# A method to observe field-region oxide charge and inter-electrode isolation
from $CV$-characteristics of $n$-on-$p$ devices

T. Abdilov  N. Akchurin  C. Carty  Y. Kazhykarim  V. Kuryatkov  T. Peltola
<EMAIL_ADDRESS>A. Wade  Department of Physics and Astronomy, Texas Tech
University, 1200 Memorial Circle, Lubbock, Texas, U.S.A.  Nanotech Center,
Texas Tech University, 902 Boston Ave, Lubbock, Texas, U.S.A.  Department of
Physics, Florida State University, 77 Chieftan Way, Tallahassee, Florida,
U.S.A.

###### Abstract

$N$-on-$p$ silicon sensors will be utilized in the Compact Muon Solenoid (CMS)
detector’s tracker and High Granularity Calorimeter (HGCAL) in the High
Luminosity upgrade of the Large Hadron Collider (HL-LHC). Among their several
advantages in terms of radiation hardness over the traditional $p$-on-$n$
sensors in the extreme radiation environment of the HL-LHC are electron
collection instead of holes and overlapping maxima of weighting and electric
fields at the charge-collecting electrodes. The disadvantage of the multi-
channel SiO2-passivated $n$-on-$p$ sensors is the generation of an inversion
layer under the Si/SiO2-interface by a positive interface-oxide-charge
($N_{\textrm{ox}}$) that at high densities can compromise the position
resolution by creating a conduction channel between the electrodes. This issue
is typically addressed by including additional isolation implants ($p$-stop,
$p$-spray) between $n^{+}$-electrodes. Focusing on the guard-ring regions of
$n$-on-$p$ sensors where no isolation implants are applied between the
electrodes, a capacitance-voltage ($CV$) characterization study of both 6-inch
wafer test diodes and 8-inch HGCAL prototype and pre-series sensors showed a
distinct threshold voltage ($V_{\textrm{th,iso}}$) in the $CV$-characteristics
of a biased $n^{+}$-electrode when its enclosing guard-ring was left floating.
When reproduced by simulations, the measured $V_{\textrm{th,iso}}$ was found
to contain information on the field-region $N_{\textrm{ox}}$ and indicate the
threshold where the two electrodes become electrically isolated by the
influence of the reverse bias voltage. Together with previous studies on the
inter-electrode isolation of irradiated $n$-on-$p$ sensors, the results
indicate that position sensitive $n$-on-$p$ sensors without isolation implants
may be feasible in future HEP experiments.

††journal: Journal of Instrumentation

##  1 Introduction

In order to cope with the extreme radiation environments of the Large Hadron
Collider and future hadron colliders like FCC-hh111Future Circular Hadron
Collider and SPPC222Super Proton-Proton Collider, one extensively studied
approach to improve the radiation hardness of planar silicon particle
detectors is the application of $n^{+}/p^{-}/p^{+}$ ($n$-on-$p$, $n$-in-$p$)
structures instead of the conventional $p$-on-$n$ configuration [1, 2]. Since
radiation introduces acceptor-like bulk defects, no type inversion occurs in
the $p$-type bulk resulting in a favorable combination of the maxima of the
weighting and electric fields after irradiation, which maximizes the signal
and charge carrier velocity in the vicinity of the collecting electrode [3].
The readout at $n^{+}$-electrodes results in a signal generated by the drift
of electrons, and since electrons have about three times higher mobility and
longer trapping times than holes, the amount of trapped charge carriers during
their drift is reduced. This enables a high-speed readout and higher collected
charge in $n$-on-$p$ devices than in conventional sensors. Also, after
irradiation the electric fields at the $n^{+}$-electrodes are lower than in
$p$-on-$n$ sensors, resulting in better noise performance [1, 4]. Another
asset of the $n$-on-$p$ sensor is the reduced dependence of the charge
collection on the reverse annealing of the effective space charge in highly
irradiated detectors [5, 6]. As a consequence, $n$-on-$p$ sensors are the
baseline technology for the detector upgrades in, for example, the Compact
Muon Solenoid (CMS) experiment’s tracker and High Granularity Calorimeter
(HGCAL) [7], where the replacement of the endcap calorimeter will involve
about 600 m2 of 8-inch silicon modules [8, 9] that will need to sustain
fluences of about $1\times
10^{16}~{}\textrm{n}_{\textrm{eq}}\textrm{cm}^{-2}$3331-MeV neutron equivalent
fluence and doses in excess of 1.5 MGy.

The disadvantage of $n$-on-$p$ devices is the more complex fabrication
technology due to the required isolation structures between the
$n^{+}$-electrodes. For example, conventional AC-coupled, poly-Si biased,
$p$-on-$n$ sensors can be processed with 6–7 lithography mask levels, while
$n$-on-$p$ devices require two more lithography steps and additional ion
implantations [2]. The isolation implants are utilized to counter the effect
from the inherent positive charge that is introduced by impurities during the
growth process of SiO2 inside the oxide and at the Si/SiO2-interface
($N_{\textrm{ox}}$). The positive $N_{\textrm{ox}}$ attracts electrons
(minority carriers in $p$-type bulk) from the Si-bulk that form an inversion
layer under the interface which acts as a conduction channel between the
segmented $n^{+}$-electrodes. Radiation induced accumulation of surface damage
can lead to a substantial increase of net $N_{\textrm{ox}}$ [10]. The negative
space charge of the additional highly $p$-doped implant between the
$n^{+}$-electrodes breaks the inversion layer by suppressing the electron
density at the vicinity of Si/SiO2-interface, thus preserving the inter-
electrode isolation and position resolution. Two solutions for the isolation
implants are commonly utilized; $p$-stop and $p$-spray (or the combination of
the two, ‘moderated’ $p$-spray [3]), with localized and uniformly distributed
doping concentrations, respectively, along the surface in the inter-electrode
gap [11, 12, 13, 14, 15, 16, 17]. For stable device performance, careful
tuning of the processing parameters is needed, since high doping
concentrations in the isolation implants ($\gtrsim 5\times
10^{16}~{}\textrm{cm}^{-3}$) increase the probability of discharges or
avalanche effects due to excessive localized electric fields [4, 17, 18]. For
the same reason the actual contact between the isolation and $n^{+}$ implants
should also be avoided [3].

However, previous studies have reported high levels of inter-electrode
isolation in $n$-on-$p$ microstrip sensors without isolation implants before
and after irradiations with protons [19, 20] and neutrons [20]. Thus, to
investigate further possibilities of planar $n$-on-$p$ sensor configurations,
this study focuses on the properties of the regions of $n$-on-$p$ devices
without isolation implants between $n^{+}$-electrodes, i.e., the region
between a diode and its guard-ring, and the observed threshold voltage of
inter-electrode isolation ($V_{\textrm{th,iso}}$). $V_{\textrm{th,iso}}$
introduced in this paper is the threshold voltage where the applied reverse
bias voltage becomes sufficiently high to sweep electrons from the inter-
electrode gap to the positively biased n+-electrode to the extent that breaks
the conduction channel and electrically isolates the electrodes. Simultaneous
to this, $V_{\textrm{th,iso}}$ provides information on the level of
$N_{\textrm{ox}}$ in the field-region of an $n$-on-$p$ sensor.

Two substantially different device types were included in the study: test
diodes from a 6-inch HGCAL prototype wafer and the guard-ring periphery region
of hexagonal 8-inch HGCAL multi-channel sensors. An accompanying study [10]
discusses the mechanisms behind the beneficial impact on inter-electrode
isolation introduced by irradiation.

The paper is arranged by first introducing the test-structure samples from
6-inch wafers and the 8-inch HGCAL-prototype and pre-series sensors in Section
2. Next, the measurement and simulation setups are described in Section 3. The
experimental and simulated $CV$-characterization results start in Section 4.1
with the observations and interpretation of $V_{\textrm{th,iso}}$ in the test-
diode $C^{-2}V$-curves, and the investigation of its relation to the oxide
charge density at the Si/SiO2-interface ($N_{\textrm{ox}}$), active thickness
of the sensor ($t$) and Si-bulk doping ($N_{\textrm{B}}$), as well as the
correlation of $V_{\textrm{th,iso}}$ to the inter-electrode isolation of
$n^{+}$-electrodes without isolation implants. The results of 8-inch HGCAL
sensors are presented in Section 4.2 by first determining the field-region
$N_{\textrm{ox}}$ for the various sensor $t$ and configurations, followed by
the investigation of $V_{\textrm{th,iso}}$ of inter-electrode isolation with
$N_{\textrm{ox}}$. Finally, the results are discussed in Section 5, while
summary and conclusions are given in Section 6.

##  2 Test-structure samples and HGCAL sensors

The three ‘half-moon’ samples in the study with ‘Large’, ‘Half’ and ‘Quarter’
test-diodes and MOS444Metal-Oxide-Semiconductor-capacitors (with active areas
of $4.0\times 4.0$, $2.5\times 2.5$ and $1.25\times 1.25~{}\textrm{mm}^{2}$,
respectively) were diced from a 6-inch Hamamatsu Photonics K.K. (HPK)
320-$\upmu\textrm{m}$-thick $n$-on-$p$ sensor-wafer555Early prototype wafer
for the HGCAL.. The test structures on the samples in Figure 1a were designed
at Institut für Hochenergiephysik (HEPHY). The standard-diffusion process was
utilized in the heavily doped backplane blocking contact to produce
300-$\upmu\textrm{m}$ active thickness test diodes. More extensive details of
the test-diode design and bulk properties are given in [21].

The HGCAL version 2 prototype (or ‘proto-A’) and pre-series666Consecutive
advanced HPK production stages towards the final HGCAL sensor production
parameters. 8-inch multi-channel $n$-on-$p$ sensors777For shortness, the
prototypes will be referred to as ‘HGCAL sensors’ in the following sections.,
designed at Fermi National Accelerator Laboratory (FNAL) and produced by HPK,
included in the study are presented in Figure 2. The low-density (LD) sensors
included both 300- and 200-$\upmu\textrm{m}$ thicknesses, which were produced
from physically thinned $p$-type float zone silicon wafers, resulting in
essentially equal active and physical thicknesses. The high-density (HD)
sensors with an active thickness of 120 $\upmu\textrm{m}$ were produced by
growing epitaxial silicon on a lower resistivity substrate, resulting in a
total physical thickness of 300 $\upmu\textrm{m}$ [7]. The $n^{+}$-electrodes
of the several hundred sensor cells (= channels) displayed in Figure 2 are
isolated from each other by ‘common’ $p$-stop implants, i.e., one $p$-stop
divides the inter-cell gap (as opposed to ‘individual’ $p$-stop where each
cell has a dedicated $p$-stop). Corresponding ‘Quarter’ MOS-capacitors from
the 8-inch sensor wafers in Figure 1b designed at HEPHY were also included in
the electrical characterization investigation.

Both the test structures and the HGCAL sensors have $\langle 100\rangle$
crystal orientation, and about 700-nm-thick silicon dioxide (SiO2) as the
passivation layer with inherent positive oxide charge. The gap between the
$n^{+}$-implant of the test diode and its guard-ring implant is 100
$\upmu\textrm{m}$ for all three test-diode sizes, while the periphery region
of the HGCAL sensors is presented in Figure 3.

(a)

(b)

Figure 1: Test structure samples. (a) ‘Half-moon’ samples with test structures
diced from a 6-inch wafer [21]. Top: three test diodes, two MOS-capacitors
(second and third from left) and other test structures. Bottom: nine test
diodes. (b) Close-up of a test-structure sample diced from an 8-inch HGCAL
wafer with the MOS-capacitor connected to the measurement circuit by a probe
needle. A test diode enclosed by its guard-ring is visible on the left-side of
the MOS-capacitor.

(a)

(b)

(c)

Figure 2: HGCAL 8-inch multi-channel sensor designs included in the study. (a)
Full low-density (LD) float-zone Si-sensor with 198 channels (pre-series). (b)
Full high-density (HD) epitaxial Si-sensor with 444 channels (pre-series). The
cell area of the HD sensors is less than half of the area of the LD-sensor
cells to control the cell capacitance. (c) Multi-Geometry Wafer (MGW) HD
epitaxial Si-sensor (version 2 prototype). Boundary of the ‘bottom-cut’
partial sensor with 288 channels is shown by the horizontal blue line in the
middle part of the sensor. The channels of the full sensors are enclosed by a
single biased guard-ring (channels 199 and 445 in Figures 2a and 2b,
respectively), while the channels of the ‘bottom-cut’ partial HD-sensor are
divided into three regions by three biased guard-rings (channels 472, 473 and
474 in Figure 2c).  Figure 3: Cross-sectional sketch of the front-side of the
periphery region of an HGCAL sensor. The horizontal dimensions are in
$\upmu\textrm{m}$. Gray: 1-$\upmu\textrm{m}$-thick Al-layer for DC-coupled
electrical contacts, dark yellow: 700-nm-thick SiO2 layer. The backplane of
the sensor has the $p^{+}$-blocking contact with 1-$\upmu\textrm{m}$-thick
uniform Al-layer. The biased guard-ring (bias-GR) is grounded during the
measurements of the cells of the multi-channel sensor, while the high voltage
(HV)-ring is used for the front-side biasing scheme [22], where the applied
$-$HV connects to the backplane via the low-resistivity edge-region under the
HV-ring (with a $p^{+}$/$p^{-}$/$p^{+}$ configuration).

##  3 Measurement and simulation setups

For the electrical characterizations of both the test structures and the
multi-channel HGCAL sensors, two measurement setups were utilized at Texas
Tech University (TTU). The capacitance-voltage ($CV$) characterizations of the
test structures were carried out with a single-channel custom probe station.
The reverse bias voltage of the test diode (or the gate voltage of the MOS-
capacitor) was supplied by a Keithley 2410 source measure unit (SMU) while the
capacitance was read out by a Keysight E4980AL LCR-meter. The negative high
voltage ($-$HV) was provided to the backplane of the test structure by a
vacuum chuck, and the connection to the measurement circuit was realized with
a probe needle on the segmented front surface, as shown in Figure 1b. A second
probe needle was applied for the grounding of the test-diode’s guard-ring. The
setup is described in detail in refs. [10, 21].

The corresponding $CV$-characterizations of the HGCAL sensors were carried out
with a multi-channel setup utilizing an automated ARRAY dual-card setup [23]
that enables the electrical characterizations of the 8-inch sensors containing
several hundred individual cells. For the connection to the measurement
circuit a dedicated probe card for each sensor type in Figure 2 was required.
Probe cards for full sensors in Figures 2a and 2b and for HD-partial sensor in
Figure 2c utilized front-side and back-side biasing, respectively. The guard-
ring next to the HV-ring in Figure 3 is left floating in all probe-card types.
The remote control and data acquisition functions were realized with a
LabVIEW™-based custom program (HexDAQ version
1.7888https://gitlab.cern.ch/CLICdp/HGCAL/). The same SMU and LCR-meter units
were used for both single-channel and multi-channel circuit measurements.

The 2D device-simulations were carried out using the Synopsys
Sentaurus999http://www.synopsys.com finite-element Technology Computer-Aided
Design (TCAD) software framework. For the test-diode and MOS-capacitor
simulations, a structure consisting of a DC-coupled $n^{+}$-pad between two
$n^{+}$ guard-rings (GR) (either grounded or floating), and a metal-oxide-
silicon structure, respectively, were implemented. The backplane doping
profile and oxide thickness were set to match the real test structures as
described in Section 2 and in [21].

For the HGCAL sensor simulations of the three active thicknesses, the
periphery-region with the dimensions displayed in Figure 3 was implemented.
Results from spreading resistance profiling (SRP) measurements of the sensors
carried out within the HGCAL community were used as an input for the doping
profiles, shown in Figure 4. The bulk-doping ($N_{\textrm{B}}$) levels were
extracted from the $CV$-measured full-depletion voltages ($V_{\textrm{fd}}$)
of the sensor-cells shown in A and implemented in the simulation.

Figure 4: Input doping profiles for the 300-$\upmu\textrm{m}$-thick HGCAL LD-
sensor periphery-region TCAD-simulation. Identical front-side
($\textrm{Depth}=0~{}\upmu\textrm{m}$) doping profiles were set for the HD-
sensors, while the low-resistivity substrate of the epitaxial sensor was
modeled by an error function starting from the backplane
($\textrm{Depth}=300~{}\upmu\textrm{m}$) with an abrupt drop to bulk-doping
level at 120-$\upmu\textrm{m}$ depth.

##  4 Experimental and simulation results

###  4.1 6-inch wafer test structures

The room-temperature $CV$-characterizations of the test structures were
carried out at a frequency of 200 kHz to control the dissipation factor and
stabilize the measurements (reduced capacitive impedance [24]) of the low-
capacitance test diodes with a minimum capacitance of 0.54 pF (‘Quarter’
diode).

The measured $CV$-characteristics of the ‘Large’ MOS-capacitor and test diode
are presented in Figure 5. The flat band voltage ($V_{\textrm{fb}}$) of the
MOS-capacitor was determined by the flat-band-capacitance method
($C_{\textrm{fb}}$ in Figure 5a). The extracted $V_{\textrm{fb}}=-4.28\pm
0.02~{}\textrm{V}$ was then used to resolve the oxide charge density at the
Si/SiO2-interface as $N_{\textrm{ox}}=(1.08\pm 0.05)\times
10^{11}~{}\textrm{cm}^{-2}$ [10]. It was also shown in [10] that in the
absence of hysteresis whether the $CV$-sweep of the pre-irradiated MOS-
capacitor is initiated from deep accumulation or from deep inversion
($-9~{}\textrm{V}$ and $0~{}\textrm{V}$ in Figure 5a, respectively), the
contribution from mobile ionic charges ($N_{\textrm{M}}$) and interface traps
($N_{\textrm{it}}$) to $N_{\textrm{ox}}$ is negligible, leading to
$N_{\textrm{ox}}$ being described essentially by the fixed oxide charge
density ($N_{\textrm{f}}$), i.e.,
$N_{\textrm{ox}}~{}{\cong}~{}N_{\textrm{f}}$. As shown in Figure 5a, the
measured $V_{\textrm{fb}}$ was reproduced by the simulation with the input
value of $N_{\textrm{ox}}=N_{\textrm{f}}$ (implemented at the
Si/SiO2-interface as a positive charge-sheet with a uniform distribution along
the interface) within uncertainty of the experimentally extracted
$N_{\textrm{ox}}$ (with contributions to uncertainty from measured
$V_{\textrm{fb}}$ and oxide capacitance ($C_{\textrm{ox}}$)). Therefore, this
approach is maintained for the field-region $N_{\textrm{ox}}$ simulations on
the test diodes and HGCAL sensors (in the following sections the simulation
tuning-parameter at the Si/SiO2-interface will be referred to as
$N_{\textrm{ox}}$).

Shown in Figure 5b, the characteristic $C_{\textrm{geom}}$-values –where
capacitance is dependent only on the material and the geometry of the device–
and the slopes in the dynamic-region of the measured $C^{-2}V$-curves from
either solely the test-diode pad (‘GR grounded’) or both the pad and its
guard-ring (‘GR + diode’) reflect the differences in the active areas $A$
involved in the measurements by the relation

$C_{\textrm{geom}}=\epsilon_{\textrm{s}}\frac{A}{d},$ (1)

where $\epsilon_{\textrm{s}}$ is the product of vacuum permittivity and the
relative permittivity of silicon, and $d$ is the active thickness of the
device [25]. Hence, the measured capacitances are $C=C_{\textrm{diode}}$ and
$C^{\prime}=C_{\textrm{diode}}+C_{\textrm{GR}}=C_{\textrm{tot}}$ for the two
configurations throughout the applied voltage range.

However, the measurement with the floating guard-ring (i.e., guard-ring is
disconnected from the biasing circuit, thus its potential is ‘floating’ with
changing conditions in the device) in Figure 5b displays a double slope in the
dynamic-region of $C^{-2}V$-curve with a distinct threshold voltage
($V_{\textrm{th,iso}}$) between the two slopes. The identical slope with
$C_{\textrm{tot}}$-curve at $V<V_{\textrm{th,iso}}$ suggests that the diode
and its guard-ring are shorted in this voltage-region. This is caused by the
conduction channel between the test-diode pad and the guard-ring –where there
is no isolation implant–, formed by the positive oxide charge
($Q_{\textrm{ox}}$) of SiO2 attracting minority carriers, i.e., electrons,
from Si-bulk to the Si/SiO2-interface. As shown by the simulated evolution of
the electron density in the vicinity of the interface in Figure 5c, at
$V~{}{\geq}~{}V_{\textrm{th,iso}}$ the Coulomb force from the positively
biased $n^{+}$-pad of the test diode overcomes the attraction from
$Q_{\textrm{ox}}$, and the electrons are swept from the inter-electrode gap
(electron density drops by about nine-orders-of-magnitude from
$V<V_{\textrm{th,iso}}$) to the $n^{+}$-pad, resulting in the test diode
becoming isolated from the guard-ring. Due to this process, the area involved
in the $CV$-measurement of the test-diode pad is reduced, which, as a
consequence of Eq. 1, is observed as an abrupt decrease of $C$ in Figure 5b,
forming a double-slope in the dynamic-region of the $CV$-curve.

With the approach presented in A, $V_{\textrm{fd}}=280~{}\textrm{V}$ was
extracted from the $C_{\textrm{diode}}$-curve in Figure 5b and the derived
value of $N_{\textrm{B}}=4.0\times 10^{12}~{}\textrm{cm}^{-3}$ (utilizing the
relation $N_{\textrm{B}}=2\epsilon_{\textrm{s}}V_{\textrm{fd}}/(ed^{2})$,
where $e$ is the elementary charge [25]) was applied as an input to the test-
diode simulation. As displayed in Figure 5b, by tuning the input
$N_{\textrm{ox}}$ both the voltage of $V_{\textrm{th,iso}}$ and the test-diode
$CV$-characteristics with its guard-ring either grounded or floating can be
closely reproduced by the simulation.

(a)

(b)

(c)

Figure 5: (a) Measured and TCAD-simulated $CV$-characteristics of a $p$-bulk
MOS-capacitor. Measured $CV$-curves were identical for the $CV$-sweeps
starting either from inversion (Inv.) or accumulation (Acc.) regions. (b)
Measured and simulated $CV$-characteristics of an $n$-on-$p$ test diode, with
its guard-ring (GR) either grounded, floating or measured together with the
test diode (GR + diode). The point of $V_{\textrm{th,iso}}$ reproduced by the
simulation with $N_{\textrm{ox}}=1.18\times 10^{11}~{}\textrm{cm}^{-2}$ is
indicated. The measured test structures in (a) and (b) were from the same
6-inch Si-wafer. (c) Simulated evolution of electron density with reverse bias
voltage at 1-nm depth from the Si/SiO2-interface and between the test-diode
pad and its floating guard-ring. The two values of $V_{\textrm{th,iso}}$, 195
and 379 V, correspond to $N_{\textrm{ox}}$ values of $1.0\times 10^{11}$ and
$1.4\times 10^{11}~{}\textrm{cm}^{-2}$ in Figure 6a, respectively. The metal-
overhang edges of the two electrodes are at 120 and 180 $\upmu\textrm{m}$,
respectively.

From further measurements and simulations with varied input $N_{\textrm{ox}}$
focusing on the $CV$-curves of a test diode with its guard-ring floating in
Figure 6a, it is evident that $V_{\textrm{th,iso}}$ is not dependent on
$V_{\textrm{fd}}$.

In Figure 6b, where
$V_{\textrm{th,iso}}{\approx}V_{\textrm{fd}}-85~{}\textrm{V}$, the influence
of the two factors in the evolution of the active volume (involved in the
test-diode pad $CV$-measurement) with reverse bias voltage is visible:

  * 1.

Isolation between the test-diode pad and the guard-ring.

  * 2.

The presence or absence of opposing electric field-lines from the guard-ring,
corresponding to whether the guard-ring is grounded or floating, respectively.

The sensitivity to $V_{\textrm{th,iso}}$ is also visible in the
$CV$-measurement with the guard-ring grounded, as the slight non-linearity in
the dynamic-region of the $C^{-2}V$-curve vanishes above
$V_{\textrm{th,iso}}$. This suggests that the conduction-channel is also
present when the guard-ring is grounded, keeping the test-diode pad and the
guard-ring shorted at $V<V_{\textrm{th,iso}}$, and indicating that
$V_{\textrm{th,iso}}$ is independent of the two $CV$-measurement
configurations in Figure 6b. The opposing field-lines from the grounded guard-
ring stop the lateral expansion of the pad’s active volume with bias voltage,
which mitigates the influence of the shorted electrodes on the $C^{-2}V$-curve
at voltages below $V_{\textrm{th,iso}}$. The same feature is also visible
throughout the dynamic-region of the measured $C^{-2}V$-curve with grounded
guard-ring in Figure 5b, where $V_{\textrm{th,iso}}$ is about 5 V below
$V_{\textrm{fd}}$. Additionally, both figures display that the aforementioned
feature in the measured $CV$-characteristics of the test diode with grounded
guard-ring is not reproduced by the 2D-simulation. This is likely to be due to
the limitation of the cross-sectional 2D-structure to reproduce the subtle
effect from the lateral expansion of the guard-ring field lines that confine
the active volume of the test-diode pad from its four sides at the voltages
where the pad and the guard-ring are still shorted. Thus, due to considerably
more pronounced influence from $V_{\textrm{th,iso}}$ on the
$CV$-characteristics of a test diode with floating guard-ring, the combined
experimental and simulation investigation of the correlation between
$V_{\textrm{th,iso}}$ and field-region $N_{\textrm{ox}}$ is focused on this
configuration.

Finally, the absence of opposing field-lines from the guard-ring in the
$CV$-measurements of the test diode with floating guard-ring in Figures 5b and
6 enables greater lateral expansion of the active volume of the test-diode pad
even when it is isolated from the guard-ring ($V>V_{\textrm{th,iso}}$),
resulting in higher $C_{\textrm{geom}}$ (with
$A=A_{\textrm{diode}}+A_{\textrm{lateral}}$ in Eq. 1) than the measurement
with the guard-ring grounded.

(a)

(b)

Figure 6: Measured and simulated $CV$-characteristics of
300-$\upmu\textrm{m}$-thick $n$-on-$p$ test diodes. ‘s1’=‘half-moon’ sample
one. (a) Influence of $N_{\textrm{ox}}$ on $V_{\textrm{th,iso}}$ for test
diodes with a floating guard-ring. The measured $C_{\textrm{geom}}$ of the
‘Half’-diode is scaled to the $C_{\textrm{geom}}$ of the ‘Large’-diodes. The
three measured values of $V_{\textrm{th,iso}}$ are reproduced by the
simulation with $N_{\textrm{ox}}$-values of $1.0\times 10^{11}$, $1.18\times
10^{11}$ and $1.245\times 10^{11}~{}\textrm{cm}^{-2}$. (b) Results for a test
diode with guard-ring grounded or floating and with
$V_{\textrm{th,iso}}(195~{}\textrm{V})<V_{\textrm{fd}}(280~{}\textrm{V})$. The
simulation applied $N_{\textrm{ox}}=1.0\times 10^{11}~{}\textrm{cm}^{-2}$.

With additional simulated data-points Figure 7a displays a power-law
dependence between $N_{\textrm{ox}}$ and $V_{\textrm{th,iso}}$ by the fit
$N_{\textrm{ox}}=7.67\times 10^{9}{|V_{\textrm{th,iso}}|}^{0.488}$ for the
100-$\upmu\textrm{m}$-width pad-to-guard-ring gap of the measured test diodes.
Doubled pad-to-guard-ring gap in Figure 7a shows a weak dependence of
$V_{\textrm{th,iso}}$ on the gap width, which becomes negligible at
$N_{\textrm{ox}}<1.2\times 10^{11}~{}\textrm{cm}^{-2}$. Thus, Figure 7a
provides a tool to determine field-region $N_{\textrm{ox}}$ from the measured
$V_{\textrm{th,iso}}$ of the $CV$-curve of an $n$-on-$p$ test diode with a
floating guard-ring or more generally, in the field-region between two
$n^{+}$-electrodes with no isolation implant.

Figures 7b and 7c present the measured $CV$-characteristics of 14 test diodes
with guard-ring floating from three ‘half-moon’ samples diced off from the
corners of one 6-inch wafer. As shown in Figure 8, the values of
$V_{\textrm{th,iso}}$ vary between the ‘half-moon’ samples and with the
position on the sample, indicating a non-uniformity of $N_{\textrm{ox}}$ over
the 6-inch wafer, while no dependence on the test-diode size is visible. One
of the test diodes (sample 1 ‘Large’ in Figure 7b) displays also a significant
sensitivity to repeated measurements with ${\Delta}V_{\textrm{th,iso}}\approx
100~{}\textrm{V}$ between the first and fourth measurements, after which no
change of $V_{\textrm{th,iso}}$ was observed with further measurements. This
could indicate a suppression of electrons pulled to the Si/SiO2-interface by
the positive oxide charge, but since repeated measurements on other test
diodes showed negligible effect on $V_{\textrm{th,iso}}$, understanding the
nature of this effect is left out of the scope of the following analysis.

Applying the fit from Figure 7a to all measured $V_{\textrm{th,iso}}$ in
Figures 7b and 7c gives for field-region $\overline{N}_{\textrm{ox}}=(1.10\pm
0.09)\times 10^{11}~{}\textrm{cm}^{-2}$, while the measurements of the MOS-
capacitors on samples 1 and 2 (sample 3 with nine test-diodes shown in the
bottom-part of Figure 1a did not contain any MOS-capacitors) result in gate
$\overline{N}_{\textrm{ox}}=(1.05\pm 0.09)\times 10^{11}~{}\textrm{cm}^{-2}$.
Thus, the measurement-simulation and direct-measurement approaches to extract
the field-region and the gate $\overline{N}_{\textrm{ox}}$, respectively, are
in agreement within uncertainty. Figure 8 displays a comparison between the
individual $N_{\textrm{ox}}$-results extracted from the field-region of the
test diodes and from the MOS-capacitor measurements.

(a)

(b) Sample 1.

(c) Samples 2 and 3.

Figure 7: (a) The simulated dependence of the field-region $N_{\textrm{ox}}$
on $V_{\textrm{th,iso}}$ in a 300-$\upmu\textrm{m}$-thick $n$-on-$p$ test
diode for two gap widths between the test-diode pad and its floating guard-
ring (‘Pad-to-GR gap’). The fit parameters for the two data sets are displayed
in the plot. (b) and (c) Measured $CV$-characteristics of 14
300-$\upmu\textrm{m}$-thick $n$-on-$p$ test diodes with guard-ring floating.
The three ‘half-moon’ samples including the test diodes are named as ‘s1–3’,
while repeated measurements on a test diode are indicated as ‘1st–4th’. The
extreme values of field-region $N_{\textrm{ox}}$, extracted fron the
simulations utilizing the fit for 100-$\upmu\textrm{m}$ pad-to-GR gap in
Figure 7a, are indicated.  Figure 8: A comparison of the field-region
$N_{\textrm{ox}}$ extracted from the test diode $V_{\textrm{th,iso}}$-values
in Figures 7b and 7c between the three ‘half-moon’ samples, as well as with
gate $N_{\textrm{ox}}$ extracted from the $V_{\textrm{fb}}$-values of the MOS-
capacitors on the samples 1 and 2 (‘s1–2’).

The correlation of $V_{\textrm{th,iso}}$ observed in $CV$-characteristics to
the change in the inter-electrode resistance ($R_{\textrm{int}}$) for
$n^{+}$-electrodes without isolation implant is presented in Figure 9a. It is
evident that the $CV$-extracted $V_{\textrm{th,iso}}$ is identical to the
voltage where $R_{\textrm{int}}$ increases abruptly by about ten-orders-of-
magnitude, i.e.,
$V_{\textrm{th,iso}}(CV)=V_{\textrm{th,iso}}(R_{\textrm{int}})$. The simulated
change of $R_{\textrm{int}}$ above $V_{\textrm{th,iso}}$ is also in close
agreement with experimental results [20]. Hence, the electron removal from the
inter-electrode gap by applied reverse bias voltage in Figures 5c and 9b
results in a high level of $R_{\textrm{int}}$ which isolates the
$n^{+}$-electrodes at a given $V_{\textrm{th,iso}}$ that can be observed in a
$CV$-measurement. Since in $R_{\textrm{int}}$-simulation both
$n^{+}$-electrodes are biased (unlike in $CV$-simulation where the guard-ring
is floating), Figure 9a also displays that $V_{\textrm{th,iso}}$ is
independent of whether one or both of the electrodes are biased. This supports
the observation of the measured $C^{-2}V$-curves with either grounded or
floating guard-ring in Figure 6b where both configurations show sensitivity to
the same $V_{\textrm{th,iso}}$. Finally, the $R_{\textrm{int}}$-curve for the
highest $N_{\textrm{ox}}$ in Figure 9a shows that for
$N_{\textrm{ox}}<1.85\times 10^{11}~{}\textrm{cm}^{-2}$, $n^{+}$-electrodes of
a 300-$\upmu\textrm{m}$-thick $n$-on-$p$ test diode, i.e., a pad-sensor,
remain isolated without an isolation implant when operated at the bias voltage
of 600 V.

(a)

(b)

Figure 9: Comparison of simulated $V_{\textrm{th,iso}}$ in the
$R_{\textrm{int}}$-characteristics of a 300-$\upmu\textrm{m}$-thick $n$-on-$p$
test diode for two $N_{\textrm{ox}}$-levels from Figure 6a, along with
$N_{\textrm{ox}}$-level that results in
$V_{\textrm{th,iso}}(R_{\textrm{int}})=600~{}\textrm{V}$ with (a)
$V_{\textrm{th,iso}}$ in the $CV$-characteristics of the two lower
$N_{\textrm{ox}}$-levels and (b) the change in electron density at 1 nm depth
from the Si/SiO2-interface in the middle of the inter-electrode gap.

The sensitivity of $V_{\textrm{th,iso}}$ to the influence of $N_{\textrm{B}}$
and the active thickness ($t$) of the sensor is presented in Figure 10. With a
constant $t$ and $N_{\textrm{ox}}$, $V_{\textrm{th,iso}}$ displays a strong
dependence on $N_{\textrm{B}}$ in Figure 10a with
$V_{\textrm{th,iso}}>V_{\textrm{fd}}$ at $N_{\textrm{B}}\leq 3\times
10^{12}~{}\textrm{cm}^{-3}$ and $V_{\textrm{th,iso}}<V_{\textrm{fd}}$ at
$N_{\textrm{B}}\geq 4\times 10^{12}~{}\textrm{cm}^{-3}$. As shown in Figure
10b, increased $N_{\textrm{B}}$ suppresses the minority carrier density close
to Si/SiO2-interface leading to reduced voltages required to isolate the
electrodes, thus moving $V_{\textrm{th,iso}}$ to lower voltages in Figure 10a.
Additionally, with a constant $N_{\textrm{B}}$ and $N_{\textrm{ox}}$,
$V_{\textrm{th,iso}}$ displays significant dependence on $t$ in Figure 10c,
with $V_{\textrm{th,iso}}>V_{\textrm{fd}}$ at $t<300~{}\upmu\textrm{m}$ and
${\Delta}V_{\textrm{th,iso}}{\approx}-60~{}\textrm{V}$ when $t$ is reduced
from 300 to 120 $\upmu\textrm{m}$. Since for a given voltage higher electric
fields are generated in a thinner sensor, a lower voltage for a thinner sensor
is required to generate sufficient field to reduce electron density in the
inter-electrode gap to a level that isolates the electrodes, displayed by
lower $V_{\textrm{th,iso}}$ with reduced $t$ in Figure 10c. As a consequence,
$CV$-extracted $V_{\textrm{th,iso}}$($N_{\textrm{ox}},N_{\textrm{B}},t$) and
therefore the results in Figures 7a and 9a should be considered for fixed
$N_{\textrm{B}}=4.0\times 10^{12}~{}\textrm{cm}^{-3}$ and
$t=300~{}\upmu\textrm{m}$.

(a)

(b)

(c)

Figure 10: Simulation results of an $n$-on-$p$ test-diode with floating guard-
ring for the influence of $N_{\textrm{B}}$ and $t$ on $V_{\textrm{th,iso}}$.
(a) Change of $V_{\textrm{th,iso}}$ with $N_{\textrm{B}}$ for constant
$t=300~{}\upmu\textrm{m}$ and $N_{\textrm{ox}}=1\times
10^{11}~{}\textrm{cm}^{-2}$. (b) Corresponding electron density to Figure 10a
close to the Si/SiO2-interface at mid-gap between pad and guard-ring for
$V=0$. (c) Change of $V_{\textrm{th,iso}}$ with $t$ for constant
$N_{\textrm{B}}=4\times 10^{12}~{}\textrm{cm}^{-3}$ and
$N_{\textrm{ox}}=1\times 10^{11}~{}\textrm{cm}^{-2}$.

###  4.2 8-inch HGCAL sensors

To extend the investigation presented in Section 4.1 to 8-inch HGCAL sensors,
the region between the two guard-rings in the periphery of a HGCAL sensor
displayed in Figure 3 was considered. To limit the lateral extension of the
active region of the multi-channel sensor toward the physical wafer edge, the
guard-ring closer to the HV-ring (‘Floating GR’ in Figure 3) is left floating
in the ARRAY setup’s probe card by default. The electrical configuration
between the biased (bias-GR) and floating guard-rings in the HGCAL sensor is
then identical to the test diode with a floating guard-ring (i.e., no
isolation implant between the biased and floating $n^{+}$-electrodes). The
main difference between the devices comes from their geometry, since instead
of a square-shaped pad of the test diode, the biased electrode is now a
$115~{}\upmu\textrm{m}$-wide strip with a hexagon shape for the full sensors
in Figures 2a and 2b, and polygon and rectangle shapes for the Multi-Geometry
Wafer (MGW)-sensor in Figure 2c. Additionally, the gap between the two
electrodes is 62 and $100~{}\upmu\textrm{m}$ for the HGCAL sensor and test
diode, respectively. Thus, despite the differences in the device geometry to
the test diodes the $CV$-characteristics of the HGCAL sensors’ bias-GR are
expected to provide an observation of $V_{\textrm{th,iso}}$.

As shown in Figures 11 and 12, bias-GR $CV$-characteristics of all measured
HGCAL sensor types display $V_{\textrm{th,iso}}$ either below (Figures 11a,
11b and 12b) or above (Figures 11c and 12a) $V_{\textrm{fd}}$ (values of
$\overline{V}_{\textrm{fd}}$ are given in A). In all cases the
$n^{+}$-electrodes without $p$-stop isolation implant become isolated at
$V_{\textrm{th,iso}}\leq 100~{}\textrm{V}$, which is significantly below the
operating voltage of 600 V considered for HGCAL [7]. The wafer-position
dependence of $V_{\textrm{th,iso}}$ observed in the test-diode results in
Figures 7b and 7c is also visible in Figure 12 where the ‘bottom-cut’ partial
sensors have three bias-GRs enclosing three regions of the sensor, as shown in
Figure 2c. The different lengths between the rectangular bias-GR at the center
of the sensor (channel 473) and the two polygonal bias-GRs adjacent to it
(channels 472 and 474) in the ‘bottom-cut’ sensor are reflected in the
different values of $C_{\textrm{geom}}$, according to Eq. 1.

With the observations from Figure 10, dedicated $t$ and $N_{\textrm{B}}$ were
applied to each of the modeled sensor structures to reproduce the measured
$V_{\textrm{th,iso}}$ by simulation. After $N_{\textrm{ox}}$-tuning the main
disagreement between simulation and measurement for
300-$\upmu\textrm{m}$-thick full sensors in Figure 11a is in the region
$V<V_{\textrm{th,iso}}$, where the lower slope of the simulated
$C^{-2}V$-curve indicates a wider lateral expansion of the depletion volume
before the biased and floating guard-rings become isolated than in the real
sensor. In Figure 11b the disagreement between simulation and measurement for
200-$\upmu\textrm{m}$-thick full sensors is now in the region
$V>V_{\textrm{th,iso}}$, where the further limited decrease of the active
volume involved in the bias-GR $CV$-measurement at $V>V_{\textrm{fd}}\approx
115~{}\textrm{V}$ is not reproduced by the simulation. The same trend is
visible in Figure 11c for 120-$\upmu\textrm{m}$-thick full sensors even though
$V_{\textrm{fd}}\approx 31~{}\textrm{V}$, thus the feature is only dependent
on $V_{\textrm{th,iso}}$ and present only in the bias-GR $CV$-characteristics
of full 200- and 120-$\upmu\textrm{m}$-thick sensors. The onset of the feature
has a dependence on active thickness, being about 20 V lower for
120-$\upmu\textrm{m}$-thick sensors than for 200-$\upmu\textrm{m}$ thickness,
while its interpretation is left out of the scope of this study. The sole
significant disagreement between simulation and measurement for the partial
‘bottom-cut’ 120-$\upmu\textrm{m}$-thick sensors in Figures 12a and 12b is in
the abruptness of the decrease of $C$ immediately after $V_{\textrm{th,iso}}$,
indicating that the electrons are being swept from the inter-electrode gap to
the positively biased guard-ring more swiftly in the simulation than in
measurement. Considering that the length-ratio of the bias-GRs in the ‘bottom-
cut’ partial and the full sensors is roughly $\frac{1}{6}$, the results
suggest that the 2D TCAD-simulation is able to reproduce more closely the
measured $CV$-characteristics of the bias-GRs that enclose a smaller sensor-
region. This is also supported by the close agreements between measurements
and simulations of test diodes in Section 4.1 with substantially smaller area
and less complex geometry to the bias-GRs of HGCAL sensors.

(a)

(b)

(c)

Figure 11: Measured and simulated $CV$-characteristics for the biased guard-
ring (‘GR’) in full 8-inch HGCAL sensors with oxide type ‘C’. Sensor IDs are
indicated in the legends, while the simulation input values of
$N_{\textrm{B}}$ are given in Figure 15. (a) Measured results of five
300-$\upmu\textrm{m}$-thick LD-sensors with $V_{\textrm{th,iso}}$ of the
sensor ‘100277’ reproduced by the simulation with the input
$N_{\textrm{ox}}=6.90\times 10^{10}~{}\textrm{cm}^{-2}$. Out of the 20
measured sensors, only $C^{-2}V$-curves with significant variation in
$V_{\textrm{th,iso}}$ are included in the plot for clarity. (b) Measured
results of five 200-$\upmu$m-thick LD-sensors with $V_{\textrm{th,iso}}$ of
the sensor ‘200148’ reproduced by the simulation with the input
$N_{\textrm{ox}}=6.45\times 10^{10}~{}\textrm{cm}^{-2}$. (c) Measured results
of three 120-$\upmu$m-thick HD-sensors with $V_{\textrm{th,iso}}$ of the
sensor ‘300066’ reproduced by the simulation with the input
$N_{\textrm{ox}}=6.65\times 10^{10}~{}\textrm{cm}^{-2}$.

(a)

(b)

Figure 12: Measured and simulated $CV$-characteristics for the biased guard-
rings (‘GR 472–474’corresponding to the channel numbers in Figure 2c) in
8-inch partial (‘bottom-cut’) 120-$\upmu$m HD HGCAL sensors. The simulation
input values of $N_{\textrm{B}}$ are given in Figure 16. (a) Measured results
of two sensors with oxide type ‘B’ with $V_{\textrm{th,iso}}$ of the ‘GR 474’
of the sensor ‘600036’ reproduced by the simulation with the input
$N_{\textrm{ox}}=5.98\times 10^{10}~{}\textrm{cm}^{-2}$. (b) Measured results
of two sensors with oxide type ‘D’ with $V_{\textrm{th,iso}}$ of the ‘GR 474’
of the sensor ‘600025’ reproduced by the simulation with the input
$N_{\textrm{ox}}=5.15\times 10^{10}~{}\textrm{cm}^{-2}$.

The investigated HGCAL sensors included three oxide-quality types:‘C’ for the
full sensors, and ‘B’ and ‘D’ for the partial sensors indicating HPK’s oxide
candidates with the oxide growth thermally and environmentally varied. By
generating additional data-points for each sensor configuration and oxide
type, the extracted $\overline{N}_{\textrm{ox}}$ are presented in Table 1. For
full sensors with oxide type ‘C’ the values of $\overline{N}_{\textrm{ox}}$
remain within uncertainty for the three thicknesses, while being distinctly
higher than $\overline{N}_{\textrm{ox}}$ of both ‘B’ and ‘D’. Comparison with
$V_{\textrm{fb}}$-extracted $\overline{N}_{\textrm{ox}}$
($\overline{N}_{\textrm{ox,gate}}$) from the MOS-capacitor measured results in
Table 1 and Figure 13 shows matching qualitative trend between the oxide
types, while the values of $\overline{N}_{\textrm{ox,gate}}$ remain lower than
$\overline{N}_{\textrm{ox}}$ by a factor $0.77\pm 0.13$ (considering average
$(6.7\pm 0.3)\times 10^{10}~{}\textrm{cm}^{-2}$ of the field-region
$\overline{N}_{\textrm{ox}}$-values for type ‘C’ in Table 1) over the three
oxide types. The disagreement between $\overline{N}_{\textrm{ox,gate}}$ and
$\overline{N}_{\textrm{ox}}$ observed here is in contrast with the observed
corresponding agreement between test structures in Section 4.1, which suggests
that $N_{\textrm{ox}}$ in the field region between the biased guard-ring and
HV-ring of HGCAL sensors is somewhat higher than the gate $N_{\textrm{ox}}$ at
their respective MOS-capacitors. Since the oxide-quality types available for
this investigation are only a subset of the multitude of oxide type candidates
provided by HPK to the HGCAL collaboration, further comparisons between the
oxide-quality types are not included in the scope of this study.

Table 1: Active thicknesses, sensor and passivation oxide types, number of measured sensors, the mean field-region oxide charge densities ($\overline{N}_{\textrm{ox}}$), number of measured MOS-capacitors and the mean gate oxide charge densities ($\overline{N}_{\textrm{ox,gate}}$) at the Si/SiO2-interface.  Active thickness | Sensor type | Oxide | Measured | $\overline{N}_{\textrm{ox}}$ | Measured | $\overline{N}_{\textrm{ox,gate}}$
---|---|---|---|---|---|---
[$\upmu$m] | type | sensors | [$\times 10^{10}~{}\textrm{cm}^{-2}$] | MOS | [$\times 10^{10}~{}\textrm{cm}^{-2}$]
300 | LD full | C | 20 | $6.74\pm 0.14$ | 6 | $5.2\pm 0.3$
200 | LD full | C | 5 | $6.64\pm 0.12$
120 | HD full | C | 4 | $6.8\pm 0.2$
120 | HD ‘bottom-cut’ | B | 2 | $6.01\pm 0.14$ | 6 | $4.5\pm 0.5$
120 | HD ‘bottom-cut’ | D | 2 | $5.32\pm 0.17$ | 4 | $4.2\pm 0.4$
Figure 13: $\overline{N}_{\textrm{ox}}$-values from Table 1 for the three
oxide quality types, extracted either from bias-GR measurements and
simulations (‘Field-$N_{\textrm{ox}}$’) or from MOS-capacitor measurements
(‘Gate-$N_{\textrm{ox}}$’).

Displayed in Figure 14a the dependence of the field-region $N_{\textrm{ox}}$
on $V_{\textrm{th,iso}}$ for the three HGCAL sensor thicknesses (with the
simulation input $\overline{N}_{\textrm{B}}$ from Figures 15 and 16) can be
described by second-order polynomial fits in the region $N_{\textrm{ox}}\leq
1.0\times 10^{11}~{}\textrm{cm}^{-2}$ (a range which includes all extracted
$\overline{N}_{\textrm{ox}}$-values in Table 1). When the simulated
$V_{\textrm{th,iso}}$-range is extended from $<200~{}\textrm{V}$ to 600 V, the
dependence is best described by linear fits in Figure 14b. The
$V_{\textrm{th,iso}}$-dependence of $N_{\textrm{ox}}$ at both high and low
$N_{\textrm{ox}}$-regions for HGCAL sensors is then distinct from the power-
law dependence of the test diodes in Figure 7a, suggesting an influence from
the substantially different geometries between the simulated device-structures
in Sections 4.1 and 4.2. Since the observed $V_{\textrm{th,iso}}$ contains
simultaneously information on $N_{\textrm{ox}}$ and on the change from low to
high levels of $R_{\textrm{int}}$, shown in Figure 9a, the simulated data-
points in Figure 14b provide threshold-values of $N_{\textrm{ox}}$ below which
$n^{+}$-electrodes without isolation implants are predicted to be isolated in
HGCAL sensors operated at $V_{\textrm{bias}}=600~{}\textrm{V}$.

(a)

(b)

Figure 14: The simulated dependence of the field-region $N_{\textrm{ox}}$ on
$V_{\textrm{th,iso}}$ for the three active thicknesses of the 8-inch HGCAL
sensors with the input values of $N_{\textrm{B}}$ indicated in the legends.
(a) Simulation results for the input $N_{\textrm{ox}}\leq 1.0\times
10^{11}~{}\textrm{cm}^{-2}$ with second-order polynomial fits to the data-
sets. (b) Input $N_{\textrm{ox}}$-range extended to the levels that result in
$V_{\textrm{th,iso}}=600~{}\textrm{V}$ with linear fits to the data-sets. The
fit parameters are displayed in the plots.

##  5 Discussion

The results in Section 4.2 indicate that pre-irradiated $n$-on-$p$ sensors
without isolation implants between the channels can reach electrical
isolation, and thus uncompromised position resolution between the channels, by
the application of sufficient reverse $V_{\textrm{bias}}$ (for the
$N_{\textrm{ox}}$-values in Table 1 at about
$V_{\textrm{bias}}>40-100~{}\textrm{V}$). As the highest
$N_{\textrm{ox}}$-values in SiO2-passivated Si-sensors with $\langle
100\rangle$ crystal orientation are typically well below $2\times
10^{11}~{}\textrm{cm}^{-2}$ [10, 26], also these levels are expected to be
within the isolation range of the operation voltage 600 V, as shown in Figure
14b (for $2\times 10^{11}~{}\textrm{cm}^{-2}$ all sensor types become isolated
in the range of about 320–500 V).

In irradiated sensors, the surface damage caused by ionizing radiation from
charged particles, X-rays or gammas includes the accumulation of
$N_{\textrm{f}}$ and deep donor- and acceptor-type $N_{\textrm{it}}$
($N_{\textrm{it,don}}$ and $N_{\textrm{it,acc}}$, respectively) that
contribute to the net $N_{\textrm{ox}}$ at the Si/SiO2-interface. Previous
experimental $R_{\textrm{int}}$-results of 200- and
290-$\upmu\textrm{m}$-thick $n$-on-$p$ strip-sensors without $p$-stop implants
neutron or proton irradiated to $\Phi=6\times
10^{14}~{}\textrm{n}_{\textrm{eq}}\textrm{cm}^{-2}$, corresponding to the
estimated Total Ionizing Doses (TID) of 6 and 870 kGy, respectively, show high
levels of inter-strip isolation at $V_{\textrm{bias}}>100~{}\textrm{V}$ (see
Figure 9 in ref. [20]). As described in ref. [10], radiation accumulated
levels of $N_{\textrm{it,don}}$ and $N_{\textrm{it,acc}}$ comparable to
$N_{\textrm{f}}$ introduce a dynamic characteristic to the net
$N_{\textrm{ox}}$, as the fractions of fully occupied $N_{\textrm{it}}$ evolve
with applied voltage. Contribution from fully occupied $N_{\textrm{it,acc}}$
results in considerably low levels of net $N_{\textrm{ox}}$ in the field-
region between the positively biased $n^{+}$-electrodes (see Figure 8 in ref.
[10]) of a position sensitive $n$-on-$p$ sensor, which remain within the
isolation range in Figure 14b. Thus, the radiation-induced accumulation of
$N_{\textrm{it,acc}}$ at the Si/SiO2-interface has a beneficial impact on the
inter-electrode isolation in irradiated $n$-on-$p$ sensors, while simulations
[10] and $R_{\textrm{int}}$-measurements [20] indicate its introduction rate
being more prominent in a radiation environment involving hadrons.

Thus, the combined observations before and after irradiation indicate that the
inter-electrode isolation and consequently position resolution between
$n^{+}$-electrodes without isolation implants can be reached and maintained by
the application of sufficient $V_{\textrm{bias}}$, with the tolerance for high
net $N_{\textrm{ox}}$-levels increasing with reduced active thickness of the
sensor.

##  6 Summary and conclusions

Measured $CV$-characteristics of 6-inch 300-$\upmu\textrm{m}$-thick $n$-on-$p$
Si-wafer test diodes with floating guard-ring display a double-slope with a
distinct $V_{\textrm{th,iso}}$ in the dynamic region of $C^{-2}V$-curve. The
corresponding TCAD-simulations show that this is due to the electron removal
along the Si/SiO2-interface from the inter-electrode gap to the positively
biased test-diode pad, until at $V~{}{\geq}~{}V_{\textrm{th,iso}}$ the
conduction channel between the two $n^{+}$-electrodes is broken. This is
reflected in the $CV$-characteristics of the test-diode pad as an abrupt drop
of capacitance. The field-region $N_{\textrm{ox}}$ is obtained by tuning its
simulation input value until a $V_{\textrm{th,iso}}$ matching with the
measurement is reproduced. The values of $N_{\textrm{ox}}$ determined by this
approach agree within uncertainty with $N_{\textrm{ox}}$ extracted from the
measured $V_{\textrm{fb}}$ of MOS-capacitors from the same samples.
$R_{\textrm{int}}$-simulations show that the threshold voltage where segmented
$n^{+}$-electrodes without isolation implants reach high levels of
$R_{\textrm{int}}$ and thus become electrically isolated is identical to
$V_{\textrm{th,iso}}$($CV$), i.e.,
$V_{\textrm{th,iso}}(CV)=V_{\textrm{th,iso}}(R_{\textrm{int}})$. Hence,
observation of $V_{\textrm{th,iso}}$($CV$) provides simultaneously information
on both field-region $N_{\textrm{ox}}$ and isolation between
$n^{+}$-electrodes without isolation implants. Further test-diode simulations
show that $V_{\textrm{th,iso}}$ also has significant dependence on both active
thickness and bulk doping of the sensor.

Measured and simulated $CV$-characteristics of the biased guard-ring on the
8-inch HGCAL-prototype and pre-series sensors with varied Si-bulk and
passivation oxide parameters reproduce the observation of
$V_{\textrm{th,iso}}$ universally. These display low values in the range of
about $40-100~{}\textrm{V}$ that correspond to field-region
$N_{\textrm{ox}}\approx(5-7)\times 10^{10}~{}\textrm{cm}^{-2}$.

The apparent high isolation levels between $n^{+}$-electrodes without
isolation implants reachable by the application of sufficient
$V_{\textrm{bias}}$ ($<200~{}\textrm{V}$ with the initial $N_{\textrm{ox}}\leq
1\times 10^{11}~{}\textrm{cm}^{-2}$) both before and after irradiation in a
hadron-dominated radiation environment make this configuration, with a similar
number of lithography and ion-implantation steps as $p$-on-$n$ sensors, a
potentially feasible $n$-on-$p$ sensor candidate for future HEP-experiments.
With respect to sensor performance, the isolation implantless configuration of
position sensitive $n$-on-$p$ sensors removes the probability of discharges or
avalanche effects due to excessive electric fields at the $p$-stops.

## Acknowledgements

This work has been supported by the US Department of Energy, Office of Science
(DE-SC0015592). We thank Ronald Lipton of FNAL for his invaluable insights on
the analysis of this investigation. We also thank K. Zinsmeyer, C. Perez, and
posthumously P. Cruzan of TTU for their expert technical support.

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##  Appendix A $V_{\textrm{fd}}$ and bulk doping of the HGCAL sensors

Data analysis in Figures 15 and 16 was realized by HGCAL Analysis Workflow
software101010https://gitlab.cern.ch/CLICdp/HGCAL/.

(a)

(b)

(c)

Figure 15: Measured $CV$-characteristics for one representative channel in
full 8-inch HGCAL sensors with oxide type ‘C’. The extracted $V_{\textrm{fd}}$
is indicated at the crossing-point of the two linear fits to the dynamic- and
static-regions of the $C^{-2}V$-data. (a) 300-$\upmu\textrm{m}$-thick LD-
sensor with global $\overline{V}_{\textrm{fd}}=255.7~{}\textrm{V}\pm 1.1\%$
and derived $\overline{N}_{\textrm{B}}=3.67\times
10^{12}~{}\textrm{cm}^{-3}\pm 1.1\%$. (b) 200-$\upmu$m-thick LD-sensor with
global $\overline{V}_{\textrm{fd}}=115.7~{}\textrm{V}\pm 0.6\%$ and derived
$\overline{N}_{\textrm{B}}=3.73\times 10^{12}~{}\textrm{cm}^{-3}\pm 0.6\%$.
(c) 120-$\upmu$m-thick HD-sensor with global
$\overline{V}_{\textrm{fd}}=31.2~{}\textrm{V}\pm 0.8\%$ and derived
$\overline{N}_{\textrm{B}}=2.80\times 10^{12}~{}\textrm{cm}^{-3}\pm 0.8\%$.

(a)

(b)

Figure 16: Measured $CV$-characteristics for one representative channel in
8-inch partial (‘bottom-cut’) 120-$\upmu$m HD HGCAL sensors. (a). Sensor with
oxide type ‘B’, and with global
$\overline{V}_{\textrm{fd}}=31.2~{}\textrm{V}\pm 0.7\%$ and derived
$\overline{N}_{\textrm{B}}=2.80\times 10^{12}~{}\textrm{cm}^{-3}\pm 0.7\%$.
(b) Sensor with oxide type ‘D’, and with global
$\overline{V}_{\textrm{fd}}=55.8~{}\textrm{V}\pm 1.0\%$ and derived
$\overline{N}_{\textrm{B}}=5.0\times 10^{12}~{}\textrm{cm}^{-3}\pm 1.0\%$.