1. Radiation Damage to Silicon Sensors DCC 11/14/02 DRAFT

2. Depletion Voltage V dep = d 2 Nq/2  – d = sensor thickness – N = Dopant concentration – q = 1.6E-19 C –  (Si) = 11.9  0 –  0 = 8.85E-12 F/m – V dep = 150V  N  3E12/cm 3  N 0 will be ~ 1 – 5 E12/cm 3. Change in V dep results from bulk damage (creation of vacancies and interstitials, and combinations of these with each other and with impurity atoms). –Bulk damage generally depends on NIEL-normalized flux. –By convention, flux is expressed in terms of “1-MeV neutron equivalent” flux, which by definition means NIEL = 95 MeVmb. –Bulk damage can be expressed in terms of a change in the effective dopant concentration, so that after exposure to radiation, V dep = d 2N eff q/2  N eff = N 0 +  N eff (due to radiation damage).

3. The Hamburg Model  N eff (  eq,t(T a )) = N A (  eq,t(T a )) + N C (  eq ) + N Y (  eq,t(T a )) –T a = Annealing temperature. –1 st term represents beneficial annealing: N A (  eq,0) = N A (  eq ); N A (  eq,  ) = 0. –2 nd term represents stable damage & has 2 components, donor removal and acceptor generation. For large doses, acceptor generation is dominant. –3 rd term represents reverse annealing: N Y (  eq,0) = 0; N Y (  eq,  ) = N Y (  eq ) For oxygenated sensors, damage does not scale with NIEL. Damage by neutrons is ~the same as for non-oxygenated sensors, but damage by charged hadrons is reduced. This is true at least for the 2 nd & 3 rd terms above (I can’t find information on the beneficial annealing term). Beneficial annealing time constant is ~ 2-3 days at 23 °C. Reverse annealing time constant is ~ 1.3 yr at 23 °C for standard silicon, & 3 – 6.5 yrs at 23 °C for oxygenated silicon. –Reverse annealing deviates from exponential for long times. –Reverse annealing of damage due to charged hadrons (not neutrons) saturates for oxygenated silicon (not for normal silicon).

4. The Hamburg Model - continued Both beneficial and reverse annealing are “frozen out” at –5 °C. Optimal scenario: run cold; heat up for ~2 weeks/yr. –Allows beneficial annealing, but ~no reverse annealing. –Only the stable damage term remains. “Warm running” scenarios also allow beneficial annealing, but do not completely freeze out reverse annealing. –Expression for N eff has 4 terms: Stable damage terms for neutrons & charged hadrons Reverse annealing terms for neutrons & charged hadrons

5. Neutrons, constant term,oxy Si Protons, constant term n, reverse annealing term, oxy Si p, reverse annealing term Plots are from the 3 rd ROSE status report. N C (n) = N C0 (1-exp(-c  eq )) + g C  eq N Y (n)=g Y  eq N C (p)=N C0 (1-exp(-c  eq )) + g C  eq Parameterization of radiation damage to oxygenated Si: N C0 = (initial dopant concentration)x0.44 c = 7.79E-14cm 2  1/1.3E13cm -2 g C = 2.00E-2cm -1 g Y = 4.7E-2cm -1 N C0 = (initial dopant concentration)x1 g C = 5.61E-3cm -1 N Y (p)=1.55E13(1-exp(-  eq /2.2E14) Donor removal Acceptor generation Note: 1) There are large variations in reported donor removal parameters (N C0 /N 0 & c). 2) Donor removal occurs rather quickly.

6. Reverse Annealing Time dependence = (1 – (1/(1+t/  Y ))) Temperature dependence:  Y (T) =  Y20 exp((1.33/8.617E-5)(1/293.15 – 1/T))

7. Leakage Current Leakage current is proportional to flux and depends exponentially on temperature. It scales with NIEL and is the same with or without oxygen. Assuming effective guard rings, leakage current is entirely bulk generated. The current is reduced by beneficial annealing. It is proportional to silicon volume and to effective flux. This dependence is reflected in the following formula by making  a function of both time and temperature: I =  eq V –Immediately after irradiation,  (room temp)  6E-17 A/cm. This drops to about 2E-17 after a long time. The ROSE result does not show a clear plateau in the value of  as time goes to infinity. –The official ROSE value of  is measured at room temperature, after 80 minutes annealing at 60 °C, and is 4E-17 A/cm. Rita’s 1 st number for SINTEF was 2.7E-17; more recent numbers for SINTEF & CiS measured with less beneficial annealing are ~4E-17 after correcting to 20 °C. –Leakage current is proportional to T 2 exp(-E g /2kT) (Eg = band gap energy = 1.12 eV; k = Boltzman constant = 8.62E-5 eV/degree K). –Example, for  eq = 1E15/cm 2 : Assuming full depletion can be maintained, the volume of a pixel =.04cm x.005cm x.025cm = 5E-6 cm 3. Using the ROSE value for , I = 4E-17 * 1E15 * 5E-6 = 200 nA. Our pixel requirements document says that the readout chip must be able to compensate for leakage current up to 100 nA.

8. From Abder Mekkaoui’s Pixel 2000 Talk Even 200 nA/pixel leakage current should not be a problem for FPIX2 (assuming the noise increase is not too large).

9. Leakage Current - continued Noise due to leakage current can be estimated using the effective integration time of the front end (50-70 ns?) Leakage current is compensated by an offsetting current. –Noise increase is due to fluctuations in the leakage current and in the compensating current. –These are two uncorrelated noise sources. –Leakage charge ~ (I leak x FE integration time)/(electron charge) –Example: I leak = 200nA Charge = (200E-9C/s x 70E-9s)/1.6E-19C/e- = 87500 e- If the initial noise is 100e-, then the noise including leakage current should be ~ sqrt(100 2 + 2x87500) = 430 e- Power dissipation due to leakage current = V bias *I leak A scale of power dissipation is given by the analog pixel cell (~50  W/pixel) and the LVDS drivers (4mA x 2.5V = 10mW/pair [21  W/pixel for innermost readout chip]).

10. Excel Model Approximate time & temperature dependence by assuming: –Luminosity = 2E32 cm -2 sec -1 for 1E7 seconds every year. –Dose occurs in one lump, ½ way through each year. –At least one warm-up per year (beneficial annealing is ignored). –Donor removal component of stable damage assumed to be proportional to total  eq with c = 7.79E-14cm 2 and N C0 = f x N 0. NOTE: N C0 =N 0 (complete donor removal) means that the depletion voltage after a large dose is independent of the original depletion voltage. –Leakage current calculated with  =2E-17. The following knobs are available: –Radial position in mm. –Initial depletion voltage. –Operating temperature. –Annealing time constant at 20  C. –f = fraction of donors removed as    –Effective front end integration time. Output: –Depletion voltage as a function of time. –Leakage current as a function of time. FE noise Power dissipation due to leakage current with V bias = V dep.

11. Model Result – Depletion Voltage Assumptions: Complete donor removal (final V dep independent of V 0 );  Y (20) = 3.2 & 6.5 yrs.

12. Model Result – Leakage Current noise = 245 e - noise = 154 e - noise = 115 e -  =2E-17; FE integration time assumed to be 55ns.

13. Tentative Conclusions Operation at 20°C is not ruled out, but is very sensitive to reverse annealing parameters. Sensitivity to reverse annealing parameters is reduced as temperature is lowered. Most of the benefit of low temperature (-10°C) operation is given by operation at +5°C.