1 | P a g e

Fabrication and Characterization of Bulk Diamond

Radiation Detectors

Park Sun Myung (A0110404E)

April 3, 2017

Supervised by: Assoc Professor Andrew A. Bettiol

2 | P a g e

Abstract

Single-crystal electronic grade CVD diamonds possess outstanding electrical properties that

makes them suitable for radiation detector use. A diamond radiation detector was fabricated

using a coplanar interdigitated electrode structure optimised through computer simulations.

The detector was tested using a Pu-239, Am-241, Cm-244 triple alpha source. The charge

collection efficiency values measured exceeded the performance of a commercial silicon

surface barrier detector that was used as a reference by 7%. The leakage current measured was

low and is in good agreement with reported values. While the energy resolution for the diamond

detector was relatively worse than the energy resolution for the reference silicon detector, the

three alpha peaks were well-defined and can be improved by optimising the fabrication process.

CONTENTS

3 | P a g e

Table of Contents 1 Acknowledgements ............................................................................................................................ 4

2 Introduction ........................................................................................................................................ 5

3 Review of Diamond Detectors ........................................................................................................... 8

3.1 Diamond Synthesis ....................................................................................................................... 8

3.2 Properties of Diamond .................................................................................................................. 9

3.3 Current Research ......................................................................................................................... 11

4 Theory ............................................................................................................................................... 13

4.1 Introduction ................................................................................................................................. 13

4.2 Charge Transport......................................................................................................................... 15

4.3 The Shockley-Ramo Theorem .................................................................................................... 18

4.4 Calculation of Charge Collection Efficiency .............................................................................. 22

5 Detector Simulations ........................................................................................................................ 23

5.1 Introduction ................................................................................................................................. 23

5.2 Methodology ............................................................................................................................... 23

5.3 Simulation Results ...................................................................................................................... 26

6 Fabrication and Testing .................................................................................................................. 30

6.1 Detector Fabrication Procedure................................................................................................... 30

6.2 Fabrication Issues ........................................................................................................................ 33

6.3 Testing and Results ..................................................................................................................... 35

7 Conclusion ........................................................................................................................................ 41

7.1 Summary ..................................................................................................................................... 41

7.2 Future Research........................................................................................................................... 41

References ............................................................................................................................................ 43

Appendix .............................................................................................................................................. 45

ACKNOWLEDGEMENTS

4 | P a g e

1 Acknowledgements

I would like to express my deep gratitude to my supervisor, Assoc Prof. Andrew Bettiol

and co-supervisors Mi Zhao Hong and Tan Hong Qi for all of the advice and help they have

given over the past year. I have learned a lot from them in the past year, not just academically

but in other aspects of life as well. Without their guidance, I would not have the many

opportunities that await me after my graduation.

I also wish to thank my parents for the unwavering support throughout my life and

especially through university. I am truly grateful for the sacrifices they have made for me and

my brother. They are my sources of inspiration when the going gets tough. I would also like

to thank my brother for putting up with all my late nights doing work or otherwise.

Park Sun Myung

INTRODUCTION

5 | P a g e

2 Introduction

Radiation detectors are instruments that detect, track and measure ionising radiation.

Ionising radiation refers to all forms of radiation that are energetic enough to eject electrons

from atoms or molecules. Some examples include gamma rays, X-rays and extreme

ultraviolet of the electromagnetic spectrum, and alpha and beta particles emitted via

radioactivity. Radiation detectors have been playing important roles in science for more than

a century, having facilitated numerous scientific breakthroughs such as the discovery of

exotic particles. Detectors can be generally classified into 2 main types, gaseous ionisation

chambers and solid state detectors. Perhaps one of the most notable examples among the

former is the Geiger counter [1]: incident ionising radiation cause a series of electron

avalanche ionisation effects that produce an amplified, measurable electrical signal. While

Geiger counters are relatively cheap and reliable for general use, they can only detect the

presence of ionising radiation; they cannot resolve the energies of ionising radiation.

Solid state semiconductor detectors, on the other hand, can measure the particle's energy

in addition to its detection and are widely used in medical applications, spectroscopy and as

particle detectors. Most semiconductor detectors used today are made of silicon. Owing to

extensive research over the past few decades, silicon detectors are highly efficient and

consistent in particle detection [2]. However, there are some drawbacks. Silicon detectors

may require cooling systems to reduce electrical noise due to leakage currents, and they are

susceptible to radiation damage. Radiation damage degrades the performance of the detector

over time and shortens the detector’s effective lifespan.

In situations where such issues are rampant, diamond presents itself as a very promising

alternative [2]. Among its many outstanding properties, diamond has a large energy bandgap,

which results in less electrical noise and a higher signal-to-noise ratio. The relatively stronger

interatomic covalent bonding make diamond more resistant to radiation damage.

Furthermore, there has been great advancements in chemical vapour deposition (CVD)

growth processes for single-crystal diamonds. Thus, it is hardly surprising that there is

significant interest in the use of diamond as radiation detectors.

INTRODUCTION

6 | P a g e

Some select applications where diamond detectors display superior performance over

silicon detectors are in detectors for excimer lasers [3] and particle accelerators. Excimer

lasers are a type of ultraviolet laser. The relatively large bandgap of diamond renders it blind

to visible light, thus improving discrimination between deep UV light and visible light.

Diamond’s superior radiation hardness and operational lifetime over silicon makes it a good

alternative for both of applications. For case of particle accelerators, significant research is

being conducted to bring the performance of diamond detectors up to par or even outperform

current silicon detectors [2].

Now I will give a brief introduction of my project, leaving further details to the rest of

this report.

The aim of my project is the optimisation, fabrication and characterisation of coplanar

interdigitated electrode designs on bulk diamond detectors for the detection of alpha particles.

The optimisation of detector performance is performed using COMSOL and MATLAB

simulations of diamond detectors with various electrode configurations. The simulations are

based on a scanning microscopy technique known as ion beam induced charge (IBIC)

microscopy. The metric used for performance comparison is the charge collection efficiency

(CCE). Based on the simulation results and fabrication limitations, an optimal electrode

configuration is chosen for fabrication. Electrodes comprised of Cr/Au bimetal layer are

deposited onto a 4 × 4 × 0.5 mm CVD single-crystal electronic grade diamond sample

provided by IIa Technologies Pte Ltd. The diamond detector is then characterised using a

radioactive alpha particle source and compared with the performance of a commercially

available silicon detector (ORTEC surface barrier Si detector). Characterisation involves the

measurement of the charge collection efficiency (CCE) of the diamond detector versus

applied bias, leakage current, energy resolution and the signal-to-noise ratio (SNR).

To summarise, my project comprises of the following:

Optimisation of coplanar interdigitated electrode configurations on bulk single-crystal

diamond detectors through simulations

Fabrication of Cr/Au interdigitated electrodes on 4 × 4 × 0.5 mm single-crystal

diamond based on the optimal electrode configuration

Characterisation of the diamond detector with a radioactive alpha particle source

INTRODUCTION

7 | P a g e

Lastly, I will give an outline of this report. In section 3, I will give a comprehensive

review of diamond detectors and their properties, with some emphasis on the advantages they

hold over silicon detectors. Section 4 will cover the physics of particle detection in intrinsic

diamond detectors. Sections 5 and 6 form the main body of my thesis. Section 5 is dedicated

to the details of the simulations used in the optimisation of interdigitated electrode geometry

and the simulation results. Section 6 illustrates the fabrication process and the problems

encountered during the process and provides the characterisation results of the fabricated

diamond detector. Section 7 summarizes the findings, concludes the report, and considers

some possible future directions for subsequent research on diamond detectors.

REVIEW OF DIAMOND

8 | P a g e

3 Review of Diamond Detectors

3.1 Diamond Synthesis

Diamond is a remarkable material that has outstanding physical, optical, electrical and

chemical properties [2]. Being the hardest naturally occurring material, diamond is already

heavily relied upon for industrial purposes such as cutting or grinding. Diamond has the

highest thermal conductivity, about 5 times that of copper. Diamond also possesses a host of

other outstanding properties such as having a large band gap, high charge carrier mobility and

high resistivity that makes it an excellent candidate for detector use. However, progress in

this area had been hampered for several decades due to the following factors:

Expensive; single-crystal diamonds could only be sourced from natural diamonds,

limited by their size and quality

Difficult to produce high quality single-crystal diamonds with low impurities via

CVD growth processes

Difficult to pattern using conventional lithography techniques due to hardness and

chemical inertness

Advancements in chemical vapour deposition diamond growth processes in recent years

have made high quality single-crystal diamonds readily available [4]. Chemical vapour

deposition is a chemical process that involves the homoepitaxial growth of diamond on a

substrate under highly controlled conditions [5]. The source of carbon is a carefully

controlled gaseous mixture containing hydrocarbons such as methane. To grow single-crystal

diamonds, the substrate must be a single-crystal diamond as well. The gaseous mixture is

heated by microwaves, direct current, hot filament, lasers or other energizing sources to form

a plasma of temperatures above 2000 °C. This causes the thermal disassociation of hydrogen,

thereby producing carbon radicals that form single bonds with the carbon atoms on the top

layer of the substrate, which is kept at a much lower temperature. Although diamond is a

metastable state of carbon in the conditions above, CVD takes advantage of the fact that

diamond has a faster nucleation and growth rate than graphite. This enables the growth of

CVD diamonds under less extreme conditions than the high pressure high temperature

REVIEW OF DIAMOND

9 | P a g e

method. Dopants may be introduced in the growth process but there are no shallow dopants

available. The closest is boron with an acceptor level of 0.37 eV.

Single-crystal CVD diamonds are available in sizes of up to 8 × 8 × 2 mm, with a high

degree of control over the impurity levels. CVD diamonds can be classified into the

following categories:

Single-crystal CVD diamond

o Optical grade: Low absorption and birefringence diamond

o Detector grade: Ultrahigh purity for electronic and quantum states

Polycrystalline CVD diamond

o Optical grade: Engineered for far infrared laser optical applications

o Electronic grade: Ultrahigh purity material for large area passive electronics

o Thermal grade: High thermal conductivity diamond for heat spreading

o Mechanical grade: High strength diamond for precision machining

o Electrochemistry grade: Boron doped diamond for electrochemical

applications

The classification of diamonds above is obtained from The Element Six CVD Diamond

Handbook [5]. The diamond used for this project is detector grade single-crystal CVD

diamond supplied by IIa Technologies Pte Ltd.

3.2 Properties of Diamond

The electronic properties of diamond pertaining to radiation detection are listed in Table

1, in contrast to the electronic properties of silicon. As some of these properties are subject to

variability from diamond to diamond, they were obtained directly from IIa Technologies Pte

Ltd, the supplier for the diamond sample used in this project.

REVIEW OF DIAMOND

10 | P a g e

Table 1 Properties of diamond and silicon relevant to radiation detection

Property Diamond Silicon Reference

Band gap (eV) 5.47 1.12 [2]

Energy to form e-h pair (eV) 13.2 3.6 [6, 7]

Electron mobility at 300 K (cm2 V-1 s-1) 2200 1500 [8]

Hole mobility at 300 K (cm2 V-1 s-1) 1600 450 [8]

Saturation carrier velocity (× 107 cm s-1) 2.7 1 [8]

Breakdown field (V cm-1) 107 3 x 105 [8]

Resistivity (Ω cm) > 1012 2.3 x 105 [2]

Dielectric constant 5.7 11.9 [8]

Thermal conductivity (W m-1 K-1) 2200 148 [8]

Atomic displacement energy (eV) 43 13-20 [9]

Density (g cm-3) 3.5 2.33 [2]

Atom density (cm-3) 1.75 x 1023 4.83 x 1022 [2]

Due to the large band gap, diamond has higher resistivity and a higher breakdown electric

field. Therefore, diamond does not require a p-n junction under reverse bias to reduce dark

current under strong electric fields. Dark current refers to leakage current in the absence of

ionising radiation. It is caused by the random thermal generation of electrons and holes. This

makes diamond suitable for use at room temperature while many types of silicon detectors

require cooling as dark currents are a source of detector noise. The high thermal conductivity

of diamond also helps in dissipating heat away during operation. A consequence of the large

band gap however, is the higher minimum energy required to produce an electron-hole pair.

Radiation detection is dependent on the movement of electron and hole pairs produced by the

ionising radiation. They are separated under the influence of the electric field between the

electrodes. The Shockley-Ramo theorem shows that the movement of the charge carriers

induces an instantaneous current in the electrodes. This current is directly proportional to the

number of electron-holes pairs and their velocities. While the measured signal is smaller in

magnitude, it is more than compensated for by the relatively lower dark current in diamond

detectors compared to silicon detectors.

Diamond has high electron and hole mobility and high saturation velocity, resulting in

faster charge collection under a given electric field and thus faster detector response time.

Diamond also has a smaller dielectric constant than silicon, yielding a smaller capacitance as

an electronic device and therefore, better noise performance of the associated front-end

electronics.

The most notable quality of diamond is its radiation hardness. It arises from the high

atomic displacement energy, energy required to displace a carbon atom from its lattice site.

REVIEW OF DIAMOND

11 | P a g e

Significant research into radiation hardness was conducted by the RD42 collaboration at

CERN. Meier et al. [10] showed that CVD diamond detector performance is unaffected even

after exposure to 24 GeV/c and 500 MeV protons for fluences of up to 1×1015 particles/cm2

while the silicon diode showed signs of radiation damage above a fluence of 1.5×1014

particles/cm2. However, recent research by Zamboni et al. [11] and Grilj et al. [12] have

shown that the opposite outcome occurs for ionising particles in the low MeV range. In these

papers, it is said that diamond detectors had greater charge collection efficiency (CCE)

degradation than silicon detectors. CCE is an important measure of performance of a

semiconductor radiation detector. The above behaviour may be attributed to the smaller

inelastic particle-carbon cross section and the lighter nuclear fragments involved in secondary

collisions. Energy loss through inelastic collisions dominate in the high MeV/GeV range.

Nevertheless, much of the motivation for radiation hard diamond detectors originates from

high-energy physics research which often involves ionising particles of at least 100 MeV, a

region where diamond holds a clear advantage.

Figure 1 Simple diagram of a sandwich semiconductor detector. Blue region represents the

semiconductor detection region. Yellow regions represent the electrodes.

3.3 Current Research

Much research has been conducted for the use of diamond detectors for alpha detection.

Various diamond dimensions and electrode structures have been studied thus far. Galbiati et

al. [13] tested a 4.7 × 4.7 × 0.5 mm single-crystal high purity CVD diamond with

239Pu/241Am/244Cm triple α source. The electrodes were of the sandwich structure as shown in

Figure 1, with DLC/Pt/Au trilayer; DLC is diamond-like carbon, obtained via energetic

bombardment of carbon atoms on the diamond substrate. Calibration was done by assigning

REVIEW OF DIAMOND

12 | P a g e

5.15 MeV, 5.48 MeV and 5.80 MeV for the 3 respective alpha sources. The energy resolution

was found to be 64 keV, approximately 1.1% of the alpha energies. This proves that diamond

detectors have excellent energy resolution. 5 MeV alpha particles have a penetration depth of

about 10 μm in diamond. Tests by Galbiati et al. using the same diamond sample with TiW

electrodes and 90Sr beta rays have shown 100% charge collection efficiency above a certain

threshold bias voltage.

Dueñas et al. [14] performed similar characterisation tests with the triple alpha source.

The diamond sample used here is also a single-crystal high purity CVD diamond but of

smaller dimensions at 4 × 4 × 0.05 mm. The thinner configuration is expected to show better

performance as the charge carriers traverse a shorter distance towards the electrodes. This

reduces signal losses due to diffusion, charge trapping and recombination of the charge

carriers. Duenas et al. reported energy resolutions of 19 and 21 keV under negative and

positive biases respectively. This is about one-third of the energy resolution reported by

Galbiati. The lower energy secondary peaks corresponding to each of the 3 alpha sources

could be resolved clearly in the result by Dueñas.

The 2 papers above show that for bulk diamond detectors (thickness > 500 μm), the

performance of the sandwich structure is not optimal. As mentioned before, the penetration

depth of 5 MeV alpha particles is only about 10 μm. It naturally follows that we can consider

a coplanar electrode design for bulk diamond detectors. One common structure is the

interdigitated design which consists of alternating strips of positive and negative electrodes.

As both electrodes are on the top surface, they should be able to collect most of the charge

carriers produced near the surface. The small electrode gap also allows for fast charge

collection, improving the time response of the detector under high particle fluences. The

interdigitated structure is commonly used for UV and γ-ray detection as the photons generally

exhibit poor penetration through the metal electrodes [3].

There has not been significant research into the optimisation of the interdigitated design.

Values for electrode width and gap used by other researchers range from 20 to 200 μm with

little justification for the choice of their values. Thus, the aim of my project is the

optimisation of the interdigitated structure with respect to those 2 parameters. For the case of

alpha detection, there is no need to consider how much exposed diamond area is required

because alpha particles lose little energy when passing through the metal electrodes.

THEORY

13 | P a g e

4 Theory

4.1 Introduction

While certain minor details may differ for different types of detectors, the general

processes involved in radiation detection are the same. The following is the chronology of

radiation detection:

1) Ionising radiation impinges on the active region of the detector, releasing electron-

hole pairs along its path trajectory as it ionises the carbon atoms.

2) The electrons and holes are separated in the electric field produced by the

electrode. Holes migrate towards the anode while electrons migrate towards the

cathode.

3) During the charge carrier drift, some charge carriers may be trapped due to point

defects such as lattice vacancies and may contribute to a build-up of space charge.

This causes polarisation in the diamond. Some charge carriers may recombine

before reaching the electrodes.

4) The movement of these charge carriers along the electric field lines induce

instantaneous currents in the electrode, described by the Shockley-Ramo theorem.

The pulse is converted into a voltage pulse using an amplifier which in ideal

situations is proportional to the energy deposited by the ionising radiation.

Simulations on Stopping and Range of Ions in Matter (SRIM) show that the average

penetration depth of 5 MeV alpha particles is approximately 11.9 μm as shown in Figure 2.

The average straggle in the lateral directions is approximately 0.2 μm, a small number

relative to the penetration depth. Most of the energy (99.76%) is lost via ionisation while the

remainder is lost through secondary recoils and phonons.

THEORY

14 | P a g e

Figure 2 SRIM data for the penetration depth of 5 MeV alpha particles in diamond

A widely-used metric for comparing the performance of semiconductor radiation

detectors is the charge collection efficiency (CCE), which is defined as the ratio of the

amount of charge collected at the electrodes to the amount of charge created inside the

detector. It is related to the charge collection distance (CCD) which is the mean distance

travelled by the electrons and holes before recombination or trapping occurs.

𝐶𝐶𝐸 =𝐶𝐶𝐷

𝑑(4.1)

where 𝑑 is the distance between the electrodes in a sandwich structure. The above equation

would not hold for arbitrary designs as 𝑑 may vary. The 𝐶𝐶𝐷 is given by the following:

𝐶𝐶𝐷 = (𝜇𝑒𝜏𝑒 + 𝜇ℎ𝜏ℎ)𝐸 (4.2)

This equation is valid only if 𝐸 is uniform throughout the detector and both 𝜇 are constant.

For all cases where the CCD is greater than 𝑑, the CCE is taken to be 100% as all of the

charges would be collected at the electrodes.

The theoretical calculation of CCE requires knowledge on both the charge transport

mechanisms and the Shockley-Ramo theorem [15] that relates the charge of the electron-hole

pairs generated to the charge induced in the electrodes.

In the subsequent subsections, the theoretical backgrounds for charge transport, the

Shockley-Ramo theorem and the calculation of charge collection efficiency (CCE) are

discussed.

THEORY

15 | P a g e

4.2 Charge Transport

Charge transport in semiconductors [16] is governed by numerous factors. For simplicity,

this subsection covers the treatment of drift motion of charge carriers relevant to intrinsic

diamond semiconductors. Without loss of generality, the derivations are performed in one

dimension 𝑥.

At all temperatures above absolute zero, all charge carriers possess thermal kinetic energy

averaging at 𝑘𝐵𝑇/2 per degree of freedom. Due to interactions with the lattice atoms, charge

carriers have an effective mass 𝑚∗ that differs from their usual mass. In general, the effective

masses of electrons and holes are not equal. The average thermal velocity 𝑣𝑡ℎ can be obtained

from the following equation:

1

2𝑚∗𝑣𝑡ℎ

2 =3

2𝑘𝐵𝑇 (4.3)

where 𝑘𝐵 is the Boltzmann constant and T is the temperature.

At thermal equilibrium without any external electric field, there is no net current from the

thermal motion of charge carriers in any direction. The charge carriers undergo frequent

collisions with the lattice. An applied electric field introduces an additional drift velocity

component parallel or antiparallel to the electric field, depending on the charge carrier. The

electron/hole mobility 𝜇 is defined as the ratio of the average drift velocity to the electric

field strength 𝐸.

𝜇 =𝑣𝑑

𝐸(4.4)

The above equation assumes that the semiconductor is in a steady state, where some

momentum gained by the charge carriers due to the electric field is lost through collisions.

Consider the electron which has a charge of −𝑒. The average increase in momentum due to

the electric field between collisions is related to the average peak drift velocity of the electron

𝑣𝑝 just before collision by the following equation:

−𝑒𝐸𝜏𝑐𝑜𝑙 = 𝑚𝑒∗𝑣𝑝 (4.5)

where 𝜏𝑐𝑜𝑙 is the average time interval between collisions. However, initial drift velocity is

not necessarily zero. An accurate statistical treatment of the collision process yields that the

THEORY

16 | P a g e

equation for the average drift velocity 𝑣𝑑 is simply the same equation, with a simple but non-

trivial replacement of 𝑣𝑝 with 𝑣𝑑.

𝑣𝑑 = − (𝑒𝜏𝑐𝑜𝑙

𝑚𝑒∗

) 𝐸 = −𝜇𝑒𝐸 (4.6)

where 𝜇𝑒 is the electron mobility. The equivalent equation for holes with charge 𝑒 is

𝑣𝑑 = (𝑒𝜏𝑐𝑜𝑙

𝑚ℎ∗ ) 𝐸 = 𝜇ℎ𝐸 (4.7)

where 𝜇ℎ is the hole mobility. The average time interval between collisions 𝜏𝑐𝑜𝑙 are not

necessarily the same for electrons and holes, as was the case for their effective masses, due to

different collision cross sections and other factors. Therefore, electron and hole mobility are

in general not equal for a given semiconductor.

Another important process for charge transport is diffusion. Diffusion is a process where

particles move from a region of high concentration to a region of low concentration. Ionising

radiation create electron-hole pairs locally along their trajectories. Diffusion affects the

charge transport because the concentration of electrons and holes in those regions are higher

than that of the surrounding regions.

The current density associated with diffusion is called the diffusion current density 𝐽𝑑𝑖𝑓

and it is related to the electron and hole density gradients as follows:

𝐽𝑑𝑖𝑓,𝑒 = 𝑒𝐷𝑒

𝑑𝑛

𝑑𝑥(4.8)

𝐽𝑑𝑖𝑓,ℎ = 𝑒𝐷ℎ

𝑑𝑝

𝑑𝑥(4.9)

𝐽𝑑𝑖𝑓 = 𝐽𝑑𝑖𝑓,𝑒 + 𝐽𝑑𝑖𝑓,ℎ (4.10)

where 𝐷𝑒 and 𝐷ℎ are the diffusion coefficients for electrons and holes respectively, and 𝑛 and

p are the electron and hole concentrations respectively at a particular point in space.

THEORY

17 | P a g e

For a non-degenerate semiconductor (i.e. a semiconductor that is not heavily doped), the

equation known as Einstein’s relationship for electrons express the relationship between

diffusion coefficient for electrons and the electron mobility as follows:

𝐷𝑒 =𝑘𝐵𝑇

𝑒𝜇𝑒 (4.11)

and likewise, for Einstein’s relationship for holes,

𝐷ℎ =𝑘𝐵𝑇

𝑒𝜇ℎ (4.12)

The overall current densities for electrons and holes due to drift and diffusion in three

dimensions are given by

𝑱𝑒 = 𝑛𝑒𝜇𝑒𝑬 + 𝑒𝐷𝑒∇𝑛 (4.13)

𝑱ℎ = 𝑝𝑒𝜇ℎ𝑬 − 𝑒𝐷ℎ∇𝑝 (4.14)

where the first term is the contribution from drift and the second term is the contribution from

diffusion. The contribution from drift is derived from the simple relation that equates current

density to the product of the individual charge, velocity and density of the charge carrier.

The last two significant factors are charge carrier generation and recombination. For the

case of undoped diamond detectors, due to the large band gap, thermal generation of charge

carriers is negligible compared to the charge carrier generation arising from ionising

particles. Thus, generation can be expressed using a Dirac delta function. Recombination rate,

𝑈, is expressed as

𝑈𝑒 =𝑛

𝜏𝑒

(4.15)

𝑈ℎ =𝑝

𝜏ℎ

(4.16)

for electrons and holes respectively, where 𝜏 is the respective average lifetime before

recombination.

THEORY

18 | P a g e

The four factors discussed above are combined to form two continuity equations for

charge transport as shown below:

𝜕𝑛

𝜕𝑡=

1

𝑒∇ ∙ 𝑱𝑒 + 𝐺 − 𝑈𝑒

= ∇ ∙ (𝑛𝜇𝑒𝑬) + 𝐷𝑒∇2𝑛 + 𝐺 −𝑛

𝜏𝑒

(4.17)

𝜕𝑝

𝜕𝑡= −

1

𝑒∇ ∙ 𝑱ℎ + 𝐺 − 𝑈ℎ

= −∇ ∙ (𝑝𝜇ℎ𝑬) + 𝐷ℎ∇2𝑝 + 𝐺 −𝑝

𝜏ℎ

(4.18)

where 𝐺 is the generation rate of electron-hole pairs due to ionisation by ionising radiation. A

more advanced treatment of charge transport is possible, with additional factors such as

temperature and bias voltage dependence of the charge carrier mobility and trapping effects

due to defects. Further discussions will be made in the later sections.

4.3 The Shockley-Ramo Theorem

When ionising radiation is incident on the active region of the detector, the number of

electron-hole pairs generated is proportional to the energy deposited by the ionising radiation.

The movement of these charge carriers induce an instantaneous charge in the electrodes that

can be shaped and amplified into an output electrical signal. The tedious calculation of the

induced charge 𝑄 due to the moving charge 𝑞 was made simple by the Shockley-Ramo

theorem. The Shockley-Ramo theorem [15] allows us to predict the CCE with relative ease if

we know the initial and final positions of the moving charge.

The Shockley-Ramo theorem states that the charge 𝑄 induced in an electrode by the

moving charge 𝑞 moving from 𝒙𝑖 to 𝒙𝑓 is given by

𝑄 = −𝑞[𝜑0(𝒙𝑓) − 𝜑0(𝒙𝑖)] (4.19)

where 𝜑0(𝒙) is the electric potential present in the detector when the particular electrode has

unit potential while the other electrodes are grounded (i.e. zero potential).

THEORY

19 | P a g e

The review of the Shockley-Ramo theorem below is based on the conservation of energy.

Consider the detector illustrated in Figure 3a. It consists of several electrodes kept at constant

voltages 𝑉𝑗 (for 𝑗 = 1, 2, … , 𝑘). The electrodes enclose surfaces 𝑆𝑗 around the entire surface 𝑆

of volume 𝜏. The outermost boundary is surrounded by the electrode of voltage 𝑉𝑘. The

electric potential 𝜑(𝒙) in the detector satisfies Poisson’s equation with the given Dirichlet

boundary conditions. Thus, by the uniqueness theorem for Poisson’s equation, the electric

field 𝑬(𝒙) = −∇𝜑(𝒙) is uniquely determined.

Figure 3 The principle of linear superposition for electric potentials

By the principle of linear superposition, the electric potential for the case in Figure 3a is

the sum of the electric potentials for the cases in Figure 3b and 3c. For Case b, the electrode

potentials are kept while the space charges 𝜌(𝒙) and the moving charge 𝑞 are removed. For

Case c, both charges are kept while the electrodes are all grounded. Assuming that the

detector is a linear and isotropic medium, the electric displacement is given by

𝑫 = 𝜀𝑬 (4.20)

where 𝜀 is the dielectric constant. The energy density 𝑢 of the electric field is given by

𝑢 =1

2𝑬 ∙ 𝑫 =

1

2𝜀𝐸2 (4.21)

The total energy of the system can be obtained by integrating the energy density over the

entire volume 𝜏. By the conservation of energy, the total energy of the field can only be

changed by energy transfers between the field and the moving charge 𝑞, and between the

field and the power supply connected to the electrodes.

THEORY

20 | P a g e

We first consider the case in Figure 3c. The work done by the electric field on a moving

charge 𝑞 is

∫ 𝑞𝑬1′ ∙ 𝑑𝒙

𝒙𝒇

𝒙𝒊

(4.22)

where 𝑬𝟏′ is equal to 𝑬𝟏, excluding the electric field due to 𝑞. As the charge 𝑞 moves from 𝒙𝒊

to 𝒙𝒇, the amount of induced charges on the electrodes change. However, as all electrodes are

grounded, no work is done arising from the change in induced charges on the electrodes. This

means that only the electric field 𝑬𝟏′ does work on charge 𝑞. Any change in the energy of

charge 𝑞 comes from the change in the energy stored in the electric field

∫ 𝑞𝑬𝟏′ ∙ 𝑑𝒙

𝒙𝒇

𝒙𝒊

=1

2∫𝜀(𝐸1,𝑖

2 − 𝐸1,𝑓2 )𝑑𝜏

𝜏

(4.23)

where 𝑬1,𝑖 and 𝑬1,𝑓 are the electric fields of the case in Figure 3c at the initial and final

positions of charge 𝑞 respectively.

For the case in Figure 3a, since the electric field excluding the charge 𝑞’s own field is

𝑬 = 𝑬0 + 𝑬1′ , the work done on charge 𝑞 by the electric field is

∫ 𝑞(𝑬0 + 𝑬1′ )𝑑𝒙

𝒙𝒇

𝒙𝒊

(4.24)

and the work done on the induced charges ∆𝑄𝑗 on each electrode by the power supply is

∑ 𝑉𝑗∆𝑄𝑗

𝑘

𝑗=1

(4.25)

The expression for the conservation of energy in this case is

∑ 𝑉𝑗∆𝑄𝑗

𝑘

𝑗=1

− ∫ 𝑞(𝑬0 + 𝑬1′ )𝑑𝒙

𝒙𝒇

𝒙𝒊

=1

2∫𝜀(𝑬0 + 𝑬1,𝑓)

2− (𝑬0 + 𝑬1,𝑖)

2𝑑𝜏

𝜏

(4.26)

Here, consider Green’s first identity, a result derived from the divergence theorem,

∫(𝜑1∇2𝜑0 + ∇𝜑0 ∙ ∇𝜑1)𝑑𝜏𝜏

= ∮𝜑1∇𝜑0 ∙ 𝑑𝑺𝑆

(4.27)

THEORY

21 | P a g e

that applies to any arbitrary function 𝜑0 and 𝜑1. Note that ∇2𝜑0 = 0 as 𝜑0 is produced solely

by the electrode potentials, i.e. the space charges and charge 𝑞 do not contribute to 𝜑0.

Furthermore, 𝜑1 = 0 on the surface 𝑺 since all electrodes are grounded. Hence, for the cross

terms on the RHS of Equation (4.25),

∫𝑬0 ∙ 𝑬1 𝑑𝜏𝜏

= ∫∇𝜑0 ∙ ∇𝜑1 𝑑𝜏𝜏

= ∮𝜑1∇𝜑0 ∙ 𝑑𝑺𝑆

− ∫𝜑1 ∙ ∇2𝜑0 𝑑𝜏𝜏

= 0 (4.28)

⇒ ∫𝜀(𝑬0 + 𝑬1,𝑓)2

− (𝑬0 + 𝑬1,𝑖)2

𝑑𝜏𝜏

= ∫𝜀(𝐸1,𝑓2 − 𝐸1,𝑖

2 )𝑑𝜏𝜏

(4.29)

Combining Equations (4.28) and (4.22) with Equation (4.25), we have

∑ 𝑉𝑗∆𝑄𝑗

𝑘

𝑗=1

= ∫ 𝑞𝑬0 ∙ 𝑑𝒙𝒙𝑓

𝒙𝑖

= −𝑞[𝜑0(𝒙𝑓) − 𝜑0(𝒙𝑖)] (4.30)

This shows that the work done by the power supply is equal to the change in kinetic energy of

the moving charge 𝑞 due to the electric field produced by the electrodes 𝑬0 alone, with no

contribution from the space charges.

For the next step, we use an important result, which is that the induced charge ∆𝑄𝑗 is

independent of the potentials 𝑉𝑗 of each electrode [15]. Thus, in setting a unit potential for 𝑉𝑗

and zero potential for the other electrodes, we can easily obtain ∆𝑄𝑗 as a fraction of charge 𝑞.

Then by Equation (4.29),

∆𝑄𝑗 = −𝑞[𝜑0(𝒙𝑓) − 𝜑0(𝒙𝑖)] (4.31)

The value of 𝜑0 ranges from 0 to 1 inclusive. Therefore, ∆𝑄𝑗 ranges from 0 to −𝑞, and is

only dependent on the initial and final positions of charge 𝑞, in the absence of energy loss

through collisions within the detector. The 𝜑0 here is called the weighting potential and it is

unitless as it is a normalised quantity. Thus, the Shockley-Ramo theorem is proven.

THEORY

22 | P a g e

4.4 Calculation of Charge Collection Efficiency

The moving charges in semiconductor detectors are the electron-hole pairs generated by

the incident ionising radiation. Applying the Shockley-Ramo theorem, we have

∆𝑄 = −𝑁𝑒[𝜑0(𝒓ℎ) − 𝜑0(𝒓0)] + 𝑁𝑒[𝜑0(𝒓𝑒) − 𝜑0(𝒓0)] (4.32)

where 𝑁 is the number of electron-hole pairs generated, 𝒓ℎ and 𝒓𝑒 are the final positions of

the holes and electrons generated, and 𝒓0 is the initial position where the electron-hole pairs

were generated.

The CCE is then given by

𝐶𝐶𝐸 = −[𝜑0(𝒓ℎ) − 𝜑0(𝒓0)] + [𝜑0(𝒓𝑒) − 𝜑0(𝒓0)]

= 𝜑0(𝒓𝑒) − 𝜑0(𝒓ℎ) (4.33)

The CCE represents the fraction of charge collected. Multiple calculations may be

required due to diffusion, resulting in different final positions even if the charge carriers

started from the same initial position. Given that all electrons drift to the positive electrode

while all holes drift to the negative electrode, 𝜑0(𝒓𝑒) = 1 and 𝜑0(𝒓ℎ) = 0. Therefore, the

CCE would be 1. Losses due to recombination and trapping reduce the CCE value as the

weighting potential value at the final position would not be 1 or 0 for electrons and holes

respectively.

DETECTOR SIMULATIONS

23 | P a g e

5 Detector Simulations

5.1 Introduction

Due to the non-uniform nature of electric fields in detectors with coplanar interdigitated

electrodes, it is difficult to calculate the CCE by hand. Through computational methods, we

are able obtain the electric field profile and estimate the performance of a detector. Accurate

modelling results can be used to predict experimental outcomes and complement

experimental results through the precise control of certain variables, even those that may be

uncontrollable in a laboratory setting. The main aim of the detector simulations in my project

is to obtain an optimised interdigitated electrode structure for the diamond detector.

In this section, the methodology for detector simulations is first discussed, followed by

the simulation results and analysis.

5.2 Methodology

The diamond sample and interdigitated electrode structure was first modelled using

SOLIDWORKS, a 3D CAD software, as shown in Figure 4. Various dimensions were

considered for the diamond sample and electrode structure. The CAD file is then imported

into COMSOL Multiphysics software. COMSOL is a general-purpose modelling and

simulation software for physics-based systems. On COMSOL, the appropriate materials and

electric potentials were assigned (i.e. diamond for the cuboid, gold for the electrode surfaces

and electric potentials for each electrode).

Electrostatics module in COMSOL uses the finite element method (FEM) to obtain the

static electric potential profile in the diamond detector by solving the Poisson equation. FEM

is a numerical method for solving partial differential equations (PDE) with various boundary

conditions [17]. The system is first discretized into many small volume elements as shown in

Figure 5. The discretization allows for the approximation of the real solution for the PDE

through the selection of linear basis functions that are non-zero in their own selected elements

and zero elsewhere.

DETECTOR SIMULATIONS

24 | P a g e

Figure 4 3D CAD design of diamond detector modelled on SolidWorks

Figure 5 Discretization of diamond detector model into small volume elements

The electric potential value was obtained at each volume element in a regular grid of

1200 by 1200 by 100 elements. The data file was exported to MATLAB. The MATLAB code

is based the ion beam induced charge (IBIC) microscopy technique [18]. Highly focussed ion

beams are used to probe various samples to determine their characteristics. For radiation

detectors, IBIC is very useful as it is equivalent to being exposed to ionising particles from

DETECTOR SIMULATIONS

25 | P a g e

other sources. IBIC has the added benefit of the high focus of the ion beam, which allows

researchers to probe specific locations of the sample. Through this technique it is possible to

obtain the detector response to ionising particles at different parts of the detector. By

scanning the ion beam across the sample, we can obtain the variation in signals received from

the detector. After energy calibration of the detector signals, the CCE can be calculated at

each point.

The MATLAB code simulates the generation of charge carriers, charge transport and

calculates the CCE using the initial and final positions of the charge carriers as explained in

the Theory section.

For 5 MeV alpha particles, Stopping and Range of Ions in Matter (SRIM) simulation

results show that the penetration depth is approximately 10 μm. The Bragg peak for alpha

particles shows that alpha particles lose most of their energy towards the end of their

trajectory. Therefore, for computational efficiency, it is assumed that all electron-hole pairs

are produced at a depth of 10 μm from the top surface of the detector. SRIM simulation

results have also shown that alpha particles lose an average of less than 1% of their energy

when transmitted through 100 nm of gold. Thus, the energy losses while passing through the

electrodes were neglected.

The 3D electric field profile was obtained by applying the gradient function on the 3D

electric potential matrix, giving the 3D electric field matrix. The charge transport was

simulated by using simple finite difference scheme for electrons and holes separately. Each

time-step has an interval of 1 ps. The distance travelled by the charge carriers at each time-

step was calculated by simply taking the product of the drift velocity and the time interval of

1 ps. The velocity is governed by Equations (4.6) and (4.7), and it varies according to the

electric field strength and direction at each point along the charge carrier’s trajectory.

Diffusion effects were neglected for various reasons. A deterministic approach to

diffusion would give similar results because the average position of the “cloud” of diffused

charge carriers follows a similar trajectory to that obtained by the current formulation while

the Monte Carlo method would be computationally intensive. Furthermore, charge collection

is a short process given the high charge carrier mobility and the strong electric fields in

radiation detectors [19]. Therefore, diffusion is expected to be limited.

DETECTOR SIMULATIONS

26 | P a g e

The termination of charge transport is triggered by either of these two conditions: a) the

charge reaches the boundary of the diamond detector; b) a time interval of 10 ns has passed

from the moment of charge carrier generation. The second condition arises from the

approximate integration time of the preamplifier 142A used for the actual detector testing.

The CCE is then calculated based on the initial and final positions using Equation (4.33)

obtained from the Shockley-Ramo theorem.

5.3 Simulation Results

The simulations discussed in this report were done under 100V bias for electrode widths

of 20μm, 30μm, 40μm, 50μm and 60μm; for electrode gaps of 5μm and 10μm. The

simulation results for electrode widths of 20μm, 40μm and 60μm at 10μm electrode gap are

shown in Figure 6. The remaining results can be found in the Appendix. The CCE values at

every point are represented by a colour on the colour scale with dark blue corresponding to

zero CCE and dark red corresponding full CCE of 1. The x and y axes are swapped relative to

the original CAD design in Figure 4.

As shown in Figure 6, full CCE is achieved near the tips of the interdigitated electrodes.

This is an expected result because the electric field strength is highest near the tips where the

radius of curvature is small, allowing for fast and efficient charge collection. The CCE is also

relatively high directly under the electrodes and near the electrodes but falls off towards the

centre of the electrode gap. Preliminary simulations on electrode gaps of up to 150 μm have

shown the same trends. Relatively lower CCE were observed between electrodes for all

simulations. Therefore, our discussion here is limited to simulations with smaller gaps of

5μm and 10μm. The CCE values also fall off rapidly in the peripheral areas of the detector.

The electric field strength in those areas are weak as they are further away from the

electrodes and the change in electric potential is more gradual.

One downside of the simulations is that the CCE values under the electrodes are lower

than expected. Based on prior tests of the interdigitated electrode structure on a single-crystal

diamond provided by the same company, the CCE values under the electrodes were in the

region of 90-100%. The electrode width and gap for that detector were 20μm and 200μm.

The simulations are unable to replicate these CCE values accurately. However, the trends in

DETECTOR SIMULATIONS

27 | P a g e

the CCE agree with the experimental data; the CCE near the tips and under the electrodes is

relatively higher than the CCE in the electrode gaps. Therefore, the simulation results still

hold some merit in comparing the relative performance for different geometries.

Figure 6 Simulation of CCE for various interdigitated electrode geometries on a 1.8 × 1.8 × 0.05 mm

single-crystal diamond detector with 5 MeV alpha particles

DETECTOR SIMULATIONS

28 | P a g e

Figure 7 Relative average CCE against electrode width. Calculated from the central region of the

CCE maps for electrode widths from 20 μm to 60 μm, and electrode gaps of 5 μm and 10 μm

Due to computational constraints, the dimensions of the diamond detector used in the

simulations are 1.8 × 1.8 × 0.05 mm. The average CCE of the middle 8 electrode strips and

gaps, 300 μm in length, were calculated for comparison of detector performance. This

method was used as the middle areas are away from the high CCE at the electrode tips, for

the average values to be less skewed. Another justification for this is that if the detector

dimensions were scaled up to the actual 4 × 4 × 0.5 mm, most of the CCE values would be

similar to the middle areas rather than the surrounding areas where the tips are.

The CCE values were normalised by taking the highest CCE value, corresponding to the

simulation with 40 μm width and 5 μm gap, to be 1 and the others were scaled accordingly.

From the graph in Figure 7, the optimal electrode widths are clearly 40 μm for electrode gaps

of 5 μm, and 30 μm for electrode gaps of 10 μm.

Therefore, for the fabrication of the diamond detector, electrode width and gap of 40 μm

and 5 μm respectively were chosen initially. However, due to difficulties encountered during

testing, an alternative configuration of 40 μm electrode width and 10 μm electrode gap was

fabricated for testing. The detector with 5 μm electrode gap encountered air breakdown easily

and no alpha detection peaks could be resolved from the noise.

0.8

0.85

0.9

0.95

1

1.05

0 10 20 30 40 50 60 70

Rel

ati

ve

Av

era

ge

CC

E

Electrode width (μm)

5 micron separation

10 micron separation

DETECTOR SIMULATIONS

29 | P a g e

Before moving on to the next section, it should be noted that the optimal electrode

configuration obtained from simulations may differ from real detectors. The mismatch

between the absolute CCE values of the simulations and actual experimental data was

touched upon earlier. There are many other real factors that may affect CCE. These include

imperfect electrode contacts, Schottky barriers near the electrode contacts and polarization

effects in diamond.

The Schottky barrier is a carrier depletion region formed at a metal-semiconductor

interface. It is caused by the introduction of metal-induced gap states in the band gap of the

semiconductor near the metal. Fermi level pinning occurs, which is the alignment of the

Fermi level of the metal and the semiconductor, due to the tendency for electrons to occupy

the gap states. These metal-semiconductor junctions behave like p-n junctions, favouring

current flow in one direction over the other. However, if the Schottky barrier is low, there

may be no rectifying effect by the junction. These are called ohmic contacts as the IV curve

shows linearity for current in both directions, similar to Ohm’s law.

FABRICATION AND TESTING

30 | P a g e

6 Fabrication and Testing

6.1 Detector Fabrication Procedure

The materials used for detector fabrication are:

1) Single-crystal electronic grade diamond sample of dimensions 4 × 4 × 0.5 mm,

provided by IIa Technologies Pte Ltd

2) Blank photomask, which consists of a uniform layer of AZ1518, on a chromium-

glass mask

3) AZ1518 photoresist solution

4) AZ400K developer solution

5) Acetone, isopropanol (IPA) and distilled (DI) water for cleaning

The instruments used for detector fabrication are, the UV laser writer, spin coater, UV

exposure station and magnetron sputtering machine.

The main fabrication steps are listed below.

1) UV laser writing of the electrode design pattern on blank photomask

2) Spin coating of diamond sample with AZ1518 photoresist. The spin coating was

done in 4 steps with the following settings:

a. Duration: 15s, RPM: 800, RPM/s: 1000

b. Duration: 75s, RPM: 6000, RPM/s: 1000

c. Duration: 30s, RPM: 7500, RPM/s: 1000

d. Duration: 10s, RPM: 0, RPM/s: 1000

3) Baking at 90°C for 90s to harden the AZ1518 on the diamond sample

4) UV exposure of diamond sample with the patterned photomask placed over it with

a power setting of 200W for 90s

5) Photoresist development using AZ400K developer for 90s

6) Magnetron sputtering of 20 nm Cr, followed by 80 nm Au for the electrodes

7) Removal of remaining photoresist and unwanted Cr/Au on the diamond sample

using acetone

8) Mounting and wire bonding of the diamond sample on a holder

FABRICATION AND TESTING

31 | P a g e

Figure 8 Fabrication process of the diamond detector. (1) Spin coating of AZ1518 on diamond

sample; (2) UV exposure under patterned photomask; (3) Photoresist development using AZ400K;

(4) Magnetron sputtering of Cr/Au interdigitated electrodes

For the first step, the desired electrode design is drawn on AutoCAD, a computer-aided

drafting software. The design file is then exported to the UV laser writer software for laser

writing. The areas exposed to the laser are then removed by submerging the photomask in a

solution consisting of 1 part AZ400K and 4 parts DI water for 90 seconds while unexposed

areas remain intact as they are unaffected by the AZ400K.

Next, the diamond sample is placed in the spin coater and a drop of AZ1518, enough to

completely cover the top surface of the diamond. The above-mentioned spin coater settings

were used to obtain a thin layer of AZ1518 on the diamond. This is followed by baking the

diamond sample at 90°C for 90 seconds to harden the AZ1518.

The diamond sample is taped onto the patterned photomask to ensure that it is as close to

the pattern as possible. UV exposure is performed on the sample over the photomask. The

power setting used is 200 watts for a duration of 90 seconds. Following the UV exposure, the

diamond sample is submerged in 1:4 AZ400K developer/DI water solution for 90 seconds to

remove the UV exposed areas. The result is an inverse of the electrode pattern consisting of

AZ1518 on the diamond surface.

The diamond sample is placed in the magnetron sputtering machine. Magnetron

sputtering is a coating technique that uses the bombardment of ions to eject sputtering

material from a target onto a sample in front of it [20]. The vacuum chamber is first pumped

down to remove air molecules, followed by the injection of argon gas. A plasma is used to

ionise the argon atoms. A high voltage is applied to accelerate the argon ions to the target.

FABRICATION AND TESTING

32 | P a g e

The argon ions eject the sputtering material which coats the diamond sample placed in front

of the target. First, a 20 nm layer of Cr is sputtered at a rate of 0.5 nm per second, followed

by a 80 nm layer of Au at a rate of 1 nm per second. Cr is chosen for the diamond-metal

boundary because Cr forms carbides that help to bind the metal onto the diamond easily. An

imperfect metal contact may affect the detector performance. Au is chosen for the upper layer

because it is an excellent electrical conductor.

After sputtering, the diamond sample is washed with acetone to remove the remaining

photoresist and the unwanted Cr/Au coating on it. The diamond sample with the

interdigitated Cr/Au electrodes is mounted on a Teflon holder with an SMA connector using

double-sided tape. The electrodes are wire bonded to electrical copper contacts on the Teflon

holder as shown in Figure 9.

Figure 9 Schematic design of detector

Figure 10 Schematic of signal processing electronics

FABRICATION AND TESTING

33 | P a g e

6.2 Fabrication Issues

Two main issues were encountered during fabrication and pre-tests. They are uneven spin

coating and suboptimal photoresist developing duration. Due to the small size of the diamond

sample and the surface tension of the AZ1518, it was not possible to obtain an even layer of

AZ1518. The AZ1518 layer was thicker near the edges than at the centre. Despite numerous

trials, the optimal settings for the spin coater could not be found. Thus, Cr/Au could not be

properly deposited near the edges of the diamond sample. One electrode strip was

disconnected from the rest of the electrode as seen in Figure 11b. However, the effect on the

performance was expected to be minimal as each electrode consists of 30 strips. Optimisation

of the spin coater settings is essential for future tests as the suboptimal coating limits the

effective area that can be used on the diamond.

(a) (b)

Figure 11 Microscope images of the electrodes

Suboptimal photoresist developing duration caused minor defects in the electrode shapes

as shown in Figures 12a and 12b. From Figure 13, we can estimate the electrode width to gap

ratio. It is found to be approximately 3.40

0.75= 4.53 > 4 =

40

10. Further calculations show that the

electrode gap is approximately 9.04 μm and the electrode width is 41.96 μm. This shows that

the photoresist developing duration of 90 seconds was insufficient. Further trials are required

FABRICATION AND TESTING

34 | P a g e

to find the optimal developing duration in order to fabricate electrode shapes as accurately as

possible.

(a) (b)

Figure 12 Microscope images of electrode defects

Figure 13 Scanning electron microscope (SEM) image of electrodes

FABRICATION AND TESTING

35 | P a g e

6.3 Testing and Results

Characterization of the diamond detector was performed using a radioactive source. The

source used is a triple alpha source of Pu-239, Am-241 and Cm-244. The source was placed 7

mm directly below the diamond detector in a vacuum chamber at 10-1 mbar. The signal from

the detector was read out by a pre-amplifier and other associated electronics as shown in the

schematic diagram in Figure 10. Measurements were taken at various positive and negative

bias voltages for 10 minutes each. The gain and shaping time of the amplifier were set at 200

and 0.5 μs respectively. The spectrum data can be found in the Appendix. A commercial

silicon detector (ORTEC surface barrier Si detector) was also tested using the same

radioactive source with +40V bias with the amplifier set at 10, 20 and 50 gain.

Table 2 Alpha particle energy of the triple alpha radioactive source

Radionuclide Alpha particle energy (MeV) and probability

Plutonium-239 5.103 (11%), 5.142 (15%), 5.155 (73%)

Americium-241 5.442 (12.5%), 5.484 (85.2%)

Curium-244 5.763(23.6%), 5.806 (76.4%)

The positions of the three spectral peaks for every spectrum were determined using a

Gaussian fit. The commercial silicon detector was taken as a reference and assumed to be

operating at 100% CCE. An energy calibration of the spectrum channels was performed using

the 3 peaks in the spectrum for the silicon detector tested at 50 gain.

The energy required to generate an electron-hole pair is 13.2 eV in diamond and 3.6 eV in

silicon. Therefore, a calibration is required to compare the CCE of the diamond detector with

the silicon detector. Taking 𝐸 to be the energy of the ionising particle, it is related to the peak

channel by the following equation:

50×𝐸

3.6×100% = 𝑘 ∙ 𝐶ℎ𝑆𝑖 (6.1)

200×𝐸

13.2×100% = 𝑘 ∙ 𝐶ℎ𝐷 (6.2)

where 𝑘 is a scaling factor, and 𝐶ℎ𝑆𝑖 and 𝐶ℎ𝐷 are the channel numbers of the peak positions

at 100% CCE. The numbers 50 and 200 account for the difference in gain used. The data for

FABRICATION AND TESTING

36 | P a g e

the silicon detector tests at 10, 20 and 50 gain were used to confirm the linear scaling of the

gain. The channel number which represents 100% CCE for diamond detectors was calculated

using Equations (6.1) and (6.2).

𝐶ℎ𝐷 = 4 ∙3.6

13.2∙ 𝐶ℎ𝑆𝑖 (6.3)

Thus, the CCE values for the diamond detector for each of the three peaks in each spectrum

were calculated by the following ratio.

𝐶𝐶𝐸 =𝐶ℎ𝑒𝑥𝑝

𝐶ℎ𝐷

(6.4)

where 𝐶ℎ𝑒𝑥𝑝 is the channel number of the peak positions from the experimental data for the

diamond detectors.

It was observed that under the negative bias, due to errors arising from the signal

processing in the electronics, the position of the peaks did not match up with the peaks found

under positive bias. A reference pulser that produces fixed positive and negative voltage

pulses was used to calibrate and account for the differences in the signal processing under

positive and negative bias.

Figure 14 CCE values for diamond detector at different bias voltages. Blue data points represent

diamond detector of electrode width = 40 μm, gap = 10 μm. Red data points represent diamond

detector of electrode width = 20 μm, gap = 200 μm

FABRICATION AND TESTING

37 | P a g e

Figure 14 shows the CCE of the diamond detector under biases ranging from -20V to

20V, represented by the blue data points. The error bars were obtained by combining the

CCE data for the 3 alpha peaks for each bias voltage. The CCE data for biases of +3V to -3V

are unavailable because the 3 alpha peaks were unresolvable due to poor charge collection as

shown in the Appendix. The red data points represent CCE data for a prior test performed on

a previous detector fabricated using single-crystal electronic grade diamond provided by the

same supplier (IIa Technologies Pte Ltd). The electrode width and gap were 20 μm and 200

μm respectively and the radioactive source used was Po-210.

The data shows that maximum charge collection efficiency of 107% was achieved from

+5V/-5V onwards. This is depicted by the flat plateau at higher biases. This is much lower

than the operating voltage of the silicon detector (+40V) as well as the previous diamond

detector (~+50V/-50V). Due to the relatively smaller electrode gaps compared to the previous

diamond detector, strong electric fields could be obtained at a lower bias voltage. Therefore,

the detector can be operated using lower voltage equipment which are often cheaper and

easier to maintain. The CCE values for the diamond detector exceed 100% under both

positive and negative bias. This may be due to minor errors in scaling the silicon detector

data in order to compare the CCE values with the diamond detector data. Also, as the silicon

detector is not new, it may have experienced a slight degradation in performance.

Nevertheless, the high CCE values of the diamond detector should not be discounted.

Figure 15 Spectrum data for diamond detector at +20V bias

-10

0

10

20

30

40

50

60

70

80

0 1000 2000 3000 4000 5000 6000 7000

Co

unts

Channels

FABRICATION AND TESTING

38 | P a g e

Figure 16 Spectrum data for previous diamond detector at -150V bias

From the spectrum data for the diamond detector at +20V bias in Figure 15, the three

alpha peaks can be easily distinguished from each other, and there are no other significant

peaks present. On the other hand, for the previous diamond detector, two peaks are observed

on the right end of the spectrum. This is even though the radioactive source Po-210 used for

the previous diamond detector releases alpha particles of only one energy (5.3 MeV). The

two peaks correspond to two different CCE values. With this detector, it would be difficult to

calculate the energy of an unknown radioactive source due to the presence of multiple peaks.

The current detector would be a better choice as there is 1 well-defined peak corresponding to

the energy of the ionising particle. It is also observed that there is a non-negligible number of

counts registered on the lower end of the channel spectrum. Those counts may correspond to

alpha particles that are incident on the peripheral areas of the detector. As these areas are

further away from the electrodes, the electric field strength would be weaker. Furthermore,

there would be incomplete charge collection as some of the charge carriers would drift away

to the sides of the detector, depending on which electrode is closest. For example, if the

closest electrode is the positive electrode, it would force holes to drift towards the edge of the

detector. Another plausible cause would be the incidence of alpha particles on the aluminium

wire bonding, resulting in an unwanted electrical signal.

FABRICATION AND TESTING

39 | P a g e

Figure 17 Gaussian fitting of 3rd alpha peaks for the diamond and silicon detector respectively

Figure 17 shows the Gaussian fitting for the 3rd peak for the diamond detector at +20V

bias and the silicon detector at +40V bias. Both peaks were fitted using a sum of 2 Gaussian

functions, representing the 5.763 MeV (23.6%) and 5.806 MeV (76.4%) alpha particles

emitted by Cm-244. The equation for the full width at half maximum is

FWHM = 2√2 ln 2 𝜎 (6.5)

where 𝜎 is the standard deviation. Both Gaussian functions were made to share the same 𝜎

value as the FWHM should be the same for both peaks. The FWHM is commonly quoted as

the energy resolution of the detector. The energy resolutions for the diamond and silicon

detectors are 92 keV and 33 keV respectively. This is far from the energy resolution of 19

keV achieved by Duenas et al. [14] with a sandwich structure diamond detector. Further

improvements in performance are necessary to make this detector more reliable.

FABRICATION AND TESTING

40 | P a g e

Figure 18 Leakage current measurements of the diamond detector

Figure 18 shows the leakage current measured under various bias voltages. The leakage

current was measured using a RBD 9103 USB picoammeter. The symmetry of the IV curve

about the origin indicates an ohmic character for the electrodes. This shows that there is no

significant Schottky barriers at the metal-semiconductor junctions. The magnitude of the

leakage current is consistent with those reported by Pernegger et al [21]. Air breakdown was

observed at 250V for both positive and negative biases. This shows that the diamond detector

has a very wide operating voltage range of 5V-240V.

0

0.05

0.1

0.15

0.2

0.25

0.3

-250 -200 -150 -100 -50 0 50 100 150 200 250 300

Lea

kag

e C

urr

ent

(nA

)

Bias Voltage (V)

CONCLUSION

41 | P a g e

7 Conclusion

7.1 Summary

Using computer simulations, the optimal coplanar interdigitated electrode configuration

was found by varying the electrode width and separations. The single-crystal electronic grade

diamond detector fabricated using the recommended dimensions of 40 μm electrode width

and 10 μm electrode gap showed an improvement in performance over a previous design of

20 μm electrode width and 200 μm electrode gap. The CCE values were higher and the

energy resolution was better as well, as the previous detector suffered from having two

detection peaks from a single alpha source. The magnitude of the leakage current measured is

low and in good agreement with other reported values.

Although the CCE values for the diamond detector were relatively higher than the silicon

detector, the silicon detector had a better energy resolution of 33 keV compared to the

diamond detector’s 92 keV.

The fabrication process can be further optimised. Due to issues encountered during

fabrication, minor defects in the shape of the electrodes were found. Better performance is

expected if the entire top surface is covered by the interdigitated electrode structure as this

ensures strong electric fields throughout the entire volume of the diamond detector.

7.2 Future Research

The computer simulation code can be further improved upon to obtain more accurate

simulation results. The absolute CCE values reported by the simulation results are not in

good agreement with experimental data. However, the simulations can give the correct trend

in the relative CCE values under the electrodes and in the electrode gaps.

Optimisation of the fabrication process would be key in achieving reproducible results.

The defects in the electrodes cause variations in detector performance (usually detrimental

CONCLUSION

42 | P a g e

effects) and this makes it difficult to accurately assess the performance of a certain electrode

structure.

Another way of optimising interdigitated diamond detector performance would be to use

3D electrode structures, where the electrode strips are etched a narrow depth into the

diamond. With the sides of the electrode strips sputtered with electrodes, it may result in

better charge collection for charge carriers generated near the surface of the detector.

Improved performance has been reported by Forneris et al. [7]. However, optimisation of the

etching depth was not performed. This aspect could be explored through computer

simulations.

REFERENCES

43 | P a g e

References

[1] Frame P. W., A history of radiation detection instrumentation, Health Physics 87 (2): p. 111-135

[2] Mainwood A., Recent Developments of diamond detectors for particles and UV radiation,

Semicond. Sci. Technol. 15 (2000) R55-R63

[3] WhitField M. D., et al, Diamond photoconductors: operational lifetime and radiation hardness

under deep-UV excimer laser irradiation, Diamond and Related Materials 10 (3-7): p. 715-721

[4] Balmer R. S., et al., Chemical vapour deposition synthetic diamond: materials, technology and

applications, Journal of Physics: Condensed Matter, 2009. 21(36): p. 364221.

[5] The Element Six CVD Diamond Handbook,

http://e6cvd.com/media/wysiwyg/pdf/E6_CVD_Diamond_Handbook_A5_v10X.pdf, [Accessed 1st

April 2017]

[6] Forneris J., et al., Modeling of ion beam induced charge sharing experiments for the design of

high resolution position sensitive detectors, Nuclear Instruments and Methods in Physics Research

Section B: Beam Interactions with Materials and Atoms, 2013. 306: p. 169-175.

[7] Forneris J., et al., A 3-dimensional interdigitated electrode geometry for the enhancement of

charge collection efficiency in diamond detectors. EPL (Europhysics Letters), 2014. 108(1): p. 18001.

[8] IIa Diamond Properties, http://2atechnologies.com/2a-diamond-properties/, [Accessed 1st April

2017]

[9] Bruzzi M., et al., Advanced materials in radiation dosimetry, Nuclear Instruments and Methods in

Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment,

2002. 485 (1–2): p. 172-177.

[10] Meier D., et al., Proton irradiation of CVD diamond detectors for high-luminosity experiments at

the LHC, Nuclear Instruments and Methods in Physics Research Section A: Accelerators,

Spectrometers, Detectors and Associated Equipment, 1999. 426 (1): p. 173-180

[11] Zamboni I., et al., Radiation hardness of single crystal CVD diamond detector tested with MeV

energy ions, Diamond and Related Materials, 2013. 31: p. 65-71

[12] Grilj V., et al., Irradiation of thin diamond detectors and radiation hardness tests using MeV

protons, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with

Materials and Atoms, 2013. 306: p. 191-194

REFERENCES

44 | P a g e

[13] Galbiati A., et al., Performance of Monocrystalline Diamond Radiation Detectors Fabricated

Using Ti/W, Cr/Au and a Novel Ohmic DLC/Pt/Au Electrical Contact, IEEE Transactions on Nuclear

Science, 2009. 56 (4): p. 1863

[14] Dueñas J. A., et al., Diamond detector for alpha-particle spectrometry, Applied Radiation and

Isotopes, 2014. 90: p. 177-180

[15] Zhong H., Review of the Shockley-Ramo theorem and its application in semiconductor gamma-

ray detectors, Nuclear Instruments and Methods in Physics Research Section A: Accelerators,

Spectrometers, Detectors and Associated Equipment, 2001. 463 (1-2): p. 250-267

[16] Leroy C., Principles of radiation interaction in matter and detection, (World Scientific

Publishing Co. Pte. Ltd., Singapore) 2016.

[17] The Finite Element Method. https://www.comsol.com/multiphysics/finite-element-method,

[Accessed 1st April 2017]

[18] Vittone E., et al., Semiconductor characterization by scanning ion beam induced charge (IBIC)

microscopy, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with

Materials and Atoms, 2008. 266 (8): p. 1312-1318

[19] Vittone E., et al., Charge collection efficiency degradation induced by MeV ions in

semiconductor devices: Model and experiment, Nuclear Instruments and Methods in Physics Research

Section B: Beam Interactions with Materials and Atoms, 2016. 372: p. 128-142

[20] Magnetron Sputtering. http://www.hauzertechnocoating.com/en/plasma-coating-

explained/magnetron-sputtering/, [Accessed 1st April 2017]

[21] Pernegger H., et al., Charge-carrier properties in synthetic single-crystal diamond measured

with the transient-current technique, Journal of Applied Physics, 2005, 97 (7)

APPENDIX

45 | P a g e

Appendix

Figure 19 CCE data for 30 μm and 50 μm electrode width, with 10 μm electrode gap respectively

APPENDIX

46 | P a g e

Figure 20 Channel spectrum data for diamond detector at +2V and +3V

APPENDIX

47 | P a g e

Figure 21 Channel spectrum data for diamond detector at +4V and +5V

APPENDIX

48 | P a g e

Figure 22 Channel spectrum data for diamond detector at +10V and +15V

APPENDIX

49 | P a g e

Figure 23 Channel spectrum data for diamond detector at -2V and -3V

APPENDIX

50 | P a g e

Figure 24 Channel spectrum data for diamond detector at -4V and -5V

APPENDIX

51 | P a g e

Figure 25 Channel spectrum data for diamond detector at -10V and -15V

APPENDIX

52 | P a g e

Figure 25 Channel spectrum data for diamond detector at -20V