Observation, modeling, and temperature dependence of doubly peaked electric fields in irradiated silicon pixel sensors

Abstract

We show that doubly peaked electric fields are necessary to describe grazing-angle charge collection measurements of irradiated silicon pixel sensors. A model of irradiated silicon based upon two defect levels with opposite charge states and the trapping of charge carriers can be tuned to produce a good description of the measured charge collection profiles in the fluence range from 0.5 x 1014 to 5.9 x 10(14) n(eq)/cm(2). The model correctly predicts the variation in the profiles as the temperature is changed from -10 to -25 degrees C. The measured charge collection profiles are inconsistent with the linearly varying electric fields predicted by the usual description based upon a uniform effective doping density. This observation calls into question the practice of using effective doping densities to characterize irradiated silicon. (c) 2006 Elsevier B.V. All rights reserved.

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arXiv:physics/0510040v2 [physics.ins-det] 5 Jan 2006
Observation,modeling,andtemperaturedependenceofdoubly
peakedelectricfieldsinirradiatedsiliconpixelsensors
M. Swartza, V. Chiochiab, Y. Allkoferb, D. Bortolettoc, L. Cremaldid, S. Cucciarellie,
A. Dorokhovb,f, C. H¨ ormannb,f, D. Kima, M. Koneckie, D. Kotlinskif, K. Prokofievb,f,
C. Regenfusb, T. Rohef, D. A. Sandersd, S. Sonc, T. Speerb
aJohns Hopkins University, Baltimore, MD 21218, USA
bPhysik Institut der Universit¨ at Z¨ urich-Irchel, 8057 Z¨ urich, Switzerland
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
Abstract
We show that doubly peaked electric fields are necessary to describe grazing-angle charge collection measurements
of irradiated silicon pixel sensors. A model of irradiated silicon based upon two defect levels with opposite charge
states and the trapping of charge carriers can be tuned to produce a good description of the measured charge
collection profiles in the fluence range from 0.5×1014neq/cm2to 5.9×1014neq/cm2. The model correctly predicts
the variation in the profiles as the temperature is changed from −10◦C to −25◦C. The measured charge collection
profiles are inconsistent with the linearly-varying electric fields predicted by the usual description based upon a
uniform effective doping density. This observation calls into question the practice of using effective doping densities
to characterize irradiated silicon.
Key words: Pixels; Radiation effects; Space charge; Simulation; Electric fields;
PACS: 29.40.Wk
1. Introduction
A silicon pixel detector [1] is currently being
developed for the CMS experiment at the CERN
LargeHadronCollider(LHC). The detectorwill be
a key component in the reconstruction of primary
and secondary vertices in the particularly harsh
LHC environment characterized by large track
multiplicities and high radiation backgrounds.
The innermost layer, located at only 4 cm from the
beam line, is expected to be exposed to a 1 MeV
neutron equivalent fluence of 3×1014neq/cm2per
year at full luminosity.
The response of the silicon sensors during the
detector operation is of great concern. It is well un-
derstoodthatthe intra-diodeelectricfields in these
detectors vary linearly in depth reaching a maxi-
mum value at the p-n junction. The linearbehavior
is a consequence of a uniform space charge density,
Neff, caused by thermally ionized impurities in the
Preprint submitted to Elsevier Science2 February 2008

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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 uniform charge density. In [2] 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 ade-
quately describe the charge collection characteris-
tics of a heavily irradiated silicon detector in terms
of a tuned double junction model which produces a
doubly peaked electric field profile across the sen-
sor. The modeling is supported by the evidence
of doubly peaked electric fields obtained directly
from beam test measurementsand presented in [3].
The dependence of the modeled trap concentra-
tions upon fluence was presented in [4]. In this pa-
per, we summarize the previous results and inves-
tigate the temperature dependence of the model.
This paper is organized as follows: Section 2 de-
scribes the experimental setup, Section 3 describes
the carrier transport simulation used to interpret
the data. The tuning of the double junction model
and its resulting predictions are discussed in Sec-
tion 4. The temperature dependence of the data
and model are summarized in Section 5. The con-
clusions are given in Section 6.
2. Experimental setup
The measurements were performed in the H2
beam line of the CERN SPS in 2003/04 using 150-
225 GeV pions. The beam test apparatus is de-
scribedin[5].A siliconbeamtelescope[6]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 detec-
tors in each module were oriented to measure hori-
zontal and vertical impact coordinates. A pixel hy-
brid detector wasmounted 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) ADCs and one custom-built flash
ADC. The entire assembly was located in an open-
geometry 3T Helmholtz magnet that produced a
magnetic field either 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 infor-
mation was used to reconstruct the trajectories of
individual 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 chargefrom
n+structures implanted into n–bulk silicon using
p-spray isolation. All test devices were 22×32 ar-
rays of 125×125 µm2pixels that were fabricated
by CiS. The substrate, produced by Wacker, was
285 µm thick, n-doped, diffusively-oxygenated
float zone silicon of orientation ?111?, resistivity
3.7 kΩ·cm and oxygen concentration in the or-
der 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 delivered
proton fluences scaled to 1 MeV neutrons by the
hardness factor 0.62 [7] were 0.5×1014neq/cm2,
2×1014neq/cm2and 5.9×1014neq/cm2. All sam-
ples 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 tem-
perature only for transport and bump bonding.
All sensors were bump bonded to PSI30/AC30
readout chips [8] 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.
3. Sensor simulation
The interpretation of the test beam data relies
upon a detailed sensor simulation that includes the
modeling of irradiation effects in silicon. The sim-
ulation, pixelav [2,9,10], incorporates the follow-
2

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ing elements: an accurate model of charge deposi-
tion by primary hadronic tracks (in particular to
model delta rays); a realistic 3-D intra-pixel elec-
tric field map; 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 simu-
lation of electronic noise, response, and threshold
effects. The intra-pixel electric field map was gen-
erated using tcad 9.0 [11] to simultaneously solve
Poisson’s Equation, the carrier continuity equa-
tions, and various charge transport models. A fi-
nal simulation step reformatted the simulated data
into test beam format so that it could be processed
by the test beam analysis software.
The effect of irradiation was implemented in the
tcad simulation by including two defect levels in
the forbidden siliconbandgapwith oppositecharge
states and trapping of charge carriers. The model,
similar to one proposed in [12], is based on the
Shockley-Read-Hall (SRH) statistics and produces
an effective space chargedensity ρefffrom the trap-
ping of free carriers in the leakage current. The ef-
fective charge density is related to the occupancies
and densities of traps as follows,
ρeff= e[NDfD− NAfA] + ρdopants
(1)
where: NDand NAare the densities of donor and
acceptor trapping states, respectively; fDand fA
are the occupied fractions of the donor and accep-
tor states, respectively, and ρdopantsis the charge
density due to ionized dopants (describes the re-
sistivity of the material before irradiation). The
donor and acceptor occupancies are related to the
trap parameters by standard SRH expressions
fD=
vhσD
hp + veσD
enieED/kT
h(p + nie−ED/kT)veσD
e(n + nieED/kT) + vhσD
(2)
fA=
veσA
en + vhσA
hnie−EA/kT
h(p + nie−EA/kT)veσA
e(n + nieEA/kT) + vhσA
where: ve and vh are the thermal speeds of elec-
trons and holes, respectively; σD
tron and hole capture cross sections for the donor
trap;σA
haretheelectronandholecapturecross
sections for the acceptor trap; n, p are the densities
of free electrons and holes, respectively; niis the
e, σD
hare the elec-
e,σA
intrinsic density of carriers; ED, EAare the acti-
vation energies (relative to the mid-gap energy) of
the donor and acceptor states, respectively. Note
thatthe singledonorandacceptorstatesmodelthe
effects of many physical donor and acceptor states
making the two-trap model an “effective theory”.
The physics of the model is illustrated in Fig. 1.
The spacechargedensity and electricfield areplot-
ted as functions of depth z for a model tuned to re-
produce the Φ = 5.9×1014neqcm−2charge collec-
tion data at 150V bias. The SRH process produces
electron-hole pairs more or less uniformly across
the thickness of the sensor. As the electrons drift
to the n+ implant, the total electron current in-
creases as z decreases. The hole current similarly
increases with increasing z. Trapping of the mobile
carriers produces a net positive space charge den-
sitynearthep+backplaneandanet negativespace
charge density near the n+implant. 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 equa-
tion and the continuity equations. The resulting
z-component of the electric field varies with an ap-
proximately quadratic dependence upon z having
a minimum at the zero of the space charge density
and maxima at both implants. A more detailed de-
scription of the double junction model and its im-
plementation can be found in [2].
n-doped
p-doped
doubly-peaked
E field
Fig. 1. The space charge density (solid line) and electric
field (dashed line) at T = −10◦C as functions of depth in
a two-trap double junction model tuned to reproduce the
Φ = 5.9×1014neqcm−2charge collection data at 150V bias.
3

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4. Model tuning and results
Charge collection across the sensor bulk was
measured using the “grazing angle technique” [15].
As is shown in Fig. 2, the surface of the test sen-
sor is oriented by a small angle (15◦) with respect
to the pion beam. Several samples of data were
collected with zero magnetic field and at temper-
ature of −10◦C and −25◦C. The charge measured
by each pixel along the y direction samples a dif-
ferent depth z in the sensor. Precise entry point
information from the beam telescope is used to
produce finely binned charge collection profiles.
Readout?chip
track
15o
z?axis
y?axis
p+?sensor?backplane
n+?pixel?implant
Bump?bond
Collected?charge
High?electric?field
Low?electric?field
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 sensor.
The charge collection profiles for a sensor irradi-
ated to a fluence of Φ = 5.9×1014neq/cm2and op-
eratedatatemperatureof−10◦Candbiasvoltages
of 150V and 300V are presented in Fig 3. The mea-
sured profiles are shown as solid dots and the simu-
lated profiles are shown as histograms. In order to
investigate the applicability of the traditional pic-
ture of type-inverted silicon after irradiation, the
simulatedprofilesweregeneratedwith electricfield
maps corresponding to two different effective den-
sities of acceptor impurities. The full histograms
arethesimulatedprofileforNeff= 4.5×1012cm−3.
Note that the 300V simulation reasonably agrees
with the measured profile but the 150V simulation
is far too broad. The dashed histograms show the
result of increasing Neffto 24×1012cm−3. At this
effective doping density, the width of the simulated
peak in the 150V distribution is close to correct
but it does not reproduce the “tail” observed in
the data at large y. The 300V simulated distribu-
tion is far too narrow and the predicted charge is
lower than the data (note that the profiles are ab-
solutely normalized). It is clear that a simulation
based upon the standard picture of a constant den-
sity of ionized acceptor impurities cannot repro-
duce the measured profiles.
m)
µ
Position (
050010001500
Charge (Arbitrary units)
0
0.5
1
1.5
2
2.5
3
=150 V
bias
V
-3
cm
12
10
×
=-4.5
eff
N
Measured
-3
cm
12
10
×
=-24
eff
N
m)
µ
Position (
0 500 1000 1500
Charge (Arbitrary units)
0
0.5
1
1.5
2
2.5
3
3.5
=300 V
bias
V
Fig. 3. The measured and simulated charge collection pro-
files for a sensor at T = −10◦C irradiated to a fluence of
Φ = 5.9 × 1014neq/cm2. The profiles measured at bias
voltages of 150V and 300V are shown as solid dots. The
full histograms are the simulated profiles for a constant
effective doping Neff= 4.5 × 1012cm−3of acceptor im-
purities. The dashed histograms are the simulated profiles
for a constant effective doping Neff= 24 × 1012cm−3.
The same measured profiles and those from bias
voltages of 200V and 450V are shown in Fig. 4.
They are compared with simulations based upon
the electric field produced by the two trap model.
The model has six free parameters (ND, NA, σD
σD
h) that can be adjusted. The activation
energies are kept fixed to the values of [12]: ED=
EV+0.48 eV, EA= EC−0.525 eV where EV and
ECare the energies of the valence and conduction
band edges. The electric field map produced by
each tcad run is input into pixelav. The electron
and hole trapping rates, Γeand Γh, are also inputs
to pixelav and are treated as constrainedparame-
ters. Although they have been measured [13], they
are uncertain at the 20% level due to the fluence
uncertainty and possible annealing of the sensors.
They are therefore allowed to vary by as much as
±20% from their nominal values. The donor con-
centration of the starting material is set to 1.2 ×
1012cm−3corresponding to a full depletion volt-
age of about 70 V for an unirradiated device. Be-
causeeachmodel iterationtook approximatelytwo
days, it was not possible to use standard statisti-
cal fitting techniques. The parameters of the dou-
ble junction model were systematically varied and
the agreement between measured and simulated
e,
h, σA
e, σA
4

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charge collection profiles was judged subjectively.
The “best fits” shown in this paper are probably
not true likelihood minima and the calculation of
eight parameter error matrices is beyond available
computational resources.Adequate agreementwas
achieved by setting the ratio of the common hole
and electron cross sections σh/σeto 0.25 and the
ratiooftheacceptoranddonordensitiesNA/NDto
0.40. There is a range of parameters in the ND-σe
spacethatproducesreasonableagreementwith the
measured profiles. The range is shown in Fig. 5a as
the solid line in the logarithmic space. If the donor
density becomes too small (ND< 20×1014cm−3),
the 150V simulation produces too much signal at
large z. If the donor density becomes too large
(ND> 50×1017cm−3), the 300V simulation pro-
duces insufficient signal at large z. Since the simu-
latedleakagecurrentvariesasIleak∝ σeND, differ-
ent points on the allowed solid contour correspond
to different leakage current. Contours of constant
leakage current are shown as dashed curves and
are labeled in terms of the corresponding damage
parameter α where α0 = 4 × 10−17A/cm is the
expected leakage current [14]. It is clear that the
simulation can accommodate the expected leakage
current which is smallerthan the measuredcurrent
by a factor of three. The same choice of parame-
ters can also account for the observed rate of signal
trapping [2].
The simulation describes the measured charge
collection profiles well both in shape and normal-
ization. The “wiggle” observed at low bias voltages
is a signature of the doubly peaked electric field
shown in Fig. 1. The relative signal minimum near
y = 700 µm (see Fig. 4) corresponds to the mini-
mum of the electric field z-component, Ez, where
both electronsand holestravelonly shortdistances
beforetrapping.Thissmallseparationinducesonly
a small signal on the n+side of the detector. At
larger values of y, Ez increases causing the elec-
trons 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 in-
creases and creates the local maximum seen near
y = 900 µm.
The charge collection profiles at T = −10◦C
m)
µ
Position (
0 5001000
Charge (Arbitrary units)
0
0.5
1
1.5
2
2.5
3
3.5
4
=450 V
bias
V
m)
µ
Position (
05001000
Charge (Arbitrary units)
0
0.5
1
1.5
2
2.5
3
=200 V
bias
V
m)
µ
Position (
0 5001000
Charge (Arbitrary units)
0
0.5
1
1.5
2
2.5
3
3.5
=300 V
bias
V
m)
µ
Position (
05001000
Charge (Arbitrary units)
0
0.5
1
1.5
2
2.5
3
=150 V
bias
V
(a)
(b)
(c)(d)
Fig. 4. The measured charge collection profiles at a tem-
perature of −10◦C and bias voltages of 150V, 200V,
300V, and 450V are shown as solid dots for a fluence of
5.9×1014neq/cm2. The two-trap double junction simula-
tion is shown as the solid histogram in each plot.
Fig. 5. The allowed region in the ND-σe space for the
best fit 5.9 × 1014neq/cm2model is shown as the solid
line. Contours of constant leakage current are shown as
dashed curves and are labeled in terms of the corresponding
damage parameter α where α0 = 4 × 10−17A/cm is the
expected leakage current [14].
for sensors irradiated to fluences of Φ = 0.5 ×
1014neq/cm2and Φ = 2 × 1014neq/cm2and op-
erated at several bias voltages are presented in
Fig. 6(a-c) and Fig. 6(d-g), respectively. The mea-
sured profiles,shown as solid dots, are comparedto
the simulated profiles, shown as histograms. Note
that the “wiggle” is present at low bias even at
5