5 Solid State Detectors
143
With F n , F p flux of electrons and holes, D n , D p diffusion constant. Electron and
hole current densities due to drift and diffusions are given by
J n = −qμ n nE + qD n ∇n, J p = qμ p pE–qD p ∇p.
(5.5)
Diffusion constant and mobility are related by Einstein’s relation D = (kT/q) μ.
It can be derived from the requirement of zero current in thermal equilibrium of a
device with non-uniform doping that has to have a constant Fermi level.
In the absence of magnetic fields charge carriers will move approximately
parallel (holes) or antiparallel (electrons) to the electric field. The magnetic field
adds a force perpendicular to the direction of motion and to the magnetic field
direction so that the charge carriers move at an angle θ p = μ H p B , θ n = μ H n B
with respect to the drift direction. The Hall mobilities μ H p and μ H n differ from the
drift mobilities μ p and μ n . B is the magnetic field component perpendicular to the
electric field and the particle velocity.
5.4 Radiation Damage
Damage by ionizing and non-ionizing radiation, represents a major limitation for the
use of silicon detectors in the harsh radiation environment of high-luminosity colliders, like the CERN LHC, where after its upgrade, fluences exceeding 10 16 cm –2
and dose values up to 5 MGy will be reached. At high-brilliance X-ray sources, like
the European X-ray Free-Electron Laser at Hamburg, dose values up to 1 GGy are
expected. Radiation damage is classified in surface and bulk damage.
Surface damage is caused by ionization by charged particles and X-ray photons
in the insulating layers, e.g. the SiO 2 , required to fabricate silicon sensors. Like
in the silicon bulk, ionizing radiation produces electron-hole pairs in the SiO 2 .
Whereas the mobility of electrons is sufficiently high so that they can move to a
nearby electrode, holes are trapped, which results in a positive charge layer and
interface traps at the Si-SiO 2 interface [4]. Positive surface charges can result in
an electron accumulation layer in the Si at the interface, which can cause shorts
between electrodes or break down. Interface traps, if exposed to an electric field,
produce surface-generation currents. As the exact conditions at the Si-SiO 2 interface
also depend on the potential on the outer SiO 2 surface, which in particular in dry
conditions has a very high surface resistance (sheet resistance > 10 18 ), it can
take days until equilibrium is reached [5]. The result can be a breakdown after
several days of operation or a humidity-dependent breakdown voltage. Surface
radiation damage also depends on the dose-rate, which together with long time
constants has to be taken into account, when studying surface damage or when
testing silicon detectors. Surface damage is also technology dependent. In addition,
already at room temperature significant annealing takes place. All these effects
make a systematic study of surface-radiation damage difficult and time consuming.
However, also thanks to the methods developed for radiation-hard electronics,
143
With F n , F p flux of electrons and holes, D n , D p diffusion constant. Electron and
hole current densities due to drift and diffusions are given by
J n = −qμ n nE + qD n ∇n, J p = qμ p pE–qD p ∇p.
(5.5)
Diffusion constant and mobility are related by Einstein’s relation D = (kT/q) μ.
It can be derived from the requirement of zero current in thermal equilibrium of a
device with non-uniform doping that has to have a constant Fermi level.
In the absence of magnetic fields charge carriers will move approximately
parallel (holes) or antiparallel (electrons) to the electric field. The magnetic field
adds a force perpendicular to the direction of motion and to the magnetic field
direction so that the charge carriers move at an angle θ p = μ H p B , θ n = μ H n B
with respect to the drift direction. The Hall mobilities μ H p and μ H n differ from the
drift mobilities μ p and μ n . B is the magnetic field component perpendicular to the
electric field and the particle velocity.
5.4 Radiation Damage
Damage by ionizing and non-ionizing radiation, represents a major limitation for the
use of silicon detectors in the harsh radiation environment of high-luminosity colliders, like the CERN LHC, where after its upgrade, fluences exceeding 10 16 cm –2
and dose values up to 5 MGy will be reached. At high-brilliance X-ray sources, like
the European X-ray Free-Electron Laser at Hamburg, dose values up to 1 GGy are
expected. Radiation damage is classified in surface and bulk damage.
Surface damage is caused by ionization by charged particles and X-ray photons
in the insulating layers, e.g. the SiO 2 , required to fabricate silicon sensors. Like
in the silicon bulk, ionizing radiation produces electron-hole pairs in the SiO 2 .
Whereas the mobility of electrons is sufficiently high so that they can move to a
nearby electrode, holes are trapped, which results in a positive charge layer and
interface traps at the Si-SiO 2 interface [4]. Positive surface charges can result in
an electron accumulation layer in the Si at the interface, which can cause shorts
between electrodes or break down. Interface traps, if exposed to an electric field,
produce surface-generation currents. As the exact conditions at the Si-SiO 2 interface
also depend on the potential on the outer SiO 2 surface, which in particular in dry
conditions has a very high surface resistance (sheet resistance > 10 18 ), it can
take days until equilibrium is reached [5]. The result can be a breakdown after
several days of operation or a humidity-dependent breakdown voltage. Surface
radiation damage also depends on the dose-rate, which together with long time
constants has to be taken into account, when studying surface damage or when
testing silicon detectors. Surface damage is also technology dependent. In addition,
already at room temperature significant annealing takes place. All these effects
make a systematic study of surface-radiation damage difficult and time consuming.
However, also thanks to the methods developed for radiation-hard electronics,