A double junction model of irradiated silicon pixel sensors for LHC
ABSTRACT In this paper, we discuss the measurement of charge collection in irradiated silicon pixel sensors and the comparison with a detailed simulation. The simulation implements a model of radiation damage by including two defect levels with opposite charge states and trapping of charge carriers. The modeling proves that a doubly peaked electric field generated by the two defect levels is necessary to describe the data and excludes a description based on acceptor defects uniformly distributed across the sensor bulk. In addition, the dependence of trap concentrations upon fluence is established by comparing the measured and simulated profiles at several fluences and bias voltages.
arXiv:physics/0506228v1 [physics.ins-det] 30 Jun 2005
Talk presented at the 10thEuropean Symposium on Semiconductor Detectors,
June 12-16 2005, Wildbad Kreuth, Germany.
A double junction model of irradiated silicon
pixel sensors for LHC
V. Chiochiaa,∗, M. Swartzb, Y. Allkofera, D. Bortolettoc,
L. Cremaldid, S. Cucciarellie, A. Dorokhova,f,C. H¨ ormanna,f,
D. Kimb, M. Koneckie, D. Kotlinskif, K. Prokofieva,f,
C. Regenfusa, T. Rohef, D. A. Sandersd, S. Sonc, T. Speera
aPhysik Institut der Universit¨ at Z¨ urich-Irchel, 8057 Z¨ urich, Switzerland
bJohns Hopkins University, Baltimore, MD 21218, USA
cPurdue University, West Lafayette, IN 47907, USA
dUniversity of Mississippi, University, MS 38677, USA
eInstitut f¨ ur Physik der Universit¨ at Basel, 4056 Basel, Switzerland
fPaul Scherrer Institut, 5232 Villigen PSI, Switzerland
In this paper we discuss the measurement of charge collection in irradiated silicon
pixel sensors and the comparison with a detailed simulation. The simulation im-
plements a model of radiation damage by including two defect levels with opposite
charge states and trapping of charge carriers. The modeling proves that a doubly
peaked electric field generated by the two defect levels is necessary to describe the
data and excludes a description based on acceptor defects uniformly distributed
across the sensor bulk. In addition, the dependence of trap concentrations upon
fluence is established by comparing the measured and simulated profiles at several
fluences and bias voltages.
The CMS experiment, currently under construction at the Large Hadron Col-
lider (LHC) will include a silicon pixel detector  to allow tracking in the
region closest to the interaction point. The detector will be a key component
Email address: email@example.com (V. Chiochia).
Preprint submitted to Elsevier Science 2 February 2008
for reconstructing interaction vertices and heavy quark decays in a particu-
lary harsh environment, characterized by a high track multiplicity and heavy
irradiation. The innermost layer, located at only 4 cm from the beam line, is
expected to be exposed to an equivalent fluence of 3×1014neq/cm2/yr at full
In these conditions, the response of the silicon sensors during the detector
operation is of great concern. It is well understood that the intra-diode electric
fields in these detectors vary linearly in depth reaching a maximum value at
the p-n junction. The linear behavior is a consequence of a constant space
charge density, Neff, caused by thermodynamically ionized impurities in the
bulk material. It is well known that the detector characteristics are affected by
radiation exposure, but it is generally assumed that the same picture is valid
after irradiation. In fact, it is common to characterize the effects of irradiation
in terms of a varying effective charge density. In  we have proved that this
picture does not provide a good description of irradiated silicon pixel sensors.
In addition, it was shown that it is possible to adequately describe the charge
collection characteristics of a heavily irradiated silicon detector in terms of a
tuned double junction model which produces a double peak electric field profile
across the sensor. The modeling is supported by the evidence of doubly peaked
electric fields obtained directly from beam test measurements and presented
in . In this paper we apply our model to sensors irradiated to lower fluences
demonstrating that a doubly peaked electric field is already visible at a fluence
of 0.5×1014neq/cm2. In addition, the dependence of trap concentrations upon
fluence is established by comparing the measured and simulated profiles at
several fluences and bias voltages.
This paper is organized as follows: Section 2 describes the experimental setup,
Section 3 describes the carrier transport simulation used to interpret the data.
The tuning of the double junction model is discussed in Section 4 with the
results of the fit procedure. The conclusions are given in Section 5.
The measurements were performed in the H2 line of the CERN SPS in 2003/04
using 150-225 GeV pions. The beam test apparatus is described in . A silicon
beam telescope  consisted of four modules each containing two 300 µm thick
single-sided silicon detectors with a strip pitch of 25 µm and readout pitch
of 50 µm. The two detectors in each module were oriented to measure hori-
zontal and vertical impact coordinates. A pixel hybrid detector was mounted
between the second and third telescope modules on a cooled rotating stage. A
trigger signal was generated by a silicon PIN diode. The analog signals from
all detectors were digitized in a VME-based readout system by two CAEN
(V550) and one custom built flash ADCs. The entire assembly was located
in an open-geometry 3T Helmholtz magnet that produced a magnetic field
parallel or orthogonal to the beam. The temperature of the tested sensors was
controlled with a Peltier cooler that was capable of operating down to -30◦C.
The telescope information was used to reconstruct the trajectories of individ-
ual beam particles and to achieve a precise determination of the particle hit
position in the pixel detector. The resulting intrinsic resolution of the beam
telescope was about 1 µm.
The prototype pixel sensors are so-called “n-in-n” devices: they are designed
to collect charge from n+structures implanted into n–bulk silicon. All test
devices were 22×32 arrays of 125×125 µm2pixels having a sensitive area of
2.75×4 mm2. The substrate was 285 µm thick, n-doped, diffusively-oxygenated
silicon of orientation ?111?, resistivity of about 3.7 kΩ·cm and oxygen concen-
tration in the order of 1017cm−3. Individual sensors were diced from fully
processed wafers after the deposition of under-bump metalization and indium
bumps. A number of sensors were irradiated at the CERN PS with 24 GeV
protons. The irradiation was performed without cooling or bias. The deliv-
ered proton fluences scaled to 1 MeV neutrons by the hardness factor 0.62 
were 0.5×1014neq/cm2, 2×1014neq/cm2and 5.9×1014neq/cm2. All samples
were annealed for three days at 30◦C. In order to avoid reverse annealing,
the sensors were stored at -20◦C after irradiation and kept at room tempera-
ture only for transport and bump bonding. All sensors were bump bonded to
PSI30/AC30 readout chips  which allow analog readout of all 704 pixel cells
without zero suppression. The PSI30 settings were adjusted to provide a linear
response to input signals ranging from zero to more than 30,000 electrons.
A detailed sensor simulation was implemented, including a physical modeling
of irradiation effects in silicon. Our simulation, pixelav [2,8,9], incorporates
the following elements: an accurate model of charge deposition by primary
hadronic tracks (in particular to model delta rays); a realistic 3-D electric field
map resulting from the simultaneous solution of Poisson’s Equation, continuity
equations, and various charge transport models; an established model of charge
drift physics including mobilities, Hall Effect, and 3-D diffusion; a simulation of
charge trapping and the signal induced from trapped charge; and a simulation
of electronic noise, response, and threshold effects. A final step reformats the
simulated data into test beam format so that it can be processed by the test
beam analysis software.
The effect of irradiation was implemented in the simulation by including two
defect levels in the forbidden silicon bandgap with opposite charge states and
trapping of charge carriers. The model, similar to one proposed in , is
based on the Shockley-Read-Hall statistics and produces an effective space
charge density ρeff from the trapping of free carriers in the leakage current.
The effective charge density is related to the occupancies and densities of traps
ρeff= e[NDfD− NAfA] + ρdopants
where: ND and NAare the densities of donor and acceptor trapping states,
respectively; fDand fAare the occupied fractions of the donor and acceptor
states, respectively, and ρdopantsis the charge density due to ionized dopants.
Each defect level is characterized by an electron and hole trapping cross sec-
activation energy, EDand EAfor the donor and acceptor trap, respectively. An
=N f -N f +
A A D D
e/h, for the donor and acceptor trap, respectively, and by an
Fig. 1. An illustrative sketch of the double trap model for a reverse biased device.
illustrative sketch of the model is shown in Fig. 1. Trapping of the mobile car-
riers from the generation-recombination current produces a net positive space
charge density near the p+backplane and a net negative space charge density
near the n+implant as shown in Fig. 1(a). Since positive space charge density
corresponds to n-type doping and negative space charge corresponds to p-
type doping, there are p-n junctions at both sides of the detector. The electric
field in the sensor follows from a simultaneous solution of Poisson’s equation
and the continuity equations. The resulting z-component of the electric field
is shown in Fig. 1(b). It varies with an approximately quadratic dependence
upon z having a minimum at the zero of the space charge density and maxima
at both implants. A more detailed description of the double junction model
and its implementation can be found in .
Charge collection across the sensor bulk was measured using the “grazing
angle technique” . As is shown in Fig. 2, the surface of the test sensor is
oriented by a small angle (15◦) with respect to the pion beam. A large sample
of data is collected with zero magnetic field and at a temperature of −10◦C.
The charge measured by each pixel along the y direction samples a different
depth z in the sensor. Precise entry point information from the beam telescope
is used to produce finely binned charge collection profiles.
Fig. 2. The grazing angle technique for determining charge collection profiles. The
charge measured by each pixel along the y direction samples a different depth z in
The charge collection profiles for a sensor irradiated to a fluence of Φ =
0.5 × 1014neq/cm2and Φ = 2 × 1014neq/cm2and operated at several bias
voltages are presented in Fig. 3(a-c) and Fig. 3(d-g), respectively. The mea-
sured profiles, shown as solid dots, are compared to the simulated profiles,
shown as histograms. The two trap model has six free parameters (ND, NA,
to the values of . Additionally, the electron and hole trapping rates, Γe
and Γh, are uncertain at the 30% level due to the fluence uncertainty and
possible annealing of the sensors. They are treated as constrained parameters.
The donor concentration of the starting material is set to 1.2 × 1012cm−3
corresponding to a full depletion voltage of about 70 V for an unirradiated de-
vice. The parameters of the double junction model were systematically varied
and the agreement between measured and simulated charge collection profiles
was judged subjectively. The procedure was repeated at the each fluence and
the optimal parameter set was chosen when agreement between measured and
simulated profiles was achieved for all bias voltages.
h) that can be adjusted. The activation energies are kept fixed
The simulation describes the measured charge collection profiles well both
in shape and normalization. In particular,the “wiggle” observed at low bias
voltages is also nicely described. The relative signal minimum near y = 700 µm
(see Fig. 3) corresponds to the minimum of the electric field z-component, Ez,
where both electrons and holes travel only short distances before trapping.
This small separation induces only a small signal on the n+side of the detector.
At larger values of y, Ez increases causing the electrons drift back into the
minimum where they are likely to be trapped. However, the holes drift into the
higher field region near the p+implant and are more likely to be collected. The
net induced signal on the n+side of the detector therefore increases and creates
the local maximum seen near y = 900 µm. The z-component of the simulated
electric field, Ez, is plotted as a function of z in Fig. 4(a) and Fig. 4(b) for
Φ = 0.5×1014neq/cm2and Φ = 2×1014neq/cm2, respectively. The field profiles