Testing of the Performance of HPK...

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


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


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


Figure 29: Collected charge versus bias voltage for HPK ECX20840 50C


46

Figure 30: Collected charge versus bias voltage for HPK ECX20840 50D


47

Figure 31: Collected charge versus bias voltage for HPK ECX20840 80B


Figure 32: Gain versus bias voltage for HPK ECX20840 50A GBGR1 at


48

Figure 33: Gain versus bias voltage for HPK ECX20840 50B GBGR1 at


Figure 34: Gain versus bias voltage for HPK ECX20840 50C GBGR1 at


49

Figure 35: Gain versus bias voltage for HPK ECX20840 80B GBGR1 at


Figure 36: Gain versus bias voltage for HPK ECX20840 80D GBGR1 at


50

Figure 37: Noise measured versus bias voltage for HPK ECX20840 50A


51

Figure 38: Noise measured versus bias voltage for HPK ECX20840 50B


Figure 39: Noise measured versus bias voltage for HPK ECX20840 50C


52

Figure 40: Noise measured versus bias voltage for HPK ECX20840 80B


Figure 41: Noise measured versus bias voltage for HPK ECX20840 80D


53

Figure 42: Pulse maximum versus gain for HPK ECX20840 50A GBGR1 at


Figure 43: Pulse maximum versus gain for HPK ECX20840 50B GBGR1 at


54

Figure 44: Pulse maximum versus gain for HPK ECX20840 50C GBGR1 at


Figure 45: Pulse maximum versus gain for HPK ECX20840 50D GBGR1 at


55

Figure 46: Pulse maximum versus gain for HPK ECX20840 80B GBGR1 at


56


gain for all six HPK ECX20840 detectors and the simulated 50D GBGR1

detector.

57



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-


59

Figure 51: Rise time versus gain for HPK ECX20840 50C GBGR1 at tem-


60

Figure 52: Rise time versus gain for HPK ECX20840 80B GBGR1 at tem-


Figure 53: The slope (dvdt) at 20% of the signal versus gain for HPK

ECX20840 50A GBGR1 at temperatures 20C, 0C, and -20C.

61


ECX20840 50B GBGR1 at temperatures 20C, 0C, and -20C.


ECX20840 50C GBGR1 at temperatures 20C, 0C, and -20C.

62


ECX20840 50D GBGR1 at temperatures 20C, 0C, and -20C.


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.


50B GBGR1 at temperatures 20C, 0C, and -20C.

64


50C GBGR1 at temperatures 20C, 0C, and -20C.



65


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-


67

Figure 65: Jitter versus gain for HPK ECX20840 50C GBGR1 at tempera-


Figure 66: Jitter versus gain for HPK ECX20840 50D GBGR1 at tempera-


68

Figure 67: Jitter versus gain for HPK ECX20840 80B GBGR1 at tempera-


Figure 68: Jitter versus gain for HPK ECX20840 80D GBGR1 at tempera-


69


pulse versus gain for all six HPK ECX20840 detectors. Timing resolution is

dependent on detector thickness, with thinner detectors having better values.

70


pulse versus gain for HPK ECX20840 50A GBGR1 at temperatures 20C,

0C, and -20C.

71


pulse versus gain for HPK ECX20840 50B GBGR1 at temperatures 20C,

0C, and -20C.

72


pulse versus gain for HPK ECX20840 50C GBGR1 at temperatures 20C,

0C, and -20C.

73


pulse versus gain for HPK ECX20840 50D GBGR1 at temperatures 20C,

0C, and -20C.

74



0C, and -20C.

75


pulse versus gain for HPK ECX20840 80D GBGR1 at temperatures 20C,

0C, and -20C.

76


pulse versus gain for HPK ECX20840 50A GBGR1 at temperatures 20C,

0C, and -20C.

77



0C, and -20C.

78


pulse versus gain for HPK ECX20840 50C GBGR1 at temperatures 20C,

0C, and -20C.

79



0C, and -20C.

80


pulse and jitter (noise measured/dvdt(20%)) versus gain for HPK ECX20840

50A GBGR1 at temperatures 20C, 0C, and -20C.

81




82



50C GBGR1 at temperatures 20C, 0C, and -20C.

83




84




85




7 References

[1] CERN, “ATLAS,” CERN, Geneva, Switzerland, February 2012,

http://home.cern/about/experiments/atlas.

[2] H. F.-W. Sadrozinski, “Sensors for ultra-fast silicon detectors,” NIM

A, Volume 765, 21 November, 2014, Pages 7-11.

[3] F. Hartmann, Evolution of Silicon Sensor Technology in Particle Physics,

STMP 231 (Springer, Berlin Heidelberg 2009), DOI 10.1007 / 978-3-540-

44774-0.

[4] N. Cartiglia, Ultra Fast Silicon Detectors, CERN Detector Seminar,

86

Geneva, Switzerland, 26 September, 2014,

https://indico.cern.ch/event/329886/attachments/641603/882830/CERN UFSD Cartiglia.pdf.

[5] F. Cenna et al., “Weightfield2: A fast simulator for silicon and di-

amond solid state detector,” NIM A, Volume 796, 1 October, 2015, Pages

149-153.

[6] N. Cartiglia, Properties of LGAD, 11th “Trento” Workshop on Ad-

vanced Silicon Radiation Detectors, Trento, Italy, 24 February, 2016.

[7] E.-L. Gkougkousis, High-Granularity Timing Detector for the upgrade

of the ATLAS Calorimeter system, International Conference on Instrumen-

tation for Colliding Beam Physics, Novosibirsk, Russia, 1 March, 2017.

[8] H. F.-W. Sadrozinski, Time Resolution of LGAD, 12th “Trento” Work-

shop on Advanced Silicon Radiation Detectors, Trento, Italy, 21 February

2017.

[9] N. Cartiglia, C. Labitan et al., “Beam test results of a 15 ps timing

system based on ultra-fast silicon detectors,” NIM A, Volume 850, 1 April,

2017, Pages 83-88.

[10] H. F.-W. Sadrozinski, “Silicon Detector Fundamentals,” CERN De-

tector Short Course, Florence, Italy, October 2012.

[11] G. Pellegrini et al., “Technology developments and first measure-

ments of Low Gain Avalanche Detectors (LGAD) for high energy physics

applications,” NIM A, Volume 765, 21 November, 2014, Pages 12-16.

[12] H. F.-W. Sadrozinski, “4D Silicon Detectors,” University of Bonn

Presentation, Bonn, Germany, 27 October, 2016.

87

[13] N. Cartiglia et al., “Performance of Ultra-Fast Silicon Detectors,”

JINST 9 C02001, Siena, Italy, 4 February, 2014.

[14] H. F.-W Sadrozinski et al., “4-Dimensional Tracking with Ultra-Fast

Silicon Detectors,” arXiv:1704.08666. Submitted on 27 April, 2017.

[15] H. F.-W Sadrozinski, “Timing Measurements on thin LGAD,” 12th

“Trento” Workshop on Advanced Silicon Radiation Detectors, Trento, Italy,

21 February 2017.

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