Radiation Damage in Sentaurus TCAD David Pennicard – University of Glasgow

Overview Introduction to trap models Radiation damage effects and defects P-type damage model Some example simulations Sentaurus Device command file

Radiation damage introduction High-energy particle displaces silicon atom from a lattice site Results in a vacancy and an interstitial Atom can have enough energy to displace more atoms After damage is caused, most vacancy-interstitial pairs recombine Left with more stable defect clusters, e.g. divacancy (V2) Defect clusters affected by annealing conditions & impurities in the silicon Defect clusters give extra energy states (traps) in bandgap Increased leakage current Increased charge in depletion region (increase in effective p-type doping) Trapping of free carriers Can simulate this in Sentaurus Device by modelling behaviour of trap levels directly NB – when dealing with different types and energies of particle irradiation, scale fluence (particles / cm2) by non-ionizing energy loss. Standard is 1MeV neutrons. See M. Moll thesis, Hamburg 1999

Traps in Sentaurus Device A statement added to the Physics section can describe the traps: Parameters Acceptor: trap has –ve charge when occupied by electron, 0 charge when occupied by hole. (Donor has +ve charge when occupied by hole) Level: specifies how we describe energy level. Here, we give the energy below the conduction band. EnergyMid gives the energy difference Concentration: given in cm-3 Electron cross-section: proportional to probability of electron moving between trap and conduction band - σe Hole cross-section: likewise, proportional to chance of carrier moving between valence band and trap level - σp Physics (material="Silicon") { Traps ( (Acceptor Level fromCondBand Conc=1.613e15 EnergyMid=0.42 eXsection=9.5E-15 hXsection=9.5E-14) ) } Electron cross-section – proportional to empty trap capturing electron from conduction band Hole – prob of trap containing electron capturing hole from valence band. But, what about other processes? Electron from trap to conduction band, hole from trap to valence band?

Traps in Sentaurus Device For each trap level, Sentaurus simulates: Proportion of trap states occupied by electrons and holes NB – “not filled by electron”=“occupied by hole” This affects charge distribution, and so has to be included in Poisson equations Rate of trapping / emission between conduction band and trap, and between valence band and trap These then have to be included in the carrier continuity equations Poisson Electron continuity Hole continuity

Increase in reverse leakage current Leakage current increases with fluence, independent of substrate type Leakage current reduced by annealing α=3.99*10-17A/cm3 after 80 mins anneal at 60˚C (M. Moll thesis) Also, temperature dependence. α normally given for 20C

Increase in leakage current 2 transitions involved: Electron from valence band moves to empty trap, leaving a hole Electron in trap moves to conduction band, giving conduction electron Then, electron and hole are swept out of depletion region by field, avoiding recombination Rate of production limited by less frequent step (larger energy difference) Trap above midgap limited by rate of valence band->trap Traps below midgap likewise limited by trap->conduction band Rate drops rapidly with distance of trap from midgap Deep level traps dominate Ec Free electron produced Trap Emid Hole produced Ev

Change in effective doping concentration Effective p-type doping increases (giving type inversion in n-type silicon) Dependent on material, particularly oxygen content and radiation type for p-type (n-type also has “donor removal” effect) My models match p-type Float Zone irradiated with protons

Change in effective doping concentration Additionally, have both “beneficial annealing) in short term, and “reverse annealing” in long term Typically, test detectors after beneficial annealing, to try to find stable damage level All this implies very complicated defect behaviour!

Change in effective doping concentration Charge state of defect depends on whether it contains electron or hole Acceptor: -ve when occupied by electron Donor: +ve when occupied by hole Source of –ve charge that gives effective p-type appears to be acceptors above midgap A small proportion of these traps are occupied by electrons Number of traps occupied once again is highly dependent on distance from bandgap Donors below bandgap can give +ve charge, but relatively minor effect Ec Acceptor Trap - - Emid Hole produced Ev

Charge trapping Number of free carriers in device decays exponentially over time Described by effective lifetime: Experimentally, effective lifetime varies inversely with fluence (this has been tested up to 1015neq/cm2) G. Kramberger, Trapping in silicon detectors, Aug. 23-24, 2006, Hamburg, Germany

Charge trapping In equilibrium, traps above Emid are mostly unoccupied Free electrons in conduction band can fall into unoccupied trap states Likewise, traps below midgap contain electrons – can trap holes in valence band Effect is less energy-dependent Similar equations for holes Ec Trap Emid Trap Ev Afterwards, carrier can be released from trap If trap levels are reasonably close to midgap, detrapping is slow So, less effect on fast detectors for LHC

University of Perugia trap models IEEE Trans. Nucl. Sci., vol. 53, pp. 2971–2976, 2006 “Numerical Simulation of Radiation Damage Effects in p-Type and n-Type FZ Silicon Detectors”, M. Petasecca, F. Moscatelli, D. Passeri, and G. U. Pignatel Ec Perugia P-type model (FZ) 0.9 2.5*10-15 2.5*10-14 CiOi Ec+0.36 Donor 5.0*10-14 5.0*10-15 VVV Ec-0.46 Acceptor 1.613 2.0*10-14 2.0*10-15 VV Ec-0.42 η (cm-1) σh (cm2) σe (cm2) Trap Energy (eV) Type - The paper here is the most recent publication from the University of Perugia, but their previous simulation papers are also useful for reference. - - Ev 2 Acceptor levels: Close to midgap Leakage current, negative charge (Neff), trapping of free electrons Donor level: Further from midgap Trapping of free holes

University of Perugia trap models Aspects of model: Leakage current – reasonably close to α=4.0*10-17A/cm Depletion voltage – matched to experimental results with proton irradiation with Float Zone silicon (M. Lozano et al., IEEE Trans. Nucl. Sci., vol. 52, pp. 1468–1473, 2005) Carrier trapping – Model reproduces CCE tests of 300m pad detectors But trapping times don’t match experimental results Experimental trapping times for p-type silicon (V. Cindro et al., IEEE NSS, Nov 2006) up to 1015neq/cm2 βe= 4.0*10-7cm2s-1 βh= 4.4*10-7cm2s-1 Calculated values from p-type trap model βe= 1.6*10-7cm2s-1 βh= 3.5*10-8cm2s-1

Altering the trap models Priorities: Trapping time and depletion behaviour Leakage current should just be “sensible”: α = 2-10 *10-17A/cm Chose to alter cross-sections, while keeping σh/σe constant Carrier trapping: Space charge: Modified P-type model 0.9 3.23*10-14 3.23*10-13 CiOi Ec+0.36 Donor 5.0*10-14 5.0*10-15 VVV Ec-0.46 Acceptor 1.613 9.5*10-14 9.5*10-15 VV Ec-0.42 η (cm-1) σh (cm2) σe (cm2) Trap Energy (eV) Type

Comparison with experiment Compared with experimental results with proton irradiation Depletion voltage matches experiment Leakage current is 30% higher than experiment, but not excessive “Comparison of Radiation Hardness of P-in-N, N-in-N, and N-in-P Silicon Pad Detectors”, M. Lozano et al., IEEE Trans. Nucl. Sci., vol. 52, pp. 1468– 1473, 2005 α=5.13*10-17A/cm α=3.75*10-17A/cm The leakage current is about 30% higher than experiment. These simulations do not attempt to model leakage current accurately – it’s only important that the leakage is physically reasonable. Experimentally, α=3.99*10-17A/cm3 after 80 mins anneal at 60˚C (M. Moll thesis)

N+ on p strip detector: CCE At high fluence, simulated CCE is lower than experimental value Looked at trapping rates using 1D sim – as expected Trapping rates were extrapolated from measurements below 1015neq/cm2 In reality, trapping rate at high fluence probably lower than predicted PP Allport et al., IEEE Trans. Nucl. Sci., vol 52, Oct 2005 900V bias, 280m thick As mentioned earlier, the simulation assumes the trapping rate measured up to 1015neq/cm2 continues up to 1016neq/cm2. Other simulations which make the assumptions give similar results. Also, the experimental results themselves aren’t completely linear; the parameter beta drops slightly at higher fluences (see V. Cindro et al., IEEE NSS conference record, Nov 2006). Back of envelope – beta gives us 0.25ns effective lifetime, vsat=1E7 cm/s, get drift distance 25um, hence 2ke- signal. From β values used, expect 25μm drift distance, 2ke- signal

Example - Double-sided 3D detector Electrode columns etched from opposite sides of silicon substrate Short distance between electrodes Expect reduced depletion voltage and faster collection (less trapping) Unlike most 3D devices, the double-sided 3D detector can be biased from the back side. Because the depletion region grows outwards from the n+ column (which is etched from the front surface) the back surfacce is difficult to deplete.

Example - Double-sided 3D at 1016 neq/cm2 Plotted electric field in cross-section at 100V bias Where the columns overlap, (from 50m to 250m depth) the field matches that in the full-3D detector At front and back surfaces, fields are lower as shown below Region at back is difficult to deplete at high fluence A. 1016neq/cm2, front surface 1016neq/cm2, back surface A. B. 100V 100V Unlike most 3D devices, the double-sided 3D detector can be biased from the back side. Because the depletion region grows outwards from the n+ column (which is etched from the front surface) the back surfacce is difficult to deplete. Undepleted B.

Example - Collection with double-sided 3D Slightly higher collection at low damage But at high fluence, results match standard 3D due to poorer collection from front and back surfaces. 20% greater substrate thickness Uniformity? Hadn’t considered this.

Sentaurus Device command file See Sentaurus/Seminar/RadDamage: StripDetectorRadDamage_des.cmd StripDetectorRadDamage_Param_des.cmd Traps added to silicon Insert appropriate concentrations, or use a “Fluence” variable in Workbench Physics (material="Silicon") { # Putting traps in silicon region only Traps ( (Acceptor Level fromCondBand Conc=@<Fluence*1.613>@ EnergyMid=0.42 eXsection=9.5E-15 hXsection=9.5E-14) (Acceptor Level fromCondBand Conc=@<Fluence*0.9>@ EnergyMid=0.46 eXsection=5E-15 hXsection=5E-14 ) (Donor Level fromValBand Conc=@<Fluence*0.9>@ EnergyMid=0.36 eXsection=3.23E-13 hXsection=3.23E-14 ) ) }

Sentaurus Device command file Extra variables can be added to “Plot” Warning – trap models are sensitive to changes in the bandgap and temperature Don’t change the “effective intrinsic density” model – alters bandgap Likewise, keep using default 300K temp. (Strictly speaking this is slightly wrong, since the standard test temp should be 20C.) Plot { ……… eTrappedCharge hTrappedCharge eGapStatesRecombination hGapStatesRecombination } Physics { # Standard physics models - no radiation damage or avalanche etc. Temperature=300 Mobility( DopingDep HighFieldSaturation Enormal ) Recombination(SRH(DopingDep)) EffectiveIntrinsicDensity(Slotboom)

Sentaurus Device command file Oxide charge increases after irradiation Electron-hole pairs produced in oxide – holes become trapped in defects in oxide, giving positive charge Saturates fairly rapidly – 1012cm-2 is a normal value after irradiation, though some papers claim up to 3*1012cm-2 X-ray irradiation causes oxide charging, but little bulk damage Other points More complicated physics tends to give slower solving, and poorer convergence: may need to alter solve conditions (smaller steps etc) For charge collection simulations, need to correct the integrated current to remove the leakage current CV simulations give strange results! Physics(MaterialInterface="Oxide/Silicon") { Charge(Conc=1e12) }

Example files See Sentaurus/Seminar/RadDamage StripDetectorRadDamage_des.cmd Basic MIP simulation at 1015neq/cm2 This has already been run You can look at the output files in the same folder .dat files taken during IV ramp .dat files taken during the MIP transient .plt files StripDetectorRadDamage_Param_des.cmd _des.cmd file for a Workbench project Use parameter “Fluence” to control the radiation damage Uses #if statements to omit “Traps” statement and use lower oxide charge if Fluence is zero Works with simple StripDetector.bnd/cmd files in Workbench folder Email: d.pennicard@physics.gla.ac.uk