144
G. Lutz and R. Klanner
surface-radiation effects are sufficiently well understood and can be avoided by a
proper design [6]. Nevertheless, there are many examples of improper designs and
several unpleasant surprises due to surface damage.
Non-ionizing interactions, which knock out silicon atoms from their lattice
points, are the main cause of bulk damage. A minimum energy transfer to the
silicon atom of about 25 eV is required to produce such a primary defect. For
energy transfers above 1 keV the silicon atom itself can knock out further silicon
atoms, resulting in defect clusters, and for energies above 12 keV multiple clusters
can be produced. These threshold numbers are the result of model calculations
and only limited experimental information is available. The primary defects are
mobile at room temperature. Some of them anneal, others diffuse to the silicon
surface or interact with crystal defects and impurities and form stable defects. Using
different spectroscopic methods a large number of defects could be identified and
their properties, like donor- or acceptor-type, position in the band gap, cross-sections
for electrons and holes and introduction rates determined [7]. The electrically active
defects have three main consequences for detectors: (1) Increase of dark current, (2)
trapping of signal charges thus reducing the charge collection, and (3) change of the
electric field in the space charge region from which the signal charge is collected.
Typical introduction rates of stable defects are of order 1 cm –1 , i.e. a fluence
if 1 particle per cm 2 , produces 1 stable defect per cm 3 . For fluences above about
10 14 cm –2 , the density of defects exceeds by far the doping density, and the
silicon properties change significantly: In non-depleted silicon the high generationrecombination rate results in an approximately equal density of holes and electrons,
and the resistivity increases from the value determined by the dopant density to
the value of intrinsic silicon, which is about 350 k·cm at room temperature. The
high dark current for a reverse biased diode, which is dominated by holes at the
cathode and by electrons at the anode, results in a position-dependent filling of
the defects and a completely different electric field distribution than in the detector
before irradiation. High field regions appear at anodes and cathodes, a phenomenon
called “double junction”, and lower field regions in-between [8, 9]. Thus the concept
of uniform doping breaks down and most of the methods used to characterize silicon
before irradiation are no more applicable.
Based on a detailed and systematic study of silicon pad diodes with different
doping and impurities irradiated by different particles and fluences, the phenomenological Hamburg model has been developed [10]. It parametrises the change
of parameters like dark current and effective doping, used to characterise nonirradiated sensors, as a function of irradiation fluence and temperature history. Up
to fluences of approximately 10 14 cm –2 , which are presently (mid 2018) reached
at the LHC, the model is remarkable successful in describing the observed effects
of radiation damage. An extension of such a model to higher fluences is badly
needed for monitoring the radiation fields at the LHC and for the planning of the
experiments at the High-Luminosity LHC.
G. Lutz and R. Klanner
surface-radiation effects are sufficiently well understood and can be avoided by a
proper design [6]. Nevertheless, there are many examples of improper designs and
several unpleasant surprises due to surface damage.
Non-ionizing interactions, which knock out silicon atoms from their lattice
points, are the main cause of bulk damage. A minimum energy transfer to the
silicon atom of about 25 eV is required to produce such a primary defect. For
energy transfers above 1 keV the silicon atom itself can knock out further silicon
atoms, resulting in defect clusters, and for energies above 12 keV multiple clusters
can be produced. These threshold numbers are the result of model calculations
and only limited experimental information is available. The primary defects are
mobile at room temperature. Some of them anneal, others diffuse to the silicon
surface or interact with crystal defects and impurities and form stable defects. Using
different spectroscopic methods a large number of defects could be identified and
their properties, like donor- or acceptor-type, position in the band gap, cross-sections
for electrons and holes and introduction rates determined [7]. The electrically active
defects have three main consequences for detectors: (1) Increase of dark current, (2)
trapping of signal charges thus reducing the charge collection, and (3) change of the
electric field in the space charge region from which the signal charge is collected.
Typical introduction rates of stable defects are of order 1 cm –1 , i.e. a fluence
if 1 particle per cm 2 , produces 1 stable defect per cm 3 . For fluences above about
10 14 cm –2 , the density of defects exceeds by far the doping density, and the
silicon properties change significantly: In non-depleted silicon the high generationrecombination rate results in an approximately equal density of holes and electrons,
and the resistivity increases from the value determined by the dopant density to
the value of intrinsic silicon, which is about 350 k·cm at room temperature. The
high dark current for a reverse biased diode, which is dominated by holes at the
cathode and by electrons at the anode, results in a position-dependent filling of
the defects and a completely different electric field distribution than in the detector
before irradiation. High field regions appear at anodes and cathodes, a phenomenon
called “double junction”, and lower field regions in-between [8, 9]. Thus the concept
of uniform doping breaks down and most of the methods used to characterize silicon
before irradiation are no more applicable.
Based on a detailed and systematic study of silicon pad diodes with different
doping and impurities irradiated by different particles and fluences, the phenomenological Hamburg model has been developed [10]. It parametrises the change
of parameters like dark current and effective doping, used to characterise nonirradiated sensors, as a function of irradiation fluence and temperature history. Up
to fluences of approximately 10 14 cm –2 , which are presently (mid 2018) reached
at the LHC, the model is remarkable successful in describing the observed effects
of radiation damage. An extension of such a model to higher fluences is badly
needed for monitoring the radiation fields at the LHC and for the planning of the
experiments at the High-Luminosity LHC.