Radiation Damage to Silicon Sensors

1
Radiation Damage to Silicon Sensors
DRAFT

• DCC 11/14/02

2
Depletion Voltage

• Vdep d2Nq/2e
• d sensor thickness
• N Dopant concentration
• q 1.6E-19 C
• e (Si) 11.9 e0
• e0 8.85E-12 F/m
• Vdep 150V ? N ? 3E12/cm3 ? N0 will be 1 5
  E12/cm3.
• Change in Vdep 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, Vdep d2Neffq/2e
  Neff N0 DNeff (due to radiation damage).

3
The Hamburg Model

• DNeff(Feq,t(Ta)) NA (Feq,t(Ta)) NC (Feq)
  NY (Feq,t(Ta))
• Ta Annealing temperature.
• 1st term represents beneficial annealing NA
  (Feq,0) NA (Feq) NA (Feq,?) 0.
• 2nd term represents stable damage has 2
  components, donor removal and acceptor
  generation. For large doses, acceptor generation
  is dominant.
• 3rd term represents reverse annealing NY (Feq,0)
  0 NY (Feq,?) NY (Feq)
• 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 2nd 3rd terms above (I cant 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 Neff has 4 terms
• Stable damage terms for neutrons charged
  hadrons
• Reverse annealing terms for neutrons charged
  hadrons

5
Parameterization of radiation damage to
oxygenated Si
Donor removal
Acceptor generation
NC(n) NC0(1-exp(-cFeq)) gCFeq
NC0 (initial dopant concentration)x0.44
c 7.79E-14cm2 ? 1/1.3E13cm-2
gC 2.00E-2cm-1
Note 1) There are large variations in
reported donor removal parameters (NC0/N0 c).
2) Donor removal occurs rather quickly.
NY(n)gYFeq
gY 4.7E-2cm-1
NC(p)NC0(1-exp(-cFeq)) gCFeq
NC0 (initial dopant concentration)x1
gC 5.61E-3cm-1
NY(p)1.55E13(1-exp(-Feq/2.2E14)
Plots are from the 3rd ROSE status report.
6
Reverse Annealing
Time dependence (1 (1/(1t/tY)))
Temperature dependence tY(T)
tY20exp((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 a function of both
  time and temperature I a Feq V
• Immediately after irradiation, a(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 a as time goes to
  infinity.
• The official ROSE value of a is measured at room
  temperature, after 80 minutes annealing at 60 C,
  and is 4E-17 A/cm. Ritas 1st 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 T2exp(-Eg/2kT)
  (Eg band gap energy 1.12 eV k Boltzman
  constant 8.62E-5 eV/degree K).
• Example, for Feq 1E15/cm2 Assuming full
  depletion can be maintained, the volume of a
  pixel .04cm x .005cm x .025cm 5E-6 cm3.
  Using the ROSE value for a, 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 Mekkaouis 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 (Ileak x FE integration
  time)/(electron charge)
• Example Ileak 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(1002
  2x87500) 430 e-
• Power dissipation due to leakage current
  VbiasIleak
• A scale of power dissipation is given by the
  analog pixel cell (50 mW/pixel) and the LVDS
  drivers (4mA x 2.5V 10mW/pair 21 mW/pixel for
  innermost readout chip).

10
Excel Model

• Approximate time temperature dependence by
  assuming
• Luminosity 2E32 cm-2sec-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 Feq with c
  7.79E-14cm2 and NC0 f x N0.
• NOTE NC0N0 (complete donor removal) means that
  the depletion voltage after a large dose is
  independent of the original depletion voltage.
• Leakage current calculated with a2E-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 F ? ?
• 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
  Vbias Vdep.

11
Model Result Depletion Voltage
Assumptions Complete donor removal (final Vdep
independent of V0) tY(20)
3.2 6.5 yrs.
12
Model Result Leakage Current
noise 245 e-
noise 154 e-
noise 115 e-
a2E-17 FE integration time assumed to be 55ns.
13
Tentative Conclusions

• Operation at 20C 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 (-10C)
  operation is given by operation at 5C.