Tests of semiconductor microstrip detectors of ATLAS detector

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Charles University in Prague

Faculty of Mathematics and Physics

DIPLOMA THESIS

Pavel ˇ Rezn´ ıˇ cek

Tests of semiconductor microstrip detectors of ATLAS detector

Institute of Particle and Nuclear Physics

Supervisor: Dr. Zdenˇ ek Doleˇ zal Study programme: Physics

Study field: Nuclear and Subnuclear Physics

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I would like to thank to my supervisor Dr. Zdenˇek Doleˇzal for his leading of my diploma thesis, for inspiring discussions and ideas. For help in building of the test setup I would like to thank all the members of the VdG accelerator lab at Institute of Particle and Nuclear Physics MFF UK, especially to Dr. Peter Kodyˇs who together with my supervisor introduced me into the problematics of the tests of ATLAS microstrip detectors.

Many thanks belong to Bettina Mikulec and Rainer Wallny for their consultations of radioactive source tests analysis and patience with testing my software during measurements at CERN. Concerning computer simulations I’m very grateful to Szymon Gadom- ski, the author of the simulation software, who instructed me how to use the software, and to Grant Gorfine for his help with Geant4 simulations. For the provided beam tests data and discussions of features of the simulation I want to thank to Marcel Vos and Jose Enrique Garcia Navarro. For help with experiencing the standard and beam module tests I wish to thank to Gareth F. Moorhead, Monica D’Onofrio, Mariane Mangin Brinet, Mauro Donega, Lars Eklund, Peter W. Phillips, the author of the standard software used for module tests, and many other ATLAS SCT developers I met during my diploma thesis training.

Finally I’m very grateful to many members and students of Institute of Particle and Nuclear Physics MFF UK for their suggestive questions.

Prohlaˇsuji, ˇze jsem svou diplomovou práci napsal samostantnˇe a výhradnˇe s pouˇzit´ım citovaných pramen˚u. Souhlas´ım se zap˚ujˇcován´ım práce.

I declare that I wrote my diploma thesis independently and exclusively with the use of the cited sources. I agree with lending the thesis.

Prague, 17^th April 2003 Pavel ˇRezn´ıˇcek

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Abstrakt: C´ılem této diplomové práce bylo provádˇen´ı a vývoj test˚u detekˇcn´ıch modul˚u vnitˇrn´ıho detektoru ATLAS. V práci jsem se zamˇeˇril na testy pomoc´ı radioaktivn´ıho β⁻ záˇriˇce. V Praze byla vyvinuta aparatura a napsán software pro mˇeˇren´ı a analýzu dat. Smyslem tˇechto test˚u bylo doplnˇen´ı mˇeˇren´ı provádˇených na svazku z SPS v CERNu, tedy provˇeˇren´ı skuteˇcných detektˇcn´ıch vlastnost´ı modul˚u. Výsledky test˚u se záˇriˇcem a na svazku byly porovnány a byl nalezen vztah mezi mˇeˇrenými signály. Mˇeˇren´ı ukázala, ˇze pomˇer stˇredn´ı energie, kterou záˇriˇcem emitovaný elektron ztrat´ı pˇri pr˚uchodu mod- ulem, ku signálu zjiˇstˇenému z dat test˚u na svazku je 1.109±0.070. Pro úplné pochopen´ı tohoto rozd´ılu byla provedena simulace obou typ˚u test˚u. Simulaci mˇeˇren´ı na svazku jsem pouˇzil k ovˇeˇren´ı simulaˇcn´ıho softwaru. Výsledkem je dobrá shoda trend˚u úhlových a jiných závislost´ı s daty, ovˇsem v absolutn´ıch hodnotách docház´ı k podhodnocen´ı mˇeˇreného signálu. Proto jsem provedl pouze relativn´ı srovnán´ı simulovaných odezev modul˚u z obou typ˚u test˚u. Simulace pˇredpov´ıdá pomˇer stˇredn´ıch signál˚u z test˚u na svazku v˚uˇci test˚um se záˇriˇcem: 1.117±0.020. Tyto testy se tedy, vzhledem k dobˇre definovanému vztahu jejich výsledk˚u v˚uci výsledk˚um mˇeˇren´ı na svazku, staly vhodným nástrojem pro ovˇeˇren´ı detekˇcn´ıch vlastnost´ı modul˚u.

Kl´ıˇcová slova: Kˇremíkové stripové detektory, Testy záˇriˇcem, Testy na svazku, Geant4, SCT, ATLAS

Title: Tests of semiconductor microstrip detectors of ATLAS detector Author: Pavel ˇRezn´ıˇcek

Department: Institute of Particle and Nuclear Physics Supervisor: Dr. Zdenˇek Doleˇzal

Supervisor’s e-mail address: Zdenek.Dolezal@mff.cuni.cz

Abstract: The setup of system for testing silicon microstrip detectors with ⁹⁰Sr source of electrons was developed. The aim of the measurements was to determine the median signal of particle passing through prototype modules for the ATLAS semiconductor tracker.

Comparison to beam tests results was performed to check the consistence of the source tests results. The ratio of signals measured in beam tests to the source tests signal is about 1.109±0.070. To fully understand the results computer simulation of the setups was performed. The beam tests simulation, used to validate the simulation software, resulted in good description of trends of observed characteristics but in underestimation of the signal. The source test simulation confirmed the relation of the beam tests results to the source tests: the ratio of simulated median signal of beam tests to source tests was about 1.117±0.020. The defined relation of beam and source tests measurements made the radioactive source tests usable for the signal determination.

Keywords: Silicon microstrip detectors, Source tests, Beam tests, Geant4, SCT, ATLAS

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1 Introduction

The semiconductor detectors in high energy physics are mostly used for precise measurement of particles’ tracks. If placed in a magnetic field the detectors provide high accuracy momentum measurement. According to relatively high energy loss (hundreds of eV/µm) of charged particle passing through the semiconductor, low energy needed to release free charge carriers (several eV for creation of electron-hole pair) and possibility of creation of fine structures (in the order of µm) of various properties, the semiconductor detectors can measure the position with an accuracy of several µm. This makes the detectors be able to detect secondary vertexes of decays of very short time living particles.

In the Center of European Nuclear Research (CERN) new hadron collider (LHC) is being built. One of 4 detector systems at the LHC will be the ATLAS, described in section 2. One part of it will be a semiconductor tracker consisting of silicon strips detector modules.

This diploma thesis deals with tests and simulations of the SCT modules. The first parts of this thesis describe general properties and usability of semiconductors as detectors, while the rest concerns SCT modules only. The standard quality assurance (QA) procedure described in section 4.3consists of detector tests and tests of readout electronics. One of the main characteristics of SCT modules is the signal to noise ratio (S/N).

While the QA tests are able to find the noise, signal can be determined by using real particles only. For this purpose SCT modules were tested in beam on SPS at CERN (see section 4.4). Because of the high cost and unavailability of beam tests, method using the β⁻ radioactive source for signal measurement has been developed and results of several modules shown insection 6.4 were compared to the results of ATLAS simulation and digitization software described in sections 5.1 and 5.2. The simulation and digitization software has been validated on the beam-tests data in section 5.3, that were analyzed by other SCT groups [10]. Because of very high luminosity of the LHC, SCT modules will operate in high radiation environment. So the tests were focused on measurement of properties of modules irradiated to dose equivalent to the dose after 10 years of operation of the ATLAS detector system. Most of the tests were done on irradiated forward modules, however several were performed on unirradiated as well.

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2 ATLAS detector system

The ATLAS (A Toroidal LHC ApparatuS) detector system [1] is general-purpose detector which is designed to exploit the full discovery potential of Large Hadron Col- lider (LHC). The LHC properties (energy of interacting protons 7 TeV, expected luminosity 10³⁴ cm⁻²s⁻¹) offer a large range of physics opportunities. The major ATLAS interest is the origin of mass at the electroweak scale based on spontaneous symmetry- breaking. One of the possible manifestation of spontaneous symmetry-breaking mechanism is the existence of standard model Higgs boson or of a family of Higgs particles.

Alternative manifestation could involve a strongly interacting Higgs system. Other goal are the searches for heavy W- and Z-like objects. Considering their leptonic decays, high resolution lepton measurements and charge identification are needed even in the range of few TeV. For supersymmetric particles searches hermecity and missing transverse energy ET capability of the detector is necessary. Another class of signatures of a new physics like the composition of the fundamental fermions can be provided by very high transverse momentum p_T jet measurements. An important chapter of the LHC will be a high rate b- and t-quark factory. The main emphasis in B-physics will be on precise measurement of CP violation, determination of the angles in CKM unitary matrix and general spectroscopy of states with b-quarks.

The set of ATLAS physics goals demonstrates that sensitivity to a variety of final states signatures is required. The basic design considerations lead to the following ATLAS detector systems: electromagnetic calorimetry for electron and photon identification and measurement, hermetic jet and missing ET calorimetry, tracking for lepton momentum measurement, forb-quark tagging, for electron and photon identification and for tau and heavy-flavour vertexing. The other features are stand-alone, precision muon momentum measurements, large acceptance in η-coverage and triggering and measurements of particles at low-pT thresholds. The ATLAS detector system is shown in figure 1 and described below.

The ATLAS magnet system consists of a solenoid and air-core toroids. The 2 T solenoid is positioned in front of the barrel electromagnetic (e.m.) calorimeter. In order to avoid degrading the e.m. calorimeter performance the thickness of the solenoid had to be minimized. The superconducting coil is integrated into vacuum vessel of the calorimeter barrel cryostat to eliminate the material and space of independent vessel walls. The dimensions of the solenoid are 1.22 m in radius and 5.3 m in length. The superconducting toroid magnet system consists of 26 m long barrel part with outer diameter 19.5 m and inner bore of 9.4 m, and of 2 end-caps with length 5.6 m and bores of 1.26 m. Magnetic induction varies from 3 Tm⁻¹ to 8 Tm⁻¹. The curved trajectories of charged particles in the magnetic field allow momentum measurement using the inner detector and muon chambers tracking data.

The calorimetry of ATLAS consists of an inner barrel cylinder and end-caps using liquid argon (LAr) technology, that is intrinsically radiation resistant, and hadronic scintillator tile calorimeter surrounding the LAr one in full length. The barrel part of the liquid calorimetry includes a presampler detector for correction to the influence of solenoid coil of the thickness of 0.83·X0 at normal incidence. The minimal thickness of the e.m. barrel calorimeter is 26·X0, while in case of end-caps calorimeters the minimal thickness is 27·X0. The hadronic scintillator tile calorimeter is based on a sampling technique with plastic scintillator plates (tiles) placed in plane perpendicular to the beam axis and embedded in iron absorber and read out by wavelength shifting fibers. The outer radius of the whole calorimetry system is 4.23 m and total length is 6.7 m. This high performance system must be capable of reconstructing the energy of electrons, protons and jets as well as

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measuring missing E_T.

The muon detector system involves 3 layers of chambers in the barrel part and 3 or 4 layers in the end-cap part. In the barrel region 2 muon chamber planes are attached to the magnetic toroids and the third one is in the mid-plane to measure the sagitta.

In the forward region the chambers are placed at the front and back faces of the toroid cryostats, with a third layer against the cavern wall to maximize the lever arm of the point- angle measurement. Every chamber consists of detectors for the precision measurement and for the triggering. In the barrel part, 2 multilayers of drift tubes are used for precision measurement while in the end-cap part cathode strip chambers are used in addition. For triggering resistive plates are used in the barrel region and thin gap chambers in the end-cap region. The basic measurement in each muon chamber is a tracks segment, providing a vector for robust pattern recognition and momentum determination.

Figure 1: The ATLAS detector system.

The inner detector system [2] shown figure 2 and covering range of pseudorapidity

|η|<2.5 is composed of 3 different detectors: semiconductor pixel detector, semiconductor strip detector and transition radiation tracker. The nearest one to the beam pipe is the pixel detector. It is designed to provide a very high-granularity and high-precision set of measurements as close to the interaction point as possible. The system consists of 3 layers in the barrel part and 4 disks in the end-cap part, and offers 140 million detector elements, each 50 µm in the Rφ direction and 300 µm in the z. The maximal radius of barrel layer is 14 cm and of forward disk is 20 cm. The total length is 2.2 m.

The furthest part of the inner detector system is the transition radiation tracker based on straw tubes. Electron identification capability is added by employing xenon gas to detect transition radiation photons created in radiator between the straws and by using 2 independent thresholds for tracking hits and transition radiation hits. The technique allows typically 36 measurements to be made on every track. The diameter of every straw is 4 mm and drift-time measurements give a spatial resolution of 170µm. The maximum

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straw length is 150 cm. In the barrel region straws are parallel to the beam direction and perpendicular in the end-cap region. The middle part of the inner detector is the silicon strip detector - semiconductor tracker (SCT) - consisting of 4 barrel layers and 9 forward wheels. The SCT system is designed to provide 4 precision measurements per track in the intermediate radial range and contributing to the momentum, impact parameter and vertex position measurement. The maximum radius of the barrel layer is 52 cm and 56 cm of the forward wheel. The system requires very high dimensional stability, cold operation of the detectors and evacuation of heat generated by the electronics and detector leakage current.

Forward SCT

Barrel SCT

TRT Pixel Detectors

Figure 2: The inner detector.

The group of VdG accelerator at Institute of Particle and Nuclear Physics (IPNP) of Faculty of mathematics and physics at Charles University in Prague has been involved in working places where QA tests of 200 SCT forward detector modules will be performed.

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3 Semiconductor detectors

3.1 Comparison to other detectors

Semiconductor detectors are in high energy physics mostly used for precision tracking that allows detection of secondary vertexes of very fast decaying particles. The advantages of semiconductor detectors compared to the others being used for tracking are following:

• The gap energy between valence and conduction band is 1.11 eV in silicon and so the average energy for creation of electron-hole pair (e-h) is 3.6 eV. That is approximately 10 times lower compared to the ionization energy of gases used in proportional chambers, drift chambers, time projection chambers etc.

• Due to high density of semiconductors, the average energy loss per unit of length is also higher according to the energy loss in gases. In case of silicon and minimum ionizing particle (MIP) the value is 390 eV/µm while for the gases the loss is 3 orders of magnitude lower. Consequently the thickness of semiconductor detectors can be very small which minimizes the multiple Coulomb scattering. Usual thickness is around 300µm.

• Another advantage connected to the high density is the reduction of range of energetic secondary electrons that leads to good spatial resolution.

• The present advanced technology of silicon detector production allows creation of very fine structures on them (in the dimensions of micrometers). The dimensions of the structures (usually strips or pixels) then mainly contribute to the resolution of the semiconductor detectors.

• Since the readout electronics is usually based on semiconductor technology, the detectors and electronics can be integrated together. Noise of such a module is than reduced.

• These detectors are mechanically rigid and so not complicated supporting structures are needed.

• High mobility of the charge carriers results in high rate of reading and lower dead time. Typical width at half maximum (FWHM) of the read out pulse is 20 ns.

But the semiconductor detectors have beside their high cost also one disadvantage compared to the gaseous detectors. It is the absence of multiplication of the amount of primary generated charge carriers and so the signal is only a function of the detector thickness.

3.2 Silicon properties

Silicon is an element of IV group of the group of elements and has 4 electrons on the valence shell. All the conductivity is realized by electrons excited from the valence band into the conducting one. Such an excitation leads to a generation of hole - empty state that left after the electron excitation and that behaves as a positively charged particle.

In the silicon without impurities the densities of electrons and holes are the same. By re- placing some of the silicon atoms by atoms from the III or V groups the p- or n-type materials are obtained. Elements from the III group (acceptors) have 3 valence electrons and easily attach an electron from silicon atoms. Elements from the V group (donors)

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have one very weakly bound electron that can be easily excited to the conduction band.

The ”binding” energy of electrons in n-type and of holes in p-type silicon semiconductor is approximately 45 meV. Very heavily doped semiconductors are marked n⁺ or p⁺ respectively. In bothn- andp-type semiconductors there are the other type carriers as well, due to thermal excitations, called minority carriers.

The density of intrinsic charge carriers is [4]:

n(T) =

Z ∞ Eg

D_e(E, T)f_e(E, T)dE (1)

whereDe(E) is the state density [3]:

D_e(E) = 1 2π²

2m_e

¯ h²

3/2

(E−E_g)^1/2 (2)

and fe(E) the Fermi-Dirac function for system of fermions:

fe(E) = 1

e^E^−EF^kT + 1 (3)

The used symbols are the energy of electrons E, the Fermi level EF, the gap energy Eg, the temperature T, the Boltzmann constant k, the Planck constant ¯h and the effective electron massmeconnected to the second derivative of energy as a function of momentum.

Application of equations (2) and (3) in (1) and use of similar relations for the density of holes p(T) results in:

n(T) = 2

mekT 2π¯h²

3/2

e^EF^kT^−Eg (4)

and

p(T) = 2

mhkT 2π¯h²

3/2

e^−EF^kT (5)

In Si without any impurity both densities are equal (ni) and do not depend on the Fermi level:

n(T)p(T) =n²_i = 4

kT 2π¯h²

3

(memh)^3/2e^−Eg^kT (6) In doped silicon of densities of NA acceptors and ND donors the relation (6) still holds since compared to intrinsic semiconductor it is the Fermi level E_{F e} that changes only.

The extrinsic carrier densities follow equations coming from zero net charge density [5]:

n =nie^{EF e−EF}^kT = 1 2

hND−NA+^q(ND −NA)²+ 4n²_iⁱ≈ND (7) and

p=nie^EF^{−EF e}^kT = 1 2

hNA−ND +^q(ND−NA)²+ 4n²_iⁱ≈NA (8) where the approximations are valid when ND NA, ni , (n p) and NA ND, ni , (pn) respectively.

Properties of silicon material are written in table 1. Particle passing through the detector ionizes the Si atoms and so effectively creates the e-h pairs. For typical thickness of silicon detector 300µm the number of generatede-hpairs by MIP passing perpendicular through the detector (seesection 3.6) is 3.2·10⁴ which is 4 orders magnitude lower than the total number of free carriers in intrinsic silicon of a surface of 1 cm² and the thickness mentioned above. In doped material the S/N ratio would be even smaller. One way to increase the ratio, is to cool the semiconductor. Another way is to deplete the detector of free carriers through a reverse biases P-N junction. The second way is the principle of operation of a silicon radiation detectors.

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Atomic number 14

Atomic weight 28.08

Atomic density 4.99·10²² cm⁻³

Density 2.33 g/cm³

Dielectric constant 11.6

Gap energy 1.11 eV

Effective states density in conduction band 2.80·10¹⁹ cm⁻³ Effective states density in valence band 1.04·10¹⁹ cm⁻³ Electron mobility 1350 cm²V⁻¹s⁻¹

Hole mobility 480 cm²V⁻¹s⁻¹ Electron Hall mobility 1670 cm²V⁻¹s⁻¹

Hole Hall mobility 370 cm²V⁻¹s⁻¹ Electron diffusion constant 34.6 cm²s⁻¹

Hole diffusion constant 12.3 cm²s⁻¹ Intrinsic carrier density 1.45·10¹⁰ cm⁻³

Breakdown field 30 V/µm

Diamond type lattice spacing 0.5431 nm Mean energy for e-hpair creation 3.63 eV

Fano factor 0.115

Table 1: The physical properties of silicon at room temperature.

3.3 Drift and diffusion

Drift of charge carriers is their movement under external field E. The speed~ ~v of such a movement is proportional to the external field:

~v=∓µ ~E (9)

where the coefficientµof the proportionality is mobility of electrons and holes respectively.

Movement of charge carriers under magnetic fieldB~ results in change of the movement direction by Lorentz angle ϑL:

tanϑL =µHB (10)

The coefficient µH is Hall mobility.

For silicon with inhomogeneous carriers density the mean movement of the carriers of charge q is, due to thermal fluctuations, nonzero and follows the opposite direction of the densityn gradient:

F~ =−D ~∇n (11)

This equation expresses the proportionality of flow F~ to the density gradient ∇~n using the diffusion coefficientD. This coefficient is related to the mobility by Einstein equation:

D= kT

q µ (12)

coming from the zero value of sum of drift and diffusion flows.

3.4 The P-N junction

As mentioned above, reverse biased P-N junction reduces the number of free carriers.

Due to gradient of electrons’ and holes’ densities in the junction of n- and p-type semiconductors, the free charge carriers diffuse and recombine. The result is net positive and

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negative charge in the n- and p-type materials respectively. This region of net charge called depletion region causes built-in potential barrier that, assuming NA, ND ni, can be calculated from [5]:

VD = EF A−EF N

q = kT q ln

NAND

n²_i

(13) with EF A and EF N being the Fermi levels inn- and p-type crystals respectively.

The depletion region can be widened by applying reversed potential V_bias on the P-N junction. The barrier height would than beVB =Vbias+VD. The electric field distribution can be obtained by solving a one-dimensional Poisson equation:

d²V

dx² =∓qN

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LetWAandWD be the width of depletion layers where uniform net charge densities areNA

and ND in the p and n regions respectively. Considering the neutrality of the crystal (NAWA=NDWD) the solution of the Poisson equation is [5] (see figure 3):

W_A=

s 2V_B

qNA(1 +NA/ND) ≈

s2V_B qND · N_D

NA

(15) and

WD =

s 2VB

qND(1 +ND/NA) ≈

s2VB

qND

(16) where is the permitivity of silicon. Choosing the material so that NA ND (see the approximation), the depletion region is wide on then-side and shallow on the p-side.

Since there is a voltage dependent charge increment dQ=qNdW that appears on ei- ther side of the junction as a result of the widening of the depletion region on that side dW, caused by an increase of the barrier voltage dVB, then it is possible to define junction capacitance [5]:

Cj = dQ dVB

= dQ dW · dW

dVB

=

s qNAND

2(NA+ND)VB ≈

sqND

2VB

(17) The capacitance decreases with rising bias voltage until depletion layer reaches the back of the crystal. Such a VB is called depletion voltage Vdep.

3.5 Reverse current

The depletion region is free of majority carriers, but under equilibrium conditions e-h pairs are generated continuously anywhere within the volume of the crystal. In opposite to non-biased detector, the created carriers have little chance to recombine. The pairs are separated and electrons and holes drift under the influence of the electric field. This current is called leakage or reverse current. Depending on where the e-hpair is generated there are 2 components: a generation current of density jgen caused by charge generated within the depletion region and a diffusion current j_diff coming from charge generated in the neutral silicon and diffusing to the depletion region.

Assuming very low charge densities n, p ni in the depletion zone of width W and effective life time τ0 of minority carriers [5]:

jgen = 1

2qni(T)

τ₀ W(Vbias) (18)

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Acceptor ion hole

Donor ion electron

P N

x [mm]

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

Charge density [C/m]

-0.0015 -0.001 -0.0005 0 0.0005 0.001

x [mm]

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

Electric field [V/m]

-1 -0.8 -0.6 -0.4 -0.2 0

x [mm]

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

Potential [V]

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Figure 3: The charge density, electric field (intensity) and potential in the P-N junction.

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The temperature dependence is only through n_i(T). Considering equation (6) n_i(T) increases by factor of 2 with a temperature increase of 8 K. The current is proportional to√

Vbias, whenVbias is lower than depletion voltage, and constant above it.

Pairs e-h generated in the neutral region in the proximity of depletion one have a chance to diffuse into it before recombination. Denoting by τe and τh the lifetimes of electrons and holes in the n- and p-type region respectively, the width of the layer from which carriers would diffuse is [5]:

L=√

Dτ (19)

where D is the diffusion coefficient for proper free carriers of density n. The diffusion current can be than calculated from:

jdiff =qn

τL (20)

3.6 Interactions of particles in silicon

There are two mechanisms of energy loss of charged particles in solids: the ionization and the bremsstrahlung. Important part of the ionization process is the release of high energy electrons (δ-electrons) that increase the mean energy loss. Another important effect is the Coulomb scattering resulting in beam divergence after passing through the detector.

The mean energy loss due to ionization of particle of charge z, mass M and velocity (in units of speed of light c) β =√

1−γ⁻², is described by Bethe-Bloch formula:

−

dE dx

ion =

Z _T_max

Tmin

T ne

dσRuth

dT dT = 2· 2πα²¯h²z² meβ²

Z

AρNA·ln

Tmax

Tmin

(21) whereT is the energy loss, ne is the density of electrons of mass me in material of atomic numberZ, atomic weightAand densityρ,σRuthis the Rutherford scattering cross-section, α is the fine structure constant and NA is the Avogadro constant. The minimum energy loss Tmin is equal to the ionization potentialI0 ≈16·Z^0.9 [6], while the maximum energy loss is:

Tmax = 2mec²β²γ²

1 + 2γ^m_M^e + (^m_M^e)² (22)

The factor of 2 in relation (21) accounts for such effects as atomic excitation. Modification of the formula (21) for fast electrons was found to be [9]:

−

dE dx

ion,e⁻

= 2πα²h¯²z² m_eβ²

Z AρNA

ln

m²_ec⁴β²γ 2I²(1−β²)

−ln 2

2 γ − 1

γ²

+ 1 γ² + 1

8

1− 1 γ

2

(23) The statistical fluctuations around the mean energy loss in a layer of thickness δx are described by Landau, Vavilov or Gaussian theory, depending on ratio κ, that is proportional to the ratio of mean energy loss to the Tmax:

κ= ξ Tmax

= 2πα²¯h²NAz²Zρ meβ²A · δx

Tmax

(24) The assumptions on Landau theory are that the ratioξ/I0 1 and that the typical energy loss is small compared to Tmax and is large compared to the binding energy of the most tightly bound electrons. The Landau distribution function is shown in figure 4. The first restriction is removed in the Vavilov theory. According to the assumptions, Landau

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Energy loss [keV]

50 100 150 200 250 300

Number of events

0 50 100 150 200 250 300 350 400

Figure 4: Simulated energy loss of 180 GeV negative pions using Geant4 and distribution function of Landau theory (solid curve).

theory can be used whenκ <0.01, while the Vavilov theory is used when 0.01< κ <10.

In the region of κ > 10 which describes non-relativistic particle energy loss, Gaussian distribution can be applied, assuming a large number of collisions involving the loss of most of the incident particle energy,

The tail in the region of high energy loss in Landau distribution is caused by high energetic electrons (δ-electrons) released by the incoming particle and resulting in sig- nificantly higher average energy loss than the most probable value. Since the range of the δ-electrons is in the order of 10 µm (40 µm for 100 keV electron), they can cause displacement of the measured track position. The number ofδ-electrons of energy higher than Tδ is [8]:

dN_δ

dx = 2πα²h¯²z² meβ²

Z

AρN_A·δx Tδ

(25) A δ-electron of kinetic energy Tδ is produced at an angleθδ determined by relation [8]:

cosθδ = Te

pe · pmax

Tmax

(26) wherepmax and pe are momenta corresponding to the kinetic energies.

Another mechanism of energy loss important for e^∓ is the electromagnetic radiation (bremsstrahlung) described by formula [9]:

−

dE dx

brem,e⁻ = α²¯h²γZ(Z+ 1)N_Aρ 137meA

4 ln(2γ)− 4 3

(27) The relative influence of ionization and bremsstrahlung in solids is described by critical energy [8]:

E_c= 610

Z + 1.24·M eV (28)

Assuming thickness of the layer being passed through δx X0, with X0 = 9.36 cm being the radiation length in silicon, the mean number of radiated photons with energies

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between E_γmin and E_γmax is [8]:

Nγ = δx X0

4 3ln

Eγmax

Eγmin

−4(Eγmax−Eγmin)

3mec²γ +(Eγmax−Eγmin)² 2(mec²γ)²

(29) The coulomb scattering at small angles [8] of particle of momentum ppassing through a thin layer is described by RMS of Gaussian distribution of deflection angles:

P(Θ) = 1

q2πΘ²_{RM S} ·exp

Θ² Θ²_{RM S}

dΘ (30)

Θ_{RM S} = z·21MeV βcp

sδx X0

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3.7 Microstrip detectors

Schematic diagram of n-type microstrip detector is shown in figure 5. The main part of the depletion region is in the weakly doped n-type material (see formula (16)).

Particle traversing through the detector creates e-h pairs along its path. The number of the pairs is proportional to the energy loss described in section 3.6. Since the detector of thickness dis reverse biased the generated carriers drift along the electric fieldE(x) [7]

towards the strips and backplane:

E(z) =−V_bias+V_dep

d + 2V_dep d

z

d (32)

The carriers diffuse in the direction~x perpendicular to the electric field. The distribution of number of holes and electrons after drift to the strips and backplane respectively follows the Gaussian law:

dN = 1

q2π[2Dt(z) +δ²] ·exp

− x² 4Dt(z) + 2δ²

N(z)dzdx (33)

where dN is the charge in the element dx, at distance x from the track, and coming from the charge N(z)dz generated in the element dz of the track at distance z from the strips. N(z) is the linear density of the generated charge. The other used symbols are diffusion coefficient D, width of the track δ and the time of charge carriers driftt(z) from the place of generation to the strips and backplane. The drift time can be calculated combining definition (9) and relation (32):

th(z) = d² 2Vdepµh

ln

(Vbias+Vdep)d (Vbias+Vdep)d−2Vdepz

(34) for holes and:

te(z) = d² 2Vdepµe

ln

(Vbias+Vdep)d−2Vdepz (Vbias−Vdep)d

(35) for electrons respectively. The product of D·t(z) is independent of µand so is the width of the distribution.

When measuring the amplitude of the signal on each strip (analog readout), partial reconstruction of the distribution is possible, which results in much better localization precision compared to strip pitch p:

∆x≈ p

S/N (36)

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When binary readout is used, signal on the strips is compared to a given threshold and the RMS of the measured and real track position ∆x² can be calculated, assuming no charge loss, from formula:

∆x² = 1 p

Z +p/2

−p/2 x²dx= p²

12 (37)

The charge division between the strips can be realized in resistive or capacitive way.

The resistive one leads to noise generation. The capacitive one is naturally realized by interstrip capacitance, but there is a non-linearity and charge loss due to strip-by-strip and strip-ground capacitance.

As mentioned insection 3.1one of the advantages of semiconductor detectors is the integration of the sensitive material and the read out electronics. There are 2 possible ways of such integration: direct connection (see left part of figure 5) where reverse current flows through the electronics or capacitive connection (see right part of figure 5) where only current changes are detected by the electronics. The capacitorC can be easily implemented on the detector using a layer of SiO2 as well as the bias resistor R using polysilicon.

n⁺ Al

p⁺ p⁺

Al Al

n SiO2

+ - + - + - + - + -

+ - + -

z

d dx x

Front-end electronics

particle

C R

Figure 5: The slice ofn-type microstrip detector with DC-readout (left) and AC-readout (right).

3.8 Noise

Referring to section 3.1 there is no multiplication of the amount of generated charge carriers. In events with tracks crossing the detector between 2 strips or at large angles, due to charge sharing, only a fraction of total charge is collected on each strip. To distinguish the real signal, low noise is essential. The electronics and detector itself contribute to the noise in different ways:

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• The main contribution comes from the capacitance of the strip being read out to its neighbours and to the backplane. It causes a signal loss and acts as a load capacitance C of the preamplifier. For conventional charge sensitive amplifier the electronics noise is calculated as equivalent noise charge (ENC) from the formula:

EN Cload =A+B·C (38) whereA and B are constants depending on the preamplifier.

• Another contribution is the equivalent noise referred to the input of the amplifier from the leakage current I and is given by:

EN C_leak = e q

sqITp

4 (39)

where e is natural logarithm base, q is the electron charge. and Tp is the peaking time equal to the integration time of a CR-RC shaper. The peaking time differs from the integration time for other types of shapers.

• Bias resistor R contribute to the noise as well by following formula:

EN Cbias = e q

sTpkT

2R (40)

with k being the Boltzmann constant and T temperature.

The error in measurement of the signal caused by all these contributions can be obtained as their sum in squares:

EN C =^qEN C_load² +EN C_leak² +EN C_bias² (41)

3.9 Radiation damage

As ATLAS will operate in high radiation environment, changes to the properties particles with the nuclei in the lattice may lead to permanent material changes due to following processes:

• Displacement of lattice atoms leading to interstitials and vacancies

• Nuclear interactions

• Secondary processes from energetic displacement lattice atoms leading to possible defect clusters

Most of the primary defects are mobile at room temperature and will therefore par- tially anneal. However, there are also stable defects: combination of vacancy and oxy- gen (A-center), a vacancy phosphorus complex (E-center) and 2 vacancies next to each other (divacancy). Although the primary interaction of radiation with silicon is strongly particle-type and -energy dependent, due to smoothing out by secondary interactions and considering non-defect-producing interactions with electrons, it is possible to use scaling by the non-ionizing energy loss (NIEL) of 1MeV neutrons.

The defects can act as trapping centers reducing signal and as recombination centers leading to an increase of the leakage current. They can change the resistivity of undepleted

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regions and charge density in the depleted region, thus requiring an increase of depletion voltage. In case of n-type detector, long term radiation leads to effective type inversion.

Damage in electronics has different effect as induced change in doping concentration is not important due to much higher doping densities than in detectors. The most important effects are the damage on silicon oxide layers in metal-oxide-semiconductor field effect transistors (MOSFET) and the decrease of minority carriers lifetime in case of bipolar and junction field effect transistors (JFET). The effects lead to decrease of amplification characteristics of transistors and increase of noise.

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4 Detector modules

4.1 Construction

Every SCT module consists of 2 or 4 silicon strips detector wafers connected by fan-ins to a hybrid with 12 readout chips. The detectors are glued on a mechanical basement.

The typical surface of the sensitive wafers is 6×6 cm². There are 4 types of the SCT modules (see figure 6): a barrel module and 3 forward modules differing in the number of detectors and their geometry. In modules with 4 silicon wafers, the detector wafers are bonded to 2 pairs and so providing effectively 2 sensitive wafers of length approximately 12 cm.

Figure 6: The barrel module (top left), forward outer module (bottom left), forward middle module (bottom right), forward inner module (top right).

All the silicon wafers are single sidedp-in-ndetectors, 285µm thick and containing 768 Al strips 23µm wide. Every module has 2 parallel detector planes and thus 1536 readout channels. The 2 planes are rotated by an angle of 40 mrad to provide 2D track position measurement by combining the hit strips numbers. The strip pitch of barrel detectors is constant: 80 µm. Thus taking into account the cylindrical coordinate system (R,Φ,z) withz direction parallel to the beam pipe, the point resolution is 23µm (see formula (37)).

Combining the 2 points from both detector planes gives precision of 16 µm in the RΦ- direction and 580µm in thez-direction. The forward detectors differ from the barrel ones by non-parallel strips converging to one point close to the beam line for easy extraction of the (R,Φ,z) coordinates of the measured tracks. The strip pitch varies from 54 µm up to 95µm and consequently the point resolution is position dependent. While the plane of the barrel detectors is parallel to the beam direction, the forward modules’ detector planes are perpendicular to it and so the last mentioned precision is not in thez-direction but in the R-direction for forward modules.

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Readout buffer Compression Format Control 128 strips x 132 cells

pipeline

Data Out

Calibration pulse

Threshold Discriminator Comparator Preamplifier

Shaper

Detector

Strips

Figure 7: The FE and readout electronics.

The ATLAS SCT readout electronics is responsible for supplying the hits information to the ATLAS 2^nd level trigger and data acquisition system. To ensure low noise operation, front-end (FE) electronics is mounted immediately at the strips’ electrodes. There are 12 readout chips on hybrid of every module and every chip reads out 128 channels (strips). The chips on the first and second module side are marked M0 S1 S2 S3 S4 E5 and M8 S9 S10 S11 S12 E13 respectively (see figure 8). The ATLAS SCT uses binary

Detectors

Mechanical basement

Bonds

Chip S3 Chip S4 Chip E5

Chip S2 Chip S1 Chip M0 Fan-ins

Hybrid

Figure 8: Module description.

readout (signal on strips is compared to a given threshold) to reduce the amount of data to be transmitted and stored. The schematics diagram [11] of FE architecture is shown in figure 7. The data from the strips are every 25 ns (LHC bunch crossing rate) stored into chips’ pipelines and are held there for the duration of the level 1 trigger (L1) la- tency waiting for the decision to transmit the data or discard it. The average trigger rate of the FE electronics operation is 100 kHz. If the data are to be read out, they are compressed and transmitted out using optical fibers. To suppress noisy hits (clusters of channels where read signal is greater than set threshold), certain type of data readout and compression based on special timing pattern recognition can be applied. Important feature of the electronics is the calibration circuit allowing to associate threshold on discriminator to an appropriate charge at the input of the preamplifier. To obtain the best

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possible uniformity of the calibration process, thresholds can be adjusted individually for every channel. This process is called trimming. The chips and hybrid construction allows to bypass non-functional chips and there is a redundant optical connection to fix possible failure of the standard one.

4.2 Read out system

The schematic diagram of the readout system for QA procedures for a single module is shown in figure 9. The hardware is based on Versa Module Eurocard (VME) modules of the following functionality:

PC ROOT

VME controller SCTLV3 SCTHV MuSTARD CLOAC SLOG PPR

VME crate

Clean room

Slow control systemCooling

Module box

Support card

Figure 9: The readout system for a single module.

• SCTLV3 module [12] provides low voltages (digital 4.0 V, analog 3.5 V) to the readout electronics and assures monitoring of the temperature and power consumption.

• SCTHV module [13] provides bias voltage for the detectors and monitors the leakage current.

• MuSTARD module [14] reads out and stores the data from the hybrid

• CLOAC module [15] and SLOG module [16] generate command sequences like trigger, calibration and reset signals. The latest ones resend configuration to the chips to correct possible loss of threshold and other settings. The CLOAC module allows use of external triggers (for example from a scintillator in beam tests) and can fan- out the command sequences that were sent to the readout electronics. The later mentioned feature can be used to trigger a laser.

• VME controller assures communication of the modules with personal computer.

• The PPR together with the support card are passive components connecting data links from the hybrid and the VME modules.

The data acquisition (DAQ) software [18] is based on ROOT [17] - a C++ interpreter with additional classes for easy data manipulation and visualization. The software con- tains a buttons control panel, ROOT interactive window and a basic information panels showing data control system (DCS) monitoring and the occupancy of the strips after applied a burst of triggers, results of performed scans etc.

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As the silicon modules have to be tested in a clean environment, clean room was built for this purpose at IPNP [28]. Typical readout system for QA allows to test up to 6 modules in parallel. Since the modules have to be cooled during the tests and humidity reduction by flowing a dry air on the modules is needed to prevent shorts at the detector, the tested devices are placed into special boxes. The monitoring of the environment conditions, data backup and solving of accidents like power failure, is assured by slow- control system [26].

4.3 Standard QA tests

The standard QA procedure includes tests of the detectors and functionality tests of the readout electronics. The quality of the detector wafers is checked by measurement of the leakage current as a function of bias voltage. Example of this IV-curve is in figure 10. Accounting the dependence of depletion layer width on the bias voltage, the relation (18) for generation current is valid up to 300 V, where the avalanche effects start to modify the shape of the IV-curve, and the depletion voltage is around 60 V. Ap- plying in the relation (18) τ0 = 1 ms [4] gives the generation current of 2 µA. This value is consistent in the order with the measured one. Precise comparison is complicated due to τ0 dependence on the temperature and number of impurities in the silicon. The used value of 1 ms is a very rough approximation for weakly dopedn-type silicon. In addition the diffusion current j_diff was neglected.

0 50 100 150 200 250 300 350

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Bias [V]

Leakage current [A]m

0 100 200 300 400 500

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Bias [V]

Leakage current [A]m

Figure 10: The IV-curve of unirradiated (left) and irradiated (right) module. Monitored temperatures on the hybrids were around 25 Celsius degrees on the unirradiated module and 0 Celsius degrees on the irradiated one.

The tests of the readout electronics involve bypass and redundancy tests, but the most important part is the calibration process including trimming and noise occupancy measurement. Another issue is the long-term stability test lasting 24 hours. Since the SCT readout is binary, it is not possible to find the amplitude of the signal directly by one measurement, but integral of the spectrum of the signal can be obtained by scanning the threshold to which the signal is being compared. If the signal is generated by charged particle passing through the detector, one obtains integral of the Landau curve, while for signal coming from the calibration circuit, the result is an error function, because the charge provided by calibration circuit has a narrow Gaussian distribution. The real measured sigma of the Gaussian function is higher and is equal to the noise (see section 3.8) assuming Gaussian distribution of the noise with given sigma equal toEN C and zero mean. Example of such an error function is shown in figure 11. The noise occupancy measurement (see figure 12) is a simple high statistics threshold scan with no calibration charge applied. The trimming (see figure 13) is done for selected calibration charge

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Amplitude [fC]

-2 -1 0 1 2 3 4

Spectrum

0 0.2 0.4 0.6 0.8 1

Threshold [fC]

1 1.5 2 2.5 3 3.5 4 4.5 5

Number of hits

0 200 400 600 800 1000

Figure 11: The threshold scan (right) of single channel with 0.2 fC step and with zero- width calibration charge of 3 fC - see dashed curve in figure (left). For every set threshold, the calibration pulse was applied and signal was read out 1000 times. The his- togram (right) shows the number of events when the read out signal was greater than the threshold. The dashed curve corresponds to ideal readout with no noise, while the full one is the smeared by Gaussian distribution of the noise (left).

by scanning the threshold and tuning the readout chips’ settings so that the threshold of 50% efficiency (median) is uniform over all channels as much as possible. The calibration process consists of scanning the calibration charge and calculating the appropriate median of threshold scan for every setting of the charge. Example of such a dependence called response curve is shown in figure 14. The derivative of the response curve deter- mines gain of the FE preamplifiers. The aim of these tests is to check whether the module matches the specifications (see section 4.4) on the rate of noisy hits and the purpose of the calibration is to find the threshold of around 1 fC, where the efficiency should be high enough.

Channel number

100 200 300 400 500 600 700

Threshold [mV]

0 20 40 60 80 100 120 140

10^-7 10^-6 10^-5 10^-4 10^-3 10^-2 10^-1 1

Threshold [mV]

0 20 40 60 80 100 120 140

Noise occupancy

10^-7 10^-6 10^-5 10^-4 10^-3 10^-2 10^-1 1

4.88E-006

Figure 12: The noise occupancy scan of KB-105 module. The left figure shows the occupancy separately for every channel, while the on the right average noise occupancy of the 6 chips (1 side of the module) is shown. The marked point is the noise occupancy at 1 fC threshold.

The radiation damage influences properties of both the sensitive wafers and the readout electronics. The latter mentioned can be seen in an increase of the leakage current

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and consequently the noise occupancy, depletion voltage increases as well. From the beam tests (see section 4.4) decrease of the amount of collected charge is obvious. In the electronics the radiation affects noise and gain. The irradiation of the modules is performed at CERN PS by 24 GeV protons to the dose of 3·10¹⁴ protons/cm² during approximately 2 weeks. The typical characteristics for both the irradiated and unirradiated modules of 4 detector wafers are summed in table 2. Note the higher noise occupancy, leakage current and bias voltage needed for operation of irradiated modules compared to unirradiated ones. In spite of the fact that the median collected charge in irradiated detectors is lower and so is the efficiency, the average size of strips clusters (see section 4.4) is the same as for the unirradiated ones. This is due to stronger charge sharing in the irradiated detectors. The lower gain of the FE electronics confirms the effects of radiation on the electronics described above.

Channel number

100 200 300 400 500 600 700

Pulse amplitude [mV]

40 60 80 100 120 140 160

Channel number

100 200 300 400 500 600 700

Pulse amplitude [mV]

40 60 80 100 120 140 160

Figure 13: The points of 50 % efficiency from threshold scan of all channels of KB-105 module before (left) and after trimming (right) showing better uniformity of the measured signal amplitudes after trimming.

Calibration charge [fC]

0 1 2 3 4 5 6 7 8

Gain [mV/fC]

0 10 20 30 40 50 60 70 80 90 100

0 1 2 3 4 5 6 7 8

Median [mV]

0 100 200 300 400 500 600

0 1 2 3 4 5 6 7 8

ENC

0 500 1000 1500 2000 2500

Figure 14: The results of M0 chip calibration of module KB-105: response curve (left), FE electronics gain (center) and ENC (right).

4.4 Beam tests

To verify the efficiency of the modules in detecting particles, prototypes of the modules were tested in beam of SPS at CERN. The schematic diagram of the beam tests setup is shown in figure 15. The modules were placed in a light-tight box with integrated cooling system. To find the efficiency of the tested devices, positions of the particles’ tracks must

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Quantity Unirradiated modules Irradiated modules

Efficiency [%] 99.5 99.0

Noise occupancy 10⁻⁶ .. 10⁻⁵ 10⁻⁴ .. 10⁻³

Cluster size 1.27 1.26

Median [fC] 3.4 2.7

Leakage current [µA] 1 2000

FE gain [mV/fC] 50 35

Used bias voltage [V] 150 350

Table 2: The characteristics of SCT modules: unirradiated modules, irradiated modules.

The presented values are given at 1 fC threshold and cluster size at incidence angle 16 degrees. The values are typical as they vary from module to module. The leakage currents correspond to measurements with monitored temperatures on the hybrids around 0 Cel- sius degrees.

be known. This information is provided by 4 silicon strip detectors of strips pitch 50µm and analog readout. The precision of this telescopes is up to 5µm (see formula 36). There are 3 important characteristics of the measurements:

• Efficiency - the number of events when there is a cluster of neighbouring strips with read signal greater than the threshold and the track given by the telescopes is not too distant (<150 µm) from the position of the center of such a cluster of strips.

• Median - the threshold where the efficiency reaches 50% (see section 4.3).

• Noise occupancy - probability that there will be a signal on a strip greater than the threshold and the position of the strip is far from the track in the detector determined by the telescopes.

• Cluster size - an average width of the hit strips clusters that are assumed to be caused by the particle passing through the detector (see the definition of the efficiency).

Light-tight box

B

Tested modules Analogue

telescopes Beam

Scintillators

in coincidence Analogue

telescopes

&

trigger signal

Figure 15: The beam tests setup.

There are 3 possible effects that lead to the existence of 2- and more-strips clusters:

• δ-electrons with range sufficient to reach also the strips neighbouring to the nearest one.

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• Charge sharing between strips due to possible non-perpendicular incidence angle and due to diffusion of the generated charge carriers as they always drift to the nearest strip (see figure 17).

• Cross-talk between strips due to their capacitive coupling.

The region of interest is at around 1 fC threshold where efficiency has to be sufficiently high (>99%) and noise occupancy low (<5·10⁻⁴) as defined in the Technical Design Re- port (TDR) [2] to provide the expected reconstruction capability. Another important characteristics are the dependence of the median (and consequently the efficiency) and cluster size on the incidence angle and change of the response in magnetic field of 1.56 T.

The precise information about the track positions allowed to study the characteristics at the edges of the detectors and to measure the median and cluster size dependence on the relative position (η) of the track position with respect to the position of the strips.

Results of the beam tests can be found in [10].

Tests of semiconductor microstrip detectors of ATLAS detector

Charles University in Prague

Faculty of Mathematics and Physics

DIPLOMA THESIS

Pavel ˇ Rezn´ ıˇ cek

Tests of semiconductor microstrip detectors of ATLAS detector

Institute of Particle and Nuclear Physics

Supervisor: Dr. Zdenˇ ek Doleˇ zal Study programme: Physics

Study field: Nuclear and Subnuclear Physics

Contents

1 Introduction

2 ATLAS detector system

Forward SCT

Barrel SCT

TRT Pixel Detectors

3 Semiconductor detectors

3.1 Comparison to other detectors

3.2 Silicon properties

3.3 Drift and diffusion

3.4 The P-N junction

3.5 Reverse current

P N

3.6 Interactions of particles in silicon

3.7 Microstrip detectors

3.8 Noise

3.9 Radiation damage

4 Detector modules

4.1 Construction

4.2 Read out system

4.3 Standard QA tests

4.4 Beam tests

&