# Summary of what seen so far Overview of charged or neutral particle interaction in matter Overview of detectors providing precise time measurement -> scintillators.

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Summary of what seen so far Overview of charged or neutral particle interaction in matter Overview of detectors providing precise time measurement -> scintillators Need them for Overview of detectors providing precise space measurement -> gaseous tracking chambers Need them for trigger lifetime measurement identification of particles direction, angle measurement momentum measurement identification of particles (using dE/dx differences)

Gaseous tracking chambers Typical resolution ? 200 micrometers space point resolution is quite typical

Gaseous tracking chambers What is the typical size (radial, longitudinal) at a collider experiment? Hint : what particle property do we want to measure ? and what polar angle distribution do we want to observe ? Radial : momentum measurement s=0.3 L 2 B / 8 p T e.g. s=0.15 cm for p T =10 GeV (150 micrometers is resolution) so typically need L~ meters Longit. : have as much acceptance as possible to measure eg. differential cross sections, etc.. Depends on the goals of experiment. Typically ~ meters

Gaseous tracking chambers: literature W.Leo pages 119 - 146 D. Green pages 151 - 176 Peter’s notes on ISIS web site (all lecture slides are there !)

Problem for today

electron positron B0 BaBar detector at Stanford Accelerator PEPII Ecms=10 GeV Y(4S) -> BB  =0.56 Problem will be about evaluation of BaBar detector design

Babar measure the amount of matter transforming into antimatter B0 can transform into B0 along the way (phenomenon called mixing) N B0 - N B0 N B0 + N B0 != 0 and depends on time t

Pros and cons ? Is the design appropriate to the physics goals? Can we suggest improvements? Babar physics goals which concern us today : - Measure very precisely the travel distance of the two B mesons - Measure very precisely the momentum of the particles coming from B meson decays

The B meson travels a distance L and then decays into particles a and c > The impact parameter “b” particle “a” also carries information about the lifetime of the B meson. so it is important to be able to measure that too. What is the expected value for “b” ? (hint: assume  small) b L  a c r z > What is the resolution needed to observe the decay length “L” and the impact parameter “b” ? We are happy if L / error(L) is > 3 B mesons (hadrons containing b quarks) have a mean lifetime  = 1.5 picoseconds. At the PEP collider B mesons are produced with a boost factor  ~ 0.5 > This means that they will travel on average a distance “L” = ?

A: b L  L=average distance travelled in mean lifetime by B meson =  c  = 0.56 * 1.5 ps * 3 10 8 m/s= 230 micrometers b ≈  L if  is small  = p T /p of decay particle B ~ M B /2 / p B /2 ~ 1/(  ) B => b ~ c  = 450 micrometers a c to observe L at least a 3 sigma significance, meaning that L/error(L) >3, we need maximal resolution to be 70 micrometers. For b is 150 micrometers. Asking for 3 sigma is really the minimum, one should need more.

So we need a different tracking device than the gaseous Ones, whose resolution is too coarse. Which one ? We need > Smaller resolution (electronic readout with higher granularity) > particles should loose little energy compared to initial energy > produce electronic signal high enough to detect particle and also fast enough to be readout before next collision event occurs silicon Which one?

Goals of the lecture Silicon detectors Reference: D.Green, pages 177-201. W.Leo, pages Example of silicon detectors in past and current experiments Reference: slides (and web links) Exercise : Pros and cons of the BaBar detector? Vertex reconstruction and kinematic fitting. Reference : slides (and web links) Identification of heavy quarks Reference: slides (and web links)

Semiconductors devices (besides book reference, veryy usefull to browse here http://jas.eng.buffalo.edu/index.html ) http://jas.eng.buffalo.edu/index.html

Solid state or semiconductor detectors are made of crystalline semiconductor material, typically silicon or germanium

Development really started in 1950’s At first used for high resolution energy measurement and were adopted in nuclear physics for charged particle detection and gamma spectroscopy Last 20 years, gained attention in high energy physics for high resolution fast tracking detectors. Basic operating principle is similar to gaseous devices: charged particle ionizes and creates electron-hole pairs which are the collected by an electric field. Photons will also be detected in solid state detectors, via photoelectric effect and then electron ionizes.

When isolated atoms are brought together to form a lattice, the discrete atomic states shift to form energy bands as shown below. Affects only the outer energy levels of atoms. Basic SemiConductor properties

Intrinsic conductivity of semiconductors Thermal excitation of charge carriers across gap http://jas.eng.buffalo.edu/education/semicon/fermi/functionAndStates/functionAndStates.html

k b T=0.026 eV at T=300K

n = density of electrons in the conduction band = 1/V ∫ f(E) g(E) dE Where (density of states) n And similarly for holes (Reference : http://britneyspears.ac/physics/basics/basics.htm) http://britneyspears.ac/physics/basics/basics.htm http://jas.eng.buffalo.edu/education/semicon/fermi/levelAndDOS/index.html

n i = AT 3/2 e (-Eg/2KT) n i = concentration of e (holes). E g = energy gap at 0 Kelvin Constantly : e/h pairs are generated by thermal energy. e and holes recombine. equilibrium T=0, no conduction T=300 K, pure Si, 1.5 10 10 cm -3 (Remember there are 10 22 atoms cm -3 ) -> Silicon is a poor conductor e -Eg/2KT ~ 10 -9 n electron= n holes in pure semiconductor ?

If one applies a electric field E to a semiconductor, e and holes start moving. Drift velocity : v e =  e E, v h =  h E  =mobility=f(E,T) T=300K, E<10 3 V/cm :  is constant E ~ 10 3 - 10 4 V/cm :  ~ E -1/2 E >10 4 V/cm :  ~ 1/E saturation v=10 7 cm/s  ~ T -m m=2.5 for e, 2.7 for holes in Si  e = 1350 cm 2 /Vs in Silicon -> v= 1.3 10 6 cm/s (gas was 10 5 cm/s) J = current = e n i (  e +  h ) E Conductivity ~ 1/ resistivity

Recombination and trapping e can fall back into valence band, but need exact energy -> rare Nonetheless lifetime for e and holes is ~ ns -> what happens ? Impurities or defects in the semiconductor ! additional levels in the forbidden gap time electron is free should be >> time takes to collect electron out of detector -> impurity concentration should typically be < 10 10 impurities cm -3 Recombination centre: This center can capture electron from conduction band and either release it back to the conduction band after a while or collect also a hole and e-hole annihilate Trapping center: This center can only trap an electron or a hole. They hold it and then release it after a while. http://jas.eng.buffalo.edu/education/semicon/recombination/indirect.html

N-Type P, As, Sb 5 electrons in the M-shell  1 electron with binding energy 10-50 meV B, Al, Ga 3 electrons in the M-shell  1 electron missing P-Type Doped SemiConductors.. When doping is actually good :)

0.05 eV in Si Amount of dopant is quite small typically (10 13 cm -3 ). N D + n= N A + p In n type N A =0, N D ~n p= n i 2 / N D -> conductivity is = e N D  e Fermi level much closer to conductive band or valence band Donor concentration determines conductivity

… but how can we use a piece of Silicon for detecting a high energy particle … ? + + - - V Is this going to work? Can you foresee any Problems ?

Intrinsic silicon will have electron density = hole density ~ 10 10 cm -3 In the volume above 4.5 10 8 free charge carriers But : only 3.2 10 4 produced by MIP (dE/dx in 300um Si divided by 3.6 eV). So, to use silicon as particle detector, we need to decrease number of free carriers How? We don’t like the thermal current ! - Reduce temperature ( need cryogenics, more expensive) - Create a free zone in the semiconductor

Reverse pn junction There must be a single Fermi level Deformation of band level Potential difference http://jas.eng.buffalo.edu/education/pn/pnformation3/index.html

Difference in concentration starts diffusion Perfect candidate for detector region

Solar cell Do we know an example of what a pn junction can be usefull for?

One can quickly establish the most critical parameters for a silicon detector by looking at the p,n junction above : Poisson’s equation : With charge density from 0 to x n and from –x p to 0 defined by : N D and N A are the doping concentrations (donor, acceptor). (semi-cond is neutral) The depletion zone is defined as : By integrating once the E(x) can be determined, E(x) = -eN D x /  + Cn 0 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/14/4216629/slides/slide_30.jpg", "name": "One can quickly establish the most critical parameters for a silicon detector by looking at the p,n junction above : Poisson’s equation : With charge density from 0 to x n and from –x p to 0 defined by : N D and N A are the doping concentrations (donor, acceptor).", "description": "(semi-cond is neutral) The depletion zone is defined as : By integrating once the E(x) can be determined, E(x) = -eN D x /  + Cn 0

by integrating twice the following two important relations are found : More in detail d=xn + xp =2  V 0 (N A + N D ) 1/2 e N A N D If N A >> N D d~xn ~ ( 2  V 0 /e N D ) 1/2 So in heavily doped p side, depletion region is all on the n side and viceversa. By increasing the voltage the depletion zone is expanded and C (capacitance) decreased – giving decreased electronics noise. Si d ~ (0.53  n V 0 ) 1/2  m for n type, (0.32  p V 0 ) 1/2  m for p type If  n ~ 20000  cm (resistivity) and V0=1 V, then d=75  m (very small) A=area of depletion zone, d its width

Field in a p-n junction is not intense enough to provide efficient charge collection thickness of the depletion zone will not be enough to detect high energy particles V is potential in figure f) of pn junction http://jas.eng.buffalo.edu/education/pn/pnformation3/index.html Solution: By applying an external voltage, we can enlarge the depletion zone and therefore the sensitive volume for radiation detection. The capacitance, hence the electronic noise, will also decrease

Reversed biased junctions http://jas.eng.buffalo.edu/education/pn/biasedPN2/BiasedPN2.html

The higher external voltage also helps increasing efficiency of charge collection. Max voltage appliable depends on the resistivity of the semiconductor. At some point junction will breakdown and begin conducting. In Si n-type, with V=300V a depletion d=1mm can be obtained Bigger d bigger resistivity (to postpone breakdown)

p+ implant n+ implant Si (n type) Basic scheme for operating a pn junction p+n junction, depletion region all in the n region (as seen) To collect charge, electrodes must be placed on both ends. But the ohmic contact cannot be made by directly depositing metal on the semiconductor (else a rectifing junction extending into the semiconductor is formed). So heavily doped layers of n+ or p+ are used between the semiconductor and the metal. Signal from incoming particle Is readout Typically, a preamplifier of charge-sensitive type, with low noise characteristics, is used to collect the charge out of the detector (~ 30000 eh pairs in 300 micrometers, need ampl.)

Signal formation in general terms For ionisation detectors we used energy balance to look at how a voltage signal was created due to charge drifting in the device. More general we have to use the Shockley-Ramo theorem for induced charge: The main message is that the signal, the electrical pulse on the electrodes is induced by the motion of charge after incident radiation (not when the charge reach the electrodes). For ionisation chambers it can be used to study not only the signal on the primary anode but also for the neighbours, or the cathode strips (if these are read out). For silicon detectors to study charge sharing between strips or pixels.

Let us have look at the signal formation using the same simple model of the detector as two parallel electrodes separated by d. A electric charge q moving a distance dx will induce a signal dQ on the readout electrode : dQ = q dx / d As in the case of the proportional chamber we use : giving where The time dependent signal is then : Pulse shape and rise time Q e (t) = e/d x 0 (1-exp  e t /  h )

The final result showing (when entering real numbers and using a more complete model) time-scales of 10/25 ns for electron/hole collection : However, there are many caveats: In reality one has to start from the real e/h distribution from a particle. Use a real description of E(x) taking into account strips and over- depletion. Traps and changes in mobility can also come in, etc From Leo n+ p x 0 d E eN A d/  + V - + - Qtot=e (integrated)

Leakage current Reverse biased pn junction does not conduct, ideally. In reality a small current always exists : leakage current. Appears as noise at the detector output. Sources: 1. Movement of minority carriers (nanoAmpers/cm2) 2. Thermally generated e/h due to impurities in depletion region (microAmp/cm2) 3. Largest source: leakage current through surface channels. depends on a lot of factors (surface chemistry, contaminants, etc.) clean encapsulation is usually required http://jas.eng.buffalo.edu/education/pn/biasedPN/index.html

Intrinsic efficiency and sensitivity Basically 100%. Limiting factor on sensitivity is noise from leakage current (  I) and noise from associated electronics ( C ) and thermal noise (  KT/R ) which sets a lower limit on the amplitude that can be detected Very important to choose correct depletion thickness, to ensure good signal

often require cooling to be operated, adds to material budget of detector  To summarize

Silicon based detectors

Silicon microstrip detectors pitch Voltage roughly 160 V

Q: Formula for resolution on position strip detector with pitch P=50 micrometers Q: what is the position resolution if the information saved is: which strip is hit ? Q: If one saves also the information: charge collected at each strip, can one think of improving the resolution ? y P

y P  2  ) 2 > = ∫ (y - ) 2 dy / ∫ dy between -P/2 and P/2 (continuous form) assume uniform illumination given =0  2 = ∫ y 2 dy /∫ dy = P 2 /12 So if P=50  m, then  = 15  m A: Reading out amplitude (of charge signal) at each strip, and weigthing positions with this, we can get better precision on position The position of the particle = the center of gravity of the charges collected at several readout strips.

Charge liberated by a charged particle is collected at the electrodes within 10 ns. Signals picked up at the strips measure the position with a precision dependent on the pitch of the strips. Detector with 20  m pitch, readout every 6 or 3 strips. Resolution r is respectively : When Magnetic field applied !

One can improve by reading out more strips (every one, eg.). Simplified readout in this case if possible, to put on detector the electronics associated with each strip Magnetic field (typically applied in high energy particle physics detectors) worsens the resolution and introduces a bias. Holes less mobile -> less angle

Not optimal

How to get 2-dim information real fake

Solid state pixel detectors Avoids problem with combinatorics and gives precise 3-D information

Precise 3D information : 20 x 20 x 20 micrometers pixels

Indeed we can clearly resolve decay distance “L” and impact parameter “b”

SLD

N+ 1 Column Parallel CCD New CCD detector being designed for next linear collider Unprecedented performance This is not possible at all colliders. Requires extremely precise steering and focusing of the beams

Reconstructed B decays Other examples of silicon detectors DELPHI

In both SLD and DELPHI detector we have mentioned the resolution on impact parameter “b” seen at start b L  a c  b = a + const/ (p sin  3/2 ) - do we understand why ? - how does the resolution on “b” influence the choice of design ? r z

r2 z b r1 z1 z2 (z2-b) / r2 = (z2-z1) / (r2-r1) b= (r2 z1 -r1 z2)/(r2-r1)  b 2 = (r2 2  z1 2 + r1 2  z2 2 ) / (r2 -r1) 2 Resolution on b indeed resol. on b is a constant, depends on point resolution of detector

how close one can get depends on radiation damage suffered (see later) if after z1 particle suffers multiple scattering then z2’ = z2 + (r2-r1)*  ms so  z2 2 =>  z2 2 + (r2-r1) 2 const / p 2 so we get now the term on  b dependent on p If r1=1cm and r2=1m and  z1 =10microns and  z2 = 200 microns (case of SLD vertex detector and gaseous tracking chamber) then clearly  b is good because the “near” measurement is good.  b 2 = (r2 2  z1 2 + r1 2  z2 2 ) / (r2 -r1) 2 -> it is a good idea to insert a high resolution detector close to the interaction point and eg. B decay point

DATA From H.F-W. Sadrozinski, UC-Santa Cruz 50 cost/area (\$/cm2) Moore's Law for Silicon Detectors Blank wafer price 6'' < 2 \$/cm2 1 2 10 4'' 6'' Wafer size

Now affordable also to cover large volume with silicon. Any disadvantages in using only silicon for tracking devices at collider experiments ? :( more multiple scattering :( more material, more energy loss :( Probability of brehmstrahlung for electrons is higher in Si (~Z^2 vs ionization that goes like Z), and also photons will convert in pairs more easily

CMS All silicon Inner tracking Detector (two single sided strip detectors, mounted back to back)

Radiation damage At the moment silicon detectors are used close to the interaction region in most collider experiments and are exposed to severe radiation conditions (damage).

The damage depend on fluence, particle type ( , ,e,n,etc) and energy spectrum. It affects both sensors and electronics.

Charged particle kicks a Si atom out of place in the lattice creating a vacancy. Threshold is 25 eV. Si atom can itself create damage on its own in a cascade process. High concentration of defects called “clusters”. These defects move around by diffusion. Create irreversible damage.

Three main consequences seen for silicon detectors : (1) Increase of leakage current

(2) Change in depletion voltage, problematic (3) Decrease of charge collection efficiency (less and slower signal)

Radiation levels in CMS Inner Tracker (0 < z < 280 cm) no damage moderate damage destruction (=J/Kg)

Or more advanced methods like …

backup

Front End electronics Most detectors rely critically on low noise electronics. A typical Front End is shown below : where the detector is represented by the capasitance C d, bias voltage is applied through R b, and the signal is coupled to the amplifier though a capasitance C c. The resistance R s represent all the resistances in the input path. The preamplifier provides gain and feed a shaper which takes care of the frequency response and limits the duration of the signal. The equivalent circuit for noise analysis includes both current and voltage noise sources labelled i n and e n respectively. Two important noise sources are the detector leakage current (fluctuating-some times called shot noise) and the electronic noise of the amplifier, both unavoidable and therefore important to control and reduce. The diagram below show the noise sources and their representation in the noise analysis :

Front End electronics While shot noise and thermal noise has a white frequency spectrum (dP n /df constant), trapping/detrapping in various components will introduce an 1/f noise. Since the detectors usually turn the signal into charge one can express the noise as equivalent noise charge, which is equivalent of the detector signal that yields signal-to-noise ratio of one. For the situation we have described there is an optimal shaping time as shown below : Increasing the detector capasitance will increase the voltage noise and shift the noise minimum to longer shaping times.

Front End electronics which shows that the critical parameters are detector capasitance, the shaping time , the resistances in the input circuit, and the amplifier noise parameters. The latter depends mostly on the input device (transistor) which has to optimised for the load and use. One additional critical parameter is the current drawn which makes an important contribution to the power consumption of the electronics. Practical noise levels vary between 10 2 -10 3 ENC for silicon detectors to 10 4 for high capasitance LAr calorimeters (10 4 corresponds to around 1.6fC).

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