CMS Pixel SimulationVincenzo Chiochia

Physik Institut der Universitt Zrich-Irchel CH-8057 Zrich (Switzerland)

PIXEL 2005 WorkshopChuzenji Lake, Nikko (Japan)November 7-11, 2005Quarter pixel: Electrostatic potential

OutlineThe CMS pixel detectorRadiation damage and impact on reconstructionBeam test data and detailed sensor simulationPhysical modelling of radiation damage:Models with a constant space charge densityDouble-trap modelsFluence and temperature dependence

The CMS pixel detector3-d tracking with about 66 million channels Barrel layers at radii = 4.3cm, 7.2cm and 11.0cmPixel cell size = 100x150 m2704 barrel modules, 96 barrel half modules, 672 endcap modules ~15k front-end chips and ~1m2 of silicon

The LHC radiation environment4 cm layer F=3x1014 n/cm2/yrFluence decreases quadratically with the radiusPixel detectors = 4-15 cm mostly pion irradiationStrip detectors = 20-110 cm mostly neutron irradiationFluence per year at full luminositysppinelastic = 80 mbL = 1034 cm-2s-1What is the sensors response after the first years of operation?

Radiation effects B fieldr-f planer-z planeno B fieldEIrradiation modifies the electric field profile:varying Lorentz deflection Irradiation causes charge carrier trapping E

Prototype sensors for beam testsn-in-n type with moderated p-spray isolation, biasing grid and punch through structures (producer: CiS, Germany)285 m thick DOFZ wafer 125x125 mm2 cell size, 22x32 pixel matrixSamples irradiated with 21 GeV protons at the CERN PS facilityFluences: Feq=(0.5, 2.0, 5.9)x1014 neq/cm2 Annealed for three days at +30 CBump bonded at room temperature to non irradiated front-end chips with non zero-suppressed readout, stored at -20C

Beam test setupData collected at CERN in 2003-2004

Charge collection measurementCharge collection was measured using cluster profiles in a row of pixels illuminated by a 15 beam and no magnetic field year LHC low luminosityFeq = 51013 n/cm2

Detector simulationChargedepositPIXELAVM.Swartz, Nucl.Instr. Meth. A511, 88 (2003);V.Chiochia, M.Swartz et al., IEEE Trans.Nucl.Sci. 52-4, p.1067 (2005).

The classic pictureAfter irradiation the sensor bulk becomes more acceptor-likeThe space charge density is constant and negative across the sensor thicknessThe p-n junction moves to the pixel implants side Sensors may be operated in partial depletionafter type inversionNeff=ND-NA

Models with constant NeffA model based on a type-inverted device with constant space charge density across the bulk does not describe the measured charge collection profilesF = 6x1014 n/cm2

Two traps modelsEConductionEValenceElectrontrapsHoletraps1.12 eVModel parameters(Shockley-Read-Hall statistics):EA/D = trap energy levelfixedNA/D = trap densitiesextracted from fitse/h = trapping cross sectionsextracted from fit

The double peak electric fielda) Current densityb) Carrier concentrationc) Space charge densityd) Electric fielddetector depthdetector depth

Model constraintsThe two-trap model is constrained by:Comparison with the measured charge collection profilesSignal trapping rates varied within uncertaintiesTypical fit iteration: (8-12h TCAD) + (8-16h PIXELAV)xVbias + ROOT analysis

Fit results Data--- SimulationF1=6x1014 n/cm2NA/ND=0.40sh/se=0.25

Scaling to lower fluencesNear the type-invesion point: the double peak structure is still visible in the data!Profiles are not described by thermodynamically ionized acceptors aloneAt these low bias voltages the drift times are comparable to the preamp shaping time (simulation may be not reliable)F3=0.5x1014 n/cm2NA/ND=0.75sAh/sAe=0.25sDh/sDe=1.00

Space charge densitySpace charge density uniform before irradiationCurrent conservation and non uniform carrier velocities produce a non linear space charge density after irradiationThe electric field peak at the p+ backplane increases with irradiationp-typen-typesensor depth (mm)V.Chiochia, M.Swartz,et al., physics/0506228

Temperature dependenceComparison with data collected at lower temperature T=-25 C.Use temperature dependent variables:recombination in TCADvariables in PIXELAV (m, D, G)The double-trap model is predictive!F2=2x1014 n/cm2T=-25 CF1=6x1014 n/cm2T=-25 CV.Chiochia, M.Swartz,et al., physics/0510040

Lorentz deflectiontan() linear in the carrier mobility (E):Switching on the magnetic fieldThe Lorentz angle can vary a factor of 3 after heavy irradiation:This introduces strong non-linearity in charge sharing

Conclusions and plansAfter heavy irradiation trapping of the leakage current produces electric field profiles with two maxima at the detector implants. The space charge density across the sensor is not uniform.What is the meaning of Vdep, depletion depth and type inversion? Measurements reflecting the electric field profile (e.g. TCT, CCE, long clusters etc.) are preferable to C-V characterization to understand radiation damage in running detectorsA physical model based on two defect levels can describe the charge collection profiles measured with irradiated pixel sensors in the whole range of irradiation fluences relevant to LHC operationOur model is an effective theory: e.g. in reality there are several trap levels in the silicon band gap after irradiation. However, it is suited for applications related to silicon detector operation at LHC. We are currently using the PIXELAV simulation to develop hit reconstruction algorithms optimized for irradiated pixel sensors.

ReferencesPIXELAV simulation:M.Swartz, CMS Pixel simulations, Nucl.Instr.Meth. A511, 88 (2003)Double-trap model:V.Chiochia, M.Swartz et al., Simulation of Heavily Irradiated Silicon Pixel Sensors and Comparison with Test Beam Measurements, IEEE Trans.Nucl.Sci. 52-4, p.1067 (2005), eprint:physics/0411143V. Eremin, E. Verbitskaya, and Z. Li, The origin of double peak electric field distribution in heavily irradiated silicon detectors, Nucl. Instr. Meth. A476, pp. 556-564 (2002)Model fluence and temperature dependence:V.Chiochia, M.Swartz et al., A double junction model of irradiated pixel sensors for LHC, submitted to Nucl. Instr. Meth., eprint:physics/0506228V.Chiochia, M.Swartz et al., Observation, modeling, and temperature dependence of doubly-peaked electric fields in silicon pixel sensors, submitted to Nucl. Instr. Meth., eprint:physics/0510040

Backup slides

EVL models100% observedleakage currents=1.5x10-15 cm230% observedleakage currents=0.5x10-15 cm2The EVL model based on double traps can produce large tails but description of the data is still unsatisfactoryF1=6x1014 n/cm2

E-field profilesConstantspace chargedensityDouble trapmodel

Scaling to lower fluencesF2=2x1014 n/cm2NA/ND=0.68sAh/sAe=0.25sDh/sDe=1.00Preserve linear scalingof Ge/h and of the currentwith FeqNot shown: Linear scaling of trap densities does not describe the data!!

Temperature dependenceCharge collection profiles depend on temperatureT-dependent recombination in TCAD and T-dependent variables in PIXELAV (me/h, Ge/h, ve/h)The model can predict the variation of charge collection due to the temperature changeT=-10CT=-25CF1=6x1014 n/cm2

Lorentz deflectionLorentz angleElectric field

Lorentz angle vs biasEffective Lorentz angle as function of the bias voltageStrong dependence with the bias voltage (electric field)Weak dependence on irradiationThis is a simplified picture!!Magnetic field = 4 T

ISE TCAD simulation

PIXELAV simulation

SRH statistics

SRH generation current

Test beam setupFour modules of silicon strip detectorsBeam telescope resolution ~ 1 mSensors enclosed in a water cooled box (down to -30C)No zero suppression, unirradiated readout chipSetup placed in a 3T Helmoltz magnetMagnetic field = 3 TorPIN diode trigger