Development of AC-LGAD detector with finer pitchelectrodes for high energy physics experiments
Sayuka K ITA1 , Koji N AKAMURA2 , Tomoka I MAMURA1 , Ikumi G OYA1 ,Kazuhiko
H ARA3
1

Graduate School of Science and Technology, University of Tsukuba, 1-1-1 Tennodai,
Tsukuba, Ibaraki, 305-8571, Japan
2
Institute of Particle and Nuclear Studies, High Energy Research Organization, 1-1 Oho,
Tsukuba, Ibaraki, 305-0801, Japan
3
Faculty of Pure and Applied Sciences and Tomonaga Center for the History of the Universe,
University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8571, Japan
E-mail: kita@hep.px.tsukuba.ac.jp, Koji.Nakamura@cern.ch(Received May 23, 2023)
Low-Gain Avalanche Diode (LGAD) sensor is one of candidate sensors for the tracker at future hadron collider experiments. To use this sensor as a tracking detector, AC-LGAD sensor
is being developed which has both timing and spatial resolutions. In high luminosity environments, good timing resolution (typically 30 ps) together with O (10 µm) spatial resolution helps
to reduce pileup effect and reconstruct tracks correctly. By optimizing fabrication parameters,
80 µm pitch strip and 100 µm pitch pixel sensors are successfully produced. The signal height(MPV) was 39.26±0.08 mV and 128.9±3.3 mV, respectively, for penetrating β particles. The
observed 60% of signal reduction of the strip sensor is explained by a larger inter-electrodecapacitance compared with the pixel sensor. In this paper, we present the performance offine electrode pitch AC-LGAD sensors including the pulse height and cross-talk of pixel andstrip type sensors evaluated using a β-ray source and the detection efficiency measured in an
800 MeV electron beam.

KEYWORDS: silicon, tracker, LGAD, AC-LGAD

1.

Introduction

Tracking detectors in future high-energy and high-luminosity hadron colliders are required to correctly assign the tracks associated to the hard scattering vertex among huge
number of pileup vertices. Up to 200 collisions are expected in an event at the HL-LHC ATLAS
experiment [1] and 10 times more in the future circular hadron collider. In such an environment, a revolution in the tracking system is required, e.g., realization of a time resolution ofO (10) ps in addition to a spatial resolution of O (10) µm.
The Low-Gain Avalanche Diode (LGAD) is a semiconductor detector with improved time
resolution. Presently a time resolution of 30 ps [2] has been achieved for minimum ionizing
particles (MIPs). In realizing the spatial resolution with LGAD, we have identified potential
difficulties in improving the granularity of the electrodes [3, 4] without decreasing the active
area fraction. To solve the issue, a capacitively-coupled LGAD sensor (AC-LGAD) [5] has beendeveloped by KEK and University of Tsukuba in collaboration with Hamamatsu Photonics
K.K. (HPK). In the previous study [6], the three process parameters, n+ and p+ implant concentrations and electrode coupling capacitance, were varied and the fundamental AC-LGAD
performance was evaluated to optimize the parameters.

1

In this paper, the performance of fine electrode pitch sensors with pixel type and strip typeelectrodes is described.

2.

AC-LGAD prototypes

The LGAD sensor is basically an n+ -in-p semiconductor diode, containing an additionalp layer under the n+ electrode with a larger boron doping compared to that in the p-bulk
region. The additional layer makes an extremely high electric field, typically over 300 kV/cm,
between n+ and p+ . Such a large electric field induces avalanche multiplication, increasing
the number of electron and hole pairs by about 10-20 times of that originally produced bya MIP. Superior time resolution is a consequence of rapid movement of a large number ofelectrons and holes created in the gain region by the high electric field. Concerning the spatial
resolution improvement, the granularity of the electrodes is increased. In case where the gain
layers (combination of n+ and p+ ) are formed separately for each direct-coupled electrode,the regions between the n+ electrodes have no gain hence the fill factor is low as describedin [4]. To overcome this feature, a capacitively-coupled LGAD (AC-LGAD) sensor, as shown in
Fig. 1(a), has been developed. A single uniform gain layer is placed over the sensor active areaand for the segmented readout, patterned aluminum electrodes are placed on the oxide layer,
and the induced signal is read out capacitively. The uniform gain layer eliminates the inactive
regions as the avalanche multiplication occurs uniformly across the entire active area.
Fig. 1(b) illustrates the signal readout principle of the AC-LGAD sensor and equivalentcircuit. The signal charge produced by the avalanche (Q 0 ) flows in two paths; one is read out
via coupling capacitors (C cp ), and the other is cross-talk through the n+ implant that has aneffective resistance (R imp ). The read out charge (Q) is determined by the impedance ratio of
the two, ZCcp and Z Rimp , which are the impedances of C cp and R imp , respectively. Additionalcross-talk is expected via inter-electrode capacitance (C int ) in case ZCint is large and becomescomparable to ZCcp . Although a presence of cross-talk to the neighboring electrodes through n+
layer is a feature of AC-LGAD sensor, optimization study of n+ and p+ doping concentrations
succeeded in suppressing the cross-talk reasonably small and keeping the signal height large,
as described in [5] and [6].
+DC elec

Al

SiO2

n+
p+

n++

Cint

AC elec-- -eeee-h+e ee-e-- - h-nhhhhe h h
e eh-he ehhhh ph++h
e-

n++
eee-

-

Ccp

Cint
Ccp

Ccp

n+

h

h

Rimp

h

p-

(a) AC-LGAD detector

Rimp
Cbulk

p+

(b) Signal readout model of AC-LGAD

Fig. 1. AC-LGAD detector (left) and signal readout model of AC-LGAD (right).

According to the signal readout model, the coupling capacitance (C cp ) and inter electrodecapacitance (C int ) are the important parameters to be optimized while the effective n+ resistance (R imp ) is optimized to be as large as possible but avoiding the depletion to reach the insulator. The C cp was varied by the thickness of the insulator (a combination of silicon dioxide andsilicon nitride) layer as well as the area of the electrode. The thickness of the insulator layer2was varied so that the coupling capacitance is 120 pF/mm2 , 240 pF/mm2 and 600 pF/mm2 ,each for the two n+ resistivity points, as summarized in Table I. Since the Al electrode determines the granularity of the device, sensors with various pitches are tested. All the prototype
sensors used for the study in this article are summarized in Table II.

Table I. Summary of six prototype variations in n+ implant concentrations and coupling capacitances, C cp .

C cp [pF/mm2 ]
600
240
120
E600 E240 E120
C600 C240 C120

n resistivity [Ω/□]
1600
400
+

The p+ concentration was tuned to keep the LGAD operation voltage in a range for eachof the n+ resistivity points. The operation voltage is similarly 190 V among C-type senors and
160 V among E-type sensors, so the sensor performance of each type can be compared at thesame bias voltage.

Table II. Physical parameters of the produced sensor types; Strip and Pixel. The overall size, electrode pitch, electrode width, and the numbers of electrodes in column and row directions are summarized. "Cut Strip" contains strips of different lengths (200µm ∼ 8890µm) in one sensor.
Sensor typeoverall dimension (mm)electrode pitch (µm)
electrodedimension (µm)#column×#row

3.

Strip

Cut Strip

11.2 × 2.7
8040, 45, 60, 70
40, 60×9880
×200∼8890
16×1

Pixel
100×100
90
×90
10×10

2.4 × 2.4
150×150
140
×140
6×6

200×200
190
×190
5×5

Performance dependence on the fabrication parameters

Experimental procedure using β source
The sensor performance dependence on the sensor fabrication parameters is evaluatedby injecting 90 Sr β-ray as MIP. The reverse bias (negative voltage) is supplied to the rear of
the sensor via conductive tape attached on a KEK 16ch amplifier board [6]. The scintillation
counter read out with MPPCs is used as the trigger. The amplified signals are digitized by adesktop digitizer, CAEN DT5742 (5 GHz sampling with 1024 long memory of 12-bit ADC with
1 V full scale) [6]. Typical pulse shape is reported in elsewhere [5].
The signal pulse height is searched for among the sampled points as the largest negative
height among the all readout channels, 4×4 for the pixel and consecutive 16 for the strip
sensors. The arrival time of the signal is defined as the time at 50% of the pulse height. The
pulse height distributions as shown in Fig. 2(a) (and also in Fig. 4(a)) are for the events whose
arrival time is between 0 to 30 ns. The signal size of the distribution is evaluated as MPV ofthe distribution of the signal pulse heights separated from the "noise" fitted by a Landau andGaus convoluted function [6]. The "noise" events are for the case β-ray traversed outside the

3.1

3

105

Rejection factor

Entriesreadout area representing the largest noise observed in this time range. The noise distribution
is fitted by an asymmetric double Gaussian function.
Fig. 2(b) shows the relationship of noise rejection factor and signal efficiency. A signal
efficiency of 99.54 % is achievable at a 10−4 of noise rate (104 of rejection factor).

Data
104

Signal fit
3

10

Pedestal fit

106
105
104
103

102

102

10

10

1
0

0.05

0.1

0.15

0.2

0.25

0.3

Pulse Height [V]10.988 0.99 0.992 0.994 0.996 0.998

1

Signal efficiency(a) Pulse height distribution.

(b) Signal efficiency and rejection factor.

Fig. 2. (a) Pulse height distribution of E600 pixel sensor of 100 µm pitch evaluated using 90 Sr. Red
and blue curves correspond to fitted signal and noise distributions. (b) The signal efficiency and rejection
factor of the same sensor.

3.2

Pixel dependence on R imp and C cp
To measure the dependence on R imp and C cp , the six 150 µm pitch pixel sensors are compared for the signal size. Fig. 3(a) shows the signal size with respect to C cp for the two R imp
values. Red and blue points correspond to R imp value of 400 Ω/□ (C-type) and 1600 Ω/□ (Etype), respectively. The signal size becomes larger with C cp and R imp as expected: the sensor
with maximum signal size is of 1600 Ω/□ of R imp and 600 pF/mm2 of C cp .
3.3

Dependence on the pixel pitch
The signal size is compared among pixel sensors with different pitches, 100, 150 and
200 µm and with C cp of 600 pF/mm2 . The signal size is observed very similar in each of theR imp values, as shown in Fig. 3(b).
For the 100 µm pixel sensor with 1600 Ω/□ and 600 pF/mm2 , the obtained signal size is
128.9±3.3 mV as a fit shown in Fig.2(a), and the separation of signal and noise distributions
is excellent.
3.4 Strip sensor performance
3.4.1 signal size and cross-talk
The performance of the strip sensor is also studied using β ray as the strip sensors areuseful in reducing the total number of readout channels in experiments. Fig. 4(a) is the distribution of largest single channel pulse height in 16 consecutive readout strips of E600 type. The
signal MPV is 39.26±0.08 mV, and signal efficiency calculated as for the pixel sensor is 99.99%
at a 10−4 of noise rate. The magnitude of cross-talk is also evaluated as the pulse height ratio
to the leading strip with the largest pulse height in an event, The magnitude of the cross-talk4

Signal size [V]Signal size [V]

0.14
0.12
0.1
0.08

0.3
Rimp 400 Ω/

0.25

Rimp 1600 Ω/

0.2
0.15

0.06
0.1
0.04

Rimp 400 Ω/

0.02

Rimp 1600 Ω/

0
0

0.05
0
0

100 200 300 400 500 600 700 800

50

100

150

200

250

300

Pixel pitch [µm]2

Ccp [pF/mm ](a) Dependence on R imp and C cp .

(b) Dependence on pixel pitch.

Fig. 3. (a) The signal size evaluated using 90 Sr as a function of C cp . Each colored point corresponds
to fixed R imp value. (b) The Signal size evaluated using 90 Sr as a function of pixel pitch (C cp is
600 pF/mm2 ). Each colored point corresponds to fixed R imp value.

104
103

Pulse Height Ratio to Leading strip

Entriesis shown in Fig. 4(b) as a function of the distance to the leading strip. The cross-talk distanceis defined as the distance constant of an exponential function fitted to the profiled data points.
The cross-talk distance of E600 strip is 62.4±0.8 µm, which is smaller than 1 strip distance,
so the cross-talk suppression is reasonably achieved. The results indicate the designed strip
sensor has a good signal to noise ratio and a small cross-talk, performance being expected in
hadron collider experiments. Note that the non-zero constant at the tail is due to the featureof searching for the largest noise in the pre-defined time range of 30 ns.

Data
Signal fit
Pedestal fit

2

10

10

1

1.2

5000
0.8
4000
0.6
3000
0.4

Pulse Height [V]

2000

0.2
0

0 0.020.040.060.08 0.1 0.120.140.160.18 0.2

6000

1

1000
2

4

6

8

10

12

14

0

distance from leading strip [Strip](a) Pulse height distribution.

(b) Pulse height ratio to leading strip.

Fig. 4. (a) Pulse height distribution of strip E600 evaluated using 90 Sr. Red and blue curves are fitted
signal and noise distributions. (b) Pulse height ratios to the leading strip as function of distance fromleading strip. Black dots are profiled points and fitted by an exponential + constant function.

5

0.14

Crosstalk ratio

Pulse height [V]3.4.2 signal size dependence on the strip length
Comparing the pulse heights of the strip and pixel sensors, the strip signal size is smaller
than pixel, by a factor of about 3, although the strip is larger in the electrode area, hence larger
coupling capacitance. A larger inter-electrode capacitance in the strip sensor is in effect. To
check this, a dedicated strip sensor of which strip electrodes have different lengths is fabricatedand response to β ray is measured. The strip sensor has cut-lines in diagonal direction, cutting
16 electrodes at different lengths making 32 electrodes with different lengths (as the strip isread out from both sides). In addition, we fabricated 2 electrode widths, 40 µm and 60 µm,
at the same 80 µm pitch. The signal size is observed to become smaller with strip length asshown in Fig. 5(a). Each colored point corresponds to the strip width of 40 µm (Narrow) or
60 µm (Wide). The wide strip has a larger slope, indicating the signal reduction with lengthis due to inter-strip capacitance, which is larger in wide electrode strips. In case of the wide
strip, the signal size is reduced to 40% from 1 mm to 10 mm strip length. The cross-talk isalso measured. The cross-talk ratio in Fig. 5(b) is evaluated as pulse height ratio of leading
strip to the sum of both neighboring strips. The cross-talk increases with strip length, and incase of wide strip, the cross-talk ratio is 1.2 at 10 mm. The significant increase of cross-talk
contributes in reduction of signal size of the leading strip. The observation suggests that thesignal pickup is very similar between the strip and pixel, and the strip sensor of 10 mm lengthis useful if the magnitude of the cross-talk is taken into account.

0.12

Narrow strip

0.1

Wide strip

0.08

1.4
1.2
1
0.8

0.06

0.6

0.04

0.4

0.02

0.2

0
0

1

2

3

4

5

6

7

8

0
0

9 10

Narrow strip
Wide strip

1

2

3

4

Strip length [mm]

5

6

7

8

9 10

Strip length [mm](a) Pulse height.

(b) Crosstalk ratio.

Fig. 5. The pulse height (left) and crosstalk (right) of dedicated strip sensors with different strip
lengths which is measured by 90 Sr. Narrow and wide strips are with electrodes of 40 µm and 60 µm
widths, respectively. The cross-talk ratio is defined as pulse height of leading divided by the sum ofneighboring strips.

4.

Detection efficiency evaluated using electron beam

The efficiency of detecting MIP particles is evaluated by using an 800 MeV electron beam
available at Research Center for Electron Photon Science (ELPH), Tohoku University. Fivelayer telescope is used for tracking. The pixel size of telescope sensors is either 50×250 µm2
or 25×500 µm2 . Two scintillation counters read out with MPPCs are used for trigger with one
6Entries

Entriesof five telescope sensors used to define region of interest (ROI) in addition. Triggering is controlled by an FPGA based trigger logic unit (TLU) [6]. In evaluating the efficiency by 800 MeV
electron testbeam, 4×4 of 100 µm pitch pixels located at the center of active area are wirebonded and read out with DT5742. The threshold for each pixel signal is determined such thatthe noise rate is 10−4 . An efficiency map is constructed for the events which recorded at least
1 hit pixel divided by the number of tracks. The track pointing resolution is evaluated fromthe projected efficiency distribution across the pixel boundary edge, resulting 48.7±7.2 µm in
X direction and 105±12 µm in Y direction. The efficiency is evaluated using the tracks thatpass the region 1 sigma in pointing resolution inside from the pixel edges. The efficiency distributions projected in X and Y are shown in Fig. 6(a) and Fig. 6(b). The data points are fitted
by an error function on both edges, and the efficiency is evaluated in the top flat region of the
distributions. The efficiency is 97.6±0.7% in X and 97.4±1.1% in Y, respectively. These values
are high enough considering the residual multiple scattering effects. Note that the area withresponse is wider than the physical readout area of 400×400 µm2 , as the surrounding pixels
are not wirebonded and signals are read out via cross-talk.

1

Data
0.8

1

Data
0.8

Fit

0.6

0.6

0.4

0.4

0.2

0.2

0
−3

−2.5

−2

−1.5

0
−19

−1

Position X [mm]

Fit

−18.5

−18

−17.5

−17

Position Y [mm](a) Efficiency in direction X.

(b) Efficiency in direction Y.

Fig. 6. Efficiency of 100 um pixel (E600) in direction X(left) and Y(right) evaluated in an 800 MeV
electron testbeam.

5.

Conclusions

Development of AC-LGAD sensors with finer pitch electrodes is in progress with Hamamatsu Photonics. To make signal larger and crosstalk smaller, two parameters, n+ resistivity
and coupling capacitance, are optimized. The sensor which has largest n+ resistivity and coupling capacitance demonstrated a best and excellent performance as a tracking sensor.
Comparing different pixel pitches down to 100 µm, the pulse height is almost identical.
The signal size is 128.9±3.3 mV and signal efficiency is 99.54% at a 10−4 of noise rate: thesignal is well separated from noise. A detection efficiency of 97% is achieved in an 800 MeV
electron beam, where the observed efficiency includes residual effect of multiple scattering.
The signal efficiency of strip is 99.99% at a 10−4 of noise rate. The inter-strip capacitanceeffect is larger in strip than in pixel sensor. A signal reduction to 40% is caused at a strip
7length of 10 mm.
In summary, clear signal is observed in 100 µm pitch pixel and 80 µm pitch strip sensors, demonstrating excellent AC-LGAD sensor performance as a tracking sensor. To deploy
AC-LGAD sensors as an inner tracker in hadron collider experiments, radiation tolerance isrequired. New ideas of radiation hardening are investigated and will be implemented in next
prototypes. Also ASIC must be developed for multiple channel readout.

Acknowledgments
We would like to acknowledge Hamamatsu Photonics K.K. for the fabrication of various
types of AC-LGAD sensors and the discussions with the personnel have been very inspiringand fruitful. This research was partially supported by Grant-in-Aid for scientific research on
advanced basic research (Grant No. 19H05193, 19H04393, 21H0073 and 21H01099) from the
Ministry of Education, Culture, Sports, Science and Technology, of Japan as well as the Proposals for the U.S.-Japan Science and Technology Cooperation Program in High Energy Physics
from JFY2019 to JFY2023 granted by High Energy Accelerator Research Organization (KEK)and Fermi National Accelerator Laboratory (FNAL). In conducting the present research program, the following facilities have been very important: Research Center for ELectron PHoton
Science (ELPH) at Tohoku University.
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