Test of Basic Properties for Radiation Damage
Measurement of Silicon Detector for the ILD
Electro-magnetic Calorimeter
Chihiro Kozakai
Department of Physics, Graduate School of Science, The University of Tokyo
2014/2/5

Abstract

A silicon tungsten sampling sandwich calorimeter is being developed for the ILD,
one of the detector concepts for the ILC. The development of a high granularity electro-magnetic calorimeter is required for Particle Flow Algorithm. Silicondetector allows high granularity multi channel readout without much diﬃculty.
Therefore, detectors using silicon semiconductor can be important technology not
only for the ILD electro-magnetic calorimeter but also for other future collider
experiments. Since the use of the silicon detector will be under severe radiation in
the years ahead, radiation hardness of the sensor and the glue for the sensor andreadout electronics is concerned. In this thesis, it is discussed how to evaluate
the radiation damage from measurements of the current-voltage properties, thecapacitance-voltage properties, and the charge collection eﬃciency measurement
to extract the change of the dependence of the leakage current on temperature,
carrier concentration change, and charge collection deficiency after irradiation.

3

Contents
1 Introduction
1.1 International Linear Collider . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 International Large Detector . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Particle Flow Algorithm (PFA) . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 SiW electromagnetic calorimeter . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7
7
9
9
14
15

2 Silicon sensor basic properties
2.1 The design of silicon sensor for the ILD ECAL . . . . . . . . . . . . . . . . .
2.2 Silicon sensor properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 The PIN diode property . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Current-voltage property . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Capacitance-voltage property . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Signal collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Expected eﬀects by radiation exposure . . . . . . . . . . . . . . . . . . . . .
2.4 The requirement for silicon sensor for the ILD ECAL . . . . . . . . . . . . .

17
17
17
17
22
26
31
31
34

3 Current-voltage measurement
3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Leakage current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35
35
38
42

4 Capacitance-voltage measurement
4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Systematic error estimation study . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Depletion width, diﬀusion voltage . . . . . . . . . . . . . . . . . . . . . . . .

45
45
48
51

5 Charge collection eﬃciency measurement plan
5.1 Expected signal voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55
55
55

5

6

CONTENTS

6 Simulation of radiation damage eﬀect
6.1 Simulation tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 The requirements on the silicon sensor . . . . . . . . . . . . . . . . . . . . .

59
59
59
61

7 Irradiation experiment plan
7.1 Radiation dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Irradiation experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65
65
67

8 Conclusion

69

9 Acknowledgements

71

A NIEL73

B The Keithley2410 high-voltage source meter specification

75

C The Agilent LCR meter specification

77

Chapter 1
Introduction
1.1

International Linear Collider

The International Linear Collider (ILC) is a future electron-positron collider operating at
centre-of-mass energies between 250 GeV and 1 TeV [1][2]. The schematic layout of the ILC
is shown in Fig.1.1. It is a multi purpose experiment. One of the main physics targets at the
ILC is the precise measurement of the Higgs boson couplings. After the discovery of Higgs
boson at the LHC in July 2012, the measurement of Higgs couplings is very important probe
to test the Standard Model and to open the way to new physics. Higgs couplings can bemeasured with less than percent order precision with the ILC and the deviations from theStandard Model can be crucially tested. In addition to Higgs boson physics, broad topics inelementary particle physics such as top quark, W boson, Z boson and new physics such as
supersymmetry can be investigated with the ILC.
The physics advantage of the ILC is that the elementary electroweak coupling e of thephoton is the same for all species of quarks and leptons, and the same also for new particles
from beyond the Standard Model. It leads to comparable cross sections of beyond theStandard Model particles to those of the Standard Model backgrounds. At the LHC, thegluon couples to all the quarks and new coloured particles. However, soft, non-perturbativestrong interactions are dominant mechanism for particle production and involve only lightquarks and gluons. Further, because the proton is a composite object with parton energy
distributions that fall steeply with its energy fraction, the production cross sections aremuch lower for heavy particles than for light particles. Thus, only events with unusual andstriking properties can be recognized against the much larger samples of background QCD
events. At the ILC, since the production cross section of new particle is comparable to theStandard Model background, new particle production events are clearly distinguishable fromthe Standard Model reactions.
Moreover, because initial state e+ and e− are point-like elementary particles, coupling only
via the electroweak interactions, theoretical cross sections can be calculated with parts-per7

8

CHAPTER 1. INTRODUCTION

Figure 1.1: Schematic layout of the ILC, indicating all the major subsystems. [1]1.2. INTERNATIONAL LARGE DETECTOR

9

mil level precision. The ILC can also provide polarized beams, allowing the spin-dependenceof production and decay rate to be revealed. It also gives interesting events eﬃciently withpolarized beams.
The advantage of the ILC from the point of view of detector design is very low chronic
background from photon-photon collision. This means low occupancy rate and loose radiation
hardness requirement compared to the LHC. Therefore, the vertex detector can be placedmuch closer to the interaction point and they can achieve high precision measurement. The
ILC can record all events, with no trigger needed.

1.2

International Large Detector

There are two detector designs for the ILC. One of the detectors at the ILC interaction pointis called the ILD (Intenational Large Detector). Fig.1.2, 1.3 shows a view of the ILD concept.
For physics at the ILC, many important channels have multi jet final states. Therefore, highjet energy resolution is required for the detector.
From innermost region, the ILD consists of a pixel vertex detector, silicon strip detectors,
time projection chamber, further silicon strip detectors, electromagnetic calorimeter (ECAL),
hadronic calorimeter (HCAL), superconducting solenoid and iron return yoke. In addition,a system of two silicon-pixel disks and five silicon-strip disks (FTD), and radiation hardcalorimetric detectors (LumiCAL, BeamCAL, LHCAL) are placed in the very forward region.
The ILD detector is optimised for Particle Flow Algorithm (PFA), described in the next
section.

1.3

Particle Flow Algorithm (PFA)

The required precision is 3-4 % for 100 GeV jets. This is a requirement to distinguish W and
Z di-jet final state. Particle Flow Algorithm (PFA) for jet energy reconstruction have beendeveloped to meet this requirement [3]. The basic idea of the PFA is that each particle shouldbe measured with the most appropriate detectors. The energy of electrons and hadrons canbe measured with calorimeter. However, for charged particles up to 200 GeV transverse
momentum, the tracker measures energy with better resolution than the calorimeter in the
ILD. If it is distinguished that whether a cluster in a calorimeter was produced by a charged
particle or a neutral particle, PFA is achieved. One simulated PFA reconstruction result isshown in Fig.1.4.
This enables the required precision of 3-4 % for 100 GeV jets to be achieved, the requirement to separate W and Z di-jet final states. Fig.1.5 shows the distribution of reconstructedmass of two W bosons or two Z bosons. These plots are based on the best jet-pairing in√selected νe ν¯e WW (blue) and νe ν¯e ZZ (red) events at s = 1 TeV.

10

CHAPTER 1. INTRODUCTION

Figure 1.2: View of the ILD concept. [1]1.3. PARTICLE FLOW ALGORITHM (PFA)

Figure 1.3: Quadrant view of the ILD concept. [1]

11

12

CHAPTER 1. INTRODUCTION

Figure 1.4: Simulation of a 100 GeV jet reconstructed by PFA. [3]1.3. PARTICLE FLOW ALGORITHM (PFA)

13

Figure 1.5: a) The reconstructed di-jet mass √distributions for the best jet-pairing in selectedνe ν¯e WW (blue) and νe ν¯e ZZ (red) events at s = 1 TeV. b) The distribution of the averagereconstructed di-jet mass, (mij + mBkl )/2.0, for the best jet-pairing for νe ν¯e WW (blue) andνe ν¯e ZZ (red) events. [2]14

CHAPTER 1. INTRODUCTION

Figure 1.6: The barrel region of the electromagnetic calorimeter (blue) within the ILD
detector.[1]1.4

SiW electromagnetic calorimeter

The ECAL is one of the most challenging detectors in the ILD for PFA requirements. The SiW
ECAL is an option for it. SiW ECAL is a sandwich-type calorimeter with layers of tungsten
absorbers and silicon semiconductor detectors. Fig.1.6 shows a picture of the barrel regionof the ECAL within the ILD. For PFA requirements, each particle cluster in a ECAL should
be separated. Tungsten absorber is the best for this purpose. It is because the tungsten
has a short radiation length (X0 = 3.5 mm), small Moliere radius (RM = 9 mm), and large
interaction length to radiation length ratio. These properties lead to compact electromagnetic
showers and make it easier to distinguish electromagnetic showers from hadronic showers.
The silicon detector layer has high granularity. The segmentation is 5 × 5 mm2 in the current
design. The ECAL is longitudinally segmented into 30 layers.

1.5. OVERVIEW

1.5

15

Overview

This paper describes tests of basic properties of silicon sensors being developed for the SiW
ECAL of the ILD. This is for understanding the sensor’s behaviour and for future radiation
damage measurement of the silicon sensor.
The physics of the silicon semiconductor detector and radiation eﬀects will be describedin chapter 2. Then the measurement of each property will be shown in chapters 3-5. In
chapter 6, some eﬀects of radiation damage on the ILD performance are investigated using
the ILD full simulation. A plan for a future irradiation experiment is presented in chapter 7.

Chapter 2
Silicon sensor basic properties
2.1

The design of silicon sensor for the ILD ECAL

The silicon semiconductor detector for the ILD ECAL, shown in Fig.2.1, is a matrix of PIN
diode.
The size is 8.97×8.97 cm2 . It has 16×16 pixels. The schematic diagram of the siliconsensor for thickness direction is shown in Fig.2.2. The thickness is 350 µm, including electrodemetal and insulator. The silicon thickness itself is 320 ±15 µm. The p-type layer has asegmentation of 5.50 × 5.50 mm2 . Thus it gives higher position precision than Molièle radius.
It is surrounded by 0.5 mm wide guard ring to suppress the surface current and thus keep
dynamic range of readout electronics.
Chips with 3×3 pixels, called baby chips, have also been produced from the same wafer
as the chip noted above for testing of diﬀerent guard ring designs. The size of the baby chipis 1.75×1.75 cm2 .
The results shown in this paper are for a main chip and 3 baby chips with same guard
ring design as main chip. The baby chips will be used for radiation hardness tests.

2.2

Silicon sensor properties

2.2.1

The PIN diode property

Here, it will be described how the silicon sensor works. This section describes the PIN
diode physics applying the discussion in [4] about pn diode. In the semiconductor diode,p-type semiconductor which is doped with acceptor has holes and n-type one which is dopedwith donor has free electrons. Undoped semiconductor, intrinsic layer has few holes andfree electrons. The PIN diode is consists of p-type layer, intrinsic layer, and n-type layer.
The intrinsic layer is sandwiched between p-type layer and n-type layer. When a forward
bias voltage (p-type layer is higher side) is applied, the current becomes large because the17

18

CHAPTER 2. SILICON SENSOR BASIC PROPERTIES

Main chip

5.50 mm5.50 mmBaby chip

1.75 cm
8.97 cm
Figure 2.1: A silicon sensor main chip for the ILD ECAL and a baby chip.

2.2. SILICON SENSOR PROPERTIES

19

Gap between pixels

350 μm
320 μm
N+
Metal(Al)Figure 2.2: A schematic diagram of the silicon sensor for thickness direction.

20

CHAPTER 2. SILICON SENSOR BASIC PROPERTIES

Same existence probability
⊝

⊝
qVD

⊝
⊝

⊝
⊝

⊝ ⊝ ⊝

⊝

Diffusion
voltage⊝EF⊕ ⊕ ⊕ ⊕
⊕ ⊕ ⊕
⊕ ⊕
⊕

⊕
Same existence probability
Neutral region(p-type)

Depletion layer
Electric field

Neutral region(n-type)Figure 2.3: An energy band chart for a PIN diode.
potential barrier between p-type and n-type becomes small. However, when a reverse bias
voltage (n-type layer is higher side) is applied, current becomes significantly small because
carriers move to each electrode and disappear from the semiconductor. In this case, there isa volume with few carriers and fully ionized donors (or acceptors) out of the intrinsic layer.
This is called the depletion layer including intrinsic layer. An electric field exists only in thedepletion layer. Here, the voltage direction is defined to be positive when p-type layer is thehigher side.
The energy band chart is introduced for a description. Fig.2.3 is an energy band chart
for a PIN diode. The left side is p-type and the right side is n-type. The central region isthe depletion layer. The upper curve shows the bottom of the conductive band (EC ) andthe lower curve shows the top of the valence band (EV ). The broken line at the centre is the
Fermi level (EF ).
The energy diﬀerence between the bottom of the p-type and the n-type conducting bands

2.2. SILICON SENSOR PROPERTIES

21

at equilibrium is defined as qVD . VD is called the diﬀusion voltage. Equilibrium is reachedwhen the Fermi levels in the n-type and the p-type regions are equal.
The diﬀusion voltage VD is derived below. The electron carrier concentration n can be
represented as
n = NC fB (EC )()3/22πm∗e kTNC ≡ 2h2
fB (EC ) ≡ e−(EC −EF )/kT

(2.1)
(2.2)
(2.3)

Here, m∗e is the eﬀective electron mass in silicon. NC is called the eﬀective density of states.
fB (EC ) is the value of the Maxwell-Boltzmann distribution at E = EC . The eﬀective densityof states for the hole concentration, p, is similarlyp = NV {1 − f (EV )} = NV e−(EF −EV )/kT(
)3/22πm∗h kTNV ≡ 2h2
1
f (EV ) ≡≃ 1 − e−(EF −EV )/kT
1 + e−(EF −EV )/kT

(2.4)
(2.5)
(2.6)

From (2.1) and (2.4),
pn = NC NV e−(EC −EV )/kT

(2.7)

For an intrinsic, undoped semiconductor, n = p = ni and pn = n2i . This ni is called the
intrinsic carrier concentration.
This depends only on the temperature T and the band gap EC − EV . EC is diﬀerent in
the p-type and the n-type regions. Therefore,

nn = NC e−(ECn −EF )/kT−(ECp −EF )/kT

np = NC e

(2.8)
(2.9)

Therefore,
qVD = ECp − ECn = kT lnnnnp(2.10)At room temperature, most of donors and acceptors are ionized. Therefore, the free electron concentration nearly equals to ND , donor concentration in n-type layer, and the holeconcentration nearly equals to NA , acceptor concentration in p-type layer. Using pn = n2i ,22

CHAPTER 2. SILICON SENSOR BASIC PROPERTIES

nn ≃ ND(2.11)

np ≃(2.12)

n2i /NA

Here, ND is the donor concentration in the n-type layer and NA is the acceptor concentrationin the p-type layer. Substituting (2.11) and (2.12) into (2.10),
VD =kT NA NDlnqn2i(2.13)

Thus, the diﬀusion voltage VD depends on the impurity concentration, NA and ND .

2.2.2

Current-voltage property

If a reverse bias voltage is applied to the silicon sensor, most of the bias voltage goes tothe depletion layer because the depletion layer has a high resistance due to a low carrier
concentration. Here, the voltage diﬀerence between the Fermi levels of the p-type and then-type is equal to the applied reverse bias voltage. The energy barrier becomes q(VD + V ).
The energy band chart is shown in Fig.2.4.
To go over the energy barrier, the electron must have energy larger than q(VD + V ). If
the energy distribution can be approximated by the Maxwell-Boltzmann distribution, thecurrent density moving from n-type side to p-type side can be written as
Inp = K1 e−q(VD +V )/kT

(2.14)

Here, K1 is a constant and independent on the bias voltage.
For an electron moving from the p-type side to the n-type side, the energy barrier doesn’t
matter. Therefore, if the number of electrons moving from p-type side to n-type side per unit
area per unit time is Ipn ,Ipn = K2

(2.15)

Here, K2 is a constant and independent on the bias voltage. The total electron current
density Je is thenJe = −q(Inp − Ipn ) = −q(K1 e−q(VD +V )/kT − K2 ).

(2.16)

Because Je = 0 at V = 0,
K2 = K1 e−qVD /kT
Therefore(2.17)

2.2. SILICON SENSOR PROPERTIES

23

Electron flow (independent on V)⊝⊝q(VD+V)

⊝
⊝

⊝

EF

⊕ ⊕ ⊕ ⊕
⊕ ⊕ ⊕
⊕ ⊕
⊕

⊝

⊝ ⊝ ⊝

qV

⊝
⊝

EF

⊕

Hole flow (independent on V)
―

p

i

n

+

Ｖ

Figure 2.4: The electron flow and the hole flow.

24

CHAPTER 2. SILICON SENSOR BASIC PROPERTIES

Je = −qK1 e−qVD /kT (e−qV /kT − 1)
−qV /kT= Je0 (e− 1)(2.18)(2.19)

Je0 ≡ −qK1 e−qVD /kT(2.20)In a similar way, the hole current density Jh can be represented as
Jh = Jh0 (e−qV /kT − 1)

(2.21)

Jh0 ≡ −qK1′ e−qVD /kT(2.22)

The current density of the PIN diode is the sum of Je and Jh .
J = Je + Jh = (Je0 + Jh0 )(eqV /kT − 1) = J0 (eqV /kT − 1)

(2.23)

J0 ≡ Je0 + Jh0(2.24)

Fig.2.5 shows the plot. It is called the diﬀusion current.
The diﬀusion voltage, VD depends on the temperature and the impurity concentrationaccording to (2.13). The Je0 dependence on temperature and impurity concentration isderived below for later analysis. Substituting (2.2), (2.5), (2.7), and (2.13) into (2.20),

Je0 = −qK1 e= −qK1

−ln

NA ND
n2
i

(2.25)n2i

NA ND
NC NV −Eg /kT= −qK1e
NA ND
I0=
T 3 e−Eg /kT
NA ND
Here, Eg = EC − EV and I0 = −qK1 · 4similar to the electron current.

(

4π 2 k2 m∗e m∗hh4(2.26)(2.27)(2.28))2/3. The calculation for hole current is

In the reality, there are other current components except diﬀusion current. The empiricalexpression of the current is as follows.

25

Current denssity

2.2. SILICON SENSOR PROPERTIES

Reverse direction

Forward direction
Applied voltage

Figure 2.5: Current-voltage plot of (2.23). [4]26

CHAPTER 2. SILICON SENSOR BASIC PROPERTIESJ=

I0
T 3 e−Eg /kT (eαqV /kT − 1)
NA ND

(2.29)

Here, α is a constant usually between 0.5 and 1. In the low bias voltage region, the causesof α are current components other than diﬀusion current. At a high bias voltage, the causeof α is the series resistance component.
According to the discussion above, the leak current value, the fluctuation of the leakcurrent, and the breakdown voltage can be measured by current-voltage measurement. The
current-voltage properties also provide information about the impurity concentration, inparticular the product of donor and acceptor concentration, NA ND according to (2.28).

2.2.3

Capacitance-voltage property

In this section, the dependence of the diode capacitance on the applied reverse bias voltage
is discussed. When the silicon sensor has a depletion layer, there is charged volume. The
p-type layer has a negatively charged volume and the n-type layer has a positively charged
volume. This gives a capacitor-like property to the silicon sensor.
Here, it is assumed that the doping concentration changes as a step function, as shownin the bottom picture of Fig.2.6.
Then, the energy band chart is like the centre picture of Fig.2.6. The x-coordinate isdefined from p-type toward n-type. The origin is set on the border between the depletion
layer and the p-type layer. The P-I junction plane is x = x1 , I-N junction plane is x = x2 ,and the border between the depletion layer and the n-type layer is x = x3 . Here, a constantdI = x2 − x1 is defined as a thickness of intrinsic layer.
The potential follows Poisson’s equation:
d2 v(x)
ρ
=−
2
dx
ϵs ϵ0



−qNA
ρ= 0


qN
D

(0 ≤ x < x1 )(x1 ≤ x < x2 )(x2 ≤ x ≤ x3 )The boundary conditions are

∂v(0)

(x = 0)v(0) = 0, ∂x = 0∂v(x)v(x) and ∂x is continuous (x = x1 , x2 )v(x ) = V + V , ∂v(x3 ) = 0 (x = x )33D∂x
From Poisson’s equation and the boundary conditions,(2.30)

2.2. SILICON SENSOR PROPERTIES

―

27

p

i

n

+

Ｖ
⊝

⊝

q(VD+V)

EF

⊕⊕ ⊕⊕
⊕ ⊕ ⊕
⊕ ⊕
⊕ x=0
Neutral region(p-type)

Chargedensity

⊝

⊝

⊝ ⊝ ⊝
⊝ ⊝ ⊝ ⊝

qV

EF
x1

x2

x3

Neutral region(n-type)
qND
＋Q x3

x

Depletion layer

x=0

x1

―Q

x2

x

-qNA

Figure 2.6: Energy band chart and the charge density distribution of PIN diode.

28

CHAPTER 2. SILICON SENSOR BASIC PROPERTIESa) Charge density

qND
x=0

x1

x2

＋Q x3

x2

x3

x

―Q

-qNA

b) Electric field distribution
x=0

x1

x

c) Potential distribution

VD + V

x=0
x1

x2

x3

x

Figure 2.7: a) Charge density distribution. b) Electric field distribution. c) Potential distribution.

qNA x1 = qND (x3 − x2 )(2.31)It means that the total number of positive charges and negative charges are equal. Moreover, the depletion layer width is inversely proportional to the impurity concentration. The
electric field distribution is as in Fig.2.7 b).

In addition, following equation can be derived.

2.2. SILICON SENSOR PROPERTIES29

qNA 2 qNA
qND
x1 +x1 dI +
(x3 − x2 )2(2.32)
2ϵs ϵ0ϵs ϵ02ϵs ϵ0)2(qNA
ND
qNA ND=(NA + ND ) x1 +dI −d2I2ϵs ϵ0 ND
NA + ND
2ϵs ϵ0 (NA + ND )(2.33)

V + VD = −The potential is shown in Fig.2.7 c).
The relation between the reverse bias voltage and total depletion width is√(x1 =qNA ND
V + VD +d22ϵs ϵ0 (NA + ND ) I)

2ϵs ϵ0 ND
ND−
dI
qNA (NA + ND ) ND + NA

(2.34)

From this equation,

Q(V ) = qNA x1√(
V + VD +=qNA NDd2
2ϵs ϵ0 (NA + ND ) I)(2.35)
2qϵs ϵ0 NA ND qNA ND dI−
NA + ND
NA + ND(2.36)

Therefore,
dQ
C=
=
dV

√

√
1
A ND
V + VD + 2ϵs ϵqNd2
0 (NA +ND ) I

qϵs ϵ0 NA ND
2(NA + ND )(2.37)

This C is the depletion-layer capacitance. It also can be represented as()
2(NA + ND )qNA ND
1
2=
V + VD +dC2qϵs ϵ0 NA ND
2ϵs ϵ0 (NA + ND ) I
2(NA + ND )≡(V + V0 )qϵs ϵ0 NA ND(2.38)(2.39)A ND
d2 . The expected curve of 1/C 2 against the reverse bias voltage
Here, V0 = VD + 2ϵs ϵqN0 (NA +ND ) I
is shown in Fig.2.8.

As in (2.39), the capacitance depends on the diﬀusion voltage and impurity concentrationof both p-type layer and n-type layer. Moreover, the capacitance can be written as

30

CHAPTER 2. SILICON SENSOR BASIC PROPERTIES

1/C2

V0
O

Full depletion voltage

V

Figure 2.8: Theoretically expected curve of 1/C 2 against the reverse bias voltage V.

2.3. EXPECTED EFFECTS BY RADIATION EXPOSURE

31

Aϵs ϵ0(2.40)
dHere, A is the area of the sensor, ϵ0 is the permittivity of the vacuum, ϵs is the relative
permittivity of silicon, and d is the thickness of the depletion layer. The thickness of thedepletion layer can therefore also be measured.
The capacitance-voltage property measurement is used to measure the values V0 and
NA +ND, which depend on the impurity concentration and depletion thickness.
NA ND
C=

2.2.4

Signal collection

When a charged particle passes through the silicon sensor, it deposits energy, creating
electron-hole pairs. The number of e-h pairs depends on only the deposited energy.
MIP deposit energy in silicon is 1.664 MeV·cm2 /g [5]. The silicon thickness in our siliconsensor is 320 µm. The density of silicon is 2.3290 g·cm−3 . Therefore, energy deposit in silicon
is 0.124 MeV. The e-h pair creation energy is 3.64 eV. Therefore, the number of e-h pairs
will be 3.41 × 104 . The total charge is 5.45 × 10−15 C.
To get full depletion and to prevent recombination of the created e-h pairs, an electricfield is applied. Then, e-h pairs are separated by electric field and collected in the electrode.
As discussed later in Sec.2.3, signal collection eﬃciency will decrease after irradiation.
The signal collection eﬃciency can be measured using a radioactive source or cosmic rays.

2.3

Expected eﬀects by radiation exposure

There are three types of radiation damage eﬀects on silicon detectors: the total ionizing
eﬀect, the displacement damage dose eﬀect, and the single event eﬀect [6].
The total ionizing eﬀect is caused by gamma-rays. When charged particles pass throughthe silicon sensor, e-h pairs are created as discussed in Sec.2.2.4. The mobility of electrons isvery large, so they quickly arrive at the electrode. However, the mobility of holes is 5-6 ordersof magnitude smaller than that of electrons. The holes are swept slowly. During sweeping, ahole may become trapped by a defect due to absent of oxygen around the interface between
Si and SiO2 in the case of MOS (Metal-Oxide-Semiconductor) capacitor. Thus positive fixedcharge is made. Fixed charges shift the capacitance-voltage curve to lower bias voltage, as
if the positive fixed charge gives a positive bias voltage. In addition, interface state is also
made in the band gap at the interface between Si and SiO2 by the total ionizing eﬀect.
The interface state is produced when a Si atom has a dangling bond which is not bonded
by covalent bond with O atom. Interface states charge positively for voltages smaller thanthe mid gap voltage and negatively for voltages higher than mid gap voltage. The mid gap
voltage is the voltage at which all the interface states are neutral. The interface states make

CHAPTER 2. SILICON SENSOR BASIC PROPERTIES

Capacitance32

After irradiation
Before irradiation

Voltage

Figure 2.9: Expected capacitance-voltage property change by irradiation.[6]the capacitance-voltage curve gradual. The number of fixed charges and interface states
increases as the radiation dose increases. The eﬀect of total ionizing eﬀect is expected to be
like Fig.2.9 for MOS capacitor.
There is MOS (Metal-Oxide-Semiconductor) structure in the p-type side of our siliconsensor. From the surface, metal as an electrode, silicon oxide as a insulator, and semiconductor are placed. The MOS capacitor-like property can be seen at a low reverse bias voltage.
These total ionizing eﬀects are evaluated with the absorbed dose, defined bydE[J/kg](2.41)
dm
Here, E is absorbed radiation energy and m is mass. The unit is Gy [1 Gy = 1 J/kg].
De =Secondly, displacement damage dose eﬀects are caused by high energy particles such as
neutron, electron, heavy ion, and gamma-ray. Charged particles lose most of their energy

2.3. EXPECTED EFFECTS BY RADIATION EXPOSURE

33

by inelastic scattering, ionization and bremsstrahlung. The probability of elastic scattering
is much smaller than inelastic scattering. For the most part in elastic scattering, induced
particles give very little energy to the nucleus. In the rare case when large momentum istransferred to a nucleus, a crystal atom is displaced. The displaced atom is called a Primary
Knocked-on Atom (PKA). It creates a point defect. The original position of the PKA also
becomes a point defect (vacancy defect). The number of these defects increases as theradiation dose increases. Some defects couple with other defects or impurities. Others couple
with void and pair annihilation occurs. Finally, many kinds of complex defects are made.
These defects create energy states called creation-recombination centres in the band gap. The
lifetime and mobility of electrons and holes are decreased by creation-recombination centres,
causing an increase of leakage current and decreasing signal charge.
Some of the defects from displacement catch majority carriers. If the density of such
defects increases to the order of the original carrier concentration, the state becomes carrier
exhausted. Generally, carrier exhaustion has the relation
pϕ = p0 − Rc ϕ

(2.42)or−Rc pϕpϕ = p0 e0(2.43)

Here, ϕ is the particle fluence and p0 is the carrier concentration before irradiation. Rc is called
the carrier exhaustion coeﬃcient, representing the magnitude of the carrier concentration
decreasing eﬀect.
The absorbed dose is not appropriate for evaluating the displacement damage dose eﬀect.
It is because absorbed dose is based on energy given via ionization, but cause of the displacement damage dose eﬀect is displacement of an atom consisting the crystal. The displacement
damage dose Dd is suggested for evaluating it.
Dd = ϕ · N IEL[MeV/g](2.44)The NIEL is the Non Ionizing Energy Loss, which depends on the energy of the incident
particle. NIEL is given by the deposited radiation energy divided by the density of theirradiated substance. NIEL is defined as follows.
1
N IEL(Ein ) =M∫ Ep(max)Ed

dσp
Ep L · dEp [eV · cm2 /g]
dEp(2.45)

Here, Ein is the energy of the incident particle, M is the mass of the irradiated substance,dσpand dE
is the diﬀerential displacement cross section. Ep is the displacement energy given top
the target atom by a collision. L is a value without dimension called the Lindhard partition
factor. Ed is the threshold energy of displacement and Ep(max) is the maximum displacement

34

CHAPTER 2. SILICON SENSOR BASIC PROPERTIES

energy. There is more detailed discussion about NIEL in App.A.
Thirdly, single event upsets are caused by alpha-rays, heavy ions and neutrons. Heavy ionshave high stopping power. When it enters the p-n junction in the IC (Integrated Circuit) for
electronics, it creates e-h pairs with high density. It causes a transient current. If it occurs
in silicon sensor, it is no problem in our case because it is normal calorimeter operation.
However, if it occurs in readout electronics, it is a problem. Generally, the time scale of thetransient current is on the order of 10 ps - 1 ns. It can change the operating state of the
IC. Thus it causes many kinds of single event eﬀects such as malfunction. In the case ofneutron, nuclear reactions occur with very small probability. Thus it creates heavy ions as
fission products. The heavy ions causes single event upset as mentioned above.
There are three types of radiation damage as discussed above. However, total ionizing dose
eﬀect does not aﬀect to the PIN diode operation because it creates defects mainly between
semiconductor and semiconductor oxide. The single event eﬀect also does not provide any
problem because this eﬀect is normal calorimeter operation. The most important eﬀect isthe displacement damage dose eﬀect.
The neutron irradiation damage for silicon semiconductor detectors will be tested to measure the displacement damage dose eﬀect. The expected eﬀects from radiation damage are
increased leakage current, eﬀective impurity decreasing by carrier exhaustion, and deterioration of signal collection eﬃciency.

2.4

The requirement for silicon sensor for the ILD ECAL

The requirement for the silicon sensor is discussed in this section from the point of view ofirradiation eﬀect.
First, the leakage current should be low and stable at the operation reverse bias voltage.
It is required for low and stable noise. Secondly, suﬃciently higher breakdown voltage thanthe operation reverse bias voltage. Breakdown is that current increases steeply from a certain
reverse bias voltage. If the breakdown voltage is near the operation reverse bias voltage, it
leads to unstable high leakage current. Thirdly, full depletion is achieved at the operation
reverse bias voltage. It is required to get the maximum sensitive volume. Fourthly, enoughsignal collection eﬃciency. It directly aﬀects to the energy measurement. It also aﬀects to thenumber of noisy pixels because the MIP signal decreases and the signal threshold is set to 0.5
MIP. More detailed discussion about the requirement for signal collection eﬃciency will begiven in Sec.6.3. The last, PIN diode property should be kept. The impurity concentration
should be same order before and after irradiation.
Summarizing above, the silicon sensor properties is evaluated by leakage current ID ,capacitance C, and charge collection eﬃciency ϵ. Detailed measurement method will be
discussed in later chapters.

Chapter 3
Current-voltage measurement
The current-voltage measurement is described in this section. The leakage current and thebreakdown voltage can be directly measured. Combined with temperature dependence, impurity concentration related value was measured. The leakage current is expected to increase
after irradiation. The impurity concentration is expected to decrease or type inversion may
occur after irradiation.

3.1

Setup

The setup for current-voltage measurement is shown in Fig.3.1. A photograph of the measurement box is shown in Fig.3.2. It was used to fix the position of the silicon sensor. The
upper picture of Fig.3.2 is the cover of the measurement box. It has 16 × 16 thin pins which
are connected to each pixel in the silicon sensor. All pins are connected to a common electrode at the back of the black board. The bottom picture of Fig.3.2 shows the case for thesilicon sensor. The bottom of the case has a second common electrode which is in contact
with the other side of the sensor. A high reverse bias voltage is applied between the upperside and bottom side of the measurement box. The measurement box was designed for themain chip with 256 pixels. To measure the smaller baby chips, a sheet of plastic was used
to insulate unused pins. The measurement box was placed in a black box, since the diodes
are sensitive to light. A Keithley2410 high-voltage source meter [7] was used to apply ahigh reverse bias voltage and measure the resulting current. The detailed specification of
the Keithley2410 high-voltage source meter is summarized in App.B. The source meter wascontrolled via a GPIB interface. The temperature was measured using a thermocouple attached to the ground electrode just under the silicon sensor. The measurement was executedin room temperature and the temperature was not controlled.
35

36

CHAPTER 3. CURRENT-VOLTAGE MEASUREMENT

Black box
Temperature logger
Silicon sensor is in themeasurement box

PROLOGIX GPIB
Ethernetcontroller

Figure 3.1: Setup for current-voltage measurement3.1. SETUP

37

Baby chip

Insulator

Figure 3.2: A photograph of the measurement box. Upper picture is the cover and bottom
picture is the case with baby chip and insulator.

38

CHAPTER 3. CURRENT-VOLTAGE MEASUREMENT

Dark current[A]

I-V

10-5

10-6

0

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Bias voltage[V]Figure 3.3: Current-voltage plot for main chip. The temperature changed from 23.9 ◦ C at
the first scan to 24.4 ◦ C at the last scan.

3.2

Leakage current

Figs.3.3-3.6 show the results of the current-voltage measurement. To get these plots, thereverse bias voltage was increased in step of 10 V. At every step, the current was read 1
s after the reverse bias voltage change, and then increased to the next reverse bias voltage
value. For main chip, the voltage is fixed if the measured current reached 25 µA. For baby
chips, the scan was terminated if either the measured current exceeded 100 nA or the reverse
bias voltage reached 800 V. At the completion of a scan, the sensor was left unpolarized for
60 s before the scan was repeated. Voltage scans were repeated 39 times in succession.
The current almost saturates around 50 V. At the operation reverse bias voltage, full
depletion and stable leakage current are required for reliable operation as discussed in Sec.2.4.
Stable leakage current means that the reverse bias voltage should be well below the breakdown
voltage. For main chip, a steep increase of current is seen from around 450-600 V. Thisphenomenon is called breakdown. It was only seen in some of the scans. This breakdown
behaviour is not stable because the leakage current changes largely by small reverse bias
voltage fluctuation. For baby chip 1-1, the breakdown voltage is about 750 V. For the otherbaby chips, 1-2 and 2-1, no breakdown behaviour was observed at voltages up to 800 V.
Experimentally, the operation reverse bias voltage is set to about 120 V. At 120 V, the mean

3.2. LEAKAGE CURRENT

39

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10-9
0

100

200

300

400

500

600

700
800
Bias voltage[V]Figure 3.4: Current-voltage plot for baby chip 1-1. The temperature changed from 25.0 ◦ C
at the first scan to 25.8 ◦ C at the last scan.

40

CHAPTER 3. CURRENT-VOLTAGE MEASUREMENT

I-V
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10

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0

100

200

300

400

500

600

700
800
Bias voltage[V]Figure 3.5: Current-voltage plot for baby chip 1-2. The temperature changed from 26.3 ◦ C
at the first scan to 25.4 ◦ C at the last scan.

3.2. LEAKAGE CURRENT

41

I-V
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600

700
800
Bias voltage[V]Figure 3.6: Current-voltage plot for baby chip 2-1. The temperature changed from 25.5 ◦ C
at the first scan to 25.8 ◦ C at the last scan.

42

CHAPTER 3. CURRENT-VOLTAGE MEASUREMENT

and RMS fluctuation of the leakage current measurement of main chip, each baby chip, 1-1,
1-2, and 2-1 were 775 ± 33 nA, 11.7 ± 0.6 nA, 18.2 ± 0.5 nA, and 7.1 ± 0.4 nA, respectively.
These fluctuations correspond respectively to 4.3%, 4.8%, 2.5%, and 5.6%. If the rise timeof the pre-amplifier is 30 ns[11], the leakage current gives additional 9.09 × 10−17 C per pixel
to the signal for main chip, which has the largest leakage current of the four. It is 50 times
lower than MIP signal, 5.45 × 10−15 C. Therefore, this result is tolerable for the ILD ECAL.

3.3

Temperature dependence

As shown in (2.29), the current depends on temperature as follows:I=

I0
T 3 e−Eg /kT (eαqV /kT − 1)
NA ND

(3.1)

Here, α is a constant usually between 0.5 and 1 [4].
The current was measured within a narrow voltage range between -0.25 V and 0.25 V
many times for baby chip 1-2, allowing the behaviour to be investigated as a function oftemperature. The result of one of these measurements is shown in Fig.3.7.
The statistical error of the current measurement was estimated based on the resolution of
the Keithley2410 high-voltage source meter (see App.B) and the 2.5% of current fluctuation
which is discussed in the sec.3.2. The systematic error of the current measurement wasestimated based on the accuracy of the Keithley2410 high-voltage source meter (see App.B).
The data were fitted to a function of the form (3.1), by using the method of least squares,0
and used to estimate the factor. One value of NAIN
T 3 e−Eg /kT (equivalent to Je0 in (2.28)) canDbe gotten for each measurement. Fig.3.8 shows the dependence of this factor on temperature.
0This temperature dependence was used to extract NAIN
, assuming Eg =1.1250 eV [8]:DI0= 402.8 ± 1.1(stat.) ± 34(syst.) A · K−3
NA ND

(3.2)

Since this number depends on the impurity concentration, it will change with increasing
irradiation. According to past studies [18]-[20], it is expected that 1012 n/cm2 neutron irradiation will result in an order of 10% decreasing of impurity concentration and a few 1012 n/cm2
neutron irradiation will cause type inversion.
The fits of the current-voltage curves also yield the factor α. Fig.3.9 shows the dependenceof α on temperature. There is no significant dependence of α on temperature. The averageis 0.9346±0.0003(stat.)±0.013(syst.), within the expected range of 0.5-1 [4].

Current[A]3.3. TEMPERATURE DEPENDENCE

43

×10-6
0
-1
-2
-3
-4
-5
-6
-7
-0.3

-0.2

-0.1

0

0.1

0.2
0.3
Voltage[V]Coefficient[A]Figure 3.7: Current-voltage plot in low voltage.

×10-9
1

0.95

0.9

0.85

0.8
23.4

23.6

23.8

24

24.2

24.4 24.6 24.8
Temperature[° C]

Figure 3.8: The dependence of Je0 on the temperature.

CHAPTER 3. CURRENT-VOLTAGE MEASUREMENT

α

44

0.94
0.938
0.936
0.934
0.932
0.93
0.928
0.926
23.4

23.6

23.8

24

24.2

24.4 24.6 24.8
Temperature[° C]

Figure 3.9: The dependence of α on the temperature.

Chapter 4
Capacitance-voltage measurement
The capacitance-voltage measurement is described in this section. The full depletion voltage
and the capacitance at the time are directly measured. The full depletion depth, the voltage
oﬀset V0 and the impurity concentration related value can be extracted from the measurement. The impurity concentration is expected to decrease or type inversion may occur after
irradiation.

4.1

Setup

The setup for the capacitance-voltage measurement is described in Fig.4.1. An Agilent LCR
meter was used for the capacitance measurement [9][10]. The detailed specification of theAgilent LCR meter is summarized in App.C. This instrument measures capacitance by using
a four-terminal pair method. The four terminal pair have the name Hp, Hc, Lp, and Lc (H/L
= high/low, p/c= potential/current). A Keithley2410 was used to apply a high reverse bias
voltage.
Fig.4.2 shows the basis of the circuit inside the LCR meter. The ”Device” is the siliconsensor in this measirement. The LCR meter applies an AC signal on the silicon sensor fromthe Hc terminal. The applied AC signal is measured through the Hp terminal. The resulting
current through the sensor is measured by the Lc terminal. The capacitance is measured bycomparing the input AC voltage and output current. The Lp terminal is set to ground using
an auto-balance bridge and works to produce a current in the outer lead. This current is thesame as the current in the silicon sensor and the inner lead. They cancel the magnetic fieldeach other, thus suppressing its influence on the measurement.
Since the capacitance of the PIN diode depends on the reverse bias voltage, the signal
AC voltage is set to a low voltage of 20 mV. An additional external circuit was used toisolate the LCR meter from the DC bias. This circuit also cuts the frequency component
lower than 30 kHz, so a frequency of 100 kHz was used in the measurement. The capacitance45

46

CHAPTER 4. CAPACITANCE-VOLTAGE MEASUREMENT

Agilent LCR meter
Lc Lp
Hp
Hc
GPIB

PC
Silicon sensor

GPIB

Keithleysource meter

Figure 4.1: Setup for the capacitance-voltage measurement. C1 and C2 are 1 µF capacitors.
CR1 and CR2 are zener diodes with 47 V of the zener voltage. CR3 and CR4 are zener
diodes with 3.3 V of the zener voltage. CR5 and CR6 are rectifier diodes. [9]4.1. SETUP

47

Imaginaryshort

Outputresistance
DeviceSignalsourceCommongroundAuto-balancing
bridgeFigure 4.2: The circuit describing four-terminal pair method. [10]48

CHAPTER 4. CAPACITANCE-VOLTAGE MEASUREMENT

measurements were made with an interval of 2 minutes because the capacitor in the external
circuit required about 2 minutes to become stable.

4.2

Systematic error estimation study

According to [9], the error of the capacitance measurement is due to two components: theerror from LCR meter itself, and that due to the measurement box [9]. The error components
due to the LCR meter are the calibration accuracy, basic accuracy, sensor impedance eﬀect,
short oﬀset, and open oﬀset [10]. The calibration accuracy is 0.03 + 1 × 10−3 × Fm %. Here,Fm =100 is frequency of the signal AC voltage, in units of kHz. The basic accuracy is
rms
0.1 × 30mV
× Kt %. Here, Vrms is an unit of voltage for signal level. The signal level
Vs
Vs = 20 mVrms . Kt = 1 is a temperature coeﬃcient.
The sensor impedance eﬀect is 0.05%.
√
The short oﬀset is 0.6mΩ(1+0.400/Vs )(1+ 1000/Fm )/Zs ×100%.
√ Here, Zs is the impedanceof the silicon sensor. The open oﬀset is 0.5nS(1 + 0.100/Vs )(1 + 100/Fm ) × 100%. The sumof these four components is the error due to the LCR meter.
The error components due to the measurement box is from the residual impedance. The
external circuit and measurement box represent an additional impedance. To compensate
its eﬀect, the LCR meter performs open and short corrections. The open correction is donewith the same setup except that the silicon sensor is replaced by an insulator, while theshort correction is performed with the silicon sensor removed and the measurement box
short-circuited. The LCR meter measures the residual impedance by these two types ofcorrections.
The error components due to the measurement box were estimated by measuring the
reproducibility of the open state and the short state for the corrections. Fig.4.3 shows a plotof G = 1/R against −iωC measured with open state. The open reproducibility Y0 is definedas the distance of points from the origin (0,0). Fig.4.4 is a plot of R against −1/iωC withshort state. The distance from the origin (0,0) is the short reproducibility, Z0 . Open andshort measurements were performed one after another, with ten data points taken in eachmeasurement. From these measurement, the open reproducibility Y0 = 28 nS and the short
reproducibility ZS = 4.3 Ω. Their total contribution to the uncertainty is
Zm = (P +ZS+ Y0 · ZX )%
ZX

(4.1)

Here, ZX is the impedance of the silicon sensor. In reality, there may be proportional
component P to the impedance uncertainty. However, it can’t be measured with our setup.

4.2. SYSTEMATIC ERROR ESTIMATION STUDY

49-i ω C

-6

0

×10

-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
-0.4
-0.45
-6

-0.5
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

×10
0.2
G

Figure 4.3: Reproducibility of open state. The same colour points were measured successively.
The diﬀerent colour points were measured after reconstruction of an open state.

CHAPTER 4. CAPACITANCE-VOLTAGE MEASUREMENT-1/i ω C

50

0

-0.2

-0.4

-0.6

-0.8

-1

-1.2
0

50

100

150

200

250
R

Figure 4.4: Reproducibility of short state. The same colour points were measured successively. The diﬀerent colour points were measured after reconstruction of a short state.

51

×1015
180

2

1/C [F-2]

4.3. DEPLETION WIDTH, DIFFUSION VOLTAGE

160
140
120
100
80
60
40
20
0

0

50

100

150
200
Bias voltage[V]Figure 4.5: Capacitance-voltage plot for main chip.

4.3

Depletion width, diﬀusion voltage

The results of reverse bias voltage scans are shown in Figs.4.5-4.8, which show the dependenceof the inverse squared capacitance 1/C 2 as a function of the applied reverse bias voltage V .
As predicted by (2.39), a linear dependence of 1/C 2 on the reverse bias voltage is seen in thereverse bias voltage below around 50 V. The saturation at about 50 V is due to full depletionof the PIN diode. The statistical error of this measurement was estimated by considering
the 1/C 2 fluctuations above 70 V. As shown in (2.40), the fully depleted capacitance allows
the depletion layer depth to be estimated. The saturated capacitance is shown in the firstrow of Table 4.1, 4.2. The depletion thickness was calculated as in second row of Table 4.1,
4.2. Here, systematic uncertainty includes capacitance systematic error discussed in previous
section and baby chip area error. The length of a side of the main chip is 89.700±0.040 mm.
The length of a side of the baby chip is 16.460±0.040 mm. These result is not consistent
with the thickness of the silicon sensor, 320 ± 15 µm. It may be temperature eﬀect or theeﬀect of proportional error component. More study is required.
A ND
As shown in (2.39), the value V0 = VD + 2ϵs ϵqN
d2 gives rise to an oﬀset in the linear
0 (NA +ND ) I
region of Fig.4.6-4.8. The data were fitted to a straight line in the reverse bias voltage range
from 8 V to 41 V. V0 is shown in the third row of the Table 4.1, 4.2. The result seems notconsistent among the 3 baby chips, more study is required. In addition, the slope of the52

CHAPTER 4. CAPACITANCE-VOLTAGE MEASUREMENT

Graph
1/C2[F-2]

18

×10
180
160
140
120
100
80
60
40
20
0

0

50

100

150

200
Bias voltage[V]Figure 4.6: Capacitance-voltage plot for baby chip 1-1.

Graph
1/C2[F-2]

18

×10
120

100

80

60

40

20

0

0

50

100

150

200
Bias voltage[V]Figure 4.7: Capacitance-voltage plot for baby chip 1-2.

4.3. DEPLETION WIDTH, DIFFUSION VOLTAGE

53

Graph
1/C2[F-2]

18

×10
180
160
140
120
100
80
60
40
20
0

0

50

100

150

200
Bias voltage[V]Figure 4.8: Capacitance-voltage plot for baby chip 2-1.
D
fitted line was used to extract the value of NNAA+N. Because this equation is derived for unit
ND
area capacitor, it is rewritten as

NA + ND
1= Sqϵs ϵ0 A2
NA ND
2

(4.2)

The values are shown in Table 4.1, 4.2. Combined with the measurement of (3.2), this canbe used to measure the change in acceptor or donor concentration due to radiation damage.
Table 4.1: The summary of capacitance-voltage measurement results for main chip and baby
chip 1-1.

Saturated capacitance
Depletion thickness
A ND
d2
V0 = VD + 2ϵs ϵqN0 (NA +ND ) I
NA +NDNA ND

Main chip
Baby chip 1-1
2.44 ± 0.01(stat.) ±0.02(syst.) nF 76.98 ± 0.09(stat.) ±0.25(syst.) pF
335.6 ± 1.4(stat.) ±2.8(syst.)µm 362.51 ± 0.42(stat.) ±0.42(syst.)µm
0.50± 0.16(stat.) ± 0.58(syst.) V
8.6 ± 0.2 V−183
1.682 ± 0.014(stat.)±0.069(syst.)×10 m
6.336 ± 0.045×10−15 m3

54

CHAPTER 4. CAPACITANCE-VOLTAGE MEASUREMENT

Table 4.2: The summary of capacitance-voltage measurement results for baby chips.

Saturated capacitance
Depletion thickness
A ND
V0 = VD + 2ϵs ϵqNd2
0 (NA +ND ) I
NA +NDNA ND

baby chip 1-2
95.79 ± 0.13(stat.) ±0.30(syst.) pF
291.32 ± 0.40(stat.) ±0.40(syst.) µm−0.07 ± 0.05 V
4.369 ± 0.02010−15 m3

baby chip 2-1
76.34 ± 0.11(stat.) ±0.25(syst.) pF
365.55 ± 0.53(stat.) ±0.53(syst.) µm
6.9 ± 0.2 V
6.876 ± 0.06310−15 m3

Chapter 5
Charge collection eﬃciency
measurement plan
The charge collection eﬃciency measurement is described in this section. The charge collection eﬃciency is expected to decrease after irradiation.

5.1

Expected signal voltage

For the measurement of the charge collection eﬃciency, signals induced by cosmic rays ora radioactive source will be measured. In Sec.2.2.4, the MIP (minimum ionizing particle)
signal was estimated to be 0.124 MeV, corresponding to a charge of 5.45 × 10−15 C.
A charge sensitive pre-amplifiers such as the CAEN A1422 will be used to read the signal.
This pre-amplifier has a gain of 400 mV/MeV, giving a MIP signal of around 50 mV.

5.2

Setup

The setup for signal collection eﬃciency is shown in Fig.5.1. The measurements of currentvoltage and capacitance-voltage properties were shown as the sum of nine pixels. For thesignal collection eﬃciency measurement, each pixel will be measured separately. A printed
circuit board will be attached to the silicon sensor with indium, and the read out circuit will
be connected to a printed circuit board. A high voltage is required to reverse bias the siliconsensor. Since the pre-amplifier is a charge sensitive amplifier, the peak value of the signal
voltage is proportional to the total charge, and therefore the deposited energy. The peakvalue will be read out by an oscilloscope. There is also a shaper and an ADC read out for
digital processing. The signal read out will be triggered by coincident signal from the two
scintillator set above and below the silicon sensor.
55

56

CHAPTER 5. CHARGE COLLECTION EFFICIENCY MEASUREMENT PLAN

PMT

Scintillator

Pre-amplifier
CAEN A1422
Coincidence

ShaperSiliconsensor
HV

PMT

Scintillator

Oscilloscope

ADC

LV

Trigger

Figure 5.1: The setup for signal collection eﬃciency measurement.

5.2. SETUP

57

The signal strength and the pedestal will be measured from the distribution of the measured peak voltages, while the expected signal can be calculated from the energy of the decay
product of the radioactive source. The energy resolution will be also measured from the same
peak voltage value distribution. There are three major possible contributions to the energy
resolution: first, the Poisson distribution due to the number of created e-h pairs, given by√
3.41 × 104 /3.41 × 104 ≃ 0.5% for a MIP signal. For larger energy deposits, it will besmaller; secondly, the noise from the pre-amplifier, estimated to be less than 2 keV according to CAEN A1422H design [11]. It is equivalent to an error of 1.6% for MIP signal; andthirdly, due to the voltage resolution of oscilloscope. An oscilloscope, Tektronix DPO2024
has a sensitivity of 2 mV/div. Therefore, it will contribute an error of 0.4%. In total, theerror will be about 1.7 % except environmental nose for MIP signal.
The charge collection eﬃciency will be measured before and after neutron irradiation tomeasure the eﬀect of traps and so on.

Chapter 6
Simulation of radiation damage eﬀect
In this section, the expected the ILD performance on jet energy reconstruction is discussed.
One of the radiation damage eﬀects, noisy pixel is simulated. This discussion gives part of
the requirements for radiation hardness of the silicon sensor.

6.1

Simulation tools

Events were simulated using the detailed full simulation of the ILD detector using the Mokka[12], GEANT4-based [13] software package. The same detector model as used in the ILD
Detailed Baseline Design [2] was simulated. Event reconstruction were performed in the
Marlin framework [14]. This includes digitization of the simulated detector signals (including
a threshold cut at 0.5 MIP in each ECAL pixel), and reconstruction of events using PFA (seeSec.1.3). For the simulation of the eﬀects of radiation damage, it was assumed that somefraction of pixels is noisy in the ECAL. As a simple, conservative assumption, noisy pixels
were assigned an energy of 1.4 MIPs.
If there is no problem in a silicon sensor, the typical signal-to-noise ratio for a MIP isabout 10. Therefore, assuming a Gaussian noise distribution, noise larger than the 0.5 MIP
threshold is about 10−7 . Since there are order of 108 pixels in total, only around 10 noisy
channels will be fired per event. The noise can have 2 eﬀects: add energy to true clusters,
increasing event energy; add inducing errors in the clustering or pattern recognition in the
ECAL (e.g. making fake clusters, or causing clusters to be merged). If noise hits are isolated,
they are not clustered and are essentially ignored in the energy sum.

6.2

Result

The jet energy resolution was evaluated using Z boson at rest decaying to two light quarks(u,d, and s). Since the energy resolution is worse in the end-caps, overlapping region of barrel
59

60

CHAPTER 6. SIMULATION OF RADIATION DAMAGE EFFECT

Mean energy[GeV]Noise rate dependence

95

90

85

80
0

0.05

0.1

×10-3

Noise rate
Figure 6.1: The dependence of mean energy on noise rate for√s = 91 GeV jets.

and end-caps, and beam direction, only | cos θ| < 0.7 events were used. Here, θ is theangle of initial quark direction measured from beam direction. The energy was measured bysumming all the reconstructed particle energies. A weak point of the PFA reconstruction isthat sometimes mis-clusterings occur [3]. The mis-clusterings result in removing a particle
from the reconstructed particle list or double counting of same particle. Therefore, only
90% of all the events were used to evaluate the jet energy mean and resolution removing
mis-clustering events. These 90% of events were selected to get their reconstructed energy
distribution range minimum. RMS90 is defined as the root mean squares of the 90% of theevents and interpreted as the energy resolution of the ILD.
√
Here, the simulation result of s = 91 GeV jets events with randomly distributed noisy
pixels is shown. Fig.6.1 shows the dependence of the mean total reconstructed event energy
on the noise rate, showing a linear dependence of the reconstructed energy on the noise rate.
Fig.6.2 shows the dependence of the jet energy resolution on the noise rate. There isno significant eﬀect on the resolution for a noise rate up to 10−5 (corresponding to about1000 noisy pixels per event),while a noise rate of 10−4 has significantly degraded jet energy
resolution.
Figs.6.3, 6.4 show views of the reconstruction of the same original event, with diﬀerent
noise rates, of 10−5 and 10−3 , superimposed. In the case of the lower noise rate, no obvious

6.3. THE REQUIREMENTS ON THE SILICON SENSOR

61

RMS90/Emean

Noise rate dependence

4.4

4.2

4
0

0.05

0.1

×10-3

Noise rate
Figure 6.2: The dependence of jet energy resolution on noise rate for√s = 91 GeV jets.

reconstruction problems are visible, while the high noise rate gives rise many fake clusters
consisting of noisy pixels.

6.3

The requirements on the silicon sensor

In the previous section, it is concluded that the noise rate should be less than around 10−5 .
In this section, the requirements for the silicon sensor are discussed based on this result.
Here, it is assumed that the typical signal to noise ratio is 10 for the silicon sensor before
irradiation, and the pedestal has Gaussian distribution with RMS σ. There will be noise rateof 10−5 when the threshold is set to 4.3 σ.
The requirement for leakage current can be determined because it aﬀects to the pedestal
distribution. If the fluctuation of the leakage current increases to get pedestal σ 1.2 times
larger, it gives noise rate of 10−5 .
The requirement for charge collection eﬃciency can be determined because it decreases thesignal threshold and thus increase noisy pixel rate. From the assumed pedestal distribution,
the 1 MIP signal should be larger than 8.3 σ. Since the 1 MIP signal is 10 σ before irradiation,
17% of signal collection eﬃciency decrease is tolerable. The contribution for the statistics
error in MIP signal collection is only 0.1% at the same time, suﬃciently small to ignore

62

CHAPTER 6. SIMULATION OF RADIATION DAMAGE EFFECT

Figure 6.3: One jet event with noise rate of 10−5 . The lines are MC particle trajectories,
dots are clustered calorimeter hits.

6.3. THE REQUIREMENTS ON THE SILICON SENSOR

63

Figure 6.4: One jet event with noise rate of 10−3 . The lines are MC particle trajectories,
dots are clustered calorimeter hits.

64

CHAPTER 6. SIMULATION OF RADIATION DAMAGE EFFECT

compared to expected MIP signal error 1.7%, discussed in Sec.5.2.

Chapter 7
Irradiation experiment plan
7.1

Radiation dose

At present, no detailed radiation dose estimate for the ILC ECAL has been performed.
However, the expected ECAL radiation dose has been studied in the case of the CLIC [15],and for the ILC neutron dose for the vertex detector from the ILC extraction line beam
dump [16]. The CLIC is a future multi-TeV linear collider. The radiation dose in the CLIC
should be higher than that in the ILC because it operates with higher centre of mass energy.
Therefore, the radiation dose estimation in the CLIC should be conservative for the ILC
detector. According to [15], the maximum equivalent neutron flux is 2 × 1010 /cm2 /year,
highest in the forward part of the ECAL end-caps. Equivalent neutron flux is defined byconverting total radiation damage to the flux of 1 MeV neutrons which gives the same extent
of radiation damage. There are two main source of displacement damage dose, incoherent
pairs and γγ → hadron. The incoherent pairs include three types of processes, γγ → e+ e−(Breit-Wheeler, BW), γe± → e± e+ e− (Bethe-Heitler, BH), and e+ e− → e+ e− e+ e− (LandauLifshits, LL). The γ is induced by beamstrahlung. The γs of γγ → hadron is also induced
by beamstrahlung. There will be 2 × 103 /bunch BW events, 2 × 105 /bunch BH events, and5 × 104 /bunch BW events in the ILC [17]. While γγ → hadron event occurs 3.2 /bunch.
The incoherent pair is important because it has larger production angles than coherent pairs.
The γγ → hadron event number is much smaller, however, the radiation damage is muchlarger than that of incoherent background. The distribution in the ECAL end-cap is shownin Fig.7.1. The reason there are relatively large dose in deeper layers is that there arebackscattering neutrons from the BeamCal located in the very forward region.
As discussed in [16], there are background neutrons not only from the interaction point
but also from the extraction line beam dump. The neutron fluence at the interaction point isestimated to be 4 × 1010 n/cm2 /year 1 MeV equivalent neutrons. It gives larger contribution
than beam crossing.
Silicon detector technology has advantage in high granularity multi channel readout.
65

66

CHAPTER 7. IRRADIATION EXPERIMENT PLAN

Figure 7.1: 1 MeV equivalent neutron flux distribution in the CLIC-ECAL end-cap. The left
is from Incoherent pairs. The right is from γγ → hadron. [15]

7.2. IRRADIATION EXPERIMENT

67

Therefore, it will be important technology for the future collider experiments and applicationin space. For a reference of such a situation, there are 3 × 1014 n/cm2 /year 1 MeV equivalent
neutrons in LHC [18].

7.2

Irradiation experiment

The silicon sensor will be irradiated with neutrons in a nuclear reactor at Kyoto University.
During irradiation, the silicon sensor will be damaged. Then, it will have some degradation as
discussed in Sec.2.3. The damage will be evaluated by comparing measurements of currentvoltage, capacitance-voltage, and signal collection eﬃciency before and after radiation.
In addition, the irradiation test of glue will be performed at the same time. This glue
will be used in the ILD ECAL construction to attach the silicon sensor to the printed circuitboard.
There are some studies of neutron radiation damage on silicon sensors from other experiments (e.g.[18][19][20]). From past research, it is expected that the silicon sensor will
have a decrease of charge collection eﬃciency of order 0.1% for 5 MeV neutron irradiation of1012 n/cm2 of neutron irradiation.
As discussed in Sec.7.1, the neutron dose in the ILC will be around 4 × 1010 n/cm2 /year.
However, similar silicon sensors can be used not only in the ILC, but also in other future
experiments or in space, where higher neutron backgrounds may be expected. Therefore, awide range of irradiation tests will be useful. The irradiation test will be done for radiationdose of 1010 n/cm2 , 1012 n/cm2 , and 1014 n/cm2 for with and without glue.

Chapter 8
Conclusion
The international linear collider is a planned electron-positron collider operating at centreof-mass energy between 250 GeV and 1 TeV. The main physics targets at the ILC are theprecise measurement of Higgs properties, top quark, W boson, Z boson and new physics suchas supersymmetry.
The ILD detector is optimized according to PFA for high resolution, 3-4 % hadronic jet
energy measurement. For the electro-magnetic calorimeter, silicon sensors are one options forthe detector layers. It is required to be stable for long duration during experiment. Radiation
will give some damage to the silicon sensor. To evaluate the radiation damage, a neutron
irradiation experiment is planned.
The property of leakage current will be evaluated by current-voltage measurement. Before
irradiation, the leakage current was around 10 nA at 120 V, and it was measured withaccuracy of a few %. Breakdown voltages are 750 V or not observed up to 800 V. The
0
impurity concentration dependent value NAIN
was measured by a temperature dependenceD
study. The properties of the capacitance-voltage measurement requires more study to improvereliability of measurement system. The charge collection eﬃciency will be measured soon
using radiation source or cosmic ray signal. The neutron irradiation damage can be evaluatedby these measurements.
To get the requirement for the silicon sensor, the ILD full simulation study was done withsome fraction of noisy pixels. The noise rate of order 10−5 is tolerable and it is equivalent to
17% of charge collection eﬃciency decrease.
The radiation test will be done in a nuclear reactor in Kyoto University. The fluence rangeof 1010 n/cm2 , 1012 n/cm2 , and 1014 n/cm2 will be tested, corresponding to the ILC operation
times of approximately 1 year, 100 year, and the LHC operation time of approximately 1
year, respectively.

69

Chapter 9
Acknowledgements
I would like to show my greatest appreciation to Professor Sachio Komamiya for giving me
the chance to research on the ILC detector. I really would like to thank Daniel Jeans. He
directed my research wonderfully and is also my good English teacher. Assistant Professor
Yoshio Kamiya gave me many helpful advices and warm encouragements. Jacqueline Yankindly oﬀered feedback on my thesis and is always a brilliant senior student in Komamiya
laboratory. I would like to express my gratitude to the CALICE-Asia group members forgiving many insightful comments, especially the members of Kyushu University for giving us
silicon sensors, measurement box, and tips for the measurement. I have had the support andencouragement of my colleagues, Shion Chen, Maya Okawa, Miki Nishimura, and so on. I
would like to thank Kyoko Tanaka, Kuniko Kono, Tomomi Yoshimoto and ICEPP secretaries
for supporting me as secretaries.
Last of all, I am deeply grateful to my family support.

71

Appendix A
NIEL
Displacement energy is represented as below with scattering angle θ.
( )
( )
θ
2m0 1
θ
2
2
Ep = Ep(max) sin=(Ei + 2m0 c )Ee sin22
M m0 e2(A.1)

Here, Ei is energy of the incident particle, c is light speed.
In the case of small Z matter, diﬀerential displacement cross section is represented as
below using McKinley-Feshbach’s equation approximating Mott’s solution.
[
{(
}]
)1/2
Ep(max)4πa0 Z 2 ER2 1 − β 2
E
E
E
p
p
p
dσp =
1 − β2+ παβZ
−
dEp
2 4
4
m0 c
β
Ep(max)Ep(max)Ep(max)
Ep2(A.2)
Here, a0 is Bohr radius, ER is Rydberg energy, β = v/c, and α is fine structure constant.
The displacement cross section can be calculated from integrating (A.2) .
The Lindhard partition factor L is

L = (1 + kg)−1( )1/2Z
1/6
k = 0.1337 · Z
A3/4
g = 3.4008ϵ1/6
p + 0.40244ϵp + ϵpEpϵp =86931 · Z 7/3

(A.3)
(A.4)
(A.5)
(A.6)

for high energy incident particle.
The NIEL can also be calculated by Monte Carlo method with SRIM (The Stopping andRange of Ions in Matter) code.

73

Appendix B
The Keithley2410 high-voltage source
meter specification
The Keithley2410 high-voltage source meter specification is summarized in Tables B.1, B.2.
Table B.1: Keithley2410 high-voltage source meter source specification. [7]Voltage programming accuracy
Programme Accuracy (1 year)
Noise
◦
◦
Range
resolution
23 C ± 5 C (peak-peak)
200.00 mV
5µV
0.02% + 600µV
5µV
2.00000 V
50µV
0.02% + 600µV
50µV
20.0000 V
500µV
0.02% + 2.4 mV
5 mV
1000.00 mV
50mV 0.02% + 100 mV
20 mV
Current programming accuracy
Programme Accuracy (1 year)
Noise
◦
◦
Range
resolution
23 C ± 5 C (peak-peak)
1.00000 µA
50 pA 0.035% + 600 pA
5 pA
10.0000 µA
500 pA
0.033% + 2 nA
50 pA
100.000 µA
5 nA
0.031% + 20 nA
500 pA
1.00000 mA
50 nA 0.034% + 200 nA
5 nA
20.0000 mA
500 nA
0.045% + 4 µA
200 nA
100.000 mA
5 µA
0.066% + 20 µA
1 µA
1.00000 A
50 µA
0.27% + 900 µA
100 µA

75

76APPENDIX B. THE KEITHLEY2410 HIGH-VOLTAGE SOURCE METER SPECIFICATION
Table B.2: Keithley2410 high-voltage source meter measure specification. [7]Voltage measurement accuracy
Default
Input Accuracy (1 year)
Range resolution
resistance23◦ C ± 5◦ C
200.00 mV
1µV 0.012% + 300µV>10 GΩ
2.00000 V
10µV 0.012% + 300µV>10 GΩ
20.0000 V
100µV 0.015% + 1 mV
>10 GΩ
1000.00 mV
10 mV 0.015% + 50 mV>10 GΩ
Current measurement accuracy
Default
Voltage Accuracy (1 year)
Range resolution
burden23◦ C ± 5◦ C
1.00000 µA
10 pA<1 mV 0.029% + 300 pA
10.0000 µA
100 pA<1 mV 0.027% + 700 pA
100.000 µA
1 nA
<1 mV
0.025% + 6 nA
1.00000 mA
10 nA
<1 mV
0.027% + 60 nA
20.0000 mA
100 nA<1 mV 0.035% + 1.2 µA
100.000 mA
1 µA
<1 mV
0.055% + 6 µA
1.00000 A
10 µA
<1 mV
0.22% + 570 µA

Appendix C
The Agilent LCR meter specification
The Agilent LCR meter specification is summarized in Table C.1.

77

78

APPENDIX C. THE AGILENT LCR METER SPECIFICATION

Table C.1: The Agilent LCR meter specification. [10]Trigger delay time
Range 0 s to 999 s
Resolution 100 µs (0 s to 100 s)
1 ms (100 s to 999 s)
Step deley time
Range 0 s - 999 s
Resolution 100 µs (0 s to 100 s)
1 ms (100 s to 999 s)
Measurement terminal four-terminal pair
Test cable length 2 m
Measurement time mode 89 s (medium mode)
Averaging
Range 1 to 256 measurements
Resolution 1
Test frequency 100 kHz
Resolution 100 Hz
Measurement accuracy ±0.01%
The signal mode Normal (Program selects voltage or current at the measurement
terminals when they are opened or short-circuited, respectively.)
Test signal voltage 20 mVrms
Resolution 100 µVrms
Accuracy ± (10% + 1 mVrms)
The test signal current
Range 0 Arms to 20 mArms
Resolution 1 µArms (0 mArms to 2 mArms)
2 µArms (2 mArms to 5 mArms)
5 µArms (5 mArms to 10 mArms)
10 µArms (10 mArms to 20 mArms)
Test signal current
Accuracy ±(10% + 10µArms)
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