1
1
Testing of the Performance of HPK RunECX20840 LGADs Through β Measurements
and Simulation
Charilou Anne Lopez Labitan
June 1, 2017
Contents
1 Abstract 5
2 Introduction 5
2.1 Low-Gain Avalanche Detectors . . . . . . . . . . . . . . . . . 6
2.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 β testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Procedure 9
3.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 β Source and Setup . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Analysis and Results 14
4.1 Collected Charge & Gain . . . . . . . . . . . . . . . . . . . . . 17
4.2 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2
4.3 Pulse Maximum . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.4 Rise Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.5 Slope dvdt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.6 Signal-to-Noise Ratio . . . . . . . . . . . . . . . . . . . . . . . 33
4.7 Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.8 Timing Resolution and Landau Fluctuation . . . . . . . . . . 38
5 Conclusion 44
6 Appendix 45
7 References 86
3
Acknowledgements
I would like to thank Hartmut F.-W Sadrozinski for laying the foundation
for the opportunities I am able to pursue today. Under his mentorship, I have
learned to never take things at face value and instead always ask questions
to seek deeper understanding. Through his confidence in my abilities, I have
had the courage to embrace new challenges and face them head on.
I would also like to thank our lab manager Zachary Galloway for taking
the time to teach me not only how to do the experiments but also guide me
through the physics behind them. With every conversation with him, I always
find myself either learning something new or gaining better understanding of
the things I thought I knew.
Special thanks to Patrick Freeman, Yuzhan Zhao, Zachary Luce, and
Ravipa Losakul for their assistance throughout the process of writing this
thesis. Through knowing and working with these talented individuals, they
have reminded me of the importance of collaboration as well as made long
days in lab much more lively and enjoyable.
Last but not least, I would like to thank Mom, Faddy, and Nini. Their
hard work and sacrifices made over the years have not only allowed me to
forge my own path but also instilled in me the values necessary in order to
succeed.
4
1 Abstract
Low-Gain Avalanche Detectors (LGADs) of different doping concentra-
tions and thicknesses from HPK ECX20840 were characterized by testing
with a β particle source. β testing was done at 20C, 0C, and -20C. The
data were compared both among detectors as well as among different tem-
peratures. β measurements for the HPK ECX20840 50D GBGR1 were also
compared to Weightfield2 simulations.
2 Introduction
In order to learn about the great and vast universe, one must know the
fundamental particles that create it. Although the European Organization
for Nuclear Research (CERN) has found the Higgs Boson, a particle that
completes the Standard Model, there is still much more to be discovered,
whether it be a particle that deals with gravitational interaction or the invis-
ible particles that make up the (in)famous dark matter. Like the discovery
of the Higgs, there is hope that these unknown particles will be found at
CERN’s Large Hadron Collider (LHC).
Within the LHC are two general purpose detector systems, CMS (Com-
pact Muon Solenoid) and ATLAS. ATLAS is the largest particle collider
volume detector, with cylindrical dimensions 46m in length and 25m in di-
ameter. [1] As the LHC prepares for its next upgrade, Ultra-Fast Silicon
Detectors (UFSDs) are being researched for possible future implementation
5
in ATLAS’s High Granularity Timing Detector.
2.1 Low-Gain Avalanche Detectors
A UFSD is a type of silicon pad (SPad) detector. Currently, the most
promising UFSDs for particle detection purposes are thin Low-Gain Avalanche
Detectors (LGADs). LGADs are n-on-p (highly doped n++ implants on a
p- bulk) pad detectors with thicknesses ranging from 50-300µm. [2]
The heavily doped n++ implants on a lightly doped p- bulk compose
the PN junction. When the PN junction is reversed biased, the size of the
depletion region is increased and an electric field is created; for detection
purposes, the detector is biased at least until completely depleted. [3] This is
so that, when a minimum ionizing particle (MIP) goes through the detector,
it creates electron/hole pairs within the depleted region. The applied electric
field from the bias voltage prevents the electrons and holes from recombin-
ing; the electrons drift to the n-implant (cathode), while the holes drift to
the p-implant (anode). The moving charges generate a current, which in
turn produces a detected signal read out by the electronics, and a chain of
amplifiers amplifies the signal which can be seen in the oscilloscope.
6
Figure 1: A schematic of a n-on-p LGAD. [4] Here an ionizing particle is
depicted as a red line entering through the front of the detector. On the left
of the schematic is a graph indicating the electric field strength versus the
position within the detector; this is dependent on the doping concentration.
Figure has been modified from the original source.
Thinner detectors are being developed because the charges have less dis-
tance to travel, resulting in a faster signal and better timing resolution. To
compensate for the lack of charges due to smaller detector thicknesses, there
7
is an extra p+ layer between the n++ implants and p- bulk, which is depicted
as the avalanche region in Fig. 1. When traveling charges pass through this
gain layer, there is an avalanche effect, and the charge increases
N(x) = N0eαx, (1)
where N is the number of charges, x is the thickness of the gain region, and
α is related to the electric field strength.
2.2 Simulations
Throughout the research and development process of UFSDs, simulations
have been a crucial part of the process. Rigorous simulations are done to
prove certain detectors are worth investing in. Other times, detectors are
sent to the lab with unknown characteristics, and lab tests can be compared
with simulations to identify the specs of the detector.
2.3 β testing
β testing is when the detectors are exposed to a radiation source that
emits electrons. These electrons, or β particles, act like MIPs. By using β
particles, detectors can be tested in a similar way as their intended use.
8
3 Procedure
The detectors tested were HPK Run ECX20840 50A GBGR1, 50B GBGR1,
50C GBGR1, 50D GBGR1, 80B GBGR1, and 80D GBGR1. These detectors
were produced by Hamamatsu Photonics, Japan. The first number refers to
whether it is 50µm or 80µm thick. The letters (‘A,’ ‘B,’ ‘C,’ and ‘D’) cor-
respond to different doping concentrations of the multiplication layer, with
A having the lowest doping concentration and D having the highest doping
concentration. ‘GBGR’ indicates the guard ring, and ‘1’ indicates which de-
tector it is from the same group. For these tests, the guard ring was not
grounded.
3.1 Simulations
Weightfield2 (WF2), developed by Nicolo Cartiglia, was used to simu-
late the detectors. It is a freeware two-dimensional simulator capable of
simulating silicon as well as diamond detectors. [5] The version used was
Weightfield4.25. By inputting known parameters (such as depletion voltage,
detector capacitance, and gain layer doping), HPK ECX20840 50D GBGR1
was simulated at voltages corresponding to gain in 10 increment steps. From
previous comparisons of impact ionization models, the Massey model was
chosen. [6]
9
3.2 β Source and Setup
Figure 2: A circuit diagram of the β testing setup. DUT is the detector
under test. Mini-Circuits TB-409-52+ is an amplifier of gain 10 that requires
a voltage of +12V.
For all β testing, a Strontium-90 (90Sr) source was used, which emits
electrons through β decay with maximum decay energies of 2.8 MeV. An
EC127 Refrigeration Chamber was used to test at temperatures of 20C,
0C, and -20C. In order to read the signals, a 2.5 GHz Lecroy WP 725Zi
Oscilloscope was used.
Figure 2 is a circuit diagram of the β testing setup using a single channel
board. A Keithley 2657A high voltage (HV) power supply was used to bias
10
the detector under test (DUT). The six capacitors in parallel were for HV
return to ground. The 1MΩ bias resistor regulated the leakage current of the
biased detector. If the bias voltage over the bias resistor became too large, the
diodes turned on in order to protect the sensor. There was an amplification
stage on the board that has a gain of 10; this was powered by a voltage of
+2.25V. The signal was then amplified by the Mini-Circuits TB-409-52+,
which also has a gain of 10, before being read out by the oscilloscope.
Figure 3: A schematic of the β testing in the climatic chamber. [7] Both
the DUT and trigger sensor were connected to a chain of amplifiers, which
in turn was connected to an oscilloscope.
11
The trigger sensor used was CNM Run 9088 W5 LGA33. This is an
LGAD which has been thoroughly tested in both a beam test and in con-
junction with identical LGADs with the beta source. Thus it was used as
a “standard candle” timing detector. [8] Although the data acquisition pro-
cess for all six detectors was for intermittent time periods during January
to April 2017, the experimental setup was consistent for all measurements,
aside from the triggering process used for HPK ECX20840 50B GBGR1 and
50C GBGR1.
Using an alignment frame built by the lab, the beta source was aligned
with the DUT in the front and trigger sensor behind the DUT, as shown in
Fig. 3. [9] For a pulse to be considered a real event (i.e. a β particle), there
must be a coincidence between the two sensors. This helps eliminate acci-
dental pulses, which may occur due to lack of light tightness in the chamber
or other sources of radiation (e.g. cosmic radiation).
For HPK ECX20840 50B GBGR1 and 50C GBGR1, a cascaded multi-
stage trigger was used to ensure events acquired by the oscilloscope were only
coincidences. By using longer cables to delay the DUT signal, data were only
acquired when signals were greater than the trigger level for both the DUT
and trigger sensor that were less than 5ns apart. This method, however, was
found to skew the data towards larger DUT signals, so it was replaced by
just an edge trigger on the trigger sensor signal. The reason is that the scope
triggers only if the pulse exceeds the trigger threshold for 6 or more time
bins. Thus only large pulses are triggered. Afterwards, the data analysis
12
process accounted for coincidences by doing cuts on the data.
As there were many events in each data run, the measurements were
plotted in a histogram and fitted using an appropriate function, which in
this case is either Landau or Gaussian. For all measurements except CFD
(Constant Fraction Discriminator) timing resolution, the mean value of the
distribution was taken; the sigma was used for the CFD timing resolution.
13
4 Analysis and Results
Figure 4: Average pulse shapes for HPK ECX20840 50D GBGR1 under beta
testing at different bias voltages. 200V corresponds to a gain of 10.9786
0.0784, 270V to gain of 19.5337 0.1239, 300V to gain of 30.1941 0.1889, and
320V to gain of 40.9014 0.2233. (The gain is defined in the next section.)
From signals like the ones shown in Fig. 4, one can characterize a detector
by looking at measurements such as collected charge, rise time, amplitude,
noise, and properties associated with them. The pulse shapes in Fig. 4 were
taken from four different bias voltage runs (200V, 270V, 300V, and 320V)
14
of HPK ECX20840 50D GBGR1, which corresponds to gain (defined in the
next section) in incremental steps of roughly 10. As there are over 2000
events in each run, each signal depicted corresponds to averaging all events
from one run point by point.
Figure 5: Simulated pulse shapes for HPK ECX20840 50D GBGR1 at differ-
ent bias voltages. 200V corresponds to a gain of 10.9865, 270V corresponds
to a gain of 20.1175, and 320V corresponds to a gain of 32.0438.
WF2 simulations illustrate signals from an idealized system, with aspects
such as no noise and constant temperature. As shown in Fig. 5, the simu-
lated HPK ECX20840 50D GBGR1 pulses have larger signals than the real
15
averaged data, which corresponds to more collected charge and longer rise
times. (Both will be discussed more thoroughly later.)
One important thing to note in the data analysis is that the absolute
values of the measurements are used. Therefore, although the signals are
negative, measurements regarding the voltage of the pulse (such as noise and
the pulse maximum) are positive values. Also, the error bars on figures may
be difficult to distinguish due to scale.
16
4.1 Collected Charge & Gain
Figure 6: Collected charge versus bias voltage for all six HPK ECX20840
detectors and the simulated 50D GBGR1 detector. Higher doping concen-
tration results in more collected charge at lower bias voltages.
The collected charge refers to the electron/hole pairs that are created
when a MIP goes through the biased detector. This can be calculated by
Collected Charge =
∑i Vi∆t
terminationR× ampgain, (2)
which can be simplified as the integral of the pulse divided by both the
termination resistance and the amplifier gain. For the single channel board,
17
the termination resistance of the system is 47, and the two stage amplifiers
result in a gain multiplication factor of 100. (Each amplifier stage magnifies
the signal by 10.) The baseline average of the pulse was subtracted from the
voltage to account for the DC offset. (Calculation explained in Section 3.2.)
The amount of charges collected at a certain bias voltage is dependent
on the doping concentration of the detector, as shown in Fig. 6. The higher
the doping concentration, the more collected charge is created at lower bias
voltages. Although HPK ECX20840 50B GBGR1 and 80B GBGR1 have the
same doping concentration in the gain layer (likewise for 50D GBGR1and 80D
GBGR1), the detectors with 80µm thickness have lower collected charges at
the same bias voltage. This is because the larger detector thickness requires a
higher bias voltage to increase the magnitude of the electric field and deplete
the detector, as shown by
VFD =qN
2w2 (3)
where VFD is the depletion voltage, q is charge, N is the doping concentration,
and w is the width of the detector. [10]
Since the simulated pulses were larger than the average pulses from beta
testing, this results in the simulations having more collected charge.
18
Figure 7: Collected charge versus bias voltage for HPK ECX20840 80D
GBGR1 at temperatures 20C, 0C, and -20C. The collected charge is de-
pendent on temperature.
As the temperature decreases, the number of collected charges increases,
as shown in Fig. 7. [11] By cooling down the environment the detector is in,
and therefore also cooling the detector, both the drift velocity and the gain
factor α (Eq. 1) increases. This is the same for all detectors tested, as shown
in Fig. 27-31 in the Appendix.
19
Figure 8: Gain versus bias voltage for all six HPK ECX20840 detectors and
the simulated 50D GBGR1 detector.
Collected charge is important because it is used to determine the gain of
the detector. Here, gain is defined as
Gain =Collected Charge
MIP Charge(4)
where MIP Charge is the charge expected from a MIP in an equivalent sensor
without gain. Since more charge is generated in an 80µm no-gain detector
than a 50µm no-gain detector due to the larger thickness, the MIP Charge
factor is greater for the 80µm detectors.
20
Figure 9: Gain versus bias voltage for HPK ECX20840 50D GBGR1 at
temperatures 20C, 0C, and -20C.
Since gain is dependent on collected charge, it also increases with lower
temperature, as shown in Fig. 9. Figures 32 to 36 (located in the Appendix)
show that this is the same for all the detectors tested.
21
4.2 Noise
Figure 10: Noise measured versus bias voltage for all six HPK ECX20840
detectors. The dominating factor affecting the noise measurements was the
oscilloscope channel mV/div scale, but this is not yet well understood.
The noise was calculated by finding the root mean squared (RMS) of the
first 500 points of the waveform, which is the noise before the main part of
pulse. This measurement was also used for the baseline correction in order
to account for the DC offset. The noise is independent of detector thickness,
as shown in Fig. 10. It was found that the noise measurements were affected
by the oscilloscope’s channel mV/div scale. The higher the mV/div scale,
22
the greater the noise, as each increase in noise corresponds to a change in
mV/div scale.
Table 1: Measured scope noise for the Lecroy WP 725Zi Oscilloscope. It is
seen that the noise increases linearly with the oscilloscope channel mV/div
scale, determining that noise is independent of detector thickness.
The oscilloscope noise has been measured using a calibration pulse for
the external trigger, as shown in Table 1. Subtracting these measurements
from the β testing noise, however, does not adequately correct for the noise
seen during β testing. The noise of the detector is assumed to be constant,
and therefore independent of the bias voltage. Figure 11 shows that using
the measurements for scope noise gives inconsistent values for detector noise,
making them unreliable. Further investigation is needed to correct for this.
23
Figure 11: Noise measured and corrected versus bias voltage for HPK
ECX20840 80D GBGR1. It is assumed that the noise is constant for the
detector at each temperature. Correcting with the noise measurements in
Table 1 does not account for the oscilloscope noise correctly.
24
Figure 12: Noise measured versus bias voltage for HPK ECX20840 50D
GBGR1 at temperatures 20C, 0C, and -20C. There is small dependence on
temperature, but the measurements are mostly dominated by the oscilloscope
channel mV/div scale.
There is a slight difference between the runs at different temperatures,
but temperature does not look to be a significant contributor, as shown in
Fig. 12. Again, the jump in noise value for the point above a bias of 300V
corresponds to an increase in the oscilloscope channel mV/div scale. This is
the same for all the detectors tested, as shown by Fig. 37-41 in the Appendix.
25
4.3 Pulse Maximum
Figure 13: Pulse maximum versus gain for all six HPK ECX20840 detectors
and the simulated 50D GBGR1 detector. The pulse maximum is linearly
dependent on gain and is greater for 80µm detectors due to their smaller
capacitance.
The pulse maximum is the maximum voltage, or amplitude, of the pulse.
Figure 13 shows that it is directly proportional to the gain of the detector.
The pulse maximum is also dependent on the detector thickness, as the
values for the 80µm detectors are consistently higher than those of the 50µm
detectors after a gain of 20. This is because larger detectors have smaller
26
capacitance, which makes a smaller RC and therefore a greater pulse height.
[12] The simulation data are slightly larger than what was found during beta
testing, but they still follow the same dependence on gain.
Figure 14: Pulse maximum versus gain for HPK ECX20840 80D GBGR1
at temperatures 20C, 0C, and -20C. Pulse maximum is independent of
temperature for the same gain.
Temperature does not affect the pulse maximum, as shown in Fig. 14.
This is the same for all the detectors tested, as shown by Fig. 42-46 in the
Appendix. HPK ECX20840 80D GBGR1 is a good example of the linear
relation between pulse maximum and gain.
27
4.4 Rise Time
Figure 15: The rise time from 10% of the signal to 90% of the signal versus
bias voltage for all six HPK ECX20840 detectors and the simulated 50D
GBGR1 detector. The asymptotic rise time is faster for thinner detectors
due to the constant value of saturated drift velocity.
Rise time is calculated by the difference in time between two points on
the rising edge of the signal. Here, rise time is calculated by the time at 90%
of the signal minus the time at 10% of the signal. The full rise time is found
by dividing the value by 0.8. After the detector is fully depleted (around a
gain of 3), it decreases as the gain increases and eventually becomes constant.
28
This is because the drift velocity of the charges collected becomes saturated,
which leads to an end of the increase in rise time despite the increase of bias
voltage.
Figure 15 shows that rise time is dependent on the thickness of the de-
tector, as the rise time is greater for the 80µm detectors than the 50µm
detectors. This is due to the drift velocity saturating to the same value, but
the charges in the thicker detectors need more time to move across the de-
tectors. This is also shown by the rise times converging for 50µm detectors
when the drift velocity is saturated. HPK ECX20840 80B GBGR1 does not
reach a high enough gain to show the same effect with the 80µm detectors.
29
Figure 16: The rise time from 10% of the signal to 90% of the signal versus
gain for HPK ECX20840 50D GBGR1 and 80D GBGR1 at temperatures
20C, 0C, and -20C. Rise time is independent of temperature.
As shown in Fig. 16, rise time has no temperature dependence; it has
only gain dependence. This is the same for all the detectors tested. Figures
47 to 52 in the Appendix show that rise time is independent of gain as well.
30
4.5 Slope dvdt
Figure 17: The slew rate (slope) dvdt at 20% of the pulse versus gain for
all six HPK ECX20840 detectors and the simulated 50D GBGR1 detector.
Thinner LGADs corresponds to a higher slew rate, as the charges have less
distance to travel.
Dvdt refers to the slew rate (slope) of the signal, or ∆V/∆t. Here, dvdt
(20%) refers to the slew rate of the signal at 20% of the pulse. The slew rate of
the signal is directly proportional to the gain. While the pulse maximum was
greater for the 80µm detectors, dvdt (20%) is greater for the 50µm detectors,
as shown in Fig. 17. This is due to the 50µm detectors’ much faster rise time.
31
Despite the simulated pulses relatively longer rise times, the dvdt matches
what was measured during β testing, which indicates the charges are still
moving at the same rate.
Figure 18: The slew rate (slope) dvdt at 20% of the pulse versus gain for
HPK ECX20840 80D GBGR1 at temperatures 20C, 0C, and -20C. The
slew rate is independent of temperature.
Like both the pulse maximum and rise time, the slew rate of the signal
is not dependent on temperature when plotted versus gain, as shown in Fig.
18. This is the same for all the detectors tested, as shown by Fig. 53-57 in
the Appendix.
32
4.6 Signal-to-Noise Ratio
Figure 19: Signal-to-noise ratio (SNR) versus gain for all six HPK ECX20840
detectors. SNR is greater for the 80µm detectors due to the greater pulse
maximum values (Fig. 12). Measurements for SNR are believed to be affected
by the oscilloscope channel mV/div scale.
One interesting thing to look at when comparing detectors is the signal-
to-noise ratio (SNR). Just as the name implies, it is calculated by
SNR =Signal
Noise. (5)
Here, signal is defined as the maximum voltage of the pulse, and noise is the
33
noise RMS. SNR, similar to the pulse maximum, is linearly proportional to
the gain. However, in Fig. 19, the highest gain points for all detectors but
HPK ECX20840 80D GBGR1 do not follow this. This is due to the oscil-
loscope channel mV/div scale, as recording larger pulses requires increasing
the scale. This is yet another reason why it is important to find a way to
correct for the noise.
Figure 20: Signal to noise ratio versus gain for HPK ECX20840 50D GBGR1
at temperatures 20C, 0C, and -20C. SNR is independent of temperature.
Figure 20 is a better example of the linear dependence of SNR to gain,
although it still affected by the oscilloscope channel mV/div scale for the runs
34
done at 20C and -20C. Since it is calculated by measurements independent
of temperature, SNR is independent of temperature as well. The temperature
dependence data for the other detectors’ SNR also looks similar, as shown
by Fig. 58-62.
4.7 Jitter
Figure 21: Jitter versus gain for all six HPK ECX20840 detectors. Jitter is
calculated by both Rise T ime/SNR and Noise/dvdt(20%). Jitter looks to
be independent of detector thickness and exponentially decreases with higher
gain, yet suffers from the scope noise.
35
Another way to gauge the noise’s effect on the signal is by looking at the
jitter. Jitter can be derived in two ways. [13]
Jitter =Noise
dvdt(6)
Jitter =Rise T ime
SNR(7)
Ideally, both would have the same value, but that is not often the case. This
can be due to many factors, such as where dvdt is defined and how well the
Gaussian distribution fits. In Fig. 21, the values for jitter calculated by Rise
Time/SNR have both the highest values at low gain as well as the lowest
values at high gain. It is important to note that both definitions of jitter
give roughly the same value, and they continually become similar as higher
gain is reached.
36
Figure 22: Jitter versus gain for HPK ECX20840 80D GBGR1 at temper-
atures 20C, 0C, and -20C. Jitter is calculated by both Rise T ime/SNR
and Noise/dvdt(20%). It is not temperature dependent.
Jitter, like the factors used to solve for it, is not temperature dependent,
as shown in Fig. 22. Figures 63 to 68 (located in the Appendix) show that
this is the same for all the detectors tested.
37
4.8 Timing Resolution and Landau Fluctuation
Figure 23: Constant fraction discriminator timing resolution at 20% of the
pulse versus gain for all six HPK ECX20840 detectors. Timing resolution is
dependent on detector thickness, with thinner detectors having better values.
The most important parameter of LGADs is the timing resolution. This
is because the detectors are so fast that they reject pileup, which is when the
dead time of the detector leads to either losing events or signals affected by
more than one event. By improving the timing resolution, the detector can
match the incoming particle’s speed so that pileup does not occur. Timing
resolution is calculated by
38
σ2t = σ2
T imeWalk + σ2LandauNoise + σ2
Distortion + σ2Jitter + σ2
TDC (8)
where TDC refers to time-to-digital converter. [14] Due to the geometry
of these detectors, the path size of the MIP is comparable enough to the
detector area that distortion does not affect the timing resolution. With the
oscilloscope’s acquisition set to 25 ps/pt, TDC is also negligible. Time walk is
corrected by the CFD corrections made when looking for coincidences during
data analysis. Therefore, the Landau Noise, or Fluctuation, and jitter are
the dominating factors in calculating timing resolution. Figure 23 shows that
the CFD timing resolution for the 50µm detectors are overall better than the
80µm detectors, which is one of the main reasons why thinner detectors are
considered better. Figures 69 to 75 in the Appendix show the CFD timing
resolution at 15% of the signal versus gain.
39
Figure 24: Constant fraction timing resolution at 20% of the pulse versus
gain for HPK ECX20840 50D GBGR1 and 80D GBGR1 at temperatures
20C, 0C, and -20C. The slight temperature dependence is mainly due to
the gain’s dependence on temperature.
There is a slight temperature dependence for the CFD timing resolution,
but the dominant factor is the gain, as illustrated in Fig. 24. This is the
same for all the detectors tested, as shown by Fig. 76-79 in the Appendix.
40
Figure 25: Landau fluctuation versus gain for all six HPK ECX20840 detec-
tors. Like the timing resolution, Landau fluctuation is smaller, and therefore
better, for thinner detectors.
As the values for jitter become increasingly small, we need to assume
that the Landau fluctuation may be what is limiting the timing resolution.
(Graphs showing jitter and CFD timing resolution versus gain can be found
as Fig. 80-85 in the Appendix.) [15] Landau fluctuation is calculated by
L2 = t2 − J2, (9)
where L is the Landau Fluctuation, t is the detector’s timing resolution, and
41
J is the jitter. For finding the landau fluctuation, the value for jitter was
calculated by Jitter = Noise/dvdt, with the dvdt calculated at 20% of the
signal. The CFD timing resolution used was also at 20% of the signal.
Figure 25 shows the landau fluctuation is lowest for the HPK ECX20840
50D GBGR1, which leads it to have better timing resolution. (The CFD
timing resolution at 20% is shown in Fig. 24.) The inconstant measurement
of the landau fluctuation at the same temperature may possibly be due to
the noise’s and timing resolution’s dependence on the oscilloscope’s channel
mV/division scale.
42
Figure 26: Landau fluctuation versus gain for HPK ECX20840 50D GBGR1
and 80D GBGR1 at temperatures 20C, 0C, and -20C. Landau fluctuation
is directly proportional to temperature, with lower temperature resulting in
better measurements.
As the temperature decreases, the landau fluctuation also decreases, as
shown in Fig. 26. The temperature dependence is more pronounced for the
landau fluctuation than the timing resolution because it is affected by the
collected charge. This is the same for all the detectors tested.
43
5 Conclusion
Simulations and β measurements were performed and compared to test
the performance of HPK Run ECX20840 50A GBGR1, 50B GBGR1, 50C
GBGR1, 50D GBGR1, 80B GBGR1, and 80D GBGR1. We found that most
of the extracted LGAD parameters are a strong function of the gain alone.
A high doping concentration and small thickness (e.g. HPK ECX20840 50D
GBGR1) are the LGAD design parameters for having the best overall perfor-
mance, especially for timing resolution. Collected charge, gain, CFD timing
resolution, and Landau fluctuation were found to have temperature depen-
dence.
44
6 Appendix
Figure 27: Collected charge versus bias voltage for HPK ECX20840 50A
GBGR1 at temperatures 20C, 0C, and -20C.
45
Figure 28: Collected charge versus bias voltage for HPK ECX20840 50B
GBGR1 at temperatures 20C, 0C, and -20C.
Figure 29: Collected charge versus bias voltage for HPK ECX20840 50C
GBGR1 at temperatures 20C, 0C, and -20C.
46
Figure 30: Collected charge versus bias voltage for HPK ECX20840 50D
GBGR1 at temperatures 20C, 0C, and -20C.
47
Figure 31: Collected charge versus bias voltage for HPK ECX20840 80B
GBGR1 at temperatures 20C, 0C, and -20C.
Figure 32: Gain versus bias voltage for HPK ECX20840 50A GBGR1 at
temperatures 20C, 0C, and -20C.
48
Figure 33: Gain versus bias voltage for HPK ECX20840 50B GBGR1 at
temperatures 20C, 0C, and -20C.
Figure 34: Gain versus bias voltage for HPK ECX20840 50C GBGR1 at
temperatures 20C, 0C, and -20C.
49
Figure 35: Gain versus bias voltage for HPK ECX20840 80B GBGR1 at
temperatures 20C, 0C, and -20C.
Figure 36: Gain versus bias voltage for HPK ECX20840 80D GBGR1 at
temperatures 20C, 0C, and -20C.
50
Figure 37: Noise measured versus bias voltage for HPK ECX20840 50A
GBGR1 at temperatures 20C, 0C, and -20C.
51
Figure 38: Noise measured versus bias voltage for HPK ECX20840 50B
GBGR1 at temperatures 20C, 0C, and -20C.
Figure 39: Noise measured versus bias voltage for HPK ECX20840 50C
GBGR1 at temperatures 20C, 0C, and -20C.
52
Figure 40: Noise measured versus bias voltage for HPK ECX20840 80B
GBGR1 at temperatures 20C, 0C, and -20C.
Figure 41: Noise measured versus bias voltage for HPK ECX20840 80D
GBGR1 at temperatures 20C, 0C, and -20C.
53
Figure 42: Pulse maximum versus gain for HPK ECX20840 50A GBGR1 at
temperatures 20C, 0C, and -20C.
Figure 43: Pulse maximum versus gain for HPK ECX20840 50B GBGR1 at
temperatures 20C, 0C, and -20C.
54
Figure 44: Pulse maximum versus gain for HPK ECX20840 50C GBGR1 at
temperatures 20C, 0C, and -20C.
Figure 45: Pulse maximum versus gain for HPK ECX20840 50D GBGR1 at
temperatures 20C, 0C, and -20C.
55
Figure 46: Pulse maximum versus gain for HPK ECX20840 80B GBGR1 at
temperatures 20C, 0C, and -20C.
56
Figure 47: The rise time from 10% of the signal to 90% of the signal versus
gain for all six HPK ECX20840 detectors and the simulated 50D GBGR1
detector.
57
Figure 48: The rise time from 10% of the signal to 90% of the signal versus
gain for HPK ECX20840 50D GBGR1 and 80D GBGR1 at temperatures
20C, 0C, and -20C. Rise time is independent of temperature when plotted
vs. the gain.
58
Figure 49: Rise time versus gain for HPK ECX20840 50A GBGR1 at tem-
peratures 20C, 0C, and -20C.
Figure 50: Rise time versus gain for HPK ECX20840 50B GBGR1 at tem-
peratures 20C, 0C, and -20C.
59
Figure 51: Rise time versus gain for HPK ECX20840 50C GBGR1 at tem-
peratures 20C, 0C, and -20C.
60
Figure 52: Rise time versus gain for HPK ECX20840 80B GBGR1 at tem-
peratures 20C, 0C, and -20C.
Figure 53: The slope (dvdt) at 20% of the signal versus gain for HPK
ECX20840 50A GBGR1 at temperatures 20C, 0C, and -20C.
61
Figure 54: The slope (dvdt) at 20% of the signal versus gain for HPK
ECX20840 50B GBGR1 at temperatures 20C, 0C, and -20C.
Figure 55: The slope (dvdt) at 20% of the signal versus gain for HPK
ECX20840 50C GBGR1 at temperatures 20C, 0C, and -20C.
62
Figure 56: The slope (dvdt) at 20% of the signal versus gain for HPK
ECX20840 50D GBGR1 at temperatures 20C, 0C, and -20C.
Figure 57: The slope (dvdt) at 20% of the signal versus gain for HPK
ECX20840 80B GBGR1 at temperatures 20C, 0C, and -20C.
63
Figure 58: The signal-to-noise ratio (SNR) versus gain for HPK ECX20840
50A GBGR1 at temperatures 20C, 0C, and -20C.
Figure 59: The signal-to-noise ratio (SNR) versus gain for HPK ECX20840
50B GBGR1 at temperatures 20C, 0C, and -20C.
64
Figure 60: The signal-to-noise ratio (SNR) versus gain for HPK ECX20840
50C GBGR1 at temperatures 20C, 0C, and -20C.
Figure 61: The signal-to-noise ratio (SNR) versus gain for HPK ECX20840
80B GBGR1 at temperatures 20C, 0C, and -20C.
65
Figure 62: The signal-to-noise ratio (SNR) versus gain for HPK ECX20840
80D GBGR1 at temperatures 20C, 0C, and -20C.
66
Figure 63: Jitter versus gain for HPK ECX20840 50A GBGR1 at tempera-
tures 20C, 0C, and -20C.
Figure 64: Jitter versus gain for HPK ECX20840 50B GBGR1 at tempera-
tures 20C, 0C, and -20C.
67
Figure 65: Jitter versus gain for HPK ECX20840 50C GBGR1 at tempera-
tures 20C, 0C, and -20C.
Figure 66: Jitter versus gain for HPK ECX20840 50D GBGR1 at tempera-
tures 20C, 0C, and -20C.
68
Figure 67: Jitter versus gain for HPK ECX20840 80B GBGR1 at tempera-
tures 20C, 0C, and -20C.
Figure 68: Jitter versus gain for HPK ECX20840 80D GBGR1 at tempera-
tures 20C, 0C, and -20C.
69
Figure 69: Constant fraction discriminator timing resolution at 15% of the
pulse versus gain for all six HPK ECX20840 detectors. Timing resolution is
dependent on detector thickness, with thinner detectors having better values.
70
Figure 70: Constant fraction discriminator timing resolution at 15% of the
pulse versus gain for HPK ECX20840 50A GBGR1 at temperatures 20C,
0C, and -20C.
71
Figure 71: Constant fraction discriminator timing resolution at 15% of the
pulse versus gain for HPK ECX20840 50B GBGR1 at temperatures 20C,
0C, and -20C.
72
Figure 72: Constant fraction discriminator timing resolution at 15% of the
pulse versus gain for HPK ECX20840 50C GBGR1 at temperatures 20C,
0C, and -20C.
73
Figure 73: Constant fraction discriminator timing resolution at 15% of the
pulse versus gain for HPK ECX20840 50D GBGR1 at temperatures 20C,
0C, and -20C.
74
Figure 74: Constant fraction discriminator timing resolution at 15% of the
pulse versus gain for HPK ECX20840 80B GBGR1 at temperatures 20C,
0C, and -20C.
75
Figure 75: Constant fraction discriminator timing resolution at 15% of the
pulse versus gain for HPK ECX20840 80D GBGR1 at temperatures 20C,
0C, and -20C.
76
Figure 76: Constant fraction discriminator timing resolution at 20% of the
pulse versus gain for HPK ECX20840 50A GBGR1 at temperatures 20C,
0C, and -20C.
77
Figure 77: Constant fraction discriminator timing resolution at 20% of the
pulse versus gain for HPK ECX20840 50B GBGR1 at temperatures 20C,
0C, and -20C.
78
Figure 78: Constant fraction discriminator timing resolution at 20% of the
pulse versus gain for HPK ECX20840 50C GBGR1 at temperatures 20C,
0C, and -20C.
79
Figure 79: Constant fraction discriminator timing resolution at 20% of the
pulse versus gain for HPK ECX20840 80B GBGR1 at temperatures 20C,
0C, and -20C.
80
Figure 80: Constant fraction discriminator timing resolution at 20% of the
pulse and jitter (noise measured/dvdt(20%)) versus gain for HPK ECX20840
50A GBGR1 at temperatures 20C, 0C, and -20C.
81
Figure 81: Constant fraction discriminator timing resolution at 20% of the
pulse and jitter (noise measured/dvdt(20%)) versus gain for HPK ECX20840
50B GBGR1 at temperatures 20C, 0C, and -20C.
82
Figure 82: Constant fraction discriminator timing resolution at 20% of the
pulse and jitter (noise measured/dvdt(20%)) versus gain for HPK ECX20840
50C GBGR1 at temperatures 20C, 0C, and -20C.
83
Figure 83: Constant fraction discriminator timing resolution at 20% of the
pulse and jitter (noise measured/dvdt(20%)) versus gain for HPK ECX20840
50D GBGR1 at temperatures 20C, 0C, and -20C.
84
Figure 84: Constant fraction discriminator timing resolution at 20% of the
pulse and jitter (noise measured/dvdt(20%)) versus gain for HPK ECX20840
80B GBGR1 at temperatures 20C, 0C, and -20C.
85
Figure 85: Constant fraction discriminator timing resolution at 20% of the
pulse and jitter (noise measured/dvdt(20%)) versus gain for HPK ECX20840
80D GBGR1 at temperatures 20C, 0C, and -20C.
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88