolation (charge spreading) Signal/Noise Ratio is the quantity to watch ! 11/26/2020 36

Run I Experience: SVX’ Signal-to-Noise Radiation Damage limits the ultimate lifetime of the Detector -Need S/N >8 to perform online b-tagging with SVT -Need S/N >5 for offline b-tagging 11/26/2020 37

Surface Damage Metal (Al) o Surface damage generation over time: – Ionizing radiation creates electron/hole pairs in the Si. O 2 – Many recombine, electrons migrate quickly away – Holes slowly migrate to Si/Si. O 2 interface. Hole mobility is much lower than for electrons (20 cm 2/Vs vs. 2 x 105 cm 2/Vs) – Some holes ‘stick’ in the boundary layer o -+ -+ + - +-+- +- -++ +- +Interface (Si. Ox) + Oxide (Si. O 2) Semiconductor (Si) After electron transport: + + + ++ +- + Surface damage results in – – Increased interface trapped charge (see picture) After transport Increase in fixed oxide charges of the holes: + + + Surface generation centers Electron accumulation under the oxide interface can alter the depletion voltage (depends on oxide quality and sensor geometry) – In silicon strip sensors, surface damage effects (oxide charge) saturate at a few hundred k. Rad 11/26/2020 38

Bulk Damage o Bulk damage is mainly from hadrons displacing primary lattice atoms (for E > 25 e. V) Vacancy/Oxygen Center O – Results in silicon interstitial, vacancy, and typically a large disordered region – 1 Me. V neutron transfers 60 -70 ke. V to recoiling silicon atom, which in turn displaces Disordered ~1000 additional atoms o Defects can recombine or migrate through the lattice to form more complex and stable defects – Annealing can be beneficial, but… – Defects can be stable or unstable o Displacement damage is directly related to the non-ionizing energy loss (NIEL) of the interaction Interstitial region C Carbon-Carbon Pair C – Varies by incident particle type and energy Phosphorous – Normalize fluence to 1 Me. V n-equivalent dopant 11/26/2020 Vacancy Carbon Interstitial C Di-vacancy P Carbon-Oxygen pair O C 39

Microscopic defects Damage to the silicon crystal: Displacement of lattice atoms o Si. S particle EK>25 e. V V I EK > 5 ke. V 80 nm I V “point defects”, mobile in silicon, can react with impurities (O, C, . . ) point defects and clusters of defects Distribution of vacancies created by a 50 ke. V Si-ion in silicon (typical recoil energy for 1 Me. V neutrons): I V Vacancy + Interstitial Schematic [Van Lint 1980] Simulation [M. Huhtinen 2001] Defects can be electrically active (levels in the band gap) - capture and release electrons and holes from conduction and valence band can be charged - can be generation/recombination centers - can be trapping centers 11/26/2020 40

Impact of Defects on Detector properties Shockley-Read-Hall statistics (standard theory) Inter-center charge transfer model (inside clusters only) charged defects Neff , Vdep e. g. donors in upper and acceptors in lower half of band gap Trapping (e and h) generation CCE leakage current shallow defects do not Levels close to contribute at room midgap temperature due to fast most effective enhanced generation leakage current space charge detrapping Impact on detector properties can be calculated if all defect parameters are known: n, p : cross sections E : ionization energy Nt : concentration 11/26/2020 41

Radiation Damage: Effect on Neff Change of Depletion Voltage Vdep (Neff) …. with particle fluence: • “Type inversion”: Neff changes from positive to negative (Space Charge Sign Inversion) before inversion p+ n+ …. with time (annealing): • Short term: “Beneficial annealing” • Long term: “Reverse annealing” - time constant depends on temperature: ~ 500 years(-10°C) ~ 500 days ( 20°C) ~ 21 hours ( 60°C) - Consequence: Detectors must be cooled even when the experiment is not running! after inversion 11/26/2020 42

Depletion Voltage: Death of SVX Layer 0 Depletion Voltage (V) Steve Worm, Vertex 2003 Central Prediction +1σ Prediction – 1σ Prediction Data & Extrapolation 300 200 100 0 0 2 4 6 8 Integrated Luminosity (fb– 1) SVXII L 0 lifetime prediction based on Hamburg Model (M. Moll) - Will SVXII L 0 survive Run II ? -> Antonio’s Talk 11/26/2020 43

Radiation Damage – Leakage Current Change of Leakage Current (after hadron irradiation) …. with time (annealing): …. with particle fluence: 80 min 60 C o Damage parameter (slope in figure) Leakage current per unit volume and particle fluence o is constant over several orders of fluence and independent of impurity concentration in Si can be used for fluence measurement 11/26/2020 o Leakage current decreasing in time (depending on temperature) o Strong temperature dependence Consequence: Cool detectors during operation! Example: I(-10°C) ~1/16 I(20°C) 44

Recent Bias Current (Re-) Analysis L 0 P. Dong et. al, upcoming CDF note 11/26/2020 45

Radiation Damage – Trapping Deterioration of Charge Collection Efficiency (CCE) by trapping Trapping is characterized by an effective trapping time eff for electrons and holes: where …. . and change with time (annealing): Increase of inverse trapping time (1/ ) with fluence 11/26/2020 46

Decrease of Charge Collection Efficiency o Two basic mechanisms reduce collectable charge: – trapping of electrons and holes (depending on drift and shaping time !) – under-depletion (depending on detector design and geometry !) o Example: ATLAS microstrip detectors + fast electronics (25 ns) o p-in-n : oxygenated versus standard FZ - beta source - 20% charge loss after 5 x 1014 p/cm 2 (23 Ge. V) 11/26/2020 o n-in-n versus p-in-n - same material, ~ same fluence - over-depletion needed 47

Oxygenation Benefits • oxygenation increases radiation hardness Michael Moll, IWORID Glasgow 2004 • sometimes, standard FZ exhibits similar radiation hardness - reasons unclear • Concentrate R&D on CZ and EPI silicon 11/26/2020 48

Summary • Silicon strip detectors built on simple pn junction principle have become a ‘mature’ technology over 25 years. • Provide reliable tracking in high density/high rate environment • Widespread use thanks to cost drop and advances in microelectronic industry • Silicon Radiation hardness to a few 1015 p/cm 2 - radiation hardness frontier > 1016 p/cm 2 (SLHC inner pixel layer) - CZ, EPI, new materials/structures? • • Silicon People are fun to work with, outgoing and (usually) in a good mood (eh …) 11/26/2020 Have fun in California - You deserve it! 49

Backup 11/26/2020 50

Sensor Materials: Diamond, Si. C and Ga. N o o o R&D on diamond detectors: RD 42 – Collaboration http: //cern. ch/rd 42/ 11/26/2020 Wide bandgap (3. 3 e. V) lower leakage current than silicon Signal: Diamond 36 e/ m Si. C 51 e/ m Si 89 e/ m more charge than diamond Higher displacement threshold than silicon radiation harder than silicon (? ) Recent review: P. J. Sellin and J. Vaitkus on behalf of RD 50 “New materials for radiation hard semiconductor detectors”, submitted to NIMA 51

Microscopic defects Damage to the silicon crystal: Displacement of lattice atoms o Si. S particle EK>25 e. V V I EK > 5 ke. V 80 nm I V “point defects”, mobile in silicon, can react with impurities (O, C, . . ) point defects and clusters of defects Distribution of vacancies created by a 50 ke. V Si-ion in silicon (typical recoil energy for 1 Me. V neutrons): I V Vacancy + Interstitial Schematic [Van Lint 1980] Simulation [M. Huhtinen 2001] Defects can be electrically active (levels in the band gap) - capture and release electrons and holes from conduction and valence band can be charged - can be generation/recombination centers - can be trapping centers 11/26/2020 52

Radiation Damage in Silicon Close proximity to the interaction region means the sensors are subject to high doses of radiation o Two general types of radiation damage – “Bulk” damage due to physical impact within the crystal – “Surface” damage in the oxide or Si/Si. O 2 interface o Cumulative effects – – o Increased leakage current (increased Shot noise) Silicon bulk type inversion (n-type to p-type) Increased depletion voltage Increased capacitance Sensors can fail from radiation damage by virtue of… – Noise too high to effectively operate – Depletion voltage too high to deplete – Loss of inter-strip isolation (charge spreading) o Ratio of signal/noise is the important quantity to watch 11/26/2020 53

Bulk Damage – Depletion Voltage Depletion voltage is often parameterized in three parts (Hamburg model): DNeff(T, t, F) = NA + NC + NY o Short term annealing (NA) S NA = Feq iga, iexp(-ka, i(T)t) – Reduces NY (beneficial) – Time constant is a few days at 20 C o o Fig. 13: Annealing behaviour of the radiation induced change in the effective doping concentration Neff at 60 C. 11/26/2020 Stable component (Nc) Nc = Nc 0(1 -exp(-c. Feq))+gc. Feq – Does not anneal (does not depend on time or temperature) – Partial donor removal (exponential or limited exponential) – Creation of acceptor sites (linear) Figure 9: Dependence of Neff on the accumulated 1 Me. V neutron equivalent fluence for standard and oxygen enriched FZ silicon irradiated with reactor neutrons (Ljubljana), 23 Ge. V protons (CERN PS) and 192 Me. V pions (PSI). Long term reverse annealing (NY) NY = NY, ∞[1 -1/(1+ NY, ∞k. Y(T)t)], NY, ∞= g. YFeq – Strong temperature dependence – 1 year at T=20 C is the same as <1 day at T=60 C or ~100 years at T= -7 C (ATLAS) – Can be significant long term; must cool Si 54

Bulk Damage – Leakage Current o Defects created by bulk damage provide intermediate states within the band gap – intermediate states act as ‘stepping stones’ of thermal generation of electron/hole pairs – Some of these states anneal away; the bulk current reduces with time (and temperature) after irradiation o Annealing function (t) – Parameterized by the sum of several exponentials iexp(-t/ i) – Full annealing (for the example below) reached after ~1 year at 20ºC – At low temperatures, annealing effectively stops 11/26/2020 55

Bulk Damage Effects (Simple View) – Current depends on (t) (annealing function), V (volume), and F (fluence). – Annealing reduces the current – Independent of particle type o Depletion Voltage: Vdep = q|Neff|d 2/2 ee 0 – Depends on effective dopant concentration (Neff = Ndonors – Nacceptors), sensor thickness (d), permitivity (ee 0). – Depletion voltage is often parameterized in three parts: • Short term annealing (Na) • A stable component (Nc) • Long term reverse annealing (NY) 11/26/2020 Before Irradiation: Small area: small current Concentration (log scale) Leakage Current: DI = (t)FV P N Small difference: small depletion V After Irradiation: Large area: large current Concentration (log scale) o P N Large difference: Large depletion V 56

Bulk Damage – Leakage Results o Measured values of (t) – Typically one quotes measured values of (t) after complete annealing at T=20ºC: ∞ = (t=∞) – Some typical ‘world averages’ for ∞ are • 2. 2 x 10 -17 A/cm 3 for protons, pions • 2. 9 x 10 -17 A/cm 3 for neutrons – Recent results show (t=80 min, T=60ºC) = 4. 0 x 10 -17 A/cm 3 for all types of silicon, levels of impurities, and incident particle types (NIM A 426 (1999)86). 11/26/2020 Fig. 7. : Fluence dependence of leakage current for detectors produced by various process technologies from different silicon materials. The current was measured after a heat treatment for 80 min at 60 C [14]. Fig. 8: Current related damage rate as function of cumulated annealing time at 60 C. Comparison between data obtained for oxygen diffused silicon and parameterisation given in Ref. [14]. 57

Silicon Detectors – How They Work Rainer Wallny Silicon Detector Workshop at UCSB May 11 th, 2006 Slides ruthlessly stolen from: Paula Collins, CERN Alan Honma, CERN Christian Joram, CERN Michael Moll, CERN Steve Worm, RAL